An explicit criterion for existence of the Magnus solution for a coupled spin system under a time-dependent radiofrequency pulse

CORC > 武汉物理与数学研究所 > 中国科学院武汉物理与数学研究所 > 2011年以前论文发表（包括2011年）

	An explicit criterion for existence of the Magnus solution for a coupled spin system under a time-dependent radiofrequency pulse
	Miao, XJ
刊名	PHYSICS LETTERS A
	2000-07-03
卷号	271 期号:4 页码:296-302
关键词	convergent criterion of the Magnus expansion exponential solution to the Schrodinger equation time-dependent radiofrequency field the shaped selective RF pulse nuclear magnetic resonance
英文摘要	The explicit criterion is derived in detail for the convergence of the Magnus expansion and the existence of the Magnus solution in the interaction picture, i.e., the exponential propagator in the weakly coupled spin (I = 1/2) system S(n)AMX... (n = 1,2,3,...) in which only spin group S is subjected to a time-dependent shaped selective radiofrequency pulse. The derivation is built on the same scheme as Maricq's [3. Chem. Phys. 86 (1987) 5647]. It is shown that the criterion depends only upon amplitude of the time-dependent field applied to the system, and the Magnus expansion converges and the Magnus solution exists when the flip angle of a non-negative-amplitude shaped RF pulse or a weak-amplitude shaped pulse is smaller than 2 pi. The exponential propagator then can be decomposed into a product of a series of elementary propagators and can be used to determine time evolution of the spin system under the shaped pulse. The linear differential equations to determine the unknown parameters in the Magnus solution are obtained explicitly. An alternative propagator in an expansion form for the Magnus solution is also proposed to describe the time evolution when the criterion is not met. (C) 2000 Elsevier Science B.V. All rights reserved.
WOS标题词	Science & Technology ; Physical Sciences
类目[WOS]	Physics, Multidisciplinary
研究领域[WOS]	Physics
关键词[WOS]	PRODUCT OPERATOR-FORMALISM ; GAUSSIAN PULSES ; NMR ; EXCITATION ; INVERSION
收录类别	SCI
语种	英语
WOS记录号	WOS:000088036000011
公开日期	2015-12-01
内容类型	期刊论文
源URL	[http://ir.wipm.ac.cn/handle/112942/8541]
专题	武汉物理与数学研究所_2011年以前论文发表（包括2011年）
作者单位	Chinese Acad Sci, Wuhan Inst Phys & Math, Lab Magnet Resonance & Atom & Mol Phys, Wuhan 430071, Peoples R China
推荐引用方式 GB/T 7714	Miao, XJ. An explicit criterion for existence of the Magnus solution for a coupled spin system under a time-dependent radiofrequency pulse[J]. PHYSICS LETTERS A,2000,271(4):296-302.
APA	Miao, XJ.(2000).An explicit criterion for existence of the Magnus solution for a coupled spin system under a time-dependent radiofrequency pulse.PHYSICS LETTERS A,271(4),296-302.
MLA	Miao, XJ."An explicit criterion for existence of the Magnus solution for a coupled spin system under a time-dependent radiofrequency pulse".PHYSICS LETTERS A 271.4(2000):296-302.