Dependence of transition probabilities for non-linear photo-ionization of He atoms on the structure of the exciting radiation pulses

Abstract

We discuss the expected dependence of the probability transitions for 2-photon and 3-photon absorption in Helium gas on the spatial and temporal structure of the exciting radiation pulses. Regarding spatial structure, we assumed a Gaussian radial intensity distribution; we find, as expected, that the 2-photon and 3-photon processes become negligible at distances D away from the focus, where D is of the order of the beam waist FWHM. Regarding temporal structure, we compared transition probabilities for square, Gaussian and cosine squared temporal profiles; we find that for the same FWHM, Gaussian and cosine squared pulses give essentially the same transition probabilities, but the square pulses are about twice as efficient. We finally studied the effect of sharp versus smooth rise and fall edges in the light pulse; we find negligible correlation with the shape of the pulse edges, and strong correlation with the pulse FWHM, i.e., with pulse total energy, as might be expected.

Finite‐time stabilisation for Markov jump systems with Gaussian transition probabilities

“…As indicated in [24], for continuous type of random variable, Gaussian probability density functions (PDFs) are often used to parameterise TPs. However, the issues on such systems with Gaussian PDFs have not been investigated up until now, although there is some attention on the Markov Process containing Gaussian TPs only in purely mathematics field [25][26][27].…”

Atomic hydrogen under strong soft X-ray pulses

“…In a series of recent papers the effect on a Helium atom, of short intense pulses in the XUV spectral range, was discussed both theoretically and experimentally [1][2][3][4][5] with regard to nphoton absorption of light at ω ph = 13 eV. The theoretical model contemplated the direct numerical solution of the Time Dependent Schrödinger Equation (TDSE) in a basis of finite and rather small dimensionality.…”