A Chafa

V Tatischeff

P Aguer

S Barhoumi

A Coc

F Garrido

M Hernanz

J José

J Kiener

A Lefebvre-Schuhl

S Ouichaoui

N De Séréville

J.-P Thibaud

Experimental determination of the 17 O(p,α) 14 N and 17 O(p,γ) 18 F reaction rates

Keywords: numbers: 26.30.+k, 25.40.Ny, 25.40.Lw, 27.20.+n, 26.50.+x

The 17 O(p,α) 14 N and 17 O(p,γ) 18 F reactions are of major importance for hydrogen-burning nucleosynthesis in a number of different stellar sites. In particular, 17 O and 18 F nucleosynthesis in classical novae is strongly dependent on the thermonuclear rates of these two reactions. The previously estimated rate for 17 O(p,α) 14 N carries very large uncertainties in the temperature range of classical novae (T =0.01-0.4 GK) whereas a recent measurement has reduced the uncertainty of the 17 O(p,γ) 18 F rate. We report on the observation of a previously undiscovered resonance at Ec.m.=183.3 keV in the 17 O(p,α) 14 N reaction, with a measured resonance strength ωγpα=(1.6±0.2)×10 -3 eV. We studied in the same experiment the 17 O(p,γ) 18 F reaction by an activation method and the resonance strength was found to amount to ωγpγ=(2.2±0.4)×10 -6 eV. The excitation energy of the corresponding level in 18 F was determined to be 5789.8±0.3 keV in a DSAM measurement which yielded a value of τ <2.6 fs for the level lifetime. The 17 O(p,α) 14 N and 17 O(p,γ) 18 F reaction rates were calculated using the measured resonance properties and reconsidering some previous analyses of the contributions of other levels or processes. The 17 O(p,α) 14 N rate is now well established below T =1.5 GK with uncertainties reduced by orders of magnitude in the temperature range T =0.1-0.4 GK. The uncertainty in the 17 O(p,γ) 18 F rate is somewhat larger due to remaining obscurities in the knowledge of the direct capture process. These new resonance properties have important consequences for 17 O nucleosynthesis and γ-ray emission of classical novae.

I. INTRODUCTION

Precise knowledge of the 17 O(p,α) 14 N and 17 O(p,γ) 18 F reaction rates is required for evaluating elemental abundances in a number of hydrogen-burning stellar sites, including red giants, asymptotic giant branch (AGB) stars, massive stars, and classical novae. These two reactions are parts of the carbon-nitrogen-oxygen (CNO) cycles. They are specifically very important for the nucleosynthesis of the rare oxygen isotope 17 O. Measurements of the oxygen isotopic abundance ratios 16 O/ 17 O and 16 O/ 18 O have been performed in several types of red giant stars (see [1] and references therein) and in presolar dust grains which formed in stellar outflows [2]. These data provide important information on nucleosynthesis and mixing processes in red giant and AGB stars, as well as on galactic chemical evolution and the age of the Milky Way [3]. However, the 16 O/ 17 O surface abundance ratio in evolved stars of mass > ∼ 2.5 M critically depends on the thermonuclear rates of the reactions 17 O(p,α) 14 N and 17 O(p,γ) 18 F [4].

Classical novae are thought to be a major -if not the dominant-source of 17 O in the Galaxy [5,6]. In addition, they can produce the short-lived radio-isotope 18 F (T 1/2 =110 minutes) whose β + decay is followed by γ-ray emission from positron-electron annihilation, which could be observed with γ-ray satellites like the INTEGRAL ob-servatory [7]. As the 17 O(p,α) 14 N and 17 O(p,γ) 18 F reactions govern the destruction of 17 O and the formation of 18 F, their rates are decisive in determining the final abundances of these isotopes [8]. Moreover, they have a small but noticeable effect on the energetics of the nova explosion [9]. Stellar temperatures of primary importance for nucleosynthesis are typically in the ranges T =0.01-0.1 GK for red giant, AGB and massive stars, and T =0.01-0.4 GK for classical nova explosions (peak temperatures of 0.35 GK can be easily achieved in explosions hosting very massive white dwarfs). Thus, for classical nova studies, the 17 O(p,α) 14 N and 17 O(p,γ) 18 F reaction cross sections have to be precisely known in the center-of-mass energy range E c.m. =0.017-0.37 MeV. In the NACRE compilation of thermonuclear reaction rates [10], the uncertainty in the rate of the 17 O(p,α) 14 N reaction was very important (orders of magnitude) in the temperature range T =0.1-0.4 GK, due to an unobserved narrow resonance at E c.m. ∼180 keV whose contribution to the total 17 O(p,α) 14 N rate had to be roughly estimated using a limit for the proton partial width [10]. The corresponding resonance in the (p,γ) channel was observed for the first time by Fox et al. [9] during the course of our study. The measured strength of (1.2±0.2)×10 -6 eV [9,11] reduces the uncertainty in the 17 O(p,γ) 18 F reaction rate by as much as orders of magnitude at nova temperatures.

The 17 O(p,α) 14 N and 17 O(p,γ) 18 F resonances at E c.m. ∼180 keV correspond to a level of spin-parity J π =2 -in 18 F, which was previously observed at an excitation energy E x =5786±2.4 keV via the 14 N(α,γ) 18 F reaction [12,13]. As reported in Ref. [12], the lifetime of this state was measured to be τ =15±10 fs using the Doppler-shift attenuation method (DSAM). This value implies a somewhat surprising ratio Γ γ /Γ α ∼1. It served to estimate the 17 O(p,α) 14 N resonance strength [10] which came out to be necessarily very small in relation with the small measured total width of the level.

The aim of this study was to measure all the properties of the level of 18 F at E x =5.79 MeV needed for a detailed knowledge of the 17 O(p,α) 14 N and 17 O(p,γ) 18 F reaction rates at nova temperatures. This includes precise determination of the excitation energy, the lifetime and the three partial widths (Γ p , Γ γ , Γ α ) of this level through measurement of the resonance strengths in the (p,α) and (p,γ) channels.

A preliminary report on the present work has been given elsewhere [14,15] and this paper is essentially a detailed version of the previous ones, with special emphasis put on calculation of the reaction rates and on some experimental points which needed to be clarified.

The experimental procedures and results are presented in Sec. II. Sec. II-A describes the DSAM experiment performed to measure both the excitation energy and the lifetime of the J π =2 -level at 5.79 MeV in 18 F. The observation of the previously unknown resonance corresponding to this level in the 17 O(p,α) 14 N reaction is presented in Sec. II-B where the measurement of its strength is described. In Sec. II-C, we report on the determination of the strength of the resonance at the same energy in the (p,γ) channel, using an activation method. Sec. III is devoted to calculations of the reaction rates derived from our measurements. In this section are also discussed revaluations of the contributions coming from other levels or processes. Finally, a summary and conclusions are given in Sec. IV.

II. EXPERIMENTAL PROCEDURES AND RESULTS

A. Excitation energy and lifetime of the J π =2 - level at 5790 keV in 18 F

The excitation energy and lifetime of the J π =2 -level at 5790 keV in 18 F have been reinvestigated using the Doppler Shift Attenuation Method (DSAM) applied to the 14 N(α,γ) 18 F reaction at E lab α =1775 keV. The corresponding resonance is known to be fairly strong [12,13] and to lead to relatively simple γ-ray spectra with unidirectional and monoenergetic recoil nuclei.

As already indicated, before this study, the level excitation energy was given as E x =5786±2.4 keV and its lifetime was found to be 15±10 fs [12]. Such a short lifetime is close to the sensitivity limit of DSAM. Thus, small differences in the measured Doppler shifts can lead to variations of orders of magnitude in the extracted lifetime and consequently in the derived level partial widths and resonance strengths. Furthermore, besides a smaller uncertainty in the calculated rates, a better precision on E x was helpful in the search of the (p,γ) and (p,α) resonances associated with the considered level.

Experimental set-up

Alpha beams of energy in the range E α =1620-1775 keV were supplied by the 4 MV Van De Graaff accelerator of the CENBG laboratory (Bordeaux). Typical beam intensities on target were 20-30 µA with a 3 mm×3 mm spot. The beam settings were adjusted to furnish parallel trajectories for incoming α-particles in order to improve the angle definition of the emitted γ rays.

The three used TiN targets were fabricated at the CENBG laboratory by nitration in an atmosphere of purified nitrogen of a titanium layer evaporated on a thick copper backing. The TiN layer was made thick enough (∼200 µg cm -2 ) to allow the simultaneous excitation of at least two of the four resonant levels in 18 F between 5.6 and 5.8 MeV excitation energy [13]. The water-cooled targets were placed at 90 • relative to the beam direction. A liquid nitrogen trap was placed near the target to reduce carbon accumulation.

The γ rays were detected with three large volume high-purity Ge (HPGe) detectors placed in the horizontal plane at a distance of 9 cm from the target. They were located at the laboratory angles θ lab =0 • , 123 • and 144 • . The three angles were measured with an estimated precision of ±2 • by means of optical sightings through a theodolite. The spread in angle due to the finite size of the detectors was estimated from the knowledge of their geometry as given by manufacturers. The efficiencies of the detectors were typically 70% at 1332 keV compared to a standard 3"×3" NaI detector. Their resolution (FWHM) was typically 2.3 keV at the same γ-ray energy. The Ge detector placed at 0 • was actively shielded with Bismuth Germanate (BGO) scintillation counters for Compton suppression in a standard geometry [16]. Compton-suppression BGO shields were not installed at 123 • and 144 • in order to place the Ge detectors as close as possible to the target to keep reasonable γ-ray efficiencies. During the measurements, three radioactive sources of 137 Cs, 60 Co and 88 Y were placed near the target to detect standard calibration lines together with the beaminduced γ rays.

Conventional electronics was used and γ-ray spectra were recorded with a standard acquisition system operating in singles mode.

Data analysis tools

Gamma-ray spectra were analyzed using the leastsquares peak-fitting program gf3 especially designed by D.C. Radford [17] for use with Germanium detectors. Two components were included in all peaks, namely a Gaussian and a low-energy skewed Gaussian. The dependence on energy of the two parameters defining the shape of the peaks (relative height of the two Gaussians and distance between them) was determined from analysis of a few well-resolved strong lines. The two parameters were then kept fixed to the calculated values in the peak-fitting procedure.

A specific program was written to extract the lifetime and excitation energy of the 5790 keV level from the measured energies of the corresponding lines in the 0 • , 123 • and 144 • spectra. Using Monte Carlo techniques, the energy distribution of the studied Doppler-broadened lines is calculated as a function of lifetime for γ rays detected at a given angle. The distribution of recoil-nucleus velocities is determined as a function of time using the most recent stopping-power data given in Ref. [START_REF] Ziegler | Program SRIM-2003[END_REF]. These data include electronic as well as nuclear stopping powers. The stopping material was considered to be titanium nitride (stoichiometry TiN). Angular scattering of recoiling ions is calculated in the same way, allowing for an investigation of correlation between energy and angular scattering which are usually treated as independent processes [START_REF] Blaugrund | [END_REF]. This correlation was found negligible (mean effect of less than 1%) in the specific studied case of short lifetimes where electronic stopping is by far the dominant process. Finally, the program gives a simulation of spectra detected in real detectors, in convoluting the theoretical energy distributions with Gaussian response functions of appropriate variance. The finite size of the γ-ray detectors is taken into account by Monte Carlo techniques. Namely, corrections for efficiency and for angular distribution [12,20] of the emitted γ rays in the detection cones were evaluated from GEANT [21] for the specific used detectors. Relativistic effects including aberration corrections [22] were fully taken into account in calculating the Doppler-shifted γ-ray energy distribution.

