On the normalization of the Gamov resonant wave function in the configuration space

Abstract

The regularization of the normalization integral for the resonant wave function, proposed by Zeldovich, is valid only when |Reqres| > |Imqres|. A new normalization procedure is proposed and implemented, which is valid when this condition fails. First, an arbitrarily normalized vertex function g(k) is calculated using the formula with the potential V(r) in the integrand. This Fourier integral converges for a potential with the asymptotics V(r) → constr−nexp(−μr) if |Imqres| < μ/2. Then the function g(k) is normalized using the generalized normalization rule, which is independent of the resonance pole position. The proposed method is approved by the example of calculation for a virtual triton.