The spin-lattice relaxation time (${\mathit{T}}_{1}$) in arsenic ${(}^{75}$As nucleus; I=3/2) has been measured, using pulsed nuclear-quadrupole-resonance methods, as a function of temperature from 4 to 596 K. The results show that ${\mathit{T}}_{1}$ follows the Korringa relation (${\mathit{T}}_{1}$T=const) for temperatures below the Debye temperature (${\mathit{FTHETA}}_{\mathit{D}}$=282 K). Above ${\mathit{FTHETA}}_{\mathit{D}}$ the data break away from this relation, and the measured ${\mathit{T}}_{1}$ is shorter than that predicted by a nucleus-carrier relaxation model. Previous calculations of nucleus-carrier spin-flip transition probabilities involving a spherical Fermi surface (FS) have been extended to the nonspherical FS of arsenic. Modified expressions have been derived using a spheroidal approximation to the FS pockets. The carrier wave functions are approximated by free-atom wave functions. These calculations can account for the magnitude of measured nucleus-carrier interactions at low temperatures, and predict the usual Korringa law for the temperature dependence. The experimental results above ${\mathit{FTHETA}}_{\mathit{D}}$ can be accounted for using both nucleus-carrier processes (\ensuremath{\propto}T) and nucleus-phonon processes (\ensuremath{\propto}${\mathit{T}}^{2}$).