In the present study, the calculated line shapes were not analyzed due to the expected short values of the investigated lifetimes. Instead, we used the first moment of the simulated γ-ray energy distributions.

Data analysis and results

Since high-precision energy measurements were needed in that experiment, special care was taken to eliminate the electronic drifts of the system. In each run of typically 20 hours duration, γ-ray spectra were systematically recorded once every hour to allow for subsequent gain adjustment through the code gf3. It was checked after this adjustment that the energy resolution of peaks in the total accumulation was the same as in the short-time partial spectra. Furthermore, four independent measurements were carried out in order to check the overall consistency of the results extracted from the redundant couples of detectors 0 • -123 • and 0 • -144 • before extracting the final average values.

The 5790 keV level of 18 F was excited at the α-particle bombarding energy E lab α =1775 keV. Thanks to the appropriate target thickness, the level at 5671.6 keV was simultaneously populated to allow for measurements of energy differences relative to this reference peak whose short lifetime (total width Γ=0.13±0.05 keV) [23] ensures fully Doppler-shifted lines. Three runs were carried out in these conditions, using fresh targets for each run, and analysed independently. In addition, a run was performed at E lab α =1623 keV to excite simultaneously the 5672 keV level and the reference levels at 5603-5605 keV [13], in order to check the previously determined excitation energy of the 5672 keV level [24].

A section of a typical γ-ray spectrum taken at θ lab =0 • and E lab α =1775 keV is shown in Fig. 1. The lines used for calibration are indicated together with the resonant γ rays of interest. Figure 2 presents a relevant section of this spectrum where show up the full-energy (FE) lines R→1081 keV and R→937 keV for the resonant level at 5790 keV (the precise excitation energies of the final states are 1080.54±0.12 and 937.20±0.06 keV, respectively [13]).

In the analysis of the spectra, two separate energy calibrations were used. The first one, corresponding to the low-energy part of the spectra (E γ <4.2 MeV), was based on lines from standard sources ( 137 Cs, 60 Co and 88 Y) and from the 40 K natural radioactivity. In addition, we took advantage of boron contamination in the target to include in the set of calibration lines the 3853.807→0 keV and 3683.921→0 keV transitions [25] from the 10 B(α,p) 13 C reaction. We checked that the centroids of the corresponding peaks, fitted with the detector response function, are not significantly affected by Doppler shift due to the long lifetime of the 3854 keV level, i.e. τ =8.6 ps [25]. For the 3684→0 keV transition, two distinct components can be identified on the spectra (see Fig. 1): a narrow one coming from the feeding of the 3684 keV level by a transition from the long-lived 3854 keV level and a broad one which is from transitions implying shorterlived levels. Only the slow component of this line was considered for the energy calibration. Centroid values obtained from the fitting process were used to determine the quadratic energy calibration. Observed χ 2 values for the best estimated parameters lead to an energy uncertainty of ±200 eV at the three angles. The low-energy calibration served in determining the energies of the following transitions: 5672→3134 keV (FE), 5672→3062 keV (FE) and 5672→1081 keV (single escape).

A separate energy calibration was determined for the high-energy part (>4.2 MeV) of the spectra, using the same lines from 10 B(α,p) 13 C and the 5672→1081 keV (FE) and 5672→0 keV (FE) lines. For the latter transitions, the excitation energy of the 5672 keV level deduced from the low-energy part of the spectra (see below) was used. The involved full Doppler shifts were calculated from the Monte Carlo code taking into account the finite size of the detectors at the various angles as indicated above. A quadratic calibration was also used. The absolute energy uncertainty was larger than in the low-energy case due to the necessary introduction of Doppler-shifted reference lines. It was estimated to ±220 eV at θ lab =0 • and ±280 eV at backward angles. The high-energy calibration served to measure the shifted energies of the 5790→1081 keV (FE) and 5790→937 keV (FE) transitions.

In order to reduce the final uncertainty in the 5790 keV level, the Doppler-shifted energies of the corresponding γ-ray lines were measured relative to those deexciting the level at 5672 keV. We first did a new measurement of the excitation energy of the level at 5672 keV, given as 5672.57±0.32 keV in a previous experiment [24]. For this study, we analysed the spectra taken at θ lab =0 • in two runs at E lab α =1775 keV (using two different targets) and a third one at E lab α =1623 keV (see above). As already mentioned, the lifetime of the studied level is known to be very short, which ensures full Doppler shifts for the measured transitions R→3134 keV, R→3061 keV and R→1081 keV. For the transition R→3134 keV, the peak-fitting procedure had to take into account a doublet including a low-intensity component of close energy (∼4 keV) corresponding to the transition 5603→3062 keV.

Nine compatible results were obtained from analysis of the three lines in the three independent measurements. We finally obtained the weighted mean value of E x =5671.6±0.2 keV for the considered level. This result is ∼1 keV less than the previous value obtained in Ref. [24]. The discrepancy could be due to the erroneous value of 3853.807 keV adopted by the authors for the energy of the calibration line from the 10 B(α,p) 13 C reaction, instead of the correct one: 3853.170±0.022 keV.

The excitation energy and lifetime of the 5790 keV level were determined from the measurements of the differences in energy of the two lines 5790→1081 keV and 5790→937 keV and of the adjacent line corresponding to the transition 5672→1081 keV. These energy differences, ∆ i , were measured for the three detection angles θ i =0 • , 123 • and 144 • from analysis of spectra similar to the one shown in Fig. 2. For levels with comparable lifetimes, such a relative measurement has the advantage to strongly reduce the effect of the uncertainty in the angular position of the Ge detectors, because in this case the angular dependence is only effective on the difference in the Doppler shifts of the studied and the reference lines.

The results obtained for the 5790→1081 keV transition are shown in Fig. 3 for the couple of angles θ 0 =0 • , θ 1 =123 • . In this figure, we compare in the ∆ 0 -∆ 1 plane the measured value and the calculations from the Monte Carlo program described above. The experimental value is given together with the covariance ellipse corresponding to the bivariate normal distribution of the two in-dependent random variables ∆ 0 and ∆ 1 . The standard deviations of ∆ 0 and ∆ 1 are 0.3 keV and 0.4 keV, respectively. The calculated energy differences are given by a step of 2 fs in the lifetime range 0-22 fs for three excitation energy values of the resonant level, namely 5789.5, 5789.8 and 5790.1 keV. The effect of the uncertainties in the angular position of the detectors is negligible : when assuming a largely overestimated error of 5 • on the angle θ 1 =123 • , the corresponding error on ∆ 1 is found to be less than 0.1 keV in the whole lifetime range 0-30 fs, i.e. well below the uncertainty arising from centroid determination and energy calibration. The result extracted from Fig. 3 is E x =5789.84±0.27 keV and τ ≤5.1 fs (here the error bar on E x does not take into account the uncertainty in the energy of the reference line).

From plots similar to the one shown in Fig. 3, four consistent couples of values "Excitation energy-lifetime" were obtained from analysis of the two transitions 5790→1081 keV and 5790→937 keV. Taking into account the partial correlation between the two results obtained for the same transition (0 • -123 • and 0 • -144 • ) due to the unique measured value ∆ 0 , the weighted average amounts to E x =5789.8±0.3 keV and τ ≤2.6 fs (85% confidence level).

The error bar of E x takes into account the uncertainty in the energy of the reference level at 5671.6±0.2 keV. In view of the very short value observed for τ , the uncertainty arising from stopping power values has not been considered. The excitation energy is found to be in good agreement with the very recent result E x =5788.9±1.0 keV given in Ref. [11] from a study of the 17 O(p,γ) 18 F reaction at E c.m. =183 keV. The lifetime value is in disagreement with the previous result τ =15±10 fs of Ref. [12]. The search for the previously unobserved resonance at E c.m. =183.3 keV in the 17 O(p,α) 14 N reaction was prompted by the large width (Γ>0.25 eV) found for the corresponding resonant state at E x =5789.8 keV in 18 F. The value of E c.m. =183.3±0.6 keV for the resonance energy is calculated from our measured value of the excitation energy of the resonant level and from the Q-value for 17 O+p→ 18 F given in Ref. [26], Q=5606.5±0.5 keV. Note that the relatively large error on the resonance energy is essentially due to the uncertainty of 0.5 keV in the Q-value [26].

Targets and apparatus

The experiment was carried out at the electrostatic accelerator PAPAP of the CSNSM laboratory (Orsay), which can supply intense proton beams of energy E p <240 keV. The beam energy spread was typically 0.2 keV. More detailed characteristics of the accelerator can be found in Ref. [27]. Beam currents of 60-90 µA were typically sustained on targets. An annular electrode biased at a voltage of -300 V was mounted in front of the target to suppress the escape of secondary electrons.

Targets of tantalum oxide were used in the study of the 17 O(p,α) 14 N reaction. They were fabricated by 17 O ion implantation in 0.3 mm thick Ta foils at the SIDONIE implanter of the CSNSM. The total irradiation fluence was 1.5×10 18 atoms cm -2 , equally distributed at 30, 10, and 2.5 keV implantation energies. The resulting target thickness of a few keV is much larger than the width of the level at 5790 keV (Γ=6.8±3 eV, see Sec. III-A). Similar targets enriched in 18 O were produced using exactly the same experimental procedure in order to measure the strength of the 17 O(p,α) 14 N resonance relative to that of the well-known resonance at E lab R =150.9 keV in the 18 O(p,α) 15 N reaction (see below).

The targets were placed at 45 • with respect to the beam direction and cooled with deionized water. The target holder was surrounded with a copper assembly cooled with liquid nitrogen to limit the carbon buildup during the irradiation. No change in the target stoichiometry was noted from Rutherford backscattering spectrometry (RBS) measurements systematically performed before and after the proton irradiation, where the charge accumulated on each target was typically 1 C. The RBS measurements were performed on both 17 O and 18 O targets at the ARAMIS accelerator (CSNSM) with 4 He beams of 1.2 MeV energy.

In the PAPAP experiment, the outgoing α-particles were detected with 4 passivated implanted planar silicon detectors with active areas of 3 cm 2 . They had an energy resolution of 20 keV with a 241 Am radioactive source. They were placed at a distance of 14 cm from the target and at laboratory angles of 105 • , 120 • , 135 • and 150 • . Each detector was shielded by a 2 µm thick foil of aluminized Mylar in order to stop the intense flux of elastically scattered protons. Detector solid angles were measured with two different calibrated sources: 241 Am and a mixed source composed of 239 Pu, 241 Am and 244 Cm. Solid angle values around 1.42×10 -2 sr were found from these consistent measurements with a typical uncertainty of ±0.04×10 -2 sr.

Standard electronics was used and α-particle spectra were recorded with a data acquisition system operating in singles mode for subsequent analysis.

