# Gamma Decay

Sunday, April 3, 2022

## The Gamma Decay Process

Just like an atom, the nucleus in an excited state (such as after decaying via alpha or beta decay) will emit photons, called *nuclear gamma rays*. These gamma rays can also be absorbed by a nucleus in a ground state to excite it.

Nuclear excited states typically only have half-lives on the order of $10^{-9}$ or $10^{-12}$ seconds, but there are some instances where decay takes hours, days, or even years.

Once the gamma ray is emitted, the nucleus experiences some recoil to conserve momentum. Since the photon has energy $E_\gamma$ and momentum $p_\gamma=E_\gamma/c$, the nucleus must recoil with momentum $p_\text{R}=p_\gamma$ in magnitude. The associated kinetic energy is

$K_\text{R}=\frac{p_\text{R}^2}{2M}=\frac{p_\gamma^2}{2M}=\frac{E_\gamma^2}{2Mc^2}$

Using a gamma ray to excite a ground state nucleus results in the following relationship:

$E_\gamma=E_i-E_f-K_\text{R}\approxeq E_i-E_f$