1. Laser assisted proton collision on light nuclei at moderate energies Imre Ferenc Barna 2015.11.25.

2. 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

3. 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

4. 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

5. 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 omega 0 laser energy (eV) E P project. kin. energ. (MeV) I laser intensity (W/cm 2 )

6. The proton – nucleon interaction The total interaction is a sum of a charged sphere and a Woods-Saxon optical potential V(r,V r,R 0,a 0 )

7. 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:

8. The technical parameters for proton – 12 C This system can be easily realised in low-energy experimental nuclear physics Moderate proton kinetic Energy: 49 MeV, it is above the Coulomb barrier

9. 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

10. Results - the total Born cross section is 201 mbarn - 800 nm Ti:Sapphire laser was taken

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

12. Results Results are published:

13. Bichromatic field the former theory can be generalized for two external fields m=2,3 order of higher harmonic The arguments of the generalised Bessel function are: The cross section formula for the n th - order photo absorption and emission in a field plus the m th - order higher harmonic

14. Results

15. - 800 + 1600 nm - I 0 = 10 12 W/cm 2, adding 90 Bessel func. - 1 photon absorption relat. phase. 0, π/4, π/2, - I 2 /I 0 = 0.1 upper fig. - I 2 /I 0 = 0.5 lower fig. - Note, cross section depends on relative phase - It is enough to investigate :

16. Results From completeness: The inelastic contribution: for monocromatic: and bichromatic case: for

17. Results scattering angle is fixed at 7 degree investigate

18. Results Results are in press: Nucl. Instr, Meth. Phys. Res B http://arxiv.org/abs/1506.01926 scattering angle is fixed at 7 degree investigate

19. 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 – 12 C collision system where 800 nm Ti:Sapphire laser with almost relatistic 10 11 -10 21 W/cm 2 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

20. THANK YOU FOR YOUR ATTENTION! Questions, Remarks, Comments?…