Monopole Excitation and Nuclear Compressibility: Present and Future Perspectives

TL;DR

This paper reviews the current understanding of isoscalar giant monopole resonances, their relation to nuclear incompressibility, and emphasizes the need for new experimental data to improve theoretical models and constrain the nuclear equation of state.

Contribution

It highlights the challenges in modeling monopole resonances across different nuclei and underscores the importance of new experiments to refine nuclear matter parameters.

Findings

Relativistic and non-relativistic models determine nuclear incompressibility with 10-20% accuracy.

Current models fail to accurately describe open-shell nuclei like tin and cadmium.

New experimental data across isotopic chains are crucial for better constraints.

Abstract

Isoscalar giant resonances are nuclear collective excitations associated with the oscillation in phase of protons and neutrons according to a certain multipolarity $L$. In particular, the isoscalar giant monopole resonance ($L=0$) is the strongest nuclear compression mode, and its excitation energy is directly related to the compression modulus for finite nuclei. Typically, microscopic calculations are utilized to establish a relationship between the experimental compression modulus and the nuclear incompressibility that is a crucial parameter of the equation of state for nuclear matter. The incompressibility of nuclear matter has been determined with an accuracy of 10 to 20\% using relativistic and non-relativistic microscopic models for describing the monopole distributions in ${}^{208}$Pb and ${}^{90}$Zr isotopes. However, the same theoretical models are not able to describe data for open-shell nuclei, such as those of tin and cadmium isotopes. In fact, only effective interactions with a softer nuclear-matter incompressibility are able to predict the centroid energy of monopole distributions for open-shell nuclei. An unified description of the monopole resonance in ${}^{208}$Pb and other open-shell nuclei remains unsolved from the theory side. Most of this uncertainty is due to our poor knowledge of the symmetry energy, which is another essential component of the equation of state of nuclear matter. Therefore, new experimental data along isotopic chains covering a wide range in $N/Z$ ratios, including neutron-deficient and neutron-rich nuclei, are of paramount importance for determining both the nuclear-matter incompressibility and the symmetry energy more precisely.