Collective excitations of $\Lambda$ hypernuclei

TL;DR

This paper investigates low-lying collective excitations in $ ext{Lambda}$ hypernuclei using self-consistent mean-field methods, revealing deformation changes, rotational behavior, and a novel soft dipole mode involving $ ext{Lambda}$ particles.

Contribution

It introduces a comprehensive analysis of deformation, rotational excitations, and a new soft dipole $ ext{Lambda}$ mode in hypernuclei using advanced theoretical approaches.

Findings

Oblate deformation in $^{28}$Si may vanish with a $ ext{Lambda}$ particle.

Addition of $ ext{Lambda}$ reduces deformation and $B(E2)$ transition probability in $^{25}_{ ext{Lambda}}$Mg.

A new soft dipole $ ext{Lambda}$ mode oscillation is identified.

Abstract

We discuss low-lying collective excitations of $\Lambda$ hypernuclei using the self-consistent mean-field approaches. We first discuss the deformation properties of $\Lambda$ hypernuclei in the $sd$-shell region. Based on the relativistic mean-field (RMF) approach, we show that the oblate deformation for $^{28}$Si nucleus may disappear when a $\Lambda$ particle is added to this nucleus. We then discuss the rotational excitations of $^{25}_{\Lambda}$Mg nucleus using the three-dimensional potential energy surface in the deformation plane obtained with the Skyrme-Hartree-Fock method. The deformation of $^{25}_{\Lambda}$Mg nucleus is predicted to be slightly reduced due to an addition of $\Lambda$ particle. We demonstrate that this leads to a reduction of electromagnetic transition probability, $B(E2)$, in the ground state rotational band. We also present an application of random phase approximation (RPA) to hypernuclei, and show that a new dipole mode, which we call a soft dipole $\Lambda$ mode, appears in hypernuclei, which can be interpreted as an oscillation of $\Lambda$ particle against the core nucleus.