State-dependent calculation of three-body cluster energy for nuclear matter and the validity of the lowest order constrained variational formalism

Abstract

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 -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.

The effect of density dependent Av18 effective interaction on the ground state properties of heavy closed shell nuclei

“…But the inclusion of the three-body force and the isobar degrees of freedom ( -Reid68) [10,28,29,45,46] have improved the behavior of Coester line to the right direction [10,45,46]. For the convergence of LOCV [39,40] formalism and comparison of our result on nuclear matter with other many-body techniques, see Tables I and II of our works in [49][50][51].…”

“…But still, a reliable many-body technique and a true NN potential are needed to predict the results close the empirical nuclear matter properties. In several of our previous works it has been shown that the application of lowest order constrained variational method (LOCV) [28][29][30][31][32][33][34][35][36][37][38][39][40], to the different realistic phenomenological NN potentials [1][2][3][4][5][6][7][8][9][10][11][12], gives substantially too much binding and large saturation density than the empirical one. During the last three decades, situation has been the same for other techniques [10,[41][42][43][44][45][46][47][48] and potentials [1][2][3][4][5][6][7][8][9][10][11][12].…”

The LOCV averaged two-nucleon interactions versus the density-dependent M3Y potential for the heavy-ion collisions

“…The two-body correlation operators, f (ij), which depend on the density, are defined as follows [21,34]: where for nuclear matter, as we pointed out before, α = {J LST } and the explicit form of V α (r, ρ) and a α (r, ρ) for Reid type and Av 18 potentials are given in Refs. [24][25][26][27]. The shapes of the above density-dependent effective interactions as well as the corresponding state-dependent versions can be found in the various works of Modarres et al [21][22][23][24][25][26][27][28].…”

“…A (S) is anti-symmetrizing (symmetrizing) operator [19][20][21][22][23][24][25][26]. In the cluster expansion technique [33], the expectation value of Hamiltonian of A-body system is written as:…”

“…The validity of LOCV method, as well as its applications to the nuclear matter and the finite nuclei, have been fully discussed in the works of Owens et al [19,20] and Modarres et al [21][22][23][24][25][26][27][28]. The LOCV effective two-body interactions have been tested by calculating the properties of the light and the heavy closed shell nuclei [25][26][27], and recently it was used to calculate the in-medium nn cross section and the transport properties of neutron matter [29,30].…”