Results

We show in Fig. 4 an α-particle spectrum measured at E lab p =196.5 keV with the detector at θ lab =150 • . The strong peak at E α ∼430 keV is due to the previously unobserved resonance at E c.m. =183.3 keV in the 17 O(p,α) 14 N reaction. The energy E α ∼430 keV corresponds to that expected for α-decay from the level at 5.7898 MeV to the ground state of 14 N when taking into account both α emission at 150 • and energy loss in 2 µm thick foils of aluminized Mylar. The broad peak around 3.4 MeV in Fig. 4 originates from the reaction 11 B(p,α)2 4 He due to a slight boron contamination of the targets.

Figure 4b shows the interesting part of the α-spectrum measured at E lab p =196.5 keV. Alpha-peak intensities were derived from least-squares fits to the data assuming a Gaussian shape with intensity, position and standard deviation as free parameters. Such a fit is shown by the dashed line in Fig. 4b. Dead-time was systematically measured and controlled during the experiment and the small corresponding corrections (<3%) were applied to the derived number of counts.

The α-particle angular distribution was measured for the 17 O(p,α) 14 N resonance at E c.m. =183.3 keV. Before this measurement, we checked that the α-particle angular distribution for the 18 O(p,α) 15 N resonance at E lab R =150.9 keV was isotropic, as expected. The results for the 17 O(p,α) 14 N resonance are shown in Fig. 5. The solid line is a Legendre-polynomial fit to the data:

W c.m. (θ α ) = 1 + a 2 P 2 (cosθ α ) , (1)
which yields a 2 =0.16±0.03. Note that the Legendrepolynomial development was limited to a 2 since the capture of relative angular momentum l=3 should be weak relative to that of l=1 due to the low energy of the resonance. The adopted development for W c.m. (θ α ) is thus expected to provide a sufficient description of the angular distribution for the determination of the resonance strength.

The measured excitation function of the 17 O(p,α) 14 N reaction is shown in Fig. 6a. The typical energy step was 0.2 keV and the accumulated charge was 0.04 C per data point. Small corrections were applied on energy to account for a moderate carbon deposit on the target (∼20 eV per point). These corrections were only noticeable for the last measured data points where the carbon build-up was maximal. Alpha yields were also slightly altered by the carbon deposit due to the induced energy straggling. Corrections for this effect were evaluated by measuring excitation functions with targets already used in previous measurement. The resulting corrections were applied to the data points and found to be small (a maximum value of 10% at the end of the measurement and of 1-3% for the most important data points). The given yields result from the sum of the individual values measured at each of the four angles normalized according to the determined angular distribution. We checked that the observed depth profile (Fig. 6a) is consistent with the characteristics (fluences and successive energies) of the implantation procedure. Measurements were repeated with three 17 O implanted targets and fully compatible results were obtained.

As already mentioned, the strength of the 17 O(p,α) 14 N resonance was determined relative to that of the strong resonance at E lab R =150.9 keV in the 18 O(p,α) 15 N reaction. Two runs with fresh 18 O targets were performed in between the three 17 O ones. They also gave fully compatible results. RBS measurements (see above) performed on 17 O and 18 O targets showed no difference between the 17 O-and 18 O-implanted ones. In particular, a similar stoichiometry was found for the 17 O and 18 O targets whatever the depth and surface position, with a maximum ratio (O/Ta) max =3.1±0.3.

The similarity of the 17 O-and 18 O-implanted targets is further demonstrated in Fig. 6b which shows a comparison of measured excitation functions for the new resonance at E lab R =194.1 keV in the 17 O(p,α) 14 N reaction and for the 150.9 keV resonance of 18 O(p,α) 15 N. The data for the latter resonance were appropriately normalized and shifted in energy to be compared with those obtained with the 17 O target. The shift in energy for the data points of the 18 O(p,α) 15 N resonance was achieved according to the relation

E 18 (keV) = 194.1 + (E mes 18 -150.9) × 0.95 , (2)
where the factor 0.95 is the ratio of stopping powers of the (3) Here, ωγ 18 pα is the strength of the 18 O(p,α) 15 N resonance; m p , M 17 and M 18 are the proton, 17 O and 18 O masses, respectively; E 17 R and E 18 R are the laboratory energies of the two resonances; ( 17 / 18 )=0.95±0.05 is the ratio of the effective stopping-powers in the laboratory system [START_REF] Ziegler | Program SRIM-2003[END_REF], where the error arises from the uncertainty in the stoichiometry of the 6b). This ratio was found to be (Y 17 pα /Y 18 pα )=(7.7±0.9)×10 -3 , where the major contributions to the uncertainty come from the target composition (10%) and the beam current integration (5%). The strength of the reference resonance at 150.9 keV in the 18 O(p,α) 15 N reaction was taken as ωγ 18 pα =0.167±0.012 eV. This value, obtained in a careful measurement by Becker et al. [28], is in very good agreement with a previous measurement [29] which gave ωγ 18 pα =0.17±0.02 eV.

We finally obtain ωγ pα =(1.6±0.2)×10 -3 eV for the strength of the resonance at E lab R =194.1 keV in the 17 O(p,α) 14 N reaction. The main contributions to the [1] Note that there is a typographical error in Eq. (1) of Ref. [14], as the exponent of 3 of the mass ratio term is missing. However, the 17 O(p,α) 14 N resonance strength was deduced from the correct equation given here.

error bar have been given above. The statistical uncertainty in the number of counts was negligible as well as the uncertainty in the energies of the two involved resonances.

Our resonance strength value is in very good agreement with the results of two very recent experiments performed either in inverse kinematics [30] or using a different type of 17 O target (not implanted) [31].

The resonance energy derived from the measured excitation function was found to be E lab R =194.3±0.7 keV. To obtain this value, the energy at half the maximum yield was corrected for taking into account the mean implantation depth of the 17 O ions at the lowest of the three used energies (see Sec. II-B-1). It is in excellent agreement with the value of 194.1±0.6 keV obtained from the excitation energy of the resonant level and the Q-value for 17 O+p→ 18 F.

C. The Ec.m.=183.3 keV resonance in the 17 O(p,γ) 18 F reaction

The strength of the 17 O(p,γ) 18 F resonance at E lab R =194.1 keV was obtained from measurements by an activation method of the 18 F total production in irradiated 17 O targets. The number of produced 18 F nuclei was determined from measurement of the 511 keV γ-rays due to β + annihilation following 18 F radioactive decay. The strength was measured relative to that of the resonance at the same energy in the 17 O(p,α) 14 N channel (see above) by measuring the corresponding α-yields during the irradiation phase of the experiment.

Experimental set-up and targets

The experiment was carried out at the electrostatic accelerator PAPAP of the CSNSM laboratory. The experimental apparatus was exactly the same as described for the 17 O(p,α) 14 N experiment, except for γ-ray measurements. The 18 F β + activity was measured with two large volume HPGe detectors (of 70% efficiency) positioned opposite one another in a very close geometry, in order to register in time coincidence the two 511 keV photons from positron-electron annihilation. A standard fast-slow coincidence system was used for the measurements. The time resolution as measured from the recorded time spectrum was typically 5 ns (FWHM). The events were recorded in a multidimensional data acquisition system for subsequent analysis. The stability of the whole electronics was systematically checked with a special emphasis put on the stability of the contours in the E γ -E γ plane used to derive the number of 511-511 keV coincident events.

Targets enriched in 17 O were produced by ion implantation in the same conditions as those for the 17 O(p,α) 14 N reaction. After irradiation by protons at E lab p =196.5 keV (on resonance) or E lab p =192.7 keV (off resonance), the 17 O targets were rapidly (in ∼4 minutes) placed between the two Ge detectors for γ-ray counting. Alpha-particle yields were measured using the same αdetector arrangement as described in Sec. II-B-1.

Experimental procedure and results

The 17 O-implanted targets were bombarded for typically 5 hours (∼2.7 half-lives of the radioisotope 18 F, T 1/2 =109.77 minutes) at ∼70 µA beam intensity. During the target irradiation, α-particle spectra were recorded every 15 minutes together with the corresponding beam charge.

Apart from 18 F, only two long-lived emitters could be significantly produced during the irradiation phase, namely 11 C (T 1/2 =20.39 minutes) by the reaction 10 B(p,γ) 11 C and 13 N (T 1/2 =9.965 minutes) by the reaction 12 C(p,γ) 13 N. The former reaction was found to be negligible from systematic measurements of boron contamination in the targets via the 11 B(p,α)2 4 He reaction (see Fig. 4a). However, a moderate production of 13 N had to be taken into account (see below) because of a carbon build-up on the target measured to be about 0.5 µg cm -2 per Coulomb of accumulated proton charge. A blank Ta target irradiated in the same experimental conditions showed no β + activity but the one due to 13 N.

The efficiency β for the β + -activity detection was measured using calibrated 22 Na and 65 Zn sources. The sources were fixed at the centre of a tantalum foil identical to the 17 O target backing and the resulting assembly was positioned between the Ge detectors at the same place as the irradiated targets. With the 22 Na source, pulse pile-up due to the emission of the 1.275 MeV γray simultaneously with the two 511 keV ones must be taken into account, especially for high efficiency detection systems. This effect was incorrectly neglected in a previous analysis of our measurement [14] and we detail here how the proper value of β already reported in Ref. [15] was obtained. The value obtained without taking into account pile-up effects [14] must be multiplied by the factor

r c = 1 1 -r( A + B ) , (4)
where r=0.904 is the β + branching ratio of 22 Na [START_REF]NuDaT database[END_REF] and A ( B ) the probability for the 1.275 MeV γ-ray to be detected in the detector A (B). A and B have been measured using the 1.115 MeV line of the 65 Zn source which is not affected by pile-up (except accidental pileup, see below). A correction of 6.5% was applied to the measured A and B to take into account the difference in energy of the 1.115 and 1.275 MeV lines. Accidental pile-up was minimised by using low-activity sources and short pulse shaping constants. It was finally taken into account as a very small correction (<1%). To account for the finite size of the beam spot on the target during proton irradiation (∼8 mm), the source position was varied by 5 mm from the centre which results in a correcting factor of 0.98±0.02. Many consistent measurements were performed with two different 22 Na sources. A number of such efficiency measurements were repeated with a 65 Zn source with the advantage of no "true" pile-up effect in that case. The average value from this fully consistent set of measurements was found to be β =(4.2 ±0.2)% [15]. The total number of 18 F nuclei contained in the targets at the end of the irradiation was measured from a fit of 18 F and 13 N decay curves to the γ-ray data recorded for ∼6 hours. The best fit was obtained from the maximum of the likelihood function for Poissondistributed data. The 18 F radioactive half-life was set as a free parameter in the fit while the 13 N half-life was fixed to T 1/2 =9.965±0.004 minutes [START_REF]NuDaT database[END_REF]. The results are shown in Fig. 7 for irradiation of fresh 17 O targets at two energies (on resonance at E lab p =196.5 keV and off resonance at 192.7 keV). The relative contribution of 13 N is small at E lab p =196.5 keV, but noticeable off resonance. Also shown in Fig. 7 is the very small background contribution to the 511×511 keV coincident rate which was measured to amount to (1.9±0.2) counts per hour from numerous independent measurements. The total numbers of 18 F at the end of the irradiation were 4910±440 at E lab p =196.5 keV (on-resonance) and 422±177 at E lab p =192.7 keV (offresonance). The value of the 18 F half-life from the fit was found to be T 1/2 =105 +19 -14 minutes (103 +217 -47 minutes) at E lab p =196.5 keV (192.7 keV), which is in excellent (reasonable, inherent to the low statistics) agreement with the actual value of 109.77±0.05 minutes [START_REF]NuDaT database[END_REF]. The experiment was repeated using a fresh 17 O target obtained in the same implantation conditions. Fully consistent results were obtained in the two independent measurements.

