Acta Physica Academiae Scientiarum Hungaricae 30. (1971)

1971 / 1. szám - J. Németh: The Effect of the Density Dependence of the Forces on First Order Finite Nuclear Calculations

Acta Physica Academiae Scienliarum Hungaricae, Tomus 30 (1), pp- 39—52 (1971) THE EFFECT OF THE DENSITY DEPENDENCE OF THE FORCES ON FIRST ORDER FINITE NUCLEAR CALCULATIONS By J. Németh INSTITUTE FOR THEORETICAL PHYSICS, ROLAND EÖTVÖS UNIVERSITY, BUDAPEST (Received 18. III. 1970) Hartree—Fock type of calculations are made with density dependent forces, and we examine the effect of density dependence on the results. The single particle and total energies and the average radii of spherical nuclei are determined. The results are compared with other calculations. Good agreement is found between theoretical and experimental values. I. Introduction The most usual method to determine properties of finite nuclei is the Hartree—Fock approximation. It is applicable only for weak forces. Phase shift analysis shows, however, that the two-body forces are not weak forces. There are two ways of avoiding this difficulty. One is to deduce from the two­­body scattering some weak force which fits the scattering data relatively well, and which are already applicable in first order calculations [1, 2]. The other possibility is to use Brueckner Hartree—Fock calculations [3, 4]. There one rearranges the perturbation series by running up the ladder graphs, and in this way a new first order term is deduced which already gives a better first order approximation. The biggest problem with the Brueckner Hartree—Fock calculations is the double self-consistency. One determines first a single particle potential, from this the single particle wave functions by solving the Schrôdinger equa­tion, then one determines the G matrix elements, and from this again the single­particle potential, and so on. The single particle potential is non-local, because of the exchange term, which makes the whole calculation process even longer. One can make a short cut by using harmonic oscillator wave functions, as the real one, and forgetting about the Hartree—Fock self-consistency, keep­ing only the Brueckner one; this is, however, a bad approximation for heavier nuclei. A new way of dealing with this problem has been developed in recent years. Using the original local density approximation of Brueckner [3], one can develop it further by applying certain corrections [5] and as a result one can deduce an effective two-nucleon force, which is density dependent [6—9] and which gives quite good results for first order calculations [8 10]. Acta Physica Academiae Scientiarum Hungaricae 30, 1971

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