Unit 8 : Equations & Terms

Unit 8 : Equations & Terms#

Review material will be added for this part of the course in later weeks.

Equations#

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

Breit Wigner Form#

(41)#\[\begin{equation} \sigma_{(a,b)}B = \sigma_{a+A→C*} \times BR(C* → B + b), \end{equation}\]

Breit Wigner Form#

(42)#\[\begin{equation} \sigma_{BW}(E) = \frac{\pi}{(k)^2} \frac{(2J + 1)}{(2I_a + 1)(2I_A + 1)} \frac{\Gamma_a(E)\Gamma_b(E)}{(E - E_R)^2 + \Gamma(E)^2/4}, \end{equation}\]

Compound Branching Ratio#

(43)#\[\begin{equation} BR(C* \rightarrow b + B) = \frac{\Gamma_b}{\Gamma}. \end{equation}\]

Difference in timescales#

  • Direct reactions are fast \((\sim10^{-22}~\textnormal{s})\)

  • Compound-nucleus reactions are slower (\(~10^{-18} - 10^{-16} s\))

Terms#

In addition you should make sure you understand the following key terms in this unit.

  • Direct Reactions

  • Compound Reactions

  • Independence Hypothesis

  • Characteristics of compound-nucleus reactions

  • Resonances

  • Breit-Wigner distribution

  • Photo-nuclear reactions

  • Photodisintegration

  • Nuclear resonance fluorescence

  • Giant dipole resonance