A separable potential model for N-N interaction (II)

A two-term separable potential model for the N-N interaction in ¹S₀, ³S₁?³D₁, ¹D₂, ³D₂, ³D₃, ¹P₁, ³P₀, ³P₁ and ³P₂ partial waves is proposed. Its off-energy-shell behaviour is very similar to that of a local potential.     

Consideration of improper forbidden states in composite particle interaction

An algebraic version of the orthogonality condition model is constructed. The approach is used to solve the problem of exclusion of improper forbidden states that are typical of composite particle interaction. The phase shifts of αα scattering, found for this type of forbidden states, significantly differ from those obtained for forbidden eigenstates.     

Scattering in the attractive Yukawa potential in the limit of strong interaction

Scattering in the attractive screened Coulomb (Yukawa) potential in the limit of strong interaction is investigated. It is shown that the scattering occurs mostly with large angles. The corresponding momentum-transfer cross section is calculated. The results are applied to estimate the ion drag force acting on an isolated micron-sized grain in low-pressure bulk plasmas.     

An interaction potential for heavy-ion scattering

The long-range part of the nucleus-nucleus interaction is taken to be given by folding the density distribution of one nucleus with the real part of the single-nucleon optical potential of the other. Analytic approximations are derived for the folded potential and its derivative in the case where the density distribution and single-nucleon optical potential have Saxon-Woods form factors of equal surface thickness. The approximations are generalised to the case of different surface thicknesses and are compared with a previous parametrisation due to Broglia and Winther. The variation with mass number of the central density of the Saxon-Woods matter distribution required to obtain the correct normalisation is shown to be large and an expression for the variation is given. Some calculations are performed on various elastic scattering data using the “quarter-point recipe” of Frahn's diffraction theory. The parameters required to fit the quarter-points of the elastic cross sections are shown to be consistent with their accepted values. It is shown, however, that the quarter-point recipe leads to a larger radius for ²⁰⁸Pb than for ²³²Th. The positions and heights of the pure Coulomb barrier (L = 0) are evaluated for various nuclei. The barrier radii are found to be sufficiently large to suggest that an interaction of the folded type should be reasonable in this region.     

Statistical mechanics of bosons with attractive interaction

In order to obtain meaningful results for a system of bosons interacting via a potential containing a long-ranged attraction, the coupling of low momentum particles with high momentum particles has to be taken into account. The method of thermal Green’s functions applied to this problem leads to involved graphical calculations even for temperatures close to the absolute zero. It is shown that the problem can be tackled much more simply and profitably by obtaining an effective hamiltonian for low momentum particles in a manner similar to that adopted in the recent renormalisation group approach to critical phenomena. The occurrence of anomalous pairings is avoided by performing suitable Bogolubov transformations. The procedure gives the quasiparticle spectrum besides yielding an explicit expression for the free energy in the low temperature limit. The results agree with those derived by Green’s function methods using partial summations.     

Bound states resulting from interaction of the non-relativistic particles with the multiparameter potential

In this study, we present the analytical solutions of bound states for the Schrodinger equation with the multiparameter potential containing the different types of physical potentials via the asymptotic iteration method by applying the Pekeristype approximation to the centrifugal potential. For any n and l(states) quantum numbers, we derive the relation that gives the energy eigenvalues for the bound states numerically and the corresponding normalized eigenfunctions. We also plot some graphics in order to investigate effects of the multiparameter potential parameters on the energy eigenvalues.Furthermore, we compare our results with the ones obtained in previous works and it is seen that our numerical results are in good agreement with the literature.     

Quantum reflection times for attractive potential tails

When a wave packet with a narrow momentum distribution is quantum reflected in a purely attractive potential proportional to -1/r(alpha), alpha>2, it generally experiences a time gain compared to a free particle reflected at r=0; for alpha=3 and very low energies there are large time delays. In quantum reflection of an atomic beam by a surface, such a time gain (delay) represents an apparent plane of reflection which is shifted in front of (behind) the surface. The quantum reflected wave is always delayed with respect to the classical particle accelerated in the attractive potential.     

The extended law of corresponding states and the interaction potential

An inversion procedure is used to obtain from the extended law of corresponding states the interaction potential over a range of reduced temperature extending from 0.5 to 25. This directly determined potential is in excellent agreement with the Lee potentials in the intermediate region. The consistency between diffusion coefficients and second virial coefficients is checked.     