The far larger number of 18 F nuclei produced at the highest beam energy is clearly due to the excitation of the 17 O(p,γ) 18 F resonance at E lab R =194.1 keV. The lower 18 F production at E lab p =192.7 keV proceeds from direct capture (DC) interfering with the low-energy part of the resonant capture at E lab R =194.1 keV. The resonance strength was derived after evaluation of the DC cross section (see Sec. III-C-1) and a small contribution of (4.3±2.2)% for DC was subtracted from the 18 F total production at E lab p =196.5 keV. We also applied to the measured (p,γ) resonance strength a correction arising from the backscattering of 18 F nuclei, which could escape the target at the time of their production. This correction was evaluated to be (4±2)% from calculations performed with the program SRIM-2003 [START_REF] Ziegler | Program SRIM-2003[END_REF] for the estimated implantation profile of the 17 O targets.

We finally obtained from the weighted mean of the two measurements at E lab p =196.5 keV: ωγ pα /ωγ pγ =717±60. The advantage of measuring the strength of the (p,γ) resonance relative to that of the (p,α) channel is that the measured value is free from the uncertainties related to the target composition and the charge measurement. In the analysis, it was only assumed that the beam intensity was constant during the sub-runs (15 minutes) of the irradiation. The number of emitted α-particles was determined at the end of each sub-run in the same way as described in Sec. II-B-1.

The quoted error in this ratio mainly arises from uncertainties in the measured β + activities (statistical uncertainty of 7%), in the associated β + -detection efficiency (5%), as well as in the measured α-particle intensities (1%) and detection efficiency (3%).

The resulting (p,γ) resonance strength is ωγ pγ =(2.2±0.4)×10 -6 eV, where the uncertainty in the corresponding (p,α) strength is taken into account. Our value is somewhat larger than that obtained in a recent study [9,11]: (1.2±0.2)×10 -6 eV. The study of Refs. [9,11] is different from ours in mainly two basic points: targets prepared by anodization of tantalum in 17 O-enriched water, and in-line detection of prompt emitted γ-rays using a large-volume HPGe placed at θ =0 • very close to the target. The reason for the disagreement between the two measurements is unclear. It cannot be ascribed to the value of the (p,α) resonance strength used as a reference in our study since it appears to be in good agreement with two very recent measurements (see Sec. II-B-2).

The DC cross section has been derived from the measurement at E lab p =192.7 keV according to the equation:

Y CD = ∆E σ(E) (E) dE , (5)
where Y CD is the measured 18 F production yield per incident proton, ∆E is the target thickness and (E) is the stopping cross section. ∆E and (E) were taken from the measured excitation function for the (p,α) resonance. The astrophysical factor S DC (E) was assumed to be constant in the small energy range ∆E. To derive its value, interference between DC and resonant capture at E lab R =194.1 keV was taken into account from a calculation using the present results for the resonance cross section and S DC (E) as estimated in Sec. III-C-1 (see Eq. 13). The corresponding correction amounts to 15%. We finally found S DC =8.3±4.0 keV barn at the effective energy E c.m. =180.2 keV, where the large error bar comes essentially from the statistical uncertainty (see Fig. 7).

III. REVISED REACTION RATES FOR THE H-BURNING OF 17 O

We have calculated the revised reaction rates for the H-burning of 17 O resulting from our experimental results. We have also investigated the DC cross section of the 17 O(p,γ) 18 F reaction from an analysis of the current data. The general expression for reaction rates is given by (e.g. [10])

N A σv = N A (8/π) 1/2 µ 1/2 (k B T ) 3/2 ∞ 0 σE exp(-E/k B T )dE , (6)
where N A is the Avogadro number, µ the reduced mass of the system, k B the Boltzmann constant, T the temperature, σ the cross section, v the relative velocity, and E the kinetic energy in the center-of-mass system. We performed numerically the integration of this equation for both resonant and non resonant processes (DC capture). In the Breit-Wigner cross section formula for resonances, we took into account the variation with energy of the partial and total widths of the involved levels, when these quantities are known. It is now the case for the level at 5.7898 MeV in 18 F since the partial and total widths of this level can be extracted from the presently measured strengths of the resonances at E R =183.3 keV (in the following the resonance energies are given in the center-of-mass system, unless mentioned otherwise) in the 17 O(p,α) 14 N and 17 O(p,γ) 18 F reactions and from the previously determined strength of the corresponding resonance at E R =1.375 MeV in the 14 N(α,γ) 18 F reaction [12].

For the levels above the reaction threshold, we used the relations:

Γ p,α (E) = Γ p,α (E R ) P l (E) P l (E R ) , (7)
Γ γ (E) = Γ γ (E R ) f B f E -E f E R -E f 2λ f +1 , (8)
where E R is the resonance energy, P l is the penetration factor associated with the relative angular momentum l, B f is the γ-ray branching ratio to the final state of energy E f in the compound nucleus and λ f is the multipolarity of the corresponding γ-ray transition. In the calculation of Γ γ (E), we only considered the two decay transitions with the higher branching ratios even when the deexcitation of the involved level is more complex (branching ratios were renormalized in that case). For mixed transitions, we adopted the multipolarity of the dominant transition when the corresponding mixing ratio is known [13], the lowest allowed one otherwise. We checked that for the complex deexcitation level at 5.6716 MeV the inferred difference in reaction rate values compared to exact calculation is lower than 0.25%. In the calculation of P l , the channel radius was obtained with r 0 =1.25 fm.

For the sub-threshold levels, the proton partial width is given by

Γ p (E) = 2P l (E)C 2 Sθ 2 sp , (9)
with C 2 S being the spectroscopic factor and θ 2 sp the single-particle reduced width.

The so-called level shift [START_REF] Thomas | [END_REF] was also introduced in the Breit-Wigner expression when necessary (i.e. when the proton width amounts to more than 10% of its maximum value).

From the values ωγ pγ =(2.2±0.4)×10 -6 eV and ωγ pα =(1.6±0.2)×10 -3 eV measured in this study for the strengths of the E R =183.3 keV resonances, and from ωγ αγ =(1.57±0.60)×10 -2 eV taken from Ref. [12] for the resonance at E R =1375 keV in the reaction 14 N(α,γ) 18 F, the values of the proton, α, γ and total widths of the level at 5.7898 MeV in 18 F are found to be Γ p =(0.38±0.05)×10 -2 eV, Γ α =6.8±3.0 eV, Γ γ =(0.94±0.36)×10 -2 eV and Γ=6.8±3.0 eV, respectively. With these values, the total width is found consistent with the measured level lifetime: τ ≤2.6 fs. It is in disagreement with the previous value of (15±10) fs given in Ref. [12]. The large error bars on Γ α , Γ γ and Γ come essentially from the uncertainty in ωγ αγ [12].

B. The 17 O(p,α) 14 N reaction rate

In the calculation of the 17 O(p,α) 14 N reaction rate, we considered the levels in 18 F at 5.6034, 5.6716 and 5.7898 MeV and fifteen levels at higher energies as done in Ref. [10]. Revised values were obtained for the rate contributions of the three lowest levels. An interference effect between the presently observed resonance at E R =183.3 keV and that at E R =1202.5 keV was also investigated. Contributions from the other levels are the same as in Ref. [10] (see page 91 of Ref. [10] for the adopted resonance strengths). The parameters of the six most important levels in 18 F for the total rate at T <0.3 GK are summarized in Table I.

The proton width of the sub-threshold level at 5.6034 MeV was revaluated by calculating its singleparticle reduced width using a Woods-Saxon potential with the same parameters that were adopted in Ref. [36] to extract the spectroscopic factor. The resulting proton width is lowered by a factor of ∼3 compared to Refs. [10,36] where the single-particle reduced width was identified with the Wigner limit. For this sub-threshold state, the level shift was introduced in the Breit-Wigner formula with a mean effect of ∼5% on the calculated rates.

The total reaction rates are given by an incoherent sum of the individual contributions of the involved resonances. The only exception is for the resonance at E R =183.3 keV whose interference with the broad one at E R =1202.5 keV (Γ=79±5 keV [35]) was considered using the two-level approximation given in Ref. [37]. The effect was found to be weak and was introduced as a small increase in the uncertainty in the rate for temperatures between 0.1 and 0.2 GK.

The calculated total reaction rates are given in Table II for temperatures of T =0.01-1.5 GK, together with lower and upper limits corresponding to 1σ confidence level. If the modal rate was calculated by numerical integration as already indicated, the uncertainties corresponding to the given limits were obtained from propagation of the statistical errors on the involved parameters using the well-known approximate relations [10]:

N A σv R = 1.5394 × 10 11 (AT 9 ) -3/2 (ωγ) × exp(-11.605E R /T 9 ) , (10)
N A σv tail = 7.8318 × 10 9 (Z p Z t /A) 1/3 S(E 0 )T -2/3 9 × exp(-4.2486(Z 2 p Z 2 t A/T 9 ) 1/3 ) , (11)
where N A σv R gives the resonant contribution of a given resonance and N A σv tail represents the "tail contribution" of the considered resonance. Here the rates are expressed in cm 3 mol -1 s -1 , the center of mass energy E R and the resonance strength ωγ are given in MeV, T 9 is the temperature in units of GK, A is the reduced mass in amu, and S(E 0 ) is the astrophysical factor at the so-called Gamow energy:

E 0 (MeV) = 0.1220(Z 2 p Z 2 t AT 2 9 ) 1/3 , (12)
with Z p and Z t being the projectile and target atomic numbers, respectively. In computing error propagation, we used the formalism given in Ref. [38]. The contributions to N A σv of the resonance tails were found to be small for T 9 >0.03. But at lower temperatures, the tail contributions from the subthreshold level at E x =5.6034 MeV and from the level at E x =5.6716 MeV are dominant (see Fig. 8) and the associated errors were computed by error propagation through Eq. ( 11). We calculated the error in S(E 0 ) taking into account both uncertainties in resonance energy and strength, as it is done in Ref. [38] for the resonant contribution (Eq. 10).

The uncertainty in a weak component of the rate (∼10%, see Fig. 8) due to the relatively broad resonance at E R =1202.5 keV was also taken into account in the same way.

To check the reliability of the so-calculated errors, we performed a full Monte Carlo simulation at a few given temperatures. Random values for the involved parameters of the levels at 5.603 and 5.672 MeV (partial and total widths, level energies as well as Q values for 17 O+p→ 18 F and 14 N+α→ 18 F) were generated according to the corresponding errors (see Table 1 and Ref. [26]). They were assumed to have a Gaussian distribution. The limits for N A σv were obtained from calculation of the probability density of N A σv after numerical integration. The errors calculated from this "exact" but timeconsuming procedure were found to be very similar to those obtained from the above-described analytical procedure. The same check was performed for a few temperatures above T 9 =0.04 on the narrow resonant level at 5.7898 MeV. We also obtained a very good agreement. Finally, the limits given in Table II are the results of the analytical calculations in the whole temperature range.

