Nuclear Matter Effects Research Articles

Three-body forces in nuclear matter

An earlier claim about the smallness of three-body effects in nuclear matter is examined in the light of a criticism. Our conclusion is that, whereas the lowest-order three-body effect is small, second-order effects are larger, with the net result of ≈ 2.5 MeV per particle additional binding at the saturation density. Although these results depend on the way one extrapolates off the pion mass shell, different ways which seem to us to be reasonable give roughly the same result.

Three-Body Effect in Nuclear Matter to All Orders of Perturbation

It is shown that there are three-body clusters in all orders of the Goldstone expansion for the binding energy of nuclear matter and that they converge extremely poorly. A $\ensuremath{\Gamma}$ matrix is defined which, on expansion, is shown to generate this infinite sequence of three-nucleon clusters. It is shown that the $\ensuremath{\Gamma}$ matrix can be evaluated in terms of a three-body correlation function for which a differential equation is derived. Solving this equation leads to the evaluation of $\ensuremath{\Gamma}$. This demonstrates that a finite sum does exist for these cluster diagrams, and gives a method for finding it. Finally, it suggests that for strong short-range potentials it is better to expand the binding energy in powers of the density rather than in powers of the interaction.

Velocity dependent nuclear forces and their effect in nuclear matter

The object of this paper is to investigate whether it is possible to replace the hard core in current nucleon-nucleon potentials by a non-singular but velocity-dependent potential. This is considered in two stages. Firstly, sucho a non-singular velovity-dependent potential is adjusted to fit the experimental phase-shifts in the four states singlet, even and odd, and triplet, even and odd. The results show that a rough fir can be obtained comparable to the Gammel-Thaler fit with hard-core potentials. These data therefore do not offer a sensitive method of distinguishing the two types of potentials. Secondly, the potentials so obtained are used to calculated the energy of infinite nuclear matter by applying ordinary perturbation theory. With first-order perturbation theory it is possible to get saturation at densities in the neighbourhood of the experimental value, but with an energy that is too positive. However, it isshown that the next term in the series, which is always negative, is by no means negligible, and so must also be considered, if an accurate value of the energy is required. Even so, these terms are still sufficiently small to indicate reasonable convergence of the series.

Binding energies of Λ particles and the Λ-N interaction

The implications of Λ-binding energies for the Λ-nucleon interaction have been considered when three-body forces are included in addition to two-body Yukawa forces. In part I the light hypernuclei with baryon number ≦ 5 are considered. For ΛH 3 the effect of three-body forces is small and may be obtained by a perturbation procedure; the binding energy of ΛH 3 being almost entirely determined by the two-body forces. For ΛH 5 the He 4 core is assumed to be undistorted by the Λ. The binding energies of ΛH 4, ΛHe 4 do not seem capable of yielding significant information about the interaction strenghts. The two-body system ΛH 2 is not bound unless the three-body forces are very strongly attractive. In part II the potential felt by a Λ in nuclear matter, this being considered as a Fermi gas, is calculated using perturbation theory. Both direct and exchange two-body forces are considered. The second order contributions, the effect of nuclear pair correlations and the velocity dependence are all small. The nucleon exchange factor used for the three-body forces strongly suppresses their effect in nuclear matter. The implications of ‘empirical’ values of the Λ-potential depth are considered. In particular if the pion-baryon couplings predominate then strongly attractive three-body forces of not too large a range are favoured, corresponding to a larger singlet than triplet two-body volume integral.