Tests of the envelope theory for three-body forces

Abstract

Many-body forces, and specially three-body forces, are sometimes a relevant ingredient in various fields, such as atomic, nuclear or hadronic physics. As their precise structure is generally difficult to uncover or to implement, phenomenological effective forces are often used in practice. A form commonly used for a many-body variable is the square-root of the sum of two-body variables. Even in this case, the problem can be very difficult to treat numerically. But this kind of many-body forces can be handled at the same level of difficulty than two-body forces by the envelope theory. The envelope theory is a very efficient technique to compute approximate, but reliable, solutions of many-body systems, specially for identical particles. The quality of this technique is tested here for various three-body forces with non-relativistic systems composed of three identical particles. The energies, the eigenfunctions, and some observables are compared with the corresponding accurate results computed with a numerical variational method.

arXiv comment13 pages

References in corpus (19)

• Delta-excitations and the three-nucleon force
• Interpreting $Z_c(3900)$ and $Z_c(4025)/Z_c(4020)$ as charged tetraquark states
• Spectra of helium clusters with up to six atoms using soft core potentials
• Cubic Casimir operator of SU${}_C$(3) and confinement in the nonrelativistic quark model
• Relativistic N-boson systems bound by pair potentials V(r_{ij}) = g(r_{ij}^2)
• Universal Behavior in Excited Heavy-Light and Light-Light Mesons
• The quantum N-body problem and the auxiliary field method
• On a three-body confinement force in hadron spectroscopy
• Numerical tests of the envelope theory for few-boson systems
• Spin contribution to light baryons in different large-$N$ limits
• Many-body forces with the envelope theory
• Improvement of the envelope theory with the dominantly orbital state method
• The auxiliary field method in quantum mechanics
• Eigenstates with the auxiliary field method
• Tests of the Envelope Theory in One Dimension
• Approximate solutions for N-body Hamiltonians with identical particles in D dimensions
• Many-quark interactions: Large-$N$ scaling and contribution to baryon masses
• The envelope theory as a pedagogical tool
• Accuracy Tests of the Envelope Theory

Cited by in corpus (3)

• Three-body Forces in Oscillator Bases Expansion
• A quark core-gluon model for heavy hybrid baryons
• Upper bounds for critical coupling constants for binding some quantum many-body systems