An essentially exact many body calculation for muonic molecular ions and exotic coulombic systems

The L = 0 bound states and the structural properties of muonic molecular ions and exotic nuclear molecular ions are calculated by a hyperspherical harmonics expansion method, which is an essentially exact method for three-body systems. We examine the convergence rate of this method and also examine its crucial dependence on the mass ratio ? (ratio of the masses of similar to dissimilar particles). An a priori criterion for the rate of convergence and the required size of the expansion basis for a predetermined precision have been suggested. Our calculation reveals the cluster type of structure of these systems.     

Ab initio shell model calculations with three-body effective interactions for p-shell nuclei

We present a qualitative improvement of the ab initio no-core shell model (NCSM) approach by implementing three-body interaction capability for p-shell nuclei. We report the first calculations using three-body effective interactions derived from realistic nucleon-nucleon potentials for 6Li, 8Be, and 10B and demonstrate that the use of three-body effective interactions speeds up the convergence of the NCSM approach. For 10B, we predict JpiT = 1(+)0 ground state, contrary to the experimental observation of 3(+)0, when the AV8(') potential is used, indicating the need for true three-body forces.     

Reduced adiabatic hyperspherical basis in the Coulomb three-body bound state problem

A new version of the adiabatic hyperspherical approach (AHSA) is suggested which has significant advantages for the calculation of three-body states with total angular momentumJ> 0. The binding energies of all bound states of mesic molecules with normal parity are calculated by the suggested method. Comparison with results of variational calculations and the fast convergence of the method confirm its high efficiency.     

Investigation of halo structure of 6He by hyperspherical three-body method

Hyperspherical harmonics expansion method is applied to a three-body model of two neutron halo nuclei. Convergence of the expansion has been ensured. A repulsive part is introduced in the interaction between the core and the extra-core neutron, to simulate Pauli principle. Two neutron separation energy, r.m.s. radii, correlation factor and probability density distributions have been calculated for ⁶He. It is found that the convergence of the two neutron separation energy is relatively slow, while other quantities reach convergence quickly.     

The orthogonal projection method in scattering theory

This work gives a detailed account of the orthogonal projection method in the theory of two- and three-body scattering, which is based on the employment of orthogonal projecting pseudopotentials. The method is applied to a number of physical problems, of which the following the most important: the improvement of convergence and the rearragement of Born series to make them convergent at low energies in the presence of bound states in a system, as well as the consideration of the Pauli exclusion principle in the scattering of composite particles and in the integral theory of direct nuclear reactions. The properties of eigenvalues of kernels of the equations obtained are investigated and the conditions for the convergence of their iterations are derived. For the three-body problem, the general case of three different particles is considered, as well as two particular cases, namely, two particles in the field of a heavy core and three identical particles. The proven theorems are illustrated by numerical examples. Other useful applications of the proposed approach are listed and discussed, in particular, those in solid-state physics and in the theory of electromagnetic transitions. The approach suggested is compared with those of the other authors and the prospects of using the developed formalism are discussed.     

A three-body model of the <Superscript>11</Superscript>B nucleus

The binding energy and the rms charge and mass radii have been calculated in terms of the single-channel three-body ⁴He⁴He³H model of the ¹¹B nucleus with an expansion of the three-body wave function in a nonorthogonal Gaussian basis. Parameters of the wave function are presented and convergence of the three-body energy depending on the number of expansion terms is demonstrated.     

Low-Energy Proton-Deuteron Scattering in Configuration Space

 A new method for solving the configuration-space Faddeev equations for elastic p-d scattering below the deuteron-breakup threshold is described. Numerical solutions that demonstrate the convergence and accuracy of the method are given. The number of channels and the value of the matching radius required to obtain an accurate solution are also investigated. These calculations demonstrate that this method can efficiently solve the large matrix equations required for the three-body scattering problem. Received April 23, 2001; accepted for publication June 7, 2001     

Lowest order constrained variational method applied to liquid $^\mathsf{3}$He

The energy of normal liquid ³He is obtained using the lowest order constrained variational (LOCV) method. In order to test the convergence of the cluster expansion series, the three-body cluster energy is calculated, with the LOCV correlation functions, and by imposing the normalization constraint on the two-body distribution function which includes three-body cluster correlations (LOCVE). It is shown that the normalization constraint plays an important role in keeping the higher cluster terms small. The resulting LOCVE calculation for the ground state energy of liquid ³He is compared with the available experimental data and the prediction from different theoretical techniques.Received: 26 May 2003, Published online: 30 January 2004PACS: 61.20.Gy Theory and models of liquid structure - 61.20.Ne Structure of simple liquids - 67.55.-s Normal phase of liquid ³He     

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.     

Three-Potential Formalism for the Atomic Three-Body Problem

Based on a three-potential formalism we propose mathematically well-behaved Faddeev-type integral equations for the atomic three-body problem and describe their solutions in Coulomb-Sturmian space representation. Although the system contains only long-range Coulomb interactions these equations allow us to reach a solution by approximating only some auxiliary short-range potentials. We outline the method for bound states and demonstrate its power in benchmark calculations. We can report a fast convergence in angular-momentum channels. Received September 30, 1997; accepted in final form January 23, 1998     

An exact treatment of some integrals appearing in the three-body contributions to transport coefficients

The convergence properties of the integral corresponding to the three-body cyclic collisions in the two-dimensional density expansion of transport coefficients are investigated. It is shown exactly that the integral considered by Oppenheim et al. and by Eu diverges logarithmically in the switching parameter ε.     

