It is shown that the method of lowest order constrained variational (LOCV) which is based on the cluster expansion theory is a reliable many-body technique to calculate the nuclear matter equation of state. In this respect, the state dependent correlation functions and the effective interactions which have been produced by the LOCV calculation with the Reid and \ensuremath{\Delta}-Reid soft core interactions are used to estimate the size of higher order cluster terms such as the effect of three-body cluster energy on the nuclear matter ground state energy. Finally it is shown that the LOCV normalization constraint plays a major role in the convergence of the cluster expansion and the result of LOCV calculation can be as good as more sophisticated approaches which go beyond lowest order.
It is shown that the method of lowest order constrained variational (LOCV) which is based on the cluster expansion theory is a reliable many-body technique to calculate the nuclear matter equation of state. In this respect, the state dependent correlation functions and the effective interactions which have been produced by the LOCV calculation with the Reid and \ensuremath{\Delta}-Reid soft core interactions are used to estimate the size of higher order cluster terms such as the effect of three-body cluster energy on the nuclear matter ground state energy. Finally it is shown that the LOCV normalization constraint plays a major role in the convergence of the cluster expansion and the result of LOCV calculation can be as good as more sophisticated approaches which go beyond lowest order.
It is shown that the method of lowest order contrained variational (LOCV) which is based on the cluster expansion theory is a reliable many-body technique to calculate the nuclear matter equation of states. In this respect the state-dependence correlation functions and effective interactions which have been produce by LOCV calculation with the Reid Soft Core and Δ-Reid interactions are used to estimate the size of higher order cluster terms such as the effect of three body cluster energy in nuclear matter. We find that the three-body cluster energy is less than 1 MeV beyond the nuclear matter saturation density and it has weaker density dependence than our previous calculation with the state-averaged coorrelation functions and effective interactions. Finally, we conclude that the LOCV method is good enough to calculate other propertiesn of quantal fluids.
The nucleonic matter problem is investigated by comparing the lowest order constrained variational ( LOCV ) method with the Fermi hypernetted chain ( FHNC ) theory, emphasizing the role of the LOCV correlation functions. In this way, the central correlation functions are used in the LOCV formalism, for the Bethe homework problem. It is shown that the LOCV computations reasonably agree with those of FHNC . Moreover, the FHNC calculations are performed with the LOCV correlation functions. It is found that, assuming the LOCV or the parametrized correlation functions, the FHNC computations do not change significantly. So, one may conclude that the mentioned consistencies refer to the choice of the LOCV correlation functions. Because, the contribution of the many-body cluster terms can be ignored, if the LOCV correlation functions satisfy the normalization constraint. Then, using the AV 18 interaction, the operator-dependent ( OD ) correlation functions are employed in the LOCV calculations. Note that the LOCV OD correlation functions are obtained by averaging over the states. It turns out that the overall behaviour of the LOCV OD correlation functions are similar to those of FHNC . Although, due to the many-body effects which are considered in the FHNC calculations, the LOCV results fairly differ from those of FHNC . Finally, it is worth mentioning that, unlike the recent FHNC calculations, the spin-orbit-dependent correlation functions are included in the LOCV approach.
The free energy of an alpha particle is calculated using the local density approximation in the harmonic oscillator basis. The effective two-body interactions are generated from the lowest order constrained variational (LOCV) calculation for nuclear matter at finite temperature, with the Reid and Δ-Reid potentials. The FermiDirac distribution is used to calculate the entropy and the occupation probability of each state of alpha particle at a given temperature. The effective mass is treated as a variational parameter. Our zero temperature results with the Δ-Reid interaction agree well with the experimental saturation data of alpha particle and the other many-body techniques. The flashing temperature of ≈5 MeV is found, which is consistent with experimental evidence. It is concluded that a similar liquidgas phase transition to that of nuclear matter is most probable in the alpha particle and heavier nuclei. PACS Nos.: 21.65+f, 21.10-k, 21.10Dr, 21.60-n
The properties of hot symmetric nuclear matter for a wide range of densities and temperatures are investigated by employing the AV14 potential within the lowest order constrained variational (LOCV) method with the inclusion of a phenomenological three-body force as well as relativistic corrections. The relativistic corrections of many-body kinetic energies as well as the boot interaction corrections are presented for a wide range of densities and temperatures. The free energy, pressure, incompressibility, and other thermodynamic quantities of symmetric nuclear matter are obtained and discussed. The critical temperature is found, and the liquid-gas phase transition is analyzed both with and without the inclusion of three-body forces and relativistic corrections in the LOCV approach. It is shown that the critical temperature is strongly affected by the three-body forces but does not depend on the relativistic corrections. Finally, the results obtained in the present study are compared with other many-body calculations and experimental predictions.
A lowest-order constrained variational (LOCV) method, with modified conditions of healing on the two-body Jastrow wave function, is investigated in calculations for the ground-state energy levels of many-body spin-polarized atomic deuterium. Results are obtained for the , and phases, corresponding to equal occupations of one, two or three nuclear spin states. Estimates for the optimum healing conditions are obtained by comparison of LOCV results with current Monte Carlo benchmarks. The nature of the phases, i.e., quantum gas or quantum liquid, is discussed, the energy of the phase in our calculations always occurring above the gas-liquid interphase for healing conditions within a physically acceptable range.
The (extended) lowest order constrained variational ((E) LOCV) method was used to calculate the ground state energy of liquid helium 3 (3He) droplets at zero temperature. Different types of density distribution profiles, such as the Gaussian, the Quasi-Gaussian and the Woods-Saxon were used. It was shown that at least, on average, near 20 3He atoms are needed to get the bound state for 3He liquid droplet. Depending on the choice of the density profiles and the atomic radius of 3He, the above estimate can increase to 300. Our calculated ground state energy and the number of atoms in liquid 3He droplet were compared with those of Variational Monte Carlo (VMC) method, Diffusion Monte Carlo (DMC) method and Density Functional Theory (DFT), for which a reasonable agreement was found.