Influence of modulation field and frequency shift of spin interaction on the formation of absorption and dispersion signals of nuclear magnetic resonance when they are recorded in weak fields

The problems arising in express testing of the state of a condensed medium by the weak-field nuclear magnetic resonance method are considered. The advantages of using the modulation technique for recording the NMR signal in a weak field are substantiated in comparison with other methods in small-sized NMR meters. The difficulties arising in obtaining additional information about the medium under study using the recorded NMR signals are noted and the directions for their solution are determined. The problem of forming new coefficients in the Bloch equations taking into account the modulation of the constant magnetic field B 0 and the spin-spin interaction in the shift of the resonance frequency and in the formation of the magnetization M is considered. Using the Wagness transformations, the absorption v ( t ) and dispersion u ( t ) signals are introduced, the transition to a rotating coordinate system is carried out, and the Bloch equation for the components u ( t ), v ( t ), and Mz ¢ with new coefficients is formed. The paper presents a mathematical relationship for describing the shape of the recorded NMR signal, which at the output of the autodyne detector consists of the signals v ( t ) and u ( t ) in different proportions between them, depending on the conditions of the sygnal recording. The values of u ( t ), v ( t ), and Mz ¢ are calculated for different parameters of magnetic fields. Different versions of these calculations are compared, which makes it possible to justifiably exclude the contribution of the modulation field, which varies over time, from one of the new coefficients for the Bloch equations. A solution to the system of Bloch equations with new coefficients is developed, and relationships are obtained for u ( t ), v ( t ), and Mz ¢, in which these signals are expressed only in terms of the parameters of the magnetic fields and the times of longitudinal T 1 and transverse T 2 relaxation of the medium under study. The line shapes are calculated using the parameters of the recorded NMR signals using the modulation technique and compared with the experimental data. The obtained results confirmed the validity of the chosen approach to the description of new coefficients and to the solution of the system of Bloch equations, in which they were included, with respect to u ( t ), v ( t ), and Mz ¢. All this allows, in contrast to the solutions of the Bloch equations that were earlier, to continue the derivation of analytical relationships for the dispersion u ( t ) and absorption v ( t ) signals independently of each other and to determine critical points for them, as well as the nature of the change in the dependences themselves, which was previously impossible to do.

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