Laser assisted charge transfer in he h collisions
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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. Introduction. Does presence of a Laser Field affect charge transfer? n h ν + α + H  He + + p How much does it affect?

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Laser assisted charge transfer in he h collisions
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
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


What has been done

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
Theory

Collision Geometry

Method:

  • What are we solving?

  • How are we solving?

  • Calculations Parameters

  • Calculation of charge transferprobability


Collision scheme

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


What are we solving

Dipole moment

Electric Field

What are we solving?

We are solving 3D Time Dependent Schrödinger Equation

with

&


How are we solving crank nicholson method

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

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


Calculation parameters

Box size in our calculations

[-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 parameters

Time 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)


Calculating charge transfer probability

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

Calculating Charge Transfer Probability

We 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
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


Testing1
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.


Testing2
Testing

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


Results

Projectile with Zp=1 moving with velocity vz

EII

E┴

Target with ZT= 2 at origin

Results

Collision scheme

  • Parallel Polarization Result

    &

  • Perpendicular polarization


Parallel polarization comparison of end grid calculation
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
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 polarization1
Parallel Polarization

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


Perpendicular polarization
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 polarization1
Perpendicular Polarization

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


Perpendicular Polarization

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




Conclusion
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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