Canonical quantum potential scattering theory

A new formulation of potential scattering in quantum mechanics is developed using a close structural analogy between partial waves and the classical dynamics of many non-interacting fields. Using a canonical formalism we find nonlinear first-order differential equations for the low-energy scattering parameters such as scattering length and effective range. They significantly simplify typical calculations, as we illustrate for atom-atom and neutron-nucleus scattering systems. A generalization to charged particle scattering is also possible.

Positronium-hydrogen-atom scattering in a five-state model

The scattering of orthopositronium (Ps) by hydrogen atoms has been investigated in a five-state coupled-channel model allowing for Ps(1s)H(2s,2p) and Ps(2s,2p)H(1s) excitations using a recently proposed electron-exchange model potential. The higher (n greater than or equal to 3) excitations and ionization of the Ps atom are calculated using the first Born approximation. Calculations are reported of scattering lengths, phase shifts. elastic, Ps and H excitation, and total cross sections. Remarkable correlations are observed between the S-wave Ps-H binding energy and the singlet scattering length, effective range, and resonance energy obtained in various model calculations. These correlations suggest that if a Ps-H dynamical model yields the correct result for one of these four observables, it is expected to lead to the correct result for the other three. The present model, which is constructed so as to reproduce the Ps-H resonance at 4.01 eV, automatically yields a Ps-H bound state at - 1.05 eV that compares well with the accurate value of - 1.067 eV. The model leads to a singlet scattering length of 3.72a(0) and effective range of 1.67a(0), whereas the correlations suggest the precise values of 3.50a(0) and 1.65a(0) for these observables, respectively. [S1050-2947(99)07703-3].

MODEL INDEPENDENCE OF SCATTERING OF 3 IDENTICAL BOSONS IN 2 DIMENSIONS

Within the framework of scattering integral equations in momentum space, we present numerical results of scattering of three identical bosons at low energies in two dimensions for short-range separable potentials. An analysis of the present numerical results reveals the three-particle scattering observables to be independent of potential shape provided the low-energy two-particle binding energy and scattering length are held fixed throughout the investigation. We think that the present conclusion of model independence will be valid for any potential, local or nonlocal, whose range is much smaller than the size of the two-particle bound state.

Extraction of the s-wave pi N scattering lengths from data on pionic atoms

For many years a combined analysis of pionic hydrogen and deuterium atoms has been known as a good tool to extract information on the isovector and especially on the isoscalar s-wave pN scattering length. However, given the smallness of the isoscalar scattering length, the analysis becomes useful only if the pion–deuteron scattering length is controlled theoretically to a high accuracy comparable to the experimental precision. To achieve the required few-percent accuracy one needs theoretical control over all isospin-conserving three-body pNN !pNN operators up to one order before the contribution of the dominant unknown (N†N)2pp contact term. This term appears at next-to-next-to-leading order in Weinberg counting. In addition, one needs to include isospin-violating effects in both two-body (pN) and three-body (pNN) operators. In this talk we discuss the results of the recent analysis where these isospin-conserving and -violating effects have been carefully taken into account. Based on this analysis, we present the up-to-date values of the s-wave pN scattering lengths.

ΛΛ Correlation Function In Au+au Collisions At √[s(nn)]=200 gev.

We present ΛΛ correlation measurements in heavy-ion collisions for Au+Au collisions at sqrt[s_{NN}]=200  GeV using the STAR experiment at the Relativistic Heavy-Ion Collider. The Lednický-Lyuboshitz analytical model has been used to fit the data to obtain a source size, a scattering length and an effective range. Implications of the measurement of the ΛΛ correlation function and interaction parameters for dihyperon searches are discussed.

Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices

The existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with a linear optical lattice (LOL) in the x direction and a nonlinear optical lattice (NOL) in the y direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance is demonstrated. In particular, we show that such crossed LOLs and NOLs allow for stabilizing two-dimensional solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach, with the Vakhitov-Kolokolov necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation. Very good agreement of the results corresponding to both treatments is observed.

Generation of nonground-state Bose-Einstein condensates by modulating atomic interactions

A technique is proposed for creating nonground-state Bose-Einstein condensates in a trapping potential by means of the temporal modulation of atomic interactions. Applying a time-dependent spatially homogeneous magnetic field modifies the atomic scattering length. A modulation of the scattering length excites the condensate, which, under special conditions, can be transferred to an excited nonlinear coherent mode. It is shown that a phase-transition-like behavior occurs in the time-averaged population imbalance between the ground and excited states. The application of the technique is analyzed and it is shown that the considered effect can be realized for experimentally available condensates.

Conformational changes in SP-B as a function of surface pressure

X-ray reflectivity of bovine and sheep surfactant-associated protein B (SP-B) monolayers is used in conjunction with pressure-area isotherms and protein models to suggest that the protein undergoes changes in its tertiary structure at the air/water interface under the influence of surface pressure, indicating the likely importance of such changes to the phenomena of protein squeeze out as well as lipid exchange between the air-water interface and subphase structures. We describe an algorithm based on the well-established box- or layer-models that greatly assists the fitting of such unknown scattering-length density profiles, and which takes the available instrumental resolution into account. Scattering-length density profiles from neutron reflectivity of bovine SP-B monolayers on aqueous subphases are shown to be consistent with the exchange of a large number of labile protons as well as the inclusion of a significant amount of water, which is partly squeezed out of the protein monolayer at elevated surface pressures.

