Neutron Separation Energy and Emission Probability at High Spins

Abstract

A new formula for the neutron separation energy at high nuclear excitations and nuclear spin is derived. The statistical theory of the superfluid nucleus is used to obtain the neutron emission probability at high spins >50h. The results obtained here agree very well with the recent experimental data of Henss et al for ^lEr. The nature and consequences of the structural transitions for the isotones TV = 88 have been investigated comprehensively. A shape transition from prolate to oblate at 7 -47 h is predicted for l i$Er.PACS numbers: 21.10. Ma, 27.70.+q Recently, l single-neutron emission probabilities at high spins and high excitation energies have been investigated by an unambiguous experimental technique where it has been possible to ensure that the neutron emission is from the compound nucleus formed in the reaction 92 Zr( 64 Ni, In) I55 Er and not due to preequilibrated emission. In Ref. 1, the extrapolation of the rotational spectra of l iiEv (available up to S5h/2) to higher spins and the assumption that the single-particle level-density parameter a and the neutron separation energy S n are independent of / are found to be unjustifiable. Further, no explanation is given in Ref. 1 for the choice of the highspin state 52ft for their study. A more rigorous theoretical approach to the problem is necessary.In our approach, we use the statistical theory of the nucleus incorporating the deformation degrees of freedom, pairing correlation, and collective rotation of the system to derive a new formula to obtain the separation energy 2 " 4 of nucleons and hence the neutron emission probability from such highly excited compound systems in a very high angular momentum state. The results obtained here agree very well with the experimental data ] and also corroborate the experimental prediction that the neutrons emitted are from the compound system 1 HET, rather than from a preequilibration mechanism. The formulations presented here explain why in the reaction 92 Zr( 64 Ni,l«) l55 Er, the rotational state 52ft is conducive for the study of neutron emission. It is shown that the separation energy of neutrons in the rotational state / > 50ft is approximately 2 to 3 MeV less than the value for 7<45ft. This decrease in S n increases the neutron emission probability to a very large extent for spins I > 50ft. A shape transition from prolate to oblate occurs at 1 -41ft for an excitation energy E* -50 MeV. This seems to be a feature of TV = 88 systems, since similar structural changes have been reported by Cranmer et al. 5 for ! 68Dy» which is also a iV = 88 system. Since TV = 88 isotones lie between TV = 86 isotones, which have a spherical ground state with rotational states built up by nucleon alignments near the Fermi energy, and TV = 90 isotones, which have a prolate ground-state configuration with high spins developed by collective rotation and nucleon alignments, they are subjected to shape changes as the spin of the system increases beyond 30ft. 6 " 9 We start with the partition function Q(a,p,y) of the deformed nucle...

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