Lowest-order Constrained Variational Calculation Research Articles

LOCV calculation for nuclear and neutron matter with the Nijmegen potential

The lowest order constrained variational (LOCV) formalism is formulated for the Nijmegen soft-core potential, which is fitted by the proton-proton (pp) scattering phase shift. The calculations are performed for the equation of state (EOS) of both nuclear and neutron matter. The state-dependent correlation functions are calculated by the minimization of two-body cluster energy, and the resulting Euler Lagrange equations are solved for this kind of potential. It is shown that LOCV calculations can work with this kind of interaction as well as other interactions in configuration space. The state-dependent correlation functions are calculated by minimization of two-body cluster energy for each channel with various JLSTMT, by using Nijmegen interaction. The correlation functions are compared with those coming from UV14 interaction in LOCV formalism. It is shown that unlike UV14, AV14, and AV18 potentials, the binding energy obtained from Nijmegen in the LOCV framework is −16.81 MeV that is close to the experimental value. Finally, it is recognized our LOCV results with Nijmegen interaction are similar to calculations with different interactions and different many-body methods.

LOCV calculation of the equations of state and properties of rapidly rotating neutron stars

In this paper, we have investigated the structural properties of rotating neutron stars using the numerical RNS code and equations of state which have been calculated within the lowest order constrained variational (LOCV) approach. In order to calculate the equation of state of nuclear matter, we have used UV14 +TNI and AV18 potentials. We have computed the maximum mass of the neutron star and the corresponding equatorial radius at different angular velocities. We have also computed the structural properties of Keplerian rotating neutron stars for the maximum mass configuration, MK, RK, fK and .

Comparative study of the LOCV and the FHNC approaches for the nucleonic matter problem

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

In order to have an effective two-nucleon potential based on the microscopic many-body calculations with a bare phenomenological nucleon–nucleon potential for the heavy-ion scattering calculations, the lowest order constrained variational (LOCV) method for the symmetric nuclear matter is applied to obtain the direct and the exchange parts of the averaged effective two-body interactions (AEI). The Reid68, the Reid68-Δ, and the Av18 interactions are used as the input phenomenological potentials. Then, it is tried to decompose the AEI into a radial and a density-dependent parts, such that the fitted LOCV AEI potentials give the same equation of state for the nuclear matter as the exact LOCV calculations. The results are compared with the various density-dependent M3Y potentials. It is shown that the direct and the exchange parts of the LOCV AEI with different input potentials are reasonably in agreement with each other and besides the different behaviors of their direct terms at small relative distances (<0.6 fm), they also roughly have the same magnitude as the direct parts of those of M3Y potentials. However, in contrast to the M3Y interaction, the exchange parts of the LOCV AEI have completely different behavior, i.e. their density dependence rises with increasing density. Finally, it is concluded that, since the direct and exchange parts of the LOCV AEI are constructed based on the many-body calculations with the phenomenological nucleon–nucleon potential, they are specially more trustable for the nucleus–nucleus collision calculations, in which the double-folding model is applied.

The nucleonic matter LOCV calculations in a periodic box versus the FHNC method

Abstract The lowest order constrained variational ( LOCV ) method is reformulated for a fixed number of nucleons in a period box ( PBLOCV ) with the inter-nucleon interactions such as the Bethe homework potential, v B , and the scalar ( v 4 ) part of the Argonne interaction ( A v 8 ′ ) c ( 4 ) . The two-body cluster approximation is used in the ( PB ) LOCV formalism to obtain the energy per particle subjected to the normalization constraint for an infinite (a finite) number of nucleons. It is shown that our ( PB ) LOCV results are reasonably consistent with those of Fantoni and Schmidt (Periodic-Box) Fermi HyperNetted Chain ( ( PB ) FHNC ) calculations. In addition, unlike the thermodynamic limit, it is found that the normalization constraint in the periodic box is not exactly satisfied. However, it is realized that, by increasing the number of particles, the value of normalization constraint in the periodic box improves. Therefore, the two-body cluster approximation in the PBLOCV method becomes more reliable in the larger periodic boxes than the smaller ones. On the other hand, the PBLOCV energy per particle approaches the corresponding LOCV prediction for the large number of particles. The anisotropic behavior of the PB two-body distribution function, which is one of the main point of this report, is discussed. Finally, it is found that the PBLOCV results, i.e. the total (two-body cluster) energy and the normalization constraint, similar to the PBFHNC calculations depend on the number of particles in the periodic box and this dependence principally becomes negligible for the large number of particles.

