Bound-state calculations of the three-dimensional Yakubovsky equations with the inclusion of three-body forces

The four-body Yakubovsky equations in a three-dimensional approach with the inclusion of the three-body forces are proposed. The four-body bound state with two- and three-body interactions is formulated in the three-dimensional approach for identical particles as a function of vector Jacobi momenta, specifically, the magnitudes of the momenta and the angles between them. The modified three-dimensional Yakubovsky integral equations are successfully solved with the scalar two-meson exchange three-body force, where the Malfliet-Tjon-type two-body force is implemented. The three-body force effects on the energy eigenvalue and the four-body wave function, as well as accuracy of our numerical calculations are presented.     

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。     

Universality in Four-Boson Systems

We report recent advances on the study of universal weakly bound four-boson states from the solutions of the Faddeev-Yakubovsky equations with zero-range two-body interactions. In particular, we present the correlation between the energies of successive tetramers between two neighbor Efimov trimers and compare it to recent finite range potential model calculations. We provide further results on the large momentum structure of the tetramer wave function, where the four-body scale, introduced in the regularization procedure of the bound state equations in momentum space, is clearly manifested. The results we are presenting confirm a previous conjecture on a four-body scaling behavior, which is independent of the three-body one. We show that the correlation between the positions of two successive resonant four-boson recombination peaks are consistent with recent data, as well as with recent calculations close to the unitary limit. Systematic deviations suggest the relevance of range corrections.     

Relativistic analysis of four-body final states

The constraints of unitarity and analyticity on four-body final states are studied. It is shown that unitarity alone forces the amplitudes to be coherent and have singular behaviour. The implementation of unitarity with total energy analyticity yields a set of relativistic linear integral equations for the four-body amplitude. This is the minimal set consistent with quantum mechanics and also is the full dynamical set of equations with two-body separable interactions. These equations will provide important ingredients for the phenomenological analysis of four-body final states using the isobar model.     

Optimized Lower Bound for Four-Body Hamiltonians

Generalizing a method elaborated for three-body systems, we derive a new lower bound on four-body ground-state energies in terms of two-body binding energies in the unequal-mass case. For simple power-law potentials, this bound is compared to variational calculations and is shown to be very close to the exact result. In particular, it gives the exact answer for harmonic interactions. Received November 6, 1997; accepted in final form February 6, 1998     

Universality in Four-Body Scattering

The four-body system is studied in the limit of large two-body scattering length by solving momentum-space integral equations for the transition operators or, alternatively, configuration-space equations for wave function. A number of universal results for atom-trimer and dimer?Cdimer scattering observables are found. We furthermore address the question whether the universal four-body systems contain additional states besides the known two S-wave states.     

The isovector monopole vibration: Coulomb energies,breaking of charge symmetry and effects from α-particle correlation in the nuclear surface

Correlations involving four particles, which can be visualized as itinerant α-particles, can occur with some probability (which is hard to estimate) in the nuclear surface, as has been discussed innumerable times. We point out in this note that such clustering would lead to a small four-body effective force, which could have important effects in the Coulomb energy difference of mirror nuclei, and in the isovector isotope shift. This four-body force is viewed as a force additional to that coming out of Brueckner-Bethe type G-matrix calculations. If one used it literally, which is probably not justified — as we discuss — one would get into serious trouble with the two-body spectra, such as the spectrum of ⁴²Ca. If one uses it circumspectly, one still gets into some trouble, as Zamick has pointed out, but the trouble does not seem to be serious.     

Universality of Short-Range Nucleon-Nucleon Correlations in Nuclei

We investigate the short-range correlations in light nuclei. The highly correlated many-body states are obtained with an explicitly correlated basis which enables us to get a precise solution of a many-body Schrödinger equation for a realistic interaction. We show two-body density distributions for the different spin-isospin channels calculated from three- and four-body states to investigate the short-range correlations between nucleon pairs. At distances below 1 fm a universal behavior is found which does not depend on the many-body states. The universality is also seen in high momentum components of the two-body momentum distributions.     

