Hyperspherical explicitly correlated Gaussian approach for few-body systems with finite angular momentum

Abstract

Within the hyperspherical framework, the solution of the time-independent Schroedinger equation for a n-particle system is divided into two steps, the solution of a Schroedinger like equation in the hyperangular degrees of freedom and the solution of a set of coupled Schroedinger like hyperradial equations. The solutions to the former provide effective potentials and coupling matrix elements that enter into the latter set of equations. This paper develops a theoretical framework to determine the effective potentials, as well as the associated coupling matrix elements, for few-body systems with finite angular momentum L=1 and negative and positive parity. The hyperangular channel functions are expanded in terms of explicitly correlated Gaussian basis functions and relatively compact expressions for the matrix elements are derived. The developed formalism is applicable to any n; however, for n greater or equal to 6, the computational demands are likely beyond present-day computational capabilities. A number of calculations relevant to cold atom physics are presented, demonstrating that the developed approach provides a computationally efficient means to solving four-body bound and scattering problems with finite angular momentum on powerful desktop computers. Details regarding the implementation are discussed.

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Cited by in corpus (11)

• Universal few-body physics and cluster formation
• Non-resonant Density of States Enhancement at Low Energies for Three or Four Neutrons
• Extension of the correlated Gaussian hyperspherical method to more particles and dimensions
• Scattering properties of the $2e^{-}2e^{+}$ polyelectronic system
• Three and four identical fermions near the unitary limit
• Computing an orthonormal basis of symmetric or antisymmetric hyperspherical harmonics
• Constrained correlated-Gaussians for hyperspherical calculations
• Hyperspherical asymptotics of a system of four charged particles
• Low-Energy Scattering Properties of Ground-State and Excited-State Positronium Collisions
• Observability of modified threshold behavior near unitarity
• Deformed Explicitly Correlated Gaussians