Electron-impact study of the PH radical using theR-matrix method

Abstract

The PH radical is an interesting case to study because of its ${\ensuremath{\pi}}^{2}$ electronic configuration, which leads to the three low-lying electronic states, $X$ ${}^{3}{\ensuremath{\Sigma}}^{\ensuremath{-}}$, $a$ ${}^{1}\ensuremath{\Delta}$, and $b$ ${}^{1}{\ensuremath{\Sigma}}^{+}$. The singlet states possess long lifetimes, because direct combination with the ground state is not allowed. This is similar to the ${\mathrm{O}}_{2}$ case. The $\mathit{R}$-matrix method is employed to calculate elastic differential and integral cross sections, momentum-transfer cross sections, and inelastic cross sections. The energy range is 0--10 eV. The Hartree-Fock ground-state configuration of PH is $1{\ensuremath{\sigma}}^{2}2{\ensuremath{\sigma}}^{2}3{\ensuremath{\sigma}}^{2}1{\ensuremath{\pi}}^{4}4{\ensuremath{\sigma}}^{2}5{\ensuremath{\sigma}}^{2}2{\ensuremath{\pi}}^{2}$. We have included thirty-seven target states in the trial wave function of the scattering system in our best model. Each target state is represented by a configuration interaction (CI) wave function. In our CI model, we freeze ten electrons in orbitals $1\ensuremath{\sigma}$, $2\ensuremath{\sigma}$, $3\ensuremath{\sigma},$ and $1\ensuremath{\pi}$; the remaining six electrons are free to move among the seven orbitals $4\ensuremath{\sigma}$, $5\ensuremath{\sigma}$, $6\ensuremath{\sigma}$, $7\ensuremath{\sigma}$, $8\ensuremath{\sigma}$, $2\ensuremath{\pi},$ and $3\ensuremath{\pi}$. Our CI model yields a dipole moment of 0.67 D at the equilibrium PH bond length, ${R}_{e}$, of 2.687 ${a}_{0}$; this dipole moment compares favorably with the experimental value 0.70 D. We have carried our scattering calculations in one state with the CI wave function and thirty-seven-state model. We have detected a stable anionic bound state ${}^{2}{B}_{1}$ of PH at various bond lengths of PH molecule. The vertical electron affinity value is 0.97 eV, which is in excellent agreement with experimental value of 1.00 eV. We have included up to $g$ partial waves in the scattering calculations. The contribution of higher partial waves is accounted for by using a Born-closure procedure.