237Np nuclear relaxation rate in heavy fermion superconductor NpPd5Al2

${}^{27}$Al nuclear spin-lattice relaxation rate 1/${}^{27}{T}_{1}$ has been measured in heavy fermion superconductor NpPd${}_{5}$Al${}_{2}$ for a wide range of external fields between 0.7 and 11 T. We found that 1/${}^{27}{T}_{1}$ exhibits a strong, field-dependent behavior at low fields below $H\ensuremath{\sim}3$ T, which is attributed to unlike-spin cross relaxation between ${}^{237}$Np and ${}^{27}$Al. An analysis based on the cross relaxation process allows us to make the first quantitative estimates of the Np nuclear relaxation rate 1/${}^{237}\ensuremath{\tau}$ in an itinerant 5$f$ electron system. The estimated values of 1/${}^{237}\ensuremath{\tau}\ensuremath{\sim}6\ifmmode\times\else\texttimes\fi{}{10}^{7}$ s${}^{\ensuremath{-}1}$, with a weak temperature variation, are below the resolution of NMR relaxation times, indicating that a direct observation of the ${}^{237}$Np NMR signal would be very difficult, at least in the paramagnetic state. It is proposed that a direct observation of ${}^{237}$Np NMR might be possible in the superconducting state at $T\ensuremath{\sim}1$ K.