Extracting laws of decay in the femto–picosecond range from autocorrelation functions

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Abstract
The formalism of the resonance states is used to derive approximate expressions of the unimolecular law of decay resulting from a specific excitation. These expressions contain no cross terms and wash out the quantum interferences. We propose a method to relate them to an experimentally observable quantity, viz., the autocorrelation function C(t) obtained as the Fourier transform of a spectral profile, which is available even when the spectrum is poorly resolved. For a specific excitation, the exact initial rate of decay (valid up to the dephasing time T1) is equal to the initial slope of ‖C(t)‖2. The subsequent time evolution can be obtained by averaging ‖C(t)‖2 over its oscillations. This generates a function ‖C(t)‖2av whose area (from time T1 onwards) is directly related to an average decay lifetime. At times t>T1, a good approximation to the average decay curve Pav(t) can be derived by multiplying ‖C(t)‖2av by an appropriate constant. The method is exemplified on various diatomic and triatomic models. As an application to a real system, we study the B̃ 2B2 state of H2O+ which is coupled to the à 2A1 state via a conical intersection. State B̃ is found to undergo an ultrafast intramolecular relaxation with a lifetime of (1.6±0.2) 10−14 s.