S Cruz

K Wimmer
email: k.wimmer@csic.es

S S Bhattacharjee

P C Bender

G Hackman

R A E Andreoiu

C S Austin

Bancroft

R Krücken

F Ames

C Andreoiu

R A E Austin

C S Bancroft

R Braid

T Bruhn

W N Catford

A Cheeseman

A Chester

D S Cross

C Aa

Diget

T Drake

A B Garnsworthy

R Kanungo

A Knapton

W Korten

K Kuhn

J Lassen

R Laxdal

M Marchetto

A Matta

D Miller

M Moukaddam

N A Orr

N Sachmpazidi

A Sanetullaev

C E Svensson

N Terpstra

C Unsworth

P J Voss

Single-particle structure in neutron-rich

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I. INTRODUCTION

The shape of a nucleus is governed by the interplay of stabilizing shell gaps, which prefer a spherical shape and quadrupole correlations, which tend to deform the nucleus. In the neutron-rich zirconium (Z = 40) and strontium (Z = 38) isotopes a sharp transition between spherical ground states for nuclei with neutron number N 59 and strongly deformed ground states at N = 60 and beyond has been inferred from isotope shift measurements [1]. At the same location the excitation energy of the first 2 + state in the even-even nuclei indicates a rapid onset of collectivity [2]. This sudden drop in E (2 + 1 ) at N = 60 has been observed in Zr and Sr nuclei, but not in the heavier Mo or lighter Kr isotones. The origin of the shape transition has been attributed to the specifics of the proton-neutron interaction. Filling of the neutron (ν) g 7/2 orbital leads to a lowering of the g 9/2 proton (π ) orbital enabling proton excitations into the π g 9/2 orbital. The increase in occupation of the π g 9/2 orbital enables further promotion of particles into the νg 7/2 orbital leading to deformation [3]. Monte Carlo shell-model (MCSM) calculations in a very large model space were able to trace the effective singleparticle energies of the relevant neutron orbitals for excited states [4]. The results show that the structure of the N = 58 nucleus 98 Zr in the excited 0 + state is dominated by many particle excitations to the proton g 9/2 orbital and resembles the ground state of 100 Zr at N = 60. This suggests a coexistence and inversion of spherical and deformed structures at N = 60.

The sharp drop of the 2 + energy is accompanied by a drop in energy of the first excited 0 + [E (0 +

2 )] state. The E (0 + 2 ) energy continuously decreases with increasing neutron number from above 3 MeV at N = 50 down to 1229 keV in 96 Sr (N = 58). At N = 60 the two structures cross, the deformed 0 + state becomes the ground state, while the spherical one is located at only E (0 +

2 ) = 215 keV. The interpretation that the ground state of the N = 60 nucleus 98 Sr is strongly deformed while the 0 + 2 state is spherical was recently confirmed by a measurement of the electric quadrupole moments obtained from Coulomb excitation [5]. Interestingly, there is a third lowlying 0 + state present in the Sr nuclei, which decreases also in energy, but not as dramatically as the deformed configuration.

In 96 Sr the excited 0 + states are connected by a very strong electromagnetic transition matrix element [6]. A measurement of the (d, p) transfer reaction cross section from the ground state of 95 Sr to the 0 + states of 96 Sr showed that the excited 0 + states can be understood resulting from the strong mixing of two configurations with very different deformation [7].

In this paper we investigate the single-particle structure of the neutron-rich 93-95 Sr nuclei by (d, t ) neutron removal reactions. Spin and parity assignments in the odd-A 93,95 Sr are constrained and spectroscopic factors give insights into the single-particle structure approaching the shape transition.

In 94 Sr the selectivity of the (d, t ) reaction allowed for the identification of excited 0 + states. The spectroscopic factors are interpreted as resulting from the mixing of two distinct structures and show that there is strong mixing at N = 56.

II. EXPERIMENTAL DETAILS

The present 2 H( 94,95,96 Sr, t ) experiments were carried out at the TRIUMF-ISAC II rare isotope facility [8]. The neutronrich Sr isotopes were produced when a 480 MeV proton beam (with 10 μA current) bombarded a thick uranium carbide (UC x ) target. After element selective two-step resonant laser excitation and ionization of Sr with the TRIUMF laser ion source [9] the extracted beam was mass separated, charge bred, and accelerated to 5.5 AMeV using the ISAC I and II heavy-ion accelerators. Details of the beam production can be found in Refs. [7,10]. The postaccelerated beams were impinging upon ≈0.5 mg/cm 2 , CD 2 deuterated polyethylene targets (>90% deuterium/hydrogen ratio) at the center of the SHARC/TIGRESS setup. The light charged particles from elastic scattering, fusion, and transfer reactions were detected and identified by using the highly segmented silicon detector array (SHARC) [11]. SHARC provides good angular coverage (35 • < θ lab < 80 • downstream of the target) and resolution ( θ lab ≈ 1 • ), ideal for measurements of angular distributions of light-ion induced reactions. A detailed description of the configuration and performance of the array is presented in Ref. [10]. For the present work, only the laboratory forward detectors were used as the (d, t ) reaction kinematics restricts the scattering angles for the tritons to 50-60 • . The downstream section of SHARC is composed of silicon E-E detectors (thickness ≈150 μm and ≈1500 μm) covering the angular range 35 • < θ lab < 80 • in the laboratory system. The setup allowed for the identification of tritons with kinetic energy above about 8 MeV. The particle identification plot is presented in Fig. 1 of Ref. [10]. The kinematics plot for the 2 H( 95 Sr, t ) reaction is shown in Fig. 1.

The γ rays emitted from excited states in the Sr residue nuclei were detected by TIGRESS (TRIUMF-ISAC Gamma-Ray Escape Suppressed Spectrometer) [12] consisting of twelve segmented clover detectors surrounding the SHARC array. Eight (four) clover detectors were placed at 90 • (135 • ) with respect to the beam direction. The distance from the target to the front face of the detectors in the high-efficiency configuration is 11.0 cm resulting in a full-energy peak efficiency of ≈10% at a γ -ray energy of 1 MeV.

III. DATA ANALYSIS AND RESULTS

The data collected with SHARC were calibrated using a standard triple-α source ( 239 Pu -241 Am -244 Cm) as well as light ions from elastic scattering, 2 H(Sr, d ) and 1 H(Sr, p). The excitation energies of final states in the Sr transfer residues were derived from the measured energies and angles of identified tritons. The in-beam excitation energy resolution was limited to σ ≈ 270 keV due to beam energy loss in the thick target. This resolution was determined from isolated (or γ -ray gated) peaks in the excitation energy spectrum (see Fig. 6). It is almost independent of the scattering angle for the range covered in this experiment. The energy and efficiency calibrations of the TIGRESS Ge detectors were carried out using standard radioactive 152 Eu and 60 Co sources, placed at the target position. Level schemes were constructed using triton-γ (and triton-γ -γ where possible) coincidences. Gating on the excitation energy allows one to associate γ rays with excited states, while the reverse gating gives information on whether the state was directly populated or fed from above.

The differential cross sections were analyzed with finiterange distorted wave Born approximation (DWBA) calculations using the FRESCO code [13]. It is assumed that in the present 2 H( 94,95,96 Sr, t ) experiments the final states are populated in a single-step process in which a valence neutron is removed from the 94,95,96 Sr ground states. In order to determine the absolute cross section the luminosity of each experiment was determined by fitting the elastic scattering data as shown in Fig. 2 of Ref. [10]. The optical model parameters for the deuteron-nucleus potentials were also determined for the 2 H( 94,95,96 Sr, d ) data. They are given in Table II of Ref. [10].

For the triton-nucleus potential a global parametrization [14] was employed. The (d, t ) overlap function was taken from Green's function Monte Carlo calculations which give a (d, t ) spectroscopic factor of 1.30 [START_REF] Brida | Green's function Monte Carlo results for one-nucleon overlaps[END_REF]. For the Sr nuclei, the boundstate wave functions were calculated in a Woods-Saxon potential with r = 1.3 and a = 0.66. The depth of the well was adjusted to match the binding energy of the state. The 1g 9/2 , 2d 5/2 , 3s 1/2 , 1g 7/2 , and 2d 3/2 single-particle orbitals were considered in the analysis. Neutron removal from the 1g 9/2 orbital below N = 50 is, however, unlikely to contribute to the population of low-lying states in the Sr nuclei. Orbital angular momentum transfers and spectroscopic factors were obtained by comparing the experimental differential cross sections with the reaction model calculations. This analysis carries substantial systematic uncertainties in the reaction modeling, the optical model parameters, and the potential used to calculate the nucleon bound-state wave function. The normalization of the elastic scattering cross section used to determine the absolute transfer cross sections depends on the optical model parameters chosen for the deuteron-nucleus potentials. When the analysis is restricted to the most forward angles in the laboratory system, the different parametrizations result in a 3% systematic uncertainty for the absolute cross sections. The effect of the optical model parameters has been estimated by calculating the spectroscopic factors for different parametrizations taking into account the angular range of covered in the experiment. These vary by 10% for L = 0 and 13% for L = 2, respectively. Lastly, the potential used to calculate the wave functions, and in particular the radius assumed, affect the extracted spectroscopic factors. By varying the parameters of the Woods-Saxon potential within 10%, the uncertainty for the spectroscopic factors was estimated as 13% for L = 0 and 22% for L = 2 in the angular range covered by the SHARC detectors. The total systematic uncertainty related to the reaction modeling thus amounts to 17 and 26% for L = 0 and 2, respectively. The spectroscopic factors are quoted below only with the statistical uncertainty. For the absolute comparison with the shell-model calculations or other works, the systematic uncertainty has to be considered in addition.

A. 93 Sr

93 Sr was populated via the 2 H( 94 Sr, t ) reaction. The excitation energy spectrum is shown in Fig. 2. As evident from the γ -ray spectra shown in Fig. 3, the ground and excited FIG. 2. The total excitation energy (E x ) spectrum for states in 93 Sr populated in the 2 H( 94 Sr, t ) reaction. The excitation energy spectrum was fitted with three components corresponding to the observed states at 0, 213, and 1143 keV. A small contribution from 94 Y and 93 Rb appearing a negative excitation energies in the spectrum was subtracted (see text).

states at 213 and 1143 keV have been populated directly in the reaction. The excitation energy spectrum has been fitted with three Gaussian peaks. The separation between the centroids is constrained using the excitation energies and the widths are constrained in accordance with the excitation energy resolution [see Fig. 6 for the 2 H( 95 Sr, t ) reaction]. Additionally, a constant background has been added to the fit, representing background events from fusion evaporation reactions. The excitation energy E x -E γ and the γ -ray energy spectra are presented in Fig. 3.

