Pandya, S P

Praharaj, C R

Rath, A K

IACS Institutional Repository

Indian J. Phys. 70A(1), 161-165 (1996)I J P  A— an international journalS h ap e a n d  a lig n m en t e ffec ts  in  X e  n u c le iS P Pandya, C R Praharaj* and A K Rath**Physical Research Laboratory, Ahmedabad-380 009, India * Institute of Physics, Bhubaneswar-751 005. IndiaAbstract : Even mass Xe nuclei have received much attention recently. In this work we study the structures of even-even ,,R-,26Xc nuclei'by deformed Hartree-Fock and angular momentum projection The systematics of the alignments of nhur2 and vhim oibits are emphasised Some observations are made about the band structures of neighbouring odd mass xenon and iodine nuclei.Keywords : Xe nuclei, shape and alignment effects, nuclear structure FACS No. : 21.60Jz1. IntroductionSeveral features like shape changes, interplay of collective and single particle like behaviour, rotation alignment effects have been inferred from recent observations and theoretical calculations in A = 120-140 region [1-4]. In this paper, we investigate the above features in 1,8-,26Xe nuclei in a microscopic shell model approach (i.e. Deformed Hartree- Fock with angular momentum projection) which has been described in detail by S P Pandya el al in their contribution to this proceedings. In the HF approach the shape and its dynamics with other nuclear parameters emerge automatically. The deformed HF intrinsic configuration designated by a K quantum number contains all the relevant information regarding the collective dynamics of the nucleus. Thus angular momentum projection from this configuration reveals the dynamical effects of the observed spectrum. Without going into details of formalism, we directly discuss our results.2. Deformed Hartree-Fock calculation for ng~,26Xe nucleiAxially deformed HF calculations are carried out for the valence nucleons in a model space consisting of two major shells both for protons and neutrons lying out side the 56Ni inertPresent address : P G Department of Physics, Sambalpur University, Jyoti Vihar, Barla,Sambalpur-768 019, Orissa, India© 19% I ACS162 S P Pandya, C R Praharaj and A K Rathcore. The energies of the spherical single particle states 2pm> 2p\n< I/5/2- l#9/2. l#7/2» 2dv2> 2^3/2. 3j |/2 and lhun are taken to be -30.0, -29.0, -29.8, -26.0,0.8, 0.26, 2.8, 1.3 and 2.5 MeV respectively. We use surface delta interaction of strength 0.85 for pp, nn and pn. Both the prolate and oblate HF energies and deformations are given in Table 1. Among all ,20XeTable 1. The intrinsic HF energy (E in MeV), deformations (/J) are given for the prolate and oblate solutions for Xe nuclei.A E (0 E ( 0prolate oblate118 -1746.3 .206 -1743.3 -.158120 -1778.1 .212 -1775.3 -.15122 -1803.3 209 -1802.2 -.169124 -1831.5 209 -1830.1 -.169126 -1859.5 .192 -1857.3 -.15PROLATE HF ORBITS OF l20XeK/lMeV MeV-11-- 1 2I 3- 149/2"7 /2*5/2*7 /2 "1/ 2 *5/2"5/2*3/2*3/2"1/ 2 "5 /2 ~ ”\- 15- 17- 184 * 3 /I t  \ _ . t^ 3 / 2 43/21/ 2 "I /2 1/ 2*3/2*' I / 2 ** 1617- 16 -20-23-2 4-im-9/2*N EU TR O N  11 M >  P R O TO N  1 1 M >Figure 1. Prolate HF orbits for protons and neutrons near the Fermi surface are shown for '“ Xe. Crosses indicate occupied orbits. M (same as* in text) is the magnetic quantum number.was found to be maximally deformed and is expected to have good band structures. Observations of excited oblate shapes are more probable for higher (A > 120) isotones. In the following we describe the band structure of l2®Xe, results for other Xe nuclei will be reported elsewhere.Shape and alignment effects in Xe nuclei 1633. Band structures in 120XeThe HF orbits (see Figure 1) for protons and neutrons show contrasting features, (i) Large gaps are seen around the Fermi surface of protons whereas for the neutrons the singleFigure 2a. The lowest energy states obtained by angular momentum projection from the K = T, 2 ' HF configurations are compared with experiment. The K  = r  and K = 2' bands have same intrinsic structure except the fact that the !zlin neutrons in K = 2" band are arranged in a kH = 1 rotation aligned (RAL) configuration. The T  state, of the K  = 1" band being lowest in energy, appears as the band head in the experiment. The low spin members of this band