کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5420884 | 1395478 | 2007 | 20 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Beyond Euler angles: Exploiting the angle-axis parametrization in a multipole expansion of the rotation operator
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موضوعات مرتبط
مهندسی و علوم پایه
شیمی
شیمی تئوریک و عملی
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چکیده انگلیسی
Euler angles (α,β,γ) are cumbersome from a computational point of view, and their link to experimental parameters is oblique. The angle-axis {Φ,n^} parametrization, especially in the form of quaternions (or Euler-Rodrigues parameters), has served as the most promising alternative, and they have enjoyed considerable success in rf pulse design and optimization. We focus on the benefits of angle-axis parameters by considering a multipole operator expansion of the rotation operator D^(Φ,n^), and a Clebsch-Gordan expansion of the rotation matrices DMMâ²J(Φ,n^). Each of the coefficients in the Clebsch-Gordan expansion is proportional to the product of a spherical harmonic of the vector n^ specifying the axis of rotation, Yλμ(n^), with a fixed function of the rotation angle Φ, a Gegenbauer polynomial C2J-λλ+1(cosΦ2). Several application examples demonstrate that this Clebsch-Gordan expansion gives easy and direct access to many of the parameters of experimental interest, including coherence order changes (isolated in the Clebsch-Gordan coefficients), and rotation angle (isolated in the Gegenbauer polynomials).
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Solid State Nuclear Magnetic Resonance - Volume 31, Issue 1, February 2007, Pages 35-54
Journal: Solid State Nuclear Magnetic Resonance - Volume 31, Issue 1, February 2007, Pages 35-54
نویسندگان
Mark Siemens, Jason Hancock, David Siminovitch,