RELAXATION OF ANISOTROPICALLY ORIENTED I=3 2 NUCLEI IN THE MULTIPOLE BASIS - EVOLUTION OF THE 2ND RANK TENSOR IN THE DOUBLE-QUANTUM FILTERED NUCLEAR-MAGNETIC-RESONANCE EXPERIMENT/
Trj. Dinesen et Bc. Sanctuary, RELAXATION OF ANISOTROPICALLY ORIENTED I=3 2 NUCLEI IN THE MULTIPOLE BASIS - EVOLUTION OF THE 2ND RANK TENSOR IN THE DOUBLE-QUANTUM FILTERED NUCLEAR-MAGNETIC-RESONANCE EXPERIMENT/, The Journal of chemical physics, 101(9), 1994, pp. 7372-7380
The relaxation of an I=3/2 spin system in an anisotropic environment c
haracterized by a finite residual quadrupolar splitting omega(q) is mo
deled by analytically solving for the density operator from Redfield's
relaxation theory. The resulting equations are cast into the multipol
e basis in order to describe the tensorial components of the spin dens
ity matrix. Included in the relaxation matrix are off-diagonal element
s J(1) and J(2), which account for anisotropic systems with omega(q) v
alues less than the width of the resonant line. With the Wigner rotati
on matrices simulating hard pulses, the response to an arbitrary pulse
sequence can be determined. An analytical expression for the response
to the double quantum filtered (DQF) pulse sequence (pi/2)-(tau/2)-pi
-(tau/2)-theta-delta-theta-AQ for theta=pi/2 is presented, showing exp
licitly the formation of a second rank tenser owing only to the presen
ce of a finite omega(q). This second rank tenser displays asymptotic b
ehavior when the (reduced) quadrupole splitting is equal to either of
the off-diagonal spectral densities J(2) and J(1). Line shape simulati
ons for omega(q) values of less than a linewidth reproduce the general
features of some recently reported Na-23 DQF line shapes from biologi
cal systems. Distinct relaxation dynamics govern each of the tensorial
components of the resonant signal revealing the influence of the expe
rimental variables on the line shape.