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Evolution of Intrinsic Nuclear Structure in Medium Mass Even-Even Xenon Isotopes from a Microscopic Perspective*

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Evolution of Intrinsic Nuclear Structure in Medium Mass Even-Even Xenon Isotopes from a Microscopic Perspective* Chinese Physics C Vol. 44, No. 7 (2020) 074108 Evolution of intrinsic nuclear structure in medium mass even-even Xenon isotopes from a microscopic perspective* Surbhi Gupta1 Ridham Bakshi1 Suram Singh2 Arun Bharti1;1) G. H. Bhat3 J. A. Sheikh4 1Department of Physics, University of Jammu, Jammu- 180006, India 2Department of Physics and Astronomical Sciences, Central University of Jammu, Samba- 181143, India 3Department of Physics, SP College, Cluster University Srinagar- 190001, India 4Cluster University Srinagar - Jammu and Kashmir 190001, India Abstract: In this study, the multi-quasiparticle triaxial projected shell model (TPSM) is applied to investigate γ-vi- brational bands in transitional nuclei of 118−128Xe. We report that each triaxial intrinsic state has a γ-band built on it. The TPSM approach is evaluated by the comparison of TPSM results with available experimental data, which shows a satisfactory agreement. The energy ratios, B(E2) transition rates, and signature splitting of the γ-vibrational band are calculated. Keywords: triaxial projected shell model, triaxiality, yrast spectra, band diagram, back-bending, staggering, reduced transition probabilities DOI: 10.1088/1674-1137/44/7/074108 1 Introduction In the past few decades, the use of improved and sophisticated experimental techniques has made it pos- sible to provide sufficient data to describe the structure of The static and dynamic properties of a nucleus pre- nuclei in various mass regions of the nuclear chart. In dominantly dictate its shape or structure, and these prop- particular, the transitional nuclei around mass A ∼ 130 erties depend on the interactions among its constituents, have numerous interesting features, such as odd-even i.e, protons and neutrons. Most nuclei exhibit an axially staggering (OES) in the gamma band at low spins, triaxi- symmetric, dominantly quadrupole, deformed shape in al deformation, etc. [4–6]. The even-even nuclei close to the ground state. However, there are several regions, the proton shell closure at Z = 50 have been the subject of known as transitional regions, in the nuclear chart where numerous theoretical [7–15] and experimental studies axial symmetry is not conserved; the triaxial mean-field [16] in the past. The Xenon (Z = 54) nucleus with four approximation may be used to characterize the properties protons more outside the 50-proton closed shell is posi- of these nuclei. Nuclei in the transitional region Z > 50 tioned in the transitional region of nuclear chart, where and N 6 82 are characterized by softness to the γ-deform- nuclear structure varies from a spherical nature to a de- ation [1], which accounts for shape coexistence in these formed one. Thus, this region is observed to be rich in the nuclei [2]. In these nuclei, protons in the valence shell be- nuclear structure, as it provides a testing ground to probe gin to fill the h11=2 shell, while the neutrons remain in the the interplay between triaxial and axially deformed nucle- middle of that shell. Rotational alignment of these ar shapes. This region is an exciting field in nuclear- valence protons and neutrons trend to drive the nucleus structure studies because of the reported presence of low- towards prolate and oblate shapes, respectively [3]. lying intruder states, as well as the occurrence of a triaxi- Therefore, the nuclei lying in the above referred trans- al shape. Hence, the present study attempts a theoretical itional region are good candidates for the study of vari- investigation of a chain of even-even Xe nuclei within the ous interesting phenomena, such as the effect of orbitals application of the TPSM approach. In recent times, as on deformation, investigation of shape changes, new ex- well as in the past few decades, various theoretical stud- citations with regard to triaxial deformations, etc. ies had been used to investigate various nuclear structure Received 29 January 2020, Published online 25 May 2020 * Arun Bharti acknowledges the financial support from the Science and Engineering Research Board, under the project file no. CRG/2019/001231 and Ridham Bak- shi acknowledges the financial support from The Department of Science and Technology, Government of India, INSPIRE Fellowship under sanction no. DST/INSPIRE Fellowship/2018/IF180368 1) E-mail: [email protected] ©2020 Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Sciences and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd 074108-1 Chinese Physics C Vol. 44, No. 7 (2020) 074108 properties, such as energy levels, electric quadrupole mo- momentum projection