The $B(E2)$ anomaly: Evidence for a low-lying mixed-symmetry collective excitation mode

TL;DR

This paper investigates the anomalously low $B(E2)$ ratios in certain nuclei, proposing that a low-lying mixed-symmetry collective mode explains the phenomenon, which standard models fail to reproduce.

Contribution

It introduces an extended IBM Hamiltonian and benchmarks it against shell model calculations to explain the $B(E2)$ anomaly as a mixed-symmetry collective excitation.

Findings

The $B(E2)$ anomaly is linked to a low-lying mixed-symmetry mode.

Standard models do not reproduce the observed $B_{4/2}$ ratios.

The extended IBM captures the anomaly by incorporating collective and single-particle dynamics.

Abstract

Exceptionally low values of the ratio of electric quadrupole transition rates, $B_{4/2}\equiv B(E2;4^+_1\rightarrow2^+_1)/B(E2;2^+_1\rightarrow0^+_{\mathrm{gs}})<1$, have been observed in neutron-deficient nuclei near $N\approx94$ (W, Os, Pt) and $N\approx62$ (Te, Xe) with few and comparable numbers of valence nucleons outside closed shells. Remarkably, the suppressed $B_{4/2}$ ratios coincide with low-lying energy level patterns characteristic of collective motion. Standard approaches, including large-scale shell model, collective models, and density functional theory, fail to reproduce this behavior, commonly referred to as the $B{4/2}$ (or $B(E2)$) anomaly. Recent work has reproduced the effect in selected Pt and Os isotopes via mapping a triaxial rotor Hamiltonian onto the interacting boson model (IBM), attributing it to triaxial rotational motion. However, this interpretation is unexpected as collectivity typically emerges first through vibrational modes with increasing valence nucleon number along isotopic chains. Here, we address this discrepancy using an extended IBM Hamiltonian across nuclei exhibiting the anomaly, benchmarked against large-scale shell model calculations, and propose that the $B(E2)$ anomaly arises from a low-lying mixed-symmetry collective mode that bridges single-particle and collective dynamics.