Effect of Octupole correlations on Fission of Light Nuclei

TL;DR

This paper investigates how octupole correlations influence the fission fragment mass asymmetry in light nuclei, focusing on shell effects at N=56 and Z=34 through systematic Hartree-Fock calculations.

Contribution

It provides a systematic analysis of shell effects on fission asymmetry in light nuclei, highlighting the dominant role of N=56 in this process.

Findings

N=56 shell effects determine fission asymmetry in the studied nuclei.

Deformed shell effects at Z=34 are less influential.

Systematic Hartree-Fock calculations support the dominance of N=56 in asymmetry.

Abstract

Fission of $^{180}$Hg produces mass asymmetric fragments which are expected to be influenced by deformed shell-effects at N=56 in the heavy fragment and Z=34 in the light fragment [G. Scamps and C. Simenel, arXiv:1904.01275 (2019)]. To investigate both shell-effects and to determine which one has the main influence on the asymmetry in the region of the $^{180}$Hg, we produce a systematic of Constraint-Hartree-Fock calculations in nuclei with similar N/Z ratio than the $^{178}$Pt. It is found that N=56 determines the asymmetry of systems in this region of the nuclear chart.

Equations

$$Q_{20}$$

$$Q_{30}$$

Full text

I Introduction

The configuration at scission is expected to strongly influence the symmetric or asymmetric nature of fission Wil74 . Indeed, the shell structure of the fragments can play an important role in stabilizing the number of neutrons and protons in each fragment. Spherical magic numbers sometimes play a role as in 258Fm Hul86 . However, due to strong Coulomb interaction, and the presence of a neck between the fragments in which strong interaction between the fragments is still present, both pre-fragments are deformed with a strong quadrupole shape or a strong octupole deformation. As a result, deformed shell effects are expected to dominate Sca18 ; Sca19 .

Experimental data on the fission of actinides show that the heavy fragment is centered in Z = 54 Uni74 ; Sch00 ; Boc08 for a large number of actinides. This empirical result has been explained by the role of the octupole deformation in Ref. Sca18 . Indeed the region around the 144Ba is expected to have strong octupole deformation Lea85 ; Buc16 ; Buc17 . This octupole deformation is associated with shell gaps with Z = 52, Z = 56, N = 84 and N = 88.

To test the universality of the effect of octupole shell structure on the asymmetry of fission, neutron-rich mercury isotopes have been studied with a similar approach Sca19 . The 180Hg case is particular since it was expected to fission symmetrically leading to two 90Zr which is a magic nuclei with N = 50. However, experience reveals that 180Hg fissions asymmetrically leading to fragments around 80Kr and 100Ru And10 . The deformed shell effects associated to this fission mode are predicted to be at N = 56 and Z = 34 which are the numbers associated to octupole shell effect due to the repulsion of states with $\Delta$j = $\Delta$l = 3 But16 . Nevertheless, the light fragment is found to be strongly elongated. Then the Z = 34 gap is due to a more complex deformation Sca19 .

The goal of the present manuscript is to determine which of the N = 56 and Z = 34 shell-effects is the strongest by varying the fissioning system mass while the N/Z ratio is preserved.

II Constrained-Hartree-Fock calculation

The calculations are done using a version of the ev8 code Bon05 modified in order to have only one plane of symmetry. The self-consistent Constrained-Hartree-Fock equations augmented by the BCS pairing (CHF+BCS) are solved with a constraint on the quadrupole and octupole moment defined respectively as

[TABLE]

The interaction used is the Sly4d Kim97 Skyrme functional with a surface type of pairing with interaction strength $V_{0}^{nn}$ = 1256 MeV$\cdot$fm3 and $V_{0}^{pp}$ = 1462 MeV$\cdot$fm3 Sca13a . To determine the fission valleys the following procedure has been used. First, a calculation is performed with a constraint on $Q_{20}$ = 47.3 b and different values of the $Q_{30}$ moment. Then, the octupole constraint is released and the value of $Q_{20}$ are changed gradually to explore the valley in both directions. The calculation is done until $Q_{20}$ = 0 and until the system scissions respectively when $Q_{20}$ is decreased and increased.

III Results

To investigate the strength of the deformed shell effects, we determine the asymmetric fission path of the systems that have similar initial N/Z ratio to the 178Pt (1.25 $\leq N/Z\leq$ 1.3). The value of the average number of protons and neutrons just before scission is shown in Fig. 1. We see that up to A = 186, all heavy fragments have N $\simeq$ 56, while $Z_{L}$ varies and show no particular stabilisation at Z $\simeq$ 34, indicating a dominance of the shell gap N = 56 over Z = 34.

Note that in the case of the 188Pb, 192Po and 196Rn the potential energy surface as a function of asymmetry is essentially flat. This is due to the presence of different shell-gap that arise at different asymmetries. For example in 196Rn the N = 56 shell-gap favor the symmetric fission while the Z = 34 and the Z = 44 favor two different asymmetric valleys. As a consequence, the shell effect does not fix strongly a particular value for the asymmetry at the scission in the 3 nuclei.

We show in Fig. 2 the potential energy curves for three of those systems. The 178Pt is the system for which the gap between the symmetric and asymmetric energy around scission ($Q_{20}\simeq$ 90 b) is the most important (about 5 MeV). It benefits from the shell-gaps at Z = 34 and N = 56 that reduce the energy of the asymmetric mode. For the 170W, this difference is only $\sim$2.5 MeV, which could be due to the fact that the $N_{H}$ $\simeq$ 54 and $Z_{L}$ $\simeq$ 32.5 values deviate slightly from 56 and 34. Nevertheless, asymmetric fission is still predicted to dominate in this system. The case of 196Rn is interesting because the symmetric path becomes more energetically favorable than the asymmetric one. The asymmetric mode has $N_{H}\simeq$  60 and $Z_{L}\simeq$ 38.5 values that deviate significantly from 56 and 34. The symmetric path, however, produces fragments with N $\simeq$ 55 which is close to N = 56. Compact octupole deformed shell effects are then expected to favour symmetric fission in this nucleus.

Summary

CHF+BCS calculations have been performed to determine the main fission asymmety valley in the 180Hg region. We conclude that, with the sly4d functional and our choice of pairing interaction, the N = 56 is stronger to fix the asymmetry than the Z = 34.