M Gudmundsson

D Fischer

D Misra

A Källberg

A Simonsson

K Støchkel

H Cederquist

T Schmidt
email: schmidt@fysik.su.se

H T Schmidt

Two-site double-core-hole

published or not. The documents may come

I. INTRODUCTION

With the development of the COLTRIMS technique (COLd Target Recoil-Ion-Momentum Spectroscopy) in the 1990s an efficient tool for extraction of detailed information on ion -atom collisions became available and revolutionized this area of research [1,2]. In the case of pure electron-transfer collisions, in which no electrons are emitted from the collision system, analyses of longitudinal recoil-ion momenta have been used to extract detailed final state information [3,4], while transverse recoil-ion momenta give information on, e.g., very small projectile scattering angles with high precision. For example, the detailed investigations of the Thomas capture mechanism [START_REF] Thomas | Proc. R. Soc[END_REF][START_REF] Horsdal-Pedersen | [END_REF][7], its velocity dependence [8] and related phenomena [9] became possible with this technique [1,2].

While the use of COLTRIMS in photo-ionization studies is widespread for both atomic and molecular targets [10,11], there is so far only a very limited number of ion-molecule collision studies. This is somewhat surprising as the detection of the final-state momentum of a charged fragment gives direct information on the orientation of the molecule at the moment of the collision when the time scales for the collision and subsequent dissociation are short compared to molecular rotation periods. There are several examples of theoretical work on ionmolecule collisions revealing interesting features which cannot be isolated without information on the molecular orientation [12,13]. Fixing or measuring the orientations of target molecules thus open new dimensions for experimental studies of ion-molecule collisions. Cocke and co-workers measured the molecular orientation dependence for 2-16 MeV O 8+ +H 2 electron transfer collisions by detecting target protons with a pre-COLTRIMS setup in 1993 [14]. This was the first partly successful attempt to establish effects of two-slit projectile wave interference in fast electron-transfer collisions. Much later, similar effects were investigated in more detail by means of a COLTRIMS apparatus where strong interference effects were observed for electron-transfer reactions in H + + H 2 [15] and He 2+ + H 2 [16] collisions as variations in the total projectile neutralisation cross sections with molecular orientation. Further the two-slit interference was demonstrated more directly through measurement of markedly different projectile angular scattering distributions for different molecular orientations in the p + H 2 case [17]. Also in much lower-energy ionatom collisions heavy-particle interference in the form of Stückelberg oscillations have been clearly observed for electron-transfer collisions [18,19]. Other aspects of the hydrogen molecule acting as an atomic sized double-slit have been elucidated for charged-particle-induced pure ionization processes [20][21][22][23][24], for photoionization [11] and for low-energy molecular ion-atom collisions [25].

In the present work we consider electron transfer in 1.04 MeV p + N 2 collisions accompanied by emission of one or more additional target electrons. We record the charge state and momentum of one of the atomic product ions from dissociating N 2 ions in coincidence with the detection of fast hydrogen atoms formed when electrons are transferred to the proton projectiles. We find that the cross section depends on the molecular orientation, but in different ways for different charge states of the detected atomic fragment ion. For N + fragments, the intensity is highest when the molecular axis is perpendicular to the incoming projectile beam. For the N 2+ and N 3+ fragments, however, the intensities peak for molecular orientations along the beam which most likely is due to higher probabilities to form core holes at both atomic centers for such orientations and thereby to reach higher charge states. The reason for the higher N + intensity for perpendicular orientations is at the moment not clear but we speculate that it possibly may be related to twocenter interference effects as observed earlier for hydrogen targets [15,17], but here involving inner shell electrons.

II. EXPERIMENT

The experiment was performed in the electron cooler heavy-ion storage ring CRYRING at Stockholm University [26]. The protons were produced in a plasma discharge ion source, extracted by a 20 kV potential difference and transported to a linear radio-frequency quadrupole accelerator, which accelerated the beam to 300 keV. At this energy the beam was injected into CRYRING and electron cooled to allow injection of further beam pulses to reach total currents of several µA. When sufficient beam was accumulated the electron cooler was switched off and the synchrotron acceleration was performed to increase the energy to 1.04 MeV. Then, again electron cooling was applied in order to limit the velocity spread in the ion beam and to increase the storage lifetime by eliminating losses through multiple small-angle scattering on residual-gas molecules. For the present experiment we had typical values of beam current of 2 µA, beam width at the gas-jet interaction region of 1.5 mm FWHM, and storage lifetimes of 20 minutes. The molecular target beam was formed in a supersonic expansion where pre-cooled N 2 gas at 2 bar and 165 K expanded through a 30 µm diameter nozzle into a vacuum chamber pumped to 10 -3 mbar by a 1000 l/s Balzer's turbomolecular pump. The container with the nozzle could be adjusted with µm precision relative to the first of a set of four skimmers defining the jet and separating the four differential pumping stages toward the storage ring. Opposite to its entrance to the storage ring vacuum system the gas-jet was collected by a three-stage jet dump. The jet was collimated to a diameter of 1.3 mm, a density of 10 11 cm -3 , and it caused no detectable increase in the CRYRING background pressure of ≈10 -11 mbar [27].

The crossing of the narrow proton and molecular nitrogen beams is in the center of a recoil-ion momentum spectrometer. A homogeneous electric field is projecting all charged target collision products toward a 95 % transmission grid after which they enter a field-free region where they travel twice the distance they have travelled in the homogeneous field region for Wiley-McLaren time focusing [28]. Finally the ions are accelerated onto a position-sensitve detector consisting of a double microchannel plate in a chevron configuration and a resistive anode encoder. To collect all nitrogen atomic ions from the molecular dissociations, a high extraction field of 200 V/cm was applied. As this detector system has no multihit capability it was necessary to cover one half of its surface to only detect one of the two atomic nitrogen fragment ions. In addition, by letting the foil cover a little more than half the detector, we could very strongly reduce a large contribution to the recoil-ion detector count rate from (mostly) single-ionization events yielding N + 2 that would have hit close to the center of the detector due to small recoil-ion momenta (in comparison to those of N q+ dissociation products). A schematic of this part of the experimental setup is shown in figure 1. Neutralized projectiles were recorded by a second position-sensitive detector 3.2 m downstream of the ion beam/gas jet crossing.

The experimental data were recorded in the following manner. After a proton beam has been electron cooled at 1.04 MeV, the data acquisition system is enabled. When a signal is registered at the projectile detector an 'open gate' signal is sent to an 8-channel analog-to-digital converter (ADC), the four corner signals of the resistive anode encoder are amplified by charge-sensitive amplifiers and sent to this ADC and a time-to-digital converter (TDC) is started. If a signal is recorded on the recoilion detector, the four corner signals from that detector are also recorded by the ADC, the gate of which is then closed and the time difference between the hits of the two detectors is recorded by the TDC. Finally the ADC and TDC information is transferred by a VME64 crate to an Alpha station and written to an event-mode data file. If no recoil-ion is recorded within a 25 µs time range, the ADC and TDC are reset to be ready for the next projectile detection and no information is saved.

In the off-line analysis the charge state of each detected target ion fragment is determined from the time-of-flight. Further, the momentum vector of each fragment ion is calculated from its position on the recoil-ion detectordetermined from the pulse heights of the corner signalsand the time-of-flight.

III. RESULTS AND DISCUSSION

In figure 2 we display the histogram of the recorded time differences between signals from the projectile and recoil-ion detectors on a logarithmic scale. We observe atomic fragment ions from dissociations of N 2 ions in charge states q=1-3+ and there is a narrow peak corresponding to intact molecular nitrogen ions, N + 2 . This peak corresponds to single-electron capture without further ionization and fragmentation, and is thus likely related to capture of a valence electron from N 2 . Note that this peak is strongly reduced due to the foil (see figure 1). Even though the recoil-ions in single-electron capture are emitted in the backward direction, their momenta are very small in comparison to those of the atomic fragment ions for which the spectrometer voltages are set, and the vast majority of the N + 2 ions travel too close to the spectrometer axis to avoid the foil. The considerable broadenings of the atomic N q+ peaks are due to the momentum FIG. 1: Schematic of the recoil-ion-momentum spectrometer. The metal foil that covers slightly more than half the detector ensures that only the fragment ion emitted into the backward hemisphere relative to the projectile direction may be detected. This is necessary in order to suppress an otherwise very large backgound from single-ionization events producing mainly intact N + 2 with low momenta (c.f. text).

gained in the dissociation process itself and it is through the time difference for the individual events in relation to the peak centers that the momentum components along the spectrometer axis are extracted.

It is remarkable that we observe atomic ions up to charge state q=3+. Since there is time for the electrons to redistribute themselves during the dissociation, the charge is likely to be shared equally between the two fragments. This equal sharing of the total charge is expected to be a general feature for covalently bound systems and in the case of N 2 such an effect has been demonstrated directly in multi-electron transfer processes [29]. Recently it was shown in a free-electron laser experiment that also after sequential multiionization by XUV photons N 2 dissociates with symmetrical (or close to symmetrical) sharing of the total charge [30]. Even in some [31], but not all [32] van der Waals bound dimers, it is found that the charge is shared equally. Thus, the present observation of triply charged atomic ions from a covalently bound molecule strongly suggests that at least five electrons were removed from the target molecule in the corresponding collision events. A key to understanding this lies in the fact that the present projectile velocity (6.45 a.u.) is considerably higher than the expectation values of the magnitude of the velocity for the bound valence electrons, reducing dramatically the cross section for capture of those. An N 2 1s core electron, on the other hand, is bound by about 400 eV, which is then also the expectation value of its kinetic energy in that state. Thus the projectile velocity for 1.04 MeV protons is close to typical speeds of the K-shell electrons of N 2 and capture of core electrons is much more likely than capture of valence electrons. Core-hole states will decay through Auger processes and the multiply charged molecular ion will then rapidly dissociate after redistribution of the charge. For photoionization above the threshold for K-shell ionization, a similar three-step mechanism (Khole formation-Auger decay-Coulomb dissociation) for the formation of multiply charged atomic fragments has been discussed [33]. This emphasizes interesting similarities between electron transfer in fast collisions with ions and photoionization as discussed also in [34].

