Nucleon-nucleon interactions

Nucleon-nucleon interactions are at the heart of nuclear physics, bridging the gap between QCD and the effective interactions appropriate for the shell model. We discuss the current status of {ital NN} data sets, partial-wave analyses, and some of the issues that go into the construction of potential models. Our remarks are illustrated by reference to the Argonne {ital v}{sub 18} potential, one of a number of new potentials that fit elastic nucleon-nucleon data up to 350 MeV with a {Chi}{sup 2} per datum near 1. We also discuss the related issues of three-nucleon potentials, two-nucleon charge and current operators, and relativistic effects. We give some examples of calculations that can be made using these realistic descriptions of {ital NN} interactions. We conclude with some remarks on how our empirical knowledge of {ital NN} interactions may help constrain models at the quark level, and hence models of nucleon structure

Weak Transitions in A=6 and 7 Nuclei

The $^6$He beta decay and $^7$Be electron capture processes are studied using variational Monte Carlo wave functions, derived from a realistic Hamiltonian consisting of the Argonne $v_{18}$ two-nucleon and Urbana-IX three-nucleon interactions. The model for the nuclear weak axial current includes one- and two-body operators with the strength of the leading two-body term--associated with $\Delta$-isobar excitation of the nucleon--adjusted to reproduce the Gamow-Teller matrix element in tritium $\beta$-decay. The measured half-life of $^6$. He is under-predicted by theory by $\simeq$ 8%, while that of $^7$Be for decay into the ground and first excited states of $^7$Li is over-predicted by $\simeq$ 9%. However, the experimentally known branching ratio for these latter processes is in good agreement with the calculated value. Two-body axial current contributions lead to a $\simeq$ 1.7% (4.4%) increase in the value of the Gamow-Teller matrix element of $^6$He ($^7$Be), obtained with one-body currents only, and slightly worsen (appreciably improve) the agreement between the calculated and measured half-life. Corrections due to retardation effects associated with the finite lepton momentum transfers involved in the decays, as well as contributions of suppressed transitions induced by the weak vector charge and axial current operators, have also been calculated and found to be negligible.Comment: 23 pages 8 tables. submitted to Phys. Rev.

Quantum Monte Carlo Calculations of Pion Scattering from Li

We show that the neutron and proton transition densities predicted by recent quantum Monte Carlo calculations for A=6,7 nuclei are consistent with pion scattering from 6Li and 7Li at energies near the Delta resonance. This has provided a microscopic understanding of the enhancement factors for quadrople excitations, which were needed to describe pion inelastic scattering within the nuclear shell model of Cohen and Kurath.Comment: 10 pages, REVTeX, 3 postscript figures; added calculation of elastic and inelastic pion scattering from 6Li at multiple energie

Spin-orbit induced backflow in neutron matter with auxiliary field diffusion Monte Carlo

The energy per particle of zero-temperature neutron matter is investigated, with particular emphasis on the role of the $\vec L\cdot\vec S$ interaction. An analysis of the importance of explicit spin--orbit correlations in the description of the system is carried out by the auxiliary field diffusion Monte Carlo method. The improved nodal structure of the guiding function, constructed by explicitly considering these correlations, lowers the energy. The proposed spin--backflow orbitals can conveniently be used also in Green's Function Monte Carlo calculations of light nuclei.Comment: 4 pages, 1 figur

Many-body effects in 16O(e,e'p)

Effects of nucleon-nucleon correlations on exclusive $(e,e'p)$ reactions on closed-shell nuclei leading to single-hole states are studied using $^{16}O(e,e'p)^{15}N$ ($6.32$ MeV, $3/2^-$) as an example. The quasi-hole wave function, calculated from the overlap of translationally invariant many-body variational wave functions containing realistic spatial, spin and isospin correlations, seems to describe the initial state of the struck proton accurately inside the nucleus, however it is too large at the surface. The effect of short-range correlations on the final state is found to be largely cancelled by the increase in the transparency for the struck proton. It is estimated that the values of the spectroscopic factors obtained with the DWIA may increase by a few percent due to correlation effects in the final state.Comment: 21 Pages, PHY-7849-TH-9

