The Effects of Multi-$\Lambda$ Hyperons on Collective Modes in Nuclei

TL;DR

This study investigates how multiple $\Lambda$ hyperons influence collective excitation modes in various hypernuclei, revealing systematic energy shifts and increased nuclear incompressibility with more hyperons using advanced theoretical models.

Contribution

It provides the first systematic analysis of the impact of multi-$\Lambda$ hyperons on collective nuclear modes and incompressibility using self-consistent Hartree-Fock + RPA calculations.

Findings

Energy of collective modes shifts upward with more hyperons.

Nuclear incompressibility $K_A$ increases with hyperon number.

Dynamical effects of hyperons are mainly in phase with protons.

Abstract

The dynamical influence of $\Lambda$ hyperons on the excited-state properties of closed-shell multi-$\Lambda$ Ca, Ni, Sn and Pb hypernuclei is investigated using the self-consistent Hartree-Fock + Random Phase Approximation in coordinate space. The strength distributions for the isoscalar monopole, isovector dipole, and isoscalar quadrupole modes are calculated, revealing a systematic upward energy shift with increasing $\Lambda$ hyperon number $-S$. The scaling behavior of the computed centroid energies $\sqrt{m_1/m_{-1}}$ with respect to both the mass and hyperon number is determined. The nuclear incompressibility modulus $K_A$ is found to increase monotonically with $-S$. The largest value is found in the $^{258}_{50\Lambda}$Pb hypernucleus, reaching $K_A = 322 $ MeV. Calculations in uniform hypernuclear matter confirm that this stiffening is a bulk effect driven by both the $N\Lambda$ and $\Lambda\Lambda$ interactions. Analysis of the transition densities for states with maximal collective coherence indicates that the dynamical effect of $\Lambda$ hyperons is predominantly in phase with the protons, especially in the case of the isovector E1 modes.