Binding and saturation of nuclear matter by the reference-spectrum method (original) (raw)

The problem of lambda-particle binding in nuclear matter

Nuclear Physics B, 1968

Extensive variational calculations of the binding energy of a A particle to nuclear matter are performed in the framework of the Jastrow method, assuming velocity-independent two-body potentials. All cluster contributions of zeroth and first order in the cluster expansion of the expected A binding energy B A are evaluated. (The total zeroth-order contribution is the sum of all two-body terms; the total first-order contribution, the sum of all three-body terms plus special four-body terms.} Truncated versions of B A which include first-order contributions are maximized with respect to parameters in the nucleon-A correlation factor. The resulting cluster convergence appears very satisfactory in all cases. For the most refined spin-dependent effective central nucleon-A potentials (fitting the data on s-shell hypernuclei and A-p scattering} the theoretical lower limits obtained exceed empirically determined upper limits on the A binding energy by about a factor two.

The binding energy of a Λ-particle in nuclear matter: A comparison of two formulations

Nuclear Physics B, 1970

Two approaches to the problem of calculating the binding energy BA of a A-particle in nuclear matter are discussed. The first method is via the Bethe-Goldstone equation for the problem in the independent-pair approximation. The second method is a Green-function formulation which sums the ladder diagrams for the self-energy of the A-particle. Using an S-wave separable potential fitted to the AN scattering data, exact analytic expressions for BA are found for both methods and compared. The relation between the two approaches is discussed and it is shown how to extend the Green-function formulation to include the effect of the higher-order cluster diagrams, contributing to the A-particle self-energy, in a consistent manner. It is pointed out that this approach provides a more systematic formulation than the usual extended Bethe-Goldstone approach. The model AN hard core problem is also investigated in the Green function approach in an appendix: the ground-state energy is rederived and expressions are found for the effective mass and damping of the A-quasi-particle up through terms of order (kFa)2.

Single particle spectrum and binding energy of nuclear matter

Physics Letters B, 2000

In non-relativistic Brueckner calculations of nuclear matter, the self-consistent single particle potential is strongly momentum dependent. To simplify the calculations, a parabolic approximation is often used in the literature. The variation in the binding energy value introduced by the parabolic approximation is quantitatively analyzed in detail. It is found that the approximation can introduce an uncertainty of 1-2 MeV near the saturation density.

A variational approach to nuclear matter with realistic potentials

Nuclear Physics A, 1977

matter, pravtous~y proposed by the passant authors, is eateaded to treat the stronj tenwr force components of realistic NN potential. Numerical a+ecults are jives for three early poteadal of Gammel, ChristiansadThaler, sad reasonable aja+eementlfoundwhh a pmviouscalcalatioa of Rictij, Tar Louw sad Clark which inchded three-body cluster contrtbutio~to the eaerjy. A rangeof flue potential jivlnjj~ood flta to them~perimental two-body NN data is also studied, sad bindinj anerjiea of typically 22 MeV per nueleoa at saturation deanities coranspondinj to kr se 1 .6-1 .7 fm'', are found. For three of the potentials oomidesed, comparieoa is made with the recast results of PaadhsrIpeade and Wirinja, which include the eontributiona to the aletjy from all of the moat cijniflcant many-body closters, and msoellent ajaeamant is found. It l sujjested that e~xpücit inctodoa of some of the nejlected internal dejreee of freedom of the nucteoms, such u the possibility of m~citadon to d(123~states, caijht brinj the equilibrium nuclear matter resuhs clover to the i values.

Approximate Calculation of Nuclear Binding Energy

Physical Review, 1960

The binding energy, size, and shape of finite nuclei are studied using a method which tests the "local uniformity" assumption. This assumption implies that the properties of finite nuclei can be obtained from those of infinite nuclear matter. The energy is computed using as a trial wave function an amplitude-and frequency-modulated plane wave; this permits the use of nuclear-matter results in a straightforward manner. The calculation gives a binding energy which is too low, a radius which is too small, and a nuclear surface which is too diffuse. Several possible corrections to this result are examined.

Nuclear binding energy and symmetry energy of nuclear matter with modern nucleon–nucleon potentials

2011

The binding energy of nuclear matter at zero temperature in the Brueckner-Hartree-Fock approximation with modern nucleonnucleon potentials is studied. Both the standard and continuous choices of single particle energies are used. These modern nucleon-nucleon potentials fit the deuteron properties and are phase shifts equivalent. Comparison with other calculations is made. In addition we present results for the symmetry energy obtained with different potentials, which is of great importance in astrophysical calculation.

Comparative study of three-nucleon potentials in nuclear matter

Physical Review C, 2012

A new generation of local three-body potentials providing an excellent description of the properties of light nuclei, as well as of the neutron-deuteron doublet scattering length, has been recently derived. We have performed a comparative analysis of the equations of state of both pure neutron matter and symmetric nuclear matter obtained using these models of three-nucleon forces. None of the considered potentials simultaneously explains the empirical equilibrium density and binding energy of symmetric nuclear matter. However, two of them provide reasonable values of the saturation density. The ambiguity concerning the treatment of the contact term of the chiral inspired potentials is discussed.