S-wave scattering length ($k\cot {\delta }_0(k)=-1/a_s+O(k^2)$)

The zero-energy parameter of the angular-momentum-zero partial wave. For a short-range interaction in three dimensions, its leading elastic scattering amplitude is $f_0(k)\simeq -a_s/(1+ik{a}_s)$ when effective-range corrections are negligible. For identical dilute bosons this parameter fixes the leading contact coupling $g_B=4\pi {\hslash }^2{a}_s/m_B$.