Theory of autoionization

A new theory of autoionization is presented which makes no reference to decay channels and which treats the process as a bound-state problem. The starting point is a postulative definition, describing autoionizing—or resonance—states as time-stability maxima within the set of bound functions. The outcome of the mathematical formulation of the postulate is a variational expression for the mean-square deviation of energy. The resulting Euler expression is a nonlinear pseudoeigenvalue equation whose solutions include autoionizing as well as stationary bound states. A second equation, similar to the first, is derived, whose solutions correspond to most stable bound functions at any given energy. Using the second equation, it is possible to obtain a plot of lifetime versus energy—the time stability spectrum. The theory is applied to some ${}_{}{}^1{}_{}{}^{}S$ autoionizing states of He below the $n=2, 3, \mathrm{and} 4$ ionization thresholds. The present results are within error bounds of experimental measurements. Agreement with Feshbach-type calculations is also good.