The scattering amplitude is The phase shift d 0 is a function of E . Therefore The total cross section is now given by This is the Breit-Wigner resonance formula .
G is the width of the resonance curve.
Assume that the potential has enough depth so that a bound state with a small binding energy exists. Now let us look at a continuum state in the same potential. Now We also have tan ka ka . The quantity a is defined as the scattering length , and the quantity r 0 is defined as the effective range . Since we can infer the energy of a loosely bound state by performing a near zero energy scattering experiment.