Nuclear Relaxation Rates in Unconventional Multi-band Triplet Superconductors

Motivated by the unconventional multi-band triplet superconductivity in the material $\text{LaNiGa}_2$, we phenomenologically explore the behavior of Nuclear Relaxation Rates in such superconductors. We consider a model of equal spin s-wave triplet pairing between electrons in two bands with a non-unitary time reversal symmetry breaking order parameter. Modifications of this complex-valued order parameter allow one to tune between a single-gap and two-gap system. We show that by varying the hyperfine Hamiltonian and the order parameter, one can obtain the \textbf{presence} or \textbf{absence} of a Hebel-Slichter peak. We apply these results to recent measurements of Nuclear Relaxation Rates in $\text{LaNiGa}_2$.