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PX388 Magnetic Resonance

Lecturer: Andy Howes

Weighting: 7.5 CATS

You have probably heard about the use of Magnetic Resonance Imaging (MRI) in medical diagnosis. In fact, magnetic resonance in nuclei - Nuclear Magnetic Resonance (NMR) - and in electrons - Electron Paramagnetic Resonance (EPR) - had existed as powerful tools used across science for several decades before being applied in the medical arena. This module describes the physics behind the magnetic resonance techniques - NMR and EPR are excellent experimental evidence for the existence of nuclear and electron spin - and shows why these techniques have found numerous applications in diverse fields including biology, chemistry, medicine, and materials science.


To show how quantum and classical physical principles may be combined to explain how the spin of nuclei and electrons is exploited in Nuclear Magnetic Resonance (NMR) and Electron Paramagnetic Resonance (EPR). It should explain why magnetic resonance methods are indispensable analytical tools in science today, in particular how NMR is used to form three-dimensional images (magnetic resonance imaging, MRI), and how molecular-level structure is revealed by the interactions that lead to fine detail in NMR and EPR spectra.


At the end of the module you should:

  • understand the physics of the NMR and EPR phenomena, i.e. the behaviour of nuclear and electron spins in magnetic fields
  • know how NMR and EPR experiments are performed, i.e. what hardware is required
  • appreciate how simple pulsed MR experiments work, e.g. the inversion recovery and spin-echo experiments for measuring the T1 and T2 relaxation times
  • be able to explain how three-dimensional images are formed in the MRI technique by the combination of pulsed MR with magnetic field gradients
  • understand how the interaction of a nuclear or electron spin with its atomic environment leads to fine structure in NMR and EPR spectra and how this can reveal structural detail on the atomic scale


The NMR and EPR phenomena
spin and angular momentum; inherent magnetism, precession at the Larmor frequency in an external magnetic field; thermal equilibrium and bulk magnetisation; resonance and electromagnetic induction: continuous wave and pulsed experiments
NMR and EPR hardware
NMR and EPR magnets (super-conducting and electro-); radiofrequency (rf) (NMR) and microwave (EPR) equipment
The Bloch equations
classical physics: precession of transverse magnetisation; the rotating frame, resonance offsets and nutation frequency; pulsed NMR: rf Pulses; longitudinal (T1) and transverse (T2) relaxation; continuous-wave MR: the steady-state magnetisation
Pulsed MR
inversion recovery and T1 relaxation; spin-echoes and T2 relaxation; Fourier transformation and frequency-domain spectra; sensitivity and signal averaging
Magnetic resonance imaging (MRI)
MRI is one of the most important diagnostic tools in modern medicine (note that the companion course Medical Physics (PX308) describes other important examples of Physics in the service of medicine).
one-dimensional imaging: frequency encoding using magnetic field gradients; two-dimensional imaging: phase encoding; slice selection (3D to 2D); gradient echoes
NMR and EPR spectrocopy: probing chemical structure
chemical shielding & the chemical shift (NMR); the g-value (EPR); through-bond J coupling and through-space dipole-dipole coupling (NMR); nuclear hyperfine and exchange interactions (EPR); solid-state NMR: anisotropic interactions and magic-angle spinning; quadrupolar interaction (nuclear spin I > 1/2)

Commitment: 15 Lectures

Assessment: 1.5 hour examination

Recommended Text: MH Levitt, Spin Dynamics: Basic principles of Nuclear Magnetic Resonance Spectroscopy , Wiley;
J. A. Weil, Electron Paramagnetic Resonance, Wiley-Interscience

This module has its own website.

Leads from: PX262 Quantum Mechanics and its Applications.