As shown in Fig. 3 the 433 keV γ rays are in coincidence with population of the 1143 keV state. The 433 keV state has not been directly populated in the 2 H( 94 Sr, t ) reaction. While the 219 keV transition from this state to the 213 keV state cannot be resolved, the intensity of the 710 keV and 433 keV γ -ray transitions as function of the excitation energy allow extraction of the direct population of the 433 keV state. A 2σ upper limit of 4% of the population of the 1143 keV state was determined. The 213 keV state is almost exclusively populated directly, a small contribution of indirect feeding from above is observed in the γ -gated excitation energy spectrum. Note that this state is isomeric with a half-life of T 1/2 = 4.3(1) ns [START_REF] Sasanuma | [END_REF], therefore the efficiency for detecting this transition in the present experiment is much reduced, similar to the case of the decay of the 0 + 2 state in 96 Sr [7]. No evidence for the population of the 986 keV J π = (9/2 + ) state was found. In the γ -ray energy spectrum gated on negative excitation energy FIG. 6. Exclusive excitation energy (E x ) spectra for the 0 + states populated in the 2 H( 95 Sr, t ) 94 Sr reaction. The ground state was extracted from the total spectrum by removing contributions from the 837 keV state using a γ -ray gate. A linear background was estimated using the negative excitation energy region and subtracted from the spectrum. For the excited states, a gate was placed on the corresponding 0 +

x → 2 + 1 transitions and the spectrum was scaled by the respective γ -ray detection efficiency. The Gaussian fits were used to determine the excitation energy resolution. a small contribution from 93 Rb was found. This contribution has been subtracted by gating on the respective transition energies and subtracting an efficiency-scaled Gaussian from the distribution as shown in Fig. 2. This subtraction affects the relative contribution of the ground and 213 keV state to the peak. The relative population is also affected by the energy calibration, but for the spectroscopic factors (see below) only the sum of all contributions was taken into account. The observed γ rays were placed in the level scheme as presented in Fig. 13.

The limited resolution for the excitation energy and the insufficient statistics for γ -ray coincidences does not allow extraction of the angular distributions for individual states. Instead the combined angular distribution for the ground and 213 keV states was extracted. These states are rather well separated from the 1143 keV state. The data are compared to DWBA reaction model calculations assuming removal of a neutron from the 3s 1/2 , 2d 5/2 , and 1g 9/2 orbitals in Fig. 4(a).

The data are in good agreement with calculations assuming angular momentum transfer L = 2, with exclusion of pure L = 0 or L = 4 distributions with 98.71 and 99.99% probability, respectively. Using a two component fit the angular distribution shown in Fig. 4 does not allow for an additional L = 4 component, a J π = 9/2 + assignment for the 213 keV state can thus be excluded. Furthermore, the cross section for the population of the 213 keV state is rather high and population of hole states in the deeply bound 1g 9/2 orbital are not expected at low excitation energy. Fitting the angular distribution with a combination of L = 2 and L = 0 slightly improves the reduced χ 2 value. The combined fit together with the individual components is shown in Fig. 4(b). The spin and parity of the 213 keV state is thus assigned as (1/2) + , based on the present work only, while (3/2, 5/2) + can not be excluded. The spectroscopic factors extracted from the combined fit in Fig. 4(b) amount to C 2 S = 3.37(67) for the L = 2 ground state and 0.44(34) for L = 0 for the 213 keV state, where the uncertainties account for the statistical uncertainty only. The systematic uncertainty related to the contamination discussed above amounts to 10%. The fit with only the L = 2 component results in a summed spectroscopic factor of C 2 S = 4.24 (11). The spectroscopic factors are summarized in Table II. Regarding the 1143 keV state, statistics are not sufficient to conclude on the spin and parity from the angular distribution. Assuming L = 2 the spectroscopic factor for this state amounts to C 2 S = 0.65 [START_REF] Brida | Green's function Monte Carlo results for one-nucleon overlaps[END_REF].

B. 94 Sr

Low-spin states in 94 Sr were populated by the 2 H( 95 Sr, t ) reaction. In this case much higher statistics were obtained such that the level scheme was constructed using the triton-γ coincidences shown in Fig. 5 as well as γ -γ coincidences. The excitation energy (E x ) versus E γ spectrum in Fig. 5(a) shows the direct population of several states. The transitions at 1043, 1456, 2690, 3075, and 3172 keV are observed for the first time. It is evident from Fig. 5(a) that the 837, 3075, and 3172 keV transitions are direct ground-state decays. All other transitions feed the first excited 2 + state at 837 keV. This was further verified using γ -γ coincidences.

0 + states

The ground state of 94 Sr was strongly populated in the present experiment. The angular distribution for the reactions to the ground state was extracted using two methods. First, a constrained Gaussian peak fit was employed to fit both the ground state and the 837 keV state for each angular bin. The width of the Gaussians has been fixed to σ = 270 keV. In the second method, the distribution gated on the 837 keV transition was subtracted from the combined angular distribution, after scaling for efficiency. An additional gate was placed on excitation energies E x < 1.4 MeV to exclude states that decay directly to the ground state. This excitation energy spectrum is shown in Fig. 6.

The angular distribution for the reactions to the ground state extracted using both methods is shown in Figs. 7(a) and 7(b). The differential cross sections are fitted with DWBA calculations described in Sec. III. The data extracted both ways clearly favors a calculation with angular momentum transfer L = 0. This corresponds to the removal of a 3s 1/2 neutron from the J π = 1/2 + ground state of 95 Sr. The spectroscopic factors amount to C 2 S = 0.336 (7) for the peak-fit method, and 0.314 (7) for the subtraction method. This value for the spectroscopic factor agrees very well with the one obtained for the 2 H( 94 Sr, p) 95 Sr reaction measured within the same campaign (C 2 S = 0.41(9) [10]).

The newly observed 1043 and 1456 keV transitions were found to be in coincidence with the 837 keV 2 + 1 → 0 + 1 transition. The excitation energy spectra gated on these two transitions are shown in Fig. In both cases the agreement with the L = 0 calculations is significantly better than for L = 2. This suggests that the states have spin and parity of 0 + or 1 + . The population of a 1 + state by L = 0 transfer would require seniority ν = 0 components in the ground-state wave function of 95 Sr, which results in a small spectroscopic factor. As discussed below such states are expected in the shell model at higher excitation energies. Together with the decay branching limit to the ground state, J π = 0 + is therefore assigned to both states. Spectroscopic factors extracted from the DWBA analysis amount to 0.067(4) and 0.105 (6) for the 1880 and 2293 keV states, respectively.

2 + states

The 2 + 1 state has been directly and indirectly populated in the present experiment, and thanks to the separation in the excitation energy spectrum, the angular distribution can be obtained from a γ gate or from a combined fit of the ground state and the 837 keV state similar to the case of the ground-state angular distribution. The latter is shown in Fig. 8(a). The spectroscopic factor extracted from the fit with the L = 2 DWBA calculation amounts to C 2 S = 0.725 [START_REF] Brida | Green's function Monte Carlo results for one-nucleon overlaps[END_REF].

The two states at 2614 and 2704 keV have sufficient statistics to analyze the angular distributions. They are shown in Figs. 8(b) and 8(c), respectively. The spectroscopic factors amount to 0.21(1) and 0.45(2), respectively. The states at 2270, 2921, and 3527 keV are also in agreement with L = 2, although the angular distributions are less clear. Populating these states via the removal of a d 5/2 neutron from the 1/2 + ground state of 95 Sr restricts the spin and parity to (2, 3) + . This is consistent with previous assignments [17]. The 2270 keV state directly decays to the ground state, therefore J π = 2 + is preferred.

2414 keV state

A state a 2414 keV has been previously assigned as J π = 3 -based on its strong feeding in the β decay of 94 Rb and the measured angular correlation [17]. In the present experiment the 2414 keV state has also been strongly populated. A gate on the 1577 keV transition confirms that the state is almost exclusively (>95%) directly populated in the (d, t ) reaction. Population of negative parity states is not expected as all available neutron orbitals are of positive parity. By removing a neutron from the naively fully occupied ν2d 5/2 orbital the coupling with the neutron in the 3s 1/2 orbital results in a 3 + state. The differential cross section for the transfer reaction to the 2414 keV state is shown in Fig. 8(d). It is compared to a calculation assuming removal of a 2d 5/2 neutron with L = 2 and also the hypothetical removal of a 1 f 5/2 neutron giving rise to the negative parity. While this is still consistent with the data, the much better fit of the L = 2 calculation together with the strong population supports the assignment of 3 + for this state. The spectroscopic factor amounts to C 2 S = 0.99(3).

1 + states

Two states at 3075 and 3172 keV have been observed for the first time in the present work. The former is close to a a previously observed state at 3078 keV [6], however, the main branch of the decay of the 3078 keV state is via a 1158 keV transition to the (3 -) state at 1926 keV. The two states observed in the present work decay only directly to the ground state. This indicates that their spins and parities are (1, 2) + . Comparison of the differential cross sections with the reaction model calculations shown in Fig. 9 suggests L = 0 transfer, i.e., removal of a neutron from the s 1/2 orbital.

Since the ground-state wave function of 95 Sr contains a significant contribution of components that have two neutrons in the 3s 1/2 orbital [10], such J π = 1 + states can be populated by the reaction. The spectroscopic factors resulting from the fits with L = 0 shown in Fig. 9 amount to 0.058(5) and 0.053 (5). FIG. 9. Angular distribution of tritons for the J π = 1 + candidates in 94 Sr. The L = 0 and L = 2 DWBA calculations are fitted to the data, and shown by the blue (solid) and green (dashed) lines and labeled with their respective reduced χ 2 values. Both states clearly agree better with L = 0.

Other states

While many states in 94 Sr are known, very few have definite spin and parity assignments. Population via the β decay of the 3 (-) ground state of 94 Rb limits the spin to J = (2, 3, 4) for several states [17]. The 4 + 1 state at 2146 keV has been only weakly populated directly in the present work. The transition at 2141 keV likely corresponds to the decay of the 2981 keV state to the first 2 + 1 state. The population of the (3 -) state at 1926 keV is indirect from unresolved states around 3.5 MeV. A summary of all observed transitions and their placement in the level scheme is presented in Table I.

