SPIN-ORBIT SPLITTING AND TENSOR FORCE

Journal Article · Mon Aug 01 04:00:00 EDT 1960 · Nuclear Phys.

DOI:https://doi.org/10.1016/0029-5582(60)90400-4· OSTI ID:4147927

Arima, A

The second-order effect of the tensor force was calculated in nuclei that had several nucleons outside closed shells. This second-order effect caused a modification of the first-order secular equation of the degenerate shellmodel states (nl)P, where nl is an orbit of the L-S coupling shell model and p is the number of nucleons outside closed shells. This modification is equivalent to the introduction of a slight change in the one-particle energy, one-body spin-orbit interaction SIGMA ?s/sub i/ - l/sub i/, effective nonlocal two- and three-body forces, and an energy depression that is common to all states. Here ? = C/sub 0/ + (p--l)C/sub 1/, where C/sub 0/ and C/sub 1/ are constant as long as the average potential of the shell model does not change. C/sub 0/ and C/sub 1/ were calculated in the (lp)-shell, and C/sub 0/ approximately 4C/sub 1/. The constant C/sub 0/ is about --1.0 to --1.5 Mev. In this numerical calculation, the harmonicoscillator wave functions were adopted as individual wave functions, and either the tensor force suggested by meson theory or the phenomenological strong tensor force was assumed. It is very interesting to note that ? (N/sup 15/ )/? (He/sup 5/) approximately 3.5. If the three-body effect is neglected, the modified secular equation results in the intermediate-coupling shell-model Hamiltonian, provided that the two-body effective potential is replaced by the usual potential which has the same matrix elements as the effective one. (auth)

• Research Organization: Argonne National Lab., Ill.
• NSA Number: NSA-15-000921
• OSTI ID: 4147927
• Journal Information: Nuclear Phys., Journal Name: Nuclear Phys. Vol. Vol: 18
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

ENERGY
MANY BODY PROBLEM
NUCLEONS
PARTICLES
PHYSICS
SPIN