I am studying the laser-induced dissociation of O₂⁺ via the a ⁴Π_u → f ⁴Π_g transition using an ultra-fast Ti:sapphire laser with pulse durations of approximately 28 femtoseconds. The experimental kinetic energy release (KER) spectra is recorded using photons with energies of 3.2 eV (Ref [1]) and 4.8 eV, which are created by second (390 nm) and third (263 nm) harmonic generation of a 790 nm laser pulse. We produce the second harmonic by passing the 790 nm laser pulse (ω) through a second harmonic generation (SHG) BBO crystal, which combines two photons of frequency ω into a single photon with frequency 2ω. To produce the third harmonic, photons with frequencies of ω and 2ω are phase matched and passed through a third harmonic generation (THG) BBO crystal. This crystal uses sum-frequency generation to combine the ω and 2ω photons into a single photon with a frequency of 3ω.

  Theoretical calculations are performed using first-order time-dependent perturbation theory to determine the transition probabilities between the vibrational states found in the figure 2. Specifically, the probabilities are given by:

where Ψ _v represents the wave function of the initial state, Ψ_{v '} represents the wavefunction of the of final state and D(R) represents the dipole transition moment. The wavefunctions are computed at specific energies using the phase amplitude method (LAP2 program, Ref [2] ).

  We are interested in the Cooper minima effect, which describes the low rate of transitions between two electronic states at specific vibrational states (Ref [3]). Current theoretical calculations of the Cooper minima do not match our experimental results. The goal of my project is to compare the positions of the Cooper minima in our experimental and theoretical results to determine if there are inaccuracies in the theory.

Figure 2: This graph shows the a ⁴Π_u → f ⁴Π_g transition, where the molecule is excited by a photon. The wavefunction of the bound state (Ψ _v), the wavefunction of the continuum state Ψ_{v '} and the dipole transition moment D(R) are shown.

[1] M. Zohrabi, J. McKenna, B. Gaire, Nora G. Johnson, K. D. Carnes, S. De, I. A. Bocharova, M. Magrakvelidze, D. Ray, I. V. Litvinyuk, C. L. Cocke, and I. Ben-Itzhak, Phys. Rev. A 83, 053405 (2011).

[2] E. Sidky and I. Ben-Itzhak, Phys. Rev. A 60, 3586 (1999).

[3] J. McKenna, F. Anis, B. Gaire, Nora G. Johnson, M. Zohrabi, K. D. Carnes, B. D. Esry, and I. Ben-Itzhak, Phys. Rev. Lett. 103, 103006 (2009).