Sizes and shapes of very heavy nuclei in high-K states

TL;DR

This study investigates the shapes and sizes of high-K nuclear states in nobelium and rutherfordium isotopes using a microscopic-macroscopic model, providing insights into their deformations and potential experimental measurements.

Contribution

It introduces a detailed microscopic-macroscopic approach to analyze high-K states, including shape calculations and comparison with experimental data, highlighting the role of higher-order deformations.

Findings

Differences in quadrupole moments and charge radii between high-K and ground states.

Identification of promising high-K isomer candidates based on excitation energies.

Emphasis on the importance of quadrupole and hexadecapole deformations.

Abstract

We have investigated shapes and sizes of selected two- and four-quasiparticle \mbox{high-$K$} states in nobelium and rutherfordium isotopes within the microscopic-macroscopic model with the deformed Woods-Saxon potential. Excited nuclear configurations were obtained by blocking single-particle states lying close to the Fermi level. Their energies and deformations were found by the four-dimensional energy minimization over shape variables. We have selected the most promising candidates for \mbox{$K$-isomers} by analyzing the isotopic dependence of excitation energies, and compared our results to available experimental data. We calculated differences in quadrupole moments and charge radii between nuclei in their \mbox{high-$K$} and ground states and found their quite different pattern for four-quasiparticle states in neighboring No and Rf isotopes. The leading role of the quadrupole and hexadecapole deformations as well as the importance of higher rank symmetries are also discussed. The current development of laser techniques and the resulting ability to measure discussed effects in the near future is the motivation of our study.