EI-Mallah, E A

Keshk, Y H

Salem, S A

IACS Institutional Repository

Indian J. Phys. 73A (2), 2 5 3 -2 5 9  (1999) NOTEU P  Aan international journalOctupole transitions in Ip shell nucleiS A Salem, E A EI-Mallah and Y H KeshkDepartment of Physics, Uriversity of Alexandria. Alcxandrii. i^gypt andM  HusseinDepartment of Physics, University of Zagazig, Zaga/ig, Hgypi Received 12 November 1997, an epted 10 Au^ u^ t 199SAbstract Significant differences aie ohserved in the tornpan.son of LleLtrv>n skalleiingdata from the octupole transitions in ^ a n d  ^ '^() with ilic re.sulis of a large basis shell model calculations A good de.scnpiion of the octupole data is obtained for the longitudinal fromfactors in  ^ and when (.oniriburjons from collectne siait' are allowed in the shell model transition density. The amplitude of this admixture is nleiitjeai in the three nucleiKeywords : Nuclear structure, sliell model, electron scrdteringPACS Nos. : 21.60 Cs, 27 20.+n15k 16,A detailed test of Uie radial shape of nucicur excited stale wave luneiions is provided by inelastic electron scattering (c, e ')  form lactors. The (c, e ')  lorni laetor is a l\)imer* Bessel transform of the transition density which may \ x  then compared to a nuclear model prediction. The shell model has been reasonably succcs.siul in explaining a huge body o< data in l/?-sheIl nuclei and in this Idler wc examine radial octupole iransition den.sities predicted by the shell model lor and Octupole uansiiions ate pariiculailyinteresting for nuclei in upper half of the lp>shell since such transitions me expected to have, within the approximation of a IffO) shell model, a unique radiai shape of V i / 2,3/2 “ 1 ^ 5/ 2,3/2 transitions. I he use ol a .V/w model space [11 gives little modilications to the shape of the octupole transitions. Saxon-Woods wave functions do not change tiic ^-dependence in any significant way and the use of Harmonic-Oscillator (110) wave functions, to define the radial shape of basis states, is justif ied.For a stringent test of tlie wave functions, it is necessary to define (c, e ')  form factors over as large a ^-rangc as possible. The experimental data used here me from Ref. [2] for Ref. [3] for and Ref, [41 for©  199^ IA(\S254 S A Salem. E A EhMallah. Y H Keshk and M HusseinFigure 1. The longiludinal form factors for the octupole transiUons in andExperimental values are indicated by solid circles; Ok:. and data arc from Refs. [2-4]. Solid curvc.s are the predictions of ifie shell model with no effective charges. The dashed curve.s are tliosc with Se chosen to repro<luce the maximum of the experimenul form factor^ see Table 1.Octupole transitions in Ip shell nuclei 255W e com pare the longitudinal octupole transitions in '*N and '®0 with shell model predictions o f M illener in F igure 1. Tw o observations are obvious from  this comparison : the shell m odel form factors do not have the correct ^-dependence, tending to be too broad relative to the experimental data and the longitucttnal form factors obtained in the shell m odel calculations are too small com pared with the experim ental data. This is particularly true for the so called collective transitions. Conventionally, the discrepancy between the experimental and theoretical form factcvs is explailied by the inu-oduction o f an additive effective charge defined a s :e = €i +Se,where e, is the charge o f the free nucleon (Cp = 1, e„ = 0) and Se is the effective charge. Some flexibility in the choice o f different values o f Se for the neutron and the proton has been found to provide a better description o f the experim ental data. This approach was investigated by Brown et al [5] for nuclei near '* 0  and they found effective charges for the neutron Se„ -  0 .34 and for proton SCp = 0.0. For octupole transitions, it has been found that the 5e„ is bigger than the Scp, explained the experimental data very well [5,6]. M illener [9] has suggested that the octupole transitions in can be explained by 6e„ -  0.385, Sep «0.095. In fact, the effective charge needed to reproduce the strength at the m aximum o f  the form factors varies from  0.1 for the 5 /2*  to 2 .2 . for 5 / 2 j  in with other transitions requiring interm ediate values. The effective charge values are presented in Table 1. In Figure 1, the solid curves represent the shell model predictions with no effective charges, while the dashed curves are those with effective charges. It should be hoted that the predicted C3 form factors with the effective charges chosen to reproduce the m aximum o f the experim ental form factor can also be obtained by choosing different values o f the eff ective charges for protons and neutrons.Table 1. Collective state mijung parameters.Transitions Excitation energy (McV)Se a'2c. 3- 9.64 0.24 0.03110.002'*0.3- 6.13 0.‘16 0.032 ± 0.002'*N. 5/2* 5.27 0.1 0.00410.0004*5n . 