The in-medium nn cross section and the transport properties of neutron matter using the LOCV effective two-body interaction

Abstract In order to calculate the in-medium neutron–neutron (nn) differential cross section and the transport properties of the pure neutron matter, the lowest order constrained variational (LOCV) method is applied to obtain the effective nucleon–nucleon (NN) interactions from the various bare realistic phenomenological NN interaction. The wide range of potentials, such as the Reid 68 , the Δ - Reid 68 , the V 8 ′ and the Av 18 are used as the input phenomenological interactions. The approach, based on the effective NN interaction, allows for a consistent description of the neutron matter and the nucleon–nucleon scattering in the nuclear medium. In this work, by using the above LOCV effective NN interactions, beside the nn differential cross section, the related quantities such as the shear viscosity and the thermal conductivity of the pure neutron matter, which are the important gradient for the stellar structure, are calculated within the Landau–Abrikosov–Khalatnikov (LAK) formalism. It is shown that, while the density dependence of effective mass are not important, the choice of in-medium effective interaction has crucial rule on the resulting nn differential cross section as well as the shear viscosity and the thermal conductivity of pure neutron matter. Finally, our above LOCV calculations are compared with those predicted by the other theoretical methods.

Lowest-order constrained variational calculation of asymmetric nuclear matter in a strong magnetic field

In the present work we study asymmetric nuclear matter in the presence of strong external magnetic fields using the lowest-order constrained variational (LOCV) method with the AV${}_{18}$ potential and employing a microscopic point of view. According to our results, the induced phase transition to antiferromagnetic states occurs for asymmetric nuclear matter in a strong magnetic field.

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

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 {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.

Ground state of heavy closed shell nuclei: An effective interaction and local density approximation approach

We study the ground-state properties of heavy closed-shell nuclei such as {sup 48}Ca, {sup 90}Zr, {sup 120}Sn, and {sup 208}Pb as well as {sup 4}He, {sup 16}O, and {sup 40}Ca. Similar to our recent work, the local density approximation in the harmonic oscillator basis and different channel-dependent effective two-body interactions that are generated through the lowest-order constrained variational calculation for asymmetric nuclear matter with the Reid68Day, Reid68, and {delta}-Reid68 potentials are used. Unlike nuclear matter, it is shown that Reid68 potential gives ground-state binding energies closer to the experimental data with respect to the {delta}-Reid68 potential and there is not much difference between Reid68 and Reid68Day potentials, which have been define up to J=5. The different channel-dependent effective interactions (J>2) and one- and two-body density distribution functions are discussed and they are compared with the results of other approaches such as the Brueckner local density approximation, correlated basis function, variational fermion hypernetted chain, variational cluster Monte Carlo, Brueckner-Hartree-Fock, fermionic molecular dynamics, and coupled cluster. Finally it is concluded that the three-body force (isobar degrees of freedom) is very important for light (heavy) nuclei because in the most of recent many-body calculations, it is observed that the available two-body nuclear forcesmore » usually underbind light nuclei and overbind heavy nuclei and nuclear matter.« less

Lowest Order Constrained Variational Calculation for Nuclear and Neutron Matter with a New Charge-Dependent Reid Potential

The lowest order constrained variational (LOCV) method is reformulated to calculate the equation of state of nuclear and neutron matter with a new charge-dependent Reid potential (Reid93). The state-dependent correlation functions are calculated by performing a full functional minimization for each JLSTM T -channel and the resulting Euler Lagrange equations are solved up to J = 9. The correlation functions are compared with those coming from LOCV calculation with the old Reid68 potential. It is shown that unlike ∆-Reid68 and AV18 interactions, the new Reid93 over binds nuclear matter at much larger saturation density than Reid68. Finally, the results are being compared with similar calculations with other potentials and many-body techniques.

