Spin (physics)

Last revised by Michael Francois Nel on 5 Jun 2024

Spin, an intrinsic quantum property associated with elementary particles, challenges classical intuition by presenting an angular momentum quantized in half-integer (fermions) or integer values (bosons) 1,2.

The quantum nature of spin does not imply a physical rotation of particles. Instead, spin is a unique manifestation of quantum mechanics, introducing intrinsic angular momentum without classical analogies 1.

Nuclear spin

Nuclear spin exists in discrete half integer values.

Protons are composed of three quarks: 2 up quarks and 1 down quark. Each quark has a spin value of 1/2. The net spin value for a single proton is 1/2.

Neutrons are also composed of three quarks: 1 up quark and 2 down quarks. Neutrons also have a net spin of 1/2.

Both protons and neutrons have a tendency to pair with other protons and neutrons, respectively. When two protons or two neutrons pair up within the nucleus, their net spin value is 0. Atoms with an unpaired proton or neutron will have a non-zero nuclear spin value.

Non-zero spin particles have a vector-like quantity known as a magnetic moment. The magnetic moment determines how a particle will interact with an external magnetic field.

When placed in an external magnetic field, atoms with a non-zero spin value will align either parallel or anti-parallel to the magnetic field lines. Parallel spins are in a lower energy state compared to anti-parallel spins. A slight predominance of atoms will align parallel to the magnetic field.

The averaged sum of the angular momentum/magnetic properties for all atoms in a given sample can be represented by a quantity known as the net magnetization vector. The net magnetization vector is used to generate signal in MRI imaging.

In the context of MRI, this means that the atoms that can be used to generate signal are those with a non-zero spin value.

Hydrogen, comprising approximately 10% of a human body by mass 3, with its single unpaired proton and no neutron, forms the basis of routine clinical MRI as it has a net spin of 1/2.

Similarly, sodium-23 (11 protons, 12 neutrons) has a net spin of 1/2 and can, albeit with more difficulty, be used for MRI.

In contrast, carbon-12 (6 protons, 6 neutrons) and oxygen-16 (8 protons, 8 neutrons) together comprising approximately 83% of a human bodies' mass 3, have no net spin and therefore cannot be used.

Electron spin

Electrons, also fermions, are charged particles central to atomic structure and possess a spin of 1/2, leading to an associated magnetic moment. Although the electron's magnetic moment is significantly larger than the proton's magnetic moment, making the electron’s spin the dominant factor in determining the atom's overall magnetic properties, it is not used in clinical MRI. The reason is that the precession frequency induced by the electron's spin would need radiofrequency pulses in the microwave spectrum, depositing unacceptably high amounts of energy in the tissues 2.

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