Pairing with polarization effects in low-density neutron matter

We study the properties of the 1S0 pairing gap in low-density neutron matter. Different corrections to the lowest-order scattering length approximation are explored, resulting in a strong suppression with respect to the BCS result.

η'-nucleus optical potential and possible η' bound states

Starting from a recent model of the η′N interaction, we evaluate the η ′-nucleus optical potential, including the contribution of lowest order in density, tρ/2mη′, together with the second-order terms accounting for η′ absorption by two nucleons. We also calculate the formation cross section of the η′bound states from (π, p) reactions on nuclei. The η′-nucleus potential suffers from uncertainties tied to the poorly known η′N interaction, which can be partially constrained by the experimental modulus of the η′N scattering length and/or the recently measured transparency ratios in η′nuclear photoproduction. Assuming an attractive interaction and taking the claimed experimental value |aη′N|= 0.1 fm, we obtain an η′optical potential in nuclear matter at saturation density of Vη′=−(8.7 + 1.8i) MeV, not attractive enough to produce η′bound states in light nuclei. Larger values of the scattering length give rise to deeper optical potentials, with moderate enough imaginary parts. For a value |aη′N|= 0.3 fm, which can still be considered to lie within the uncertainties of the experimental constraints, the spectra of light and medium nuclei show clear structures associated to η′-nuclear bound states and to threshold enhancements in the unbound region.

Pairing with polarization effects in low-density neutron matter

We study the properties of the 1S0 pairing gap in low-density neutron matter. Different corrections to the lowest-order scattering length approximation are explored, resulting in a strong suppression with respect to the BCS result.

Asymptotic model for shape resonance control of diatomics by intense non-resonant light: universality in the single-channel approximation

Non-resonant light interacting with diatomics via the polarizability anisotropy couples different rotational states and may lead to strong hybridization of the motion. The modification of shape resonances and low-energy scattering states due to this interaction can be fully captured by an asymptotic model, based on the long-range properties of the scattering (Crubellier et al 2015 New J. Phys. 17 045020). Remarkably, the properties of the field-dressed shape resonances in this asymptotic multi-channel description are found to be approximately linear in the field intensity up to fairly large intensity. This suggests a perturbative single-channel approach to be sufficient to study the control of such resonances by the non-resonant field. The multi-channel results furthermore indicate the dependence on field intensity to present, at least approximately, universal characteristics. Here we combine the nodal line technique to solve the asymptotic Schrödinger equation with perturbation theory. Comparing our single channel results to those obtained with the full interaction potential, we find nodal lines depending only on the field-free scattering length of the diatom to yield an approximate but universal description of the field-dressed molecule, confirming universal behavior.

Generation of nonground-state condensates and adiabatic paradox

The problem of resonant generation of nonground-state condensates is addressed aiming at resolving the seeming paradox that arises when one resorts to the adiabatic representation. In this picture, the eigenvalues and eigenfunctions of a time-dependent Gross-Pitaevskii Hamiltonian are also functions of time. Since the level energies vary in time, no definite transition frequency can be introduced. Hence no external modulation with a fixed frequency can be made resonant. Thus, the resonant generation of adiabatic coherent modes is impossible. However, this paradox occurs only in the frame of the adiabatic picture. It is shown that no paradox exists in the properly formulated diabatic representation. The resonant generation of diabatic coherent modes is a well defined phenomenon. As an example, the equations are derived, describing the generation of diabatic coherent modes by the combined resonant modulation of the trapping potential and atomic scattering length.

One-dimensional trapped atoms: critical coupling parameter and critical number of particles

In this paper we consider the case of a Bose gas in low dimension in order to illustrate the applicability of a method that allows us to construct analytical relations, valid for a broad range of coupling parameters, for a function which asymptotic expansions are known. The method is well suitable to investigate the problem of stability of a collection of Bose particles trapped in one- dimensional configuration for the case where the scattering length presents a negative value. The eigenvalues for this interacting quantum one-dimensional many particle system become negative when the interactions overcome the trapping energy and, in this case, the system becomes unstable. Here we calculate the critical coupling parameter and apply for the case of Lithium atoms obtaining the critical number of particles for the limit of stability.

Dissipative dynamics of matter-wave solitons in a nonlinear optical lattice

Dynamics and stability of solitons in two-dimensional (2D) Bose-Einstein condensates (BEC), with one-dimensional (1D) conservative plus dissipative nonlinear optical lattices, are investigated. In the case of focusing media (with attractive atomic systems), the collapse of the wave packet is arrested by the dissipative periodic nonlinearity. The adiabatic variation of the background scattering length leads to metastable matter-wave solitons. When the atom feeding mechanism is used, a dissipative soliton can exist in focusing 2D media with 1D periodic nonlinearity. In the defocusing media (repulsive BEC case) with harmonic trap in one direction and nonlinear optical lattice in the other direction, the stable soliton can exist. Variational approach simulations are confirmed by full numerical results for the 2D Gross-Pitaevskii equation.