High-order perturbation theory of the imaginary part of the resonance eigenvalues of the Stark effect in hydrogen and of the anharmonic oscillator with negative anharmonicity

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Abstract
The "perturbation theory" for the imaginary part of the resonance energies of the hydrogen atom in the Stark effect and of the two-dimensional anharmonic oscillator with negative anharmonicity, which is a separation constant in the Stark problem, is solved to high order. The solution is based on the Langer-Cherry generalization of the JWKB method, which can be carried out in closed form, order by order. The numerical results should be useful both in interpreting experimental measurements of excited-state lifetimes and in understanding the analytic properties of the Stark and anharmonic-oscillator resonances.