Subsidiary conditions and variational calculations of nuclear and neutron matters

The energy of nuclear and neutron matter is calculated within the framework of the variational approach including the contribution from three-body clusters. Two types of constrains for the two-body correlation function and realistic S-wave forces are used. It is shown that the energy strongly depends upon the type of constraint and that the variational calculation may lead to much more energy than the lowest order Brueckner theory calculations.     

Cluster-variational calculations for extended nuclear systems

The energy as a function of density is calculated for neutron matter and for symmetrical nuclear matter, based on Jastrow trial wave functions. The energy expectation value is truncated in low cluster order. A detailed analysis of the two- and three-body cluster contributions and a special portion of the four-body contribution is given. Variation of a parameterized two-body correlation function is subjected to constraints designed to confine the trial wave function to the domain corresponding to rapid cluster convergence. Results are presented for a variety of model central potentials containing hard cores, for different sets of constraints, and for two- and three-parameter correlation functions. Calculations constrained by the “average Pauli condition” are found to yield results very close to those constrained by the “normalization” or “unitarity” condition, and the two-parameter correlation function appears to be quite adequate. The convergence of the cluster expansion, as reflected in the low orders, is good except at the highest densities considered. The three-body cluster contribution displays, in all cases, a remarkable internal cancellation between its “two-correlation-line” addends.     

The properties of nuclear matter at zero and finite temperatures

The properties of nuclear matter are studied in the frame of the Brueckner theory. The Brueckner-Hartree-Fock approximation plus two-body density-dependent Skyrme potential which is equivalent to three-body interaction are used. Various modern nucleon-nucleon potentials are used in the framework of the Brueckner-Hartree-Fock approximation, e.g.: CD-Bonn potential, Nijm1 potential, and Reid 93 potential. These modern nucleon-nucleon potentials fit the deuteron properties and are phase shifts equivalent. The equation of state at T = 0, pressure at T = 0, 8, and 12 MeV, free energy at T = 8 and 12 MeV, nuclear matter incompressibility, and the symmetry energy calculation are presented. The hot properties of nuclear matter are calculated using T ²-approximation method at low temperatures. Good agreement is obtained in comparison with previous theoretical estimates and experimental data, especially at low densities.     

Symmetry energy,unstable nuclei and neutron star crusts

We present an upgraded review of our microscopic investigation on the single-particle properties and the EOS of isospin asymmetric nuclear matter within the framework of the Brueckner theory extended to include a microscopic three-body force. We pay special attention to the discussion of the three-body force effect and the comparison of our results with the predictions by other ab initio approaches. Three-body force is shown to be necessary for reproducing the empirical saturation properties of symmetric nuclear matter within nonrelativistic microscopic frameworks, and also for extending the hole-line expansion to a wide density range. The three-body force effect on nuclear symmetry energy is repulsive, and it leads to a significant stiffening of the density dependence of symmetry energy at supra-saturation densities. Within the Brueckner approach, the three-body force affects the nucleon s.p. potentials primarily via its rearrangement contribution which is strongly repulsive and momentum-dependent at high densities and high momenta. Both the rearrangement contribution induced by the three-body force and the effect of ground-state correlations are crucial for predicting reliably the single-particle properties within the Brueckner framework.     

On the relation between Brueckner theory and Jastrow theory of nuclear matter

The two- and three-hole-line contributions to the ground state energy as calculated from Brueckner theory are derived from a cluster expansion followed by variation of the trial function. The implications of that derivation both for Brueckner theory and for Jastrow theory are worked out in detail. It is argued that the Jastrow theory is able to give simpler methods to calculate the ground state energy which may be of the same accuracy as current Brueckner calculations. It is shown that the single-particle potential of Brueckner theory is intimately related to a subsidiary condition used in the variation of the trial function. The main steps which have to be taken in a derivation of the general hole-line expansion from Jastrow theory are indicated. It is shown that the hole-line expansion is not a cluster expansion in the sense of Jastrow theory, and an interpretation is given of the “self-consistent choice” of the single-particle potential advocated in Brueckner theory.     

Three-body force effect on the properties of nuclear matter under the gap and continuous choices within the BHF approach

We have calculated and compared the three-body force effects on the properties of nuclear matter under the gap and continuous choices for the self-consistent auxiliary potential within the Brueckner-Hartree-Fock approach by adopting the Argonne V₁₈ and the Bonn B two-body potentials plus a microscopic three-body force (TBF). The TBF provides a strong repulsive effect on the equation of state of nuclear matter at high densities for both the gap and continuous choices. The saturation point turns out to be much closer to the empirical value when the continuous choice is adopted. In addition, the dependence of the calculated symmetry energy upon the choice of the self-consistent auxiliary potential is discussed.     

