The Yang-Mills theory for the Nuclear Collective Model(YMCM) [1] provides a theo- retical framework that predicts the experimental values for moments of inertia associated with the collective rotational spectra of nuclei. The coupling parameter g in YMCM can take on values between 0 and 1, and couples the circulation degrees of freedom to the an- gular momentum degrees of freedom in the theory, which then allows for the true moments of inertia to be quantitatively derived. We probe the nature of this coupling by investigating the dynamics of the current source J, which is associated with the interaction Lagrangian of YMCM. Specifically, we calculate the covariant divergence and covariant curl of the current source J. Under the assumption that the nucleus is not heavily deformed, we can employ a perturbation approach in our calculations, where terms in higher order (defor- mation parameter) can be discarded. We find that the covariant divergence is zero, up to but not including O(2) and the covariant curl was found to be exactly zero, up to any order in . Furthermore, the Covariant Divergence and curl are calculated for the connection field AIF, and the divergence was zero, up to but not including O(), while the curl was zero up to any order.