多体作用对氦原子团簇He9压缩特性的贡献

 采用Lowdin方法计算了处于压缩状态的氦原子团簇He₉体心立方向型的排斥势及其多体分量，并由此计算出团簇微观压强及其多体分压强。结果发现，多体作用对氦原子团簇He₉压缩特性贡献较大。在相同体积下，由两体近似方法计算的体系压强比多原子体系实际压强偏高10%~30%；考虑三体分压强修正后，近似理论的计算值又会偏低1.5%~10%；只有同时考虑三体、四体修正后，近似理论计算值与实际多原子体系的压强值基本一致。团簇He₉所表现出的压缩特性与固态氦的实验结果相符合。     

四体相互作用对固氦压缩特性的贡献

运用从头计算自洽场方法和原子团簇理论计算了高压下固氦原子间的四体势分量.计算结果表明四体分量对结合能的贡献为正；随着压缩度增大四体势的贡献比例变大.采用两体、三体、四体势和Aziz吸引势计算固氦零温状态方程并与实验测量相比较，结果表明两体势对固氦的压缩性贡献了过多的正效应，加入三体分量的修正，仅在低于10GPa时理论值与实验值相符很好，但考虑了四体势修正后能将理论值与实验值符合程度提高到 27GPa. 关键词： 状态方程 固氦 四体势 从头计算     

Rearrangement Collisions between Four Identical Particles as a Four-Body Problem

Nuclear reactions between composite particles with rearrangement processes are considered. The cluster model is used in describing the structure of the nuclei. With this structure we have in the initial channel as well as in the final channel, four interacting particles. These reactions are studied as a four-body problem. The scattering amplitudes are approximated by using a separable expansion for the separable potential model. The four-body equations are reduced to integral equations in the form of exact effective two-particle Lippmann-Schwinger equations. These equations are solved by standard methods in a form suitable for numerical calculations. The present four-body treatment is applied calculating the differential cross-sections for different scattering and transfer nuclear reactions. Distorted wave Born approximation calculations are used in calculating the angular distributions. The present theoretical calculations are in good agreement with the experimental angular distributions.     

Neutron Resonances in Systems of Few Nuclei and Their Possible Role in Radiation of Overdense Stars

Exact analytical solutions of three- and four-body systems made of one light particle and other heavy particles have been obtained in the model of Born?COppenheimer approximation with two-body separable interactions. In the case of neutron scattering on a subsystem of few fixed nuclei the appearance of new resonance quantum states has been shown as well as their dependence on distances between heavy nuclei. The applications of new phenomena to overdense stars radiation are considered.     

Four-body problem and BEC-BCS crossover in a quasi-one-dimensional cold fermion gas

The four-body problem for an interacting two-species Fermi gas is solved analytically in a confined quasi-one-dimensional geometry, where the two-body atom-atom scattering length a(aa) displays a confinement-induced resonance. We compute the dimer-dimer scattering length a(dd) and show that this quantity completely determines the many-body solution of the associated BEC-BCS crossover phenomenon in terms of bosonic dimers.     

A variational approach to distribution function theory

We present a novel formalism for the generation of integral equations for the distribution functions of fluids. It is based on a cumulant expansion for the free energy. Truncation of the expansion at theKth term and minimization of the resulting approximation leads to equations for the distribution functions up toKth order.The formalism is not limited to systems with two-body interactions and does not require the addition of closure relations to yield a complete set of equations. In fact, it automatically generates superposition approximations, such as the Kirkwood three-body superposition approximation or the Fisher-Kopeliovich four-body one.The conceptual approach is adapted from the cluster variation method of lattice theory.     

