Unit 3 : Equations & Terms

Unit 3 : Equations & Terms#

Equations#

To aid with exam revision below is a list of all equations that you should learn for this unit in the course.

MAGIC NUMBERS

(13)#\[\begin{equation} \bf \textnormal{Magic Nuclei -}~ Z~\textnormal{or}~N=2, 8, 20, 28, 50, 82, 126... \end{equation}\]

BINDING ENERGY PARABOLA ESTIMATE

(14)#\[\begin{equation} M(A,Z) = aA + bZ + cZ^{2} \end{equation}\]

BINDING ENERGY SOLVING

(16)#\[\begin{split}\begin{equation} \frac{dM(A,Z)}{dZ} \rightarrow 0\\ \end{equation}\end{split}\]

PARABOLA DIFFERENCE

(16)#\[\begin{equation} \frac{-\hbar^{2}}{2m} \nabla^{2} \psi(r,\theta,\phi) + V(r,\theta,\phi) \psi(r,\theta,\phi) = E \psi(r,\theta,\phi) \end{equation}\]

SHELL MODEL POTENTIAL

(17)#\[\begin{equation} V(r) = \frac{-V_{0}}{1+\textnormal{exp}(\frac{r-b}{a})} \end{equation}\]

SHELL QUANTUM NUMBERS AND PROJECTIONS

(18)#\[\begin{equation} \langle l^{2} \rangle = \hbar^{2}l(l+1) \end{equation}\]
(19)#\[\begin{equation} \langle l_{z} \rangle = \hbar m_{z} ~~~~\textnormal{where}~~~~ m_z=0,\pm1,\pm2,...,\pm l \end{equation}\]
(20)#\[\begin{equation} \langle s^{2} \rangle = \hbar^{2} s(s+1) \end{equation}\]
(21)#\[\begin{equation} \langle s_z\rangle = \hbar m_{s} ~~~~\textnormal{where}~~~~ m_{s} = \pm \frac{1}{2}. \end{equation}\]

SHELL MODEL SIMPLE STATES

\[ n_{\textnormal{states}} = 2(2l+1) \]

SPIN ORBIT COUPLING POTENTIAL OPERATOR

\[ V=V(r) \hat{L} \cdot \hat{S}. \]

Terms#

The following represent the key terms you should be able to explain after reviewing this module.

  • SEMF, Binding Energy Equation, Binding Energy Curve

  • Nuclear Spin, Parity, Magnetic Moment, Nuclear Material

  • Collective Body, Energy Levels, Collective Body Model

  • Individual Particle Model, Symmetry Term in SEMF, Pairing Term in SEMF

  • Magic Number Nuclei, Concentric Shells in Shell Model

  • Nuclear Potential Well, Harmonic Oscillator

  • Nuclear Decay, Mirror Nuclei, Relative Abundance

  • Neutron Binding Energy, Neutron Capture Energy, Neutron Seperation Energy

  • Neutron Shielding, Pauli Blocking, Reduced Quadrupole Moment

  • Nuclear Excitation Energy

  • Ground State, First Excited State, Doubly Magic Nuclei

  • Double Closed Shell Nucleus, Decay Chain Sequences

  • Principal Radioactive Series, Decay Chain

  • Total Angular MOmentum, Nuclear Spin, Angular Momentum Substates

  • Spin-Orbit Correction, Spin Up, Spin Down, Degeneracy

  • Unpaired Nucleon, Parity, Parity Operator, Collective Models