by
H. S. Köhler(Physics Department, University of Arizona, USA)
→
Europe/Stockholm
132:028
132:028
Description
The
scattering cross-section can be expressed as a function of phase-shifts
δ(k), k being the momentum. It will have a maximum for δ(k) = π/2,
implying a scattering length as → inf and effective range r0 = .0. This
situation is referred to as the Unitary Limit.
Taking advantage of Feshbach resonances atomic scattering lengths can
be tuned magnetically making it possible to study properties of systems
in this limit experimentally. The large scattering length in the
nucleon- nucleon 1 S0 state (as = −18.5f m, r0 = 2.8f m) is also of
interest here.
Theory predicts the total energy of interacting spin 1/2 fermions in
this limit to be proportional to the free Fermi-gas energy; i.e. E =
ξEF G with varied results: 0.24 < ξ < 0.5 at zero temperature. I
will show results of many-body calculations representing the
interaction by a separable potential that reproduces the Unitary Limit
exactly. I find ξ = 0.24 with a Brueckner p − p ladder summation at
temperature T = 0, but ξ increasing with effective range, yielding ξ ∼
0.45 for r0 = 2.8. Green’s function calculations (with h − h ladders
and spectral widths) for T > 0 yield higher values of ξ. They also
yield a critical temperature Tc = 0.29Ef , Ef being the fermi-energy of
the free Fermi gas at T = 0.
