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Laser Assisted Charge transfer in He ++ + H Collisions

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Laser Assisted Charge transferin He++ + H Collisions

Presented by

Fatima Anis

Dr. Brett D. Esry

V. Roudnev & R. Cabrera-Trujillo

Dr. Ben-Itzhak

Dr. Cocke

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

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

Reference:

T.Kirchner, PRL 89, 093203 (2002)

Thomas did 3D grid calculations for same alpha on Hydrogen using circular polarized light.

What has been done?Theory

Collision Geometry

Method:

- What are we solving?
- How are we solving?
- Calculations Parameters
- Calculation of charge transferprobability

Projectile with Zp=1 moving with velocity vz

EII

E┴

And Laser Field is given as

Target with ZT= 2 at origin

Collision scheme- 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

Operator- Splitting for Time Evolution

- Unitary operators of Cayley-Hamilton form is used for operator exponentials

- Relaxation Method to get the ground state of Hydrogen

- Our lattice solution utilizes a uniform grid and three-point finite-difference method

[-4, 15]x x [-4, 4]yx [-25, 25]z a.u.

Grid spacing = 0.2 a.u. supports

EH = - 0.49 a.u. EHe+= - 1.90 a.u.

Calculation parametersTime Step = 0.06 a.u.

Time Range: ti = - 200.0 a.u. to tf = 200.0 a.u.

Projectile Velocity = 0.1 a.u.

xinitial(b,0,-20.0) → xfinal(b,0,20.0)

Fig. A typical He++ + H final state density function

Calculating Charge Transfer ProbabilityWe estimate the reaction probability by integrating the electron density function around a box ΩT surrounding the target at tf

Where,

We define ΩT as

ΩT = [-4, 15]xx [-4, 4]y x [-25, 10]z a.u.

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

Testing

- No Laser Field
- Collision Energy = 2keV/amu

Reference:

T.Kirchner, PRL 89, 093203 (2002)

T. Kirchner, PRA 69, 063412 (2004)

Fig. He++ + H charge transfer probability as a function of b with no Laser Field for projectile energy of 2keV/amu.

Testing

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

Projectile with Zp=1 moving with velocity vz

EII

E┴

Target with ZT= 2 at origin

ResultsCollision scheme

- Parallel Polarization Result

&

- Perpendicular polarization

Parallel PolarizationComparison 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

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 5.28

Fig. He++ + H weighted charge transfer probability as a function of b for collision energy of 1keV/amu

Parallel Polarization

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

Perpendicular Polarization

σ(a.u.2)

Field Free 0.95

E0 = 0.01a.u.

α = 0.0 8.35

α = π/5 5.61

α = 2π/5 1.83

Total 4.66

Fig. CEP-Averaged weighted charge transfer probability as a function of b for different orientation of the laser field and collision plane

Perpendicular Polarization

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

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

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.

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