An Approximation to the Reaction Matrix in Nuclear Matter

DWE Blatt; BHJ McKellar

doi:10.1071/ph720001

An Approximation to the Reaction Matrix in Nuclear Matter

Australian Journal of Physics ◽

10.1071/ph720001 ◽

1972 ◽

Vol 25 (1) ◽

pp. 1 ◽

Cited By ~ 1

Author(s):

DWE Blatt ◽

BHJ McKellar

Keyword(s):

Nuclear Matter ◽

Hard Core ◽

Reference Spectrum ◽

Nucleon System ◽

Core Potential ◽

Reaction Matrix ◽

T Matrix

It has been shown by Butler et al. that a good approximation to the Bethe-Goldstone wavefunction can be constructed from eigenfunctions of the free two-nucleon system. The approximation is therefore closely related to the T-matrix. In this paper, it is used to derive an approximate G-matrix in terms of the T-matrix. As an illustration of this approach, the resulting approximate G-matrix is compared with the reference spectrum approximation of Bethe, Brandow, and Petschek for the simple case of a pure hard core potential.

MICROSCOPIC OPTICAL POTENTIAL FROM ARGONNE INTER-NUCLEON POTENTIALS

International Journal of Modern Physics E ◽

10.1142/s0218301311020319 ◽

2011 ◽

Vol 20 (11) ◽

pp. 2317-2327 ◽

Cited By ~ 2

Author(s):

DIPTI PACHOURI ◽

MANJARI SHARMA ◽

SYED RAFI ◽

W. HAIDER

Keyword(s):

Binding Energy ◽

Nuclear Matter ◽

Optical Potential ◽

Hard Core ◽

Soft Core ◽

Scattering Data ◽

Test Case ◽

Hartree Fock ◽

Reaction Matrix ◽

Microscopic Optical Potential

In the present work we describe our results concerning the calculation of equation of state of symmetric zero temperature nuclear matter and the microscopic optical potential using the soft-core Argonne inter-nucleon potentials in first order Brueckner–Hartree–Fock (BHF) theory. The nuclear matter saturates at a density 0.228 nucleon/fm 3 with 17.52 MeV binding energy per nucleon for Argonne av-14 and at 0.228 nucleon/fm 3 with 17.01 MeV binding energy per nucleon for Argonne av-18. As a test case we present an analysis of 65 and 200 MeV protons scattering from 208 Pb . The Argonne av-14 has been used for the first time to calculate nucleon optical potential in BHF and analyze the nucleon scattering data. We also compare our reaction matrix results with those using the old hard-core Hamada–Johnston and the soft-core Urbana uv-14 and Argonne av-18 inter-nucleon potentials. Our results indicate that the microscopic potential obtained using av-14 gives marginally better agreement with the experimental data than the other three Hamiltonians used in the present work.

Hard-Core Potential and the Boundary-Condition Model for Nuclear Matter

Physical Review ◽

10.1103/physrev.143.783 ◽

1966 ◽

Vol 143 (3) ◽

pp. 783-789 ◽

Cited By ~ 2

Author(s):

Y. C. Lee ◽

K. W. Wong

Keyword(s):

Boundary Condition ◽

Nuclear Matter ◽

Hard Core ◽

Core Potential ◽

Condition Model ◽

Boundary Condition Model

VELOCITY-DEPENDENT NUCLEON–NUCLEON POTENTIALS AND SATURATION IN NUCLEAR MATTER

Canadian Journal of Physics ◽

10.1139/p64-066 ◽

1964 ◽

Vol 42 (4) ◽

pp. 696-719 ◽

Cited By ~ 18

Author(s):

R. K. Bhaduri ◽

M. A. Preston

Keyword(s):

Wave Function ◽

Nuclear Matter ◽

Short Range ◽

Potential Model ◽

Hard Core ◽

Nucleon Nucleon ◽

Core Potential ◽

Dependent Potential

Recently, nonsingular velocity-dependent potentials have been constructed which fit the the two-nucleon data, but do not give saturation in nuclear matter at reasonable densities. In this paper, we have asked what features a potential should have in order to give saturation, and we have found that the short-range wave-function distortion (defined in the text) is important. Reasons are given for the failure of the earlier potentials to saturate, and a new velocity-dependent potential is proposed which gives results similar to the standard hard-core potential model. We speculate on the usefulness of such potentials for future calculations of nuclear properties.

