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Canadian Journal of Physics

Lowest order constrained variational and local density approximation approach to the hot alpha particle

Majid Modarres, H. R. Moshfegh, Hodjat Mariji

Published Aug 1, 2002• 6 citations
Publisher

Abstract

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 Fermi–Dirac 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 liquid–gas 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

DOI
10.1139/p02-041

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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 Fermi–Dirac 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 liquid–gas 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 AV14A{V}_{14}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.
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 ΔΔΔ-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.
Some properties of polarized neutron matter at finite temperature have been studied using the lowest order constrained variational (LOCV) method with the Argonne V18 (AV18) potential. Our results indicate that a spontaneous transition to the ferromagnetic phase does not occur. Effective mass, free energy, magnetic susceptibility, entropy, and the equation of state of polarized neutron matter at finite temperature are also calculated. A comparison is also made between our results and those of other many-body techniques.
How do protons and neutrons bind to form nuclei?This is the central question of ab initio nuclear structure theory.While the answer may seem as simple as the fact that nuclear forces are attractive, the full story is more complex and interesting.In this work we present numerical evidence from ab initio lattice simulations showing that nature is near a quantum phase transition, a zero-temperature transition driven by quantum fluctuations.Using lattice effective field theory, we perform Monte Carlo simulations for systems with up to twenty nucleons.For even and equal numbers of protons and neutrons, we discover a first-order transition at zero temperature from a Bose-condensed gas of alpha particles ( 4 He nuclei) to a nuclear liquid.Whether one has an alpha-particle gas or nuclear liquid is determined by the strength of the alpha-alpha interactions, and we show that the alpha-alpha interactions depend on the strength and locality of the nucleon-nucleon interactions.This insight should be useful in improving calculations of nuclear structure and important astrophysical reactions involving alpha capture on nuclei.Our findings also provide a tool to probe the structure of alpha cluster states such as the Hoyle state responsible for the production of carbon in red giant stars and point to a connection between nuclear states and the universal physics of bosons at large scattering length.
We present first-principles predictions for the liquid-gas phase transition in symmetric nuclear matter employing both two- and three-nucleon chiral interactions. Our discussion focuses on the sources of systematic errors in microscopic quantum many-body predictions. On the one hand, we test uncertainties of our results arising from changes in the construction of chiral Hamiltonians. We use five different chiral forces with consistently derived three-nucleon interactions. On the other hand, we compare the ladder resummation in the self-consistent Green's functions approach to finite-temperature Brueckner-Hartree-Fock calculations. We find that systematics due to Hamiltonians dominate over many-body uncertainties. Based on this wide pool of calculations, we estimate that the critical temperature is ${T}_{c}=16\ifmmode\pm\else\textpm\fi{}2$ MeV, in reasonable agreement with experimental results. We also find that there is a strong correlation between the critical temperature and the saturation energy in microscopic many-body simulations.