1. Tunneling Ionization of Hydrogen atom in an Electric Field 1113201 Hillary Ssemanda 森下研

2. Tunneling Ionization of Hydrogen Atom in Electric Field Introduction : Ionization of Hydrogen (1 ) Photo electric effect(EUV) : 1 photon-1 electron interaction, (2) Intense Laser (IR) Many photons- 1 electron interaction, (Classical Period)<<(Laser cycle period). (non perturbative) Why the Hydrogen atom? – Basic Schrodinger eq. is separable into 2 equations.[1] – There are already codes for Hydrogen in general potentials [1] Pavel A. Batishchev, Oleg I. Tolstikhin and Toru Morishita (PHYSICAL REVIEW A 82, 023416 (2010))

3. Tunneling Ionization of Hydrogen Atom in Electric Field Contents Theory Numerical Method Results – Energy and Ionization rate – TMD – Energy for complex F

4. Tunneling Ionization of Hydrogen Atom in Electric Field Contents Theory Numerical Method Results – Energy and Ionization rate – TMD – Energy for complex F

5. Tunneling Ionization of Hydrogen Atom in Electric Field Theory Potential Barrier : System’s Schrodinger eqn. ɛ is the Energy and Γ is the Ionization rate

6. Tunneling Ionization of Hydrogen Atom in Electric Field Theory Parabolic coordinates:

7. Tunneling Ionization of Hydrogen Atom in Electric Field Contents Theory Numerical Method Results – Energy and Ionization rate – TMD – Energy for complex F

8. Tunneling Ionization of Hydrogen Atom in Electric Field Numerical Method are Laguerre Polynomials The coefficients of [a] form a 5 diagonal Matrix in both cases

9. Tunneling Ionization of Hydrogen Atom in Electric Field Numerical Method

10. Tunneling Ionization of Hydrogen Atom in Electric Field Contents Theory Numerical Method Results – Energy and Ionization rate – TMD – Energy for complex F

11. Tunneling Ionization of Hydrogen Atom in Electric Field Results ɛ is the Ionization energy and Γ is the Ionization rate The quantum states are in the form REFERENCE’ Pavel A. Batishchev, Oleg I. Tolstikhin and Toru Morishita (PHYSICAL REVIEW A 82, 023416 (2010))

12. Tunneling Ionization of Hydrogen Atom in Electric Field Results and Comparison A flux of ionized electrons leaving the atom in the direction opposite to the field. The momentum distribution of the electrons ejected in this direction is TMD(Transverse Momentum Distribution) REFERENCE’ Pavel A. Batishchev, Oleg I. Tolstikhin and Toru Morishita (PHYSICAL REVIEW A 82, 023416 (2010))

13. Tunneling Ionization of Hydrogen Atom in Electric Field Energy in Complex Fields

14. Tunneling Ionization of Hydrogen Atom in Electric Field Complex Field At the Branch point: More Calculations will be done. Reference: J. S Briggs, V I Savichev, E A Solov’evPhys. B: At. Mol. Opt. Phys. 333363 2000 Re[F]Im[F] Our work0.0508―0.0393 Reference0.057988―0.0392454

15. Tunneling Ionization of Hydrogen Atom in Electric Field CONCLUSION We studied hydrogen atom in an electric Field We established an effective code for calculating complex energies and transverse momentum distribution(TMD). We checked the accuracy of the results by comparing them with results from earlier researches. The numerical method we used in this research has a shorter computation time compared to the general methods that work arbitrary potentials. Studies on the physics of Tunneling Ionization amongst other phenomena can be studied faster. We observed the existence of Branch points in the (0,0,0)&(0,1,0) surfaces.

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