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Manuscript Title: GAMOW: a program for calculating the resonant state solution of the radial Schrodinger equation in an arbitrary optical potential.
Authors: T. Vertse, K.F. Pal, Z. Balogh
Program title: GAMOW FUNCTIONS
Catalogue identifier: AAOD_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 27(1982)309
Programming language: Fortran.
Computer: ES-1040.
Operating system: OS 28.F.
RAM: 94K words
Word size: 8
Keywords: Atomic physics, Normalized gamow, Scattering, Resonant states, Single particle solution, Schrodinger equation, Decaying states, Complex eigen-solution, Poles of scattering, Bound states in complex Potential, Other, General purpose, Differential equation.
Classification: 2.6, 4.3.

Nature of problem:
The program calculates the normalized Gamow solution of the radial Schrodinger equation, i.e. the solution which is regular at the origin and has purely outgoing wave asymptotics, in a spherically symmetric complex potential of arbitrary form. Optionally either the complex energy eigenvalue in a given potential, i.e. the position of the pole of the scattering function S(E) or the strength of the short range potential belonging to a given energy value is computed.

Solution method:
Internal and external solutions satisfying the boundary conditions in the origin and the asympotic region, respectively, are generated by integrating the radial equation with the Fox-Goodwin method and from the mismatch of their logarithmic derivatives a correction to the eigen energy/potential strength is determined. The procedure is repeated with the corrected value till convergence. The wave function is normalized in the Zel'dovich sense by integrating numerically along a contour in the complex r-plane.

The present method does not work in the vicinity of zero energy and for unphysical resonances and antibound states.

Running time:
0.5-3 s per iteration.