C. 95 Sr

Several states in 95 Sr have been populated in the 2 H( 96 Sr, t ) 95 Sr reaction. The γ -ray energy spectrum is shown in Fig. 10. Four γ -ray transitions belonging to 95 Sr have been observed. It is evident that the population of the first excited state at 352 keV is mostly indirect via the 681 keV state, which decays by a 329 keV transition to this state. The excitation energy spectrum is shown in Fig. 11.

The resolution is not sufficient to separate the close-lying states. In order to determine the level scheme and the population of the states, the γ yield (corrected for efficiency and branching ratios) for bins in excitation energy has been determined. 95 Sr has a transition at 683 keV, belonging to the FIG. 10. γ -ray energy spectrum for the 2 H( 96 Sr, t ) 95 Sr reaction. A gate on excitation energies below 1800 keV has been applied. FIG. 11. Excitation energy spectrum for 95 Sr. The total γ -ray yield has been used to constrain the area of Gaussian peaks and the excitation energy spectrum has been fitted with four components and a constant background. The component representing the 352 keV state has been fixed to the upper limit obtained from the γ -ray analysis.

decay of the 1239 keV state to the isomeric state at 556 keV. Using the known branching ratio of the 681 keV and 329 keV transitions depopulating the 681 keV state [18], the yield for the 1239 keV state has been obtained. In contrast to the 2 H( 94 Sr, p) 95 Sr reaction [10], this state is not populated in the present reaction. The direct population strength of the first excited state at 352 keV is consistent with zero. The excess of 352 keV counts in Fig. 10 is likely from states above 1.5 MeV. In order to crosscheck this analysis and to obtain the ground-state population, the excitation energy spectrum has been fitted with four components corresponding to the ground, 352, 681, and 1247 keV states as well as a constant background. The number of counts in the components for the excited states is consistent with the results of a fit to the total γ -ray energy spectrum shown in Fig. 10. The result is shown in Fig. 11. This allows for the extraction of the population of the ground state and shows that the data is well described by taking into account only these four states.

The angular distribution combined for the ground and 681 keV states has been extracted similarly to the case of the 2 H( 94 Sr, t ) 93 Sr reaction. A gate on excitation energies below 1000 keV has been applied in order to limit the contribution from the 1247 keV state. The spectroscopic factor has been corrected for the fact that the 681 keV state is only partially included in the excitation energy gate. The 352 keV state has been ignored in the angular distribution fit shown in Fig. 12.

The angular distribution for the 1247 keV state has large uncertainties but is best described by L = 0, which is in agreement with the proposed total angular momentum (1/2) + [18]. The spectroscopic factors amount to 0.23 [START_REF] Brida | Green's function Monte Carlo results for one-nucleon overlaps[END_REF] for the ground state, 2.15(50) for the 681 keV state, and 0.46 [START_REF] Brida | Green's function Monte Carlo results for one-nucleon overlaps[END_REF] for the 1247 keV state assuming J π = 1/2 + for the latter.

IV. DISCUSSION

A. Structure of 93 Sr

The present data represents the first reaction study of 93 Sr. Excited states have previously been studied only by β decay FIG. 12. Angular distribution of tritons gated on both the ground and 618 keV states in 95 Sr. The data are compared to DWBA reaction model calculations assuming removal of a neutron from the 3s 1/2 orbital with L = 0 for the ground state (blue) and from the 2d 5/2 orbital with L = 2 for the 681 keV state (green). The combination of L = 0 and L = 2 best fitting the data is shown by the solid black line.

and spin and parity assignments are based on log f t values. The ground state of 93 Sr is known to be J π = 5/2 + [19]. For the 213 keV state both (9/2 + ) and (3/2 + ) assignments have been proposed, the latter is favored based on the g-factor measurement [START_REF] Sasanuma | [END_REF]. Other spin and parity assignments for 93 Sr were based on assumptions about the ground-state spin of the β decay mother 93 Rb [20,21]. The present data limits the possible values for the 213 keV state to (1/2, 3/2, 5/2) + , with a slight preference for 1/2 + based on the measured angular distribution for the ground and 213 keV states. The conversion coefficient for the 213 keV transition has been measured and points to a pure E 2 transition [22], therefore we assign J π = (1/2) + to the state at 213 keV. The 433 keV state has not been populated directly in the transfer reaction, which is expected for a 3/2 + state since the 2d 3/2 orbital is higher in energy and is expected to have a low occupancy in the ground state of 94 Sr. A state at 986 keV, which exclusively decays to the ground state was also not observed in the present experiment. The assignment is consistent with (9/2 + ) because direct population in the (d, t ) transfer reaction can only populate the (1g 9/2 ) -1 component of the wave function, and hole states in the deeply bound 1g 9/2 orbital below N = 50 are unlikely to occur at low excitation energy. This state has been assigned as a member of a rotational band built on the ground state and is interpreted as weak coupling of the 2d 5/2 neutron hole to the 2 + state of the 94 Sr core [23]. The state at 1143 keV decays to the first three states of 93 Sr and direct population in the (d, t ) reaction favors positive parity. Therefore, J π = (5/2) + is tentatively assigned to this state. The proposed spin and parity assignments for 93 Sr are shown in Fig. 13.

The proposed level ordering matches the first few states in the isotone 95 Zr. The first excited state, located at 954 keV, is a 1/2 + state and the spectroscopic factor determined from a (d, t ) reaction measurement amounts to 0.18 [24]. The spectroscopic factor extracted for the ground state in the 96 Zr(d, t ) 95 Zr reaction is 5.75, larger than the present result, C 2 S = 3.37(67). This suggests that the N = 56 subshell closure is stronger in the Zr isotopic chain than in Sr. The (1/2) + assignment for the first excited state is in agreement with the log f t values measured for the decay of 93 Rb [21] although the present interpretation differs. The log f t value of 7.9(3) is at the lower limit for known first forbidden unique transitions required for the decay of the 5/2 -ground state of 93 Rb to the (1/2) + state. A total absorption spectrometry measurement suggests an even smaller β decay branch to the 213 keV state [25] in agreement with the present interpretation. Furthermore, the angular moment sequence of 5/2 + , 1/2 + , and 3/2 + for the first three states of 93 Sr also matches with the measured conversion coefficients [22], which indicates M1 (and/or E 2) transitions for the decay of the 433 keV state to the ground and first excited state. As a consequence any state that decays to the 213 keV (1/2) + state has to have low angular momentum (1/2 ± , 3/2 ± , or 5/2 + ). This means that the weak 1566 keV transition observed in the β decay of 93 Rb and assigned to the decay of the 1780 keV state is likely misplaced as the latter was observed in the spontaneous fission of 252 Cf and assigned (11/2 -) [23].

Figure 13 compares the proposed level scheme to shellmodel calculations. The shell-model calculations have been performed using the GLEK effective interaction [26]. The model space consisted of the neutron 2d 5/2 , 3s 1/2 , 3d 3/2 , and 1g 7/2 and the proton 2p 3/2 and 2p 1/2 orbitals. The singleparticle energies of the neutron 2d 5/2 , 3s 1/2 , 3d 3/2 , and 1g 7/2 orbitals have been adjusted, the interaction and model space is the model [Fig. 13(b)] to analyze the (d, p) reactions. This gave the best overall results for 94-97 Sr [10].

The results of the shell-model calculations are shown on the right side of Fig. 13. The level ordering, energies, and relative transition strengths are in good agreement with the proposed assignment. The 9/2 + state belonging to the groundstate rotational band is predicted at higher energies. This is also reflected by the excitation energies of the 2 + states in 92,94 Sr, which are calculated 200-400 keV higher than experimentally observed. The calculated energy of the first 2 + is strongly dependent on the proton space used in the calculations [10]. The relative spectroscopic factors of the first five states are in good agreement with the calculated spectroscopic factors for the 2 H( 94 Sr, t ) reaction. The shell model predicts spectroscopic factors of 4.03 and 0.87 for the ground and 213 keV states in good agreement with the experimental result, 3.37(67) and 0.44(34), respectively. For the second 5/2 + state the shell-model calculations predict 0.26, smaller than the experimental value of 0.65 [START_REF] Brida | Green's function Monte Carlo results for one-nucleon overlaps[END_REF], however, the spin and parity assignment is not certain. The calculations also predict a rather small value for the 3/2 + 1 state, C 2 S = 0.30, which is consistent with the nonobservation of direct population.

In addition to the states shown in Table II and Fig. 13, the shell-model calculation also predicts the 3/2

B. Structure of 94 Sr

The level scheme together with the spectroscopic factors obtained from the experimental cross sections is shown in Fig. 14.

The summed spectroscopic strength for the 3s 1/2 orbital amounts to 0.62(2) while one would naively assume that the ground state of 95 Sr has one neutron in 3s 1/2 . Taking into account the usual quenching of the spectroscopic strength by a factor of about 0.6, this means that the observable expected 3s 1/2 strength is accounted for. For the 2d 5/2 orbital the summed strength is 2.53(9) compared to the independent particle expectation of 6. There are several states for which the angular distribution and the spectroscopic factor could not be determined, the experimental value thus represents only a lower limit.

Also shown in Fig. 14 are the results of shell-model calculations. The energy of the 2 + state as well as the newly discovered 0 + states is slightly overpredicted. The 3 + state on the other hand is predicted at lower energies than experimentally observed. Overall the agreement is very good, in particular, much better than for the isotope 96 Sr [10]. Concerning the spectroscopic factors, for the ground and the 2 + 1 state the agreement is very good. The summed spectroscopic strength for the 3s 1/2 and 2d 5/2 orbitals in the calculations amount to 0.97 and 5.06 for the states shown on the right side of Fig. 14. The biggest discrepancy is observed for the 3 + state. The shell model predicts a large spectroscopic factor of C 2 S = 2.80 for this state. This can be understood in a naive independent particle model where the ground state of 95 Sr has a configuration with the ν2d 5/2 orbital fully occupied, and a single neutron in the 3s 1/2 orbital, (2d 5/2 ) 6 (3s 1/2 ) 1 . The removal of a 2d 5/2 neutron results in (2d 5/2 ) 5 (3s 1/2 ) 1 coupled to J = 2 or 3. The experimental strength for the 3 + state is only about one-third of the calculated one. It can not be excluded that this strength of the 2d 5/2 orbital is split over several states, which could not be identified experimentally. This state was initially assigned as 3 -, based on angular correlation measurements, which suggest a 3 → 2 → 0 cascade decay, and limit the quadrupole components for the 3 → 2 + 1 decay to less than 0.1% L = 2. Assuming a pure M1 transition for this decay, the measured lifetime, τ = 5.7(23) ps [27], corresponds to B(M1) = 2.5(10) × 10 -3 μ 2 N , compatible but smaller than the shell model result of B(M1) = 0.070 μ 2 N . The systematics of the 0 + states along the Sr isotopes is shown in Fig. 15.

