Realistic Two-body Forces Research Articles

Maximum mass of neutron stars with a quark core

Massive neutron stars (NS) are expected to possess a quark core. While the hadronic side of the NS equation of state (EOS) can be considered well established, the quark side is quite uncertain. While calculating the EOS of hadronic matter we have used the Brueckner-Bethe-Goldstone formalism with realistic two-body and three-body forces, as well as a relativistic mean field model. For quark matter we employ the MIT bag model constraining the bag constant by exploiting the recent experimental results obtained at CERN on the formation of a quark-gluon plasma. We calculate the structure of NS interiors with the EOS comprising both phases, and we find that the NS maximum masses fall in a relatively narrow interval, $1.45 M_\odot \leq M_{\rm max} \leq 1.65 M_\odot$, near the lower limit of the observational range.

Bandcrossings at high spin: Level interactions and diabolic points

Cranking calculations have been performed for many particles in a deformed single- j shell interacting via realistic two-body forces. Although the particle number is conserved in our problem, it can still be treated as a continuous variable. This allows us to consider the diabolic structure of our hamiltonian, which is important in understanding the two-particle transfer reaction. We also discuss the level interaction which determines whether a system will backbend or upbend. We find an analytic solution for the level interaction strength for small deformations and calculate numerical ones for large deformations. These permit a comparison with other models and a general discussion of the AB interaction strength.

Few-body anharmonic oscillators and the matrix continued fractions

For both identical and distinguishable particles and for an arbitrary polynomial approximation to the realistic two-body forces, the A-body Hamiltonian may be converted into an infinite block-three-diagonal matrix in the properly arranged, translationally invariant, oscillator basis. As a consequence, the exact Green function and all the projections of eigenstates of the microscopic Schrodinger equation become expressible in terms of the matrix continued fractions. This generalises the recent reformulation of the one-dimensional A=1 anharmonic problem by Graffi and Greechi (1975). The quick convergence of this non-perturbative method of solving the many-body bound-state problem is demonstrated for the simplest three- and four-body examples. With the core-possessing type V(r)=-r2+r4 of the spin- and isospin-independent two-body interaction, only the 10-3 error in the three-bosonic ground-state energy arises from restricting the formulae to 5*5 dimensional matrices.

Phenomenological Study of Three-Body Force Based on the Energy Levels of the Alpha-Particle

The contributions of the three· body force to the energies of the alpha-particle are estimated both in the ground state and in the first three T = 0 negative parity (j = 0', 2 -, l' ) excited states. These contributions just correspond to the deviations of the theoretical values of the energies of the alpha-particle, which are obtained with the realistic two-body force only, from the experimental ones not only in the ground state but also in the excited states. From this fact, it is shown that the three-body force is indispensable to reproducing the energies of nuclei with realistic nuclear interactions and that the three-body force may be determined in a phenomenological way. There have been no experimental phenomena which constitute a direct evidence of the nuclear three-body force. In the present paper, it is pointed out that there exists a fact taking the place of such phenomena, and it is shown that rough features of the three-body force such as its strength and type can be deduced. Recently A TMS method 1) has been proposed to solve few-particle systems under realistic two-body interactions. This method is of powerful one. In fact, the method gives the very close upper and lower bound energies of the ground states for three- and four-alpha-particle systems, where the alpha-particles in­ teract through phenomenological inter-particle potential with a strong repulsive part. 2 ) This means that ATMS method can make it possible to solve almost completely these alpha-particle systems. Using this method, wave functions and energy values have been evaluated for the triton and the alpha-particle with several realistic two-body forces. 1),3) We pay attention to the deviations of the theoretical energy values obtained with the realistic two-body force from the experimental ones in the first three T =0 negative parity (j=0-, 2-, r) excited states of the alpha-particle as well as in the ground state. The theoretical value of the ground state energy of the alpha-particle, which is obtained by the use of ATMS method, deviates to a large extent from the experimental one in any case of the realistic two-body forces, and this deviation is considerably large compared with the differences among several theoretical values calculated with different types of the two-body force.

Helium at zero temperature with hard-sphere and other forces

Various theoretical and numerical problems relating to heliumlike systems in their ground states are treated. New developments in the numerical solution of the Schr\"odinger equation permit the solution of 256-body systems with hard-sphere forces. Using periodic boundary conditions, fluid and crystal states can be described; results for the energy and radial-distribution functions are given. A new method of correcting for low-lying phonon excitations so as to extrapolate the energy of fluids to an infinite system is described. A perturbation theory relating the properties of the system with pure hard-sphere forces to those with smoother, more realistic two-body forces is introduced. As in recent work on classical systems the potential is divided into two continuous parts: One is repulsive, one attractive, the latter being treated as a perturbation. The solution for the repulsive part is taken directly from the hard-sphere problem when the radius is identified as the scattering length of the repulsive part of the smooth potential. The convergence for the Lennard-Jones potential is very good. Using our numerical results for the hard-sphere problem, with phonon corrections, together with this perturbation theory, results for energy versus density agree with experiment within our error of (3-10)% except at high crystal densities. We carry further Schiff's recent application of this perturbation theory to ${\mathrm{He}}^{3}$ and conclude that antisymmetrization by the method of Wu and Feenberg is the reason for lack of agreement with experiment in that system.

On the wave functions of spherical odd-mass nuclei

A procedure presented in a previous paper has been generalized in order to describe collective properties of odd-mass nuclei. The problem has been considered first in the general case of fermions interacting by realistic two-body forces. The present classification of low lying states of odd nuclei has been confirmed. The lowest states can be separated in two groups: one-quasi-particle and phonon-particle states. From the general case a schematic model grounded on (pairing+P(2)) forces has been derived and applied to205Pb, in order to study the general features of wave functions.

Nuclear binding energy parameters in terms of realistic two-nucleon-potentials

Effective forces are derived from realistic two-body forces, and renormalizations coming from excitation of closed shells are shown to be important in achieving agreement with empirical binding energies.