Analysis of angular distribution

Finally, an estimate of the counting rate / p(max) at the maximum of the photoline can be derived. Approximating the measured photoline with a Gaussian distribution of fwhm = A exp one derives from equ. (2.28c) 

A comparison between experimental and theoretical values for the J (2p) parameter in neon is shown in Fig. 2.14. (The corresponding comparison between experimental and theoretical values for the partial cross section r(2p) of the 2p main photoline is omitted because most calculations give only r(2p, main) + r(2p, satellites), see Section 5.2.) The experimental data are given by the solid curve surrounded by a hatched area which takes into account the error bars. Theoretical results from advanced photoionization theories (many-body perturbation theory, R-matrix theory, and random-phase approximation) are represented by the other lines, and they are in close agreement with the experimental data (for details see [Sch86]). The theoretical / (2p) data of Fig. 2.13 are also close to the experimental values, except in the threshold region. 

Finally, a comment will be made concerning the relative simplicity of 2p photoionization in neon. Atoms other than neon have more interesting features in the observables which could be due to the photoionization of an electron with higher ( value, to potential barrier effects, to stronger influences from electron-electron interactions, to the appearance of Cooper [Coo62] and correlation 

---

For the analysis of angular distribution measurements involving two electronic surfaces, readers are referred to refs. 83 and 84. 

The more obvious and consistent deviations from the hard sphere theory occur, at the low density values, due to the effects of attractive forces in the real system. We can attempt to correct for these effects using a method described previously (27-30) for the analysis of angular momentum correlation times in supercritical CFjj and CFjj mixtures with argon and neon. We replace the hard sphere radial distribution function at contact hs with a function gp (0) which uses the more realistic... 

The alpha particle spectrum at all resonances is complicated by the fact that the transitions aj leading to the broad excited state of Be are accompanied by particles aj2 due to the break-up in flight of the recoil Be nuclei these form a continuous distribution between certain limits. The analysis of this distribution by Dee and Gilbert to prove the existence of an excited state of Be , was the first successful treatment of a three-body reaction. The ground state of Be is also unstable to break-up into alpha particles angular correlations in the alpha particle reactions have confirmed previous assignments for the Be levels. 

N (pd) Standing observed the deuterons from this reaction using a scintillation detector and pulse height analysis. The angular distribution of ground state deuterons obtained with 18.7 MeV protons is shown in Fig. 59 and may be fitted by a pick-up curve with /n = l No trace was found of deuterons corresponding to the first excited state of... 

Corrections for this type of effect are possible, but they require knowledge of angular distributions. We conclude that angular distributions are therefore normally necessary even for an analysis of velocity data. However, with an apparatus providing velocity spectra only, such errors do become small for very-high-energy reactions. Here, the laboratory velocity is so large that the sensitivity of the detector is similar for products emitted in any direction from the center of mass. Fortunately, most of the early uses of... 

Computational approaches to trajectories studies have been refined and generalized. " Theoretical attention has focused on the analysis of product distributions with the aim of improving upon histogram methods. Methods of moments have been developed by fitting angular distributions to functional expansions. Information theoretical S3mtheses may also be used to extract product properties. The classical-quantal correspondence principle has been used for vibrational energy distributions. ... 

Other techniques in which incident photons excite the surface to produce detected electrons are also Hsted in Table 1. X-ray photoelectron Spectroscopy (xps), which is also known as electron spectroscopy for chemical analysis (esca), is based on the use of x-rays which stimulate atomic core level electron ejection for elemental composition information. Ultraviolet photoelectron spectroscopy (ups) is similar but uses ultraviolet photons instead of x-rays to probe atomic valence level electrons. Photons are used to stimulate desorption of ions in photon stimulated ion angular distribution (psd). Inverse photoemission (ip) occurs when electrons incident on a surface result in photon emission which is then detected. 

---