Prog. Theor. Phys. Vol. 18 No. 4 (1957) pp. 345-356

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Cluster Development Method in the Quantum Mechanics of Many Particle System, II

— Saturation of Nuclear Forces —

Department of Physics, University of Tokyo, Tokyo
^*Nuclear Data Group, National Research Council, Washington, D. C., U.S.A.

(Received July 1, 1957)

Abstract:

The cluster development method formulated in the first paper is applied to the discussion on the saturation of nuclear forces. We assume Serber type two-body forces with hard cores, in which central potentials are assumed to be spin independent (eqs. (1) and (2)). The potential depth and range are determined from the scattering length and the effective range in the spin singlet state, and the hard core radius is taken as D = 0.6 × 10^-13 cm. The Coulomb forces are neglected. The usual variational method is used with a simple trial correlation function (eq. (6)). By using the one- and two-nucleon clusters only, the energy minimum per nucleon is found to be -5.2 Mev at r₀ = 1.1 × 10^-13 cm (for r₀ see eq. (5)). At this minimum point the three-nucleon cluster terms are evaluated. They are one order of magnitude smaller than the leading term, and the convergency of the development seems to be fairly good. It is seen that the effective potential for the single particle motion in the nuclear matter is much weakened after separating the short range correlations between nucleons.

URL : http://ptp.ipap.jp/link?PTP/18/345/
DOI : 10.1143/PTP.18.345

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