Renormalization in Perturbation Theory of Multi-photon Ionization of Molecules

Abstract

We study the appearance of divergences in stationary perturbation R matrix theory applied to the calculation of multi-photon above threshold ionization pro- cesses. We remove divergent parts of the amplitude using projection formalisms by renormalized T matrix and discuss problems of this approach. Furthermore, we show that by summing up indistinguishable ionization paths in the velocity gauge at the third order of perturbation theory, divergences can be removed. Moreover, we study the same processes at third order of perturbation theory using time-dependent perturbation theory and illustrate that even the time- dependent perturbation theory diverges. Finally, by using summation of indis- tinguishable processes in time-dependent and stationary perturbation theory in velocity gauge, we obtain comparable finite results for divergent processes. 1

Studujeme vy 'skyt divergencı ́ ve staciona ́rnı ́ poruchove ́ R maticove ́ teorii popisujı ́cı ́ nadprahovou vı ́cefotonovou ionizaci. Pomocı ́ projekc ̌nı ́ch formalismu ̊ zaloz ̌eny ́ch na renormalizovane ́ T matici odstran ̌ujeme divergentnı ́ c ̌a 'sti ampli- tudy a zaby ́va ́me se proble ́my spojeny ́mi s tı ́mto pr ̌ı 'stupem. Da ́le ukazujeme, z ̌e sec ̌tenı ́m principia ́lne ̌ nerozlis ̌itelny ́ch ionizac ̌nı ́ch procesu ̊ v rychlostnı ́ kalibraci lze divergence ve tr ̌etı ́m r ̌a ́du odstranit. Take ́ studujeme procesy tr ̌etı ́ho r ̌a ́du pomocı ́ c ̌asove ́ poruchove ́ teorie a ilustrujeme, z ̌e i tento popis vede k diver- gencı ́m. Konec ̌ne ̌ pomocı ́ sec ̌tenı ́ nerozlis ̌itelny ́ch procesu ̊ v c ̌asove ̌ za ́visle ́ a sta- ciona ́rnı ́ poruchove ́ teorii v rychlostnı ́ kalibraci zı 'ska ́va ́me srovnatelne ́ konec ̌ne ́ vy 'sledky pro divergentnı ́ procesy. 1