The newly discovered states at 1880 and 2293 keV fit well into this systematics and complete it up to N = 60. The excited 0 + states smoothly come down in energy until 94 Sr. In 96 Sr a drop by about 600 keV is observed. A similar behavior is seen is the Zr isotopes where at N = 56 the energies of the 0 + states have a local maximum. This, and the local maximum seen in the energies of the 2 + states for both Sr and Zr is an indication of the N = 56 subshell closure.

The shell-model calculations predict only one excited 0 + state with substantial spectroscopic strength, while experimentally the strength is about equally shared between the state FIG. 15. Energy systematics of the 0 + states in even-mass Sr isotopes. Levels drawn with dashed lines are tentative assignments [17,[28][29][30][31][32][33]. The newly observed 0 + states 94 Sr from the present experiment are marked with an asterisk. at 1880 and 2293 keV. This resembles the situation in 96 Sr where the two excited 0 + states share a significant amount of spectroscopic strength and are strongly mixed. Using the same approach as was discussed for 96 Sr the mixing of the two excited 0 + states can be extracted as a 2 = 1/(1 + R) with the ratio of spectroscopic factors R = 1.55 (14). The mixing amplitude derived from the experimental results is a 2 = 0.39(2). This means that the two excited states result from the strong mixing of almost degenerate states (2042 and 2131 keV) with a mixing matrix element of V = 202(2) keV. The mixing of the excited 0 + states in 94 Sr is thus very similar to the one in 96 Sr. 98 Sr at N = 60, however, behaves completely different with very weak mixing (between the ground state and first excited 0 + state). Returning to the evolution of the 0 + states in the Sr isotopic chain as shown in Fig. 15, it is clear that the ground-state shape transition at N = 60 is accompanied by a clear structural change of the 0 + states. In the lighter strontium isotopes the two excited 0 + states strongly mix among each other, but not with the ground state, while at N = 60 one of the excited 0 + states drop in energy, becomes the ground state, and a rather pure, strongly deformed state. It would be interesting to further investigate the structure of the 0 + states in 98 Sr by one-neutron transfer reactions as in the present study, however, this is complicated by the highly complex structure of the 97 Sr ground state [10,19].

C. 95 Sr

The level structure of 95 Sr is well reproduced by the shellmodel calculations. The level scheme is shown in Fig. 16. The 3/2 + state is not or only very weakly directly populated in the present experiment; this is in agreement with the shell-model prediction that in the ground state of 96 Sr the 2d 3/2 orbital occupation is small.

While the agreement with the shell model points to the fact that 95 Sr is still dominated by spherical configurations, the spectroscopic factors are not expected to agree. For the inverse reaction 2 H( 95 Sr, p) 96 Sr a small spectroscopic factor of 0.19(3) was determined for the ground-state transfer reaction [10]. The present result of 0.23 [START_REF] Brida | Green's function Monte Carlo results for one-nucleon overlaps[END_REF] is in agreement with that. In contrast the shell model predicts a spectroscopic factor of 1.57 for the ground state of 95 Sr. This shows that the ground state of 96 Sr has only little overlap with the ground state of 95 Sr, indicating that the transition towards strongly deformed ground-state configurations at 98 Sr (and potentially already 97 Sr) is more complex then predicted. For the 352, and 681 keV states in 95 Sr the shell-model calculations predict spectroscopic factors of 0.38, and 4.80. While these numbers are in qualitative agreement with the observation, the interpretation is not straightforward as the 96 Sr ground state does not resemble the shell-model predictions.

V. SUMMARY

The 2 H( 94,95,96 Sr, t ) reactions have been studied to examine the single-particle structure of the 93-95 Sr isotopes toward the N = 60 shape transition. The spin and parity assignments for excited states in 93 Sr have been revised. The revised level scheme is in good agreement with shell-model calculations. Two excited 0 + states in 94 Sr have been observed for the first time. The similar population strength suggests strong mixing between the two 0 + states, resembling the situation in 96 Sr. Further studies, such as low-energy Coulomb excitation, could provide additional support for this interpretation. For other states, except the 3 + state in 94 Sr, good agreement with the shell model for excitation energies and spectroscopic factors is observed indicating that the structure of low-lying states in 95 Sr is not yet affected by the shape transition at N = 60. The 2 H( 96 Sr, t ) 95 Sr reaction is not well suited to determine the nature of states in 95 Sr as the ground-state configuration of 96 Sr deviates significantly from the shellmodel prediction. The large overlap of the 5/2 + state in 95 Sr with the projectile ground state indicates a similar structure and suggests that this state is slightly oblate deformed. The deformation and nature of states in 95 Sr could be further explored by low-energy Coulomb excitation as well as lifetime measurements. Lastly, it should be mentioned that the development of shell-model calculations in much larger model spaces than the ones discussed here could provide more insights in the nature of the shape transition at N = 60.

FIG. 1 .

 1 FIG. 1. Kinematics plot for the 2 H( 95 Sr, t ) transfer reaction (only identified tritons are shown). The transfer to states at excitation energies at 0, 2, 4, 6 MeV are denoted by the dashed lines.

FIG. 3 .FIG. 4 .

 34 FIG. 3. (a) Excitation energy (E x ) versus E γ spectrum obtained from the 2 H( 94 Sr, t ) reaction. (b) corresponds to the γ -ray energy spectrum.

FIG. 5 .

 5 FIG. 5. (a) Excitation energy (E x ) versus E γ spectrum for 94 Sr populated via the 2 H( 95 Sr, t ) reaction. The dashed lines indicate the location of direct ground-state decays and decays to the first excited 2 + state at 837 keV. (b) corresponds to the γ -ray spectrum. The newly observed transitions are marked with asterisks.

FIG. 7 .

 7 FIG. 7. Angular distribution of tritons for L = 0 transfer reactions to final states in 94 Sr. (a) and (b) show the results of the two methods to extract the ground-state distribution. The newly discovered 0 + states are shown in (c) and (d). The L = 0 and L = 2 DWBA calculations are fitted to the data, and are shown by the blue (solid) and green (dashed) lines and labeled with their respective reduced χ 2 values.

FIG. 8 .

 8 FIG. 8. Angular distribution of tritons for L = 2 transfer reactions to final states in 94 Sr. (a) shows the 837 keV 2 + state angular distribution extracted with the peak-fit method. (b) and (c) show states that were previously discussed as candidates for 2 + states. (d) The 2414 keV state was previously assigned tentatively as 3 -, which is in clear contradiction to the present result, which is consistent only with L = 2. The L = 0, L = 2, and L = 3 DWBA calculations fitted to the data are shown by the blue, green, and red lines and labeled with their respective reduced χ 2 values.

FIG. 13 .

 13 FIG.13. Proposed level scheme of93 Sr. The left side shows the experimental levels with energies in keV and the spin and parity assignments from this work. The widths of the arrows are proportional to the relative intensity of the observed γ -ray transition. Dashed levels and transitions have not been observed in the present work. The right side shows the result of shell-model calculations.Here the widths of the arrows indicate the branching ratios. A 3/2 + state at 695 keV cannot be associated with any of the low-lying experimental states.

FIG. 14 .

 14 FIG.14. Level scheme of94 Sr. The left side shows the experimental levels with energies in keV and the spin and parity assignments from this work. The thick lines indicate the magnitude of the experimental spectroscopic factors and the color the orbitals. The right side shows the result of shell-model calculations.

FIG. 16 .

 16 FIG.[START_REF] Sasanuma | [END_REF]. Proposed level scheme of95 Sr. The left side shows the experimental levels with energies in keV and the spin and parity assignments from this work. The widths of the arrows are proportional to the relative intensity of the observed γ -ray transition. Dashed levels and transitions have not been observed in the present work. The right side shows the result of shell-model calculations.Here the widths of the arrows indicate the branching ratios.

TABLE I .

 I Summary of observed levels, transitions, and relative intensities for the 2 H( 95 Sr, t ) 94 Sr. The transition and level energies with their uncertainties are obtained from the present work, they agree within the uncertainties with the results obtained in β decay[6]. The spin and parity assignments are from the present work.

	E γ (keV)	I (%)	assignment		E i (keV)
	836.7(3) 1043.0(5) 1089.5(6) 1308.8(9) 2270.4(19) 1456.1(5) 1577.4(4) 1777.1(6) 1867.4(4) 2084.3(17) 2094.1(20) 2140.9(28) 3075.0(21) 3171.7(16) 2690.3(21)	57.0 2.4 1.8 2.4 0.4 3.7 15.0 3.3 6.7 0.9 0.4 0.6 2.5 1.7 1.3	2 + 1 0 + 2 (3 -1 ) 4 + 1 (2) + 0 + 3 3 + 1 (2, 3) + (2) + (2, 3) + (2,3,4) (2,3,4) 1 + 1 + (2, 3) +	→ → → → → → → → → → → → → → →	0 + 1 2 + 1 2 + 1 2 + 1 0 + 1 2 + 1 2 + 1 2 + 1 2 + 1 2 + 1 2 + 1 2 + 1 0 + 1 0 + 1 2 + 1	836.7(5) 1879.7(6) a 1926.2(7) 2145.5(9) 2270.4(19) 2292.8(6) a 2414.1(5) 2613.8(7) 2704.1(5) 2921.0(17) 2930.8(20) 2977.6(28) b 3075.0(21) a 3171.7(16) a 3527.0(21) a

a Observed for the first time in the present work. b Likely corresponds to the transition at 2144.2(2) from the 2981.1(5) keV state observed in the β decay of 94 Rb

[6]

.

TABLE II .

