Laser Assisted Charge transfer in He++ + H Collisions

Presented byFatima Anis

Dr. Brett D. EsryV. Roudnev & R. Cabrera-Trujillo

Dr. Ben-ItzhakDr. Cocke

IntroductionIntroduction

Does presence of a Laser Field affect Does presence of a Laser Field affect

charge transfer?charge transfer?

nnhhνν + + αα + H + H He He++ + p + p

How much does it affect?How much does it affect?

Can we control charge transfer during Can we control charge transfer during

collision through CE phase?collision through CE phase?

Possibility for doing such an experimentPossibility for doing such an experiment

What has been done?What has been done?

Reference:T.Kirchner, PRL 89, 093203 (2002)

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

Remi did some preliminary calculations using END1- p + H2 H + H2

+

2- He+ + He He + He+

3- Li++ + He Li+ + He+

4- Li++ + Li Li+ + Li+

FWHM = 10fsλ = 790nmI = 3.5x1012 W/cm2

TheoryTheory

Collision Geometry Collision Geometry

Method:Method:

What are we solving?What are we solving?

How are we solving?How are we solving?

Calculations ParametersCalculations Parameters

Calculation of charge transferCalculation of charge transfer probability probability

Collision schemeCollision scheme

)cos()(2)(

0

teEtEt

And Laser Field is given as

Collision Energy = 1keV/amuLaser parameters:

Intensity = 3.5x1012W/cm2

FWHM ≈ 6.0fs λ = 800nm φ is CEP

Projectile with Zp=1 moving with velocity vz

Target with ZT= 2 at origin

EII

E┴

! Capture is possible for almost 1-2 optical cycles

What are we solving?What are we solving?We are solving 3D Time Dependent Schrödinger EquationWe are solving 3D Time Dependent Schrödinger Equation

with

),()]([),( trtVTtrt

i

2

2

1T

dtEtRr

Z

r

ZtV

p

PT

)()(

)(

zvtxbtRP ˆˆ)( Electric Field Dipole moment

&

How are we solving? Crank-Nicholson methodHow 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

)(),(),( 3)2/()2/( Otreeetr iViTiV

Operator- Splitting for Time Evolution

)()2

1()2

1( 31 OAi

Ai

eiA

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

Calculation parametersCalculation 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. supportsEH = - 0.49 a.u. EHe+= - 1.90 a.u.

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 ProbabilityCalculating Charge Transfer Probability

max

min

),(),( 32z

z

fzfct dztzrdtrPT

max

min

max

min

2),(),(

x

x

y

y

z dxdytrtz

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]x x [-4, 4]y x [-25, 10]z a.u.

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

TestingTesting

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

TestingTesting

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, 093203 (2002)T. Kirchner, PRA 69, 063412 (2004)

No Laser Field

Collision Energy = 2keV/amu

TestingTesting

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

ResultsResults

Parallel Polarization ResultParallel Polarization Result

&&

Perpendicular polarizationPerpendicular polarization

Collision schemeCollision scheme

Projectile with Zp=1 moving with velocity vz

Target with ZT= 2 at origin

EII

E┴

Parallel PolarizationParallel PolarizationComparison of END & Grid CalculationComparison 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 PolarizationParallel Polarization

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

σ(a.u.2)Field Free 0.95E0 = 0.01a.u.CEP=π 5.83CEP=3π/2 4.58CEP Averaged 5.28

Parallel PolarizationParallel Polarization

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

Perpendicular PolarizationPerpendicular Polarization

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

σ(a.u.2)Field Free 0.95E0 = 0.01a.u.α = 0.0 8.35α = π/5 5.61α = 2π/5 1.83Total 4.66

Perpendicular PolarizationPerpendicular Polarization

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

Perpendicular PolarizationPerpendicular Polarization

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

Without FieldWithout Field

With Laser FieldWith Laser Field

ConclusionConclusion

4-5 fold enhancement in capture cross section in case of both 4-5 fold enhancement in capture cross section in case of both parallel and perpendicular Laser polarizationparallel and perpendicular Laser polarization

Enhancement is CEP dependent for parallel and perpendicular Enhancement is CEP dependent for parallel and perpendicular Laser polarizationsLaser polarizations

For Parallel polarization capture cross section is enhanced For Parallel polarization capture cross section is enhanced significantly independent of CEPsignificantly independent of CEP

For perpendicular polarization effect of CEP and relative angle For perpendicular polarization effect of CEP and relative angle αα are related to each other. are related to each other.

Thank YouThank You