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

Bahruz Suleymanli, Kutsal Bozkurt, Elias Khan, Haşim Güven, Jerome Margueron

Abstract

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

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

Abstract

The dynamical influence of hyperons on the excited-state properties of closed-shell multi- 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 hyperon number . The scaling behavior of the computed centroid energies with respect to both the mass and hyperon number is determined. The nuclear incompressibility modulus is found to increase monotonically with . The largest value is found in the Pb hypernucleus, reaching MeV. Calculations in uniform hypernuclear matter confirm that this stiffening is a bulk effect driven by both the and interactions. Analysis of the transition densities for states with maximal collective coherence indicates that the dynamical effect of hyperons is predominantly in phase with the protons, especially in the case of the isovector E1 modes.
Paper Structure (13 sections, 22 equations, 11 figures)

This paper contains 13 sections, 22 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Hartree-Fock-Random Phase Approximation approach for multi-$\Lambda$ hypernuclei
  3. Formalism
  4. Numerical details
  5. Results
  6. The Isoscalar Monopole Response in Multi-$\Lambda$ Hypernuclei
  7. The Isovector Dipole Response in Multi-$\Lambda$ Hypernuclei
  8. The Isoscalar Quadrupole Response in Multi-$\Lambda$ Hypernuclei
  9. Giant Resonance Energies
  10. Nuclear Incompressibility
  11. Hypernuclear matter at nuclear saturation density
  12. Transition densities
  13. Conclusions

Figures (11)

  • Figure 1: Isoscalar monopole strength distributions for multi-$\Lambda$ hypernuclei $^{48-S}_{-S\Lambda}$Ca,$^{48-S}_ {-S\Lambda}$Ni, $^{48-S}_{-S\Lambda}$Sn, and $^{48-S}_{-S\Lambda}$Pb calculated within the HFRPA approach.
  • Figure 2: Low-energy segment ($0$–$12$ MeV) of the isoscalar monopole strength distributions for the same nuclei and $\Lambda$ configurations as in Fig. \ref{['fig:monopole_full']}. The insets display the corresponding high-energy segment ($25$–$30$ MeV).
  • Figure 3: Isovector dipole strength distributions for multi-$\Lambda$ hypernuclei $^{48-S}_{-S\Lambda}$Ca, $^{48-S}_{-S\Lambda}$Ni, $^{48-S}_{-S\Lambda}$Sn, and $^{48-S}_{-S\Lambda}$Pb calculated within the HFRPA approach.
  • Figure 4: Low-energy segment ($0$–$12$ MeV) of the isovector dipole strength distributions for the same nuclei and $\Lambda$ configurations as in Fig. \ref{['fig:dipole_full']}. The insets display the corresponding high-energy segment ($25$–$30$ MeV).
  • Figure 5: Isoscalar quadrupole strength distributions for multi-$\Lambda$ hypernuclei $^{48-S}_{-S\Lambda}$Ca, $^{48-S}_{-S\Lambda}$Ni, $^{48-S}_{-S\Lambda}$Sn, and $^{48-S}_{-S\Lambda}$Pb calculated within the HFRPA approach.
  • ...and 6 more figures