The Geometrical Phase in the PEANUT Experiments for the NQR Spectroscopy for the Spins I = 3/2

Abstract

The results of the research of a non-cyclic geometrical phase of the ³⁵Cl nuclear quadrupole resonance (NQR) signals are presented, caused by the character of nuclear magnetization trajectory under radio-frequency excitation by means of PEANUT sequence for powdered samples. The analytical math expressions for a geometrical phase in NQR for a spin I = 3/2 while rotating nuclear magnetization by means of the PEANUT pulse sequence with frequency detuning and variable duration of the pulse were obtained. It is shown that the measured phase for this sequence is a geometrical phase and it may accumulate up to Δω ≠ 0 with a change of duration of the radio-frequency pulse \(t_{\text{w}}^{\prime }\). The experiment with the phase inversion and with nutation detection by means of echo amplitude was first applied in NQR jointly with measuring a geometrical phase. Since nutations detection and excitation in the PEANUT method are completely separate in time, experiments with high nutation frequencies become possible. The experimental examples supporting theoretically predicted distinctions of the geometrical phase for the PEANUT method in ³⁵Cl NQR are presented. An alternative nutation experiment is proposed to determine asymmetry parameter η for the nuclei with the spin I = 3/2 in powders proceeding from the nature of a non-cyclic geometrical phase accumulation.