Symmetries of the master equation and long-lived states of nuclear spins

Abstract

In terms of the master equation of relaxation, long-lived states in systems of n interacting spin-1/2 nuclei are described as those with eigenvalues much less than the characteristic T(1) rate. It is demonstrated that degeneracies of correlations between interacting dipole-dipole pairs are responsible for their presence. The case n=3 is considered in full detail.

Symmetry constraints on spin dynamics: Application to hyperpolarized NMR

“…The transformation of total spin magnetization into singlet order, and back again, is an important manipulation in the NMR of long-lived states [13,14,15,16,17,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44] and in parahydrogen-enhanced NMR [18,19,20,21,22,45,46,47,48,49].…”

Creating Long-Lived Spin States at Variable Magnetic Field by Means of Photochemically Induced Dynamic Nuclear Polarization

“…The experimental dependences were fitted with the formula derived for W 4 . For systems with more coupled spins analytical results can be obtained [12][13][14] only for low fields (close to zero) or very high fields but not in the intermediate field range. For modeling field-dependent relaxation data for such systems it is necessary to perform a numerical analysis of the relaxation rates using the same strategy as described here (computation of the relaxation matrix and its eigen-values).…”

“…In the first case, there is a two-spin 1/2 system with properties, as discussed above, whereas in the second case, at least three coupled spins have to be considered (if the weaker couplings between the β-CH 2 protons and the ring protons are neglected). It is known that LLSs can exist in coupled three- and four-spin systems ,, at B = 0; however, it is not yet studied in detail in what field range they can be found. Theoretical treatment of such a problem can only be done numerically because the Hamiltonian of three coupled spins at arbitrary field cannot be solved analytically.…”

Singlet NMR methodology in two-spin-1/2 systems

“…Since its discovery in the Levitt group [24,25,26] a number of research groups have investigated the field of singlet NMR over the past 12 years with the purpose of defining and characterising singlet order relaxation properties [3,27,28,29,30], and the conditions for its existence [31,32,33,34], and of developing the methodology to access singlet order in different magnetic regimes [24,26,35,36,37,38,39,9,40,11,41,42,43] and to demonstrate the existence of long-lived singlet order in multiple-spin systems [44,45,46,47,48,49] and in heteronuclear systems [50]. Significant studies on the chemical requirements for obtaining long-lived spin order have been also conducted [17,51,52,53,54] with a record lifetime of 70 min for a 13 C-pair [54], 26 min for a 15 N-pair [51], and 10 min for a 1 H-pair [17] demonstrated.…”