The distributions of the magnitudes of final-state momenta of the atomic nitrogen fragment ions are shown in figure 3 for the N + , N 2+ and N 3+ dissociation products. As expected, the more highly charged ions also have higher momenta due to the Coulomb repulsion. As we only detect one of the atomic fragment ions we do not know the total number of electrons removed in each event, but we do observe for example that the maximum in the N 2+ distribution coincides with a 'shoulder structure' in the N + momentum distribution. This indicates that this N + -structure is related to dissociating N 3+ 2 . The structures in the N + distribution for lower momenta are probably due to different dissociating states of N + 2 and N 2+

2 . The high-momentum tails of the N 2+ and N 3+ distributions seem to coincide and this would indicate that N 5+ 2 → N 2+ + N 3+ is responsible for the highest kinetic energies in both cases. Thus, N 5+ 2 should be the most highly charged molecule produced in this experiment, and given the equal sharing of charge we may conclude that the observed N 3+ ions come from dissociating N 5+ 2 exclusively.

In figure 4 we show the orientation dependence in dσ/d(cosθ) summed over all three observed atomic charge states, where θ is the angle between the direc- tion of emission of the detected dissociation product and the projectile beam direction. The sharp cut in the signal for cos(θ)≥-0.1 is due to the foil that covers a little over one half the detector area. We find a significant variation with the angle θ with about 50 % higher signal for the molecular axis close to perpendicular to the beam direction as compared to the molecular axis aligned with the beam direction. In earlier studies of transfer and excitation in p + H 2 collisions [15] a similar strong orientation dependence could be explained by the welldefined changes in projectile momentum (and thus de-Broglie wavelength) that accompanies the electron capture in the vicinity of either target proton. For capture of a target electron from an initial state of gerade symmetry it was predicted [35,36] and later found [15,17] that constructive interference gives a maximum in the cross section for the transverse orientation of the molecular axis with respect to the incoming projectile direction. The same reasoning predicts that there should be minima due to destructive interferences at other specific orientations (θ) determined by the momentum gained by the projectile (≈ v P /2, where v P is the projectile velocity) when an electron is captured from H 2 . Such projectileenergy dependent minima were clearly identified in [15]. It was further shown [37] that the inverse orientation dependence should be expected when an electron from an intial state of ungerade symmetry is captured. The hydrogen molecule, H 2 , is unique in that both electrons (neglecting small configuration interaction effects) occupy single-electron states of gerade symmetry. In a larger system like N 2 single-electron states of both symmetries are occupied and similar interference as observed in electron capture from H 2 can only be expected in the case of a strong preference for capture from states of either initial symmetry. The longitudinal momentum transfer to the projec- The measured orientation-dependent relative cross section dσ/dcosθ as functions of cosθ summed over all three observed atomic ion charge states. This entity would be constant for an isotropic distribution of the emitted atomic nitrogen ions.

tile in the initial electron-transfer process is given by (in atomic units):

δk = v P /2 + Q/v P , (1)
where Q is the inelasticity of the collision. In atomic units the change in momentum is equal to the change in wave number of the de Broglie wave and the phase shift accumulated as the wave front propagates from one nuclear center to the other is given by:

δΦ = δka cos θ, (2)
where a = 2.1 a 0 is the internuclear distance in N 2 .

In the case of capture of a valence electron, the Q/v Pterm in (1) is negligible as was the case for capture from H 2 . Thus δka ≈ 6.7 for valence capture from N 2 and the phase shift would vary from zero (for capture from a gerade symmetry initial state) to more than -2π when the molecular axis orientation is varied from transverse (θ = 90 • , δΦ = 0) to parallel (θ = 180 • , δΦ = -δka). Thus if capture of initial gerade symmetry valence electrons would dominate, we should find a variation with a maximum at cos θ=0, an intermediate minimum and another maximum close to the parallel orientation. Such a behaviour is definitely ruled out from the data shown in figure 4.

In the case of inner-shell capture from N 2 , on the other hand, the Q/v P -term is significant and the momentum gained by the projectile is strongly reduced so that δka ≈ 2.0 according to (1). Therefore, a minimum due to destructive interference (δΦ = -π) is never reached when the molecular axis orientation is varied. Rather we go from a maximum at θ = 90 • towards lower intensity when approaching θ = 180 • . Our observations resembles this behaviour as is shown in figure 4. This observed behavior is what is expected for capture of electrons from an initial state of gerade symmetry and consistent with what was found experimentally for p + H 2 [15,17]. As mentioned above the expectation for capture of electrons from states of initial ungerade symmetry will be the reverse, and thus our experimental result seems to indicate that there is a higher probability of capture of an electron in an initial gerade state. The full curve in figure 4 is the result of treating the projectile wave functions after the electron transfer process as the sum of two plane waves with a phase shift given by (2) for a case where capture of electrons initially occupying states of gerade symmetry is dominating. There is good agreement between the data and this simple model result, but rather than drawing any conclusions from this we propose further experimental investigations to be made. In the p + H 2 case [15], the projectile-wave interference was nicely demonstrated by the variation of the position of the minimum with projectile velocity. In the case of p + N 2 core-electron capture a 2.0 MeV projectile kinetic energy would give δka ≈ 6.0 and a minimum in the orientation dependent cross section for θ ≈ 58 • as an example. It would be really interesting if such an experiment could be performed in the near future-unfortunately it cannot be done with the present setup for practical reasons as the CRYRING is no longer available for experiments.

Irrespective of how the orientation variations of dσ/dcosθ in figure 4 should be understood, we may consider whether these dependences differ for different atomic ion fragment charge states. For this purpose, the relative yields of N + , N 2+ and N 3+ to the summed yields are shown in figure 5 as functions of cosθ where θ again is the angle of emission of the detected fragment. We find that multiply charged atomic fragments are more likely to be found in electron transfer events where cosθ is close to -1, i.e. for the molecular axis aligned with the projectile beam. This means that there is a higher probability for higher atomic fragment ion charge states for this orientation and we ascribe this to steric effects. When a projectile comes sufficiently close to one nuclear center for a high probability for electron transfer, it must also come close to the other atomic center for molecules close to parallel with the ion beam, which will increase the probability for impact ionization of a K-shell electron at the other atomic center. In a scenario where one core hole is created through electron transfer and another core hole is created at the other nuclear center by impact ionization, it is natural that high charge states are formed. Currently, such two-site double-core hole states are being sought for in sequential X-ray photoionization by means of the Stanford Linear Coherent Light Source free-electron X-ray laser, while single-site molecular nitrogen double core hole states produced with that technique [38] and in single X-ray photon experiments [39,40] have been reported recently.

IV. CONCLUSION

We have reported the results of relative cross section measurements differential in the orientation of the molecular axis for electron transfer processes in 1.04 MeV p + N 2 collisions. We find that electron transfer leading to dissociation into charged products is more likely if the molecular axis is oriented perpendicular to the incoming H + trajectory. This behaviour resembles that found for molecular hydrogen target molecules in earlier work and may possibly be explained by de Broglie wave interference due to electron transfer in close vicinities of either atomic core. If this is indeed the case, it is a very surprising result as such interferences should be unique for molecular hydrogen as only there both electrons are in gerade-symmetry initial single-electron states. Rather than concluding that quantum interference is responsible for the observed orientational variation of the cross sections, we propose to repeat the experiment at a higher projectile beam energy around 2 MeV in order to investigate if there is also a minimum (around θ=58 • ) when the molecular orientation is varied between parallel and perpendicular orientations. In the present work we have observed that the relative intensities of the N 2+ and N 3+ dissociation products increase significantly for orientations close to aligned with the direction of the incoming ion beam. We ascribe this observation to the formation of two-site double-core-hole states formed when one core electron is captured while another one from the other atomic core is ionized by the projectile.

FIG. 2 :

 2 FIG.2: Time-of-flight spectrum of target ions and fragments recorded in coincidence with neutralized projectiles. Note that the N + 2 peak corresponding to molecular ions is strongly reduced due to the coverage of a little more than one half of the detector area by a foil (cf. text).

FIG. 3 :

 3 FIG.3:The distributions of the absolute values of the momenta for the three different charge states of atomic fragments from dissociations of N2 ions.

  FIG.4:The measured orientation-dependent relative cross section dσ/dcosθ as functions of cosθ summed over all three observed atomic ion charge states. This entity would be constant for an isotropic distribution of the emitted atomic nitrogen ions.

FIG. 5 :

 5 FIG.5:The relative yields of N + , N 2+ and N 3+ as functions of cos θ.

Acknowledgments

Financial support from the Knut and Alice Wallenberg Foundation and the Swedish Research Council is gratefully acknowledged. Further, we would like to acknowledge many fruitful discussions with Charles Lewis Cocke, Erik Horsdal, Horst Schmidt-Böcking, and Reinhold Schuch.


P Lambropoulos

K G Papamihail

P Decleva

Theory of Multiple Ionization of Xenon under strong XUV radiation and the role of the Giant Resonance

Keywords: numbers: 32.80.Rm, 32.80.Fb, 30.80.Hd, 42.50.Hz

We examine the conditions under which multiple ionization of Xenon, under strong radiation of photon energy 93 eV and pulse duration 10 fs, leading up to Xe 21+ can be observed. Through a set of rate equations, we show that the dominant sequential channels are sufficient for and consistent with the observed ionic species. Addressing the possible role of the giant resonance in this context, we evaluate the evolution of the neutral which is responsible for that resonance, examining its depletion during the pulse. We show that, owing to the large value of the cross section and in combination with the pulse duration, as the intensity rises towards the peak value, the neutral is depleted very early, at lower intensities, thus precluding its exposure to the higher peak intensities above 10 15 W/cm 2 . But we do point out that under much shorter pulse duration, direct many-electron multiple ejection may be a possibility, but not under the presently available conditions of intensity and pulse duration at the FEL (Free Electron Laser) facilities.

