NQR Spin Echo in the Effective Fields of Multiple-Pulse Sequences * G. B. Furman, I. M. Kadzhaya, G. E. Kibrik, A. Yu. Poljakov, and I. G. Shaposhnikov Theoretical Physics Department and Radiospectroscopy Laboratory, Perm University, Perm 614005, Russia Z. Naturforsch., 47a, 409-411 (1992); received November 21, 1991 Results of a study, both theoretical and experimental, of a new kind of NQR spin echo technique are reported and discussed. Key words: NQR, Spin echo, Multiple-pulse sequence. The action on a spin system by a multiple-pulse sequence may be described in terms of an effec- tive time-independent field, whose co e and direction n(n x , n y , n z ) are determined via the period t c , pulse duration t w , and frequency offset A of the sequence [1, 2], As has been shown [3], a resonant response of the system can be obtained in the effective field. In this paper results, both theoretical and experimental, on the NQR spin echo in the effective field are presented. We consider a quadrupolar nuclear spin system acted on by two pulsed magnetic Fields: a sequence of pulses (frequency co, amplitude HJ along the X-axis of the electric field gradient (EFG) tensor and a three- pulse low frequency (l.f.) field (frequency Q<gco, ampli- tude H 2 ) along the Z-axis of the EFG. In the represen- tation used in [3], the equation of motion of the den- sity operator g(t) is ^ i ^ = [ß t (n  S) + co 2 (t) S z (t) cos (Q t) + H d (t), ö (t)], at where (i) Q k = co e + 2 n k/t c , t c is the multiple-pulse sequence period, k = 0, ±1, +2, ±3,..., 2 (ii) co e = —cos 1 {cos((p/2) cos(zk c /2)}, t c (iii) n x = sin (<p/2)/sin (ß 0 tj2), n y = 0, n z = cos (tp/2) sin(zlr c /2)/sin(ß 0 tj 2), tp = yH l t w , y being the gyromagnetic ratio and t w the pulse duration of a multiple pulse sequence. * Presented at the Xlth International Symposium on Nuclear Quadrupole Resonance Spectroscopy, London, U.K., July 15-19, 1991. Reprint requests to Dr. G. B. Furman, Department of Theoretical Physics, Perm University, Bukirev St. 15, Perm 614005, Russia. (iv) co 2 (t) = tH 2 (t), H-, for 0 <t<t H 2 (t)=< T 0 < t < T 0 - K W 2 , To + Ti^j^To + ^ + L 0 otherwise, (see Fig. 1, bottom) t 0 and ii are the intervals between the first and second pulse of the three-pulse sequence and be- tween the second and third pulse of this sequence, respectively, and f Wi , r W2 , f W3 are the durations of the first, the second, and the third pulses of the sequence, M x (t) M x (o) 1.0 . b 2.o t, ms Fig. 1. Top: Time dependence of the magnetization M x , a) in the absence of the l.f. pulse sequence, b) in the presence of this sequence. Bottom: The diagram of the l.f. pulse sequence (c). 0932-0784 / 92 / 0100-0409 $ 01.30/0. - Please order a reprint rather than making your own copy.