Exploring the structure of Xe isotopes in A ∼ 130 region: Single particle and collective excitations

R. Banik1,2,∗, S. Bhattacharyya1,2, S. Biswas3, S. Bhattacharya1,2, G. Mukherjee1,2, S. Rajbanshi4, S. Dar1,2, S. Nandi1,2, S. Ali5,2, S. Chatterjee6, S. Das6, S. Das Gupta7, S. S. Ghugre6, A. Goswami5,2, D. Mondal1, S. Mukhopadhyay1,2, H. Pai5, S. Pal1, D. Pandit1, R. Raut6, P. Ray5,2, and S. Samanta6 1Variable Energy Cyclotron Centre, 1/AF Bidhannagar, Kolkata 700064, India. 2Homi Bhabha National Institute, Training School Complex, Anushaktinagar, Mumbai-400094, India. 3GANIL, CEA/DRF-CNRS/IN2P3, Bd Henri Becquerel, BP 55027, F-14076 Caen Cedex 5, France. 4Department of Physics, Presidency University, Kolkata 700073, India. 5Saha Institute of Nuclear Physics, Kolkata 700064, India. 6UGC-DAE CSR, Kolkata Centre, Kolkata 700098, India. 7Victoria Institution (College), Kolkata 700009, India.


Introduction
The transitional nuclei in the A ∼ 130 region are of current interest to explore the variety of nuclear structures arising from interplay between the single particle and the collective degrees of freedom. The shape driving nature of the h 11/2 orbital, available for both protons and neutrons, and the corresponding particle-hole interactions drag the nucleus towards various exotic shapes and structures. The role of the unique parity h 11/2 orbital is thus important in inducing deformation to the system and having deformed band structures based on both one quasi-particle (qp) and multi qp configurations. 131 Xe(Z = 54, N = 77) is one of the suitable candidate to study various band structures and interesting features of the nuclear shape in A ∼ 130. Only one qp (νh 11/2 ) band structure in 131 Xe is known [1,2], whereas, high spin band structures in 125 Xe [3] and triaxial bands in 129 Xe [4] have been reported. Availability of highj h 11/2 orbital for both proton particles and neutron holes makes 131 Xe also a suitable candidate to exhibit Magnetic Rotation (MR) at high spin. Such MR band is reported in 123 Xe [5] and described using the tilted axis configuration with πh 11/2 ⊗ νh 11/2 . As one approaches the N = 82 shell closure the MR band becomes favourable for its proximity to spherical shape. The lower spin states of 131 Xe are generated from single par- * e-mail: ranabir.banik@vecc.gov.in ticle excitations of four proton particles and five neutron holes (with respect to 132 Sn) in various available orbitals. The understanding of the configurations of these states helps us to explain the underlying nucleon-nucleon interactions. Thus 131 Xe can be an interesting nuclei to study the various mechanisms of generation of angular momentum in a single nuclei. Population of 131 Xe is difficult due to lack of stable target-projectile combinations. Previous spectroscopic studies on this nuclei were carried out from decay spectroscopy [6,7], Coulomb excitations [8], (α , 3n) [1] and (α , n) [9] measurements. But these studies are limited by the detection system used. A recent study on 131 Xe [2] reports only the extension of the yrast band to higher spin. But no detail information about the other high spin structures is available prior to the present study.
Xenon isotopic chain is also known for its shape change from γ-soft rotor to spherical one. The possible phase transition for the even-A Xe isotopes can be described using E(5) symmetry, where the nucleus undergoes from spherical vibrator to γ-soft rotor. Clark et al. [10] has predicted that the E(5) symmetry can be investigated in 128 Xe. The spectroscopic study on 128 Xe [11] has indicated that 130 Xe can possibly be a better candidate to look for such E(5) symmetry breaking. The structure of 130 Xe was studied using Coulomb excitation in inverse kinematics [11] and (n , n') reaction [12], which concluded that this nucleus may not be the candidate for E(5) symmetry.   But to know the detail low lying structures, it is worth to re-investigate the non-yrast and yrast states of 130 Xe.

