Experimental data on energy levels of the odd-odd deformed nucleus¹⁸⁰Re obtained from radioactive-decay and heavy-ion reaction studies are analysed to deduce spin-parity and configuration assignments for the six observed rotational bands based on the selection rules for fast beta transitions, criteria for the relative-energy ordering of the triplet and singlet bandheads, two-particle-plus-rotor model calculations including Coriolis mixing, rotational energy systematics involving staggering features, and considerations of gyromagnetic ratios, signature splittings and rotational band alignments.

A trace formula for the oscillating part of the level density for a spherical billiard has been obtained in spherical polar coordinates. The Jacobian of stability and the length of the orbits are obtained from the classical mechanics of the problem. The same formula is applicable to both the planar and the diametric orbits. Numerical results have been obtained with this formula and compared with the results from exact quantum theory, EBK quantization, and Balian and Bloch.

The deformed mean field of nuclei exhibits various geometrical and dynamical symmetries which manifest themselves as various types of rotational and decay patterns. Most of the symmetry operations considered so far have been defined for a situation wherein the angular momentum coincides with one of the principal axes and the principal axis cranking may be invoked. New possibilities arise with the observation of rotational features in weakly deformed nuclei and now interpreted as magnetic rotational bands. More than 120 MR bands have now been identified by filtering the existing data. We present a brief overview of these bands. The total angular momentum vector in such bands is tilted away from the principal axes. Such a situation gives rise to several new possibilities including breaking of chiral symmetry as discussed recently by Frauendorf. We present the outcome of such symmetries and their possible experimental verification. Some possible examples of chiral bands are presented.

We show for the first time that the generalized seniority scheme explains reasonably well the $B(E3)$ systematics for the $(0^{+} → 3^{−}_{1})$ transitions in the Sn isotopes, which are odd-tensor $E3$ transitions connecting different seniority states $(\Delta\upsilon = 2)$. Additionally, we also present large scale shell model (LSSM) calculations to support our interpretation. The generalized seniority scheme points to the octupole character of these 3− states in Sn isotopes.

We have recently shown that the general trends of partition-wise fission fragment mass distribution in heavy-ion-induced compound nuclear (CN) fission of heavy nuclei can be reproduced reasonably well by using theconcept of isospin conservation, hence providing a direct evidence of isospin conservation in neutron-rich systems [Jain et al, Nucl Data Sheets 120, 123 (2014); Garg and Jain, Phys. Scr. 92, 094001 (2017); Jain and Garg, EPJ Web of Conference 178, 05007 (2018); Garg et al, Phys. Scr. 93, 124008 (2018)]. In this paper, we test the concept of isospin conservation to reproduce the fission fragment mass distribution emerging from thermal neutron-inducedCN fission reaction, $^{245}\rm{Cm}(n_{th}, f)$. As earlier, we use Kelson’s conjectures [I Kelson, Proceedings of the Conference on Nuclear Isospin (Academic Press, New York, 1969)] to assign isospin to neutron-rich fragments emitted in fission, which suggest the formation of fission fragments in isobaric analogue states. We calculate the relative yields of neutron-rich fragments using the concept of isospin conservation and basic isospin algebra. The calculated resultsreproduce the experimentally known partition-wise mass distributions quite well. This highlights the usefulness of isospin as an approximately good quantum number in neutron-rich nuclei. This also allows us to predict the fragment distribution of the most symmetric Cd–Cd partition and the heavier mass fragment distributions, both not measured so far.