Many-body forces with the envelope theory

Abstract

Many-body forces are sometimes a relevant ingredient in various fields, such as atomic, nuclear or hadronic physics. Their precise structure is generally difficult to uncover. So, phenomenological effective forces are often used in practice. Nevertheless, they are always very heavy to treat numerically. The envelope theory, also known as the auxiliary field method, is a very efficient technique to obtain approximate, but reliable, solutions of many-body systems interacting via one- or two-body forces. It is adapted here to allow the treatment of a special form of many-body forces. In the most favourable cases, the approximate eigenvalues are analytical lower or upper bounds. Otherwise, numerical approximation can always be computed. Two examples of many-body forces are presented, and the critical coupling constants for generic attractive many-body potentials are computed. Finally, a semiclassical interpretation is given for the generic formula of the eigenvalues.

References in corpus (8)

• Sinc approximation of algebraically decaying functions
• Delta-excitations and the three-nucleon force
• Comment on "Fractional quantum mechanics" and "Fractional Schroedinger equation"
• A general comparison theorem
• Numerical tests of the envelope theory for few-boson systems
• Improvement of the envelope theory with the dominantly orbital state method
• Duality relations in the auxiliary field method
• Bound cyclic systems with the envelope theory

Cited by in corpus (11)

• Tests of the Envelope Theory in One Dimension
• Many-quark interactions: Large-$N$ scaling and contribution to baryon masses
• Quantum support to BoHua Sun's conjecture
• Envelope Theory for Systems with Different Particles
• Improvement of the Envelope Theory for Systems with Different Particles
• The envelope theory as a pedagogical tool
• Compact equations for the envelope theory
• Tests of the envelope theory for three-body forces
• Classical and Quantum Kepler's Third Law of N-Body System
• Accuracy Tests of the Envelope Theory
• Upper bounds for critical coupling constants for binding some quantum many-body systems