Exclusive cross sections for the ${}^{43}\mathrm{P}(-1p){}^{42}\mathrm{Si}$ 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 coexisting shapes. Using the formalism developed for deformed nuclei, we calculate the spectroscopic amplitudes and exclusive cross sections in the strong-coupling limit, where for ${}^{43}\mathrm{P}$ the schematic wave function 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. Model predictions for excitation energies and electromagnetic observables, which could motivate further studies of both nuclei, are also presented.

• Received 16 August 2021
• Accepted 10 December 2021

DOI:https://doi.org/10.1103/PhysRevC.105.014309