Catching the PEG-induced attractive interaction between proteins

We present the experimental and theoretical background of a method to characterize the protein-protein attractive potential induced by one of the mostly used crystallizing agents in the protein-field, the poly(ethylene glycol) (PEG). This attractive interaction is commonly called, in colloid physics, the depletion interaction. Small-Angle X-ray Scattering experiments and numerical treatments based on liquid-state theories were performed on urate oxidase-PEG mixtures with two different PEGs (3350 Da and 8000 Da). A “two-component” approach was used in which the polymer-polymer, the protein-polymer and the protein-protein pair potentials were determined. The resulting effective protein-protein potential was characterized. This potential is the sum of the free-polymer protein-protein potential and of the PEG-induced depletion potential. The depletion potential was found to be hardly dependent upon the protein concentration but strongly function of the polymer size and concentration. Our results were also compared with two models, which give an analytic expression for the depletion potential. Received 29 April 2002 RID="a" ID="a"Present address: CRMC2-CNRS, Campus de Luminy, case 913, F-13288 Marseille Cedex 09, France; e-mail: vivares@crmc2.univ-mrs.fr RID="b" ID="b"e-mail: bonnete@crmc2.univ-mrs.fr RID="c" ID="c"Laboratory associated to Universities Aix-Marseille II and III.     

Quantum instability of a Bose-Einstein condensate with attractive interaction

We study the quantum and the mean-field Gross-Pitaevskii (GP) dynamics of a Bose-Einstein condensate gas confined in a toroidal trap. According to GP, if the interatomic interaction is attractive, the rotational states of the system can be dynamically stable or unstable depending on the strength of the mean-field energy. The full quantum analysis, however, reveals that the condensate is always unstable. Quantum fluctuations are particularly important close to the GP stability borderline, even for systems with a relatively large number of condensate atoms.     

Novel magnetic properties of the Hubbard chain with an attractive interaction

The magnetic properties of an attractive Hubbard chain are considered. Based on the Bethe Ansatz equations of the problem, exact analytic expressions are derived for the magnetization and susceptibility. These formulae can be evaluated after solving certain derivatives of the Bethe Ansatz equations. These derivative equations are also given. We give the magnetization and susceptibility curves for several values of the interaction-strength and bandfilling. We find that the susceptibility at the onset of magnetization (at the critical field) isfinite for all bandfillings, except for the cases of half filled and empty bands, and in the limit of vanishing interaction. We argue that the finiteness of the initial susceptibility is due to the fermion-like behavior of the bound pairs. We also give the gap (what is equal to the critical field) and the initial susceptibility as functions of the interaction-strength and bandfilling for the cases of nearly half filled and almost empty bands as a function of the interaction, and in the weak coupling limit as a function of the bandfilling. To our knowledge, this is the first Bethe Ansatz calculation for the gap in this latter limit.     

Exact energy eigenvalues for an attractive Coulomb potential with zero-radius hard core

Following a peratization procedure, the exact energy eigenvalues for an attractive Coulomb potential, with a zero-radius hard core, are obtained as roots of a certain combination of di-gamma functions. The physical significance of this entirely new energy spectrum is discussed.     

Short range behaviour of the N-N potential within the quark Model

The short range behaviour of the nucleon-nucleon (NN) potential is studied in terms of the quark model, where nucleons are assumed to consist of three colored quarks. By considering the overlap kernel of the wave function of the resonating group method (RGM), it is found that the Pauli effect does not produce a ‘hard core’. Instead, the gluon exchange interaction with the confinement requirement suggests a rather soft one. TheΔ-Δ isobar interaction is also considered. In the (S, T) = (3, 3), (3, 2) and (2, 3) channels we find a ‘hard core’, while calculations in some other cases indicate even strong short range attractions.     

Sufficient conditions for the existence of bound states of N particles with attractive potentials

We provide simple sufficient conditions for the existence of a bound state in a system of N particles interacting via a purely attractive two-body potential. Our method is based on a variational approach.     

