Related papers: On-shell approximation for the s-wave scattering t…
We investigate the on-shell approximation in the context of s-wave scattering for ultracold two-body collisions. Our analysis systematically covers spatial dimensions D=1,2,3 , with the aim of identifying the regimes in which the…
We analyze the scattering problem of identical bosonic particles confined on a spherical surface. At low scattering energies and for a radius much larger than the healing length, we express the contact interaction strength in terms of the…
We reexamine the relations between the Bethe-Salpeter (BS) wave function of two particles, the on-shell scattering amplitude, and the effective potential in quantum filed theory. It is emphasized that there is an exact relation between the…
A solution of the scattering problem is obtained for the Schr\"odinger equation with the potential of induced dipole interaction, which decreases as the inverse square of the distance. Such a potential arises in the collision of an incident…
We discuss an exact relation between the two-particle scattering amplitude and the Bethe-Salpeter (BS) wave function inside the interaction range in quantum field theory. In the relation the reduced BS wave function defined by the BS wave…
We derive the asymptotic expansions of the wave function of three particles having equal mass with finite-range interactions and infinite or zero two-dimensional scattering length colliding at zero energy and zero orbital angular momentum,…
We consider many-body effects on particle scattering in one, two and three dimensional Bose gases. We show that at zero temperature these effects can be modelled by the simpler two-body T-matrix evaluated off the energy shell. This is…
Scattering processes are a fundamental way of experimentally probing distributions and properties of systems in several areas of physics. Considering two-body scattering at low energies, when the de Broglie wavelength is larger than the…
We introduce a nonperturbative approximation scheme for performing scattering calculations in two dimensions that involves neglecting the contribution of the evanescent waves to the scattering amplitude. This corresponds to replacing the…
Using improved experimentally based $X{}^1\Sigma^+$ and $a{}^3\Sigma^+$ molecular potentials of NaRb, we apply the variable phase method to compute new data for low energy scattering of $^{23}$Na atoms by $^{85}$Rb atoms and $^{87}$Rb…
The zero-temperature equation of state is analyzed in low-dimensional bosonic systems. In the dilute regime the equation of state is universal in terms of the gas parameter, i.e. it is the same for different potentials with the same value…
A new approach is described to the evaluation of the S-matrix in three-dimensional atom-diatom reactive quantum scattering theory. The theory is developed based on natural collision coordinates where progress along the reaction coordinate…
We demonstrate an interference method to determine the low-energy elastic scattering amplitudes of a quantum gas. We linearly accelerate two ultracold atomic clouds up to energies of 1.2 mK and observe the collision halo by direct imaging…
We analyze the zero energy collision of three identical bosons in the same internal state with total orbital angular momentum $L=2$, assuming short range interactions. By solving the Schr\"odinger equation asymptotically, we derive two…
We consider the three-boson problem with $\delta$-function interactions in one spatial dimension. Three different approaches are used to calculate the phase shifts, which we interpret in the context of the effective range expansion, for the…
In three spatial dimensions, in the unitary limit of a non-relativistic quantum Bose or Fermi gas, the scattering length diverges. This occurs at a renormalization group fixed point, thus these systems present interesting examples of…
We propose an alternative approach to L\"uscher's formula for extracting two-body scattering phase shifts from finite volume spectra with no reliance on the partial wave expansion. We use an effective-field-theory-based Hamiltonian method…
We propose a systematic T-matrix approach to solve few-body problems with s-wave contact interactions in ultracold atomic gases. The problem is generally reduced to a matrix equation expanded by a set of orthogonal molecular states,…
Using the finite-temperature path integral Monte Carlo method, we investigate dilute, trapped Bose gases in a quasi-two dimensional geometry. The quantum particles have short-range, s-wave interactions described by a hard-sphere potential…
We analyze the collision of three particles with arbitrary mass ratio at zero collision energy, assuming arbitrary short-range potentials, and generalize the three-body scattering hypervolume $D$ first defined for identical bosons in 2008.…