Constrained variational calculations on nuclear matter with state dependent correlations

Constrained variational calculations on the binding energy of nuclear matter have been performed employing three potentials with differing mixtures of central and tensor components. We present numerical results on the energy expectation value in two- and three-body cluster approximation as function of the separation distance at which the central and tensor correlations heal smoothly.     

Lambda-Nucleon and Nucleon–Nucleon Interactions on the Lattice

Lattice QCD study of nuclear potentials is reported. A lattice QCD method to calculate realistic nuclear potentials is developed. In this method, Bethe–Salpeter wave functions generated on the lattice are used to reconstruct nuclear potentials by using Schrödinger equation. It is one of the possible extensions of Lüscher’s finite volume method for scattering phase shifts. Hence the resulting potential can reproduce the scattering data. The method was first applied to the central potential in NN system. It is now applied to various objects, such as tensor potential, hyperon potentials both in quenched QCD and 2 + 1 flavor QCD generated by PACS-CS Collaboration.     

A cluster-variational investigation of static density waves in nuclear matter

A detailed comparison of the energy of the uniform phase and of phases exhibiting periodic density fluctuation is presented for extended nuclear systems. The short-range correlations are taken to be of Jastrow type and the calculations are carried through two-body cluster order. With semi-realistic central potentials containing hard cores, no energetic advantage of a non-uniform state is detected, either in symmetrical nuclear matter or in pure neutron matter. However, the analysis gives useful information on the conditions favoring an instability of the homogeneous phase and points to the essential role of the tensor force in the formation of spin-(isospin-) density waves.     

Nuclear Forces in the Odd Parity Sector and the LS Forces from Lattice QCD

The first lattice QCD calculation for the spin-orbit potential as well as the central and the tensor potentials in parity odd sector is presented for the two-nucleon system. These potentials are extracted from the Nambu-Bethe-Salpeter (NBS) wave functions for total angular momenta ${J^{P}=A_1^{-}(0^-),T_1^{-}(1^-),T_2^{-}\oplus E^{-}(2^-)}$ based on the representation theory of the cubic group.     

Cluster-variational calculations for extended nuclear systems

The energy as a function of density is calculated for neutron matter and for symmetrical nuclear matter, based on Jastrow trial wave functions. The energy expectation value is truncated in low cluster order. A detailed analysis of the two- and three-body cluster contributions and a special portion of the four-body contribution is given. Variation of a parameterized two-body correlation function is subjected to constraints designed to confine the trial wave function to the domain corresponding to rapid cluster convergence. Results are presented for a variety of model central potentials containing hard cores, for different sets of constraints, and for two- and three-parameter correlation functions. Calculations constrained by the “average Pauli condition” are found to yield results very close to those constrained by the “normalization” or “unitarity” condition, and the two-parameter correlation function appears to be quite adequate. The convergence of the cluster expansion, as reflected in the low orders, is good except at the highest densities considered. The three-body cluster contribution displays, in all cases, a remarkable internal cancellation between its “two-correlation-line” addends.     

Dirac equation for the Hulthén potential within the Yukawa-type tensor interaction

Using the Nikiforov-Uvarov (NU) method, pseudospin and spin symmetric solutions of the Dirac equation for the scalar and vector Hulthén potentials with the Yukawa-type tensor potential are obtained for an arbitrary spin-orbit coupling quantum number κ. We deduce the energy eigenvalue equations and corresponding upper- and lower-spinor wave functions in both the pseudospin and spin symmetry cases. Numerical results of the energy eigenvalue equations and the upper- and lower-spinor wave functions are presented to show the effects of the external potential and particle mass parameters as well as pseudospin and spin symmetric constants on the bound-state energies and wave functions in the absence and presence of the tensor interaction.     

Exact matrix elements for general two-body central-force interactions,expressed as sums of products

ABSTRACT

In a manner similar to but distinct from concurrent tensor efforts in electronic structure, it is shown that the Laplace transform can serve as a generator for a sum-of-products (SOP) form that allows one to write essentially any function of distance between two particles (i.e. any central force potential) as an exact two-body matrix. In particular, exact expressions for the Coulomb, Yukawa and long-range Ewald two-body operators are evaluated in a band-limited (Sinc function) basis. The resultant exact, full-basis, SOP representations for these interaction potentials – acting in conjunction with an external harmonic confining field – are validated via comparison with energy eigenstate solutions obtained via an independent calculation based on separation of variables. The new two-body matrix representations may have substantial impact in any of the many disciplines in which pair-wise central force interactions are relevant – especially, electronic structure and dynamics.     

Remove Degeneracy in Relativistic Symmetries for Manning-Rosen Plus Quasi-Hellman Potentials by Tensor Interaction

The relativistic Dirac equation under spin and pseudo-spin symmetries is investigated for Manning-Rosen plus quasi-Hellman potentials with tensor interaction. For the first time we consider the Hulthen plus Yukawa for tensor interaction. The Formula method is used to obtain the energy eigen-values and wave functions. We also discuss about the energy eigen-values and the Dirac spinors for the Manning-Rosen plus quasi-Hellman potentials for the spin and pseudo-spin symmetry with Formula method. To show the accuracy of the present model, some numerical results are shown in both pseudo-spin and spin symmetry limits.     