 II Experimental and shell-model spectroscopic factors for the 2 H( 94,95,96 Sr, t ) reactions. The uncertainties in the spectroscopic factors are statistical ones only. Additional reaction model uncertainties as discussed in Sec. III must be considered for absolute comparisons. For the odd-N isotopes the ordering of the lowest predicted states are in good agreements with the experimental level schemes. For 94 Sr the shell-model states are associated with their most probable experimental counter part. States with very low spectroscopic factors have been omitted in this table for clarity.

		experiment			shell model
	J π	E (keV)	C 2 S	J π	E (keV)	C 2 S
			2 H( 94 Sr, t ) 93 Sr
	5/2 +a	0	3.37(67)	5/2 +	0	4.03
	(1/2 + )	213	0.44(34)	1/2 +	196	0.87
	(3/2 + )	433		3/2 +	532	0.30
	(5/2 + )	1143	0.65(15) b	5/2 +	924	0.26
			2 H( 95 Sr, t ) 94 Sr
	0 +	0	0.336(7)	0 +	0	0.45
	2 +	837	0.725(25)	2 +	1279	1.14
	0 +	1880	0.067(4)	0 +	2315	0.35
	4 +	2146		4 +	2474	0
	0 +	2293	0.105(6)	0 +	2441	0.03
	3 +	2414	0.99(3)	3 +	1989	2.80
	(2, 3) +	2614	0.21(1)	2 +	2456	0.86
	(2) +	2704	0.45(2)	3 +	2600	0.12
	(2, 3) +	2921	0.07(1)	2 +	3525	0.13
	1 +	3075	0.058(5)	1 +	2811	0.00
	1 +	3172	0.053(5)	1 +	3231	0.11
	(2, 3) +	3527	0.079(8)	2 +	3525	0.13
			2 H( 96 Sr, t ) 95 Sr
	1/2 +a	0	0.23(15)	1/2 +	0	1.57
	3/2 +	352		3/2 +	412	0.39
	5/2 +	681	2.15(50)	5/2 +	585	4.80
	(1/2 + )	1247	0.46(15) c	1/2 +	1833	0.20
	ground state have not been observed. The upper limit for
	the nonobservation of 1880 keV (2993 keV) γ rays rela-
	tive to the 1043 keV (1456 keV) transition amount to 2%
	(1%). The extraction of an upper limit for the ground-state
	decay of the 1880 keV transition is complicated by the
	nearby 1867 keV transition. The angular distributions of
	tritons following the population of the 1880 and 2293 keV
	states are shown in Figs. 7(c) and 7(d).

a From Ref.

[19]

. b Assuming J π = 5/2 + . c Assuming J π = 1/2 + .

ACKNOWLEDGMENTS

The efforts of the TRIUMF operations team in supplying the 94,95,96 Sr beam are highly appreciated. K.W. thanks A. M. Moro for his help regarding the input of the overlap function in FRESCO. We acknowledge support from the Science and Technologies Facility Council (UK, Grants No. EP/D060575/1 and No. ST/L005727/1), the National Science Foundation (US, Grant No. PHY-1306297), the Natural Sciences and Engineering Research Council of Canada, the Canada Foundation for Innovation and the British Columbia Knowledge and Development Fund. TRIUMF receives federal funding via a contribution through the National Research Council Canada. K.W. acknowledges the support from the Spanish Ministerio de Economía, Industria y Competitividad, Gobierno de España RYC-2017-22007.


A Ramos

I Raggio

F Zanon

M Assié

E Clément

A Lemasson

D Ramos

A Raggio

I Zanon

F Galtarossa

C Lenain

J Casal

F Flavigny

A Matta

D Mengoni

D Beaumel

Y Blumenfeld

R Borcea

D Brugnara

W Catford

F De Oliveira

N De Séréville

F Didierjean

C Aa

Diget

J Dudouet

B Fernández-Domínguez

C Fougères

G Frémont

V Girard-Alcindor

A Giret

A Goasduff

A Gottardo

J Goupil

F Hammache

P R John

A Korichi

L Lalanne

S Leblond

A Lefevre

F Legruel

L Ménager

B Million

C Nicolle

F Noury

E Rauly

K Rezynkina

E Rindel

J S Rojo

M Siciliano

M Stanoiu

I Stefan

L Vatrinet

The MUGAST-AGATA-VAMOS campaign : set-up and performances

Keywords: Direct nuclear reactions, Solid-state detectors, Spectrometer, Triple coincidences, Radioactive beams

Introduction

Direct reactions are one of the keys to our understanding of nuclear structure and nuclear astrophysics. Their reaction mechanism involves few degrees of freedom and allows precise theoretical calculations such that they can supply crucial nuclear structure information. Transfer reactions, in particular, are an efficient tool to study nuclear structure effects such as shell evolution, pairing and clustering. Astrophysically important cross-sections can also be inferred through these measurements. For decades light ion beams were used to probe the heavier target nuclei of interest in direct kinematics. The inception of radioactive beams allowed the extension of direct reaction studies to the broad domain of unstable nuclei. In this case, the reactions are performed in inverse kinematics where the radioactive beam impinges on the light probe. The excitation energy and scattering angle are generally determined through two-body kinematics from the kinetic energy and recoiling angle of the light particle. This technique has been employed by the first generation of Silicon-strip arrays such as MUST [1], Orruba [2]... The straggling of the light charged particle in the target and the fact that dE/dE * (where E is the kinetic energy of the recoiling particle and E * the excitation energy) is smaller than 1 for pick-up reactions (kinematic compression) limits the excitation energy resolution attainable. Therefore, a simple particle measurement is only useful in cases when the level spacing is large, such as light or closed-shell nuclei. For more general cases, coupling of the particle detectors with a γ-ray array becomes crucial for precise spectroscopy and moreover brings additional information such as decay modes of the populated states. A further combination with a zero-degree spectrometer provides event-by-event identification of the reaction products, separation between the beam and contaminants as well as rejection of the background contributions of fusion-evaporation residues from target-like products for example.

Measuring direct reactions in inverse kinematics and coupling with state-of-the-art γ-detector arrays requires the development of powerful and sophisticated devices. In particular, the detection of the light ejectile requires high accuracy both in angle and energy combined with compacity and as much as possible transparency to γ-rays. Silicon technology offers a combination of good energy resolution together with high granularity. TIARA [3], T-REX [4], ShARC [5] and GODDESS [6] arrays have been built in this spirit with maximal solid-angle coverage and integration into γ-detector arrays but they offer limited particle identification. On the other hand, the MUST2 array [7] provides particle identification by ∆E-E and time-of-flight techniques and can be arranged in a forward and backward four-telescope configuration to be coupled with 4 EXOGAM clovers [8] at 90 degrees [9,10,11,12]. Its poor transparency to γ-rays is due to its integrated electronics and cooling blocks which stand right behind the detectors and prevents coupling them with state-of-art HPGe γ-ray detectors such as AGATA [13,14,15].

The present paper focuses on the MUGAST-AGATA-VAMOS campaign at GANIL [START_REF]Grand Accélérateur national d'ions lourds[END_REF] using the post-accelerated radioactive beams produced by the SPIRAL1 facility [START_REF] Villari | [END_REF]. The combination of the MUGAST Silicon array with the state-ofthe-art AGATA array and the large acceptance VAMOS spectrometer [18] gives a unique opportunity to perform exclusive measurements with radioactive beams. The triple coincidence provides both the particle and γ-ray spectroscopy of the nucleus of interest, the entry point for the γ decay through particle measurement, excellent background rejection, precise monitoring of the target thickness and Doppler correction from the twobody kinematics of the reaction. These features will be illustrated using three distinct data sets acquired with the MUGAST-AGATA-VAMOS setup: (i) the commissioning data, where the well-studied 16

Implementation of the MUGAST-AGATA-VAMOS setup

The MUGAST-AGATA-VAMOS campaign was performed at GANIL using the radioactive SPIRAL1 beams postaccelerated by the CIME cyclotron up to 12A MeV. Beam tracking devices, CATS [19], were available on the line for beam diagnostics and also time-of-flight measurement and beam rate monitoring. The beam was impinging either on a solid tar-get (such as CD 2 or LiF) or a cryogenic 3 He target, HeCTOr [20]. The low beam energy is well suited for stripping reaction measurements, for example (d,pγ), where the light ejectile is emitted backward. The MUGAST array surrounded the target to provide energy and angle of the light particles together with their identification. The AGATA array surrounded MUGAST in the backward hemisphere and featured high resolution with line shape information and high efficiency. Finally, the VA-MOS large acceptance spectrometer was used as a separator to provide identification of the heavy residue, rejection of the parasitic reactions and target thickness monitoring. Each element of the set-up is detailed in the following subsections.

The MUGAST array

The MUGAST array is composed of 12 double-sided Silicon strip detectors (DSSD) (see Fig. 1) which are arranged in order to cope with the mechanical constraints of the AGATA array and to fit into a sphere of 18 cm diameter. The transparency to γ-rays in the backward direction is ensured by deporting the front-end electronics to a circular mechanical support (see Fig. 1b)) located at 90 degrees.

In the backward direction, 5 (in 2019) and then 7 (starting from 2020) trapezoidal nTD type DSSDs and a float zone annular DSSD are assembled as shown in Fig. 1 to cover about 50% (70% with 7 trapezoidal detectors) of the backward hemisphere. The trapezoidal detectors are 500 µm-thick, reverse mounted and placed at 13 cm from the target. Their custom packaging from Micron Semiconductors Ltd [21] features very narrow frames with two kapton cables bent at 80 degrees. Each side is divided into 128 strips with a pitch of 710 µm and 760 µm on the front and rear side, respectively. The annular detector is a customized 500 µm-thick Si DSSD (S1 type) from Micron Semiconductor Ltd. It is divided into 4 quadrants each comprising 16 rings on the junction side and 4 sectors in the ohmic side. The inner diameter of the active zone is 48 mm and the external one 96 mm. The angular resolution of the backward array due to the geometry is better than 0.4 degrees. Fig. 2a) shows the comparison between the measured (with an α source) and simulated total efficiencies of the backward detectors as a function of the position angle. The simulation is performed with the nptool package [22] in a realistic way i.e. taking into account the detector geometry, the dead layers and the missing strips during the experiment. The averaged efficiency is about 70% for the trapezoidal ring which is consistent with the geometrical coverage. For the annular detector, the efficiency is close to 80% as there were 3 missing sectors during the experiment (see Fig. 2). There is a slight overestimation of the efficiency in the simulations around 110 degrees. This effect can be seen in Fig. 2b) and c) where the impact matrix in the backward detectors is displayed. In the data, there are missing counts at the top and the bottom that are present in the simulated data. This loss of efficiency is attributed to the target holder frame, casting a shadow on the detectors.

