Atomic polarizability: A periodic descriptor

Atomic polarizability is an essential theoretical construct to define and correlate many physicochemical properties. It exhibits periodicity and has a relationship with other periodic descriptors. Although a number of scales are available to compute atomic polarizability, the final scale is yet to be designed. In this venture, we have invoked a new empirical approach to compute the atomic polarizability of 103 elements of the periodic table, considering the conjoint action of other periodic descriptors, namely effective nuclear charge (Zeff) and absolute radii (r). The proposed approach is [Formula: see text], where “e” represents the electronic charge, Zeff is the effective nuclear charge, r is the absolute radius, and α is the polarizability. Our computed atomic polarizability follows all sine qua non of the periodicity. Our model significantly exhibits the relativistic effect too. A close agreement between our computed data and other available theoretical and experimental results demonstrates the efficacy of our proposed approach. Furthermore, we have established the polarizability equalization principle in terms of our computed data.

MULTIPOLE MATRIX ELEMENTS ν FOR H-LIKE ATOMS, THEIR ASYMPTOTICS AND APPLICATIONS (AS β=1, n ≤ 4, n' ≤ 10)

This article deals with the connection between multipole matrix elements <nl|rβ|n'l' >ν for H-like atoms and new properties of Appell's function F2(x,y) to the vicinity of the singular point (1, 1), where ν is the so-called "auxiliary" parameter of Heun-Schrödinger's radial equation, |1 - ν| = o(1), [Formula: see text] is the "effective" nuclear charge. Exact numerical values for the dipole matrix elements, the average oscillator strengths, the transition probabilities and the line intensities, as n ≤ 4 and n' ≤ 10, in the form of regular rational fractions are given (in Tables 1–4), that make more precise the well-known Tables 13–16 by Hans A. Bethe.

Improved (1s)2 variational model for helium

The ground-state energy of neutral helium is estimated variationally with a trial wavefunction of the form ϕ≈e −γ(rA/a o)ne−γ(rB/a o)n. This model represents a modification of traditional textbook examinations of this problem via inclusion of the power “n” as a second nonlinear variational parameter in addition to the usual effective nuclear charge γ and leads to an upper-limit on the ground state energy of −2.86107 Eh (Eh=1 hartree) in comparison with the traditional (n=1) result of −2.84766 Eh. This result represents a reduction of the percentage overestimate from the true ground-state energy (−2.90373 Eh) of from 1.93 to 1.47. In comparison with the maximum accuracy obtainable from an uncorrelated trial wavefunction, −2.86168 Eh, the present trial wavefunction reduces the percentage overestimate from 0.49 (n=1) to 0.021. The optimum values of (n, γ) are determined to be ≈(0.897, 1.825).