Recombination rates from potential models close to the unitary limit

Abstract

We investigate universal behavior in the recombination rate of three bosons close to threshold. Using the He-He system as a reference, we solve the three-body Schrödinger equation above the dimer threshold for different potentials having large values of the two-body scattering length $a$. To this aim we use the hyperspherical adiabatic expansion and we extract the $S$-matrix through the integral relations recently derived. The results are compared to the universal form, $\alpha \approx 67.1{\sin }^2[s_0\ln ({\kappa }_{\ast }a)+\gamma ]$, for different values of $a$ and selected values of the three-body parameter ${\kappa }_{\ast }$. A good agreement with the universal formula is obtained after introducing a particular type of finite-range corrections, which have been recently proposed by two of the authors in Ref.[1]. Furthermore, we analyze the validity of the above formula in the description of a very different system: neutron-neutron-proton recombination. Our analysis confirms the universal character of the process in systems of very different scales having a large two-body scattering length.

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Cited by in corpus (10)

• Efimov Physics: a review
• Few-body physics in resonantly interacting ultracold quantum gases
• Universality and scaling in the $N$-body sector of Efimov physics
• Efimov Physics and Connections to Nuclear Physics
• $N$-boson spectrum from a Discrete Scale Invariance
• Universal Relations for Range Corrections to Efimov Features
• Breakup of three particles within the adiabatic expansion method
• An effective-field-theory analysis of Efimov physics in heteronuclear mixtures of ultracold atomic gases
• Three-body systems in physics of cold atoms and halo nuclei
• Three-body continuum states and Efimov physics in non-integer geometry