Experiment and Data Analysis
The excited states of 130,131 Xe have been populated using the reaction 130 Te (α , xn) 130,131 Xe, at a beam energy of 38 MeV, obtained from the K-130 Cyclotron at Variable Energy Cyclotron Centre (VECC), Kolkata, India. The Indian National Gamma Array (INGA) at VECC [13] consisting of seven Compton suppressed Clover HPGe detectors were used to detect the de-exciting γ rays. Four detectors of the array were at 90 • , two detectors were at 125 • and one detector was at 40 • with respect to the beam direction. PIXIE based digital data acquisition system [14] was employed to record the time stamped LIST mode data in both singles (M γ ≥ 1) and coincidence mode (M γ ≥ 2).
The LIST mode data were sorted using the IUCPIX sorting programs [14] and further analysed using the RADWARE [15] and LAMPS [16] data analysis packages to construct the symmetric and angle-dependent E γ -E γ matrices and E γ -E γ -E γ cube. In the present work, the multipolarities of the observed γ rays were determined from the Ratio of the Directional Correlation of the Oriented states (R DCO ) measurements, as described in Ref. [17]. The parities of the excited states have been assigned from the polarization asymmetry measurements (∆ asym ). The measured values of the ∆ asym give an idea about the electromagnetic nature of the decaying transition. The description of the method can be found in the Ref. [18].

Results
The existing level scheme of 131 Xe is significantly extended with the placement of 72 new transitions from the current measurement. The details of this will be given in a forthcoming publication. The partial level scheme of  131 Xe, related to the present paper, is shown in Fig. 1. The R DCO vs ∆ asym plot for the transitions of 131 Xe, reported in this paper are shown in the Fig. 2.
The main yrast negative parity band (Band A) of 131 Xe is observed upto 4945 keV excitation energy as also observed by Kaya et al. [2]. The present work confirms the 31/2 − (3814 keV) and 35/2 − (4945 keV) spin assignments to the top two levels of this band, respectively, which could not be assigned in Ref. [2]. In the present work, a new band structure (Band B) (∆J = 2) is identified, which decays to the main yrast band by M1 transitions of energy 682, 574, 881 and 834 keV. The M1 nature of these transitions are established from their deduced R DCO and ∆ asym values. This band B is the possible signature partner band of the main yrast sequence. Fig. 3(a) and (b) represent the coincidence spectra double gated on the 810 -902 keV and 810 -295 keV transitions respectively, from the E γ -E γ -E γ cube. The presence of two different sets of new γ rays in these two spectra establishes another new band structure above 1617 keV level. The transitions of the main yrast band and the partner band are evident from Fig. 3(a). Fig. 3(b) shows another new set of γ-rays which are observed above the 19/2 + state and are in coincidence with each other. This new band is extended upto 5172 keV, 33/2 (+) , level with the observation of seven transitions and named with band C in the level scheme. Among these transitions, the 444 keV γ-ray was known from previous studies, but other transitions of energy 1105, 295, 503, 119, 311 and 592 keV are newly observed from the present work. The placement of these transitions are determined from their relative intensities. The deduced R DCO values of ∼ 0.5 in a quadrupole gate along with negative ∆ asym values establish these transitions as of M1 character.
Another set of new γ-rays are observed above the 11/2 − state and parallel to the yrast band in 131 Xe. Six new transitions of energies 316, 334, 602, 857, 1045 and 1205 keV are seen in the sequences D1, D2 and D3, which extends this part of the level scheme upto 3108 keV excitation.
As the yield of 130 Xe is less at the beam energy chosen for the present reaction, only a limited set of data could be obtained on this nucleus. In this work, the main yrast structure in 130 Xe is observed above the particle alignment. Various non-yrast states are also observed parallel to the main yrast structure in the 130 Xe.

