Theoretical study of autoionizing states and lifetimes in multiply excited argon

Autoionization transition rates have been calculated for a representative selection of spectroscopic terms of multiply excited argon atoms. The states selected consist of two highly excited electrons in the Rydberg states ($n=4, 5$) together with one or two vacancies in the valence shell ($n=3\mathrm{}$) and a single vacancy in the inner shell ($n=2\mathrm{}$). Configuration mixing was found to be important. The eigenvalues and eigenstates were found by the truncated diagonalization method (i.e., $\mathrm{QHQ}$ is diagonalized). The effect of term splitting was included by calculating the contributions of the quadrupole terms in the interelectron repulsive potentials. The applicability of the $\mathrm{msnp}\pm$ classification scheme suggested by Cooper, Fano, and Prats for helium was investigated for the outer electrons. Among the doubly excited outer-shell states found here are pairs of states which predominantly have the characteristics of $45sp+$ and $45sp-$ levels. However, states of the less-ionized system show less ± character because the shielding of the nucleus by the core electrons removes the degeneracy in energy of $4s5p$ and $5s4p$ levels, so there is less mixing when there is more shielding. The lifetimes of the valence-electron ($n=3\mathrm{}$) shell decay range from ∼${10}^{-15\mathrm{}}$ to ∼${10}^{-13\mathrm{}}$ sec. The lifetimes of the highly excited electrons separate into two widely disparate ranges: from ∼${10}^{-17\mathrm{}}$ to ∼${10}^{-16\mathrm{}}$ sec and from ∼${10}^{-13\mathrm{}}$ to ∼${10}^{-11\mathrm{}}$ sec. The outer-shell states that have lifetimes shorter than the inner shell are those from which it is energetically possible for an electron to fall to a $4s$, $4p$, or $3d$ subshell, while the longer lifetimes are for states which can decay only to the $n=3\mathrm{}$ core.