Onset of collectivity in neutron-rich Sr and Kr isotopes : Prompt spectroscopy after Coulomb excitation at REX-ISOLDE , CERN

A rapid onset of quadrupole deformation is known to occur around the neutron number 60 in the neutron-rich Zr and Sr isotopes. This shape change has made the neutronrich A = 100 region an active area of experimental and theoretical studies for many decades now. We report in this contribution new experimental results in the neutron rich 96,98Sr investigated by safe Coulomb excitation of radioactive beams at the REX-ISOLDE facility, CERN. Reduced transition probabilities and spectroscopic quadrupole moments have been extracted from the differential Coulomb excitation cross section supporting the scenario of shape coexistence/change at N = 60. Future perspectives are presented including the recent experimental campaign performed at ILL-Grenoble. ae-mail: clement@ganil.fr This is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/20136201003 EPJ Web of Conferences


Introduction
Fission fragment spectroscopy has been used for decades to probe shells and shape evolution far from stability.In particular, the evolution of the deformation in n-rich isotopes around N = 60 has attracted many theoretical and experimental works.Already in the 60's, S. A. E. Johansson has shown that the light fission fragments of a 252 Cf source with mass around A = 110 belong to an island of large stable deformation [1].First theoretical work carried out with phenomenological approaches predicted that Sr and Kr with mass greater than 100 belong to a region for which the equilibrium shape is axially symmetric and oblate.The maximum of deformation should be observed in 98−102 Sr and 96−102 Kr and a transition from the spherical shape at N = 50 to highly deformed nuclei is predicted [2].
From the systematics of the 2-neutron separation energies extracted from mass measurements for Z = 32 to Z = 45, an increase of the binding energy is observed in Rb, Sr, Y and Zr isotopes at N = 60 [3].The onset of stability observed for these elements has been interpreted as a consequence of the deformation.The low Z border of the phenomenon has been recently established in the Kr isotopic chain where no deviation from the standard trend toward the drip line is observed [3].In addition, the first excited states have been observed in all even-even nuclei up to N = 60.The systematics of the excitation energy of the first 2 + states for Sr and Zr isotopes shows a sudden drop at N = 60 for both isotopic chains and by applying a simple geometrical model one can relate it to a change of deformation from = 0.17 to = 0.4.Consistently with the mass measurement [3], the decrease of the energy of the first 2 + between 94 Kr and 96 Kr is smooth [4].In addition, low lying 0 + states have been identified in the Zr and Sr chains and similarly to the 2 + 1 state, an abrupt drop of the 0 + 2 energy is observed at N = 60.Low lying 0 + 2 states are a long standing indication of shape coexistence.In this picture, excited 0 + states for N < 60 might correspond to a deformed configuration which becomes the ground state at N = 60 as the spherical configuration becomes non-yrast.The strong dependence of related spectroscopic properties on the number of protons and/or neutrons makes of these nuclei a very challenging case for various theoretical models.In this framework, we have investigated the shape transition in the Sr isotopic chain using Coulomb excitation reaction.Collectivity and nuclear deformation have been studied in 96,98 Sr via the measurement of reduced transition probabilities connecting different states and their spectroscopic quadrupole moments, being a direct measurement of the shape.

