Treatment of renormalization, potential energy of intermediate states, and re-arrangement effects in Brueckner calculations of closed shell nuclei

Journal Article · Tue Jan 01 04:00:00 EST 1974 · Nucl. Phys., A, v. A219, no. 2, pp. 266-294

DOI:https://doi.org/10.1016/0375-9474(74)90066-9· OSTI ID:4332834

Grange, P; Preston, M A

In the Brueckner-Hartree-Fock theory of finite nuclei, the problems of renormalization, potential energy of intermediate states and re-arrangement effects are examined. For practical calculations it is shown that satisfactory solutions to them can be obtained if the parametrization chosen for the single- particle potential in finite nuclei is linked closely to nuclear matter results. The link is made with similar problems in the density dependent Hartree-Fock theory, and the possibility of such a parametrization is emphasized by recalling the existence of a formal solution for the Hartree-Fock single-particle potertial if the effective interaction is of the delta -function type. A method of solution of the Bethe-Goldstone equation is then presented which separates the intermediate states into those of an open shell'' and of a continuum''. Finally results of model calculations of /sup 16/O and /sup 40/Ca with harmonic oscillator functions are presented in which the parametrization chosen for the DHF singleparticle potential is taken from the Skyrme-Vautherin delta -function force. A self-consistent determination of certain parameters of this form of force leads to values in close agreement with the empirical estimate made by Vautherin and Brink in /sup 16/O, with the exception of the spin-orbit splittings. Limitations and possible iraprovements of this type of approach are discussed for /sup 40/Ca. (auth)

• Research Organization: McMaster Univ., Hamilton, Ont.
• Sponsoring Organization: USDOE
• NSA Number: NSA-29-028243
• OSTI ID: 4332834
• Journal Information: Nucl. Phys., A, v. A219, no. 2, pp. 266-294, Journal Name: Nucl. Phys., A, v. A219, no. 2, pp. 266-294; ISSN NUPAB
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

*CALCIUM 40-- ENERGY LEVELS
*OXYGEN 16-- ENERGY LEVELS
BETHE- GOLDSTONE EQUATION
BRUECKNER METHOD
HARMONIC OSCILLATORS
HARTREE-FOCK METHOD
L-S COUPLING
N68332 --Physics (Nuclear
Theoretical)--Nuclear Properties & Reactions
6 <= A <= 19--Energy Levels & Transitions
N68532* --Physics (Nuclear
Theoretical)--Nuclear Properties & Reactions
39 <= A <= 58--Energy Levels & Transitions
NUCLEAR FORCES
NUCLEAR POTENTIAL
POTENTIAL ENERGY
RENORMALIZATION
SHELL MODELS