Discussion
The ground state of 131 Xe is determined by the odd valence neutron. The lowest two levels of this nucleus are 3/2 + (0 keV) and 11/2 − (164 keV), which originate from the odd neutron occupying the available d 3/2 and h 11/2 orbitals. The large spin difference between these two states enforces the 11/2 − state to be a long lived isomer (11.84 d) in 131 Xe. This isomeric state decays to the 3/2 + ground state by IT decay [19]. The rotational structure built on the 11/2 − state is reported in Kaya et al. [2] and also seen in this work. Fig. 4 represents the variation of single particle alignment as function of rotational frequency for the yrast negative parity νh 11/2 band (Band A) of 131 Xe and 129 Xe. Backbending with large alignment gain is observed for this band in 131 Xe, whereas 129 Xe shows an upbending. Such gain in alignment in 131 Xe takes place due to the alignment of a pair of protons in h 11/2 orbital. Band A and band B in 131 Xe are found to have large staggering parameter, similar to its isotopic and isotonic partners. Large signature splitting as observed for this band indicates a large Ω mixing. The sequence of M1 γ-rays (Band C) above the 23/2 + state is connected to the 21/2 + state by a relatively higher energy 1105 keV transition. This implies that these two parts have different configurations, with a 5-qp configuration to the upper part of the band (above 27/2 + ) and a 3-qp configuration to the lower part. The upper part of this band is likely to have an extra pair of proton aligned which gives rise to a configuration π[(d 5/2 g 7/2 ) 3 h 11/2 ] ⊗ νh −1 11/2 . This structure may possibly a MR band and thus discussed in the framework of Shears mechanism with the Principle Axis Cranking (SPAC) model [20][21][22][23]. The description of this theoretical model can be found in the Ref. [22]. For the present case, SPAC calculation is carried out considering the aforesaid configuration and assuming J π = 12 and J ν = 5.5 . The level energies with respect to the band head energy as a function of level spin for the dipole band is plotted in the Fig. 5. Those experimental points are compared with the present calculation (solid line) and are found to be matching well. The calculated transition probabilities, B(M1), are also plotted as a function of level spin and shown in the inset of Fig. 5. It is clearly seen from the figure, that the B(M1) values go on decreasing as the spin increases, which is one of the signature of magnetic rotational band. But a concrete evidence for this band to be a MR band would be an experimental observation of decreasing B(M1) values, which is out of the scope of the present experiment. Present SPAC model calculations also predicts that the 91% of the total angular momentum of the levels of this band is generated via shears mechanism.
The levels in the sequences, marked as D1, D2 and D3 in the level scheme ( Fig. 1), are found to decay via various non-stretched transitions, indicating these states to be of single particle origin. Shell Model calculations are carried out for these states employing the code NUSHELLX [24] in the gdsh model space with the jj55pna Hamiltonian (referred as SN100PN interaction) [25]. The available orbitals consisting in the shell N , Z = 50 -82 are g 7/2 , d 5/2 , d 3/2 , s 1/2 and h 11/2 for both protons and neutrons. The calculations are carried out without any restriction in proton and neutron model space. The comparison between the calculated energy levels and the experimental levels of sequences D1, D2 and D3 are shown in Fig. 6. For this purpose, the experimental levels with increasing order of excitation energy for a given spin are compared with the corresponding states of shell model calculations. A good agreement between experimental states and shell model calculations for sequences D1, D2 and D3 are obtained.

Summary
The excited states in 130,131 Xe have been studied using αinduced fusion evaporation reaction and INGA detection setup. The existing level scheme of 131 Xe is extended with the observation of signature partner band of the yrast band and a MR band. Other new set of low-lying levels above the 11/2 − isomer are also observed. The MR band is discussed using SPAC model calculations and the non yrast states are interpreted in terms of Shell Model calculations.