I. INTRODUCTION

Photo-absorption at short wavelength radiation, by which we mean the XUV and X-ray range, traditionally studied at synchrotron facilities, owing to limitations in the intensity of even the most advanced sources of that type, had been confined to singlephoton processes. This has changed with the recent appearance of new radiation sources at that wavelength range, such as the accelerator-based Free Electron Lasers (FEL) [1],

which have made possible the observation of photo-absorption driven by sub-picosecond pulses of intense radiation, leading inevitably to multiphoton (non-linear) processes. A number of experimental data, as well as related theoretical studies, especially in the rare gases, have already been published [2,3,4]. The first issue arising in this new context is whether the coupling to the radiation can still be described by LOPT (Lowest (non-vanishing) Order of Perturbation Theory). As long as the ponderomotive energy U p (cycle averaged kinetic energy of a free or loosely bound electron, in the field) is significantly smaller than the photon energy, LOPT is valid. To provide a point of calibration, note that for infrared radiation of photon energy 1 eV and intensity 10 13 W/cm 2 , U p = 1.43 eV, while it scales proportionally to the radiation intensity and inversely proportionally to the square of the photon energy. Then it follows that, for photon energies around 100eV, the range of interest in this paper, LOPT is valid, as long as the intensity is below 10 19 W/cm 2 , which is three orders of magnitude larger than the intensities employed in our calculations and related experiments. In addition, for the notion of the cross section to be applicable, the pulse duration should be at least 10 cycles of the field; a condition amply satisfied, at this photon energy, even for a pulse as short as 1 fs.

Due to the large peak intensity (up to about 10 16 W/cm 2 ), however, multiple ionization leading to the appearance of ionic species up to Xe 21+ have been reported in TOF (Time of Flight) data [3,4]. The first question that multiple ionization raises is whether sequential processes, leading to successive ionic species, represent the dominant mechanism, or whether the simultaneous ejection of several electrons is also a major contributing process and if so, what would the underlying mechanism be? This is of particular relevance to Xe, known to exhibit a so-called giant resonance at photon energy 100 eV, which involves a single-photon ejection from the 4d shell. An overall Theory of Multiple Ionization of Xenon under strong XUV radiation and the role of the Giant Resonance.3 theoretical interpretation [5], in so far as the dependence of the ionic species on laser intensity is concerned, up to about Xe 15+ , has shown that the underlying mechanism is indeed compatible with sequential ionization; beginning with the single-photon ejection of a 4d electron and the subsequent Auger process producing (with known branching ratios) one or two more electrons [6]. As a consequence of the relevant branching ratios, the most abundant species, throughout the intensity range covered in the experiments [2,3], is Xe 2+ , followed by Xe 3+ .

Although the photon energies of the two sets of data, namely 93eV [2] and 90.5eV [3], do not fall on the peak of the giant resonance, they are well within its broad width of about 30 eV, which implies relatively large cross section (about 22 Mb) very close to the peak value. This has prompted the speculation, albeit in rather vague terms, that the proximity to the giant resonance, in the presence of high intensity, may somehow play a role in the creation of multiply ionized species; other than producing Xe 2+ and Xe 3+ , which initiates the sequential route to the higher ions. Specifically, as stated in [3], under "high irradiance" i.e. 10 16 W/cm 2 , "due to the higher amplitudes, the collective oscillations within the 4d shell may lead to the emission of more than one 4d electron, up to all ten, more or less simultaneously and coherently". Clearly, for this scenario to be of any relevance, it is necessary for the neutral to be exposed to that "high irradiance". Given that, at these photon energies, the creation of up to Xe 7+ is due to a sequence of single-photon absorptions, the issue is amenable to detailed calculation, which is the chief objective of this work. This type of single-photon resonance has been studied, theoretically, as well as experimentally, quite extensively over the last few decades [6,[START_REF] Starace | Handbook der Physik[END_REF][START_REF] Andersen | [END_REF]9]. The magnitude of this feature is unusually large in Xenon, due to the double well shape of the potential and the strong localization of the continuum f-wave in the inner well at the resonance energy [START_REF] Starace | Handbook der Physik[END_REF]10,11]. It appears also in some of the ionic species of Xenon, as well as in the neighboring elements, gradually disappearing in the higher ionization stages, as the resonance is drawn below threshold and is transferred to the bound 4f state [START_REF] Andersen | [END_REF]9].

Although terminology may vary, it is well known that this resonance is essentially due to the d → f coupling matrix element and the overall behavior can be obtained even in a single-particle calculation [START_REF] Starace | Handbook der Physik[END_REF]12]. Accurate reproduction of the experimental cross section and its dependence on photon energy does of course require a sophisticated ap-Theory of Multiple Ionization of Xenon under strong XUV radiation and the role of the Giant Resonance.4 proach, such as RPA (Random Phase Approximation) [13] or Density Functional [14,15] which takes into account the correlation in this multielectron system. It must be emphasized at the outset that this giant resonance represents a photo-absorption process within lowest order perturbation theory (LOPT), as far as the coupling of the electrons to the radiation is concerned; which means that it is described by a transition probability per unit time (Fermi's golden rule), expressed in terms of a cross section. The intra-atomic couplings between the electrons are of course non-perturbative, as already mentioned above. And although the term collective is occasionally used in this context, it should be kept in mind that it is only one electron that is ejected by the photon. The Auger events that follow, leading to Xe 2+ and Xe 3+ , represent intra-atomic processes which occur even far away from the resonance.

Our main objectives in this paper are: (a) To provide an extension and more detailed exposition of our earlier work [5], including now ionic species up to Xe 21+ , thus confirming that the sequential channels alone account for the appearance of species as high as Xe 21+ . (b) To present a quantitative assessment of the role of the giant resonance. (c) To connect the underlying physics to more recent data, pertaining to the validity of LOPT. (d) To discuss the notion of direct multielectron ejection, a process that may turn out to be observable in future experiments, if sub-fs pulses become available in this wavelength range.

A few comments on terminology may be helpful here, before entering the technical aspects of the work. What we mean by sequential ionization is the chain of processes in which the absorption of one or more photons, depending on the ionization potentials, leads to successive ionic species (see Appendix). It is understood that the time scales are such that the ion produced relaxes to its ground state, before the next step in the sequence. This does not preclude the possibility of an ion left in an excited state, from which the next absorption event can occur. Whether this is a significant contribution will depend on the specific situation, i.e. atomic species, photon energy, pulse duration and intensity, as well as on how detailed the experimental data are. Be that as it may, in our equations below, it is assumed that the ions relax to the ground state, before the next event and that this relaxation includes the possible Auger process, as in the case with neutral Xenon. In strong-field radiation-atom interactions, at long wavelength (infrared), the term non-sequential is used to denote a process in which, the first (valence)

Theory of Multiple Ionization of Xenon under strong XUV radiation and the role of the Giant Resonance.5 electron pulled by the field from the atom, is set into oscillation acquiring the ponderomotive energy and upon returning to the atom, ejects another electron via a collision.

That is why this process is referred to as recollision. Obvioulsy, for this to be possible, the U p of the returning electron must be larger than the binding energy of the valence electron. This type of process is out of the question, in our context, because as already mentioned, the ponderomotive energy is too small to eject even a valence electron. Obviously, it is even smaller compared to the binding energy of a sub-valence electron.

What is in principle possible is the direct multiphoton ejection of two or more electrons, by means of multiphoton absorption of the necessary number of photons, which has nothing to do with recollision. That is why the proper term is direct multielectron ejection. The case of 2-photon direct two electron ejection in Helium, first proposed in [16], is a problem that has already received considerable attention [17,18,19]. Its generalization to several electron multiphoton direct ejection was introduced very recently in [20], while its possible relevance to this case is presented later on, in section V.

II. THEORETICAL FRAMEWORK AND MODELING.

In an experiment under a pulsed source such as the FEL, the atoms are exposed to radiation that rises from zero to the peak value and then falls off to zero, within tens of femtoseconds. Specifically in [3], the full temporal width of the pulse at half maximum (FWHM) was about 10 fs, which is by far sufficiently long for the notion of the cross section to be applicable. Since the conditions of the radiation-atom interaction in that experiment were well within the validity of LOPT, the evolution of the ionic species during the pulse is describable in terms of a set of differential equations, referred to as rate or kinetic equations. Such rate equations are perfectly adequate for the interpretation of experiments in which only total ionic yields are measured. When more detailed data, such as photoelectron energy spectra and angular distributions are measured, a more detailed description in terms of density matrix equations may be required. The input to these rate equations is the temporal behavior of the pulse -a Gaussian being sufficient for our purposes -as well as the relevant cross sections. As already mentioned above, the sequence from Xe to Xe 7+ , via the intermediate ionic stages Xe + , Xe 2+ ,...,

Theory of Multiple Ionization of Xenon under strong XUV radiation and the role of the Giant Resonance.6

Xe 6+ , proceeds by means of single-photon absorptions. The cross sections for all of these processes exist in the literature [6,[START_REF] Andersen | [END_REF]9,10], having been obtained through ab initio calculations, as well as measured in related experiments. The sequence beyond Xe 7+ involves 2-photon, 3-photon, etc. up to 7-photon absorption; the latter in the steps leading from Xe 19+ to Xe 21+ . Cross sections for these multiphoton processes can be obtained through an approach of scaling [21] which has been tested repeatedly over the last 25 years (including successful comparison to experimental data) and was employed in [5]. The complete list of the differential equations as well as the relevant cross sections, are given in the Appendix, while a schematic outline of the channels involved in the process is shown in Fig. 1.

