Excitation and charge transfer in H-H+ collisions at 5-80 keV and application to astrophysical shocks

In astrophysical regimes where the collisional excitation of hydrogen atoms is relevant, the cross-sections for the interactions of hydrogen atoms with electrons and protons are necessary for calculating line profiles and intensities. In particular, at relative velocities exceeding ∼1000 km s−1, collisional excitation by protons dominates over that by electrons. Surprisingly, the H–H+ cross-sections at these velocities do not exist for atomic levels of n≥ 4, forcing researchers to utilize extrapolation via inaccurate scaling laws. In this study, we present a faster and improved algorithm for computing cross-sections for the H–H+ collisional system, including excitation and charge transfer to the n≥ 2 levels of the hydrogen atom. We develop a code named BDSCX which directly solves the Schrödinger equation with variable (but non-adaptive) resolution and utilizes a hybrid spatial-Fourier grid. Our novel hybrid grid reduces the number of grid points needed from ∼4000n6 (for a ‘brute force’, Cartesian grid) to ∼2000n4 and speeds up the computation by a factor of ∼50 for calculations going up to n= 4. We present (l, m)-resolved results for charge transfer and excitation final states for n= 2–4 and for projectile energies of 5–80 keV, as well as fitting functions for the cross-sections. The ability to accurately compute H–H+ cross-sections to n= 4 allows us to calculate the Balmer decrement, the ratio of Hα to Hβ line intensities. We find that the Balmer decrement starts to increase beyond its largely constant value of 2–3 below 10 keV, reaching values of 4–5 at 5 keV, thus complicating its use as a diagnostic of dust extinction when fast (∼1000 km s−1) shocks are impinging upon the ambient interstellar medium.

Brain sources of EEG gamma frequency during volitionally meditation-induced, altered states of consciousness, and experience of the self.

Multichannel EEG of an advanced meditator was recorded during four different, repeated meditations. Locations of intracerebral source gravity centers as well as Low Resolution Electromagnetic Tomography (LORETA) functional images of the EEG 'gamma' (35-44 Hz) frequency band activity differed significantly between meditations. Thus, during volitionally self-initiated, altered states of consciousness that were associated with different subjective meditation states, different brain neuronal populations were active. The brain areas predominantly involved during the self-induced meditation states aiming at visualization (right posterior) and verbalization (left central) agreed with known brain functional neuroanatomy. The brain areas involved in the self-induced, meditational dissolution and reconstitution of the experience of the self (right fronto-temporal) are discussed in the context of neural substrates implicated in normal self-representation and reality testing, as well as in depersonalization disorders and detachment from self after brain lesions.

Directional statistics: introduction

In many of the natural and physical sciences, measurements are directions, either in two or three dimensions. The analysis of directional data relies on specific statistical models and procedures, which differ from the usual models and methodologies of Cartesian data. This chapter briefly introduces statistical models and inference for this type of data. The basic von Mises-Fisher distribution is introduced and nonparametric methods such as goodness-of-fit tests are presented. Further references are given for exploring related topics such as correlation and regression.

Guessing Solutions to the H-atom Schrodinger Equation

In teaching elementary quantum chemistry, the concept of eigenfunctionality is explored using the H-atom's Hamiltonian and various guessed functions. This is done in Cartesian coordinates, in Spherical Polar coordinates, and in Confocal Elliptical coordinates.