Preface

Schmid, Erich W.; Ziegelmann, H.

doi:10.1016/b978-0-08-018240-7.50004-9

Cited by 11 publications

(15 citation statements)

References 0 publications

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“…The interaction (2) is separable and the Lippmann-Schwinger equation for the two-body problem can be solved analytically. The two-body t-matrix can be written as [32]:…”

Section: A the Two-body Sectormentioning

confidence: 99%

Universal properties of the four-body system with large scattering length

2007

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Few-body systems with large scattering length have universal properties that do not depend on the details of their interactions at short distances. We study the universal bound state properties of the four-boson system with large scattering length in an effective quantum mechanics approach. We compute the four-body binding energies using the Yakubovsky equations for positive and negative scattering length. Moreover, we study the correlation between three-and four-body energies and present a generalized Efimov plot for the four-body system. These results are useful for understanding the cluster structure of nuclei and for the creation of weakly-bound tetramers with cold atoms close to a Feshbach resonance.

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“…The interaction (2) is separable and the Lippmann-Schwinger equation for the two-body problem can be solved analytically. The two-body t-matrix can be written as [32]:…”

Section: A the Two-body Sectormentioning

confidence: 99%

Universal properties of the four-body system with large scattering length

2007

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“…This kernel, as is well known [27], is proportional to the product of the Dirac delta and Heaviside theta functions. However, due to "packetting" (i.e integration over momentum bins in Eq.…”

Section: B Three-body Lattice Basis and The Permutation Matrixmentioning

confidence: 99%

Three-body breakup within the fully discretized Faddeev equations

et al. 2012

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A novel approach is developed to find the three-body breakup amplitudes and cross sections within the modified Faddeev equation framework. The method is based on the lattice-like discretization of the three-body continuum with a three-body stationary wave-packet basis in momentum space. The approach makes it possible to simplify drastically all the three-and few-body breakup calculations due to discrete wave-packet representations for the few-body continuum and simultaneous lattice representation for all the scattering operators entering the integral equation kernels. As a result, the few-body breakup can be treated as a particular case of multi-channel scattering in which part of the channels represents the true few-body continuum states. As an illustration for the novel approach, an accurate calculations for the three-body breakup process n+d → n+n+p with non-local and local N N interactions are calculated. The results obtained reproduce nicely the benchmark calculation results using the traditional Faddeev scheme which requires much more tedious and time-consuming calculations.

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“…Let the considered atomic system be composed of one Rb atom and two Xe atoms. Following Schmid and Ziegelmann 4 we denote the Rb atom by 1 and the two Xe atoms by 2 and 3. When neglecting three-particle potentials, the Hamiltonian for the considered svstem has the form where the potentials Vi describe the two-particlc interactions according to:…”

Section: Three-body Scattering Problemmentioning

confidence: 99%