Effect of three-body interaction on hot asymmetric nuclear matter

The properties of hot asymmetric nuclear matter are studied in the framework of the finite temperature Brueckner－Hartree－Fock theory that is extended to include the contribution of microscopic three-body forces. We give the variation of the critical temperature with the asymmetry parameter and show the effect brought by this three-body repulsive potential on the value of the critical asymmetry of the phase transition for asymmetric nuclear matter. Owing to the additional repulsion provided by three-body forces, this value decreases. In addition, the domain of mechanical instability for hot nuclear matter is also indicated, which gradually shrinks with increasing asymmetry and temperature.     

Three-body force effect on the properties of nuclear matter underthe gap and continuous choices within the BHF approach

We have calculated and compared the three-body force effects on the properties of nuclear matter under the gap and continuous choices for the self-consistent auxiliary potential within the Brueckner-Hartree-Fock approach by adopting the Argonne V₁₈ and the Bonn B two-body potentials plus a microscopic three-body force (TBF). The TBF provides a strong repulsive effect on the equation of state of nuclear matter at high densities for both the gap and continuous choices. The saturation point turns out to be much closer to the empirical value when the continuous choice is adopted. In addition, the dependence of the calculated symmetry energy upon the choice of the self-consistent auxiliary potential is discussed.     

压缩氦原子团簇Hen（n＝3，4，5）排斥势及其多体展开分量计算

 采用Lowdin方法计算了处于压缩状态的氦原子团簇He_n（n＝3，4，5）的排斥势及其多体展开分量。发现随原子数目或压缩度增大，多体展开式的收敛性变差。多体展开式中两体势分量、四体势分量为正值，三体势分量和五体势分量为负值。因此，在进行近似处理时，两体近似法计算的排斥势偏高。经三体修正后的排斥势必然偏低。该计算结果与最新的实验结果定性符合。发现四体势和五体势分量对高密度氦状态方程仍然具有重要贡献。     

A cluster-variational investigation of static density waves in nuclear matter

A detailed comparison of the energy of the uniform phase and of phases exhibiting periodic density fluctuation is presented for extended nuclear systems. The short-range correlations are taken to be of Jastrow type and the calculations are carried through two-body cluster order. With semi-realistic central potentials containing hard cores, no energetic advantage of a non-uniform state is detected, either in symmetrical nuclear matter or in pure neutron matter. However, the analysis gives useful information on the conditions favoring an instability of the homogeneous phase and points to the essential role of the tensor force in the formation of spin-(isospin-) density waves.     

Transformation of a Three-Body Interaction into a Sum of Pairwise Potentials: Application to the Quark-String-Junction and the Urbana Potentials

A transformation of a three-body potential into a sum of two-body potentials is derived. It is applied to the quark-string-junction potential, which becomes the sum of three linear potentials, and to the three-body part of the Urbana nuclear potential. Received October 4, 1996; revised February 16, 1997; accepted for publication June 20, 1997     

Accumulation of three-body resonances above two-body thresholds

We calculate resonances in the three-body system with attractive Coulomb potential by solving homogeneous Faddeev-Merkuriev integral equations for complex energies. The equations are solved using the Coulomb-Sturmian separable expansion method. This approach allows us to study the exact behavior of the three-body Coulomb systems near the threshold. A negatively charged positronium ion is used as a test case. In addition to locating all previously known S-wave resonances of the positronium ion, we also find a large number of new resonant states that accumulate just slightly above the two-body thresholds. The pattern of accumulation of resonant states above the two-body thresholds suggests that probably they are infinite in number. We conjecture that this may be a general property of the three-body system with an attractive Coulomb potential.     

Effect of three-body cluster on the healing properties of the Jastrow Correlation function

A variational equation for the Jastrow Correlation function is derived from the energy functional expanded up to three-body cluster terms. The asymptotic behaviour of this nonlinear equation is studied. The solutions show a healing at least of the type cos(tαr)/r ². The influence of higher cluster contributions is studied. Finally, it is discussed, how one can reduce the many-body cluster contributions to healing conditions to be used in the two-body cluster treatment.     

Jastrow-type calculations for nuclear matter with the normalization condition

Results are given of constrained Jastrow calculations for the energy per particle and the density of nuclear matter using the test potentials IY and OMY-6, as well as several others, and various correlation functions involving parameters. The constraint chiefly employed is the normalization condition in first order, a condition naturally entering the Jastrow formalism. The energy in the minimization is approximated by the first two and in some cases by the first three terms of its FIY cluster expansion. In addition to the three-body terms in the FIY expansion, the corresponding terms of the AHT expansion are also calculated for comparison. From the computations which were performed it seems that, at least in some cases, the normalization condition constitutes a quite satisfactory constraint, leading to reliable results, when used in low order calculations. In addition, conclusions are drawn as to the sensitivity of the results to the constraint, correlation function and minimized energy expression.     

