4th Week: Decays, Tunneling and Cross Sections

Nuclear Radiation

Figure 1. A table of known stable and radioactive nuclides

When looking at the table of nuclides it is obvious that the valley of stability is only a small percentage of all known nuclei. So most nuclei are considered unstable. To become stable these nuclides emit ionizing particles and radiation, resulting in a loss of energy from the original nuclei. This Process is called radioactive decay.

Alpha Decay

Alpha decay, which is usually seen in heavier elements, is the transformation of a parent nucleus to a daughter nucleus through the emission of a helium nucleus.

$_{Z}^{A}{\textrm {X}}\to \;_{Z-2}^{A-4}{\textrm {Y}}+\;_{2}^{4}{\textrm {He}}$

Beta Decay

There are three types of Beta decays, $\beta ^{-}$-decay, $\beta ^{+}$-decay, and electron capture. All three of these decays can be characterized by $\Delta A=0$ and $\left|\Delta Z\right|=1$.

The first one, $\beta ^{-}$decay, occurs when a nucleus with an over abundance of neutrons transforms to a more stable nucleus by emitting an electron. This process can be denoted as:

$_{Z}^{A}{\textrm {X}}\to \;_{Z+1}^{A}{\textrm {Y}}+\;e^{-}$

From electric-charge conservation, the proton number in such decays is increased by one unit.

Likewise, a $\beta ^{+}$-decay occurs when a proton-rich nucleus emits a positron, therefore reducing the nuclear charge by one.

$_{Z}^{A}{\textrm {X}}\to \;_{Z-1}^{A}{\textrm {Y}}+\;e^{+}$

Gamma Decay

$E_{\alpha }=E_{centerofmass}{\frac {M_{product}+M_{reaction}}{M_{reaction}}},\;\;\;\;E_{centerofmass}=E_{\alpha }{\frac {M_{reaction}}{M_{reaction}+M_{product}}}$