magic angle

https://doi.org/10.1351/goldbook.MT07419
Upon excitation of an '@[email protected]' sample (assuming an ultra short excitation pulse) the relationship between the @[email protected] intensity detected at a time \(t\) and through a @[email protected] analyser oriented at an @[email protected] \(\beta\) with respect to the electric @[email protected] of the exciting beam is given by \[I(t,\beta ) \propto N(t)\left [ 1 + (3\, \text{cos}^{2}\, \beta - 1)R(t) \right ]\] where \(R(t)\) is the degree of alignment of the emitting transition dipole in the laboratory frame and \(N(t)\) is the excited-state population, both at time \(t\). For \(\beta = 54.7^{\,\unicode{x26ac}}\) (the magic @[email protected]), the dipole-alignment contribution vanishes and \(I(t,\,\beta = 54.7^{\,\unicode{x26ac}} ) \propto N(t)\).
Notes:
  1. This concept also applies for time-resolved absorption measurements in cases in which @[email protected] occurs because the detected species do not freely rotate fast enough to make the measurement @[email protected] within the time of the experiment.
  2. Applies for steady-state measurements on fixed samples. In this case \[I(\beta ) \propto N\left [ 1 + (3\, \text{cos}^{2}\, \beta - 1)R \right ]\] with \(I(\beta)\) the intensity of the effect observed at an analyser @[email protected] \(\beta\) with respect to the electric @[email protected] of the exciting beam, \(N\) the excited-state population at steady-state equilibrium, and \(R\) the degree of alignment of the @[email protected] of the excited molecular entity.
  3. The term magic @[email protected] is also used in NMR @[email protected]
Source:
PAC, 2007, 79, 293. (Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)) on page 367 [Terms] [Paper]