The scattering length of a radial short-range potential is the coefficient determining its zero-energy scattering solution at large distance. For a bounded
nonnegative radial potential 
of finite range in three dimensions,
in the Bose-gas kinetic convention, the solution regular at the origin satisfies
 |
The normalization is 
outside the potential's support, and 
is the scattering length. For a nonzero
potential on a set of positive
measure, 
. For an impenetrable sphere
of exclusion distance 
, the exterior solution has this
same form and vanishes on the sphere. The factor 
in the equation is part of the pair-energy
normalization.
