We present a calculation of the static and dynamic dipole polarizability of the helium atom using a variationally stable treatment that incorporates the coupled-channel hyperspherical representation of the wave functions. Inclusion of logarithmic terms in intermediate functions as well as the effect of an optimization procedure for the variational parameter are analyzed. When available, our coupled-channel results are compared with other values in the literature.

Binding energies for excitons trapped by impurities in ZnSe and CdS are calculated within the hyperspherical adiabatic approach. Nonadiabatic couplings are included in the radial equations, leading to energies lower than the variational values available in the literature. Resonant states similar to autoionizing lines in atoms are predicted to lie above the first electron-impurity ionization threshold.

This work is part of a broader research that focuses on ocular health. Three outlines are the basis of the pyramid that comprehend the research as a whole: authors’ previous work, which has provided the public to self-check their own sunglasses regarding the ultraviolet protection compatible to their category; Brazilian national survey in order to improve nationalization of sunglasses standards; and studies conducted on revisiting requirements of worldwide sunglasses standards, in which this work is inserted. It is still controversial on the literature the ultraviolet (UV) radiation effects on the ocular media, but the World Health Organization has established safe limits on the exposure of eyes to UV radiation based on the studies reported in literature. Sunglasses play an important role in providing safety, and their lenses should provide adequate UV filters. Regarding UV protection for ocular media, the resistance-to-irradiance test for sunglasses under many national standards requires irradiating lenses for 50 uninterrupted hours with a 450 W solar simulator. This artificial aging test may provide a corresponding evaluation of exposure to the sun. Calculating the direct and diffuse solar irradiance at a vertical surface and the corresponding radiant exposure for the entire year, we compare the latter with the 50-h radiant exposure of a 450 W xenon arc lamp from a solar simulator required by national standards. Our calculations indicate that this stress test is ineffective in its present form. We provide evidence of the need to re-evaluate the parameters of the tests to establish appropriate safe limits for UV irradiance. This work is potentially significant for scientists and legislators in the field of sunglasses standards to improve the requirements of sunglasses quality and safety.

Energies and wavefunctions are calculated for the bound states of the helium atom in the hyperspherical adiabatic approach by the full inclusion of nonadiabatic couplings. We show that the use of appropriate asymptotic radial boundary conditions not only allows the efficient calculation of energies accurate up to a few ppm for the ground state but also gives increasingly precise results for high-lying excited states with a unique set of equations. The accuracy of the wavefunctions is demonstrated by the calculation of oscillator strengths in the length form for transitions between states n ¹S^e and (n + 1) ¹P^o up to n = 29, in agreement with variational calculations.

The nonadiabatic ground state for the helium atom is obtained with the hyperspherical adiabatic approach. Potential curves, nonadiabatic couplings, and channel functions are calculated by a numerically exact procedure based on the analytical expansion of the channel functions. The coupled radial equations are solved by standard techniques. The convergence of the procedure is investigated as nonadiabatic couplings are systematically introduced. The inclusion of 11 potential curves and channel functions gives a ground-state energy that differs from the best variational calculation by 0.1 parts per million.