5/2* 7.15 2.2 0.00610.0006'*N. 1/2* 7.57 0.21 0.01310.001>*N. 5/2* 9.15 1.2 a 006 1  0.0006£  = 0.029 ± 0.002The m ajor inadequacy  o f  the shell m odel is the neg lec t o f  m ixing w ith configurations outside the restricted m odel space. However, significant extension of the 73A (2)-n256 5 A Salem, E A El-Mallah, Y H Keshk and M Husseinshell m odel basis requires knowledge o f m any more two-body interaction m atrix elem ents and even if  these w ere know n, the size o f  such a  calculation w ould  rapidly becom e prohibitive. Although the shell model description o f the C3 transitions is not consistentlyFigure 2. Possible C3 form factors calculated from different configurations» in the upper curves. In the lower curves, comparison between data and theory for the 7,57 MeV level. The curves are predictions of the shell model mixed with the configurations shown above as defined in eq. 1.Octupole transitions in Ip shell nuclei 257good in term s o f  the predicted strength, from the com parison, it w ould appear that the model w ave function is missing only a  small contribution from configurations not included in the  shell m odel space.It is possible to utilize th e  experimental data to obtain soine feeling for the reasons o f this contribution by writing the physical transition density as fo llow s;Ptr<'’> = PsM('')+aPadd('‘)- (1)Here, a  is an adjustable param eter and p^a^r) is the contfibution from configurations which are outside o f the space considered by the shell model. Such conHgurations will in general, be expected to have a ^-dependence which is different from that o f the shell model form factors. W ith this model space, it was possible to give a  reasonable description o f the octupole transitions [8]. However, the shapes o f these configurations are displayed in figure 2. with com parison betw een data and theory for the 7.57 M eV level, as an example.An alternative choice for pujuC'') ^  fbat o f a collective vibrational state, how ever, can provide an overall satisfactory agreem ent for all six states w ith very significant improvements in both the shape and strength o f the predicted form factors. This procedure has som e theoretical [10,11] and experim ental [12,13] justiflca tion  even though the application to explain octupole transition data in this way has not been attem pted so far. However, the existence o f  low -lying octupole collective states is well established and considerable evidence for the existence o f a  giant octupole resonance (G O R) at an excitation energy o f -llO /A ^'^^ MeV [14] has accumulated in recent years.The radial shape o f the collective state to be used in eq. (1) was chosen asPadd('-) = A'rp;..(r), (2)where N  is adjusted to give the strength required by the sum rule [10] and p ' . ,  ( r )  is the radial derivative o f the ground state charge distribution o f the nucleus which was obtained fr(»n [15] in terms o f a Fourier-Bessel s a le sp j . f ( f ) == 0, r ^ R , .The values o f q/fic gives the p -th  zero o f the spherical Bessel fu nc tion : -  0, whereRc — 1 fm, is the cu t-o ff radius and are the Fourier-Bessel coefficients [15]. The description o f  In eq. (2) was then used in eq. (1) and a w a s  treated as an adjustable param eter for each transititm studied. In P sm(0 .  no effective charges were used. The results are presented in Table 1, and Figure 3. The admixture is always such that the strength o f the transition is enhanced. Considerable im provem ent in the ^-dependence o f all the studied transitions is observed for values o f  or which are needed to reproduce the experim entally observed form factor maxima.258 S A Salem, E A El-MaUah. Y H Keshk and M HusseinFifurt'3. The experimenta] form factors as in Figure 1. The solid curves are the predictions of the model defined in eqs. 1 and 2. The values of a  are listed in Table 1. The dashed curves show the sensitivity of the admixture a.AcknowledgmentsWe are indebted to Dr. John Millener for providing us with shell model calculations presented here.References[1] D J Millener and D Kurath Nucl. Phys. A255 315 (1975)[2] H Crannel Phys. Rev. 148 1107 (19$6)[3] S A Salem PhD Thesis (Glasgow University) (1988)[4] T N Buti PhD Thesis (MIT) (1984)[5] B A Brown et al. NUcl. Phys. M i l  77 (1977)[6] C L BUlie et al, Phys. Rev. C30 1989 (1984)[7] S C i^akravarti etal, Phys. Rev. C35 2197 (1987)[8] S Salem (to be published)[9] D J Millener (private communication)[10] Bohr and Mottelson Nuclear Structure V d. 2 (New York : Benjamin) (1975)[11] T Suzuki Phys. Rev. C8 2111 (1973)[12] R H Bassel etal J. Phys. G8 1215 (1982)[13] M W S Macauley et d. J. Phys. G2 751 (1976)[14] T Carey et d, Phys. Lett. 45 239 (1980)[15] J W deVnes et al, Phys. Lett. B205 22 (1988)Octupole transitions in Ip shell nuclei 259

OctupoleTransitions in 1p Shell Nuclei

http://arxiv.iacs.res.in:8080/jspui/bitstream/10821/5585/1/Octupole%20Transitions%20in%201P%20Shell%20Nuclei_S%20A%20Salem.pdf

OctupoleTransitions in 1p Shell Nuclei

Abstract

Similar works

Full text

Available Versions

IACS Institutional Repository