To complete the set-up, 4 MUST2 telescopes [7] cover the forward angles from 8 to 50 degrees at 18 cm from the target. They consist of a 300 µm-thick square DSSD backed by [START_REF]Grand Accélérateur national d'ions lourds[END_REF] with 128 strips on each side. Around 90 degrees, a single square DSSD of 300 µm thickness with 128 strips on each side is used to measure the elastic scattering of the beam on target. The reaction chamber is designed such that the MUGAST array fits into the AGATA array and preserves the large angular acceptance of VAMOS. The backward removable part of the reaction chamber is an aluminium spherical shell of 18 cm outer radius and a 3 mm thickness. The central part of the reaction chamber is made of stainless steel and opens with two large doors, one on each side. A system of guide rails facilitates moving of the MUST2 detectors and the backward ring upstream by 20 cm such that a moving cart can extract the backward ring out of the chamber and give full access to the detectors and their associated electronics (see Fig. 3). The reaction chamber can also host the HeCTOr cryogenic He target [20] with a dedicated mechanical support to hold its cryostat.

The position of the detectors inside the chamber is determined with a 3D arm which measures the position of holes made in the PCB frame of the detectors. Each detector is measured individually and the target position is measured consistently with a mask set at the target position. The precision of the measurement is 0.2 mm.

The AGATA array

Details about the AGATA array at GANIL have been published in ref. [23]. During the MUGAST campaign, the AGATA spectrometer consisted of up to 41 Ge crystals organized in triple clusters and placed in the backward hemisphere of the laboratory frame 18 cm away from the target. Resulting efficiency, taking into account the presence of the MUGAST detectors, is discussed in section 5.

VAMOS configuration

The large acceptance VAMOS++ magnetic spectrometer [18] was centered at 0 degrees to detect the forward focused beam-like residues of the reactions. The spectrometer entrance was placed at 73 cm from the target resulting in an angular acceptance of 4.6 degrees in the current configuration. The focal plane was equipped with 150 × 1000 mm 2 multi-wire parallel plate avalanche counters (MWPPAC), a pair of position sensitive drift chambers (DC) operated at 6 mbar of isobutane and a stack of segmented ionization chambers operated between 50 and 120 mbar of CF 4 . The MWPPAC provided measurement of the time-of-flight relative to the radio-frequency (RF) of the beam. The DC pair allowed measurement of the track of the heavy ions and the segmented ionisation chamber was used to measure energy loss and total energy of the ions. The identification of the ions is obtained based on the time-of-flight, rigidity and energy measurement following the reconstruction procedure discussed in Ref. [18]. A dedicated focalized optics is used to ensure a focalisation of the beam at the entrance of the focal plane. Depending on the beam intensities, the focal plane was equipped with a movable finger/shutter, placed upstream from the detection system to block the direct beam from entering the focal plane.

Electronics and data acquisition

The MUGAST, AGATA and VAMOS electronics are based on different data acquisition (DAQ) technologies which will be presented in this section before discussing the coupling of the three systems.

MUGAST electronics

The MUGAST array comprises about 3000 strips, all read out by the integrated electronics of MUST2 [7], which provide energy and time information for each strip. The front-end boards, called MUFEE, are placed under vacuum at a distance between 20 and 40 cm from the detectors on a ring surrounding the target (see Fig. 1). Each board hosts 9 ASICs and a pair of MUFEE boards reads 256 strips, i.e. one DSSD. The power consumption is approximatively 15 W per DSSD and is drained via a water cooled copper heat exchanger sandwiched between the two MUFEE boards. The ASICs deliver energy, time and leading edge discriminator (LED) information via a multiplexed bus to the MUVI board. MUVI is a single width unit in VXI C standard and ensures the slow control and data coding for 4 telescopes. The full MUGAST electronics comprise 4 MUVI boards in 4 common dead time VXI crates with parallel readout to reduce dead time.

AGATA electronics

The AGATA front-end electronics are based on a full digital system using 14 bit FADC at 100 MHz sampling. The clock and trigger are distributed to each AGATA crystal independently and correlated to the VAMOS and MUGAST subsystem through the AGAVA VME board. Details can be found in Refs. [23,13]. In the present configuration, the AGATA electronics were run in trigger-less mode, with no data reduction, since the individual counting rate per detector during the beam time was barely above that of the room background. Pulseshape analysis of digitized traces from all AGATA channels is performed in real-time and hit positions and energies are stored on disks. Individual AGATA crystal data are then merged by software with a time coincidence window of 500 ns using the individual time stamps of each channel. Finally, the coincidence of heavy-ions in VAMOS and light charged particles with AGATA events is performed on the timestamp difference between the AGATA crystals and the AGAVA board with a maximum time window of 2 µs.

VAMOS electronics

The readout of the detection system of the VAMOS spectrometer was obtained using NUMEXO2 digitizer modules [24]. Each module consists of 16 channel independent FADC with 100 MHz sampling. The VAMOS GTS clock [25] is distributed over each NUMEXO module independently and correlated to the VAMOS and MUGAST sub-system with an AGAVA VME board. In the present configuration, the preamplifier outputs of the 10 pads of the ionization chamber and the 4 amplification wires of the drift chambers were digitized and treated in real-time using a trapezoidal filter so that only amplitude and time information are stored upon an external validation of the MUGAST triggered acquisition signal. The time-of-flight information between the parallel plate detector at the focal plane and the MUGAST array or the RF of the cyclotron or CATS detectors (depending on the configuration) were measured using ORTEC TACs, which signal outputs were digitized using a dedicated NUMEXO2 firmware. The charges of the 4 drift chambers are read out using GASSIPLEX chips and a CAEN V551 sequencer [18] where the charges are multiplexed. The demultiplexing of the signal is done using NU-MEXO2 modules with dedicated firmware.

Data acquisition

The MUGAST-AGATA-VAMOS campaign couples three heterogeneous acquisitions systems: VAMOS and AGATA are based on the GTS system and events are respectively timestamped with the VAMOS TimeStamp (VTS) and AGATA TimeStamp (ATS); the MUGAST acquisition system is based on the GANIL DAQ, coupling 8 VME and VXI crates in common dead time through CENTRUM modules in event number mode [START_REF] Wittwer | 14th Conference on Real Time (RT2005)[END_REF]. The MUGAST acquisition system is triggered by an OR of the individual LED signal from the MUGAST telescopes. The VAMOS events are validated by triggered events in MUGAST to achieve data reduction. The AGATA system operates in trigger-less mode. Triggered events in the MUGAST system are timestamped with both ATS and VTS clocks using two AGAVA modules [13]. A scheme of the data acquisition and data flow is given in Fig. 4. The correlation of data produced by the systems proceeds in three steps :

1. On the MUGAST subsystem, the events are built on a common dead time event number basis in the GANIL event builder. The ATS and VTS timestamps are embedded in the built event headers. 2. A second event builder, based on the VAMOS TimeStamp (VTS) is used to correlate the VAMOS and MUGAST data. A typical building window of 1 µs was used. 3. A third event builder, based on the AGATA TimeStamp (ATS) is used to correlate the pre-built AGATA [23] data and the VAMOS+MUGAST data. A typical building windows of 1 µs was used.

MUGAST performances

The MUGAST array provides particle identification and precise energy and angle measurement of the light ejectiles. Some of its performances are discussed in this section.

Particle identification

The identification of particles that stop in the first layer of Silicon is usually deduced from time-of-flight (ToF) measurement. In the present case, the ToF is taken between MUGAST and the CATS beam tracking device placed upstream. The typical time resolution is 1.5 ns. An example of particle identification from the time-of-flight versus energy spectrum is shown in Fig. 5 for the 16 O(d,p) reaction measurement. The line corresponding to the protons is clearly seen, with the punchthrough at 9 MeV for a 500 µm-thick detector. ToF MUGAST-CATS (a.u.)

Energy (MeV) Depending on the beam mass, charge and kinetic energy, the CATS devices cannot always be inserted due to large straggling effects. When no time reference is available, the particle identification at backward angles relies on the energy-angle kinematic correlation for a two-body reaction, as the background contribution is quite low. From the energy and angle matrix shown in Fig. 6, the 16 O(d,p) reaction kinematic lines are identified (the solid lines correspond to the theoretical lines). The hole around 155 degrees corresponds to the detector frames. The ground state and the first excited state at 871 keV of 17 O are well separated. The energy resolution for this measurement will be discussed in section 7.1.

During the MUGAST-AGATA-VAMOS campaign, another technique for particle identification was developed, based on the reconstruction of the trajectories in the VAMOS spectrometer as it will be detailed in section 7. In the forward direction, in addition to ToF identification useful for low energies, particles having enough energy to punch through the first layer (DSSD) are identified from their energy loss in the first layer (∆E) and their remaining energy measured in the CsI crystals.

Excitation energy resolution

The excitation energy of the populated nucleus of interest is deduced by the missing mass method relying on the two-body kinematics and the measurement of the energy and angle of the light ejectile. For inverse kinematics measurement, the resolution in excitation energy is dominated by target effects and kinematic compression, so that the typical values are several hundreds of keV. The thinner and the more homogeneous the target, the better the excitation energy resolution.

During the campaign, the thinnest target was used for the measurement of 19 O(d,pγ) 20 O at 8A MeV with a 0.3 mg/cm 2 (corresponding to 3 µm) thick CD 2 target. The measured excitation energy spectrum is shown on Fig. 7 ,where the background contribution is removed by gating on the time between the PPAC of VAMOS and the RF of the beam that selects 20 O ejectiles. The experimental excitation energy resolution is 179±4 keV for the 2 + excited state of 20 O at 1.67 MeV. A similar measurement was performed with HELIOS at 8.06A MeV and a slightly thinner target of 0.26 mg/cm 2 [START_REF] Hoffman | [END_REF]. An excitation energy resolution of approximatively 175 keV (FWHM) was obtained, very similar to our value. In order to get deeper insight into the contributions to the excitation energy resolution, simulations using the nptool package are performed in a consistent way with the analysis of our data for the measurement 19 O(d,pγ) 20 O. The impact of the target thickness on the excitation energy resolution of the 2 + excited state of 20 O is shown on Fig. 8 (top). The simulation taking into account the target thickness and the associated straggling in energy and angle, the energy resolution of the detectors and the beam spread on target leads to an excitation energy resolution of 191 keV. The experimental result is shown by the red point for comparison. The uncertainty on the target thickness as given by the manufacturer is quite large 3±0.5 µm and may explain the discrepancy between the simulated and experimental resolutions. In principle, the target thickness can be accurately determined with the VAMOS spectrometer, taking advantage of the Bρ resolution of 2 per mil. The energy loss of the beam inside the target is precisely determined and the target thickness deduced. But this measurement could not be performed for the 19 O(d,pγ) 20 O reaction because we were using a gold backing on the target for lifetime measurement purpose.

