The dynamical influence of $\mathrm{\Lambda }$ hyperons on the excited-state properties of closed-shell multi-$\mathrm{\Lambda }$ 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 $\mathrm{\Lambda }$ 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 ${}_{50\mathrm{\Lambda }}{}^{258}\mathrm{Pb}$ hypernucleus, reaching $K_A=322$ MeV. Calculations in uniform hypernuclear matter confirm that this stiffening is a bulk effect driven by both the $N\mathrm{\Lambda }$ and $\mathrm{\Lambda }\mathrm{\Lambda }$ interactions. Analysis of the transition densities for states with maximal collective coherence indicates that the dynamical effect of $\mathrm{\Lambda }$ hyperons is predominantly in phase with the protons, especially in the case of the isovector $E1$ modes.

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• Hypernuclei & mesic nuclei
• Nuclear forces
• Nuclear matter
• Nuclear structure & decays
• Nucleon-nucleon interactions
• Hyperons
• Hartree-Fock methods
• Nuclear density functional theory
• Nuclear many-body theory
• Random phase approximation
• Shell model