Shape Transition at N = 60
The nuclear structure of neutron rich Sr and Zr isotopes has been extensively studied experimentally in the past [5,[12][13][14].In 96 Sr, the ground-state band has a vibrational-like character.Two low-lying 0 + states were established by Jung et al. [15] at 1229 and 1465 keV and were interpreted as candidates for a deformed band head.An extremely strong electric monopole transition was observed between the 0 + 3 and 0 + 2 states [13,16], indicating the presence of a sizable deformation and strong mixing of the configurations.The sequence of the 0 + 3 (1465 keV), 2 + 3 (1629 keV) and 4 + 2 (1975 keV) states was interpreted as a well-deformed rotational band equivalent to the ground-state band in 98 Sr, even though the 2 + 3 → 0 + 3 transition remained unobserved.Lifetimes could be established for the 10 + and 12 + states in this band [5], from which a moderate deformation of only 2 = 0.25 was derived.It was argued that the 0 + 2 (1229 keV) and 2 + 2 (1506 keV) states are the low-spin members of this moderately deformed band, and it was concluded that the onset of deformation around N = 58 is not as abrupt as previously thought, but rather gradual [5].The 0 + 3 and 2 + 3 states could still be interpreted as being based on a very deformed configuration, especially in the light of the strong E0 transition.In 98 Sr, one can expect a different scenario.Beyond N = 60, the observed rotational ground-state band of 98 Sr points to a large ground-state deformation and the 0 + 2 state at 215 keV, which decays to the ground state via an enhanced E0 transition of 2 (E0) = 0.053 [18], supports the scenario of shape coexistence with a high mixing.However, the rotational ground-state band follows almost a perfect rigid rotor in opposition with a Fission 2013 large mixing of the wave functions which should disturb the sequence.A 2 + 2 state has been established 656 keV above the low lying 0 + 2 state.The sequence of the 0 + 2 and 2 + 2 states, very similar to the groundstate band in 96 Sr, supports the scenario of shape coexistence.
From the microscopical point of view, the sudden shape change is associated with a sharp modification of the shell structure at N = 60.In the deformed shell model approach, the onset of collectivity can be understood as a results of a competition between the spherical gaps at Z = 38, 40 and N = 56, and the deformed subshell closures at Z = 38, 40 and N = 60, 62 and 64.In the Sr and Zr isotopic chains, a spherical-to-deformed transition takes place when going from 58 to 60 neutrons, thus when the νg 7/2 orbital is being filled.Recently, Shell Model calculations were performed in the Zr isotopic chain in an extended model space [6].In this work the − ν interaction between the spinorbit partner 1 g 9/2 and 1ν g 7/2 was pointed out as the main mechanism for the shape modification: as the ν g 7/2 orbital is being filled, the Z = 40 subshell closure between the 1 f 5/2 and 1 g 9/2 effective single-particle energies (ESPE) is reduced.The 1 g 9/2 ESPE has an increasing slope while the 1 f 5/2 ESPE decreases more slowly when neutrons are added (see Fig. 1 in [6]).It is now established that this mechanism is responsible for the rapid onset of deformation in n-rich isotopes around N = 20 and N = 28 with different spin-orbit partners [7].In addition, the shell model calculations propose an interpretation for the 0 + 2 states for N < 60 as being a 2p-2h proton excitation from the 1f 5/2 orbital.The description beyond N = 60 where extruder orbits from a 78 Ni core and the h 11/2 intruder orbital make the shell model description very challenging.
While theoretical calculations, for example using the Nilsson-Strutinsky method with a Woods-Saxon potential [8], the relativistic mean field theory [9], or the Hartree-Fock-Bogoliubov approach with Gogny interaction [10] reproduce this onset of deformation qualitatively, they differ in the magnitude of the deformation parameters and excitation energies.Most calculations predict slightly oblate ground-state deformations for the lighter isotopes and strongly deformed prolate shapes for the heavier ones.In the transitional region around N = 60 the different shapes are expected to coexist in a narrow energy range.In the potential energy surfaces, the absolute minimum in 96 Sr is found to be oblate, while a strongly deformed prolate minimum is found about 1 MeV higher.Oblate and prolate minima are almost degenerate in 98 Sr.This scenario is supported by the observation of the excited 0 + states at 1229 and 1465 keV in 96 Sr and at only 215 keV in 98 Sr.However, the sign of the deformation is difficult to access experimentally, and so far there is no clear experimental evidence for oblate shapes in the neutron-rich Sr or Zr isotopes.Finally by comparing the different mean field approaches one can notice that calculations carried out with axial symmetry predicted coexisting prolate and oblate minima with almost the same deformation.Calculations using more degrees of freedom predict a slightly oblate configuration coexisting with a large deformed prolate minimum [8][9][10].Up to now there is no experimental proof for a large prolate or oblate deformation beyond N = 60.
The goal of the present experimental program is to measure spectroscopic quadrupole moments in both ground state and excited bands around N = 60.In addition, B(E2)'s between coexisting structures and between the states belonging to the excited configuration will provide fundamental information required for a proper description of these nuclei.

Coulomb excitation of 96,98 Sr
Post-accelerated radioactive beams of 96,98 Sr were delivered by the REX-ISOLDE facility at CERN with an average intensity of 1-0.5 10 4 pps (pure 96 Sr) and 6.10 4 pps (80% pure 98 Sr) at 2.87 MeV/A and 2.82 MeV/A respectively to the Coulomb excitation setup of the MINIBALL HPGe array [11].Each of the beams was scattered on two different targets: 109 Ag, 120 Sn for 96 Sr and 60 Ni, 208 Pb for 98 Sr. De-excitation -ray spectra are sorted in prompt coincidence with scattered particles detected in the annular silicon strip detector for scattering angles ensuring a pure electromagnetic process [19].Doppler correction is applied for the projectile assuming detection of 96,98 Sr recoils using both the position information of the particle detector and the electric segmentation of the MINIBALL detectors.The -ray spectra following the Coulomb excitation of the 96 Sr beam are presented in Figure 1.In both spectra, the 2 + 1 → 0 + 1 transition in 96 Sr is observed as well as the excitation of the target.In case of the heavier target a weak transition corresponding to the 0 + 2 decay is visible in the insert.The Coulomb excitation analysis was performed using the least squares fitting code GOSIA [20,21].A standard 2 function is constructed from the measured -ray yields of both the projectile and the target, and those calculated from a complete set of electromagnetic matrix elements, both transitional and diagonal, between all known states involved in the excitation process.Combining the data set from both target and using the differential Coulomb excitation cross section, we have significantly improved the measurement of the B(E2,2 + 1 → 0 + 1 ) = 462(11) e 2 fm 4 and extracted for the first time a preliminary value for the spectroscopic quadrupole moment of the first 2 + 1 state equal to Q s = −6(9) efm 2 .From the measurement of the spectroscopic quadrupole moment a weak static deformation can be assigned to the first excited state.For indication, using the deformed liquid drop model, one can extract ≤ 0.14.The mean deformation of the first 2 + state is null as its B(E2) is rather large (20 W.u) supporting a quasi-vibrator character for the 96 Sr in its ground-state band structure.This deformation is also compatible with a moderate oblate deformation in the ground state calculated in the triaxial mean-field approach.

