The spherical tensor formalism applied to relaxation in magnetic resonance

Concepts in Magnetic Resonance Part A: Bridging Education and Research

Volumn 28, Issue 4, 2006, Pages 270-290

  Nielsen, Robert D ^a   Robinson, Bruce H ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

EPR; Liouville space; Redfield equation; Relaxation; Spherical tensor; Spin lattice relaxation; Spin spin relaxation

Indexed keywords

EID: 33747159935     PISSN: 15466086     EISSN: 15525023     Source Type: Journal    
DOI: 10.1002/cmr.a.20055     Document Type: Review

References (49)

1. Smith SA, Palke WE, Gerig JT. 1994. The Hamiltonians of NMR Part IV: NMR relaxation. Concepts Magn Reson 6:137-162.
2. Pyper NC. 1971. Theory of symmetry in nuclear magnetic relaxation including applications to high resolution NMR line shapes. Mol Phys 21(1):1-33.
3. Szymanski S, Binsch G. 1989. A Liouville space formulation of Wangsness-Bloch-Redfield theory of nuclear spin relaxation. II. Scalar relaxation. J Magn Reson 81:104-120.
4. Biedenharn LC. 1981. Angular momentum in quantum physics, theory and application. Reading, MA: Addison-Wesley.
5. Sakurai JJ. 1994. Modern quantum mechanics. New York: Addison-Wesley.
6. Edmonds AR. 1985. Angular momentum in quantum mechanics. Princeton, NJ: Princeton University Press.
7. Slichter CP. 1996. Principles of magnetic resonance. Berlin: Springer.
8. Matthias E, Olsen B, Shirley DA, Templeton JE. 1971. Theory of nuclear magnetic resonance detected nuclear radiations. Phys Rev A 4(4):1626-1658.
9. Rose ME. 1957. Elementary theory of angular momentum. New York: Dover.
10. Happer W. 1972. Optical pumping. Rev Mod Phys 44(2):169-238.
11. Szymanski S, Gryff-Keller AM, Binsch G. 1986. A Liouville space formulation of Wangsness-Bloch-Redfield theory of nuclear spin relaxation suitable for machine computation. I. Fundamental aspects. J Magn Reson 68:399-432.
12. Sanctuary BC. 1985. Multipole NMR. X. Multispin, multquantum multilinear operator bases. J Magn Reson 61:116-129.
13. Sanctuary BC. 1986. Comments on spin-dynamics calculations. J Magn Reson 67:166-168.
14. Sanctuary BC, Krishnan MS. 1986. Rotating and principal-axis frames in multipole NMR. J Magn Reson 69:210-217.
15. Temme FP, Sanctuary BC. 1986. Symmetry-adapted bases and projection superoperators of multiquantum NMR under the groups S2[×]S2 and S4[×]S2. J Magn Reson 69:1-27.
16. Pyper NC. 1971. Theory of symmetry in nuclear magnetic resonance: part II. Mol Phys 22(3):433-458.
17. Buckmaster HA, Chatterjee R, Shing YH. 1972. The application of tensor operators in the analysis of EPR and ENDOR Spectra. Physica Status Solidi 13:9-50.
18. Bloch F. 1946. Nuclear induction. Phys Rev 70(7):460-474.
19. Weil JA, Bolton JR, Wertz JE. 1994. Electron paramagnetic resonance: elementary theory and practical applications. New York: Wiley.
20. Fano U. 1957. Description of states in quantum mechanics by density matrix and operator techniques. Rev Mod Phys 29(1):74-93.
21. Fano U. 1995. Density matrices as polarization vectors. Atti Della Accademia Nazionale Dei Lincei Classe Di Scienze Fisiche, Matematiche E Naturali 6(2):123-130.
22. Redfield AG. 1965. The theory of relaxation processes. In: Waugh JS, editor. Advances in magnetic resonance. Vol. 1. New York: Academic Press, p 1-32.
23. Robinson BH, Reese AW, Gibbons E, Mailer C. 1999. A unified description of the spin-spin and spin-lattice relaxation rates applied to nitroxide spin labels in viscous liquids. J Phys Chem B 103(28):5881-5894.