Xe

2+ * : 4d A pivotal issue in our present inquiry is the evolution of the lower ionic species and in particular neutral Xenon, during the pulse. That is because, if we are to speculate on the possibility that, owing to the giant resonance, neutral Xenon when exposed to the higher intensities reached in the experiment may exhibit unusual behavior, we need to ascertain that it will not be depleted during the rise of the pulse. Even if one were to be skeptical about the level of accuracy of the multiphoton cross sections entering the sequence of processes beyond Xe 7+ , they are of no consequence as far as the evolution of the neutral is concerned (see also relevant discussion in the Appendix). It should be obvious, but it bears emphasizing, that what happens to the neutral does affect the Theory of Multiple Ionization of Xenon under strong XUV radiation and the role of the Giant Resonance.7 yield of the higher species, but not the other way around. Actually, mere inspection of the experimental ionic yields (Fig. 4 in [2]) suggests that, at the intensity at which Xe 8+ begins appearing in the data (around 8 × 10 13 W/cm 2 ), the neutral must have been depleted having given rise to the ionic species. And if we are to speculate about the possibility of all ten 4d electrons being ejected "simultaneously", we should examine in particular the intensity at which Xe 10+ begins appearing. We should at the same time examine whether the neutral, with its ten 4d electrons, is still intact, when that intensity is reached. Again, on the basis of the experimental data (Fig. 4 of [2]; where unfortunately the yield of Xe 10+ is not shown), we see that the yields of species like Xe 9+ and Xe 11+ , even at the highest peak intensity in the experiment 10 16 W/cm 2 , are two orders of magnitude below the yields of species like Xe 2+ , Xe 3+ and Xe 4+ . Thus it is evident that, even at the qualitative level, the data themselves suggest that up to Xe 7+

it is the single-photon processes that control the chain of events leading to the higher ions; simply because, if some 10-electron process played a significant role, one would expect a surge of Xe 10+ quite early in the pulse, while the neutral is still available. And here is where the crucial dilemma has already surfaced. Early in the rise of the pulse, the neutral is available, but the intensity is low. Later, as the intensity approaches its peak, the neutral will have been depleted. But the experimental data alone cannot

provide a definitive answer, as they do not contain information on the population of the neutral. Moreover, measured ionic yields, as shown in Fig. 4 of [2], come not only from the focal region, where the highest peak intensity is reached, but also from an expanded peripheral volume of lower intensities. It is therefore theory that can provide the missing link, by examining the population of the neutral during the pulse in the focal region.

Proceeding now beyond the qualitative assessment, we consider the sequential channels, depicted schematically in Fig. 1. Using an expanded version of the rate equations of [5] (23 differential equations, shown in the Appendix) to calculate the ionic yields, as a function of peak intensity, for a pulse duration of 10 fs, including the population of the neutral, we obtain the result shown in Fig. 2. We have, on purpose, left out the spatial integration over the interaction volume [5], in order to exhibit the evolution (the appearance and disappearance) of the ionic species as a function of the laser peak intensity, at the focal region where the intensity is maximum. The effect of the spatial Theory of Multiple Ionization of Xenon under strong XUV radiation and the role of the Giant Resonance.8

integration (essentially an instrumental, albeit unavoidable effect) is well known and has, in the context of this problem, been included in [5]. In any case, as already noted above, the signal produced in the peripheral (outside the focal region) interaction volume is due to lower intensities.

Examining now the population of the neutral in Fig. 2, first note that it is practically gone (reduced by 5 orders of magnitude from its initial value of 1) at a peak intensity of about 6 × 10 14 W/cm 2 , well below 10 16 . Note moreover that Xe 10+ begins appearing with a population of 10 -5 at an intensity of about 1.5 × 10 14 W/cm 2 , while it never exceeds the populations of Xe 7+ , Xe 8+ and Xe 9+ . Actually, the whole picture points rather clearly to the gradual leaking of the initial population through the sequence of ions. The peak values of the various ionic species, resulting from an interplay between the order of non-linearity and the value of the relevant cross section, reflect the rate of flow to and out of each ionic species. The abrupt changes of peak heights, as for example from Xe 11+ to Xe 12+ , are due to changes of the order of non-linearity, as determined by the corresponding ionization potentials. The overall picture then demonstrates that, if we were to postulate some unusual, even if unspecified, process that sets in at the higher intensities, say above 5 × 10 15

Theory of Multiple Ionization of Xenon under strong XUV radiation and the role of the Giant Resonance.9

W/cm 2 , leading to multiple electron ejection, it would have to originate from a species like Xe 6+ and not from the neutral with its giant resonance. It should be clear by now that, ironically, the effect of the relatively high cross section around that "giant" resonance is to cause the rapid depletion of the neutral at lower intensities, precluding thus the possibility of its exposure to the higher peak intensity.

A few further remarks concerning certain details of the sequence of processes are perhaps in order here. The photo-ejection of one 4d electron opens a hole whose filling by an Auger process, leads predominantly to the net ejection of 2 electrons, with (it bears repeating) known cross sections. That is why the dominant species up to intensities of about 5 × 10 13 W/cm 2 is Xe 2+ . The Auger lifetimes in this case are somewhat shorter than the pulse duration. Thus, in the scale of the pulse duration, the hole is in effect filled quickly, which means that the ejection of a 4d electron from Xe 2+ represents a significant channel, which is of course included in the calculation leading to the results of Fig. 2. It is true that Xe + and Xe 2+ do exhibit a resonance at around that photon energy, but with values of the cross section significantly smaller than that of the neutral;

which have anyway been incorporated in the rate equations. Beginning with Xe 3+ and beyond, single-photon ionization is dominated by electron ejection from the 5s and 5p shells. Be that as it may, all processes with significant cross sections, from all shells of importance, have been included in the rate equations. It is important to keep in mind that, in the experimental data which include yields from the peripheral volume of lower intensities, beyond the focal region, Xe 2+ will always dominate as is actually the case in [2], Fig. 4, as well as in our earlier work [5].

Theory can in addition provide a direct quantitative assessment of the evolution (depletion) of the neutral during the pulse. This is shown in Fig. 3, for pulses of various peak intensities, ranging from 10 13 to 10 16 W/cm 2 , all of 10 fs duration, confirming the picture discussed above in terms of the ionic yields. It is obvious, in particular, that for a peak intensity of 10 16 or even 10 15 , the neutral has been depleted severely, long before the peak intensity is reached. Note, moreover, that although at 10 14 W/cm 2 about 30 % of the neutral is still available at the peak intensity (Fig. 3 ), the population of Xe 10+ at that intensity is about 7 orders of magnitude lower.

Despite the apparent complexity of the problem, involving 23 differential equations and processes of non-linearity up to 7, we came across a rather interesting surprise, contained in the results of Fig. 4 in comparison to those of Fig. 2. In Fig. 2, the yield of Xe 3+ , over a range of intensities spanning two orders of magnitude, is visibly lower than what it is in Fig. 4. The difference is due to the values of the single-photon partial cross section leading from Xe to Xe 3+ , employed in the two calculations (as indicated in the caption of Fig. 4). Although theoretical and experimental values do exist in the literature [6], a difference by a factor of 1.66 between the values employed in Fig. 2 and 4 is well within the known uncertainties. Surprisingly, or maybe not, the relative yields of Xe 2+ and Xe 3+ in Fig. 4 are in much better agreement with the experimental results of [2]. It appears therefore that despite the high intensity and many stages of ionization, the data (taken at face value) can provide a clue as to the most appropriate value of the cross section for Xe → Xe 3+ . Incidentally, this provides an additional redundancy check of the decisive role of single-photon transitions in the sequence of ionization events, as well as the validity of the rate equations. In case there was a lingering doubt as to the validity of LOPT under the conditions of these experiments, further confirmation has been provided by a more recent experimental paper [22], in which the additional absorption of one photon, above that exciting the giant resonance, has been documented through the analysis of the photoelectron energy spectrum. This is an ATI (Above Threshold Ionization) process, corresponding to a net 2-photon absorption from a 4d electron. The slope of the respective photoelectron yield, as a function of FEL intensity (Fig. 4, [22]) in a log-log plot, has been found to be equal to 2, an unmistakable signature of LOPT. As is well known from strong field non-perturbative behavior, the onset of deviation from LOPT is characterized by the departure of the slope of ATI from that corresponding to the number of absorbed photons (see, for example, [23]). On the basis of our results in Fig. 2 and 3 above, this is hardly surprising, since we have shown that the neutral is depleted at the lower intensities. As a consequence, any photo-absorption product originating directly from the neutral, as

Theory of Multiple Ionization of Xenon under strong XUV radiation and the role of the

III. FURTHER EXPERIMENTAL CONFIRMATION OF LOPT

Theory of Multiple Ionization of Xenon under strong XUV radiation and the role of the Giant Resonance.12 the ATI electrons must be, will inevitably appear at the lower intensities, during the rise of the pulse, while the neutral is still around. Thus it goes without saying that any speculation about the behavior of Xe with its giant resonance at 10 16 W/cm 2 is devoid of meaning in the context of these experiments. But even if the neutral were exposed to an intensity near 10 16 W/cm 2 at this photon energy, as it might under a much shorter pulse, the behavior would still be within LOPT, as explained in our introduction above.

In the meantime, Pi and Starace [22] have published an ab initio value 5 × 10 -52 cm 4 sec for this ATI 2-photon (generalized) cross section at photon energy 93 eV, as obtained within LOPT. Using this cross section and that for single-photon absorption (22 Mb), it is straightforward to calculate the ratio of the two-photon to the singlephoton rate, at a given intensity. For example, at an intensity of 10 14 W/cm 2 , that ratio turns out to be 2 × 10 -4 , which means that the ATI yield is about four orders of magnitude smaller than the single-photon one, in reasonable agreement with what has been reported in [22]. On the other hand, if we were to use an intensity of 10 16

W/cm 2 , we would find this ratio to be 2 × 10 -2 or 2 % which is in the ballpark of the theoretical estimate of 0.5 % given in [22], but still quite different from the experimental value. Be that as it may, it should be clear by now that estimates for this ratio at such a high intensity are meaningless, because the neutral will never "see" an intensity of 10 16 W/cm 2 , for a 10 fs pulse. It is a simple exercise to show that the lifetime of the neutral (against ionization) at that intensity is less than 10 -16 sec.

