A comprehensive account of the theoretical analyses of the Efimov effect and the universal properties of three-body bound states is provided. Recent experimental studies are reviewed and shown how the few-body analysis also yields insights into many-body phenomena, accessible by the experimental ability to tune the range and strength of the forces between cold atoms.

Universal few-body physics and cluster formation

The potential harmonic expansion method

https://cds.cern.ch/record/224237/files/CM-P00062481.pdf

The Nonrelativistic three-body problem for baryons

First order of the hyperspherical harmonic expansion method

Fast convergent hyperspherical harmonic expansion for three-body systems

In the framework of the hyperspherical formalism, we present a study of the coupled adiabatic approximation for the case of three nucleons interacting via central spindependent two-body potentials. We analyze the convergence of the ground state eigenvalues versus the grand orbital quantum number ($2K$) and compare the results to that of the coupled equations. We also compare with two simpler but less accurate approximations: the uncoupled adiabatic approximation and the extreme adiabatic approximation. The former provides an upper and the latter provides a lower bound to the ground state energy.NUCLEAR STRUCTURE Few body bound states, reduction of hyperspherical equations applied to triton, quantum few-body problem.

Coupled adiabatic approximation in the three-body problem

We use the lowest hyperspherical harmonic to find the wave function for the 1−, isospin-3/2 state reached byE1 transitions. The Ballot-Beiner-Fabre wave function is used for the3He ground state. Our calculated cross-section is in agreement with Fetisov’s measurements of photodisintegration into three nucleons for photon energy from 18 to 85 MeV, but we find too low a cross-section below 18 MeV.

Photodisintegration of3He into 3 nucleons

We study the hypertriton using the formalism of hyperspherical harmonics, for spin-independent NN and N..lambda.. two-body potentials of Gaussian shape. We use up to 19 Simonov harmonics for the Verma-Sural potential, and obtain a ground state energy 240 keV below their value of -2.35 MeV found for 9 Simonov harmonics. The partial waves are used to calculate various expectation values for the hypertriton. We readjust the strength of the ..lambda..N potential to obtain agreement between the calculated energy and the experimental value.

Hypertriton and hyperspherical harmonics

We extend the Fabre-Levinger calculation of the /sup 3/He photoeffect (E1 transition to final isospin 3/2) by including an additional grand orbital (L = 3) in the final state wave function The coupled differential equations between L = 1 and L = 3 for the final state are given We solve for two model potentials, and find the Blatt-Biedenharn eigenphase shifts and the mixing parameter, and also the total cross section for photodisintegration We find reasonable agreement (generally within 10%) with the cross section found for one hyperspherical harmonic The convergence speed of the hyperspherical harmonic expansion for the outgoing channel is also examined by comparison with sum rules for the integrated cross section: We find rapid convergence for both models

J. S. Levinger

Papers

Coupled adiabatic approximation in the three-body problem

Photodisintegration of3He into 3 nucleons

Hypertriton and hyperspherical harmonics

Trinucleon photoeffect to isospin 3/2, using coupled hyperspherical harmonics

Photodisintegration of 3 He into 3 nucleons. Errata and addendum