Abstract
The first step toward the application of an effective non partial wave (PW) numerical approach to few-body atomic bound states has been taken. The two-body transition amplitude which appears in the kernel of three-dimensional Faddeev-Yakubovsky integral equations is calculated as function of two-body Jacobi momentum vectors, i.e. as a function of the magnitude of initial and final momentum vectors and the angle between them. For numerical calculation the realistic interatomic interactions HFDHE2, HFD-B, LM2M2 and TTY are used. The angular and momentum dependence of the fully off-shell transition amplitude is studied at negative energies. It has been numerically shown that, similar to the nuclear case, the transition amplitude exhibits a characteristic angular behavior in the vicinity of 4He dimer pole.
Highlights
In recent years the 4 He trimer and tetramer have been the center of several theoretical investigations
The limitation arises from eccentricities of the interatomic interactions, since interatomic interactions often contain very strong short range repulsion which leads to tedious and cumbersome numerical procedure
In calculations of atomic systems, because of the short range correlations, one needs a large number of partial wave (PW) to obtain the converged results
Summary
In recent years the 4 He trimer and tetramer have been the center of several theoretical investigations (see, for example, Refs. [1,2,3] and references therein). The three and four-body atomic bound states have been studied with short-range forces and large scattering length at leading order in an Effective field theory approach [9]-[11], but these investigations are based on PW decomposition and the interactions are restricted to only s-wave sector. By these considerations we are going to extend a numerical method, which has been successfully applied to nuclear bound and scattering systems and avoids the PW representation and its complexity, to atomic bound states.
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