Alpha clusters in nuclei with 41 ≦ A ≦ 45

The effect of pairing and surface α-clustering structure was studied by means of a Hamiltonian with pairing and four-body interaction terms in a simple two-level model in odd nuclei with 41 ≦ A ≦ 45. It was shown that the dynamical α-structures can be induced by the pairing correlation alone, but with an unusually large value of the strength G of the pairing interaction. The addition of a small four-body interaction term allowed us to diminish the G-value to a physically reasonable one and, at the same time, to get meaningful α-clustering. The four-body term added to the Hamiltonian is a simplified way to improve, in this respect, the two-body pairing interaction (itself a simplified model interaction). For example, in the ground state of ⁴⁵Ti the “α-clusters” appeared with larger probability than that for separate nucleons, while in ⁴⁵Ca both probabilities are approximately equal. The calculated binding energy was also applied to reproduce the experimental difference of the masses of neighbouring nuclei. With the eigenstates of the Hamiltonian, schematic spectroscopic factors for two-nucleon transfer, α-transfer, and elastic scattering of α-particles were also calculated. Spectroscopic factors for the transitions from ground state to ground state and from ground state to excited state were then used to distinguish between superfluid or normal behaviour of these nuclei. In addition to the superfluidity induced by pairing forces, a superfluidity due to four-body correlations was also predicted.     

B decays to baryons

From inclusive measurements, it is known that about 7% of all B mesons decay into final states with baryons. In these decays, some striking features become visible compared to mesonic decays. The largest branching fractions come with quite moderate multiplicities of 3?C4 hadrons. We note that two-body decays to baryons are suppressed relative to three- and four-body decays. In most of these analyses, the invariant baryon?Cantibaryon mass shows an enhancement near the threshold. We propose a phenomenological interpretation of this quite common feature of hadronization to baryons.     

Baryonium and the four-body problem

A stochastic variational method is used to solve the Schrödinger equation for the non-relativistic $\text{qq}\text{q}\text{q}$ system. The quarks are considered as interacting with the two-body one-gluon exchange potential and a linear four-body confining potential. The mass spectrum for the non-strange baryonium states is predicted, and a preliminary estimate made for the strength of the coupling of M-baryonium states to T-baryonium. The stability of baryonium states with respect to decay into mesons is investigated.     

The Painlevé Property for Quasihomogenous Systems and a Many-Body Problem in the Plane

We investigate a many-body problem in the plane introduced by Calogero and intensively studied by Calogero, Françoise and Sommacal. An ad hoc complexification transforms the many-body problem to a system of second order autonomous complex equations depending on some complex constants that describe the two-body interactions. We investigate the sets of two-body interaction constants that make the complexified equation have the Painlevé Property, this is, its solutions are given by single-valued meromorphic functions. In this case the original system has only periodic isochronous solutions. We exhibit a family of settings where the system displays this property and show that it is not present in the three- and four-body problems that do not fall within our class. For this, we introduce a necessary condition for the presence of the Painlevé Property in some quasihomogenous systems.     

Several versions of the integro-differential equation approach to bound systems

We find that a single two-variable integro-differential equation, which includes all two-body correlations, produces results for three- and four-body bound systems in good agreement with those obtained with the most accurate methods and also that for sixteen fermions, interacting by means of local Wigner-type potentials our results agree with those obtained with the Variational Monte-Carlo and the Fermi-Hypernetted chain methods.This equation includes a hypercentral potential. When it is set equal to zero it reduces to theS-state projected potential version of the formalism, which for three nucleons is identical to the exact Faddeev equation forS-state projected potentials.We show that the inclusion of the hypercentral component of the two-body local potential, which operates on all orbitals, takes the effect of the higher partial waves largely into account without the need of solving a system of coupled integro-differential equations. We, furthermore, show that by using the Weight-Function Approximation our integro-differential equation is transformed into a simple inhomogeneous differential equation, which becomes accurate forA16.The major advantages of our approximate method are, firstly, that unlike the exact Faddeev-Yakubovsky and Alt-Grassberger-Sandhas equations or the Monte-Carlo methods, it does not become rapidly unmanageable, but even simplifies with increasingA and, secondly, the speed and simplicity of our numerical calculations.     

Four-body adiabatic model applied to elastic scattering

Elastic scattering of a projectile, composed of three clusters, from a spherical target is analysed using a four-body adiabatic model. The model is a generalisation of the three-body adiabatic model of Johnson and Soper. Calculations of the elastic scattering of ¹¹Li from ¹²C are compared to both experimental data and the results of recent four-body eikonal model calculations.