Ratios of individual reaction rate contributions and the total modal rate are displayed in Fig. 8 as a function of temperature. The strong effect of the previously unknown resonance at E R =183.3 keV is clearly visible since this resonance dominates the total reaction rates in the temperature range (1-4)×10 8 K which is of most importance in nova nucleosynthesis. Below T 9 =0.02, the dominant contributions arise from the levels at 5.603 and 5.672 MeV with a small component due to the broad high-energy levels at 6.163, 6.633 and 6.809 MeV.

We show in Fig. 9 a comparison of present and previous [10] total reaction rates for the 17 O(p,α) 14 N reaction. Also given are the associated uncertainties. Large differences can be seen in both ranges T 9 <0.02 and T 9 =0.1-0.4. For T 9 <0.02, the difference is mainly to be ascribed to the lowered value of the single particle width of the subthreshold level at 5.603 MeV. In the temperature range of T 9 =0.1-0.4, the reaction rate increase of more than an order of magnitude is due to the present observation of the previously unknown resonance at E R =183.3 keV. The slight difference observed between T 9 =0.02 and T 9 =0.1 (∼30%) originates in the revaluation of the excitation energy of the level at 5.6716 MeV.

Besides the very large differences with previous studies found in the range of temperatures attained during nova outbursts, the second important point shown in Fig. 9 is the drastic improvement in accuracy observed for T 9 =0.1-0.4. For example, at T 9 =0.2, the uncertainty in the reaction rate is reduced from more than two orders of magnitude to ∼15% due to the precise measurement of the strength of the resonance at E R =183.3 keV, whereas estimating the latter strength previously was some tricky guessing game. The two very recent measurements of the strength of this resonance at Oak Ridge National Laboratory [30] and Triangle Universities Nuclear Laboratory [31] will probably allow to further reduce the uncertainty of the 17 O(p,α) 14 N reaction rate in the range T 9 =0.1-0.4, as it appears that the results obtained in these experiments are fully compatible with those from the present work.

C. The 17 O(p,γ) 18 F reaction rate

In the calculation of the 17 O(p,γ) 18 F rate, we considered the levels at 5.6033, 5.6716 and 5.7898 MeV in the same way as for the 17 O(p,α) 14 N reaction (see Table I for the adopted level parameters) and sixteen levels above E R =183.3 keV. For the latter contributions, we followed the study of Ref. [10] (see page 89 of that reference for the resonance strength values) except for the resonance at E R =489.9 keV for which we used a new measurement [11] of the resonance strength and for the resonance at E R =501.5 keV for which the wrong limit (ωγ pγ <0.33) quoted in Ref. [10] was corrected to the value of ωγ pγ <0.33×10 -3 given in Ref [12].

As already pointed out [10,11,39], the direct capture process strongly affects the total reaction rates for T 9 <0.8. In Refs. [10,36,39], the DC contribution was extrapolated from high-energy experimental cross sections of Ref. [39]. Recently, Fox et al. [11] employed an alternative method based on theoretical calculations. A Woods-Saxon single-particle potential served to generate the radial wave functions of the 21 final bound states in 18 F to which E1 DC transitions are allowed. The spectroscopic factors of the 21 considered levels were taken from the literature. The total S DC (E) values were finally obtained as an incoherent sum of the calculated individual contributions. We have re-examined the evaluation of the cross sections for the DC process in the 17 O(p,γ) 18 F reaction in view of its strong influence on the total reaction rate.

Analysis of the direct capture contribution

We show in Fig. 10 the existing experimental measurements of the DC cross sections in 17 O(p,γ) 18 F (Ref. [39] and the present low-energy measurement described in Sec. II-C-2). In his study [39], Rolfs assumed a pure DC process in the energy ranges E c.m. =0.27-0.44 MeV and E c.m. =0.88-1.78 MeV (see Fig. 11 of Ref. [39]). On the contrary, Fox et al. [11] argue that the data points in the low-energy range should be "influenced by the tails of higher lying broad resonances", as indicated by their calculation of the incoherent sum of the cross sections from the broad resonances at E R =556.7 keV and E R =676.7 keV. Then, as the energy dependence obtained in Ref. [39] using a square-well potential is quite different from the one they calculate using more realistic Woods-Saxon potentials, they conclude that "it is surprising that the extrapolated S-factor of Ref. [39] agrees with the four low-energy data points" given in the same study in the energy range E c.m. =0.27-0.44 MeV. In view of this argument, they finally disregard all the data points of Ref. [39] (including those above E c.m. =0.88 MeV) and rely on calculations based on measured spectroscopic factors to estimate the absolute scale of the DC cross section. The calculations are described in detail in Ref. [11] and the obtained results are displayed in Fig. 10. The disagreement with the experimental values (Ref. [39] and this work) is evident for the low-and high-energy data points.

We reinvestigated the DC process S-factor by correcting the low-energy data points of Ref. [39] from the contribution of the broad resonances at E R =556.7 keV and E R =676.7 keV according to the statement of Ref. [11]. The corrections were calculated from the Breit-Wigner formula with energy-dependent partial widths (see Table I for the values at the resonance energies). The DC cross sections were then calculated in the same way that was used in Ref. [11] (i.e. with a Woods-Saxon potential) except for the used specific computer code (code RACAP obtained from P. Descouvement, private communication). We obtained very similar results for the shape of the S-factor energy dependence and for its magnitude as well. In an attempt to fit the quadratic function describing the so-calculated energy dependence to the whole set of data, we simulated the high-energy (>0.88 MeV) results of Ref. [39] by a set of 19 points distributed according to the spread of the corresponding data as appreciated from Fig. 17 of Ref. [39] (see Fig. 10).

The result of the fit is given as a solid line in Fig. 10. It is clear from this figure that the energy dependence calculated with a Woods-Saxon potential is inconsistent with the high-energy data points of Ref. [39], given their very small estimated relative error bars (∼3%). With this fit, we get for the DC S-factor:

S DC (E) = 6.2 + 1.61E -0.169E 2 (13)
where E is in MeV and S DC (E) in keV barn. This result is not significantly dependent on the way we simulated the high-energy results of Ref. [39] (e.g. the number of representative data points). If the fit is restricted to the five low-energy points for lack of a detailed report of the high-energy results in Ref. [39], the obtained S DC (E) is 13% higher.

In an attempt to understand the inconsistency of the data above 0.88 MeV with the S DC (E) of Eq. ( 13), we corrected the simulated high-energy data points from the contributions of the broad resonances at 556.7, 676.7 and 1170 keV. These contributions, calculated from the resonance parameters given in table I and in Ref. [13], were found to be non negligible (15% at the maximum) in a significant part of the high-energy range of the data of Ref. [39]. Fitting a quadratic function proportional to that of Eq. ( 13) to the so-corrected data and assuming relative error bars of 5% for these data, we obtained a fit of good quality (χ 2 red =1.3). The corresponding S DC (E) values are lowered by 3% compared to those given by Eq. ( 13). This result suggests that many of the data points of Ref. [39], in both the low-and high-energy ranges, could suffer from some mixing of DC and resonant processes. Obviously, new data which could allow to clearly disentangle the DC cross section from resonance contributions would be highly valuable. However, we retained in the present work the relation (13) as the final result for S DC (E). But considering the bad quality of the corresponding fit and following a suggestion of Ref. [11], we took the overall fractional uncertainty in S DC (E) to be 50%.

The present S DC (E) values are higher by a factor of ∼1.7 than those given in Ref. [11], but still in agreement with them given the uncertainty of 50% estimated in both studies. At low energy, they are lower than those given in Ref. [39] (see Fig. 10), essentially due to the Woods-Saxon potential used in the present work in place of the square-well potential of Ref. [39].

The DC contribution to the total rate was calculated by numerical integration of Eq. (6). Interference between DC and resonant capture was neglected since these processes mainly proceed through different orbital angular momenta and/or different γ-ray multipolarities. Note that the interference effect considered in the analysis of the present (p,γ) measurement at E lab p =192.7 keV (Sec.II-C-2) only affects the S-factor value near E c.m. =180 keV. It was checked that its effect on the reaction rate is negligible.

Total reaction rates

Total reaction rates and lower and upper limits corresponding to 1σ confidence level were calculated using the procedure described above for the 17 O(p,α) 14 N reaction. The results are listed in Table III for temperatures of T 9 =0.01-1.5. The main uncertainty in the 17 O(p,γ) 18 F rate comes from the DC contribution (50%). Clearly, additional measurements of the DC cross sections of the 17 O(p,γ) 18 F reaction including more precise studies at low energy (E<0.4 MeV) would be highly valuable to further reduce this uncertainty.

Individual rate contributions relative to the total modal rate are shown in Fig. 11. The direct capture process dominates the total rate below T 9 =0.03 and in the range T 9 =0.09-0.4. This indicates that the importance of the resonance at E c.m. =183.3 keV is less pronounced than in the 17 O(p,α) 14 N case, but its contribution is still significant around T 9 =0.2.

Ratios of present to previous [10,11] total reaction rates for 17 O(p,γ) 18 F are shown in Fig. 12. The modal rates are given as well as the lower and upper limits. The comparison with the NACRE compilation [10] shows (see Fig. 12a) that the modal rates are in agreement above T 9 =0.4, whereas the present upper limit is significantly lower due to the corrected value used for the strength of the resonance at E R =501.5 keV. Between T 9 =0.1 and T 9 =0.4, the present rates are smaller than the NACRE values by up to a factor ∼5, but still within the previous very large error bars mainly caused by the unmeasured resonance at 183.3 keV. It can be seen from Fig. 12a that the fractional uncertainty in the rates (about ±30% in the present study) has been reduced by more than two orders of magnitude in this temperature range. Below T 9 =0.1, a smaller reduction of the rate values is observed, which is mainly due to our analysis of the DC contribution.

The comparison with the recent work of Ref. [11] shown in Fig. 12b indicates moderate differences which are to be ascribed to a different estimation of the DC cross section and to the somewhat divergent values obtained for the strength of the resonance at 183.3 keV.

IV. SUMMARY AND CONCLUSIONS

We reported on the observation of a previously undiscovered resonance at E c.m. =183.3±0.6 keV in the 17 O(p,α) 14 N reaction, with a measured resonance strength ωγ pα =(1.6±0.2)×10 -3 eV. The strength of the 17 O(p,γ) 18 F resonance at the same energy was measured to be ωγ pγ =(2.2±0.4)×10 -6 eV by an activation method. From these values combined with the known strength of the 14 N(α,γ) 18 F resonance feeding the same level, we calculated the partial and total widths of the 18 F level at E x =5.7898 MeV. The lifetime of this level was also measured by DSAM and the observed limit was found to be consistent with the total width calculated from partial widths, contrary to a previous DSAM measurement [12].

A precise value of the excitation energy of the resonant level was also obtained in the lifetime measurement.

We calculated the 17 O+p thermonuclear rates using the presently measured properties of the 18 F level at E x =5.7898 MeV and clarifying the situation for the subthreshold state at 5.6034 MeV and for the level at 5.6716 MeV. In the analysis of the 17 O(p,γ) 18 F rate, the contribution of the DC process was revisited, with the conclusion that new data would be helpful to further reduce the potential systematic uncertainties in this reaction rate. The previous uncertainties in the 17 O+p rates are finally reduced by orders of magnitude at temperatures in the range 0.1-0.4 GK. The rate uncertainties are now reasonably small, especially for the 17 O(p,α) 14 N rate, which can be considered to be firmly established below 1.5 GK.

