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

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