Size shrinking of composite bosons for increasing density in the BCS to Bose-Einstein crossover
Dipartimento di Matematica e Fisica, Sezione INFM,
Università di Camerino, 62032 Camerino, Italy
Revised: 29 July 1999
Published online: 15 February 2000
We consider a system of fermions in the continuum case at zero temperature, in the strong-coupling limit of a short-range attraction when composite bosons form as bound-fermion pairs. We examine the density dependence of the size of the composite bosons at leading order in the density ("dilute limit"), and show on general physical grounds that this size should decrease with increasing density, both in three and two dimensions. We then compare with the analytic zero-temperature mean-field solution, which indeed exhibits the size shrinking of the composite bosons both in three and two dimensions. We argue, nonetheless, that the two-dimensional mean-field solution is not consistent with our general result in the "dilute limit", to the extent that mean field treats the scattering between composite bosons in the Born approximation which is known to break down at low energy in two dimensions.
PACS: 74.20.Fg – BCS theory and its development / 74.25.-q – General properties; correlations between physical properties in normal and superconducting states / 74.20.-z – Theories and models of superconducting state
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000