IV. RELEVANCE OF COLLECTIVE PLASMA-LIKE OSCILLATIONS

The above experimental data on ATI and their quantitative theoretical interpretation have direct bearing on a very recent attempt [25] at interpreting the multiple ionization of Xe in terms of an ad hoc semiclassical model, in which the eighteen 4d, 5s and 5p electrons are modeled by a one-dimensional, damped, harmonically driven oscillator. By representing ionization in terms of damping constants, and through an adjustment of parameters, a curve resembling the giant resonance has been obtained in Fig. 2 of [25]. We shall refrain from commenting on the appropriateness and validity of such a model at this point in time, in view of the exhaustive information, accumulated

Theory of Multiple Ionization of Xenon under strong XUV radiation and the role of the Giant Resonance.13

over the last decades, on a well-established quantum phenomenon. But it is relevant and important to point out that any attempt at alternative theoretical models should at least be compatible with existing experimental data and of course self-consistent. There is, however, a serious difficulty in this case, because the model of [25] cannot possibly account for ATI which in view of [22] is an experimental fact, indisputably and quantitatively compatible with single-atom multiphoton theory. As we have shown above in detail, the behavior, magnitude and intensity dependence of that ATI yield prove, beyond any doubt, that the process begins with the ejection of one electron from the 4d shell. The 4d shell therefore begins breaking up very early in the pulse; precisely because of the large value of the cross section. One cannot have an ATI photoelectron without having an electron raised into the continuum by the absorption of one photon.

And of course the observed energies of the photoelectrons correspond exactly to those dictated by energy conservation. It is evident therefore that the experimental data are incompatible with the assumption of the 4d, 5s and 5p shells oscillating at high intensity.

Curiously, the experimental ATI paper [22] is not cited in [25], although its author is one of the co-authors of [22].

A few further remarks on this issue are in order at this point. (a) The fact that by adjusting parameters one can fit one feature of photoabsorption does not entail its validity, especially when it concerns a thoroughly studied and settled process, such as the giant resonance in Xenon. The above discussed ATI process is one of many others that cannot possibly be accommodated by the model of [25]. (b) The assertion that the model is not valid below 4×10 13 W/cm 2 poses another difficulty. As we have seen above, by the time this intensity is reached, the neutral has been depleted significantly. If we were to assume that the neutral remaining after that intensity, suddenly loses many electrons (of the order of 18), we would expect a sudden surge of ions around Xe 18+ . This however flies against the experimental data themselves (Fig. 4, [2]), as well as our theory, because in both the ions are seen to follow a sequence of appearance. (c) The modeling in [25] is based on a sudden turn on of the coupling which is incompatible with the real pulse. And it is not an academic issue but a very practical one, because as it was demonstrated a long time ago [21] and reconfirmed here, the wings in the rise of the pulse play a decisive role on the depletion of species through the sequential channels. That is why, non-perturbative behavior at long (infrared) wavelengths came into play when what the order of the photo-absorption process may be.

Finally, it may be helpful to remind the reader that ad hoc models for multiple ionization have been attempted long ago ( [21] and references therein), with reasoning similar, but not identical, to that in [25]. Careful and detailed investigations, however, demonstrated that the claims were incompatible with the rules governing radiation-atom interactions, in relation to the pulse duration. That in fact was the motivation for the introduction of the scaling approach [21] which was instrumental in demonstrating the fallacy of the so-called collective multiple ionization. Ultimately, it was the examination of photoelectron energy spectra that settled the issue [26]. In the present case, the signature of the ATI photoelectron energy alone provides a valuable, in fact crucial, clue. Nevertheless, more detailed studies of photoelectron energy spectra, such as a recent example in Kr [27], will provide further insight as to the relative magnitude of the channels leading to multiple ionization.

V. DISCUSSION AND OUTLOOK

Through a quantitative analysis of the time evolution of the Xe ionic species under radiation of photon energy 93 eV, pulse duration 10 fs and intensity up to 10 16 W/cm 2 , we have shown that neutral Xe is depleted well before that intensity is reached. As a result, the giant resonance with its large cross section cannot be a contributor to whatever may happen at intensities, say, above 5 × 10 14 W/cm 2 . The fact that, with increasing peak intensity, significant yields of ionic species are produced within a larger part of the interaction volume (outside the focal region), does not affect the argument, because the intensity in the expanded volume is lower. Moreover, whatever approximations may be involved in the values of the higher order -3-photon and above

Theory of Multiple Ionization of Xenon under strong XUV radiation and the role of the Giant Resonance.15

-cross sections, they do not affect the issue of the role of the giant resonance, since species up to and including Xe 7+ are produced via single-photon sequential absorptions, with known cross sections, within LOPT. This has in fact been verified directly through a parametric study, in which we have varied the values of the higher order cross sections, within a reasonable range, with the result that it is only the populations of the higher ionic species that are redistributed somewhat, without affecting the overall picture (see Appendix). It should be further noted that the known intensity fluctuations of the FEL pulses [1,20], do not affect our central argument. The yield of single-photon processes is not affected by the fluctuations, while their effect on N-photon processes is to increase the apparent N-photon cross section by at most a factor of N!, which again affects only the relative yields of the higher ionic species and not the neutral or the lower ionic species.

Still, in anticipation of future improvement of sources, there is a process of direct many electron ejection which is in principle possible and perhaps worth pondering.

Given sufficient intensity, it is conceivable (technically speaking there is a Feynman diagram) that ten 4d electrons can be ejected via an approximately 17-photon process, for photon energies in the range of 100 to 200 eV, leading to the creation of a Xe atom with a hollow 4d shell. This would be a process still within LOPT, but it would require a pulse duration well below 1 fs, so that the depletion of the neutral in the rise of the pulse can be avoided. The quantitative dynamics, lifetime and channels of decay of such a hollow state represent of course terra incognita and an enormously challenging problem.

This idea of direct multiphoton multielectron processes, involving up to 8 electrons, has been discussed most recently [20] in a specific quantitative context. Thus if and when FEL sources can provide sub-fs, intense pulses, it will be worthwhile to explore in more detail the feasibility of the observation of such direct multielectron processes. Although the details of the underlying dynamics represent a daunting task, still multiphoton cross sections for such direct processes can be estimated through scaling [20]. It is then a matter of extending our rate equations, by including such higher non-linearity direct processes, and assessing their contribution to the laser power dependence of ionic species, as compared to that of the sequential alone, as discussed in [20]. Such a project must, however, await the development of sub-fs, intense pulses in this short wavelength range; because otherwise it may simply remain as an academic theoretical exercise.

Theory of Multiple Ionization of Xenon under strong XUV radiation and the role of the Giant Resonance.16

There is, however, one point that should be made clear at this point in time.

The above direct, multielectron, multiphoton process has nothing to do with the giant resonance, which in any case is a single-photon process. All of the electrons in such direct processes are driven by the field, while in the giant resonance only one electron is ejected by the field, the role of correlation between the electrons in the shell being to lend enhanced oscillator strength to the single-photon transition. In contrast, in the direct process envisioned here, electron correlation would not be a major influence [20], since in a real sense each electron is pushed out by a photon. In fact, for a sufficiently short pulse, electron-electron interaction is completely negligible. Nevertheless, although in some sense the electrons would be ejected "together", instead of sequentially, we would refrain from using the term collective, as it may not be particularly helpful, if not misleading, since it conjures images of collective processes in heavy nuclei or mesoscopic systems which have hardly any resemblance to an atom.

Figure 1 .

 1 Figure 1. Schematic diagram of the main channels leading to sequential multiple ionization of Xe under radiation of photon energy 93 eV.

Figure 2 .

 2 Figure 2. Calculated population of the neutral and generated ionic yields of Xe, as a function of FEL peak intensity, under 93 eV radiation of 10 fs pulse duration.

Figure 3 .

 3 Figure 3. Evolution of the population of the neutral during the pulse for various peak intensities. The dashed line represents a pulse of 10 fs duration (FWHM).

Figure 4 .

 4 Figure 4. Sensitivity of the yields of Xe 2+ and Xe 3+ to the single-photon cross sections. The cross section for Xe → Xe 3+ employed in the calculation for this Figure is 10 Mb as compared to 6 Mb in the calculation for Fig. 2.

  Theory of Multiple Ionization of Xenon under strong XUV radiation and the role of the Giant Resonance.14 pulse durations broke the picosecond barrier. The corresponding barrier at XUV and beyond is of the order of sub-femtosecond. (d) The data moreover clearly demonstrate the sequential generation of successive ions according to well-known cross sections and the associated Auger processes, with Xe 2+ dominating the onset of ionization, followed by Xe 3+ , as expected by LOPT. (e) Atoms are neither clusters nor plasmas. They have well known structure and their coupling to radiation obeys selection rules, no matter

Acknowledgments

The authors are grateful to George M. Nikolopoulos for helpful discussions and comments, to A. F. Starace for clarifying information related to the value of the ATI cross section and to Hugo van der Hart for supplementary information on his estimate of the ATI contribution in [22]. Also detailed information on Xe cross section measurements by J. M. Bizau is gratefully acknowledged. Support by the European COST Action CM0702 is also acknowledged.

Appendix A.

The purpose of this Appendix is to provide the complete set of differential (rate) equations governing the production of the Xe ionic species by sequential multiphoton ionization, under radiation of photon energy 93 eV. The symbol N j (j = 0,1,2,,22) indicates the time-dependent population of the species of charge j+, and Ṅj the time derivative.

