  We present a NMR pulse double-irradiation method which allows one to separate
magnetic from quadrupolar contributions in the spin-lattice relaxation. The
pulse sequence fully saturates one transition while another is observed. In the
presence of a Delta m = 2 quadrupolar contribution, the intensity of the
observed line is altered compared to a standard spin-echo experiment. We
calculated analytically this intensity change for spins I=1, 3/2, 5/2, thus
providing a quantitative analysis of the experimental results. Since the pulse
sequence we used takes care of the absorbed radio-frequency power, no problems
due to heating arise. The method is especially suited when only one NMR
sensitive isotope is available. Different cross-checks were performed to prove
the reliability of the obtained results. The applicability of this method is
demonstrated by a study of the plane oxygen 17O (I = 5/2) in the
high-temperature superconductor YBa_2Cu_4O_8: the 17O spin-lattice relaxation
rate consists of magnetic as well as quadrupolar contributions.
