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

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.

5 pages, 3 figures