The symbol σ

(n) ij denotes the single-or multiphoton cross section for the transition from ionic species Xe i+ to Xe j+ , with the superscript n indicating the order of the process which appears also as the exponent of the time-dependent photon flux F(t). Absence of a superscript indicates a single-photon process. The calculation is limited to species up to and including Xe 22+ , because the highest species indicated in the experimental data in [3] is Xe 21+ . Strictly speaking, there should also be terms in the right-hand Theory of Multiple Ionization of Xenon under strong XUV radiation and the role of the Giant Resonance.17 side of the equations representing the creation of the excited hole state and its decay, via the appropriate cascade. It turns out, however, that such terms do not affect the results appreciably, because the pulse duration is longer than the relevant lifetimes [6]. Such terms will be necessary when pulse durations shorter than the leading lifetimes become available. Since only data in the form of TOF peaks have been given in [3], a quantitative comparison with the laser power dependence shown in Fig. 2, as well as Fig. A1 below, is not possible. Qualitative comparison through visual inspection of the TOF spectra in [3] appears to show reasonable resemblance with theory.

The rate equations are:

13,14 F 4 N 13 -σ For single-photon processes (up to Xe 7+ ), the cross sections have been taken

from [6,[START_REF] Andersen | [END_REF]9], as well as checked through independent calculation using Cowan's code (http://aphysics2.lanl.gov/cgi-bin/ION/runlanl08d.pl ). Multiphoton cross sections have been obtained mainly through scaling [21], while some 2-photon cross sections have also been calculated through a truncated summation.

It may be useful to devote here some space on the level of accuracy of the multiphoton cross sections, as obtained through scaling. First recall that a single-photon cross section is proportional to the square of a dipole matrix element between the initial and Theory of Multiple Ionization of Xenon under strong XUV radiation and the role of the Giant Resonance.19 final state. An N-photon transition amplitude involves a summation over (N-1) manifolds of intermediate states, in which a product of N dipole matrix elements appears in the numerator [21]. As usual, the cross section is given by the square of the absolute value of the transition amplitude. Dimensionally, therefore, it involves a product of N squared matrix elements. Now, an error of a factor of 2 in the squared single-photon matrix element, entails an error of a factor of 2 in the single-photon cross section. It follows then that, an error of a factor of 100 in the value of, say, a 6-photon cross section, is equivalent to an error of 100 1/6 =2.16, essentially the same as a factor of 2 in the single-photon case. As explained in detail in [21], the scaling procedure is exact for hydrogen-like systems. Its systematic extension to other atoms takes into account the size of the atom, as well as the ionization potential, both of which reflect the particular atomic structure of the species under consideration. Thus although no longer exact, through numerous applications and testing over the years, it has been found to be well within the accuracy of the relevant experiments in which the only measured quantity is the laser power dependence of ionic yields.


Christine S Autenrieth

Jens Baumert

Sebastian E Baumeister

Beate Fischer

Annette Peters

Angela Döring

Ph.D Barbara Thorand
email: thorand@helmholtz-muenchen.de.

Association between domains of physical activity and all-cause, cardiovascular and cancer mortality

Keywords: domains of physical activity, exercise, health-promoting effects, mortality

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

The health-promoting effects of regular physical activity on cardiovascular disease (CVD), chronic morbidity and premature death are well-established [START_REF] Nocon | Association of physical activity with all-cause and cardiovascular mortality: a systematic review and meta-analysis[END_REF][START_REF]Physical activity and health: A report of the surgeon general[END_REF][START_REF] Wannamethee | Physical activity in the prevention of cardiovascular disease: an epidemiological perspective[END_REF]. Despite the knowledge of its health-enhancing effects, engagement in exercise, especially in industrialized societies, remains poor across many European countries [START_REF] Sjöström | Health-enhancing physical activity across European Union countries: the Eurobarometer study[END_REF]. In recent years, efforts have been made to counter the increasing physically inactive lifestyle of many individuals through campaigns, on both national and international levels (e.g. by Federal Ministries of Health or the World Health Organization), to incorporate physical activity into daily living. Recent recommendations advocate a minimum of 30 minutes of at least moderate-intensity activities on most days of the week [START_REF] Haskell | Physical activity and public health: updated recommendation for adults from the American College of Sports Medicine and the American Heart Association[END_REF]. Although the association between physical activity and mortality has been examined extensively in the past several years [START_REF] Arrieta | Effects of leisure and non-leisure physical activity on mortality in U.S. adults over two decades[END_REF][7][START_REF] Mensink | Physical activity and its association with cardiovascular risk factors and mortality[END_REF], few studies have focused on domain-specific activities performed during daily routines [START_REF] Andersen | All-cause mortality associated with physical activity during leisure time, work, sports, and cycling to work[END_REF][START_REF] Barengo | Low physical activity as a predictor for total and cardiovascular disease mortality in middle-aged men and women in Finland[END_REF][START_REF] Matthews | Influence of exercise, walking, cycling, and overall nonexercise physical activity on mortality in Chinese women[END_REF]. Specifically, analyses of the four most common domains (domestic, transportation, work, leisure time) of physical activity on mortality are sparse [START_REF] Besson | Relationship between subdomains of total physical activity and mortality[END_REF]. For people not willing or not able to engage in leisure time activities at all, information on the effects of physical activity beyond leisure time is crucial. The importance of incorporating regular activities into daily routines has been averred by several physical activity experts in their recommendations, suggesting a protective effect from premature morbidity and mortality [START_REF] Dunn | Lifestyle physical activity interventions. History, short-and long-term effects, and recommendations[END_REF][START_REF] Murphy | Lifestyle physical activity for health[END_REF]. Especially household physical activity in relation to mortality has not been given sufficient attention; the distinct effect of regular housework in terms of all-cause and CVD mortality has only recently been investigated [START_REF] Besson | Relationship between subdomains of total physical activity and mortality[END_REF][START_REF] Stamatakis | Physical activity, mortality, and cardiovascular disease: is domestic physical activity beneficial? The Scottish Health Survey --1995, 1998, and 2003[END_REF]. In addition, few population-based data exist on different types and intensities of activity undertaken during daily routines and their relation to cause-specific mortality [START_REF] Matthews | Influence of exercise, walking, cycling, and overall nonexercise physical activity on mortality in Chinese women[END_REF][START_REF] Hu | The effects of physical activity and body mass index on cardiovascular, cancer and allcause mortality among 47 212 middle-aged Finnish men and women[END_REF][START_REF] Schnohr | Long-term physical activity in leisure time and mortality from coronary heart disease, stroke, respiratory diseases, and cancer. The Copenhagen City Heart Study[END_REF]. These considerations, and the insufficient prior systematic investigation of physical activity, subdivided into different domains, on all-cause, CVD and cancer mortality in a population-based cohort, were the motivation for this study.

METHODS

Study population

The presented data were derived from the second MONICA/KORA Augsburg survey (S2), conducted in 1989/1990 in the city of Augsburg and two adjacent counties. The study design, sampling, and data collection have been described in detail elsewhere [START_REF] Health Organization | The World Health Organization MONICA Project (monitoring trends and determinants in cardiovascular disease): a major international collaboration. WHO MONICA Project Principal Investigators[END_REF][START_REF] Lowel | The MONICA Augsburg surveys--basis for prospective cohort studies[END_REF]. In brief, for

Covariables

Baseline information on socio-demographic factors, medical history, and lifestyle habits were gathered by trained medical staff during a standardized interview. Educational attainment was estimated by recording years of school completed and then dichotomized into low (≤11 years of school) and high educational level (≥12 years of school).

Assessment of alcohol intake (in grams per day) was based on data regarding weekday and weekend consumption of beer, wine, and spirits and categorized into no, moderate (for men: >0-<40 g/day, for women: >0-<20 g/day) and high alcohol consumption (for men: ≥40 g/day, for women: ≥20 g/day). Study participants provided information about whether they had ever smoked cigarettes regularly (current, past, never).

Blood pressure (BP) and body mass index (BMI) were measured by trained medical staff.

BMI was calculated as weight in kilograms divided by height in square meters. BP was measured with a Hawksley Random Zero sphygmomanometer. Three BP recordings were taken from each individual after completion of the interview, i.e. after being at rest in a sitting position for an average of 30 minutes. The BP results provided are based on the mean of the second and third BP recordings. Further details on the measurement procedures are reported elsewhere [START_REF] Hense | Ten year trends of cardiovascular risk factors in the MONICA Augsburg region in southern Germany: Results from the 1984/1985, 1989/1990, and 1994/1995 surveys[END_REF]. Actual hypertension was defined as blood pressure values ≥140/90 mmHg and/or the usage of antihypertensive medication, given that the subjects were aware that they had hypertension [START_REF] Hense | Ten year trends of cardiovascular risk factors in the MONICA Augsburg region in southern Germany: Results from the 1984/1985, 1989/1990, and 1994/1995 surveys[END_REF].

Nonfasting blood samples were collected from all subjects under standardized conditions in 1989/1990 [START_REF] Keil | The cardiovascular risk factor profile in the study area Augsburg. Results from the first MONICA survey 1984/85[END_REF]. Total cholesterol was measured by an enzymatic method (CHOD-PAP, Boehringer Mannheim, Mannheim, Germany) and high-density lipoprotein (HDL) cholesterol was measured after precipitation with phosphotungstic acid/Mg2+ (Boehringer Mannheim, Mannheim, Germany) on fresh samples.

Statistical analyses

Baseline characteristics are presented by means and standard deviations for continuous variables. Categorical variables are expressed as relative frequencies. Pearson correlation was computed to determine the relationships between the continuous variables of interest. To avoid multicollinearity, only BMI was used for further analyses, as waist circumference was highly correlated with BMI (r =0.79).

Cox proportional hazards models, with days as the timescale, were applied to compute the hazard ratios and 95% confidence intervals (HR, 95% CI) for all-cause, CVD, and cancer mortality. The proportional hazards assumption was tested by the inspection of log((log)event) versus log of event times and proved to be sufficient. Persons categorized in "no physical activity" were defined as the reference group in each physical activity domain, except for work and total activity, in which light physical activity served as the comparison group. To take the non-linear increase of death risk with age into account, stratification by age groups (25-49, 50-59, 60-69, 70-74 years) was included in the Cox models. For each of the four physical activity domains, we calculated HR adjusted for sex, BMI, systolic blood pressure, total-to-HDL cholesterol ratio, education, smoking status, alcohol consumption, myocardial infarction, stroke, diabetes, cancer, self-reported limited physical activity due to health problems and the remaining other domains of physical activity. For total activity, the same model was calculated, but no adjustments for other domains of physical activity were made.

