The asymptotics of total scattering cross sections for a three-body quantum system with two heavy particles are studied when the masses tend to infinity. It is assumed that the initial channel is a two-cluster channel such that a light particle and a heavy one form a bound state and the relative velocity of another heavy particle to the pair is fixed. It is shown that the limits exist and they can be expressed in terms of transition probabilities which appear in the scattering theory for the charge transfer models.The asymptotics of total scattering cross sections for a three-body quantum system with two heavy particles are studied when the masses tend to infinity. It is assumed that the initial channel is a two-cluster channel such that a light particle and a heavy one form a bound state and the relative velocity of another heavy particle to the pair is fixed. It is shown that the limits exist and they can be expressed in terms of transition probabilities which appear in the scattering theory for the charge transfer models.

Journal of Mathematical PhysicsJan 1, 19953 citations

Mathematical problems of the quantum theory of scattering for a three-particle system

L. D. Faddeev

Jan 1, 196437 citations

Three-Body Bound States in Atomic Mixtures With Resonant p -Wave Interaction

Maxim A. Efremov, Lev I. Plimak, Misha Ivanov +1 more

We employ the Born-Oppenheimer approximation to find the effective potential in a three-body system consisting of a light particle and two heavy ones when the heavy-light short-range interaction potential has a resonance corresponding to a nonzero orbital angular momentum. In the case of an exact resonance in the p-wave scattering amplitude, the effective potential is attractive and long range; namely, it decreases as the third power of the interatomic distance. Moreover, we show that the range and power of the potential, as well as the number of bound states, are determined by the mass ratio of the particles and the parameters of the heavy-light short-range potential.We employ the Born-Oppenheimer approximation to find the effective potential in a three-body system consisting of a light particle and two heavy ones when the heavy-light short-range interaction potential has a resonance corresponding to a nonzero orbital angular momentum. In the case of an exact resonance in the p-wave scattering amplitude, the effective potential is attractive and long range; namely, it decreases as the third power of the interatomic distance. Moreover, we show that the range and power of the potential, as well as the number of bound states, are determined by the mass ratio of the particles and the parameters of the heavy-light short-range potential.

arXiv:1303.5939Physical Review LettersSep 10, 201311 citations

Thermodynamics of the two-component Fermi gas with unequal masses at unitarity

K. M. Daily, D. Blume

We consider mass-imbalanced two-component Fermi gases for which the unequal-mass atoms interact via a zero-range model potential with a diverging $s$ -wave scattering length ${a}_{s}$ , that is, with $1/{a}_{s}=0$ . The high-temperature thermodynamics of the harmonically trapped and homogeneous systems are examined using a virial expansion approach up to third order in the fugacity. We find that the universal part of the third-order virial coefficient associated with two light atoms and one heavy atom is negative, while that associated with two heavy and one light atom changes sign from negative to positive as the mass ratio $\ensuremath{\kappa}$ increases and diverges when Efimov physics sets in at $\ensuremath{\kappa}=13.61$. By examining the Helmholtz free energy, we find that the equilibrium polarization of the trapped and homogeneous systems is 0 for $\ensuremath{\kappa}=1$, but finite for $\ensuremath{\kappa}\ensuremath{\ne}1$ (with a majority of heavy particles). Compared to the equilibrium polarization of the noninteracting system, the equilibrium polarization at unitarity is increased for the trapped system and decreased for the homogeneous system. We find that unequal-mass Fermi gases are stable for all polarizations.We consider mass-imbalanced two-component Fermi gases for which the unequal-mass atoms interact via a zero-range model potential with a diverging $s$-wave scattering length ${a}_{s}$, that is, with $1/{a}_{s}=0$. The high-temperature thermodynamics of the harmonically trapped and homogeneous systems are examined using a virial expansion approach up to third order in the fugacity. We find that the universal part of the third-order virial coefficient associated with two light atoms and one heavy atom is negative, while that associated with two heavy and one light atom changes sign from negative to positive as the mass ratio $\ensuremath{\kappa}$ increases and diverges when Efimov physics sets in at $\ensuremath{\kappa}=13.61$. By examining the Helmholtz free energy, we find that the equilibrium polarization of the trapped and homogeneous systems is 0 for $\ensuremath{\kappa}=1$, but finite for $\ensuremath{\kappa}\ensuremath{\ne}1$ (with a majority of heavy particles). Compared to the equilibrium polarization of the noninteracting system, the equilibrium polarization at unitarity is increased for the trapped system and decreased for the homogeneous system. We find that unequal-mass Fermi gases are stable for all polarizations.

arXiv:1110.1400Physical Review AJan 5, 201231 citations

Quantum Scattering Theory for Several Particle Systems

L. D. Faddeev, S. P. Merkuriev

Springer eBooksJan 1, 1993455 citations

We consider mass-imbalanced two-component Fermi gases for which the unequal-mass atoms interact via a zero-range model potential with a diverging

s

-wave scattering length

{a}_{s}

, that is, with

1/{a}_{s}=0

. The high-temperature thermodynamics of the harmonically trapped and homogeneous systems are examined using a virial expansion approach up to third order in the fugacity. We find that the universal part of the third-order virial coefficient associated with two light atoms and one heavy atom is negative, while that associated with two heavy and one light atom changes sign from negative to positive as the mass ratio $\ensuremath{\kappa}$ increases and diverges when Efimov physics sets in at $\ensuremath{\kappa}=13.61$. By examining the Helmholtz free energy, we find that the equilibrium polarization of the trapped and homogeneous systems is 0 for $\ensuremath{\kappa}=1$, but finite for $\ensuremath{\kappa}\ensuremath{\ne}1$ (with a majority of heavy particles). Compared to the equilibrium polarization of the noninteracting system, the equilibrium polarization at unitarity is increased for the trapped system and decreased for the homogeneous system. We find that unequal-mass Fermi gases are stable for all polarizations.