LOCV calculation for the uniform electron fluid at finite temperature

The free energy of the homogeneous electron fluid at finite temperature is obtained using the lowest order constrained variational (LOCV) method. In order to test the convergence of cluster expansion series the three-body cluster terms are calculated with the LOCV correlation functions. The results agree reasonably with those of Monte Carlo, coupled-cluster, perturbational expansion etc, techniques at zero temperature. The flashing and critical temperatures as well as the critical exponent are found to be about 0.6, 1.3 eV and 0.384 respectively. A similar liquid-gas phase transition to that of nuclear matter and liquid He3 is observed.

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

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 , 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 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.

Modified LOCV Calculations for Normal and Fully Spin-Polarized Liquid 3 He

In a comparative study between recent interaction models, a modified lowest-order constrained variational (LOCV) approach is used to obtain results for normal and fully spin-polarized liquid 3 He. With a truncated energy expansion, correlation functions are optimized by adjusting the healing conditions on a Jastrow two-body wave function. Using the HFDHE2 model, results of such modifications are consistent with FHNC/S results. At 0.0164 A −3 , our results with the HFD-B2 model are −2.46 K and −2.13 K, respectively, for the ground-state binding energy.

LOCV calculation of nuclear matter with phenomenological two-nucleon interaction operators

The lowest-order constrained variational (LOCV) method is developed for the wide range of phenomenological two-nucleon interaction operators such as , and U potentials. The calculation is performed for both nuclear and neutron matter with the state-dependent correlation operators. The validity of our lowest-order approximation is tested by calculating the three-body cluster energy with the state-averaged correlation functions. It is shown that while the three-body cluster energy improves the nuclear matter saturation density, the LOCV method still overbinds nuclear matter with the above potentials. Finally, we find that our LOCV results are similar to those calculations which have been performed by using more sophisticated many-body techniques.

Lowest-order constrained variational calculation for hot asymmetric nuclear matter

The method of lowest-order constrained variational that reasonably predicts the nuclear matter saturation data is used to calculate the equation of state of asymmetric nuclear matter at finite temperature. The Reid soft-core potential with and without the N - interaction, which fits N - N scattering data, is taken as the nuclear Hamiltonian. The calculation is performed for a wide range of density, asymmetry parameter and nuclear temperature, which are of interest in heavy-ion collisions and astrophysics. Beside spin, isospin, total angular momentum and density dependence of the correlation functions, they are also arranged to depend on the temperature and asymmetry parameter of the system. The free energy, pressure, effective mass etc of asymmetric nuclear matter are calculated. It is shown that while the calculated symmetry coefficient defined in the semi-empirical mass formula is roughly constant and is near its empirical value at zero temperature, it depends on the proton-to-neutron ratio at finite temperature. Finally, the dependence of the liquid - vapour phase transition, as well as the effective mass dependence on the temperature and asymmetry parameter, is investigated.

The effect of the N-N interaction on pion condensation in neutron matter

The influence of an isospin-dependent N-N interaction on the critical density for pion condensation is considered. The authors use the technique of lowest-order constrained variational calculations to predict the influence of a realistic N-N interaction on the properties of pion-condensed neutron matter, including the explicit allowance for N*(1236) excitations in intermediate states in the 1S0 channel in the N-N potential. They find a reduction in the critical density, but an increase in the energy density for high densities compared with that obtained using a pure neutron matter potential energy.

LOCV calculations with a self-consistent treatment of isobars

The results of a series of lowest-order constrained variational calculations for various nucleon fluids are presented. The calculations are based upon the Reid soft-core potential (1968) and allow in a self-consistent fashion for the explicit excitation of a nucleon into an N*(1234) state via a recent transition potential proposed by Green, Niskanen and Sainio (1978). For nuclear matter a binding energy of 16 MeV per nucleon is obtained at a saturation density 0.25 N fm-3. The compressibility of nuclear matter is calculated to be 300 MeV. From a study of asymmetric matter a symmetry coefficient of 33 MeV is obtained. It is found that the inclusion of N*'s in beta-stable matter leads to a suppression of the proton abundance at high densities.

Constrained variational calculations for finite nuclei

The technique of lowest-order constrained variational calculations used by the authors to study the bulk properties of homogeneous, quantal fluids (1978) is extended for use in discussing the ground-state properties of finite nuclei. The significance of various constraints in finite systems is discussed. It is shown that the saturating effects of explicit allowance for N*(1234) excitations is essential if the calculations are to yield sensible binding energies and RMS radii. Specific application is made to the light closed-shell nuclei 4He, 12C and 16O.