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Manuscript Title: Solution of bound state problems in nuclear shell model with momentum dependent potentials.
Authors: M.A.K. Lodhi, B.T. Waak
Catalogue identifier: ACWK_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 10(1975)182
Programming language: Fortran.
Computer: IBM 360/50.
Operating system: OS 360.
RAM: 21K words
Word size: 32
Keywords: Nuclear physics, Energy levels, Wave functions, General purpose, Differential equation, Morse functions, Analytic solution, Schroedinger equation, Nonlocal potential, Momentum-dependent Potential, Shell model.
Classification: 4.3, 17.19.

Nature of problem:
Investigations of the structure of nuclei show that a nonlocal effect should be included in the nucleon-nucleus or nucleon-nucleon interaction. A nonlocal potential can be understood as reflecting the correlations existing in nuclear matter, whereby the presence of a particle at positionr influences the probability of finding another nucleon at a point r' in the neighborhood of r. This in turn affects the energy of the particle at r'. The nonlocal potential can be expressed as an effective energy-dependent potential. From the effective potential, the single-particle wave functions and eigenvalues are calculated.

Solution method:
The effective potential is approximated by a function for which the Schrodinger equation is analytically solvable. The wave function and eigenvalue are then expressable in terms of the parameters of the analytically solvable function. The program finds the values of the parameters that give a "best" fit to the effective potential and then computes the corresponding eigenvalue.

The parameters of the effective potential are chosen to be suitable for nuclei along the beta stable line with A>10.

Unusual features:
The input data is read under the NAMELIST option of FORTRAN IV(g). The variable DUMMY is used for the sole purpose of reading the card identification/sequence field in columns 77-80. Under normal running conditions, the data cards will not be sequenced and the variable DUMMY can be eliminated.

Running time:
(IBM360/50) The running time for one single-particle state can range from 1-15 mins. The variation in running time strongly depends on the number of iterations required for convergences and the number of points considered in matching procedure. A good initial energy estimate significantly reduces the number of iterations, so an energy formula has been provided which generates a reasonably accurate estimate. The running time for the example is 1.3 min (2.8 min including compilation).