Structure of $^{43}$P and $^{42}$Si in a two-level shape-coexistence model

TL;DR

This paper investigates the shape coexistence in $^{43}$P and $^{42}$Si using a two-level mixing model, successfully explaining experimental cross sections and suggesting both nuclei are predominantly oblate in shape.

Contribution

It introduces a two-level shape-coexistence model to interpret reaction data for $^{43}$P and $^{42}$Si, providing insights into their nuclear shapes and configuration mixing.

Findings

Both nuclei are predominantly oblate in shape.

The model accurately reproduces experimental cross sections.

Oblate configuration amplitude exceeds 80%.

Abstract

Exclusive cross sections for the $^{43}$P$(-1p)^{42}$Si reaction to the lowest $0^+$ and $2^+$ states, measured at NSCL with GRETINA and the S800, are interpreted in terms of a two-level mixing (collective) model of oblate and prolate co-existing shapes. Using the formalism developed for deformed nuclei we calculate the spectroscopic amplitudes and exclusive cross-sections in the strong coupling limit, where for $^{43}$P the schematic wavefunction includes the coupling of the Nilsson [211]$\frac{1}{2}$ proton orbit. Good agreement with the experimental data is obtained when the amplitude of the oblate configuration is $\gtrsim$ 80\%, suggesting that both nuclei are predominantly oblate, in line with theoretical expectations.