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The -ray spectra following the Coulomb excitation of the 98 Sr beam are presented in Figure 2. In agreement with the shape transition scenario, the spectra are rather different from those of 96 Sr.In both spectra, the decay from the rotational ground-state band populated up to spin 8 + and the decays from the 2 + 2 are observed.Unknown transitions visible in the spectra are marked with asterisks.They neither belong to the known level scheme of 98 Sr, nor exhibit − coincidences with known decays.Therefore, we assume that they belong to the main contaminant of the beam, 98 Rb, for which no excited state have been reported so far.The known lifetimes of the 2 + 1 , 4 + 1 , 8 + 1 , 10 + 1 and 0 + 2 states were used as additional data points in the GOSIA fit.As a results, a preliminary value for the B(E2,6 + 1 → 4 + 1 ) = 5600(1800) e 2 fm 4 has been extracted.The value fits perfectly with the systematics of the rotational ground-state band which is consistent with the behavior of a very good rotor with an almost constant transitional quadrupole moment in the intrinsic reference frame.Preliminary B(E2) connecting the 2 +   98 Sr, respectively, supporting the shape coexistence scenario.This complete set of electromagnetic matrix elements will be compared with advanced theoretical models and in particular with calculations beyond the mean-field which provide B(E2)'s and spectroscopic quadrupole moments for a large number of excited states.

Spectroscopy at EXILL and perspective
The Kr isotopes will be the subject of the next experimental investigations.In opposition to the Sr and Zr at N = 60, the two-neutron separation energy and the excitation energy of the first 2 + state do not show any abrupt change in the systematics.Does the 2 + energy in 96 Kr reflect a large mixing of the different configurations as established in the light isotopes close to the N = Z line [22] or the gain in binding energy due to the deformation and/or correlation is not strong enough only 2 proton away from the Sr isotopes?Does any shape isomer exist in this isotope?Extending the level scheme in 96 Kr is the purpose of experiment being part of the EXOGAM campaign at ILL (EXILL).Future measurements in next generation ISOL facilities using the post-accelerated fission fragment beams and the Coulomb excitation technique will allow to determine the electromagnetic properties.

Conclusion
We have investigated the collectivity and the deformation in 96,98 Sr at N = 60 using the Coulomb excitation technique at REX-ISOLDE.Spectroscopic quadrupole moments have been extracted and are compatible with the shape inversion and shape coexistence scenario between a deformed and a spherical configuration.Detailed comparisons with theoretical models will be performed with advanced calculations based on the mean-field approach.A microscopical interpretation based on exact shell model or Monte Carlo shell model should also be investigated.A recent experiment performed at the ILL reactor will soon provide new spectroscopic data in the Kr isotopic chain and in the future, the use of the post-accelerated fission fragment beams from ISOL facilities will allow us to investigate the electromagnetic properties of the transitional key nucleus 96 Kr. 01003-p.5

Figure 1 .
Figure 1.Top: -ray spectrum detected in MINIBALL, Doppler corrected for the projectile and following the excitation of a 96 Sr beam impinging on a 109 Ag target.Bottom: same spectrum for the excitation of 96 Sr on a 120 Sn target.The insert shows a zoom on the weak 0 + 2 decay.

2 01003Figure 2 .
Figure 2. Left: -ray spectrum detected in MINIBALL, Doppler corrected for the projectile and following the excitation of a 98 Sr beam impinging on a 60 Ni target.Right: same spectrum for the excitation of 98 Sr on a 208 Pb target.
+ 1 states with an average value of -150 efm 2 indicating a large prolate deformation and for the 2 + 2 state equal to |Q s | ≤ 48 efm 2 .One can notice the similarity in terms of B(E2) and Q s between the 2 + 1 → 0 + 1 and 2 + 2 → 0 + 2 in 96 Sr and