Unitary-Model-Operator Approach to Nuclear Many-Body Problem. I: --The Ground-State and One-Body Energies of 16O--
Year: 1986
Type: article
Abstract: A theory is formulated to derive an effective interaction in nuclei in the framework of the unitarymodel-operator approach.A unitary operator is introduced to describe two-body correlations, and it is determined from the condition that the effective interaction should be decoupled between the lowmomentum model space and the high-momentum space.The unitary-transformed Hamiltonian is represented in a cluster expansion form.The one-and two-body cluster terms are mainly discussed.The theory is applied to the calculation of the energies of the ground-and one-body states with the Reid soft core potential.A large gain of the energy has been obtained for the ground state in comparison with the result of the usual G-matrix theory.As for the one-body energies obtained, agreement with the experimental values is fairly good.Although the discrepancies with the experiments still remain at the 1O~ 15 % level, the present approach shows to have some desirable features compared with the nuclear many-body theories proposed so far. § 1. IntroductionA fundamental problem in nuclear physics is to clarify the properties of nuclei in terms of the interaction among their constituent particles.Although there have been many theories or approaches, we have not yet reached the goal of reproducing successfully the experimental data.The investigation of nuclear properties, in the usual nonrelativistic approach, proceeds in two steps: The first one is to determine the interaction among nucleons, and the second is to solve the many-body SchrOdinger equation.Concerning the nucleon-nucleon force, it seems that the phenomenological potential, such as the Reid potential, would be incomplete and one should wait until quark dynamics, probably quantum chromodynamics (QCD), solves finally the problem o~ nuclear force.It is of no doubt that in order to fit the experiments we need more accurate knowledge on the nuclear force including the threebody force.However, if we want to reach the goal, we need also a good many-body theory.Regardless of the accuracy of the nuclear force, we shall not be able to solve the problem unless we have a way of constructing an accurate solution for a many-body system.We believe that many-body theory should share the responsibility for the discrepancy between theory and experiment.It will be sure that nuclear many-body theory is still to be improved.Among many theories for nuclear many-body problem, the most widely applied method is, needless to say, the linked-diagram perturbation theory.This approach may also be referred to as the folded-diagram theory based on the G-matrix interaction especially due 'to Brandow 1l and Kuo et al. 2l An outstanding problem in this approach is the convergence of the perturbation expansion.Since Schucan and Weidenmliller 3 ) pointed out the divergence of the perturbation expansion due to the presence of intruder states, this difficulty has long been a serious problem.Present status of this problem is
Source: Progress of Theoretical Physics
DOI: 10.1143/ptp.75.1388
Authors: K. Suzuki, R. Okamoto
Institution: Kyushu Institute of Technology
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W2107924403