As shown in Ref. [14] from hydrodynamic simulations of classical nova outbursts, the results of the experiments described in this paper have important consequences for 17 O and 18 F nucleosynthesis in classical novae. Besides the 17 O+p rates, the final abundance of 18 F in nova ejecta is also strongly dependent on the rate of the reaction 18 F(p,α) 15 O, which is presently the subject of strong experimental efforts (e.g. [40][41][42]). A significant reduction of the uncertainty in this reaction rate should soon allow accurate predictions for the synthesis of 17 O and 18 F in nova outbursts. f From Ref. [11]. g From Ref. [34]. h Based on the resonance strengths ωγpγ and ωγpα from Ref. [10] and the total width Γ from Ref. [13]. i From Ref. [35], which also gives ωγpα=(4.93±0.34)×10 3 eV and Γ=(79±5)×10 3 eV. We did not take into account other values of Γ given in the literature, because they could include extra contributions from higher-energy levels (see [35]). The partial width Γγ of this level is not known. Ref. [39] present work

Ref. [39] (corrected)

1.8

Fox et al. [11] Rolfs [39] present work FIG. 10: Previous [11,39] and present estimates of the direct capture S-factor in the 17 O(p,γ) 18 F reaction for Ec.m.=0-1.8 MeV. The data points are from Ref. [39] and the present work (triangle at Ec.m.=180.2 keV). The four squares at low energy (<0.45 MeV) are original data from Ref. [39] and circles are corrected low-energy values (see text). The 19 data points above Ec.m.=0.88 MeV are representative of the larger number of measured values, which cannot be accurately extracted from Fig. 17 of Ref. [39]. They were generated from a draw in a band around the best estimated value [39] of the DC S-factor (dotdashed line) with a distribution (and error bars) in accordance with the data spread appreciated from Fig. 17 of Ref. [39]. The solid line shows the present calculations of the DC S-factor, whereas dot-dashed and dotted lines are the previous calculations from Refs. [39] and [11], respectively (see text). Note that the upturn of the S-factor at energies below 0.1 MeV visible in Fig. 17 of Ref. [39] has no influence on the fit and was not considered. the ratio of the present rates to the rates evaluated in Ref. [10] (Ref. [11]). The hatched area gives the present uncertainties in the reaction rates. Upper and lower limits for the rates of Refs. [10,11] are given as dashed lines.

B

  . The Ec.m.=183.3 keV resonance in the 17 O(p,α) 14 N reaction

FIG. 1 :FIG. 2 :FIG. 3 :

 123 FIG.1:(Color online) Section of a typical γ-ray spectrum obtained at E lab α =1775 keV with the HPGe detector at θ lab =0 • . The two resonances corresponding to the 5671.6 and 5789.8 keV levels in 18 F were simultaneously populated. A small component due to the weak excitation of the resonant levels at 5603-5605 keV is also visible. The ordinate scale of the figure has been chosen to illustrate some γ-ray peaks of relatively low intensities, leading to a truncated drawing for the two lines arising from the 10 B(α,p)13 C reaction. The labels "C" and "R" indicate some of the lines used for calibration and the reference peak for energy difference measurements, respectively (see text). The primary γ-ray decays of the resonant level at 5790 keV are labeled with stars. All lines correspond to full-energy peaks unless labeled SE (single-escape line).

FitFIG. 4 : 1 )FIG. 5 :FIG. 6 :FIG. 7 :

 41567 FIG. 4: (Color online) (a) Sample α spectrum obtained in the 17 O(p,α) 14 N experiment with the detector at θ lab =150 • . The proton energy is E lab p =196.5 keV and the accumulated charge is equal to 0.93 C. The broad peak labelled 11 B(p,α)2 4 He is due to a slight contamination of boron in the used target. (b) Relevant part of the spectrum with a least-squares fit to the data points: dotted line -fitted linear background; dashed line -fitted Gaussian function with intensity, position and standard deviation as free parameters.

FIG. 8 :

 8 FIG. 8: (Color online) Ratios of individual reaction rate contributions to the total modal rate for the 17 O(p,α) 14 N reaction. The unlabelled solid and dashed lines below 0.02 GK correspond to tail contributions of the resonances at 0.557+0.677 MeV and 1.202 MeV, respectively (see text).

FIG. 9 :

 9 FIG. 9: (Color online) Ratio of present and previous[10] reaction rates for 17 O(p,α)14 N given as the solid line with hatched area representing uncertainties. The dashed lines indicate the previous[10] lower and upper limits for the total rate.

FIG. 11 :

 11 FIG. 11: (Color online) Ratios of individual reaction rate contributions to the total modal rate for the 17 O(p,γ) 18 F reaction.

FoxFIG. 12 :

 12 FIG.12:(Color online) Comparison of present and previous reaction rates for the 17 O(p,γ)18 F reaction. In part a (b) is given the ratio of the present rates to the rates evaluated in Ref.[10] (Ref.[11]). The hatched area gives the present uncertainties in the reaction rates. Upper and lower limits for the rates of Refs.[10,11] are given as dashed lines.

  17 O and18 O targets for protons of the appropriate energy.The strength of the 17 O(p,α)14 N resonance was obtained from the relation 1 ωγ pα = ωγ18

	pα	M 17 M 17 + m p	M 18 + m p M 18	3 E 17 R E 18 R	17 18	Y 17 pα pα Y 18	.

  17 O and18 O targets; and (Y 17 pα /Y 18 pα ) is the ratio of the measured reaction yields for the two resonances, which was obtained from the plateau of the excitation functions measured with the 17 O and 18 O targets (energy range of E lab

p =195.2-196.5 keV in Fig.

TABLE I :

 I Summary of the parameters of the six most important levels in18 F for the 17 O(p,α)14 N and 17 O(p,γ)18 F reaction rates at temperatures T <0.3 GK. Based on the Q-value for 17 O+p→ 18 F: Q=5606.5±0.5 keV[26].

	ER a	Ex	J π	Γp	Γα	Γγ
	(keV)	(keV)		(eV)	(eV)	(eV)
	-3.12±0.57	5603.38±0.27 b	1 +	-c	42.8±1.6 d	0.485±0.046 d
	65.1±0.5	5671.6±0.2 e	1 -	(19±3)×10 -9 f	130±5 d	0.45±0.02 g
	183.3±0.6	5789.8±0.3 e	2 -	(3.8±0.5)×10 -3 e	6.8±3.0 e	(9.4±3.6)×10 -3 e
	556.7±1.0	6163.2±0.9 b	3 +	(14.0±0.5)×10 3 h	3.86±0.72 h	(37.7±8.6)×10 -2 h
	676.7±1.0	6283.2±0.9 b	2 +	(10.0±0.5)×10 3 h	13.9±0.5 h	0.64±0.14 h
	1202.5±5.0	6809±5 b	2 -	14.5×10 3 i	64.5×10 3 i	-

a b From Ref.

[13]

. c Γp(E) calculated from Eq. (

9

) with C 2 S=0.12±0.04

[36]

and θ 2 sp =0.89 MeV (this work). d From Ref.

[23]

. e From present work (see text).

TABLE II :

 II Total thermonuclear reaction rates for 17 O(p,α) 14 N.

	T (GK)	Lower limit	Modal rate	Upper limit
	0.01	4.02×10 -25	4.97×10 -25	5.92×10 -25
	0.011	4.27×10 -24	5.23×10 -24	6.18×10 -24
	0.012	3.50×10 -23	4.24×10 -23	4.99×10 -23
	0.013	2.31×10 -22	2.79×10 -22	3.26×10 -22
	0.014	1.29×10 -21	1.54×10 -21	1.80×10 -21
	0.015	6.23×10 -21	7.44×10 -21	8.65×10 -21
	0.016	2.75×10 -20	3.26×10 -20	3.77×10 -20
	0.018	5.12×10 -19	6.19×10 -19	7.26×10 -19
	0.02	1.11×10 -17	1.53×10 -17	1.94×10 -17
	0.025	1.10×10 -14	1.54×10 -14	1.99×10 -14
	0.03	1.30×10 -12	1.76×10 -12	2.22×10 -12
	0.04	4.77×10 -10	6.14×10 -10	7.52×10 -10
	0.05	1.52×10 -8	1.92×10 -8	2.32×10 -8
	0.06	1.46×10 -7	1.81×10 -7	2.17×10 -7
	0.07	7.09×10 -7	8.73×10 -7	1.04×10 -6
	0.08	2.28×10 -6	2.79×10 -6	3.30×10 -6
	0.09	5.96×10 -6	7.16×10 -6	8.36×10 -6
	0.1	1.56×10 -5	1.80×10 -5	2.05×10 -5
	0.11	4.62×10 -5	5.20×10 -5	5.77×10 -5
	0.12	1.45×10 -4	1.64×10 -4	1.83×10 -4
	0.13	4.35×10 -4	4.96×10 -4	5.57×10 -4
	0.14	1.18×10 -3	1.35×10 -3	1.52×10 -3
	0.15	2.85×10 -3	3.27×10 -3	3.69×10 -3
	0.16	6.19×10 -3	7.12×10 -3	8.04×10 -3
	0.18	2.25×10 -2	2.59×10 -2	2.92×10 -2
	0.2	6.25×10 -2	7.18×10 -2	8.11×10 -2
	0.25	3.84×10 -1	4.39×10 -1	4.94×10 -1
	0.3	1.48×10 0	1.65×10 0	1.82×10 0
	0.35	6.02×10 0	6.50×10 0	6.97×10 0
	0.4	2.56×10 1	2.75×10 1	2.94×10 1
	0.45	9.28×10 1	9.99×10 1	1.07×10 2
	0.5	2.73×10 2	2.95×10 2	3.16×10 2
	0.6	1.42×10 3	1.53×10 3	1.63×10 3
	0.7	4.64×10 3	4.96×10 3	5.28×10 3
	0.8	1.12×10 4	1.20×10 4	1.27×10 4
	0.9	2.24×10 4	2.38×10 4	2.51×10 4
	1.	3.91×10 4	4.12×10 4	4.34×10 4
	1.25	1.09×10 5	1.14×10 5	1.19×10 5
	1.5	2.29×10 5	2.38×10 5	2.47×10 5

TABLE III :

 III Total thermonuclear reaction rates for 17 O(p,γ) 18 F.

