What is the origin of the nuclear magnetic dipole

moment (m) and how is it oriented relative to an

external magnetic field B0?

From Quantum Mechanics (I ½-particle 1H,

13C,31P,)

z

m

q

y

f

x

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)

Solution Larmor Equation - the basic NMR equation

w -gB

Conclusion

- THE LARMOR EQUATION (w -gB) IS DERIVED FROM A

CLASSICAL MECHANICAL APPROACH - THE SPIN MOTION IS WITHIN THE MHz-RANGE

(Radio-frequencies)

MOTION OF m IN A ROTATING FRAME OF REFERENCE

w rotation frequency of the reference frame

relative to the static frame

- 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

One dipole (mi) ? Many dipoles (

)

Mxy 0 !!!!!

LINEAR POLARIZED FIELD B1 B1cos(wt)

Rf-irradiation

Conclusion A LPF is composed of two opposite

rotating fields

RFR Application of an rf-pulse along the

u-direction (Why and what effect ?)

Excersize 1.5 What effect will B1have on the

magnetization when on resonance (w0 w) ?

Discuss

a

B1

The magnetization is rotated an angle a during

the duration t of the rf-pulse

Show experiment !

Decaying FID? show experiment

Including (phenomenologicaly) relaxation terms in

the Bloch equation (RFR)

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)

Water Confined between Solid Glass beads -

Experiment

Effect of various types of magnetic field

inhonogeneities on the FID decay Let 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 ?

What if N(B)

Why doesnt the FID decay exponentially with time

as expected from theory? (Perform a CPMG pulse

sequence)

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

Principles for Measuring T2 Spin gymnastics

Controlled sequence of rf-pulses Hahn spin-echo

p/2-t-p-t-deteksjon

(p/2)-puls

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

Magnetization in the rotating frame

100 meter

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EKKO

SPIN-ECHO-EKSPERIMENT

1/T2

1/T21/T2INH

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

T1-experiment