Journal of Experimental and Theoretical Physics

One-parametric dependences of the spectra, scattering lengths, and recombination coefficients for a system of three bosons

Ф. М. Пеньков

Published Sep 1, 2003• 11 citations

Abstract

A model of a two-pole pair t -matrix for the description of three-boson systems with r 0 / a 0 ≪ 1 is studied. The position of the second pole on the nonphysical sheet is treated as a parameter of the Faddeev integral equation. Close agreement with the calculations performed for realistic potentials was obtained, and interaction parameters for three bosons that were not calculated earlier were predicted.

DOI: 10.1134/1.1618335

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Journal of Experimental and Theoretical Physics

One-parametric dependences of the spectra, scattering lengths, and recombination coefficients for a system of three bosons

Ф. М. Пеньков

Published Sep 1, 2003• 11 citations

Publisher

Abstract

DOI: 10.1134/1.1618335

Related papers

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Ф. М. Пеньков, Werner Sandhas

Physics of Atomic NucleiApr 1, 20140 citations

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The threshold recombination coefficient for three bosons whose two-body scattering length $a$ is positive and large compared with the nominal range of the potentials is shown to proceed via a crossing of hyperspherical adiabatic potential curves at $R\ensuremath{\approx}2.6a$. The hidden crossing theory gives a simple expression for the rate in terms of the scattering length and a phase $\ensuremath{\Delta}$. The phase depends upon the details of the interaction, and varies from species to species, however an upper limit to the rate which depends only upon the scattering length emerges from the hidden crossing theory.The threshold recombination coefficient for three bosons whose two-body scattering length $a$ is positive and large compared with the nominal range of the potentials is shown to proceed via a crossing of hyperspherical adiabatic potential curves at $R\ensuremath{\approx}2.6a$. The hidden crossing theory gives a simple expression for the rate in terms of the scattering length and a phase $\ensuremath{\Delta}$. The phase depends upon the details of the interaction, and varies from species to species, however an upper limit to the rate which depends only upon the scattering length emerges from the hidden crossing theory.

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S

-matrix element. This result is then compared to a variational calculation in the adiabatic hyperspherical representation, and to a numerical solution to the momentum-space Faddeev equations. We find excellent agreement with the exact phase shifts, and comment on some of the important features in the scattering and bound-state sectors. In particular, we find that the

1+2

scattering length is divergent, marking the presence of a zero-energy resonance which appears as a feature when the pairwise interactions are short range. Finally, we consider the introduction of a three-body interaction, and comment on the cutoff dependence of the coupling.

The threshold recombination coefficient for three bosons whose two-body scattering length

a

is positive and large compared with the nominal range of the potentials is shown to proceed via a crossing of hyperspherical adiabatic potential curves at $R\ensuremath{\approx}2.6a$. The hidden crossing theory gives a simple expression for the rate in terms of the scattering length and a phase $\ensuremath{\Delta}$. The phase depends upon the details of the interaction, and varies from species to species, however an upper limit to the rate which depends only upon the scattering length emerges from the hidden crossing theory.