Tài liệu Magnetic resonance potx

Applied physics group,
Physics department, CBNU

Contents:
Introduction
Theory basis
The basis of experiments
Summary

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Applied physics group,
Physics department, CBNU

Magnetic resonance is a phenomenon found in
magnetic systems that
possess both magnetic moments and angular
momentum.
Magnetic resonance is an analytical technique
based on a property of
matter called spin.
Magnetic resonance techniques include:
Magnetic resonance imaging (MRI),
Nuclear magnetic resonance (NMR),
Electron spin resonance (ESR),
Electron paramagnetic resonance (EPR).
Magnetic resonance techniques are generally
non-invasive and non-destructive.

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Applied physics group,
Physics department, CBNU

Magnetic resonance technique applications
MRI is used by clinicians to produce
tomographic images of
the inside of the human body. MRI is also
used by scientists
to study materials as it is a non-destructive
imaging technique.
NMR is used by scientists to study the
structure and dynamics
of molecules.
ESR and EPR are used by scientists to study
structure and reactions of free radicals.

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Applied physics group,
Physics department, CBNU

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Applied physics group,
Physics department, CBNU

A system such as a nucleus may consist of many particles coupled
together so that in any given state, the nucleus possesses a total
magnetic moment µ and a total angular momentum J. Two vectors
may be taken as parallel

µ = γJ

where γ is a scalar called the “gyromagnetic ratio”
In quantum theory, we have

J = I
where I stands for a dimensionless angular momentum operator.
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Applied physics group,
Physics department, CBNU

 As an external magnetic field is applied, this field produces an
interaction energy of nucleus of amount -µ H.
The Hamiltonian:

H = - µH

H = -γ  H0Iz in the z-direction,
and E = γ  H0m

with m = I, I-1, ….-I (2I + 1 values)

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Applied physics group,
Physics department, CBNU

m
H0

3 3

 +1
2 2


-3/2

3 3

 µH 0 
2 2


-1/2

1 3

H
 µ 0
2 2


+1/2
+3/2

0

1 3

−  µH 0 
2 2

3 3

−  µH 0 
2 2


The energy of the four sublevels of a nucleus with
spin I=3/2 when placed in a magnetic field H0

 To satisfy the conservation of energy,
ω = ∆ E
∀ ∆E is the energy difference between the initial and final
nuclear Zeeman energies.
∀ ω is an angular frequency
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Applied physics group,
Physics department, CBNU

 For producing magnetic resonance, an
alternating magnetic field is applied
perpendicularly to the static magnetic field,
and is written by
H pert= -γ  H0x Ixcosω t
Consequently, the allowed transitions are
between levels adjacent in energy, giving
ω = ∆ E = γ  H0

H

0
x

H0

or ω = γ H0
 On the other hand, for a particle with mass m
and charge e moving in a circular path of
radius r with period T
J = mvr = m.2π r2/T
While the magnetic moment is
µ = iA,
because i = (e/c)(1/T),
we have µ = eπ r2/cT, then deducing γ =
e/2mc.

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Applied physics group,
Physics department, CBNU

Experiments
1
m =+
2
A

Oven

dH
dz

C
dH
=0
dz
1
m =−
2

B

dH
dz

Detector
1

m =+
2

Slit

The atomic beam arrangement of I. Rabi and collaborators used to
detect magnetic resonance transitions in atomic energy levels

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Applied physics group,
Physics department, CBNU
X -in

Electromagnet pole faces

Magnet
Power
supply

X–Y
recorder
B

Y -in

Keithley
610A

D
Crystal

Magic
T

Cavity and
sample
A

Sync in
Microwave
Oscillator
And power supply

C
Dummy
load

Schematic arrangement of apparatus for an electron
paramagnetic resonance experiment in the
microwave region.

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Applied physics group,
Physics department, CBNU

Conclusion
With a large masses have low γ’s, a factor of 1000
lower γ for nuclei than for electrons.
We can change ω by changing Ho, but in most
cases it is advantageous to use as large a magnetic
field as possible.
The electronic systems have a resonance in the
microwave frequency region.
The nuclear systems have a resonance in the radio
frequency region.
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Applied physics group,
Physics department, CBNU

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Applied physics group,
Physics department, CBNU

Thanks for your attention!

The end