	T (GK)	Lower limit	Modal rate	Upper limit
	0.01	2.37×10 -25	4.55×10 -25	6.73×10 -25
	0.011	2.52×10 -24	4.84×10 -24	7.15×10 -24
	0.012	2.04×10 -23	3.91×10 -23	5.79×10 -23
	0.013	1.32×10 -22	2.54×10 -22	3.76×10 -22
	0.014	7.14×10 -22	1.37×10 -21	2.03×10 -21
	0.015	3.30×10 -21	6.34×10 -21	9.37×10 -21
	0.016	1.34×10 -20	2.57×10 -20	3.80×10 -20
	0.018	1.60×10 -19	3.07×10 -19	4.53×10 -19
	0.02	1.39×10 -18	2.62×10 -18	3.85×10 -18
	0.025	1.47×10 -16	2.37×10 -16	3.26×10 -16
	0.03	8.02×10 -15	1.08×10 -14	1.36×10 -14
	0.04	2.10×10 -12	2.66×10 -12	3.23×10 -12
	0.05	6.55×10 -11	8.19×10 -11	9.83×10 -11
	0.06	6.66×10 -10	8.27×10 -10	9.89×10 -10
	0.07	3.60×10 -9	4.55×10 -9	5.50×10 -9
	0.08	1.35×10 -8	1.78×10 -8	2.22×10 -8
	0.09	4.09×10 -8	5.77×10 -8	7.44×10 -8
	0.1	1.12×10 -7	1.68×10 -7	2.23×10 -7
	0.11	2.95×10 -7	4.54×10 -7	6.13×10 -7
	0.12	7.53×10 -7	1.16×10 -6	1.57×10 -6
	0.13	1.84×10 -6	2.79×10 -6	3.74×10 -6
	0.14	4.25×10 -6	6.29×10 -6	8.33×10 -6
	0.15	9.16×10 -6	1.32×10 -5	1.73×10 -5
	0.16	1.84×10 -5	2.61×10 -5	3.38×10 -5
	0.18	6.13×10 -5	8.50×10 -5	1.09×10 -4
	0.2	1.66×10 -4	2.27×10 -4	2.89×10 -4
	0.25	1.07×10 -3	1.48×10 -3	1.89×10 -3
	0.3	4.24×10 -3	5.98×10 -3	7.71×10 -3
	0.35	1.53×10 -2	2.08×10 -2	2.62×10 -2
	0.4	5.73×10 -2	7.20×10 -2	8.67×10 -2
	0.45	2.01×10 -1	2.38×10 -1	2.75×10 -1
	0.5	6.02×10 -1	6.95×10 -1	7.89×10 -1
	0.6	3.41×10 0	3.88×10 0	4.35×10 0
	0.7	1.21×10 1	1.37×10 1	1.53×10 1
	0.8	3.14×10 1	3.55×10 1	3.95×10 1
	0.9	6.57×10 1	7.38×10 1	8.19×10 1
	1.	1.18×10 2	1.32×10 2	1.45×10 2
	1.25	3.26×10 2	3.64×10 2	4.03×10 2
	1.5	6.34×10 2	6.98×10 2	7.62×10 2

Acknowledgments

We wish to thank E. Virassamynaiken and D. Ledu for the preparation of the TiN and O-implanted targets, respectively, as well as the technical staff of the CSNSM for their constant help. We are also indebted to C. Iliadis for several useful discussions. This work was supported by the CMEP agreement for scientific cooperation between France and Algeria under the project No. 01MDU518 and by AYA2004-06290-C02.


Sonia Desmoulin-Canselier
email: sonia.desmoulin-canselier@univ-nantes.fr

Scientific approximation and ethno-racial categories in French Jurisprudence: an ambivalent situation

Positive French law and, more deeply, French legal culture seem to follow a model that is diametrically opposed to the one shaping American law. Referring to universalistic and egalitarian values, related to scientific discourses denying the existence of racial characteristics (notably elaborated at the end of the 50"s at UNESCO headquarters in Paris 1 ), French law clearly demonstrates that itis hostile to the use of ethnic and racial classifications. French lawyers, particularly constitutional-law specialists, have repeatedly debated expunging all reference to "race" from legal texts, even when the word is used to combat racism and discrimination 2 , and this topic appears from time to time on the political agenda (for example during the last presidential campaign and inseveral billsdrafted to remove the word "race" 3 ). From thislegal angle, France appears to be a color-blind country. Nevertheless, doubts may be raised about the robustness of this supposed "counter-model." Does this color-blind basic premise really systematically apply in judicial proceedings? And do all the safeguards really protectFrance from an awkwarduse of ethnic or racial distinctions? These questions have to be asked taking into account two contextual elements. Firstly, ethno-racial categories are still used in medical and scientific fields, with recent developments in genomics and pharmacogenomics. Secondly, some "scientistic" belief still pervades French culture(in Descartes and Pasteur Country). How this context is affecting the field of law enforcement?

To assess the impact of such phenomenaon judicial proceedings, the most relevant material to study may not be court rulings punishing racist crimes or discriminatory practices. Paradoxically, it may be also very enlightening to analyzecourt orderswhere the terms "race" or "ethnicity" appear marginally, or implicitly, without being at the core of the debate.Indeed, certaincourt rulings mention ethnic or racial origins incidentally to disputes that center on other questions. Most of the time, "race", "ethnic origin", or "apparent physical characteristics" are then referred to in the context of forensic (scientific or medical)expertise. To date, we have to remember that in the French judicial system, experts work for the judge (and not for the claimant 1 Le racisme devant la science, [1956] UNESCO / Gallimard, 1960. 2 See, in particular, Sans distinction de race, Numéro dédié de la revue Mots. Les langages du politique, Année 1992, Volume 33, n° 1; P. Mbongo, "Un antiracisme scripturaire: la suppression du mot "race" de la législation," Recueil Dalloz 2013 p. 1288; N. Malherbe, "Quelles seraient les conséquences juridiques de la suppression du mot "race" de notre Constitution?," Recueil Dalloz 2013, p. 1012 3 Proposition de loi constitutionnelle n° 559 visant à supprimer le mot "race" de l"article 1er de la Constitution, 2007; Assemblée nationale, proposition de loi (n° 218) tendant à la suppression du mot "race » de notre législation, 16 mai 2013. (Constitutional law proposal n° 559 aimed at bannning the word "race" from Article 1 of the Constitution, 2007; Assemblée nationale, Bill (n° 218) suggesting a ban on the word "race" from our legislation, 16 May 2013.)

Workshop Quantifying Race: How Politics, Economics, andMedical Myopia Drive Color-Coded Data, Brocher Foundation, June 2015 2 or the defender) who appoints them. And one can find that, through the expertise, ethno-racial origins or categories may be used without being stigmatized.Some recent cases, both in civil and criminal matters, attest to this fact.

One first example, in civil matter,concerns the liability of a drug manufacturer.A person who developed multiple sclerosis after being vaccinated decided to sue the laboratory in order to establish its liability. Such a claim was not new, but appears to be one between several others very similar. Nevertheless, in a ruling dated 10 July 2013, the Court of Cassationthe highest jurisdiction in France for civil and criminal mattersrecognized for the first time that the ethnic origins of the claimant could be taken into consideration. Here, the ethnicity became a piece of serious, precise, and corroborative circumstantial evidence enabling to establish proof of a causal link between a medical productthe vaccineand damage suffered. 4 In doing so, the Court broke ground for differential treatment of victims depending on the ethnic or racial category to which they belong. And the color-blind basic principleseems to be forgotten. At the same time, the Court remained silent about the controversy surrounding the role of ethnic background in a disease of unknown aetiology.

In other rulings, a person"s racial background was discussed in relation to the results of bone X-rays carried out in order to establish whether that person was a minor, as he claimed. 5 Illegal aliens on French territory attempted to avoid deportation by claiming protectedminor status. However, authorities suspected the birth dates on identity documents might have been falsified and, to detect such fraud, had carried out clinical examinations and bone X-rays. The purpose was to establish an approximate age by comparing the suspect"s bone measurements with a table of average measurements at various stages of child development. As part of the trial proceedings, the judges had to decide whether or not such table was a reliable and acceptable evidence. On one hand, some experts testified that the bone-development tables to which the police referred had been established on the basis of data collected from "North American "Caucasian"populations, which therefore failed to account for development and particularities specific to African populations" 6 . And, in 2005,an opinion published by the Comité Consultatif National d"Ethique (the National Consultative Ethics Committee) stated that "such reference tables contain the risk of major errors in relation to non-Caucasian children from Africa or Asia, whose bones may develop at entirely different ages in relation to North American and British averages." 7 On the other hand, a 2007 report from the Académie Nationale de Médecine concluded "the simplest and most reliable method for estimating bone age is to compare X-rays of the left wrist and hand to the Greulich & Pyle Atlas, the reference most commonly used. Note that, to date, no racial difference has been demonstrated." 8 In most of the court-orders, the judges chose to follow the latter opinion and admitted as evidence the comparisonto bone-growth tables in addition to clinical examinations. In all these cases, they seem to follow a half pragmatic and half scientistic reasoning. Their decisions neglected controversies relative to the scientific consistency of the tablesandmedical expertise seem to have neutralized the socio-political implications of ethno-racial categories. By ruling in this manner, judges strengthen the fallacious idea that medical and scientific interpretation of racial categories is not open to question. Again, that brings us to the conclusion that even in the French legal order ethno-racial distinctions are not absent. Consequently, on may say that there is no pure "French alternative model."

Examples may also be found outside the domain of civil law. A recent criminal case deserves plenty attention. The issue is DNA phenotyping. Certain laboratories claim to be capable of producing a facial composite sketch of a suspect on the basis of a DNA sample. Once again, France might seem to be exempt from any risk of abuse. For example, in 2007-08, an attempt to implement the practice in France raised a furor in the press. Evoking the "Test d"Orientation Géo-Génétique" (TOGG, Geo-Genetic Orientation Test) 9 , journalists spoke out against an "ethnic database" and possible abuse of the "genetic composite portrait" in the hands of the police. As it is oftendone, theypointed to British and American law enforcement practices as examples to be shunned. 10 When French judges were interviewed, they expressed their "alarm at such aninadmissible program." 11 In June2011, the French justice ministry took the precaution of circulating a memorandum to the State"s Prosecutors, judges, and officers of the crimeinvestigating police, enjoining them to turn down proposals for anatomical profiling from phenotyping laboratories. 12 Signed by the head of the Criminal Matters and Pardons Division, it read: "My attention has been drawn to the fact that in criminal investigations, new methods for determining a person"s physical features or ethnic or geographic origin, based on the results of DNA phenotyping of biological material collected at the scene of the crime, have been offered to certain investigating police or judges.The method was referred for deliberation to the commission that approves the persons qualified to carry out identification assignments using DNA phenotyping within the framework of legal procedures. The commission has concluded that such methods must be considered with the utmost caution. Being in full agreement with this position, I 8 Académie nationale de Médecine, Rapport 07-01 Sur la fiabilité des examens médicaux visant à déterminer l"âge à des fins judiciaires et la possiblité d"amélioration en la matière pour les mineurs étrangers isolés. 9 According to its designers, TOGG is theoretically capable of determining, with a reliability rate of 95 to 99.99%, the "ancestral" or "geographic source" of a DNA sample; i.e., if the source is "Caucasian," "Sub-Saharan Africa," "Eastern Asian," "Mediterranean African," or "Indian" in type. 10 thank you for your cooperation with my request that you ensure that such proposals berefused. To me, they present prohibitive legal and scientific disadvantages." The question seemed to be settled, once and for all. However, on 25 June 2014, theCriminal Division of the Court of Cassation handed down an especially revealing decision. The point was to legitimate or refuse the possibility that a French investigating judge could order an expertise to be carried out, aimed at obtaining information describing a suspect"s physical appearance using traces found at a crime scene. In this case, the victim of a rape was unable to provide the police with any description of her attacker. Investigators had found biological material, and compared the DNA to profiles archived in a national DNA database, the Fichier National Automatisé des Empreintes Génétiques (FNAEG) made up of samples taken from persons suspected in connection with crimes. 13 However, the comparison led nowhere. In the absence of an eyewitness, clues about the identity of the rapist were severely limited. At that point, the investigating judge asked an approved laboratory to carry out tests to extract "essential data from the DNA" and to give investigators "all the components related to the suspect"s apparent physical features." The judge"s request was daring and unprecedented, and a rejection would have harmed both the procedure and his career. To avoid this outcome, the judge himself then requested the annulment of the order by the investigating chamber. He was thereby forcing the justice system to take a stand on whether this type of evidence from DNA profiling was admissible in French courts.