technique was successfully adop- ments, and B(E2) of the Xe nuclei [14, 17–21]. These ted to study the γ-vibrational band structures in triaxially studies suggest that these nuclei are soft with regard to deformed nuclei. The TPSM approach has also provided the γ-deformation with a almost maximum effective tri- theoretical support for observation of the γγ-band in ◦ axiality of γ = 30 [7]. Nuclei above the closed shell at Z those nuclei [33]. Because the studied 118−128Xe isotopes = 50 and with a neutron number close to the N = 66 mid- are of the even-even type with even protons and neutrons, shell exhibit large ground-state deformations, with β2 ≈ the TPSM basis chosen for carrying out the present study 0.2 –0.3 [22, 23]. For the Z = 54 Xenon isotopes, the is composed of the projected 0-qp state (or qp-vacuum), 120 ground state deformation is at its maximum for Xe66, two-proton qp, two-neutron qp, and 4-qp configurations, which is evident from the minimum value of excitation namely, + + 120 energy of the first 2 state [E(21 )]. Below Xe, the val- ˆ I jΦ >; + PMK ues of [E(21 )] increase down to the lightest known iso- y y 114 Pˆ I a a jΦ >; tope Xe, indicating a decrease in the deformation as the MK p1 p2 y y (1) N = 50 closed shell is approached. This trend is quantitat- Pˆ I a a jΦ >; MK n1 n2 ively supported by calculations presented in Ref. [24], I y y y y Pˆ ap ap an an jΦ >; which predict that the tendency continues all the way to MK 1 2 1 2 the closed shell. Furthermore, 120Xe is a well-studied nuc- where jΦ> represents the triaxial vacuum state. The leus [25, 26] with a ground state rotational band three-dimensional angular-momentum projection operat- = ≈ : (E4+ E2+ 2 5) and a quasi-band with a band head at or [34] is given by Z 876.0 keV. Furthermore, 120Xe lies in a complex nuclear 2I + 1 Pˆ I = dΩ DI (Ω)Rˆ(Ω); (2) transition region, which evolves from a vibration-like MK 8π2 MK structure near N = 82, through a γ-soft region near N = with the rotational operator 74, towards rotational configurations for lighter neutron- −ıαJˆ −ıβJˆ −ıγJˆ deficient nuclei. In the N = 66 region, 120Xe is the heav- Rˆ(Ω) = e z e y e z ; (3) iest even-even nucleus showing a signature of shape co- Ω denotes a set of Euler angles (α,γ = [0, 2π], β = [0, π]) existence [27]. Moreover, quasi-ground-state bands and and J denotes angular-momentum operators. In this γ γ quasi-rotational -vibrational bands with unstable -de- present approach, triaxiality is included in the deformed formations have also been studied for Xe in this nuclear basis, which helps perform an exact three-dimensional region [28]. angular momentum projection. In this manner, the de- The Xenon nucleus thus belongs to the region of the formed vacuum state obtained is significantly improved, nuclear segre chart where the effect of triaxiality on the as it permits all possible components of K. The projected nuclear structure is evident. Therefore, the purpose of the shell model version employed for the description of axi- present study is to investigate the observed band struc- ally deformed nuclei uses the pairing plus quadrupole- tures and, in particular, the observed triaxiality in quadrupole Hamiltonian [35] with a quadrupole-pairing 118−128Xe isotopes using the triaxial projected shell model term also included, as follows: (TPSM) approach [29, 30] in a simple and comprehens- X X 1 y y y ive manner. The formalism of the TPSM that we are us- Hˆ = Hˆ0 − χ Qˆ µQˆ µ −GM Pˆ Pˆ −GQ PˆµPˆµ; (4) ing in the present study has been successfully employed 2 µ µ in the past [31–33] to study high-spin structures of triaxi- and the equivalent triaxial Nilsson mean-field Hamiltoni- ally deformed nuclei. Further, the present chain of iso- an is given by topes 118−128Xe has not been studied to date with the ap- ( ) ˆ + ˆ plication of TPSM; therefore the present work was taken 2 0 Q+2 Q−2 Hˆ N = Hˆ0 − h¯! ϵQˆ 0 + ϵ p ; (5) up as a challenge to describe their structure within TPSM. 3 2 The paper is organized as follows. Section 2 provides where the first term in Eq. (4) is the single-particle spher- a brief overview of the theoretical approach (TPSM) used ical Hamiltonian, which has a proper spin-orbit force rep- in the present work. The results of the measurement for resented by Nilsson parameters [36]. The force strength the Xenon isotopes, followed by a discussion and their quadrupole-quadrupole (QQ) χ is determined in such a comparison with the available experimental data, are way that it holds a self-consistent relation with the quad- presented in Section 3. Finally, the study is summarized rupole deformation. In Eq. (5), ϵ and ϵ0 specify the de- in Section 4. formation parameters corresponding to the axial and tri- axial deformation, respectively, and they are related to −1 ϵ0 2 Theoretical outline the triaxiality parameter by γ = tan ( ϵ ).
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