Structure of P43 and Si42 in a two-level shape-coexistence model

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