Atomic Nuclei: Nuclear Magnetic Moment

Atomic nuclei are positively charged. When they possess nonzero spin, they behave like rotating charges. This rotation of charge generates a magnetic field, B, and produces a magnetic moment, μ. The magnetic moment is the property that allows nuclei to interact with external magnetic fields in nuclear magnetic resonance applications.

In the absence of an external magnetic field, magnetic moment vectors are randomly oriented. When an external magnetic field B0 is applied, the magnetic moment vectors align with or against the field in 2I + 1 possible orientations. For a hydrogen nucleus with I = ½, there are two possible orientations: spin-up aligned with the field and spin-down aligned against it.

A proton has two possible spin orientations in an external magnetic field. The spin-up state, also called α or spin +½, is aligned with the field and has lower energy. The spin-down state, called β or spin −½, is aligned against the field and has higher energy. This energy difference is fundamental to nuclear magnetic resonance.

The spin quantum number I determines how many possible orientations a nucleus can adopt in an external magnetic field. The total number of orientations is given by 2I + 1. For hydrogen nuclei, I = ½, yielding two orientations. Different nuclei with different I values have different numbers of possible spin states, affecting their behavior in nuclear magnetic resonance.

Without an external magnetic field, a proton's magnetic moment is randomly oriented in space with no preferred direction. The magnetic moment exists due to the proton's charge and spin, but lacks any directional preference. Only when an external magnetic field is applied does the magnetic moment adopt specific allowed orientations relative to the field direction.

Alpha (α) and beta (β) are labels for the two spin states of a proton in an external magnetic field. The alpha state, or spin +½, aligns with the field and is the lower energy state. The beta state, or spin −½, aligns against the field and is the higher energy state. This energy difference enables radiofrequency pulses and pulse sequences to induce transitions between states.

A hydrogen nucleus, which is a proton, has a spin quantum number I of ½. Using the formula 2I + 1, this yields exactly two possible spin orientations in an external magnetic field. These two states correspond to the magnetic moment aligning either with or against the applied magnetic field direction.