The Core of $^{25}$F studied by the $^{25}$F(-1p)$^{24}$O reaction

TL;DR

This study investigates the structure of $^{25}$F via the ($5/2^+ o 24$O) reaction, revealing a significant depletion of proton strength and suggesting $^{24}$O is more vibrational and less rigid than previously thought.

Contribution

The paper provides experimental spectroscopic data and interprets it using Particle-Vibration Coupling models, challenging the view of $^{24}$O as a rigid doubly-magic core within $^{25}$F.

Findings

Significant depletion of proton $d_{5/2}$ strength in $^{25}$F.

$^{24}$O acts as a softer, more collective core than expected.

Effective $^{24}$O* core exhibits quadrupole vibrational behavior.

Abstract

The $^{25}$F($5/2^+) (-1p) ^{24}$O reaction was studied at the NSCL using the S800 spectrometer. The experimental spectroscopic factor for the ground-state to ground-state transition indicates a substantial depletion of the proton $d_{5/2}$ strength compared to shell-model expectations. Our result supports the findings reported by Tang \textit{et al.}, from their study of the $(p,2p)$ reaction at RIBF. The overlap between the $^{25}$F and $^{24}$O ground-states is considerably less than anticipated if $^{24}$O acted as a robust and rigid doubly-magic core in $^{25}$F. We interpret the results within the framework of the Particle-Vibration Coupling (PVC) of a $d_{5/2}$ proton coupled to a quadrupole phonon of an effective core. This approach provides a good description of the experimental data by requiring an effective $^{24}$O* core with a phonon energy of $\hbar\omega_2$= 3.2 MeV, and a $B(E2) ~ 2.7$ W.u., softer and more collective than a bare $^{24}$O. Both the Nilsson deformed mean field and the PVC models appear to capture the properties of the effective core of $^{25}$F, suggesting that the additional proton tends to polarize the free, doubly magic $^{24}$O in such a way that it becomes either slightly deformed or a quadrupole vibrator.