Few-body systems with large scattering length $a$ have universal properties that do not depend on the details of their interactions at short distances. The rate constant for three-body recombination of bosonic atoms of mass $m$ into a shallow dimer scales as $\ensuremath{\hbar}{a}^{4}∕m$ times a log-periodic function of the scattering length. We calculate the leading and subleading corrections to the rate constant, which are due to the effective range of the atoms, and study the correlation between the rate constant and the atom-dimer scattering length. Our results are applied to $^{4}\mathrm{He}$ atoms as a test case.Few-body systems with large scattering length $a$ have universal properties that do not depend on the details of their interactions at short distances. The rate constant for three-body recombination of bosonic atoms of mass $m$ into a shallow dimer scales as $\ensuremath{\hbar}{a}^{4}∕m$ times a log-periodic function of the scattering length. We calculate the leading and subleading corrections to the rate constant, which are due to the effective range of the atoms, and study the correlation between the rate constant and the atom-dimer scattering length. Our results are applied to $^{4}\mathrm{He}$ atoms as a test case.

arXiv:cond-mat/0611769Physical Review AMar 22, 200722 citations

Recombination in the universal four-fermion system

Arnoldas Deltuva

In the systems of spin 12 fermions with resonant S-wave interactions supporting only weakly bound dimers the antisymmetry forbids recombination of three (or more) fermions at zero energy. However, the fermion-fermion-dimer recombination is only partially suppressed. It is studied in the framework of momentum-space integral equations for the four-particle transition operators. In the vicinity of the unitary limit the fermion-fermion-dimer recombination rate, rescaled to build dimensionless quantity, is found to be linear in the effective range parameter, enabling a simple and accurate parametrization as well as evaluation of finite-range effects for any potential model. This feature makes the present results very useful in benchmarking different methods for three-cluster breakup and recombination calculations in four-particle systems. The interplay of the three-fermion and fermion-fermion-dimer recombination processes and their consequences for ultracold mixtures of fermions and dimers is discussed.In the systems of spin 12 fermions with resonant S-wave interactions supporting only weakly bound dimers the antisymmetry forbids recombination of three (or more) fermions at zero energy. However, the fermion-fermion-dimer recombination is only partially suppressed. It is studied in the framework of momentum-space integral equations for the four-particle transition operators. In the vicinity of the unitary limit the fermion-fermion-dimer recombination rate, rescaled to build dimensionless quantity, is found to be linear in the effective range parameter, enabling a simple and accurate parametrization as well as evaluation of finite-range effects for any potential model. This feature makes the present results very useful in benchmarking different methods for three-cluster breakup and recombination calculations in four-particle systems. The interplay of the three-fermion and fermion-fermion-dimer recombination processes and their consequences for ultracold mixtures of fermions and dimers is discussed.

arXiv:2105.09033Physics Letters BAug 25, 20210 citations

Four-Boson Systems Close to a Universal Regime

Lauro Tomio, M. R. Hadizadeh, Marcelo Takeshi Yamashita +2 more

Few-Body SystemsJan 10, 20131 citation

Few-body systems with large scattering length

a

have universal properties that do not depend on the details of their interactions at short distances. The rate constant for three-body recombination of bosonic atoms of mass

m

into a shallow dimer scales as $\ensuremath{\hbar}{a}^{4}∕m$ times a log-periodic function of the scattering length. We calculate the leading and subleading corrections to the rate constant, which are due to the effective range of the atoms, and study the correlation between the rate constant and the atom-dimer scattering length. Our results are applied to

^{4}\mathrm{He}

atoms as a test case.