Model Study of Three-Body Forces in the Three-Body Bound State

The Faddeev equation for the three-body bound state with two- and three-body forces is solved directly as three-dimensional integral equation. The numerical feasibility and stability of the algorithm, which does not employ partial wave decomposition is demonstrated. The three-body binding energy and the full wave function are calculated with Malfliet-Tjon-type two-body potentials and scalar two-meson exchange three-body forces. For two- and three- body forces of ranges and strengths typical of nuclear forces the single-particle momentum distribution and the two-body correlation function are similar to the ones found for realistic nuclear forces.     

Computation of some thermodynamics, transport, structural properties, and new equation of state for fluid methane using two-body and three-body intermolecular potentials from molecular dynamics simulation

Molecular dynamics simulation has been performed to obtain pressure, radial distribution function, and self-diffusion coefficient of fluid methane using one site OPLS (optimized potentials for liquid simulations), five sites OPLS-SITE, and two-body HFD (Hartree-Fock dispersion)-like potentials. To take higher-body forces into account, three-body potential of Hauschild and Prausnitz (1993) has been used with the two-body HFD-like potential. The significance of this work is that the three-body potential of Hauschild and Prausnitz extended as a function of density and temperature and used with the HFD-like potential to improve the prediction of the results of pressure of fluid methane without requiring an expensive three-body calculation. The molecular dynamics simulation of methane has been also used to determine a new equation of state. The results are in a good agreement with experimental and theoretical values.     

三体核力重排项的同位旋效应

在同位旋相关的Brueckner理论框架内, 研究了三体核力重排贡献对同位旋对称势及其动量相关性和密度依赖性的影响，特别是研究了三体核力重排效应对于非对称核物质中质子和中子有效质量同位旋劈裂的影响. 结果表明: 三体核力重排效应对质子和中子单核子势均具有排斥性，而且其贡献随动量和密度增加而迅速增大. 在低密度区域，三体核力重排贡献对同位旋对称势的影响相当小，然而随着密度的升高，三体核力重排效应的贡献显著增强. 在高密度区域，三体核力重排效应使得同位旋对称势明显增大，而且当密度足够高时，三体核力重排贡献甚至导致对称势的动量相关性质发生改变. 三体核力的重排效应对核子有效质量同位旋依赖性的影响是使高密度丰中子核物质中质子-中子有效质量同位旋劈裂的幅度显著减小.     

Spinodal instabilities of asymmetric nuclear matter within the Brueckner–Hartree–Fock approach

We study the spinodal instabilities of asymmetric nuclear matter at finite temperature within the microscopic Brueckner–Hartree–Fock (BHF) approximation using the realistic Argonne V18 nucleon–nucleon potential plus a three-body force of Urbana type. Our results are compared with those obtained with the Skyrme force SLy230a and the relativistic mean field models NL3 and TW. We find that BHF predicts a larger spinodal region. This result is a direct consequence of the fact that our Brueckner calculation predicts a larger critical temperature and saturation density of symmetric nuclear matter than the Skyrme and relativistic mean field ones. We find that the instability is always dominated by total density fluctuations, in agreement with previous results of other authors. We study also the restoration of the isospin symmetry in the liquid phase, i.e., the so-called isospin distillation or fragmentation effect, finding that its efficiency increases with increasing proton fraction and decreases as temperature and density increase. In general, we find that the Brueckner results are comparable to those obtained with the Skyrme and the relativistic mean field models, although the restoration of isospin symmetry is not so efficient in this case.     

Ground state baryons in the non-relativistic quark model

We analyse the properties of the ground state bayons in the non-relativistic quark model. The three-body problem is solved by means of the hyperspherical expansion. We consider various two-body potentials of power law type and also a three-body linear potential. In displaying the results, we insist on quantities like ratios of splittings which are scale independent and are functions only of the power of the potential and of the ratio of quark masses.     

Low Energy D(p, p)D Elastic Scattering Including Coulomb Force

The motivation of this paper is to obtain the three-body amplitudes for the Coulomb potential plus a nuclear force in momentum space. Not only the two-body off-shell nuclear amplitude but also the two-body off-shell Coulomb amplitude is important in the three-body calculation. For calculating the Coulomb amplitude, the modified Coulomb potential whose Fourier transformation is analytically equivalent to the pure configuration space Coulomb potential, is introduced. In addition, the decisive screening range parameter is also utilized instead of the screening range. The modified Coulomb potential plus the parameter is called decisive modified Coulomb potential. The three-body proton-deuteron elastic scattering is calculated by using the proper two-body off-shell amplitude for the decisive modified Coulomb potential.