An energy-independent nonlocal potential model for bound and scattering states

The general expression of the nucleon-nucleus optical potential has been obtained using Watson's multiple scattering theory and Wolfenstein's parametrization of the nucleon-nucleon scattering amplitude. The resulting theoretical potential is nonlocal and consists of an energy-independent central volume plus surface real and imaginary potential and of a Thomas-like spin-orbit term. The analysis has been restricted to N = Z spherical nuclei, so that neither isospin-isospin nor spin-spin interactions have been included. The widely used Perey-Buck, Greenlees, and Watson expressions of the optical potential are easily obtained as particular cases. For practical purposes, the nonlocal potential has been parametrized in the Frahn-Lemmer form, using Woods-Saxon radial form factors, and the equivalent local potential (ELP) has been calculated by a Perey-Buck-like transformation.The ELP has a radial behavior very similar to the original nonlocal one, but the potential depths and radii are energy dependent. The six free parameters in the ELP have been adjusted to fit the available experimental data in the ?70 to + 150 MeV range of interest in nuclear reactions, namely, energies of single hole and single particle states, charge distributions, proton elastic scattering cross sections, and polarizations. The fitted potential depths show an energy dependence in remarkable agreement with the model predictions with a central nonlocality range β ? 1 F and a spin-orbit nonlocality range β₃ ? 0.8 F. The relative importance of surface and volume dependence in the real central potential in also discussed.     

Matter rogue wave in Bose-Einstein condensates with attractive atomic interaction

We investigate the matter rogue wave in Bose-Einstein condensates with attractive interatomic interaction analytically and numerically. Our results show that the formation of rogue wave is mainly due to the accumulation of energy and atoms toward to its central part; and the decay rate of atoms in unstable matter rogue wave can be effectively controlled by modulating the trapping frequency of external potential. The numerical simulation demonstrate that even a small periodic perturbation with small modulation frequency can induce the generation of a near-ideal matter rogue wave. We also give an experimental protocol to observe this phenomenon in Bose-Einstein condensates.     

Scaling of dynamics with the range of interaction in short-range attractive colloids

We numerically study the dependence of the dynamics on the range of interaction Delta for the short-range square well potential. We find that, for small Delta, dynamics scale exactly in the same way as thermodynamics, both for Newtonian and Brownian microscopic dynamics. For interaction ranges from a few percent down to the Baxter limit, the relative location of the attractive-glass line and the liquid-gas line does not depend on Delta. This proves that, in this class of potentials, disordered arrested states (gels) can be generated only as a result of a kinetically arrested phase separation.     

Ne-BeH体系的相互作用势和能级结构的理论研究

本文对Ne-BeH体系采用单双迭代(包括非迭代三重激发)耦合簇理论CCSD(T)方法,对Be , H 和 Ne原子采用aug-cc-pVQZ基组和3s3p2d1f1g中心键函数.利用非线性最小二乘法拟合该理论水平下的相互作用能,得到了Ne-BeH弱相互作用体系在冻结BeH键长情况下的二维的全程势能面,在 和 处存在一全局最小值-34.43607 .利用该势能面,计算了Ne-BeH体系的J=0-9的能级结构.以期对Ne-BeH的相关的实验和理论研究提供必要的参考和借鉴.     

Ne-BeH体系的相互作用势和能级结构的理论研究

本文对Ne-BeH体系采用单双迭代(包括非迭代三重激发)耦合簇理论CCSD(T)方法,对Be , H 和 Ne原子采用aug-cc-pVQZ基组和3s3p2d1f1g中心键函数.利用非线性最小二乘法拟合该理论水平下的相互作用能,得到了Ne-BeH弱相互作用体系在冻结BeH键长情况下的二维的全程势能面,在 和 处存在一全局最小值-34.43607 .利用该势能面,计算了Ne-BeH体系的J=0-9的能级结构.以期对Ne-BeH的相关的实验和理论研究提供必要的参考和借鉴.     

Classical limit of relativistic quantal system with attractive Coulomb interaction

Using the appropriate harmonic oscillator states and reasonable approximations, we construct coherent wavepackets corresponding to the solutions of the Klein-Gordon equation for the attractive potentialV(r)=−k/r, k>0, in two and three space dimensions. We deduce the corresponding classical limit in two dimension by requiring that the expectation value 〈r〉 of the radial variable is large. In the case of three dimensions, besides the condition of large 〈r〉, we make the uncertainty Δr=[〈r ²〉 − 〈r〉²]^1/2 a minimum with respect to certain parameter of the wavepacket. We then investigate the trajectory traversed by the wavepacket in the classical limit. We find that the classical limit of this relativistic quantal problem gives, in the leading order, the same expression for the rate of motion of the perihelion as that given by the solution of the corresponding special relativistic classical dynamical problem. We also briefly discuss some of the subtle aspects of the classical limit of the relativistic quantal system, in general.