Neutron matter at zero temperature with auxiliary field diffusion Monte Carlo

The recently developed auxiliary field diffusion Monte Carlo method is applied to compute the equation of state and the compressibility of neutron matter. By combining diffusion Monte Carlo for the spatial degrees of freedom and auxiliary field Monte Carlo to separate the spin-isospin operators, quantum Monte Carlo can be used to simulate the ground state of many nucleon systems (A\alt 100). We use a path constraint to control the fermion sign problem. We have made simulations for realistic interactions, which include tensor and spin--orbit two--body potentials as well as three-nucleon forces. The Argonne $v_8'$ and $v_6'$ two nucleon potentials plus the Urbana or Illinois three-nucleon potentials have been used in our calculations. We compare with fermion hypernetted chain results. We report results of a Periodic Box--FHNC calculation, which is also used to estimate the finite size corrections to our quantum Monte Carlo simulations. Our AFDMC results for $v_6$ models of pure neutron matter are in reasonably good agreement with equivalent Correlated Basis Function (CBF) calculations, providing energies per particle which are slightly lower than the CBF ones. However, the inclusion of the spin--orbit force leads to quite different results particularly at relatively high densities. The resulting equation of state from AFDMC calculations is harder than the one from previous Fermi hypernetted chain studies commonly used to determine the neutron star structure.Comment: 15 pages, 15 tables and 5 figure

LOCV calculation for Beta-stable matter at finite temperature

The method of lowest-order constrained variational, which predicts reasonably the nuclear matter semi-empirical data is used to calculate the equation of state of beta-stable matter at finite temperature. The Reid soft-core with and without the N-$\Delta$ interactions which fits the N-N scattering data as well as the $UV_{14}$ potential plus the three-nucleon interaction are considered in the nuclear many-body Hamiltonian. The electron and muon are treated relativistically in the total Hamiltonian at given temperature, to make the fluid electrically neutral and stable against beta decay. The calculation is performed for a wide range of baryon density and temperature which are of interest in the astrophysics. The free energy, entropy, proton abundance, etc. of nuclear beta-stable matter are calculated. It is shown that by increasing the temperature, the maximum proton abundance is pushed to the lower density while the maximum itself increases as we increase the temperature. The proton fraction is not enough to see any gas-liquid phase transition. Finally we get an overall agreement with other many-body techniques, which are available only at zero temperature.Comment: LaTex, 20 page

In medium T matrix for neutron matter

We calculate the equation of state of pure neutron matter, comparing the G-matrix calculation with the in-medium T-matrix result. At low densities, we obtain similar energies per nucleon, however some differences appear at higher densities. We use the self-consistent spectral functions from the T-matrix approach to calculate the 1S0 superfluid gap including self-energy effects. We find a reduction of the superfluid gap by 30%

Chiral Effective Field Theory Calculations of Weak Transitions in Light Nuclei

We report quantum Monte Carlo calculations of weak transitions in A 10 nuclei, based on the Norfolk two-and three-nucleon chiral interactions, and associated one-and two-body axial currents. We find that the contribution from two-body currents is at the 2-3% level, with the exception of matrix elements entering the rates of Li-8, B-8, and He-8 beta decay. These matrix elements are suppressed in impulse approximation based on the (leading order) Gamow Teller transition operator alone; two-body currents provide a 20-30% correction, which is, however, insufficient to bring theory in agreement with experimental data. For the other transitions, the agreement with the data is satisfactory, and the results exhibit a negligible to mild model dependence when different combinations of Norfolk interactions are utilized to construct the nuclear wave functions. We report a complete study of two-body weak transition densities which reveals the expected universal behavior of two-body currents at short distances throughout the range of A = 3 to A = 10 systems considered here

New Forms of Deuteron Equations and Wave Function Representations

A recently developed helicity basis for nucleon-nucleon (NN) scattering is applied to th e deuteron bound state. Here the total spin of the deuteron is treated in such a helicity representation. For the bound state, two sets of two coupled eigenvalue equations are developed, where the amplitudes depend on two and one variable, respectively. Numerical illustrations based on the realistic Bonn-B NN potential are given. In addition, an `operator form' of the deuteron wave function is presented, and several momentum dependent spin densities are derived and shown, in which the angular dependence is given analytically.Comment: 19 pages (Revtex), 9 fig