In order to understand the situation better, and because the question is technique, I shall present the state of French law in detail. Positive law provides, on the one hand, for free evaluation of evidence in criminal matters, in the absence of a conflicting legal presumption, 14 and, on the other hand, for a distinction between the examination of genetic characteristicsadmitted solely for medical or research purposes -andDNA sequencesthat are admissible for the purposes of identification, notably within the framework of law enforcement. Thus, article 16-10 of the French Civil Code states: "An examination of the genetic characteristics of a person may only be undertaken for medical purposes or for scientific research. The express consent of the person must be obtained in writing before the carrying out of the examination, after the person has been duly informed of its nature and its purpose. The consent shall specify the purpose of the examination. It may be revoked at any time without any formality." 15 This law is supposed to be applied to any analysis of a DNA sequence carried out under the authority of French law enforcement. Article 16-11 ( §1-2)of the same code provides that"The identification of a person by his genetic fingerprint may only be sought: 1°) Within the framework of investigative measures or the preparation of a case during a judicial proceeding; 2°) For medical purposes or for scientific research; 3°) In order to establish, when it is unknown, the identity of deceased persons." This text allows for the comparison of DNA sequences if needed to establish identity or kinship. Therefore, the question that arose concerned the qualification of DNA profiling aimed at establishing a "composite sketch" of physical features. Was the purpose of such profiling the identification of an individual, and therefore legal within the context of criminal investigation? Or was it more a matter of examining genetic characteristics, which are supposed to be barred from admission as evidence?The first jurisdiction to examine the matterthe Chamber of Investigationreplied by ruling that articles 16-10 and 16-11 of the French Civil Code were not applicable to traces collected at the crime scene, but only to samples taken from the human body. The Court of Cassation confirmed thisinterpretation and moreover specified that"as long as the expertise requested by the investigating judge on the grounds of article 81 of the code of criminal procedure consisted solely of revealing apparent physical features for the sole purpose of facilitating identification of the unknown culprit of a crime, using a DNA sequence left at the crime scene, the order shall not be censured." This ruling is eminently contestable, as a statement of grounds and by its implications.

Both parts of the statement of grounds can be contested. First of all, it is not at all convincing to limit the application of articles 16-10 and 16-11 of the Civil Code to samples that are taken from the human body. 16 This ruling by the Chamber of Investigation, upheld by the Court of Cassation, actually undermines the scope of these laws significantly, depriving them of any value. The purpose of these provisions is to protect personal privacy and dignity, and to combat any discrimination that might result from abusive usage of genetic data. If it is admissible to proceed with sequencing in the absence of consent, as long as the information is derived from traces of DNA that are detached from a human body, the laws fail to achieve their goal. To assert that the need for informed consent applies only to samples taken directly from the body (of a living person or a corpse) is the same as saying that it is freely permissible to carry out DNA testing on biological material that is detached from another"s body: hair, flakes of skin, or fingernail clippings. Yet this is a direct contradiction of the legislators" intention.

Next, the conditions under which the Court of Cassation upheld the legality of DNA profiling for the purpose of revealing physical features can be criticized sharply. Two types of remarks can be made with regard to the Court"s validation for the expertise consisting "solely of revealing apparent physical features for the sole purpose of facilitating identification of the unknown culprit of a crime, using a DNA sequence left at the crime scene." First, the Court of Cassation decision infers that the analysis ordered does indeed consist of "identification." It implies that finally, there is no difference between comparing DNA sequences and extracting information from a sequence. Many commentators expressed concern about the implications for French law of abandoning the distinction between coding and noncoding genomic DNA. Until then, the law had stipulated that of the two types of DNA, coding and noncoding, only the lattershould be archived for the purposes of comparing sequences. 17 Actually, the legislation was drafted at a time when scientificand technical knowledge led experts to believe that personal data could not be extracted from noncoding DNA. It is important to note that it was only on the basis of thepresumption that noncoding DNA yielded no more than a "genetic fingerprint" that the legislationcreating the FNAEG, a huge database of DNA sequences, was declared constitutional. 18 This archive includes samples collected from convicted offenders, but also DNA from suspects, as well as from biological materials collected at crime sceneswhere several persons with no link to the crime may have deposited such traces. 19 However, progress in genetics and biotechnologies has partially negated the presumption that noncoding DNA is innocuous. Currently, noncoding DNA can be made to yield a profile indicating physical features. 20 For example, the document written by the laboratory manufacturing the TOGG Test,which elicited indignation in 2007-08, already mentioned that indications regarding ethnic origins were obtained from noncoding segments of DNA. We can therefore state that coding versus noncoding is no longer a valid criterion "for differentiating the examination of physical features from identification by profile." 21 Secondly, it can be noted that, according to the statement of grounds, extracting information from a DNA sequence for the purposes of profiling is acceptable, as long as this information concerns only visible physical features, and that it is extracted and used within the framework of a legal proceeding. Certain scholars may interpret this ruling as an effort to reassert the "sensitive" nature of certain data still disqualified from use in a criminal proceeding, such as the predisposition to develop a disease. However, this statement implies a contrario that physical features are not sensitive data. Yet there is nothing convincing about this assertion and, moreover, the solution allows us to assume that information about physical appearance is based unequivocally on the sequence tested, and that the extraction is not liable to either doubt or interpretation. Such a vision of current DNA profiling capabilities is totally inaccurate. Once again, it illustrates the temptation to find infallible proof in the expertise. On the contrary, it would be wiser to take account of the conjectural nature of scientific 17 Article 706-54 of the Code of Criminal Procedure provides that "The DNA sequences recorded in this database may only be taken from uncoded segments of deoxyribonucleic acid, with the exception of the segments corresponding to the sex markers.." 18 Article 706-54 of the Code of Criminal Procedure thus provides that "The national automated database of DNA sequences, placed under the supervision of a judge, is designed to centralize the DNA sequences resulting from biological traces, and also the DNA sequences of persons convicted of the offenses outlined in article 706-55, in order to facilitate the identification of and the search for the perpetrators of these offenses.The DNA sequences of persons prosecuted for one of the offenses mentioned in Article 706-55 who have been ruled unfit to stand trial on the grounds of Articles 706-120, 706-125, 706-129, 706-133 or 706-134 are regulated by the same statutes. The DNA sequences of persons against whom there is serious or corroborating evidence rendering it likely that they have committed any of the offenses mentioned in article 706-55 are also stored in this database by order of the judicial police officer either automatically or at the request of the district prosecutor or of the investigating judge. This decision is recorded in the case file.[…]" 19 Conseil Constitutionnel, Décision n° 2010-25 QPC du 16 septembre 2010. 20 O. Millot, interview with geneticist Catherine Bourgain,"L"ADN va révéler de plus en plus d"informations," Libération, 31 janvier 2012. 21 E. Verges, "Vers un portrait-robot génétique? Le profil morphologique d"un suspect face aux droits fondamentaux," RDLF 2014, chron. n°25 (http://www.revuedlf.com/droit-penal/vers-un-portrait-robot-genetique-leprofil-morphologique-dun-suspect-face-aux-droitsfondamentaux-cass-crim-25-06-2014-n-13-87-493-pbri/) knowledge and the possibility of different interpretations.Furthermore, how can we be sure that "genetic composite portraits" derived from DNA traces collected on crime scenes will not be used following a hidden racial pattern?

To conclude, in civil matters, ethno-racial origins do take a role in judicial proceedings in France (notably through forensic (medical or scientific) expertise). Today, French judges take into account ethnic origin to prove a causal link between a medical product and damage. In criminal matters, investigating judges have the power, from now on, to request that physical features such as the color of a suspect"s skin, eyes, and hair be "revealed" to them on the basis of biological items found at the scene of the crime. Tomorrow, on the same grounds, they will also be able to ask about the shape of the ears or nose, because progress in that field of DNA research is underway. 22 We therefore have no choice but to note that by accepting DNA profiling for physical features, the Court of Cassation is doing today what the Justice Ministry and judges claimed they expressly wished to avoid doing yesterday, with the "Test d"Orientation Géo-Génétique." A ruling like this has socio-political implications that must not be ignored. Not only does France"s highest legal jurisdiction support the principle that "genes contain everything" and that a DNA sequence can simply be "read," it also opens the door to a form of ethnic genetic archiving for the purposes of police work. What will the national DNA database, the FNAEG (Fichier National Automatisé des Empruntes Génétiques), do with this information about skin color? Will it be fine-tuned somehow, to take mixed racial backgrounds into account? Is there a way to articulate such specifics without virtually reverting to racial distinctions reminiscent of law in slave-trading times? It is to be feared that the egalitarian color-blind banner will not be sufficient to protect the French legal order from pitfalls. Likewise, hiding our half-pragmatic, half-scientistic way of dealing with the usage of ethno-racial categories may have driven us in a totally ambivalent situation.

  C. Louis, "Le nouvel arsenal de la police scientifique," 11/11/2008, Le Figaro; G. Charles, "Les apprentis sorciers du fichage ethnique," 28/03/2007, L'Express. 11 F. Arfi, "Des juges contournent la loi pour utiliser des tests ADN "ethniques"," Mediapart.fr, et "Un juge dit son

	"éffarement"	devant	un	programme		"inadmissible","	Mediapart.fr:
	http://www.mediapart.fr/journal/france/280508/un-juge-dit-son-effarement-devant-un-programme-inadmissible
	12	CRIM-PJ	N°	08-28.H5	du	29	juin	2011:
	http://www.syndicatmagistrature.org/IMG/article_PDF/JSM/Circulaire%20ADN.pdf

Cour de cassation, 1 ère chambre civile, 10 juillet 2013, pourvoi n° 12-21314.

See, in particular, Cour d"appel de Rennes,

6ème chambre b, 28 octobre 2014, quatre affaires: RG n° 13/07652; n° 13/08852; n° 14/01051 et n° 13/08052; Cour d"appel Metz, Ordonnance 24 Mars 2014, n° 14/00154; Cour d"appel de Limoges, chambre spéciale des mineurs, Audience publique du lundi 13 mai 2013, deux affaires, RG n° 12/00088 et n° 13/00057; Cour d"appel de Limoges, chambre spéciale des mineurs, 7 octobre 2013, RG n° 13/00043. 6 Cour d"appel de Limoges, 13 mai 2013, cited above. 7 Comité Consultatif National d"Ethique pour les Sciences de la Vie et de la Santé (CCNE), Avis n° 88 Sur les méthodes de détermination de l"âge à des fins juridiques

Article 706-54 du Code de procédure pénale.

Paragraph 1 of Article 81 of the Code de procédure pénale states "In compliance with the law, the investigating judge proceeds with all of the investigative measures he deems useful to demonstrating the truth. He investigates incriminatory and exculpatory information."

Violation of the provisions of article

16-10 of the Civil Code constitutes the offense punished in article 226-25 of the criminal code.

See, esp., J. Danet, "Poussée de fièvre scientiste à la chambre criminelle, le recours au "portrait robot génétique » (mais approximatif) est validé," Revue de science criminelle 2014 p. 595. Contra C. Girault, "La tentation du portrait-robot génétique," AJ Pénal 2014 p. 487.

See, for example, reports by the forensic hematology laboratory in Bordeaux.