Magnetic properties of nuclei - Structure of matter

Question 1

Explain angular momentum, conjugated spin dipole magnetic moment in protons and neutrons.

Answer 1

Similar to electrons, protons and neutrons also have angular momentum (spin) and conjugated spin dipole magnetic moment.

For proton, these vectors are of the same direction.

For neutron, these vectors are antiparallel.

The value of spin is half-integer (in multiples of ћ).

Therefore, nuclei, which contain odd number of protons, neutrons or odd number of nucleons, possess a resulting spin (given as vector su, spins of individual nucleons) different from zero.

These nuclei also possess a non zero magnetic moment since protons as well as neutrons are formed by electrically charged quarks.

Examples of these nuclei may be the following nuclides:

¹H₁, ²D₁, ⁷Li₃, ¹²C₆, ¹⁴N₇, ¹⁹F₉, ²³Na₁₁, ¹²⁷I₅₃ etc.

There are more than one hundred of stable atoms with the magnetic moments and non-zero spins.

All the nuclei composed of even numbers of protons or neutrons.

E.g. ¹²C₆, ¹⁶O₈, ³²S₁₆, ⁴⁰Ga₂₀ etc possess a zero spin.

Question 2

What yields the spin of the nucleus?

Answer 2

Product of the nuclear spin number, I, and Dirac constant, I.e. Iћ yields the spin of the nucleus.

Nuclei with even mass numbers have integer values of the spin (in units ћ) while nuclei with odd mass number possess half integer spins.

Effects of the nuclear magentic resonance are observed for nuclei with I>0.

Question 3

How is the magnitude of the magnetic moment of the nucleus expressed?

Answer 3

Analogously to the Bohr’s magneton (eћ/2m_e) as a unit of the magnetic moment of the lectron, the magnitude of the magnetic moment of the nucleus μ_j is expressed in units of the nuclear magneton (n.m.) defined by 1n.m. = eћ/2m_p where m_p is the mass of the proton.

It is obvious that the numerical value of the nuclear magneton is lower than that of Bohr magneton by a factor m_e/m_p, which is approximatly 1/1836.

The value of 1n.m. = 5.5 * 10^-27 J.T^-1.

Magnetic moments of proton and neutrons are 2.8 and 1.9 n.m. respectively.

Thus magnetic moment of proton is 1.41 * 10^-26 J.T^-1 and it is about 658 times lower than that of electron.

That is why magnetic phenomina of nuclei are so weak and sophisticated devices had to be designed for the observation of their effects.

Magnetic properties of the nuclei serve as a basis of the most modern imaging method, nuclear magnetic resonance imaging.