4th Week: Decays, Tunneling and Cross Sections

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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.

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle _{Z}^{A}\textrm{X}\to \; _{Z-2}^{A-4}\textrm{Y} + \;_{2}^{4}\textrm{He}}

Beta Decay

There are three types of Beta decays, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \beta^-} -decay, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \beta^+} -decay, and electron capture.

The first one, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle _{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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \beta^+} -decay occurs when a proton-rich nucleus emits a positron, therefore reducing the nuclear charge by one.

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle _{Z}^{A}\textrm{X}\to \; _{Z-1}^{A}\textrm{Y} + \;e^+}

Gamma Decay

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_{\alpha } = E_{center of mass} \frac{M_{product}+M_{reaction}}{M_{reaction}}, \; \; \; \; E_{center of mass} = E_{\alpha} \frac{M_{reaction}}{M_{reaction}+M_{product}}}