To assess the a priori assumed dose-response relation between domain-specific physical activity and type of mortality, linear trend tests across physical activity levels were performed by entering the categorical activity variable as a continuous variable into the Cox model.

Effect modifications were tested between physical activity and sex, as well as selected covariates, on mortality by additionally entering an interaction term of the respective variables into the model.

Due to the identified interactions, we then examined the joint effects of leisure time activity and systolic blood pressure, as well as leisure time activity and BMI, on all-cause mortality.

Tests were considered statistically significant with a two-sided p<0.05. The statistical software package SAS 9.1.3 (SAS Institute, Inc., Cary, NC) was used to perform all statistical analyses.

RESULTS

Between 1989 and 2007 (median follow-up period 17.8 years), 995 participants died; 452 from CVD and 326 from cancer. Baseline information of the study sample is presented in Table 1. Participants can be described as middle-aged and mostly free of chronic conditions.

One fifth of the subjects died during the 17.8 years of follow-up.

With regard to total and work activity, the majority of both men and women were moderately active, whereas during leisure time, light activities were most frequently reported. Different activity patterns for men and women were observed for transportation activity, in which most men reported no activity and women mainly engaged in moderate activities. This was similar in the household domain, whereby most men reported no activity and light intensity activities predominate among women.

As shown in Table 2, significant risk reductions for all-cause and CVD mortality can be reported for work, household, leisure time (only all-cause) and total physical activity (p trend <0.05). Engagement in leisure time and total activity was inversely associated with cancer mortality (p trend <0.01).

Being moderately active at work compared to the light activity group significantly reduced the risk for all-cause and CVD mortality by 31% (95% CI, 0%-52%) and 46% (95% CI, 7%-69%), respectively. For the household domain, significant risk reductions were only observed in light activities (all-cause mortality: 18%; 95% CI, 5%-29%; CVD mortality: 28%, 95% CI, 11%-42%). Compared to being sedentary, being vigorously active during leisure time significantly reduced the risk for all-cause and CVD mortality by 52% (95% CI, 35%-64%) and 50% (95% CI, 21%-69 %), respectively. However, neither moderate nor light activities during leisure time were associated with a significantly decreased CVD mortality risk.

Participants engaging in vigorous leisure activity lowered their risk of cancer mortality by 64% (95% CI, 41%-77%). The remarkable decrease in cancer mortality associated with leisure time physical activity is actually already present in light (42%; 95% CI, 20%-58%) and moderately (44%; 95% CI, 23%-60%) active subjects. For total activity, subjects categorized in vigorous activities were at reduced risk for all-cause (27%; 95% CI, 10%-41%) and cancer mortality (38%; 95% CI, 12%-57%). With regard to CVD mortality, a significant trend was observed, but the individual HR did not reach significance.

For transportation activity, however, no significant results or clear trends can be noted for either all-cause, CVD, or cancer mortality.

We also calculated the Cox model with each activity domain entered individually into the multivariable-adjusted model. Almost no statistical differences were observed, indicating that the domains are, in fact, independent of each other. In addition, the above-mentioned results

in the fully adjusted model did not change after excluding those persons who died during the first two years of follow-up (n=55, data not shown). Because the relationship between mortality and physical activity was not altered by sex, except for CVD mortality and transportation activity (p=0.049), when examining the interactions in any combination, all analyses were performed using combined data with both men and women (range of the pvalues across all activity domains: 0.133 to 0.846 for all-cause, 0.190 to 0.886 for CVD and 0.058 to 0.834 for cancer mortality).

Both systolic BP (p=0.030) and BMI (p=0.023) showed a significant interaction with leisure time physical activity on all-cause mortality. We therefore assessed the joint effects of systolic BP as well as BMI and different levels of leisure time activity. Persons engaging in vigorous leisure activity, in combination with a systolic BP<140 mm Hg (Figure 1) and a BMI<30 (Figure 2), respectively, served as reference groups.

As shown in Figure 1, the effect of increasing activity levels during leisure time was stronger among participants with a systolic BP≥140 mm Hg on reducing all-cause mortality.

Compared with the reference group, inactive persons with an increased systolic BP had the highest mortality risk (HR=2.10; 95% CI, 1.36-3.24) in our sample (p< 0.001). We recalculated the same model, in which we additionally considered antihypertensive medication, but the results were very similar (data not shown).

Figure 2

DISCUSSION

In our population-based prospective cohort study among middle-aged men and women, work, household, leisure time and total physical activity were significantly associated with a reduced risk of all-cause and CVD (except for leisure activity) mortality. The inverse relationship between leisure time as well as total activity with cancer mortality was highly significant, whereas walking and cycling for transportation was associated with neither all-cause nor cause-specific mortality.

To our knowledge, only one previous European study has individually examined the four most common physical activity domains (domestic, transportation, work, sports/exercise) on mortality, and reported similar results. In addition to total and sports/exercise activities being inversely associated with all-cause and CVD mortality, the authors also found evidence for the benefits of domestic activities, but none for work and transportation-related physical activity [START_REF] Besson | Relationship between subdomains of total physical activity and mortality[END_REF]. Two other studies have investigated several different forms of physical activity independently in relation to all-cause mortality [START_REF] Andersen | All-cause mortality associated with physical activity during leisure time, work, sports, and cycling to work[END_REF][START_REF] Matthews | Influence of exercise, walking, cycling, and overall nonexercise physical activity on mortality in Chinese women[END_REF]. With regard to the beneficial impact of leisure time physical activity or total activity, our results are consistent with a previous study which showed a dose-response relationship, predominantly in the leisure time domain, with all-cause mortality [START_REF] Lee | Physical activity and all-cause mortality: what is the doseresponse relation?[END_REF]. In contrast, the significant results for walking or biking as a means of transportation detected by Andersen et al. [START_REF] Andersen | All-cause mortality associated with physical activity during leisure time, work, sports, and cycling to work[END_REF] and Matthews et al. [START_REF] Matthews | Influence of exercise, walking, cycling, and overall nonexercise physical activity on mortality in Chinese women[END_REF] were not observed in the present study which may be explained by the use of different instruments.

In our study, among all three types of mortality investigated, the greatest risk reductions through engagement in leisure time activities are found for overall cancer mortality. Some population studies and reviews detected a reduced risk of cancer mortality through enhanced physical activity among men [START_REF] Orsini | Association of physical activity with cancer incidence, mortality, and survival: a population-based study of men[END_REF], women [START_REF] Matthews | Influence of exercise, walking, cycling, and overall nonexercise physical activity on mortality in Chinese women[END_REF] or both sexes [START_REF] Hu | The effects of physical activity and body mass index on cardiovascular, cancer and allcause mortality among 47 212 middle-aged Finnish men and women[END_REF][START_REF] Schnohr | Long-term physical activity in leisure time and mortality from coronary heart disease, stroke, respiratory diseases, and cancer. The Copenhagen City Heart Study[END_REF][START_REF] Lee | Physical activity and cancer prevention--data from epidemiologic studies[END_REF][START_REF] Thune | Physical activity and cancer risk: dose-response and cancer, all sites and site-specific[END_REF], but none of them has independently examined work, transportation, household and leisure time physical activity. A large prospective follow-up study from Finland [START_REF] Hu | The effects of physical activity and body mass index on cardiovascular, cancer and allcause mortality among 47 212 middle-aged Finnish men and women[END_REF] reported a 21% and 27% lower risk of cancer mortality for men and women, respectively, when comparing high versus low occupational and leisure time physical activity. With regard to our study sample, moderately active individuals almost halved their risk of premature deaths due to cancer, while vigorously active persons reduced their risk by almost two thirds. Likewise, a recent study among 2,560 men investigating the intensity level needed to reduce cancer mortality concluded that people have to engage in at least moderate leisure (sports, exercise) activities (>4.5 METs) to benefit from its effects [START_REF] Laukkanen | Intensity of leisuretime physical activity and Cancer mortality in men[END_REF]. Nonetheless, in our population, even light leisure activities (<3.0 METs) offer a 42% risk reduction compared to the inactive reference group.

Our findings emphasize the necessity to engage in sports activities and suggest that physical activity in daily routines (e.g. transportation and household activities) do not seem to be sufficient in the prevention of cancer mortality.

The results regarding the interactions of leisure time physical activity with systolic BP and BMI, merit some comment. Subjects who reported to be inactive, had a considerably higher risk of all-cause mortality than participants engaging in vigorous activities in both the systolic BP<140mm Hg and the systolic BP≥140 mm Hg group. Men and women with an increased systolic BP seem to benefit slightly more from enhanced leisure time in contrast to those with a normal systolic BP. These findings are in accordance with other studies reporting that high levels of physical activity or aerobic exercise may protect against the adverse effects of elevated systolic BP [START_REF] Vatten | Combined effect of blood pressure and physical activity on cardiovascular mortality[END_REF][START_REF] Whelton | Effect of aerobic exercise on blood pressure: a meta-analysis of randomized, controlled trials[END_REF].

Previous studies have hypothesized that high physical activity may attenuate the increased risk of mortality that is related to adiposity [START_REF] Hu | The effects of physical activity and body mass index on cardiovascular, cancer and allcause mortality among 47 212 middle-aged Finnish men and women[END_REF][START_REF] Koster | Joint associations of adiposity and physical activity with mortality: the National Institutes of Health-AARP Diet and Health Study[END_REF]. In our population sample, the beneficial effects of physical activity on mortality seem to be present in non-obese men and women (BMI<30) only.

