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[en] The focus of this research project was atoms with scattering lengths that are large compared to the range of their interactions and which therefore exhibit universal behavior at sufficiently low energies. Recent dramatic advances in cooling atoms and in manipulating their scattering lengths have made this phenomenon of practical importance for controlling ultracold atoms and molecules. This research project was aimed at developing a systematically improvable method for calculating few-body observables for atoms with large scattering lengths starting from the universal results as a first approximation. Significant progress towards this goal was made during the five years of the project.
[en] The constraining power of the present experimental data, combined with the general theoretical knowledge about ππ scattering upon the scattering lengths of this process is investigated by means of a rigorous functional method. We take as input the experimental phase shifts and make no hypotheses about the high energy behaviour of the amplitudes, using only absolute bounds derived from axiomatic field theory and exact consequences of crossing symmetry. In the simplest application of the method, involving only the π0π0 S-wave, we explored numerically a number of values proposed by various authors for the scattering lengths a0 and a2 and found that no one appears to be especially favoured. (author)
[en] For small values of the scattering length α (vertical strokeαvertical stroke approx.= 0) the effective range function kcot delta shows a pole for small k2. The usual effective range expansion cannot produce such a pole. We provide an alternative expansion which reduces to the usual one for vertical strokeαvertical stroke > 0 and shows a pole for vertical strokeαvertical stroke approx.= 0. The present expansion explains the low energy properties of the S-wave spin-doublet trinucleon system and in particular the linear correlation between the trinucleon energy and the neutron-deuteron scattering length. (orig.)
[en] The textbook effective-range expansion of scattering theory is useful in the analysis of low-energy scattering phenomenology when the scattering length is much larger than the range R of the scattering potential: . Nevertheless, the same has been used for systems where the scattering length is much smaller than the range of the potential. We suggest and numerically study an effective-range expansion for as well as improved two-parameter effective-range expansions for the cases and . The improved effective-range expansions for and reduce to the expansions for and , respectively, in appropriate limits. (paper)
[en] An effective field theory for the three-body system with large two-body scattering length a is applied to three-body recombination into deep bound states in a Bose gas. The recombination constant α is calculated to first order in the short-distance interactions that allow the recombination. For a<0 , the dimensionless combination mα/(ℎa4) is a periodic function of ln< hspace SPACE=''-0.167''>|a| that exhibits resonances at values of a that differ by multiplicative factors of 22.7. This dramatic behavior should be observable near a Feshbach resonance when a becomes large and negative
[en] The derivation and qualitative analysis of the nonlinear and linear equations adopted for calculation of the scattering length and effective range are given. In the case of the central square-well potential, the exact solutions of these equations are found and studied. The connection between the effective range and scattering length is revealed. Special attention is paid to the cases of zero and unrestricted scattering lengths.
[en] The nonlinear Ramsey interferometry of Fermi superfluid gases in a double-well potential is investigated in this paper. We found that the frequency of the Ramsey fringes exactly reflects the strength of nonlinearity, or the scattering length of the Fermi superfluid gases. The cases of sudden limit, the adiabatic limit and the general case are studied. The analytical result is in good agreement with the numerical ones. The adiabatic condition is proposed. In general situation, the zero-frequency point emerge. Finally the possible applications of the theory are discussed. (general)