Application of the method of moments to three-body scattering

The method of moments is investigated as a possible iterative method of solution of the Faddeev equations. The method is shown to converge rapidly to the three-body wave function for the case of zero energy neutrons scattering off deuterium. It is suggested that the method should be appropriate for the treatment of three-body break-up with separable or local potentials.     

Operation of the Faddeev Kernel in Configuration Space

We present a practical method to solve Faddeev three-body equations at energies above the three-body breakup threshold as integral equations in coordinate space. This is an extension of a previously used method for bound states and scattering states below three-body breakup threshold energy. We show that breakup components in three-body reactions produce long-range effects on Faddeev integral kernels in coordinate space, and propose numerical procedures to treat these effects. Using these techniques, we solve Faddeev equations for neutron-deuteron scattering to compare with benchmark solutions.     

计及两体和三体作用下的二维凝聚体中的孤子特性

使用多重尺度法,解析地研究计及粒子间两体和三体同时作用下二维凝聚体中孤子的特性. 结果发现,当凝聚体粒子间两体作用为排斥、三体作用为吸引时,凝聚体内会产生暗孤子环,且随着三体吸引作用的减弱,暗孤子环中心峰的高度逐渐降低,并当三体吸引作用消失时暗孤子环演化为一个完美的二维暗孤子. 当两体和三体作用均为排斥时,凝聚体中的暗孤子的宽度和幅度随着三体排斥作用的加强而减小,且当三体作用强度增加到与两体作用同一数量级时,凝聚体产生坍塌现象. 关键词： 玻色-爱因斯坦凝聚体 两体和三体作用 暗孤子     

Faddeev calculations on lambda hypertriton with potentials from Gel'fand-Levitan-Marchenko theory

Effective lambda-proton and lambda-neutron potentials, restored from theoretical scattering phases through Gel'fand-Levitan-Marchenko theory, are tested on a lambda hypertriton through three-body calculations. The lambda hypertriton is treated as a three-body system consisting of lambda-proton, lambda-neutron and proton-neutron subsystems. Binding energy and root mean square radius are computed for the ground state of lambda hypertriton (${J}^{\pi }=1/{2}^{+}$). In coordinate space, the dynamics of the system is described using a set of coupled hyperradial equations obtained from the differential Faddeev equations. By solving the eigenvalue problem derived from this set of coupled hyperradial equations, the binding energy and root mean square matter radius computed are found to be −2.462 MeV and 7.00 fm, respectively. The potentials are also shown to display a satisfactory convergence behaviour.     

Faddeev-Noble Versus Sasakawa-Sawada Equations for the Nuclear Three-Body Coulomb Problem

We compare the efficiency of two Faddeev-type approaches for the nuclear three-body Coulomb problem. The first one is a modification of Noble’s approach, the second one is due to Sasakawa and Sawada. In an integral-equation formulation both of these methods rely on the same Green’s operators and driving terms. The differences lie in the treatment of the long-range Coulomb potentials. Numerical examples show that the modified Faddeev-Noble approach provides for faster convergence.     

耦合腔系统中的三体纠缠演化

研究由耦合腔和四个全同的二能级原子构成的系统中三体纠缠态纠缠量的演化. 四个原子分别囚禁在单模耦合腔A和B中, 并且原子通过单光子跃迁与腔场发生共振相互作用. 采用纠缠张量方法, 通过数值计算研究了每个腔中三体纠缠的演化. 讨论了原子与腔场间的耦合强度对三体纠缠演化的影响. 研究结果表明: 原子与腔场间的两体纠缠强于原子间的两体纠缠, 每个腔中的三体纠缠是两体纠缠相干叠加的结果.     

Three-body inverse scattering problem

Two methods are suggested to reconstruct three-body potentials from three-body scattering data. This was achieved by using the reduction of the corresponding Schrödinger equation to a system of ordinary differential equations (not integro-differential equations as usual in the direct problem). Exactly solvable three-body models are presented. A new simple method for solving the multi-dimensional inverse problem in a finite-difference approximation is considered in the Appendix.     

High-pressure equation of state for solid krypton from interatomic potentials

The pressure-volume isotherm for krypton at 300 K is evaluated by the Monte Carlo method using pair and three-body potentials. The pair potentials used are that of Aziz and Slaman and a slightly modified version of their potential which gives better agreement with high-energy scattering data. The three-body potentials considered are the Axilrod-Teller interaction and the first-order three-body exchange interaction as parametrized by Loubeyre. The results are compared with recent measurements at pressures up to 300 kbar and the implications of the comparison are discussed. The best agreement with experiment is found using the Axilrod-Teller interaction as the only many-body interaction, indicating that the three-body exchange interaction is to a large extent canceled by higher many-body interactions, at least in the highly symmetrical environment of the crystal.This paper is dedicted to Howard Reiss on the occasion of his 66th birthday.