The effect of three-body cluster energy on LOCV calculation for hot nuclear and neutron matter

Abstract

The two-body correlation functions, obtained in a lowest-order constrained variational calculation for hot nuclear and neutron matter, with the Reid potential and the explicit inclusion of (1234), are state averaged and used to calculate the three-body cluster energy. The three-body cluster energy is found to vary between about 1 and 2 MeV through and beyond twice the nuclear-matter saturation density for temperatures between 5 and 20 MeV. However, the inclusion of a three-body cluster reduces the nuclear-matter flashing and critical temperatures. A critical temperature of 15.8 MeV and a critical exponent of 0.35 is found. The results of entropy calculations are in good agreement with experimental prediction and other theoretical results. Finally it is shown that by allowing an explicit (1234) degree of freedom through the Reid potential up to and including the three-body clusters, the lowest-constrained variational calculation yields other nuclear-and neutron-matter properties close to the available semi-empirical and experimental data at zero and finite temperatures.

The Bethe Homework Problem for Hot Neutron Matter in the Static Fluctuation Approximation

“…Neutron matter was studied at both zero and finite temperatures by several groups using different techniques [17][18][19][20][21][22][23]. Our results are, by and large, consistent with those works.…”

“…In addition, the lowest-order constrained variational (LOCV) method was used [20,21] to investigate both neutron and nuclear matter. The pressure was studied [20] at different values of temperature as a function of density, using the modified Reid potential.…”

“…These authors find that the pressure increases with increasing density and temperature, which is in agreement with our results. The effect of three-body cluster energy on the thermodynamic properties was also studied [21]. Even with this additional contribution, there is still good Fig.…”

Lowest-order constrained variational calculation forβ-stable matter at finite temperature

“…In a series of papers the lowest order constrained variational (LOCV) method has been developed [3][4][5][6][7][8] for calculating the properties of homogeneous nuclear fluids with realistic nucleon-nucleon interaction. This approach has been further generalized to include more sophisticated interactions such as the V 14 [8], the AV 14 and the new argonne AV 18 [8] as well as the Reid [3] and ∆-Reid [3] potentials.…”

“…Despite this agreement for model problems, there has been some dispute about convergence of LOCV results in calculation employing realistic nucleon-nucleon interactions which are strongly spin-dependent and which, in particular, contain a sizeable tensor force. This argument was tested by us by calculating the energy of the three-body cluster contribution in nuclear matter and the normalization integral < ψ | ψ > both at zero and finite temperature [4,7].…”