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

TL;DR

The paper addresses the $B_{4/2}$ anomaly, where the ratio $B_{4/2}$ dips below unity in two neutron-deficient regions around $N\approx 94$ (W-Os-Pt) and $N\approx 62$ (Te-Xe). It develops an extended interacting boson model (IBM) including mixed-symmetry neutron–proton modes and higher-order SU(3) terms, and compares predictions with large-scale shell-model calculations. The main finding is that a low-lying mixed-symmetry collective mode can reproduce both the energy systematics and the anomalous $B_{4/2}$ values, providing a bridge between single-particle and collective dynamics, while LSSM reproduces spectra but not the anomaly. This suggests a general mechanism for emergent collectivity and motivates cross-model validation with LSSM, PSM, and beyond-mean-field approaches.

Abstract

Several instances of exceptionally low values of the ratio $\frac{B(E2; 4^+_1\rightarrow 2^+_1)}{B(E2; 2^+_1\rightarrow 0^+_{\mathrm{gs}})}$ (''$B_{4/2}$'') < 1 have been observed in two neutron deficient regions of the nuclear chart: tungsten, osmium, platinum isotopes with neutron numbers around $N=94$ and tellurium, xenon isotopes with neutron numbers around $N=62$. The striking feature of these observations is that they coincide with low-lying energy level structures that are consistent with what is normally characterized as collective motion of the nucleus. Standard nuclear structure model calculations including large-scale shell model, collective model and density functional theory calculations fail to reproduce the effect. %In the heavier group of nuclides these cases initiate a smooth evolution of increasing $B_{4/2}$ values as a function of increasing neutron number, reminiscent of a phase transition from the ``anomalous" regime to fully developed collective excitations with ''normal'' $B_{4/2}$ values whereas in the Te-Xe region only a limited number of cases with $B_{4/2} < 1$ have been observed so far. Recent theoretical work has, however, successfully reproduced the ''anomalous'' $B_{4/2}$ phenomenon in some of the platinum and osmium isotopes by mapping a triaxial rotor Hamiltonian onto the interacting boson model (IBM), thereby extending the model's SU(3) degrees of freedom. The extended IBM Hamiltonian encompasses quadrupole vibrations, rotations as well as mixed-symmetry neutron-proton modes. We here successfully apply an extended IBM Hamiltonian to nuclei in both mass regions, which notably are characterized by similar boson numbers in the IBM. The results point to the emergence of a low-lying mixed-symmetry collective excitation mode, representing an additional form of nuclear collectivity that effectively bridges single-particle and collective behaviors.

Figures (2)

• Figure 1: (Color online) Experimental excitation energy ratios, $R_{4/2}$, and ratios of reduced E2 transitions rates, $B_{4/2}$, (when available) for tungsten, osmium, and platinum isotopes with neutron numbers $88 \leq N \leq 106$ (bottom), as a function of the number of valence neutron pairs, $N_\nu$. The experimental data are taken from Refs. zhang2021zanon2024milanovic2025grahn2016saygi2017cederwall2018goasduff2019, and nudat. The theoretical IBM predictions are from Refs. zhang2022zhang2024teng2025pan2024. Some data points have been somewhat displaced horizontally for clarity.
• Figure 2: (Color online) Experimental and calculated excitation energy ratios ($R_{4/2}=E_{4^{+}_1}/E_{2^{+}_1}$ and B(E2:$4^+_1\rightarrow 2^+_{1}$)/B(E2:$2^+_1\rightarrow 0^+_{gs}$) ratios for tellurium and xenon isotopes with neutron number $57 \leq N \leq 64$ as a function of the number of valence neutron pairs, $N_\nu$. The experimental data are taken from Refs. deangelis2002juradophdsiciliano2020doncel2017, and from nudat. The theoretical IBM and LSSM calculations are from this work, see text for details.