Related papers: Pseudopotential in resonant regimes
Atom-atom scattering of bosonic one-dimensional (1D) atoms has been modeled successfully using a zero-range delta-function potential, while that of bosonic 3D atoms has been modeled successfully using Fermi-Huang's regularized s-wave…
The general formulas to calculate the phase shifts of wave function of a particle scattering on a target formed by a pair of non-identical zero-range potentials are derived. It is shown that at asymptotically great distances from the target…
We solve the Klein-Gordon equation in the presence of a spatially one-dimensional cusp potential. The scattering solutions are obtained in terms of Whittaker functions and the condition for the existence of transmission resonances is…
Propagation of whispering gallery modes in Surface Nanoscale Axial Photonics (SNAP) microresonators, fabricated at the optical fiber surface, is commonly described by a one-dimensional wave equation, resembling the Schr\"odinger equation,…
In the present work, we start from a minimal Hamiltonian for Fermi systems where the s-wave scattering is the only low energy constant at play. Many-Body Perturbative approach that is usually valid at rather low density is first discussed.…
A new effective field theory has been developed to describe shallow $P$-wave resonances using nonlocal, momentum-dependent two-body potentials. This approach is expected to facilitate many-body calculations and has been demonstrated to…
Anisotropic pseudopotential relevant to collisions of two particles polarized by external field is rigorously derived and its properties are investigated. Such low-energy pseudopotential may be useful in describing collective properties of…
A multi-channel scattering problem is studied from a point of view of integral equations system. The system appears while natural one-particle wave function equation of the electron under action of a potential with non-intersecting ranges…
We develop ultratransferable pseudopotentials for the contact interaction that are 100 times more accurate than contemporary approximations. The pseudopotential offers scattering properties very similar to the contact potential, has a…
The long-standing question of finding the momentum representation for the s-wave zero-range interaction in three spatial dimensions is here solved. This is done by expressing a certain distribution, introduced in a formal way by S. Tan…
We show that a purely s-wave interaction in three dimensions (3D) can induce higher partial-wave resonances in mixed dimensions. We develop two-body scattering theories in all three cases of 0D-3D, 1D-3D, and 2D-3D mixtures and determine…
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…
Following a strong analogy with two-dimensional physics, the three-body pseudo-potential in one dimension is derived. The Born approximation is then considered in the context of ultracold atoms in a linear harmonic waveguide. In the…
Finite size effects alter not only the energy levels of small systems, but can also lead to new effective interactions within these systems. Here the problem of low energy quantum scattering by a spherically symmetric short range potential…
More than 65 years ago, Jost and Kohn [R. Jost and W. Kohn, {Phys. Rev.} {\bf 87}, 977 (1952)] derived an explicit expression for a class of short-range model potentials from a given effective range expansion with the $s$-wave scattering…
We consider the effective field theory (EFT) treatment of two-body systems with narrow resonances. Within this approach, an $s$-wave scattering amplitude can be expanded in powers of a typical momentum scale of a system $Q\ll \Lambda$,…
The fundamental quantities of potential scattering theory are generalized to accommodate long-range interactions. New definitions for the scattering amplitude and wave operators valid for arbitrary interactions including potentials with a…
We develop the contact theory for spin-orbit-coupled Fermi gases. By using a perturbation method, we derive analytically the universal two-body behavior at short distance, which does not depend on the short-range details of interatomic…
We consider the resonant Fermi gas, that is, two-component fermions in three dimensions interacting by a short-range potential of large scattering length. We introduce a quantity, the three-body contact, that determines several observables.…
The definition of the scattering volume for $p$-wave collisions needs to be generalized in the presence of dipolar interactions for which the potential decreases with the interparticle separation as $1/R^3$. Here, we propose a generalized…