The strengths of our study include a long follow-up period and its population-based representative design, while including a wide age range. The careful evaluation of important covariates in the MONICA/KORA Augsburg Surveys at baseline allowed for the adjustment of the most common risk factors related to all-cause, CVD and cancer mortality. Furthermore, data on the concurrent assessment of the four most important domains of physical activity is sparse in the literature, with the majority of previous studies focusing on leisure and/ or workrelated physical activity [START_REF] Lee | Physical activity and all-cause mortality: what is the doseresponse relation?[END_REF][START_REF] Oguma | Physical activity and all cause mortality in women: a review of the evidence[END_REF]. Besides these strengths, the study has also some limitations that need to be considered. As our data on physical activity were self-reported, reporting bias cannot be fully avoided. However, we used a validated and widely-applied questionnaire [START_REF] Iqbal | Validating MOSPA questionnaire for measuring physical activity in Pakistani women[END_REF][START_REF] Roeykens | Validity and reliability in a Flemish population of the WHO-MONICA Optional Study of Physical Activity Questionnaire[END_REF]. Another limitation is that physical activity was only recorded at baseline, making it impossible to report changes of activity patterns over time. We do not have follow-up data on physical activity at an individual level; therefore, we must assume that physical activity patterns remain fairly stable over time. This is a general problem in epidemiological studies and previous studies have also addressed this matter in their limitations [START_REF] Barengo | Low physical activity as a predictor for total and cardiovascular disease mortality in middle-aged men and women in Finland[END_REF][START_REF] Besson | Relationship between subdomains of total physical activity and mortality[END_REF][START_REF] Hu | The effects of physical activity and body mass index on cardiovascular, cancer and allcause mortality among 47 212 middle-aged Finnish men and women[END_REF]. Further research is needed to consider subsequent modifications in physical activity patterns during lifetime. The stringent categorization into low, moderate and vigorous physical activity may have led to misclassification, in some cases. Regardless, this solution worked best to combine the multiple answer options in the MOSPA questionnaire (e.g. subjects engaged in moderate and vigorous physical activity were categorized as vigorously active) and our division most probably reflects the participants' activity level correctly. We do not have data on other transportation-related exposures and participants who frequently walk or bike close to heavily travelled roads may be exposed to hazardous substances such as diesel exhausts and other fumes, which may counterbalance the positive effects of physical activity.

In conclusion, the physical activity domains work, household and leisure time as well as total activity showed inverse associations with mortality. The benefits of physical activity in terms of lower all-cause mortality were greatest among participants with an increased systolic BP who were non-obese. In light of the positive health effects ascribed to regular exercise, it is highly important to disentangle the different forms of physical activity, in order to promote those domains that contribute the most to positive health outcomes. It is therefore important that public health agencies endorse physical activity campaigns of any kind.

Nonexercise activities such as housework or work physical activity should be fully integrated into daily routines as their preventive nature has been proven in previous studies on various health outcomes. The findings of this study specifically underline that engagement in nonexercise activities beyond leisure time physical activity may be conducive to successfully reduce all-cause, CVD and cancer mortality risk. a Adjusted for sex, BMI, total-to-HDL cholesterol ratio, education, smoking status, alcohol consumption, myocardial infarction, stroke, diabetes, cancer, self-reported limited physical activity due to health problems and other domains of physical activity.

p=0.030 for interaction between leisure time physical activity and systolic BP a Adjusted for sex, systolic blood pressure, total-to-HDL cholesterol ratio, education, smoking status, alcohol consumption, myocardial infarction, stroke, diabetes, cancer, self-reported limited physical activity due to health problems and other domains of physical activity.

p=0.023 for interaction between leisure time physical activity and BMI

Figure 1 .

 1 Figure 1. Hazard Ratios (HR) a of all-cause mortality according to the joint effects of leisure

Figure 2 .

 2 Figure 2. Hazard Ratios (HR) a of all-cause mortality according to the joint effects of leisure

  For instance, subjects who engaged in light and moderate physical activity were categorized as moderately active, whereas cohort members who reported light and vigorous activity were classified in the highest activity level. A

	household (no, light, moderate) and total (light, moderate vigorous), and two for work activity
	(light, moderate).
	minimum time spent while executing the level of physical activity in each category was Outcome definition
	determined a priori. Thus, the four activity levels can be characterized as follows: End points used in this study were all-cause mortality and mortality from any CVD, cancer or
	S2, 6,637 individuals were drawn from a target population of 349,050 residents aged 25 -74 Participants who are represented in the category "no physical activity" did not report any other causes that occurred until December 31 st , 2007. Deaths were ascertained by regularly
	years, using two-stage random sampling stratified by age and sex. Of those, 4,940 individuals light, moderate or vigorous activity in the respective domain of physical activity. "Light checking the vital status of all sampled persons of the MONICA surveys through the
	participated in the baseline survey (baseline response: 76.9%). All subjects are currently physical activity" was defined as activities causing no or little increase in breathing or heart
	rate (<3.0 METs). "Moderate physical activity" was defined as activities causing little to
	moderate rise in breathing and heart rate (3.0-6.0 METs). Participants below the cut-off point
	of 120 minutes per week spent on moderate physical activity were reassigned to light physical
	activity. The highest activity level, "vigorous physical activity", classifies persons who
	engage in activities causing moderate to large increase in breathing and heart rate (>6.0
	METs). Participants below the cut-off point of 90 minutes per week were reassigned to
	moderate physical activity.
	The MET-minutes per week of the four domains of physical activity were then summed up,
	thereby creating a fifth rubric (total physical activity) that represents the overall activity level
	in the study participants. 36 persons who stated no physical activity at all, in any of the four
	physical activity domains, were allotted to "no physical activity" in each single domain, but
	were assigned to "light physical activity" for the total activity, in order to avoid a reference
	group of only 36 subjects.
	After restricting the analyses of occupational activity to employed participants only, data from
	2,538 cohort members were available for further analyses of work physical activity. With
	considerations for the activity levels reported in our population, we amended the MOSPA
	questionnaire to include the following categories for the activity domain variables; four
	activity levels for transportation and leisure time (no, light, moderate, vigorous), three for

followed within the framework of the Cooperative Health Research in the Region of Augsburg (KORA). Individuals with incomplete data on outcome (mortality, n=6), exposure (physical activity, (n=26)), or co-variables (n=268), were sequentially excluded from further analyses. Thus, 4,672 participants (2,373 men and 2,299 women) were available for the final analyses. The study was approved by the local authorities and all subjects provided a written informed consent.

Baseline measurements

MONICA Optional Study on Physical Activity (MOSPA)

The MOSPA questionnaire was designed to assess different domains of physical activity, asking participants to report the time usually spent on being physically active during work, transportation (walking or biking), household and/or leisure time, during a normal week over the past year. Based upon the subjects' indications, metabolic equivalents (METs, expressed in minutes per week) were calculated by means of a standardized program derived from the Compendium of Physical Activities

[START_REF] Ainsworth | Compendium of physical activities: classification of energy costs of human physical activities[END_REF]

and provided by the Centers for Disease Control and Prevention (CDC). Following the recommendations of the CDC and the American College of Sports Medicine

[START_REF] Pate | Physical activity and public health. A recommendation from the Centers for Disease Control and Prevention and the American College of Sports Medicine[END_REF]

, intensity categories (no, light, moderate, vigorous) were defined for each physical activity domain. Individuals were graded into the category according to the highest intensity level of their activities. population registries inside and outside the study area. Death certificates were obtained from local health authorities. Using the 9 th revision of the International Classification of Diseases (ICD), death certificates were coded for the underlying cause of death. Until December 31 st , 2007, 995 subjects died from all-cause mortality (ICD-9: 001-999), 452 from CVD (ICD-9: 390-459), and 326 from cancer (ICD-9: 140-208). 20 individuals were lost to follow-up in the final dataset.

Table 1 . Baseline characteristics

 1

	Men	Women	Total
	(n = 2,372)	(n = 2,299)	(n = 4,672)

Table 2 . Hazard Ratios (HR) by domain and physical activity level for all-cause, CVD and cancer mortality

 2 Adjusted for sex, BMI, systolic blood pressure, total-to-HDL cholesterol ratio, education, smoking status, alcohol consumption, myocardial infarction, stroke, diabetes, cancer, self-reported limited physical activity due to health problems, and other domains of physical activity. No adjustments for other types of physical activity in total activity.

				All-cause		CVD		Cancer
				995 events		452 events		326 events
		No. of	No. of	HR a	No. of	HR a	No. of	HR a
		subjects	deaths	(95% CI)	deaths	(95% CI)	deaths	(95% CI)
	Work b
	Light	328	36	Reference	17	Reference	13	Reference
	Moderate	2210	198	0.69 (0.48-1.00)	75	0.54 (0.31-0.93)	78	0.84 (0.46-1.54)
				p=0.048		p=0.028		p=0.574
	Transportation
	No	1633	333	Reference	145	Reference	108	Reference
	Light	485	86	1.08 (0.85-1.37)	31	0.94 (0.63-1.39)	40	1.49 (1.03-2.15)
	Moderate	1533	374	1.16 (1.00-1.35)	180	1.23 (0.98-1.55)	121	1.19 (0.91-1.56)
	Vigorous	1021	202	0.95 (0.80-1.14)	96	1.02 (0.78-1.34)	57	0.89 (0.64-1.24)
				p trend =0.774		p trend =0.395		p trend =0.836

a b Analyses restricted to working participants (n=2,538).

ACKNOWLEDGEMENTS

The KORA research platform (KORA, Cooperative Health Research in the Region of Augsburg) and the MONICA Augsburg studies were initiated and financed by the Helmholtz Zentrum München, German Research Center for Environmental Health (formerly GSF, National Research Center for Environment and Health), which is funded by the German Federal Ministry of Education and Research and by the State of Bavaria. The present study was performed within the KORA Age project which was financed by the German Federal Ministry of Education and Research (BMBF FKZ 01ET0713).

We thank all members of the Institute of Epidemiology of the Helmholtz Zentrum München and the field staff in Augsburg who were involved in the planning and conduct of the MONICA/KORA Augsburg. We are thankful to Prof. Dr. med Ulrich Keil, PhD, the principal investigator of the WHO MONICA Augsburg project. Finally, we express our appreciation to all study participants.