lie above T  and should be looked for in special experiments.particle levels are evenly spaced at the Fermi surface, (ii) The neutron Fermi surface is in the mid hj shell whereas the low m proton /i1 orbits lie about 2-3 MeV above the Fermi164 S P Pandya, C R Praharaj and A K Rathsurface. From our HF calculation, we find that all most all the states above the neutron Fermi surface are oblate in nature and hence neutron excitation will lead to reduction inFigure 2b. The staggering in the h lu2and g 1/2 proton alignment (/RAL) are shown for band 5 and 6 The /t1W2and gll2 alignment for the odd / branch is consistently larger than the even I states and hence the odd / sequence is energetically favoured. For band 6 the g lf2 alignment smoothly increases with angular momentum and hence no splitting is observed m this band.collectivity. In fact this is manifested in the observed [1] intensities (of the E2 transitions in the ground band) which decreases at the band crossing. The characterstics of all the observed bands are reproduced by angular momentum projection from relevant HF configurations, whose intrinsic structures are listed in Table 2. The agreement of the excitation energies (see Table 2), with experiment in some of the bands could be improvedTable 2. The intrinsic structures of protons and neutrons, deformations, (0), band heads and excitation energies (£* in MeV) of all the bands observed in ,20Xe are given Band 3 could not be identified uniquely.Band Experiment [1]Band E* headE* .TheoryBand pheadkP kn1 0+ 00 0.0 0+ .212 0* 0*2 2* 0.876 1.072 i + 211 -l/2+, 3/2+ 03 18+ 6.2064 8+ 2.63 2.47 1 + .19 -do- (l/2+)25 T 2.496 3 655 r .207 l/2~, l/2+6 5~ 2.073 1.416 3~ .208 l/2+, 5/2'by using modified Nilsson single particle energies f6] which has been used [3] in this region for better reproduction. We find band crossings due to the alignment oihw n  neutrons in theShape and alignment effects in Xe nuclei 165ground band, band 2 ,4  and 5 (see Table 2). In band 6 the odd neutron in /i I1/2 blocks the corresponding alignment and related band crossing is not observed. Band crossings arising due to h\ 1/2 proton alignment are not considered in the present calculation but nevertheless such crosssings can occur at high spins (> 20). However, we find that alignment o f protons m h\ 1/2 and g w  orbits lead to large signature splitting in band 5 (see Figure 2). The even /  sequence in this band has been pushed up in energy and has escaped detection. This could he due to weak inter-signature transitions.4. ConclusionsThe important conclusions drawn from our investigation are : (i) Among all the isotopes, l2()Xe has larger ground state deformation since the intruder neutron h\ ,/2 shell is just half filled. Our calculation reproduces the observed features o f the collective bands in 120Xe  quite well, (ii) In the particle rotor model it is essential to assume gamma deformation to explain the signature splitting in both the positive and negative parity bands in this region [5J, however in our model splitting for both parities comes out naturally with axial symmetry, ( iii)  Rotation alignment of g7/2 protons play an important role in understanding the band structures in this region, (iv ) Drastic change o f shape was not evident from our calculation though we find relative decrease in prolate collectivity at band crossing. Transition from collective rotational behaviour to single particle like behaviour at relatively low spins has been predicted in 122- ,24Xe [3,4]. However, shape changes at relatively high spins (> 30) could not be ruled out in 120Xe.References111 J Goswamy, N Singh et al Z  Phys A in press(2) S Juutinen et al Z  Phys A338 365 (1983); Nucl Phys A553 531c (1993)(3| J Simpsone ta lP h y s  Leu  B262 388 (1991)[4| W  Gaste t a l Z  P h ys.A318 123(1984)15] A Gelberg el a l Nucl Phys A5S7 439c (1993), D Lieberz et a l Phys U n  B282 7 (1992) N  Jing-Ye-Zhang e ta l  Phys. Rev. C39714 (1989)

Shape and Alignment Effects in Xe Nuclei

http://arxiv.iacs.res.in:8080/jspui/bitstream/10821/4825/1/Shape%20and%20Alignment%20Effects_By%20A%20K%20Rath.pdf

Shape and Alignment Effects in Xe Nuclei

Abstract

Similar works

Full text

Available Versions

IACS Institutional Repository