Microscopic calculations of nuclear structure and nuclear correlations Page: 3 of 15
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pairs sharing one nucleon. The practical effect of adding such an NNN potential is additional
binding in light nuclei where the attractive long-range two-pion-exchange dominates, and more
repulsion in nuclear matter where the intermediate-range repulsive term produces a more rapid
saturation. The strengths of the attractive and repulsive parts, A and U, are adjusted to give an
overall best fit to nuclear binding energies in these two regimes.
Below we report results for two models: Urbana VII, which was fit to earlier variational
calculations of light nuclei and nuclear matter  and is used here for closed-shell nuclei, and
Urbana VIII, which was fit to more recent exact Faddeev and Green's function Monte Carlo
(GFMC) calculations and is used here for few-body nuclei . Other NNN potentials are
available, such as the Tucson-Melbourne model [101, which has a more complete two-pion-
2. VARIATIONAL TRIAL FUNCTIONS
The variational method can be used to obtain approximate solutions of the many-body
Schrodinger equation for Hamiltonians of the kind given above and for a wide range of nuclear
systems: few-body nuclei [7-9] such as 3H and 4He, light nuclei  such as 1 0 and 40Ca,
nuclear matter [12,13] and neutron stars . A suitably parametrized trial function Tv is used
to calculate an upper bound Ev to the ground-state energy E0 using the Rayleigh-Ritz
The parameters in Tv are varied to minimize Ev, and the lowest value is taken as the
approximate ground-state energy. The corresponding Tv can then be used to calculate other
properties of interest. A better energy may be obtained by using Yv as a starting point for a
perturbation or GFMC calculation . The key steps are always to 1) find a good ansatz for
Tv, and 2) accurately evaluate the expectation value (H).
The strong state-dependence of the interactions induces corresponding correlations in the
wave function. A good trial function can be constructed from a product of correlation
JYV) = [1 + E.U, s + . UTN ][S fI(1+Uij)]lI'') , (8)
i<j 1ij~ <j
where Pj is a Jastrow wave function, and Uij, U S, and U are two- and three-body
1L -- -
Figure 2. Diagrams contributing to the NNN 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/m1/3/: accessed January 18, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.