Third-order corrections to the Hartree–Fock approximation for the binding energy of 4He

1970 ◽  
Vol 48 (18) ◽  
pp. 2123-2129
Author(s):  
H. J. Kreuzer
Keyword(s):  
Binding Energy ◽  
Plane Waves ◽  
Nucleon Nucleon ◽  
Second Order ◽  
Nucleon Interaction ◽  
Third Order ◽  
Hartree Fock ◽  
Nucleon Nucleon Interaction

We present third-order calculations of the binding energy of 4He with an effective (finite) nucleon–nucleon interaction of the Hamada–Johnston type. The intermediate (unoccupied) states are approximated by plane waves in a first calculation and in a second by oscillator functions. In both approximations third-order graphs contribute only a few percent of the second-order terms to the binding energy.

POTENTIAL OF NUCLEON INTERACTION WITH ODD NUCLEI IN THE HARTREE-FOCK THEORY

1999 ◽  
Vol 08 (02) ◽  
pp. 137-157 ◽  
Author(s):  
S. M. KRAVCHENKO ◽  
A. P. SOZNIK
Keyword(s):  
Optical Potential ◽  
Nucleon Nucleon ◽  
Effective Density ◽  
Nuclear Surface ◽  
Nucleon Interaction ◽  
Hartree Fock ◽  
Order Of Magnitude ◽  
Nucleon Nucleon Interaction ◽  
Analytical Expressions ◽  
Strong Spin

An expression for the real part of the optical potential of nucleon interaction with odd nuclei is derived in the Hartree-Fock approximation with effective density-dependent nucleon-nucleon interaction. It is shown for 13 C nucleus, as an example, that this potential contains the central interaction, as well as two spin-orbit forces connected with the spins of scattered nucleon and nucleus, and quite strong spin-spin and tensor interactions. The simple analytical expressions have been obtained for these potentials. The radial distributions of the interactions obtained and their energy dependences are investigated. It is shown that all potentials differ for neutron and proton scattering while the spin-spin and tensor forces in both cases have opposite signs, complicated radial dependences and are the same by an order of magnitude on the nuclear surface.

scholarly journals Nuclear structure study of some tin isotopes using the self-consistent mean field method

2019 ◽  
Vol 13 (26) ◽  
pp. 112-120
Author(s):  
Mohammed F. Majid
Keyword(s):  
Mean Field ◽  
Nucleon Nucleon ◽  
Field Method ◽  
Structure Study ◽  
Nucleon Interaction ◽  
Skyrme Interaction ◽  
Hartree Fock ◽  
Nuclear Structure Study ◽  
The Mean ◽  
Nucleon Nucleon Interaction

Hartree-Fock calculations for even-even Tin isotopes usingSkyrme density dependent effective nucleon-nucleon interaction arediscussed systematically. Skyrme interaction and the general formulafor the mean energy of a spherical nucleus are described. The chargeand matter densities with their corresponding rms radii and thenuclear skin for Sn isotopes are studied and compared with theexperimental data. The potential energy curves obtained withinclusion of the pairing force between the like nucleons in Hartree-Fock-Bogoliubov approach are also discussed.

The Nuclear Three Body Problem with Phase Equivalent Separable Interactions

1975 ◽  
Vol 53 (18) ◽  
pp. 1749-1763 ◽  
Author(s):  
N. J. McGurk ◽  
H. Fiedeldey
Keyword(s):  
Binding Energy ◽  
Scattering Length ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Bound State ◽  
Nucleon Nucleon ◽  
Triton Binding Energy ◽  
Nucleon Interaction ◽  
Global Features ◽  
Nucleon Nucleon Interaction

The triton ground state energy and the neutron–deuteron doublet scattering length have been calculated with two families of phase equivalent separable interactions in the 1S0 and 3S1–3D1 states of the nucleon–nucleon interaction. Generating the interactions from a solution of the inverse scattering problem, a separable representation of the nucleon–nucleon interaction is fully exploited to fit the scattering and bound state data as well as possible. Off shell constraints on the interactions are then discussed. Results for the three nucleon quantities are compared to those obtained with realistic local and one boson exchange potentials. It is shown that all results for potentials obeying the known off shell constraints lie on the Phillips band, which appears to be independent of the potential model employed. This is a consequence of the fact that the triton binding energy and doublet scattering length are only sensitive to the broad detail of the nucleon–nucleon S matrix in the 1S0 and 3S1–3D1 states and to certain global features of the residues at the singlet deuteron and deuteron poles. Relatively large off shell variations in the triton binding energy and doublet scattering length along this Phillips band are possible and the plausibility that the experimental values could be fitted is discussed.

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