Scattering length

The scattering length in quantum mechanics describes low-energy scattering. It is defined as the following low-energy limit,

where ${\displaystyle a}$ is the scattering length, ${\displaystyle k}$ is the wave number, and ${\displaystyle \delta (k)}$ is the phase shift of the outgoing spherical wave. The elastic cross section, ${\displaystyle \sigma _{e}}$, at low energies is determined solely by the scattering length,

...
Wikipedia