1. Laser Assisted Charge transfer in He++ + H Collisions
Presented by
Fatima Anis
Dr. Brett D. Esry
V. Roudnev & R. Cabrera-Trujillo
Dr. Ben-Itzhak
Dr. Cocke

2. Introduction Does presence of a Laser Field affect charge transfer?
nhν + α + H  He+ + p
How much does it affect?
Can we control charge transfer during collision through CE phase?
Possibility for doing such an experiment

3. What has been done? Remi did some preliminary calculations using END
Reference:
T.Kirchner, PRL 89, (2002)
Remi did some preliminary calculations using END
1- p + H2  H + H2+
2- He+ + He  He + He+
3- Li++ + He  Li+ + He+
4- Li++ + Li  Li+ + Li+
FWHM = 10fs
λ = 790nm
I = 3.5x1012 W/cm2
Thomas did 3D grid calculations for same alpha on Hydrogen using circular polarized light.

4. Theory Collision Geometry Method: What are we solving?
How are we solving?
Calculations Parameters
Calculation of charge transfer probability

5. Collision scheme Collision Energy = 1keV/amu Laser parameters:
Projectile with Zp=1 moving with velocity vz
Target with ZT= 2 at origin
EII E┴
And Laser Field is given as
Collision Energy = 1keV/amu
Laser parameters:
Intensity = 3.5x1012W/cm2
FWHM ≈ 6.0fs
λ = 800nm
φ is CEP
! Capture is possible for almost 1-2 optical cycles

6. What are we solving?
We are solving 3D Time Dependent Schrödinger Equation
with
&
Electric Field
Dipole moment

7. How are we solving? Crank-Nicholson method
Relaxation Method to get the ground state of Hydrogen
Our lattice solution utilizes a uniform grid and three-point finite-difference method
Operator- Splitting for Time Evolution
Unitary operators of Cayley-Hamilton form is used for operator exponentials

8. Calculation parameters
Box size in our calculations
[-4, 15]x x [-4, 4]y x [-25, 25]z a.u.
Grid spacing = 0.2 a.u. supports
EH = a.u. EHe+= a.u.
Time Step = 0.06 a.u.
Time Range: ti = a.u. to tf = a.u.
Projectile Velocity = 0.1 a.u.
xinitial(b,0,-20.0) → xfinal(b,0,20.0)

9. Calculating Charge Transfer Probability
We estimate the reaction probability by integrating the electron density function around a box ΩT surrounding the target at tf
Fig. A typical He++ + H final state density function
Where,
We define ΩT as
ΩT = [-4, 15]x x [-4, 4]y x [-25, 10]z a.u.

10. Testing
The time step of 0.06 a.u. ensures energy conservation within 0.7% of its initial value
No Soft Core by making sure our vector lies exactly between the two grid points
&
Comparison with other results
END
Kirchner’s

11. Testing No Laser Field Collision Energy = 2keV/amu
Fig. He++ + H charge transfer probability as a function of b with no Laser Field for projectile energy of 2keV/amu.
Reference:
T.Kirchner, PRL 89, (2002)
T. Kirchner, PRA 69, (2004)

12. Testing
Fig. He+++H weighted transfer probability as a function of b for Eo = 0.0 a.u. and collision energy 1 keV/amu

13. Results Collision scheme Parallel Polarization Result &
Projectile with Zp=1 moving with velocity vz
Target with ZT= 2 at origin
EII E┴
Parallel Polarization Result
&
Perpendicular polarization

14. Parallel Polarization Comparison of END & Grid Calculation
Fig. He+++H weighted Laser induced charge transfer probability as a function b for collision energy 1keV/amu, E0 = 0.01a.u. and CEP = - π/2

15. Parallel Polarization
σ(a.u.2)
Field Free 0.95
E0 = 0.01a.u.
CEP=π 5.83
CEP=3π/2 4.58
CEP Averaged
Fig. He++ + H weighted charge transfer probability as a function of b for collision energy of 1keV/amu

16. Parallel Polarization
Fig. Charge transfer total cross section as a function of CEP for a collision energy 1keV/amu

17. Perpendicular Polarization
σ(a.u.2)
Field Free 0.95
E0 = 0.01a.u.
α =
α = π/
α = 2π/
Total
Fig. CEP-Averaged weighted charge transfer probability as a function of b for different orientation of the laser field and collision plane

18. Perpendicular Polarization
Fig. CEP-Averaged cross section as a function the relative angle α

19. Perpendicular Polarization
Fig. Capture cross section as a function of CEP for different orientations of the laser field and the collision plane

20. Without Field

21. With Laser Field

22. Conclusion
4-5 fold enhancement in capture cross section in case of both parallel and perpendicular Laser polarization
Enhancement is CEP dependent for parallel and perpendicular Laser polarizations
For Parallel polarization capture cross section is enhanced significantly independent of CEP
For perpendicular polarization effect of CEP and relative angle α are related to each other.

23. Thank You