Inter-band B(E1) Strengths in Heavy Nuclei based on the Proxy-SU(3) Scheme

TL;DR

This paper introduces a method to calculate inter-band B(E1) transition strengths in heavy nuclei using the proxy-SU(3) scheme, simplifying the complex shell-model calculations for these electromagnetic properties.

Contribution

It develops an $SU(3)$ second quantization expansion of the $E1$ operator and applies it to compute $B(E1)$ strengths in $^{224}$Th within the proxy-SU(3) framework, advancing nuclear structure modeling.

Findings

Successfully calculated inter-band B(E1) strengths for $^{224}$Th.

Demonstrated the effectiveness of the proxy-SU(3) scheme in simplifying $E1$ transition calculations.

Provided insights into the electromagnetic properties of heavy deformed nuclei.

Abstract

Rotational bands of positive and negative parity are frequently found experimentally in heavy deformed even-even nuclei along with their corresponding $E2$ intra-band and $E1$ inter-band transitions. In $SU(3)$ symmetry-based models, calculating the $B(E2)$ strengths is relatively straightforward due to the relation between the $E2$ operator and the quadrupole generator of the algebra. However, calculating the $B(E1)$ strengths is a more difficult task, requiring computations involving the shell-model expansion of the dipole operator and multi-shell matrix elements. In this work the $E1$ operator is expanded in $SU(3)$ second quantization and applied to calculate the inter-band $B(E1)$ strengths of the isotope $^{224}$Th using the semi-microscopic algebraic quartet model (SAQM) based on the recently proposed proxy-$SU(3)$ scheme.