Probing nuclear forces beyond the nuclear drip line: The cases of $^{16}$F and $^{15}$F

TL;DR

This study combines experimental and theoretical approaches to investigate the properties of unbound proton-rich nuclei $^{16}$F and $^{15}$F, revealing modifications in nucleon-nucleon interactions and mirror symmetry breaking.

Contribution

It provides new experimental data and theoretical analysis on the nuclear forces and mirror symmetry breaking in unbound nuclei beyond the nuclear drip line.

Findings

Strong asymmetry observed between mirror nuclei $^{16}$F-$^{16}$N and $^{15}$F-$^{15}$C.

Significant modification of nucleon-nucleon effective interaction involving loosely bound protons.

Mirror symmetry of the neutron-proton interaction is preserved after corrections, but differences in proton-proton versus neutron-neutron interactions are measured.

Abstract

The unbound proton-rich nuclei $^{16}$F and $^{15}$F are investigated experimentally and theoretically. Several experiments using the resonant elastic scattering method were performed at GANIL with radioactive beams to determine the properties of the low lying states of these nuclei. Strong asymmetry between $^{16}$F-$^{16}$N and $^{15}$F-$^{15}$C mirror nuclei is observed. The strength of the $nucleon-nucleon$ effective interaction involving the loosely bound proton in the $s_{1/2}$ orbit is significantly modified with respect to their mirror nuclei $^{16}$N and $^{15}$C. The reduction of the effective interaction is estimated by calculating the interaction energies with a schematic zero-range force. It is found that, after correcting for the effects due to changes in the radial distribution of the single-particle wave functions, the mirror symmetry of the $n-p$ interaction is preserved between $^{16}$F and $^{16}$N, while a difference of 63\% is measured between the $p-p$ versus $n-n$ interactions in the second excited state of $^{15}$F and $^{15}$C nuclei. Several explanations are proposed.