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Computational Study of Intense Laser-Induced Reactions in H2+ and D2+

This project investigates the behavior of H2+ and D2+ ions under intense laser pulses, focusing on quantum dynamics and the validity of the Axial Recoil Approximation. Utilizing advanced quantum mechanics equations, the work involves calculating wave function evolution using Fortran programs. Key metrics include laser intensity, pulse duration, and carrier envelope phase (CEP). The study aims to predict physical observables from the produced nuclear wave functions, contributing to the understanding of dissociation dynamics in molecular hydrogen.

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Computational Study of Intense Laser-Induced Reactions in H2+ and D2+

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  1. Intense LASER interactions with H2+ and D2+:A Computational Project  Ted Cackowski

  2. Project Description • Assisting the multiple-body-mechanics group at KSU with calculations of H2+/D2+ behavior under the influence of a short, yet intense laser pulse.

  3. Motivation • To explore the validity of the Axial Recoil Approximation • Exploring the quantum mechanics of H2+/D2+ in a time-varying electric field under various experimental conditions • Exploring the quantum dynamics there afterward

  4. Modes of Operation • Schrödinger's Equation and the associated quantum mechanics • Fortran 90/95

  5. Process Overview

  6. Physical Situation

  7. Scales of Physical Interest • Laser Intensity: ~1E14 watts/cm2 • Pulse Length: ~7E-15 s (femtoseconds) • Frequency: 790E-9 m (nanometers) • H2/D2 Nuclear Separation: • ~3E-10 m (angstroms)

  8. Diatomic Hydrogen • Two protons, two electrons • Born-Oppenheimer Approximation • First Electrons, then Nuclei

  9. Figure 1

  10. H2+ Molecule • There are two separate pulses. • Ionizing pulse gives us our computational starting point • Franck-Condon Approximation

  11. Figure 2

  12. Note on Completeness • The Overlap Integral • Where, |FCV|2 are bound/unbound probabilities • Unavoidable dissociation by ionization • Controlled dissociation

  13. Mechanics • The second pulse is the dissociating pulse. • We now have the Hamiltonian of interest • Dipole Approximation

  14. Linear Methods • We expand Yinitialonto an orthonormal basis • Overlap integral / Fourier’s trick • We then generate the matrix H as in • Propagate the vector through time using an arsenal of numerical techniques

  15. Data Production • After producing a nuclear wave function associated with a particular dissociation channel, any physical observable can be predicted. • “Density Plots” are probability density plots (Ψ*Ψ)

  16. Channels

  17. Notable Observables • Angular distribution of dissociation as it depends on: • Pulse Duration • Pulse Intensity • Carrier Envelope Phase (CEP)

  18. My Work • Computational Oversight • Two Fortran Programs • First: Calculate the evolution of the wave function when the Electric field is non-negligible • Second: Calculate the evolution of the wave function when the Electric field is negligible • Produce measurable numbers

  19. Afore Mentioned Figure

  20. Conclusions • Rotational inertia plays an important role • Pulse intensity is critical • Further analysis will be required for pulse length and CEP

  21. Future Work • Simulate H2+ under various CEP initial conditions • Confidence Testing • Data Interpretation • Connect with JRM affiliates

  22. Special Group Thanks • Dr. Esry • Fatima Anis • Yujun Wang • Jianjun Hua • Erin Lynch

  23. Special REU Thanks • Dr. Weaver • Dr. Corwin • Participants • Jane Peterson

  24. Bibliography • Figure 1 from Max Planck institute for Quantum Optics website • Figure 2 from Wikipedia, “Frank-Condon” http://images.google.com/imgres?imgurl=http://www.mpq.mpg.de/~haensch/grafik/3DdistributionD.gif&imgrefurl=http://www.mpq.mpg.de/~haensch/htm/Research.htm&h=290&w=420&sz=24&hl=en&start=0&um=1&tbnid=rOBflIUYzSm7xM:&tbnh=86&tbnw=125&prev=/images%3Fq%3DH2%252B%26svnum%3D10%26um%3D1%26hl%3Den%26sa%3DN

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