The hyperfine structure observable in atomic spectra, including the interactions with nuclei, indicates that the nuclei have spin. The nuclear spin is a vector, and its absolute value is л/I (I + 1)—, where I is the quantum number of the nuclear spin,

2n

simply called “nuclear spin.” Nuclei with even mass numbers have I = 0, 1, 2, 3…,

13 5 11

whereas nuclei with odd mass numbers have I = -, -, -… —. The nuclear spin is

2 2 2 2

the sum of the spins of all protons and neutrons. In nuclear reactions, the conservation of spins also must occur.

Parity is related to the symmetry properties of nuclei. It expresses whether the wave function of a particle is even or odd (symmetrical or asymmetrical), depend­ing on whether the wave function for the system changes sign when the spatial coordinates change their signs.

Even parity: Ф(— x, — y, — z) = Ф(х, y, z)

Odd parity: Ф(— x, — y, — z) = — Ф(х, y, z)

The conservation of parity also must occur for nuclear reactions.

The spin and the parity can be signed together: for nuclei with even parity, a + is written after the value of the spin, while for nuclei with odd parity, a — is written (e. g., 0+ or 7/2—).

The particles can be characterized by statistics describing the energies of single particles in a system comprising many identical particles, which has a close con­nection to the spin and parity of the particles. The particles with half-integral nuclear spin can be described using the Fermi—Dirac statistics. These particles obey the Pauli exclusion principle and have odd parity. These particles are called “fermions.” The particles with zero or integral spin and even parity can be described using the Bose—Einstein statistics. These particles are called “bosons.”

The movement of a charged particle causes magnetic momentum. The unit of measure for magnetic momentum is the Bohr magneton, which describes the mag­netic momentum of an electron:

eh ‘id , ,

MB = ——- = 9.274 X 10—24 J/T (2.14)

4nme

For the nucleus, the mass of the proton can be substituted into Eq. (2.14) as follows:

where T is tesla. The quantity pN expresses the unit of nuclear magnetic momen­tum. The magnetic momentum of the different nuclei is in the range of 0—5pN. Surprisingly, the magnetic momentum of the proton is not equal to the value calcu­lated from Eq. (2.15), but it is about 2.7926 times higher than the calculated value. Perhaps more surprising, the neutrons also have magnetic momentum, which is expressed by —1.9135 pN. This implies that the neutral neutron consists of smaller charged particles known as quarks, as discussed in Section 2.4. The negative sign of the magnetic momentum of the neutron indicates that the spin and magnetic momentums are in opposite directions.

Besides magnetic momentum, nuclei can have electric quadruple momentum too. The formation of quadruple momentum can be caused by the deviation of charge distribution from the spherical symmetry. Quadruple momentums have been determined for many nuclei by I > 1/2. Nuclei I = 0 or 1/2 cannot have quadruple momentums.

In conclusion, the characteristic properties of nuclei are listed as follows:

1. Rest mass

2. Electric charge

3. Spin

4. Parity

5. Statistics

6. Magnetic momentum

7. Electric quadruple momentum (not all nuclei).