Study of the Low-Energy Characteristics of Neutron-Neutron Scattering in the Effective-Range Approximation

The influence of the mass difference between the charged and neutral pions on the low-energy characteristics of nucleon-nucleon interaction in the $^{1}S_{0}$ spin-singlet state is studied within the framework of the effective-range approximation. By making use of the experimental singlet neutron-proton scattering parameters and the experimental value of neutron-neutron virtual-state energy, the following values were obtained for the neutron-neutron scattering length and effective range: $a_{nn}=-16.59(117)$fm, $r_{nn}=2.83(11)$fm. The calculated neutron-neutron scattering length $a_{nn}$ is in good agreement with one of the two well known and differing experimental values of this quantity, and the calculated effective range $r_{nn}$ is also in good agreement with present-day experimental results.