Approximate Analytical Solutions of Dirac Equation with Spin and Pseudo Spin Symmetries for the Diatomic Molecular Potentials Plus a Tensor Term with Any Angular Momentum

Approximate analytical solutions of the Dirac equation are obtained for some diatomic molecular potentials plus a tensor interaction with spin and pseudospin symmetries with any angular momentum. We find the energy eigenvalue equations in the closed form and the spinor wave functions by using an algebraic method. We also perform numerical calculations for the Pöschl-Teller potential to show the effect of the tensor interaction. Our results are consistent with ones obtained before.     

Λ-binding to nuclear matter in the fermi hypernetted chain approximation

The Fermi hypernetted chain technique (FHNC) has been extended to the problem of calculating the Λ-binding to nuclear matter. By using graphical techniques and considering the Λ-particle as an impurity, cluster expansions for ΛN and NN distribution functions have been obtained in terms of irreducible graphs. Topological analyses of the graphs have been made to obtain hypernetted chain equations for the two distribution functions for state-independent ΛN and NN correlation factors. Calculations are carried out for the Λ-binding energy including the rearrangement energy terms by employing central, state-independent and spin-averaged hard-core ΛN potentials. Results are in direct contradiction to the reaction matrix results as well as the empirical estimates.     

Deuteron form factors for the Nijmegen potentials

The deuteron form factors and tensor polarizations in elastic ed scattering are considered for four versions of the Nijmegen nucleon-nucleon potentials. The numerical deuteron wave functions in these potentials are approximated by a series of Gaussian functions with the result that it can be used in any computations of integrated characteristics. The quality of this approximation of the wave function is exemplified by comparing the results that it produces for the momentum distributions, the quadrupole moment, the D-state probability, and the deuteron radius with the results of the corresponding precise calculations.     

Correlated hyperspherical-harmonic expansion for three-nucleon systems

The hyperspherical-harmonic-expansion method is applied to solve the Schrödinger equation for a three-particle system interacting via central spin-dependent potentials. The convergence of the expansion has been improved by multiplying the hyperspherical basis by an appropriate correlation factor, chosen as a product of one-dimensional functions fixed by means of a two-body Schrödinger equation. The results obtained for three nucleons interacting via the Malfliet-Tjon potential are in close agreement with those given by the most accurate methods.     

Variational calculations of ν8 models of nuclear matter

We report variational calculations of ν8 models of nuclear matter which contain central, spin, isospin, tensor and spin-orbit potentials. These semi-realistic models can explain the nucleon-nucleon scattering in 1S0, 3S1?3D1, 1P1 and 3P2?3F2 states up to ～ 300 MeV. The variational wave function has two-body central, spin, isospin, tensor and spin-orbit correlations. The terms in the cluster expansion of the energy expectation value, that do not contain the spin-orbit correlations are summed by chain summation techniques developed for the ν6 models. Of the terms containing spin-orbit correlations, the two-body and three-body-separable ones are calculated, and the magnitude of the rest is estimated. Results for three phase-equivalent ν8 models, which differ significantly in the strength of tensor and spin-orbit potentials, are reported. They suggest that simple ν8 models may not be able to simultaneously explain the binding energy and density of nuclear matter.     

Nucleon-nucleon potentials and regge poles. II. Reggeon exchange potentials

We derive and discuss in detail a connection between the low-energy nucleon-nucleon potentials and reggeon exchanges. In particular explicit relations between coupling constants and form factors of one-boson-exchange amplitudes and Regge residues are given. Besides the traditional one-boson-exchange potentials we also obtain new contributions to the potentials which come from the J = 0 components of the Pomeron and tensor meson trajectories. In the central potential these extra contributions are repulsive and this could provide a partial explanation for the need of soft or hard cores in semi-phenomenological and some of the one-boson-exchange models.     

Relativistic symmetry of position-dependent mass particle in Coulomb field including tensor interaction

The spatially-dependent mass Dirac equation is solved exactly for attractive scalar and repulsive vector Coulomb potentials including a tensor interaction under the spin and pseudospin symmetric limit. Closed forms of the energy eigenvalue equation and wave functions are obtained for arbitrary spin-orbit quantum number κ. Some numerical results are given too. The effect of the tensor interaction on the bound states is presented. It is shown that the tensor interaction removes the degeneracy between two states in the spin doublets. We also investigate the effects of the spatially-dependent mass on the bound states under the conditions of the spin symmetric limit in the absence of tensor interaction.     

Multipole expansion of non-local coupling potentials for cluster transfer and application to 16O(16O, 12C)20Ne

When the transfer of clusters and the symmetrization (antisymmetrization) of scattering wave functions is described by cluster models within the coupled-channel formalism, non-local coupling potentials arise. We suggest a procedure to calculate these potentials by a multipole expansion of all potentials and wave functions which depend on sums of vectors. The expansion coefficients are found by least-squares fit. The method is applied to the ¹⁶O(¹⁶O, ¹²C)²⁰Ne reaction, which is treated in the cluster model with two inert ¹²C- and α-clusters as constituents.