Three-body Forces in Oscillator Bases Expansion

Abstract

The oscillator bases expansion stands as an efficient approximation method for the time-independent Schrödinger equation. The method, originally formulated with one non-linear variational parameter, can be extended to incorporate two such parameters. It handles both non- and semi-relativistic kinematics with generic two-body interactions. In the current work, focusing on systems of three identical bodies, the method is generalised to include the management of a given class of three-body forces. The computational cost of this generalisation proves to not exceed the one for two-body interactions. The accuracy of the generalisation is assessed by comparing with results from Lagrange mesh method and hyperspherical harmonic expansions. Extensions for systems of $N$ identical bodies and for systems of two identical particles and one distinct are also discussed.

18 pages

References in corpus (10)

• Minimal Length Uncertainty Relation and Hydrogen Atom
• A high-precision variational approach to three- and four-nucleon bound and zero-energy scattering states
• Glueball Spectroscopy in a Relativistic Many-Body Approach to Hadron Structure
• Spectra of helium clusters with up to six atoms using soft core potentials
• The Doubly-heavy Tetraquarks ($q{q}^{\prime }\bar{Q}\overline{Q^{\prime }}$) in a Constituent Quark Model with a Complete Set of Harmonic Oscillator Bases
• Cubic Casimir operator of SU${}_C$(3) and confinement in the nonrelativistic quark model
• On a three-body confinement force in hadron spectroscopy
• Pentaquarks $uudd\bar{q}$ with One Color Sextet Diquark
• Many-quark interactions: Large-$N$ scaling and contribution to baryon masses
• Tests of the envelope theory for three-body forces

Cited by in corpus (1)

• Diquark size effects in the quark-diquark approximation for baryons