Structure effects on the giant monopole resonance and determinations of the nuclear incompressibility

TL;DR

This paper investigates how nuclear structure influences the giant monopole resonance and refines the understanding of nuclear incompressibility, especially its dependence on isospin asymmetry, through experimental measurements and theoretical analysis.

Contribution

It provides new measurements of the ISGMR in molybdenum isotopes and clarifies the value of the asymmetry term $K_\tau$, resolving previous conflicting conclusions.

Findings

Molybdenum nuclei exhibit similar softness as tin and cadmium in ISGMR energies.

The study constrains the isospin dependence of nuclear incompressibility, finding $K_\tau$ around -510 MeV.

The measurements support a negative value for $K_\tau$, contradicting earlier positive estimates.

Abstract

Giant resonances are collective nuclear vibrations which provide a unique laboratory setting to probe the bulk properties of the nuclear force. One of the isoscalar compressional modes -- the isoscalar giant monopole resonance (ISGMR) -- is useful in constraining the equation of state (EoS) of nuclear matter. For example, the nuclear incompressibility, $K_\infty$, is a fundamental quantity in the EoS and is directly correlated with the energies of the ISGMR in finite nuclei. Previous work has shown that interactions with $K_\infty$ which reproduce the energies of the ISGMR in $^{208}$Pb and $^{90}$Zr well, overestimate those of the tin and cadmium nuclei. To further investigate where this "softness" appears in moving away from the doubly-closed nucleus $^{90}$Zr, and how this effect develops, the first portion of this thesis consists of measurements of the ISGMR in the molybdenum isotopes. Comparison of the ISGMR strengths with Random Phase Approximation calculations shows that these nuclei have ISGMR energies which are overestimated to a similar degree as seen in the tin and cadmium nuclei, while the strength of $^{208}$Pb is precisely reproduced. This suggests clearly that the molybdenum nuclei exhibit the same open-shell softness which has been documented previously. The ISGMR in isotopes encompassing a broad range of proton-neutron asymmetries constrains the dependence of the nuclear incompressibility on the isospin asymmetry, as quantified by the asymmetry term, $K_\tau$. To reconcile previously-published and highly concerning conclusions that $K_\tau = + 582$ MeV, the second portion of this thesis is focused upon independently studying this claim. A simultaneous measurement of the ISGMR in $^{40,42,44,48}$Ca has excluded the possibility of a positive value for $K_\tau$, and found consistency with previous data, placing $K_\tau$ at $-510 \pm 115$ MeV.