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Origin of Nuclear Magnetic Dipole Moment (m) and its Orientation Relative to External Magnetic Field

This text explores the origin of nuclear magnetic dipole moment and how it is oriented relative to an external magnetic field. It discusses the motion and angular momentum of the dipole, Larmor equation, and the role of a rotating frame of reference. The effects of an rf-pulse and magnetic field inhomogeneities on the observable signal intensity and FID decay are also examined. Various pulse sequences and experiments are explained, including Hahn spin-echo and CPMG-pulse sequence.

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Origin of Nuclear Magnetic Dipole Moment (m) and its Orientation Relative to External Magnetic Field

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  1. What is the origin of the nuclear magnetic dipole moment (m) and how is it oriented relative to an external magnetic field B0?

  2. From Quantum Mechanics(I = ½-particle; 1H, 13C,31P,…) z m q y f x

  3. Characterizing the motion of m in B0 m = gL L; angular momentum (spin) • = m x B • ; torque Exercise 1.1: Derive the above equation (qualitatively)

  4. SolutionLarmor Equation - the basic NMR equation w = -gB

  5. Conclusion • THE LARMOR EQUATION (w = -gB) IS DERIVED FROM A CLASSICAL MECHANICAL APPROACH • THE SPIN MOTION IS WITHIN THE MHz-RANGE (Radio-frequencies)

  6. MOTION OF m IN A ROTATING FRAME OF REFERENCE w; rotation frequency of the reference frame relative to the static frame

  7. Exercise 1.4. Find the solution of the above equation in the rotating frame, (Note w0= -gB0) mU cos(w-w0)t mV sin(w-w0)t

  8. One dipole (mi) → Many dipoles ( ) Mxy = 0 !!!!!

  9. LINEAR POLARIZED FIELD [B1= B1cos(wt)] Rf-irradiation Conclusion: A LPF is composed of two opposite rotating fields

  10. RFRApplication of an rf-pulse along the u-direction(Why and what effect ?)

  11. Excersize 1.5: What effect will B1have on the magnetization when on resonance (w0 = w) ? Discuss

  12. a B1 The magnetization is rotated an angle a during the duration t of the rf-pulse Show experiment !

  13. Decaying FID? – show experiment

  14. Including (phenomenologicaly) relaxation terms in the Bloch equation (RFR):

  15. Bloch Equation (on resonance, after magnetization is rotated onto the v-axis) Solution (after the magnetization is rotated into the uv-plane (w1 = 0); Exercise 2.2)

  16. Water Confined between Solid Glass beads - Experiment

  17. Effect of various types of magnetic field inhonogeneities on the FID decayLet N(B) represent the number of spins experiencing a magnetic field B.Since w = gB, we may write dN = N(w)dw What is the observable signal intensity M if ?

  18. What if N(B) =

  19. Why doesn’t the FID decay exponentially with time as expected from theory?(Perform a CPMG pulse sequence)

  20. Why does the FID decay faster (1/T2*) than what is predicted by the true spin-spin relaxation rate 1/T2? FID Homogeneous field lnM Inhomogeneous field Time

  21. Principles for Measuring T2 Spin gymnastics: Controlled sequence of rf-pulses Hahn spin-echo: p/2-t-p-t-deteksjon (p/2)-puls

  22. The basic (p/2)x – p-x spin-echo experiment

  23. Magnetization in the rotating frame “100 meter”

  24. EKKO

  25. SPIN-ECHO-EKSPERIMENT 1/T2 1/T2+1/T2INH

  26. CPMG-pulse sequence p/2-t-(p-t-deteksjon)n

  27. T1-experiment

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