# Microscopic study of K-Selection Rule Violation in $^{182}$W K=10$^+$ Isomer Decay

## TL;DR

This paper investigates the microscopic mechanisms behind the delayed decay of K-isomers in $^{182}$W, using angular momentum projection and deformed Hartree-Fock calculations, revealing the absence of a K selection rule and explaining experimental retardation.

## Contribution

The study introduces a microscopic model that explains K-isomer decay without relying on a K selection rule, contrasting with traditional rotational models.

## Key findings

- Decay is retarded due to poor overlap between K bands.
- K-mixing is negligible, K quantum numbers are well conserved.
- Transitions are finite but delayed, aligning with experimental observations.

## Abstract

In this paper we study the microscopic mechanism for the retarded decay of K-isomers to lower K bands. We do angular momentum projection from suitable intrinsic states. The retardation arises from poor overlap between the low K and high K bands in the integral over Euler angles. Deformed HF and angular momentum projection calculations are done for the decay of the $K=10^+$ isomer band to the ground band of $^{182}W$. K-mixing is unimportant and the K quantum numbers of the bands are quite good. There is significant difference in the reduced matrix elements of transition operators in our formalism and that in the rotational model. Angular momentum projection gives J-selection rule but there is no K selection rule for reduced matrix elements of electromagnetic multipole operators. Thus, E2 and M1 transitions from the K isomer to the ground band of $^{182}W$ are finite but retarded in angular momentum projection theory, as in experiments. This provides a theoretical basis for the study of K-isomers and their decay modes. Quantitative results are presented. The microscopic model gives J-selection rule and angular momentum conservation for combined matter and radiation systems.