Furthermore, the shape of the excitation energy spectrum is also investigated with the simulations in Fig. 8 (bottom) for three different target thicknesses 3, 6 and 10 µm. With increasing target thickness, the Gaussian shape of the excitation energy peak converts into a bell shape. This effect is attributed to the energy loss of the beam in the target and has been previously observed, for example in ref. [9,28]. If not properly accounted for, it impacts the extraction of the angular distributions and associated cross-sections. The excitation energy spectrum should, in this case, be fitted with the convolution of a Gaussian and a step function. The full width half maximum (FWHM) plotted in Fig. 8 (top) corresponds to the width of the peak evaluated at half the height of the peak by an iterative method, after obtaining the peak height from the fitting procedure.

Another contribution to the excitation energy resolution is the beam spread on target. With SPIRAL1 beams, the quality of the beam optics, with a size on target of ∆X=1.5 to 1.8 mm and ∆Y=2.7 to 3.0 mm, offers the possibility to run without tracking detectors. The simulated excitation energy spectrum for 19 O(d,p) 20 O* reaction assuming ∆X=1.5 mm and ∆Y=2.7 mm and a target of 3 µm, gives a resolution of 191 keV without beam tracking and 164 keV with no beam spread. In total, the experimental excitation energy resolution is 180 keV where 40 keV come from the intrinsic detector resolution and about 30 keV from the spatial spread of the beam. The dominant contribution is due to angular and energy straggling of outgoing protons inside the target.

AGATA efficiency with MUGAST

One of the major requirements for coupling a Silicon devices with a HPGe array is the transparency to γ-rays. The impact of the MUGAST array lying in between the target and the AGATA array on the photopeak efficiency is investigated in this section.

Photopeak efficiency

The absolute photo-peak efficiency of AGATA was measured using a standard 152 Eu source placed at the center of the MU-GAST array (see Fig. 9(top)). The photo-peak efficiency at 1.4 MeV was measured to be 4.9(1)% with 41 fully operational crystals placed at 182 mm from the source and 7.1(1)% after neighboring crystal Add-Back procedure was applied. Nevertheless, the second case results in a worsening of the peak-tototal ratio below 400 keV as compared to the first case with tracking, as, in fact, is expected from GEANT4 simulations [29].

Transparency to γ-rays

The MUGAST array transparency to γ-rays was carefully evaluated. Fig. 9 (bottom) presents a comparison between two measurements using a 152 Eu source placed at the target position. The first measurement (black points) was performed with 35 crystals at the nominal distance of 233 mm using the standard chamber and a plunger device [23]. The second measurement (red points) was performed with 39 crystals at 182 mm, placing the source in the MUGAST chamber, including fully equipped silicon detectors. As the number of available AGATA crystals and the target to detectors distances are different between the two measurements, they have been normalized to the photopeak efficiency at 1.4 MeV for the 152 Eu source. The comparison shows that the MUGAST chamber and detectors do not induce additional absorption for γ-ray energies above 200 keV and is ∼10% more transparent than a plunger set-up at 100 keV.

VAMOS performances

The VAMOS magnetic spectrometer provides full identification of the heavy residues from the reaction as well as full rejection of parasitic reactions such as fusion-evaporation when combined with MUGAST identification of light particles.

The atomic number (Z) is identified based on the correlation between the energy loss (∆E) in the two first segments of the ionization chamber and the total energy of the ions (E). No overlap between neighboring Zs is observed above the Bragg peak. Fig. 10 (upper) shows the Z identification of residues from reactions between the 15 O beam at 4.7A MeV and the LiF target. The mass number is obtained based on the combined measurement of the mass, deduced from the energy and velocity of the residues (A = E/u(γ-1)), and the mass-over-charge ratio, extracted from their magnetic rigidity (A/q = Bρ[Tm]/3.107βγ). The resolution of the mass measurement alone is not good enough to separate neighboring masses, and only the combination of both A and A/q allows for mass separation. Fig. 10 (lower) shows the mass identification matrix for the same reactions as in the upper case. The diagonal correlations indicate the different charge states of the emitted ions.

The final isotopic identification of the residues is presented in Fig. 11. For the range of masses and energies achieved in this experiment, the resolution in Z results in σ Z =1.6%, in average, and the resolution in A is σ A =0.9%. The resolution in Z is limited by the intrinsic resolution of the ionization chamber and the resolution in A is limited by the time-of-flight between the target and the VAMOS focal plane that, in this case, has a resolution of 2.5 ns.

In the current configuration, the efficiency in the determination of the magnetic rigidity is 90%, taking into account the drift chamber detection and the reconstruction method efficiencies. The detection efficiency of the ionization chamber is better than 92% for each section of the detector.

Performances of the coupled MUGAST, AGATA and VA-MOS setup

The MUGAST-AGATA-VAMOS set-up combines state-ofthe-art detectors that were specifically tuned for exclusive measurement of direct reactions. The excitation energy resolution, Doppler correction of γ-ray lines from particle measurement and developments in VAMOS to accept high beam rates and the advantages of the triple coincidences are discussed in the following sections. 16 O(d,pγ) 17 O one-nucleon transfer reaction The commissioning of the MUGAST-AGATA-VAMOS campaign was performed with an 16 O beam slowed down to 6A MeV and with a reduced intensity of 4×10 4 pps impinging on a 1 mg/cm 2 CH 2 target. The well-studied 16 O(d,pγ) 17 O reaction [30] was used as a benchmark.

Commissioning with

The excitation energy spectrum obtained by missing-mass technique is shown in Fig. 12. The background contribution comes mainly from fusion-evaporation reactions and α particles contamination and creates a tail that is clearly visible in the negative energies. A gate on VAMOS suppresses the background at the expense of statistics due to low efficiency during the commissioning experiment. The excitation energy resolution is 496 keV and 643 keV (FWHM) for the g.s. and first excited state, respectively. The main contribution comes from the 1 mg/cm 2 thick target effects. In this case, it is sufficient to separate the 871 keV first excited state from the ground state. The resolution can of course be improved by the γ-ray measurement in coincidence. The Doppler corrected γ-ray spectra are shown in Fig. 13 (a) without any condition except a time window between AGATA and MUGAST-VAMOS events (b) adding a gate on the excitation energy in MUGAST and finally (c) and adding an extra gate on the ionization chamber of VAMOS. All background contributions are strongly reduced already with a gate on MUGAST while the γ-ray line at 871 keV remains very strong.

The two angular distributions for transfer to the ground state and first excited state are presented in Fig. 14. They were obtained using a fit of two Gaussians and a background within several, width varying, angular bins. Each bin width was chosen so that the statistics is the same, hence resulting in the same statistical error bars. The efficiency normalization was performed using the nptool simulations. An absolute normalization was not possible because the beam current was not monitored during the commissioning. This current is normally measured by the CATS beam tracking devices [19]. When they cannot be used (due to too high current or too large straggling in the device), a model dependent normalisation can be deduced from measurement of the elastic scattering around 90 degrees, however no detector was available in this region during the commissioning run. A relative normalization to the theoretical distributions can still be carried out. The transfer reaction is studied with standard post-form DWBA calculations performed with the FRESCO code [31]. For the 16 O-d entrance channel, the parametrization by An&Cai [32] is adopted whereas, for the exit channel and the core-core optical potentials, the global parametrization by Watson et al. [33] is used. The binding potential for the p-n system is taken as the simple Gaussian interaction in [34], which reproduces the deuteron binding energy. For the binding potential of the 17 O nucleus, a Woods-Saxon potential with standard parameters (r 0 = 1.25 fm, a = 0.65 fm) is employed. The depth of the central and spin-orbit terms are adjusted to reproduce the energy of the d 5/2 ground state and the s 1/2 excited state in 17 O. In the DWBA calculations, spectroscopic factors equal to unity are fixed for both states, in agreement with previous measurements [35,36].

A proper description of the deuteron breakup may play a very important role in the description of the (d,p) transfer process, and could be done using the ADWA formalism. The adiabatic model using the Jonhson-Soper zero-range potential can be used to reproduce this effect [37], although it is better suited at high incident energies. The finite-range extension by Jonhson-Tandy (JT) [38] gives a more reliable description of the breakup process in a broader range. In the present work, calculations using the JT potential in the 16 O-d entrance channel were also performed, and results are found to be similar to those obtained with the global optical potential. The theoretical distributions were re-scaled to the experimental ones for comparison purposes. The ratio between g.s. and s 1/2 scaling factors with the An&Cai + Watson case is 1.19 (6) and is an estimate of the relative spectroscopic factors between the two transfer reactions. The compatibility between the factors is in agreement with the expected single particle behaviour of the residual nucleus and the unitary spectroscopic factors present in literature [35,36].

Triple coincidence measurements: full spectroscopy and background rejection

To discuss triple coincidences, we consider the α-transfer reaction 15 O( 7 Li,t) 19 Ne ( * ) , of astrophysical interest, that populates a large number of states around 4 MeV. For example, the states at 4.140 MeV and 4.197 MeV cannot be separated from particle measurement only as they are spaced by 51 keV. However their de-exciting γ-ray lines at 2632 keV and 2689 keV are well-separated with AGATA (see Fig. 15). With triple coincidence measurement, the background contribution to the γ spectrum is very low, particularly in the high energy region.

Moreover, the entry point for the γ decay can be determined from the particle-γ coincidence measurement. Fig. 16 shows the Doppler corrected γ-ray energy (E γ ) plotted against the excitation energy in 19 Ne, as derived from the triton energy and angle. The spectrum is gated by the identified 19 Ne in VAMOS. 19 Ne [START_REF]ENSDF data base[END_REF] is given in the inset.

For example, the 275-keV transition can be seen both through direct population of the 1/2 -state and collecting transition from numerous higher-lying states up to 10 MeV. This information is useful for determining top feeding of the γ-rays and can be of interest for lifetime measurements combined with transfer reactions. 7.3. Doppler correction of γ-ray spectra using two-body kinematics The Doppler correction of in-flight emitted γ-rays is usually performed event-by-event using the first hit interaction position determined by the Orsay Forward Tracking (OFT) algorithms [START_REF] Lopez-Martens | [END_REF]14] with the positions and energies as provided by the pulse shape analysis algorithms, and the averaged β of the beam. With MUGAST, the Doppler correction can also rely on the two-body kinematics by using the momentum of the heavy-ions deduced from the precise position and energy measurement of the light charged particle. A comparison of the two methods is shown in Fig. 17. A resolution (FWHM) of 7.1 keV is obtained for the 1.673 MeV γ-ray transition from the de-excitation of the 2 + 1 state in 20 O, compared to a resolution (FWHM) of 10.2 keV obtained with the Doppler Correction performed using an average beam velocity of 12.6%. During the MUGAST campaign, radioactive beams of up to 10 8 pps impinged on targets of typical thicknesses of 1 mg/cm 2 , with the VAMOS spectrometer set at zero degrees. This high intensity mode was only possible with the masking of the most forward part of the MUST2 detectors and using a movable plate in the VAMOS focal plane to intercept direct beam and non dominant charge states of residues of interest. The counting rates were 10 5 Hz in VAMOS, about 100 Hz for the full MU-GAST array and about 100 to 200 Hz per crystal resulting in about 8 kHZ in total in AGATA.

