THE QUANTUM FEW-BODY PROBLEM AND THE 1/D METHOD

Qualitative properties of the ground states and the low-lying spectra of three- and four-body systems are studied in the framework of the 1/D method, where D is the dimensionality of space. Special emphasis is laid on model-independent properties and relations between magnitudes. It is shown that the low terms of the 1/D expansion often give a good qualitative description of the system, although the 1/D series is known to exhibit poor convergence for D = 3. The Post estimate of the ground-state energy, the ordering of Wigner multiplets in the spectrum of resonances of the He-4 nucleus, the Hund rule in the two-electron atom, and other properties follow straightforwardly from the 1/D analysis.