Perturbative analysis of Colulomb-Volkov theories

R. GAYET; E. CORMIER; M. GHALIM; M. MASTOUR; V. D. RODRÍGUEZ

Rosario, Argentina

Conferencia; 24th International Conference on the Physics of Electronic, Photonic and Atomic Collision (XXIV ICPEAC) Rosario, Argentina (2005); 2005

PERTURBATIVE ANALYSIS OF COULOMB-VOLKOV THEORIES R. Gayet1  , E. Cormier1, M. Ghalim2, M. Mastour2 and V. D. Rodríguez3 1)      CELIA, Université Bordeaux 1, 351 Cours de la Libération, 33405 Talence Cedex, France. 2)      LPAN, Université Hassan II- Aïn Chock, B.P. 53 66 - Maarif, Casablanca, Maroc 3)      Departamento de Física, FCEyN, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina.         In recent works two related theories: CV2 [1] and MCV2 [2] have been employed to study the peak structure of the electron spectrum in above threshold ionization (ATI) of atomic Hydrogen by ultra-short UV laser pulses. The theories have been compared with exact 3D numerical solutions of the relevant time dependent Schrödinger equation TDSE [3].     These theories use as final states the so-called Coulomb-Volkov wave function to describe the electron continuum in the field of both the target nucleus and the laser. Through the many case studies in [1] and [2] one may conclude that CV2 is valid for photon energies exceeding the ionization potential. For smaller photon energies there is an increasing influence of intermediate bound states not accounted for in the standard theory CV2. The modified MCV2 theory is an extension of CV2 which takes into account the population of the continuum through intermediate bound states. A great success of MCV2 is to reproduce and explain a secondary peak structure that shows up in ATI spectra.     Both theories have been tested for different parameters such as photon energy, pulse duration and laser intensity. In the present work, the perturbative structure of these theories is analyzed. We demonstrate that the first order term in the CV2 perturbative expansion is identical to the first Born approximation.     On the contrary, the second order term in the same expansion is not exactly identical to the second order Born term. In fact, the intermediate bound states contribution have been dismissed in the CV2 theory while the continuum intermediate states are fully taken into account but using an approximate procedure: the larger the photon energy, the better the validity of the procedure. Therefore, we clearly delimit the validity range of CV2 theory by an analytical procedure beyond the empirical one. The procedure could be in principle extended towards higher order terms, but it becomes rather involved.     As a by-product of the present analysis we are led to modify the CV2 theory when intermediate bound state influence becomes significant. The modified theory is related, but not identical, to MCV2. The relationship arises from the perturbative analysis of the MCV2 theory. In fact, the second order term of the MCV2 perturbative series fully accounts for the bound intermediate states, and the contribution of continuum intermediate states are accounted for by the same approach as in the CV2 theory.     Comparison between full second Born approximation with CV2 and MCV2 calculations will be discussed.      References [1] G. Duchateau, E. Cormier and R. Gayet, Phys. Rev. A   66,  023412 (2002). [2] V. D. Rodríguez, E. Cormier and R. Gayet, Phys. Rev. A   69, 053402 (2004). [3] E. Cormier and P. Lambropoulos, J. Phys. B  30, 77  (1997).