Two-photon Ionisation of He through a Superposition of Higher Harmonics

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Laser assisted proton collision on light nuclei
at moderate energies
Imre Ferenc Barna 2015.11.25.
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Outline
Introduction Theory of laser asssited
potential scattering multi-photon emission and
absorption for mono and bichromatic field
Proton - nucleon interaction the
Woods-Saxon optical potential and the Coulomb
field of a charged sphere Results Summary
Outlook Outlook

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Introduction

• - we consider a nulcear scattering process
• in a simultaneous laser field
• main motivation
• - to get additional information from nuclear
• structure with an extra laser field in
  collision if possible
• - construction of Romanian ELI
• where laser physics meets nuclear physics

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Theory of laser assisted collision
non-relativistic theory
Volkov wavefunction for the projectile, anal.
sol. for free charged paricle in laser field
dipole approx, now we use linear polarization
First Born approx. for the scattering process BUT
includes all order of photon absorption and
emission in a non-perturbative way
Fourier transformed, Dirac delta
Bessel function, scattering potential
energy conservation phys. from laser phys.
from interaction
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Theory of laser assisted collision
angular differential cross section with Born
cross section
geometry of the scattering, argument of the
Bessel function contains, information about the
laser,
hbar omega0 laser energy (eV) EP project.
kin. energ. (MeV) I laser intensity (W/cm2)
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The proton nucleon interaction
The total interaction is a sum of a charged
sphere and a Woods-Saxon optical potential
V(r,Vr,R0,a0 )
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The Fourier transformed interaction
for the Coulomb term of a charged sphere Ci
integral cosinus Si integral sinus
with the help of the complex integrals and
residuum theorem the FT of the WS terms
can be obtained
new result in nucl. Physics according to
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The technical parameters for proton 12C

This system can be easily realised in low-energy
experimental nuclear physics Moderate proton
kinetic Energy 49 MeV, it is above the Coulomb
barrier
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Results

the graph of the first Born cross sections
obtained from the three Fourier transformed
Woods-Saxon terms such shapes are common for
angular differential cross sections in collisions
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Results

• - the total Born
• cross section is
• 201 mbarn
• - 800 nm TiSapphire
• laser was taken

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Results
for large argument Bessel func. has a strong
decay
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Results

Results are published
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Bichromatic field

the former theory can be generalized for two
external fields
m2,3 order of
higher harmonic
The arguments of the generalised Bessel function
are

• The cross section formula for the nth- order
  photo absorption and emission in a field plus
  the mth- order higher harmonic

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Results


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• - 800 1600 nm
• - I0 1012 W/cm2,
• adding 90 Bessel func.
• - 1 photon absorption
• relat. phase. 0, p/4, p/2,
• - I2/I0 0.1 upper fig.
• - I2/I0 0.5 lower fig.
• - Note, cross section depends
• on relative phase
• - It is enough to investigate

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Results
From completeness
The inelastic contribution for
monocromatic and bichromatic case for
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Results
scattering angle is fixed at 7 degree
investigate
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Results
scattering angle is fixed at 7 degree
investigate
Results are in press Nucl. Instr, Meth. Phys.
Res B
http//arxiv.org/abs/1506.01926
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Summary Outlook

• We presented an analytic theory for
  laser-assisted
• collisions and used for a nuclear scattering
  process
• It was applied for a 49 MeV proton 12C
  collision
• system where 800 nm TiSapphire laser with
  almost
• relatistic 1011-1021 W/cm2 intensites and for
  10 keV
• X-rax lasers
• The obtained angular differential cross
  sections are
• unfortunately(?) very small - question of the
  view point
• Investigated bichromatic laser fields, where
  the some parts of the
• cross sections can be enhanced via coherent
  control
• Speculation about alpha aplha collision, with
  analytic
• non-local potential, where exact solution can
  be obtained in laser field OR
• Two-Center shell model (Scheid,
  Antonenko-Adamian, Diaz-Torres etc.) laser
  field

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