A remark about regge poles for hard-core potential scattering

Il Nuovo Cimento ◽

10.1007/bf02785566 ◽

1963 ◽

Vol 27 (2) ◽

pp. 550-552

Author(s):

G. Berendt

Keyword(s):

Hard Core ◽

Potential Scattering ◽

Core Potential ◽

Regge Poles

Liquid helium and the properties of a Bose–Einstein gas. III. The density dependence of hard-core models

Canadian Journal of Physics ◽

10.1139/p70-167 ◽

1970 ◽

Vol 48 (11) ◽

pp. 1340-1364

Author(s):

D. F. Goble

Keyword(s):

Density Dependence ◽

Liquid Helium ◽

Hard Core ◽

Ladder Approximation ◽

Model Systems ◽

Coordinate Space ◽

Core Boundary ◽

T Matrix ◽

Bose Einstein ◽

Space Method

We have used the results of a previous paper by Goble and Trainor to compute the density dependence of the hard-core Bose–Einstein gas in the t-matrix ladder approximation, utilizing the coordinate-space method of Brueckner and Sawada as modified by Parry and ter Haar, and the pseudopotential treatment of the hard-core boundary condition presented by Liu and Wong. Various thermodynamic parameters of these model systems are compared with the properties of liquid helium four. The disagreements which are found are shown to be primarily related to differences in the magnitudes of the Landau parameters.

On angular momentum analyticity in hard core potential scattering

Physics Letters ◽

10.1016/0031-9163(63)90281-6 ◽

1963 ◽

Vol 4 (4) ◽

pp. 218-219 ◽

Cited By ~ 5

Author(s):

O. Brander

Keyword(s):

Angular Momentum ◽

Hard Core ◽

Potential Scattering ◽

Core Potential

Hyperspherical approach for the trinucleon system with hard-core potential

Physical Review C ◽

10.1103/physrevc.45.2640 ◽

1992 ◽

Vol 45 (6) ◽

pp. 2640-2647 ◽

Cited By ~ 3

Author(s):

T. K. Das ◽

H. T. Coelho ◽

J. R. A. Torreão

Keyword(s):

Hard Core ◽

Core Potential ◽

Hyperspherical Approach

Soft-Core Model in Nuclear Matter Calculations

Zeitschrift für Naturforschung A ◽

10.1515/zna-1969-0701 ◽

1969 ◽

Vol 24 (7) ◽

pp. 1037-1039

Author(s):

R Kar ◽

M Roy

Keyword(s):

Binding Energy ◽

Nuclear Matter ◽

Soft Core ◽

Core Model ◽

Equilibrium Density ◽

Core Potential ◽

Thomas Fermi ◽

Soft Core Potential

Abstract Using a Thomas-Fermi method developed by KUMAR, LE COUTEUR and ROY 1 , it is shown here that the two-body soft-core potential suggested by KÖHLER and WAGMARE 2 does not give rise to correct binding energy and equilibrium density in nuclear matter calculations.

The 1S0 two-nucleon T matrix and the interior wave function

Canadian Journal of Physics ◽

10.1139/p76-267 ◽

1976 ◽

Vol 54 (22) ◽

pp. 2225-2239 ◽

Cited By ~ 1

Author(s):

R. J. W. Hodgson ◽

J. Tan

Keyword(s):

Wave Function ◽

Nuclear Matter ◽

Symmetric Function ◽

Body Wave ◽

Binding Energies ◽

Strongly Correlated ◽

Scattering Wave ◽

T Matrix

The fully off-shell T matrix is generated from a real symmetric function σ(k,k′) which in turn can be obtained from a knowledge of the two-body wave function in the interaction interior. The resulting T matrices are employed to compute the binding energies of 16O, 40Ca, and nuclear matter. Limiting the two-body wave function to physically acceptable forms limits the allowed σ functions. A 'difference integral' is defined in terms of the two-body scattering wave function, which seems to be strongly correlated with the binding energies.

LORENTZ BOOSTED NUCLEON-NUCLEON T-MATRIX AND THE TRITON BINDING ENERGY

Modern Physics Letters A ◽

10.1142/s021773230900005x ◽

2009 ◽

Vol 24 (11n13) ◽

pp. 804-809 ◽

Cited By ~ 3

Author(s):

H. KAMADA ◽

W. GLÖCKLE ◽

H. WITAŁA ◽

J. GOLAK ◽

R. SKIBIŃSKI ◽

...

Keyword(s):

Binding Energy ◽

Nonlinear Equation ◽

Faddeev Equation ◽

Mass Operator ◽

Nucleon Nucleon ◽

Spin Rotation ◽

Triton Binding Energy ◽

Nucleon System ◽

T Matrix

The phase equivalent relativistic NN potential, which is related by a nonlinear equation to the original nonrelativistic potential, is used to construct the mass operator (rest Hamiltonian) of the 3-nucleon system. Employing the CD Bonn NN potential, the solution of the relativistic 3N Faddeev equation for 3 H shows slightly less binding energy than the corresponding nonrelativistic result. The effect of the Wigner spin rotation on the binding is very small.