Search

Overview of the recent advances in description of the few two-component fermions is presented. Themodel of zero-range interaction is generally considered to discuss the principal aspects of the few-body dynamics. Particular attention is paid to detailed description of two identical fermions of mass m and a distinct particle of mass m: it turns out that two L = 1 three-body bound states emerge if mass ratio m/m increases up to the critical value µ ≈ 13.607, abovewhich the Efimov effect takes place. The topics considered include rigorous treatment of the few-fermion problem in the zero-range interaction limit, lowdimensional results, the four-body energy spectrum, crossover of the energy spectra for m/m near µ, and properties of potential-dependent states. At last, enlisted are the problems, whose solution is in due course. [ABSTRACT FROM AUTHOR]

We develop a method for treating different quantum few-body dynamics without traditional partial-wave analysis. The key element of the method is a nondirect product discrete-variable representation (npDVR) we have suggested and developed in application to the time-dependent mutidimensional Schrödinger equations. The method is described here in details and the high efficiency and economy are demonstrated in application to the breakup cross sections of helium ion in collision with proton. We also give a brief review of the results obtained in the frame of the method in low-dimensional few-body physics. [ABSTRACT FROM AUTHOR]

We consider few-body bound state systems and provide precise definitions of Borromean and Brunnian systems. The initial concepts are more than a hundred years old and originated in mathematical knot-theory as purely geometric considerations. About thirty years ago they were generalized and applied to the binding of systems in nature. It now appears that recent generalization to higher-order Brunnian structures may potentially be realized as laboratory-made or naturally occurring systems. With the binding energy as measure, we discuss possibilities of physical realization in nuclei, cold atoms, and condensedmatter systems. Appearance is not excluded. However, both the form and the strengths of the interactions must be rather special. The most promising subfields for present searches would be in cold atoms because of external control of effective interactions, or perhaps in condensed-matter systems with nonlocal interactions. In nuclei, it would only be by sheer luck due to a lack of tunability. [ABSTRACT FROM AUTHOR]

We have suggested a method for treating different quantum few-body dynamics without traditional using of the partial-wave analysis. It happened that this approach was very efficient in quantitative analysis of low-dimensional ultracold few-body systems arising in confined geometry of atomic traps. Here we discuss its application to a recently suggested mechanism of resonant molecule formation in confined two-component atomic mixture with transferring the energy release to the center-of-mass excitation of forming molecules. The author considers this result as one of the most significant in his scientific carrier which started from the model of resonant muonic molecule formation [S.I. Vinitsky et al., Sov. Phys. JETP 47, 444 (1978)], one of the most citing works of S.I. Vinitsky. [ABSTRACT FROM AUTHOR]

The complex-rotation method adapted to solving the multichannel scattering problem in the two-body system where the interaction potential contains the long-range Coulomb components is described. The scattering problem is reformulated as the problem of solving a nonhomogeneous Schrödinger equation in which the nonhomogeneous term involves a Coulomb potential cut off at large distances. The incident wave appearing in the nonhomogeneous term is a solution of the Schrödinger equation with longrange Coulomb interaction. This formulation is free from approximations associated with a direct cutoff of Coulomb interaction at large distances. The efficiency of this formalism is demonstrated by considering the example of solving scattering problems in the α-α and p-p systems. [ABSTRACT FROM AUTHOR]

A procedure to solve few-body problems is developed which is based on an expansion over a small parameter. The parameter is the ratio of potential energy to kinetic energy for states having not small hyperspherical quantum numbers, K> K0. Dynamic equations are reduced perturbatively to equations in the finite-dimension subspace with K ⩽ K0. Contributions from states with K> K0 are taken into account in a closed form, i.e., without an expansion over basis functions. Estimates concerning the efficiency of the approach are presented. [ABSTRACT FROM AUTHOR]

Within the ( α, n, p) three-body model, the s-wave 6Li → α + d vertex constant G 01 and the asymptotic normalization coefficient C 01 (these two quantities are proportional to each other) for the wave function describing the 6Li nucleus in the α + d channel are calculated by solving Faddeev equations for various sets of nucleon-nucleon and α N potentials. The resulting values of G 01 and C 01 are used to calculate the astrophysical factor S(E) for the radiative-capture reaction d( α, γ)6Li at energies in the range E = 0–600 keV. The calculated values of G 01 and C 01 appear to be sensitive to the form of the pair potentials used. It is shown that, upon correctly taking into account the contributions of the E2 and E1 multipolarities, the values of S(E) in the region E < 150 keV are determined primarily by the values of C 01 and of the 6Li binding energy in the α + d channel. [ABSTRACT FROM AUTHOR]

Modern few-body methods for investigating Borromean two-neutron halo nuclei are discussed together with recent experiments. Advances in the studies of [sup 6]He and [sup 11]Li are analyzed. Some new problems created by a large neutron excess and a halo phenomenon are considered. [ABSTRACT FROM AUTHOR]