Gamma Decay and Internal Conversion

Alpha decay and the three β decay modes (β^–, β⁺, and electron capture) can lead to the formation of a daughter nucleus in an excited state. This excited nucleus may release energy to reach its ground state either instantaneously or with a slight delay (if in a metastable state), through one of the following two processes:

Processes Involved

Gamma (γ) Decay: The excitation energy is emitted as one or more γ photons.
Internal Conversion: The excitation energy is transferred to one of the atom's orbital electrons (usually a K-shell electron), resulting in the ejection of this electron. The vacancy left behind is filled by a transition from a higher atomic shell, often emitting characteristic X-rays or Auger electrons.

Mathematical Representation

The two processes of gamma decay and internal conversion are represented as follows:

$$ ^*X_A^{Z} \rightarrow X_A^{Z} + \gamma \, \text{(Gamma decay)} \quad \ $$ $ ^*X_A^{Z} \rightarrow X_A^{Z+1} + e^- \rightarrow X_A^{Z} + \gamma \quad \text{(Internal conversion)} $

Where:

^*X_A^{Z} represents the excited state of the nucleus.
X_A^{Z} is the stable daughter nucleus in its ground state after the decay process.
γ represents the gamma photon emitted during γ decay.
e^– is the electron emitted during internal conversion.

Example 1: Gamma Decay

One common example of gamma decay is the transition of an excited ⁶⁰Ni nucleus, which results from the β^– decay of ⁶⁰Co. The excited state of ⁶⁰Ni decays to its ground state by emitting two γ rays with energies of 1.17 MeV and 1.33 MeV:

$$ ^{60}_{28}Co \rightarrow ^{60}_{29}Ni^* \rightarrow ^{60}_{28}Ni + \gamma_1 (1.17 \, \text{MeV}) + \gamma_2 (1.33 \, \text{MeV}) $$

In this example:

⁶⁰Co undergoes β^– decay to form an excited ⁶⁰Ni nucleus.
The excited state of ⁶⁰Ni then transitions to its ground state, emitting two gamma photons in the process.
The energies of the γ rays are 1.17 MeV and 1.33 MeV.

Example 2: Internal Conversion

Another example of energy release through internal conversion is the decay of excited ¹²⁵Te, which results from the electron capture decay of ¹²⁵I. The excited state of ¹²⁵Te decays by emitting 35 keV gamma rays (7% of decays) and internal conversion electrons (93% of decays):

$$ ^{125}_{53}I + e^- \rightarrow ^{125}_{52}Te^* \rightarrow ^{125}_{52}Te + \gamma (35 \, \text{keV}) + e^- (\text{Internal conversion}) $$

In this example:

¹²⁵I undergoes electron capture, which leads to an excited state of ¹²⁵Te.
The excited ¹²⁵Te nucleus de-excites by emitting a 35 keV γ photon (7% of decays).
The majority of decays (93%) involve internal conversion, where the excitation energy is transferred to a K-shell electron, ejecting it from the atom and filling the vacancy with an electron from a higher shell.

Gamma Decay vs. Internal Conversion

The main difference between gamma decay and internal conversion lies in how the excitation energy is released:

In gamma decay, the excitation energy is emitted as gamma radiation (γ).
In internal conversion, the excitation energy is transferred to an orbital electron, which is ejected, and the vacancy is filled by a transition from a higher energy shell, leading to the emission of X-rays or Auger electrons.

Energy Released in Gamma Decay and Internal Conversion

The energy released in gamma decay and internal conversion processes comes from the difference in binding energies between the excited state and the ground state of the nucleus. In the case of internal conversion, part of this energy may be transferred to an orbital electron, leading to the emission of characteristic X-rays or Auger electrons.

The Q value for these transitions is given by:

$$ Q = M(P) - M(D) - m_{\gamma} $$

Where:

M(P) is the mass of the parent nucleus.
M(D) is the mass of the daughter nucleus.
m_γ is the mass of the emitted gamma photon.