Resonances by the exterior-scaling method within the framework of the finite-basis-set approximation

Simon’s exterior-scaling procedure is applied to model systems within the framework of the finite-basis-set approximation. We show that if the basis-set functions are scaled when r>$r_0$, a variational solution is obtained by adding the term 1/2δ(r-$r_0$)[d/dr-λ] [1-exp(-2iΘ)] to the Hamiltonian, where λ is the logarithmic derivative of the resonance wave function at $r_0$. Two computational methods are proposed. One is an ab initio linear variational iterative procedure, whereas in the second one λ is semiclassically estimated during the iteration procedure and all the variational calculations are carried out for r≤$r_0$ and therefore are exactly Θ independent. An illustrative numerical application is presented.