  We study the nature of the quasiinvariants in nematic 5CB and measure their
relaxation times by encoding the multiple quantum coherences of the states
following the JB pulse pair on two orthogonal bases, Z and X. The experiments
were also performed in powder adamantane at 301 K which is used as a reference
compound having only one dipolar quasiinvariant. We show that the evolution of
the quantum states during the build up of the quasi-equilibrium state in 5CB
prepared under the S condition is similar to the case of adamantane and that
their quasi-equilibrium density operators have the same tensor structure. In
contrast, the second constant of motion, whose explicit operator form is not
known, involves a richer composition of multiple quantum coherences on the X
basis of even order, in consistency with the truncation inherent in its
definition. We exploited the exclusive presence coherences 4, 6, 8, besides 0
and 2 under the W condition to measure the spin-lattice relaxation time T_{W}
accurately, so avoiding experimental difficulties that usually impair dipolar
order relaxation measurement such as Zeeman contamination at high fields, and
also superposition of the different quasiinvariants. This procedure opens the
possibility of measuring the spin-lattice relaxation of a quasiinvariant
independent of the Zeeman and S reservoirs, so incorporating a new relaxation
parameter useful for studying the complex molecular dynamics in mesophases. In
fact, we report the first measurement of T_{W} in a liquid crystal at high
magnetic fields. The comparison of the obtained value with the one
corresponding to a lower field (16 MHz) points out that the relaxation of the
W-order strongly depends on the intensity of the external magnetic field,
similarly to the case of the S reservoir, indicating that the relaxation of the
W-quasiinvariant is also governed by the cooperative molecular motions.