Particle identification and time-of-flight with VAMOS

One of the difficulties with the high intensity mode is the impossibility to use beam tracking devices for both normalization of the beam intensity and particle identification by timeof-flight. For the latter, the time between MUGAST and VA-MOS has been investigated by reconstructing the trajectories of heavy-ions in VAMOS.

Once the residues are identified, the start of the time-of-flight may by traced back from the VAMOS detection. The exact (integer) values of the mass number ( A ) and the ion charge ( q ) allow to translate the magnetic rigidity into velocity:

β =        3.107 Bρ[T m] A q 2 + 1        -1/2 . (1)
This velocity has inherited the resolution of the magnetic rigidity (0.2%). Hence the time-of-flight between the target and the VAMOS focal plane (ToF V AMOS ) is accurately determined from this velocity and the path travelled by the residues, also reconstructed in VAMOS with a resolution of 0.2%. The deduced time-of-flight resolution between the target and VAMOS is ∼800 ps, a factor 4 better resolved than using the cyclotron RF as the start of the time-of-flight measurement.

The time-of-flight between the target and MUGAST (ToF) may be determined using the previous method, together with the time between MUGAST and VAMOS, ToF = ToF VAMOS -T MUGAST-VAMOS , with an inherent resolution of ∼1 ns.

Figure 18 presents the identification plot in MUGAST based on the relation between the time-of-flight and the energy of the light recoils emitted in reactions between a 15 O beam and a LiF target.

The upper panel shows the ToF and the energy of the recoils detected in one of the MUST2 detectors placed at forward angles. The ToF is measured as the time difference between the cyclotron RF and the individual signal of each detector strip. The limited resolution of the RF results in a ToF resolution of 2.5 ns and it prevents the separation between different species.

The lower panel shows the same data set, but now, the ToF is determined based on the method presented above. Protons and α particles are well separated. The deuterium line is not visible in the data due to its typical low production in this type of reactions, nevertheless a shadow is present between both proton and α that corresponds to deuterium. The vertical lines indicate the punch-through of proton, deuterium and α particles in the detector. The final ToF resolution is 1.4 ns. This ToF resolution is limited by the experimental conditions: the MUGAST signal used as start of T MUGAST-VAMOS suffered from electronic jitters that imposed ∼1 ns time resolution to the signal.

Conclusion

The MUGAST-AGATA-VAMOS set-up combines simultaneous light particle, γ-ray and heavy recoil detection with stateof-the-art devices and allows for triple coincidence measurements of direct reactions with radioactive beams. The system was commissioned with the 16 O(d,pγ) 17 O * reaction for which the spectroscopy of 17 O was performed.Several stripping reactions measurements (d,pγ), ( 7 Li,tγ) performed during the campaign highlight the specificity of the MUGAST-AGATA-VAMOS set-up. In particular, it has been demonstrated that the detection of light ejectiles with good accuracy in energy and angle improves the Doppler correction of the γ-ray energies as compared with the method using the average velocity of the beam. The experimental setup shows excellent background rejection in the particle and γ-ray spectra thanks to the triple coincidence measurement. It also provides the determination of the entry point for γ-ray decay from the transfer reaction measurement. This information is crucial when applying Doppler Shift Attenuation Method (DSAM) for lifetime measurements. Moreover, a new method for particle identification based on the time-of-flight between MUGAST and VAMOS by reconstructing trajectories in VAMOS has been proposed. The time resolution obtained by this technique (1.4 ns) allows for particle identification without using beam tracking devices. The set-up has also proven to be able to run with high intensity beams (up to 10 8 pps), after masking part of the forward MUST2 detectors and using a movable plate in the focal plane of VAMOS. The MUGAST-AGATA-VAMOS campaign paves the way for direct reactions measurement with the new generation of postaccelerated ISOL facilities like SPES [41] and HIE-ISOLDE [42] and the slowed down fragmentation beams like OEDO [43] in RIKEN or the low energy branch of FAIR [44] using the GRIT-AGATA [45] in combination with high performance zero-degree detection.

Figure 1 :

 1 Figure 1: (Top) 3D view of the MUGAST set-up: a) global view with the beam coming from the left, AGATA on the left and the VAMOS spectrometer on the right; b) backward ring; c) full array. (Bottom) Photograph of the backward detectors with their electronics.

Figure 2 :

 2 Figure 2: a) Efficiency of MUGAST obtained through alpha source calibration for the configuration with 7 trapezoidal detectors in 2020. The red and black histograms represent simulation and data, respectively. The data is normalized to the simulation through the ratio of total number of counts in the annular detector. b) 2D reconstruction of the position of the alpha particles in the detectors. c) Same picture for simulated data.

Figure 3 :

 3 Figure 3: 3D view of the MUGAST reaction chamber and its mechanics.

Figure 4 :

 4 Figure 4: Schematic representation of the acquisition and data flow for MUGAST-AGATA-VAMOS.

Figure 5 :

 5 Figure 5: Reverse time-of-flight between MUGAST and the beam tracking detectors CATS as a function of the energy loss in the DSSDs. Note that for reverse ToF, the fastest particles have the longest ToF. A contamination from the triple alpha source is also present.

Figure 6 :

 6 Figure6: Energy versus angle of the light ejectiles (protons in this case) for the16 O(d,p) measurement. The red and the blue lines represent the theoretical correlation from two-body kinematics for ground state and the first excited state, respectively.

Figure 8 :

 8 Figure 8: (Color online)(Top) Full width half maximum of the excitation energy peak (see text for definition) as a function of the target thickness (in µm) for the 19 O(d,p) 20 O* reaction, populating the 2 + state at 1.67 MeV. The red point represents the experimental resolution. (Bottom) Simulated excitation energy spectra for three CD 2 target thicknesses: 3 (blue), 6 (red) and 10 (green) µm for the same reaction.

Figure 9 :

 9 Figure 9: (Top) Absolute efficiency of AGATA with the MUGAST array at 18 cm, after add-back procedure. (Bottom) Comparison of tracked AGATA efficiency between MUGAST set-up (red dots) and the standard chamber with the plunger device (black dots). The efficiency is normalized to the 1.408 MeV line.

Figure 10 :

 10 Figure 10: Particle identification in VAMOS. (Upper) Identification of the atomic number of heavy residues from 15 O +LiF reactions. (Lower) Identification of mass number and charge states of the residues from 15 O +LiF reactions. The line indicates the charge state q=8.

15 Figure 11 :

 1511 Figure 11: Isotopic identification of the heavy residues emitted in 15 O+LiF reactions, detected in VAMOS. Panels in the upper and right edges represent the projection of the mass number and atomic numbers, respectively.

Figure 12 :

 12 Figure 12: Excitation energy spectra for 16 O(d,p) 17 O obtained from the particle detection alone (MUGAST, blue line) and with an additional condition on the VAMOS ionization chamber (MUGAST+VAMOS, red line).

Figure 13 :

 13 Figure 13: γ spectra from AGATA after add-back procedure : a) with a time window between AGATA and MUGAST-VAMOS event and Doppler correction with average β of the beam; b) with multiplicity 1 in MUGAST, gating on the excitation energy of Fig. 12 on the 871 keV peak, and Doppler correction from the two-body kinematics; c) with an additional condition on the ionization chamber of VAMOS.

Figure 14 :

 14 Figure 14: Angular distributions for the g.s. and first excited 1/2 + state in 17 O. The DWBA calculations performed with two different potentials combination are represented in dashed and solid lines for the g.s. and first excited state respectively.

Figure 16 :

 16 Figure16: Doppler corrected γ-ray energy versus the excitation energy for the reaction15 O( 7 Li,t)19 Ne * . Counts located on the Ex=Eγ line correspond to state decaying directly to the ground states of19 Ne.

Figure 17 : 7 . 4 .

 1774 Figure17: γ spectra for19 O(d,p)20 O reaction gated on20 O in VAMOS and Doppler corrected: with the averaged beam energy (red) and on an event-byevent basis with the light particle detected in MUGAST (black). A zoom on the 1.9 MeV region is shown in the inset.

Figure 18 :

 18 Figure 18: Particle identification by time-of-flight versus Energy. (Upper) The time-of-flight is measured between MUGAST and the RF from the beam. (Lower) The time-of-flight is determined from the time between MUGAST and VAMOS after the reconstruction of the trajectories of the heavy residues.

  Figure 7: Excitation energy spectrum for 19 O(d,p) reaction with a time gate between VAMOS PPAC and the RF of the beam to select 20 O. The main peaks observed are labeled.

	500 1000 Counts / 25 keV		g.s	1.67 MeV 2 +		3.57 MeV 4 +	4.07 MeV 2 +	5.02 MeV 3 +
	-	1	0	1	2	3	4	5	6
				Excitation energy (MeV)

  In red, Doppler corrected γ spectrum in coincidence with MUGAST (any particle) divided by 500 and in blue the same spectrum gated by MUGAST +19 Ne ions in VAMOS for the 15 O( 7 Li,t)19 Ne ( * ) reaction. A partial list of levels for

	MUGAST /500	19 Ne partial level scheme
		3/2+ 4032.9 2497	15 (5)
			3758	5 (5)
			4033	80
		(15)
		(9/2)-4140	2632	100
		(7/2)-4197	2689.5 80 (5)
			3958.8 20 (5)
		MUGAST+VAMOS
	Figure 15:

-8 -6 -4 -2 -

Acknowledgments

The authors would like to thank the GANIL staff for their continuous help. This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 654002. A. Matta and W.N. Catford gratefully acknowledge the support of the STFC grant ST/J000051/1, ST/L005743/1, and ST/N002636/1. C. Diget acknowledges the support of the STFC grant ST/P003885/1. B. Fernández-Domínguez acknowledges the support of the Xunta de Galicia ED431B 2018/15 and Mineco PGC2018-096717-B-C22 grants.