The ground-state spins and parities of the odd-$A$ phosphorus isotopes ${}^{25-47}P$ are studied with the relativistic mean-field (RMF) model and relativistic elastic magnetic electron-scattering theory (REMES). Results of the RMF model with the NL-SH, TM2, and NL3 parameters show that the $2s_{1/2}$ and $1d_{3/2}$ proton level inversion may occur for the neutron-rich isotopes ${}^{37-47}P$, and, consequently, the possible spin-parity values of ${}^{37-47}P$ may be ${\frac{3}{2}}^{+}$, which, except for ${}^{47}\mathrm{P}$, differs from those given by the NUBASE2012 nuclear data table by Audi et al. Calculations of the elastic magnetic electron scattering of ${}^{37-47}P$ with the single valence proton in the $2s_{1/2}$ and $1d_{3/2}$ state show that the form factors have significant differences. The results imply that elastic magnetic electron scattering can be a possible way to study the $2s_{1/2}$ and $1d_{3/2}$ level inversion and the spin-parity values of ${}^{37-47}P$. The results can also provide new tests as to what extent the RMF model, along with its various parameter sets, is valid for describing the nuclear structures. In addition, the contributions of the upper and lower components of the Dirac four-spinors to the form factors and the isotopic shifts of the magnetic form factors are discussed.

• Received 18 March 2014
• Revised 21 June 2014

DOI:https://doi.org/10.1103/PhysRevC.90.024307