Zero-energy scattering length

The physical interpretation of the zero-energy scattering length a(0) (or often just a) is that, when E = V(r), the wavefunction =o(f) has zero curvature. As r oo, o(r) for zero energy is thus a straight line. The extrapolation of this straight line cuts the distance axis at a separation R = ao, which may be positive or negative. 

Although the Kohn variational method is not a bounded method (except at zero energy when, subject to certain conditions, it can yield an upper bound on the scattering length), it is found in practice that the phase shift usually becomes more positive as the flexibility of the trial function is enhanced by increasing w it converges towards what is assumed to be the exact value according to a pattern which is quite accurately represented by... 

At interatomic distances / e, where the relaxation occurs, as well as at all distances where the hyperradius p a, the wavefunction is determined by the Schrodinger equation with zero energy and, hence, depends on the scattering length a only through a normalization coefficient ... 

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