Nuclides with high N/Z ratios are neutron rich, and undergo radioactive decay to reduce this value by the emission of an electron (representing the conversion of a neutron to a proton within the nucleus). Conversely, nuclides with low N/Z ratios will decay by the emission of a positron (representing the conversion of a proton to a neutron); electron capture decay is an alternative process to positron emission, in which the unstable nucleus captures an orbiting electron to produce the same daughter nuclide.

Alpha decay becomes a dominant process above Z = 80, with the emission of an alpha particle (helium nucleus). Other relatively common modes of decay include isomeric transition (gamma-ray decay from a well-defined energy state of a radionuclide to a lower energy state in the same nuclide), spontaneous fission and delayed-neutron emission.

(a) Beta Decay

The mass number remains unchanged, and the atomic number Z increases by one unit when a radionuclide undergoes P- decay. An electron and an antineutrino are emitted, as a neutron in the nucleus is transformed into a proton:

n 4 p + в + V

Ax ч z+Y+P~+V

The maximum P-energy is represented by the equation:

Eemax = Q"- E

where Q — is the overall disintegration energy, equal to the difference in atomic masses between the ground states of the parent and daughter, and El is the energy level to which the decay occurs. Similarly, P+ decay is described by:

p 4 n + в+ +V

Ax ч z-y + в+ +v

and Eв+ = Q + — 2m0c2 — Et

where V is a neutrino, Q + is the overall disintegration energy, and

2m0c2 = 1.021998 MeV in which m0 is the mass of an electron at rest.

P+ emission occurs when

Q +- Et > 2m0c2

The P transition energy is shared between the electron (or positron) and antineutrino (or neutrino), as a continuous distribution for the two particles extending from 0 up

to E

(b) Alpha decay

A nucleus of atomic number Z and mass number A disintegrates by the emission of an a particle to give a daughter nucleus with atomic number Z — 2 and mass number A — 4:

Ax ч A-4y + Ahp

Z^ N Z-21 N-2 2^C2

The a disintegration energy can be represented by the equation:

where Ea is the energy of the emitted a particle, Et is the nuclear-level energy of

the daughter nuclide, and Er is the recoil energy:

in which MN is the mass of the recoiling daughter nucleus, and Ma is the mass of the a particle. The a particle is held within the nucleus by the Coulomb potential barrier, and escapes from the nucleus by means of a tunnelling mechanism.

(c) Gamma transitions

A gamma transition occurs when a nucleus in an excited state de-excites to a lower energy level, leading to the emission of a у ray and conversion electron (and an electron-positron pair when energy conditions permit). The gamma transition probability is defined as:

PTP — PY + Pce + Pe±

where PY, Pce and Pe± are the у -ray, conversion-electron and electron-positron pair emission probabilities, respectively.

The energy of the emitted y-ray can be represented by the equation:

EY — (i — Ef ) — Er

where Ei — Ef is the energy difference between the initial and final levels of the Ytransition, and Er is the recoil energy of the nucleus in the final state:

E —feL

r 2 M N c2

where MN is the mass of the recoiling daughter nucleus. The recoil energy is negligible, except for high Y energies and nuclei with low atomic number.

Gamma transitions can be classified in terms of multipole order, which is a function of the orbital angular momentum and quantum number L carried by the photon: L = 0, monopole; L = 1, dipole; L = 2, quadrupole, etc… If J and Jf are the total angular momenta quantum numbers of the initial and final levels connected by the Y transition, the vectorial relationship between the angular momenta is given by the formulation:

Ji J f — L — Ji +Jf I

Moreover, the angular momentum carried off by the photon cannot be zero, and consequently a 0 4 0 transition cannot occur except by internal conversion or internal-pair creation.

Gamma transitions are divided into electric and magnetic radiations:

electric radiation (emitted by the oscillation of electrical charges), with a parity change of (-1)L;

magnetic radiation (caused by the magnetic moment of the nucleus), with a parity change of (-1)^+4

A gamma transition can be a mixture of two (or sometimes three) multipole transitions. Two transitions in competition will have multipole order 2L and 2L+1, one electric and the other magnetic (e. g., mixture of M1 + E2).

The de-excitation energy of the nucleus can also be transferred directly to an electron (K, L, M..) which is ejected from the atom in preference to a gamma-ray emission:

where Ex is the binding energy of the electron in the X shell.

The internal conversion coefficient of the electron in the K shell is defined as:

Pce

ceK

PY where P and Pf are the K conversion-electron and y-ray emission probabilities, respectively; similar terms are also defined for the L, M, N… shells.

The total conversion coefficient is:

«total — OK + aL + 06m + ••• — — pe

PY

where Pce is the total conversion-electron emission probability of the related transition.