Nuclear Structure
Understanding of nuclear structure is fundamental to all detection work,
but there are a couple heuristics that can be used. This material is
common, so I’ll use
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as expected.
Constant Density Nucleus
A common estimate for the radius of a nucleus is
\[ \begin{align}\begin{aligned}R\approx1.25\left[\unit{fm}\right]\cdot A^{\nicefrac{1}{3}}\\which indicates constant density of nucleii. Also, it should be noted\end{aligned}\end{align} \]
that the \(\left(\,\right)^{\nicefrac{1}{3}}\) indicates a not very
strong dependence on the number of nucleons, and thus all atoms with
several shells are close to \(2\times10^{-10}\unit{m}\)
Nuclear Models
The Shell Model uses the Pauli exclusion principle that states that
there are \(2j+1\) possible states for substates with total momentum
\(j\), That there are orbits, and that magic numbers correspond to
closed shells in both \(N\) and \(Z\).
The liquid drop model states that nucleons are arranged like the
molecules of a spherical liquid drop. This gives way to the expression
for the mass being
\[ \begin{align}\begin{aligned}\begin{split} \begin{multline*}
M=NM_{n}+ZM_{p}-\alpha A+\beta A^{\nicefrac{2}{3}}+\gamma\frac{Z^{2}}{A^{\nicefrac{1}{3}}}\\
+\xi\frac{\left(A-2Z\right)}{A}+\delta
\end{multline*}\end{split}\\where :math:`\alpha` is the total volumetric correction or the total\end{aligned}\end{align} \]
energy of one bond, \(\beta\) is the surface tension correction,
\(\gamma\) is the columbic term from potential energy, \(\xi\)
is the symmetry term, and stronger for \(Z=N\), and \(\delta\)
is a pairing term - indicating that the bond between \(n+n\) or
\(p+p\) is stronger than \(n+p\).
Bibliography