24. Nielsen RD, Robinson BH. 2004. A novel relaxation equation of motion. J Phys Chem A 108:1589-1600.
25. Mehring M, Weberruss. 2001. Object-oriented magnetic resonance. New York: Academic Press.
26. Fano U, Rau ARP. 1996. Symmetries in quantum physics. New York: Academic Press.
27. Abragam A. 1961. The principles of nuclear magnetism. Oxford: Clarendon Press.
28. Rao SK. 1985. A note on the classification of the zeros of angular momentum coefficients. J Math Phys 9:2260-2261.
29. Schwinger J. 1977. The Majorana formula. Trans N Y Acad Sci II 38:170-184.
30. Einarsson L, Westlund PO. 1988. The effects of higher rank multipoles on relaxation measurements in isotropic high spin system. J Magn Reson 79:54-65.
31. van Der Maarel JRC. 2003. Thermal relaxation and coherence dynamics of spin 3/2.1. static and fluctuating quadrupolar interactions in the multipole basis. Concepts Magn Reson 19A(2):97-116.
32. Smith SA, Palke WE, Gerig JT. 1992. Theoretical treatment of relaxation in the presence of an RF field. J Magn Reson 100(1):18-24.
33. van Der Maarel JRC. 2003. Thermal relaxation and coherence dynamics of spin 3/2. II. Strong radio-frequency field. Concepts Magn Reson 19A(2):117-133.
34. Werbelow LC. 1996. Relaxation processes: cross correlation and interference terms. In: Grant DM, Harris RK, editors. Encyclopedia of NMR. Vol. 6. New York: Wiley. p 4072-4078.
35. Werbelow LC, London RE. 1996. Dynamic frequency shift. Concepts Magn Reson 8:325-338.
36. Robinson BH, Haas DA, Mailer C. 1994. Molecular dynamics in liquids: spin-lattice relaxation of nitroxide spin labels. Science 263(5146):490-493.
37. Kivelson D. 1960. Theory of ESR line widths of free radicals. J Chem Phys 33(4):1094-1106.
38. Hwang JS, Mason RP, Hwang LP, Freed JH. 1975. Electron-spin resonance studies of anisotropic rotational reorientation and slow tumbling in liquid and frozen media. 3. Perdeuterated 2,2,6,6-tetramethyl-4-piperidone N-oxide and an analysis of fluctuating torques. J Phys Chem 79(5):489-511.
39. Freed JH, Fraenkel GK. 1963. Theory of linewidths in electron spin resonance spectra. J Chem Phys 39(2):326-348.
40. Percival PW, Hyde JS. 1976. Saturation recovery measurements of the spin-lattice relaxation times of some nitroxides in solution. J Magn Reson 23:249-257.
41. Bruschweiler R, Ernst RR. 1992. Molecular-dynamics monitored by cross-correlated cross relaxation of spins quantized along orthogonal axes. J Chem Phys 96(3):1758-1766.
42. Levitt MH. 2001. Spin dynamic, basics of nuclear magnetic resonance. New York: Wiley.
43. Harriman JE. 1978. Theoretical foundations of electron spin resonance. New York: Academic Press.
44. Berliner LJ. 1976. Spin labeling. New York: Academic Press.
45. Hubbard PS. 1963. Theory of nuclear magnetic relaxation by spin-rotational interactions in liquids. Phys Rev 131:1155-1165.
46. van Beek JD, Carravetta M, Antonioli GC, Levitt MH. 2005. Spherical tensor analysis of nuclear magnetic resonance signals. J Chem Phys 122(24):244510.
47. Jeener J. 1982. Superoperators in magnetic resonance. In: Waugh JS, editor. Advances in Magnetic Resonance. Vol. 10. New York: Academic Press, p 1-52.
48. Greiner W, Muller B. 1998. Quantum mechanics: symmetries. Berlin: Springer-Verlag.
49. Schweiger A, Jeschke G. 2001. Principles of pulse electron paramagnetic resonance. Oxford: Oxford University Press.