Few-Body Systems最新文献

Nuclear reactions are complex, with a large number of possible channels. Understanding how different channels contribute to a given reaction is investigated by perturbing the continuous spectrum. Tools are developed to investigate reaction mechanisms by identifying the contributions from each reaction channel. Cluster decomposition methods, along with the spectral theory of proper subsystem problems, is used to identify the part of the nuclear Hamiltonian responsible for scattering into each channel. The result is an expression of the nuclear Hamiltonian as a sum over all scattering channels of channel Hamiltonians. Each channel Hamiltonian is constructed from solutions of proper subsystem problems. Retaining any subset of channel Hamiltonians results in a truncated Hamiltonian where the scattering wave functions for the retained channels differ from the wave functions of the full Hamiltonian by N-body correlations. The scattering operator for the truncated Hamiltonian satisfies an optical theorem in the retained channels. Because different channel Hamiltonians do not commute, how they interact determines their contribution to the full dynamics.

Dynamical association of Efimov trimers in thermal gases by means of modulated magnetic fields has proven very fruitful in determining the binding energy of trimers. The latter was extracted from the number of remaining atoms, which featured oscillatory fringes stemming from the superposition of trimers with atom-dimers. Subsequent theoretical investigations utilizing the time-dependent three-body problem revealed additional association mechanisms, manifested as superpositions of the Efimov state with the trap states and the latter with atom-dimers. The three atoms were initialized in a way to emulate a thermal gas with uniform density. Here, this analysis is extended by taking into account the effects of the density profile of a semi-classical thermal gas. The supersposition of the Efimov trimer with the first atom-dimer remains the same, while the frequencies of highly oscillatory fringes shift to lower values. The latter refer to the frequencies of trimers and atom-dimers in free space since the density profile smears out the contribution of trap states.

We construct approximate bound state solutions to the one-dimensional Schrödinger equation within the Dunkl formalism for a symmetrized Hulthén potential. Our method is based on reducing the governing equation to conventional Schrödinger form, such that an approximation to an inverse quadratic term becomes applicable. Conditions for computing stationary energies, as well as for establishing boundedness and normalizability of our solutions are discussed.

In this study, we present a perturbative analysis of the three-gluon vertex for a kinematical symmetric configuration in dimensions (n=4-2epsilon ) and different covariant gauges. Our study can describe the form factors of the three gluon vertex in a wide range of momentum. We employ a momentum subtraction scheme to define the renormalized vertex. We give an in-depth review of three commonly used vector representations for the vertex, and explicitly show the expressions to change from one representation to the other. Although our estimates are valid only in the perturbative regime, we extend our numerical predictions to the infrared domain and show that in (n=4) some nonperturbative properties are qualitatively present already at perturbation theory. In particular, we find a critical gauge above which the leading form factor displays the so-called zero crossing. We contrast our findings to those of other models and observe a fairly good agreement.

A special four-body quantum model in one dimension with a discrete spectrum was introduced, including harmonic oscillator and three-body interaction potentials. After reducing one degree of freedom by using the Jacobian transformation in the center of mass, the desired Hamiltonian is examined in spherical coordinate with three degrees of freedom. To investigate this model algebraically, using the gauge rotation with the ground state wave function, the relation between the Hamiltonian and the generators of (sl(3, {mathbb {R}})) and (sl(2, {mathbb {R}})) Lie algebras is examined. Finally, this algebraic form helps us to get the Hamiltonian eigenvalues.

The oscillator bases expansion stands as an efficient approximation method for the time-independent Schrödinger equation. The method, originally formulated with one non-linear variational parameter, can be extended to incorporate two such parameters. It handles both non- and semi-relativistic kinematics with generic two-body interactions. In the current work, focusing on systems of three identical bodies, the method is generalised to include the management of a given class of three-body forces. The computational cost of this generalisation proves to not exceed the one for two-body interactions. The accuracy of the generalisation is assessed by comparing with results from Lagrange mesh method and hyperspherical harmonic expansions. Extensions for systems of N identical bodies and for systems of two identical particles and one distinct are also discussed.

We give a detailed and self-contained description of a recently developed theoretical and numerical method for the simulation of three identical bosonic alkali-metal atoms near a Feshbach resonance, where the Efimov effect is induced. The method is based on a direct construction of the off-shell two-body transition matrix from exact eigenfunctions of the embedded two-body Hamiltonians, obtained using realistic parameterizations of the interaction potentials which accurately reproduce the molecular energy levels. The transition matrix is then inserted into the appropriate three-body integral equations, which may be efficiently solved on a computer. We focus especially on the power of our method in including rigorously the effects of multichannel physics on the three-body problem, which are usually accounted for only by various approximations. We demonstrate the method for ⁷Li, where we recently showed that a correct inclusion of this multichannel physics resolves the long-standing disagreement between theory and experiment regarding the Efimovian three-body parameter. We analyze the Efimovian enhancement of the three-body recombination rate on both sides of the Feshbach resonance, revealing strong sensitivity to the spin structure of the model thus indicating the prevalence of three-body spin-exchange physics. Finally, we discuss an extension of our methodology to the calculation of three-body bound-state energies.

In this work, we present a study on the role of atomic configurations in forming van der Waals molecules through three-body recombination. Fixing the angle between the two momenta associated with the Jacobi vectors, we calculate the reaction probability for a specific configuration. In this way, we elucidate the nature of the total reaction probability in reactions X + He + He(rightarrow )XHe + He, essential for understanding van der Waals molecules formation in molecular beams and buffer gas cells.