Microscopic calculations of nuclear structure and nuclear correlations Page: 2 of 15
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Opj = 1, 'ri'tj, ai-6j, (Bi-aj)(Ti-'rj), Sij, Sij('Zi-tj), L-S, L-S(ti-tj),
L2, L2(ti-'tj), L2(6i-aj), L2(Gi-Gj)(Ti-tj), (L.S)2, (L-S)2(Ti-'tj) .(3)
The first eight operators are required phenomenologically to reproduce S- and P-wave NN
scattering and deuteron properties. The additional L-dependent operators are required for
fitting higher partial waves. Examples are the Reid vg potential , an adaptation of the
standard Reid soft-core potential which uses the first eight operators above, and the Argonne
vi4 potential , which uses all fourteen operators shown. Other realistic potentials, such as
the Bonn , Nijmegen , and Paris  models, use p2 operators instead of, or in addition
to, L2 operators.
The meson-theoretic basis for the NN potential is illustrated in Figure 1. The dominant
long-range interaction is one-pion exchange, which has the operator structure:
vi = X7(ti-tj) = [Y(rij)ai'j + T(rij)Sij]ti-tj , (4)
where Y(r) and T(r) are the usual Yukawa and tensor functions. At intermediate ranges, two-
pion exchange, with the possible excitation of intermediate A-isobar resonances, is the
dominant reaction. Analysis with interaction models that include explicit A degrees of freedom
 show that these processes provide significant attraction, which is predominantly central in
character, but includes important components for the first six operators of eq.(3). At shorter
ranges the interaction may be dominated by the exchange of heavier mesons, such as the p and
o, or the quark substructure of nucleons may start to play some more complicated role; these
features contribute to the spin-orbit and higher-order terms in the potential.
Realistic models for the NNN potential also have a non-trivial operator dependence.
Meson-exchange diagrams contributing to the NNN potential are shown in Figure 2, starting
with a long-range two-pion-exchange part of the Fujita-Miyazawa form :
Vi = A C ( (X),Xk) ('ti'tjr'tik) + 4 [X),Xk[i'itjti-tk] ), (5)
which is built up from the one-pion-exchange operators, and arises from an intermediate A-
isobar excitation. In the Urbana NNN potentials  a phenomenological intermediate-range
repulsive term is added:
V k = U E T2(rij)T2(rjk) (6)
which can be viewed as an interference of the intermediate-range attraction between two NN
Figure 1. Diagrams contributing to the NN potential.
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Wiringa, R.B. Microscopic calculations of nuclear structure and nuclear correlations, article, January 1, 1992; Illinois. (digital.library.unt.edu/ark:/67531/metadc1059736/m1/2/: accessed November 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.