n−nandn−pScattering Lengths and Charge Independence

The degree of charge-independence violation for the low-energy nucleon-nucleon system is studied on the basis of a semiphenomenological meson theory. The difference between the singlet $n-p$ and $n-n$ scattering lengths induced by the ${\pi }^{\pm }-{\pi }^0$ and ${\rho }^{\pm }-{\rho }^0$ ($\Delta m$) electromagnetic mass splittings is investigated for the one-pion-, two-pion-, and $\rho$-exchange potentials. A charge-independent boundary condition is used to replace the short-range behavior. It is found that approximately 60% of the measured difference between the scattering lengths can be accounted for by the one-pion and two-pion potentials with charge-independent pseudoscalar coupling. The calculated results are sensitive to parameters of the $\rho$-exchange potential, such as $\Delta m$ and coupling constants, which are not well known. The dependence of the scattering lengths on these parameters is found. Finally, we note that a negative $\Delta m$, or a change of the order of 2% in the boundary condition or in the ratio of charged to neutral coupling constants, can account for the discrepancy that remains after pion electromagnetic mass splittings are included.