MODULATION OF CARR-PURCELL SPIN ECHOES IN MULTI-HALF SPIN SYSTEMS.

Loading...
Thumbnail Image

Date

1967

Journal Title

Journal ISSN

Volume Title

Publisher

Ohio State University

Research Projects

Organizational Units

Journal Issue

Abstract

Density matrix procedures for the analysis of Carr-Purcell spin echoes $(CPSE)^{1}$ in the presence of nuclear spin-spin coupling have been developed for several multi-half-spin systems. Since we assume the use of Mciboom-Gill $modification^{2}$ of the CPSE experiment, the quantity of interest is the x-component of magnetization, $<I_{x}>$, in the rotating frame. In general, $<I_{x}>$ for the nth echo can be expressed as: $\begin{equation}<I_{x}>_{n} \propto a_{0} + \sum\limits_{1}a\cos(2\pi F_{1} t) + \sum\limits_{m}(-1)^{n} b_{m} \cos(2 \pi F_{m} t),\end{equation}$ with $F_{1\, or\, m} = (2\pi t_{cp})^{-1}|\lambda_{j} - \lambda_{k}|,$ where $t_{cp}$ is the separation between the $180^{\circ}$ pulses and $\lambda_{i}$ is the ith eigenvalue in the $A\wedge A$, $representation.^{3}$ In Eq. (1) the amplitude factors, $a_{1}$'s or $b_{i}$'s can be determined by the use of eigen-functions of $A_{a} \wedge A$ and they are, in general, not equal. $a_{0}$ is the unmodulated contribution. The modulation frequencies and their relative amplitudes are functions not only of the relative chemical shifts and coupling constants, but also strongly dependent on $t_{cp}$. Analytical expressions for $<I_{x} >_{a}$ have been obtained in multi-half-spin systems of the type ``$A_{a}BX_{x}$'' where a and x are arbitrary numbers of half-spin nuclei. It is discussed that the general expression of $<I_{x}>_{n}$ for the type ``$A_{n}BX_{x}$'' can be obtained from those for simpler types such as AB, $A_{2}B$ and ABX. Automatic heteronuclear decoupling in CPSE is also discussed for above spin systems. $^{1}$ H. Y. Carr and E. M. Purcell, Phys. Rev. 94, 630 (1954). $^{2}$ S. Meiboom and D. Gill, Rev. Sci. Instr. 29, 688 (1958). $^{3}$A. Allerhand. J. Chem. Phys. 44, 1 (1966).

Description

Author Institution: Department of Chemistry, The Ohio State University

Keywords

Citation