https://doi.org/10.1351/goldbook.MT07419
Upon excitation of an '@I03353@' sample (assuming an ultra short excitation pulse) the relationship between the @F02453@ intensity detected at a time \(t\) and through a @P04712@ analyser oriented at an @A00346@ \(\beta\) with respect to the electric @P04712@ 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 @A00346@), the dipole-alignment contribution vanishes and \(I(t,\,\beta = 54.7^{\,\unicode{x26ac}} ) \propto N(t)\).
Notes:
- This concept also applies for time-resolved absorption measurements in cases in which @PT07461@ occurs because the detected species do not freely rotate fast enough to make the measurement @I03353@ within the time of the experiment.
- 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 @A00346@ \(\beta\) with respect to the electric @P04712@ of the exciting beam, \(N\) the excited-state population at steady-state equilibrium, and \(R\) the degree of alignment of the @T06460@ of the excited molecular entity.
- The term magic @A00346@ is also used in NMR @S05848@.