Highly excited hydrogen lines in stellar spectra. I

The solution of the hydrogenic Schrödinger equation are given with two boundary conditions imposed on the wave function, for distances of the order of magnitude of one hundred times the Bohr radius from the central nucleus. Thus the shifts and splitting of the H-H₂₆ lines are given which arise from the non-vacant environment. The Inglis-Teller limit is revised since from the shifts it follows that it gives a correct charged particle density only in the case of extremely high electron and ion densities. The gas density is derived from the number of the visible Balmer lines, and usually the widths and the contours but not the coalescence include information on the charged particle density.     

Restricted quatum-mechanical three-body problems

On the basis of a perturbative procedure in which the eigenfunctions of a helium-like ion are expanded in the Hilbert space built up from the eigenfunctions of an electron in two fixed Coulomb charges,all asymptotic eigenfunctions are constructed for the Schrödinger equation of helium-like ions. If the nuclear chargeZ ₁ is not less than 2, then our asymptotic considerations clarify the singularities of the Schrödinger equation of a helium-like ion (atr ₁=0, ,r ₂=0, ,r ₁₂=0, ), while in the case ofZ ₁=1 (negative hydrogen ion)r ₂=0 will not be treated in this paper. The established order (inr ₂) of asymptotics at 0 or in an exceptional case the zeroth-order term of the functions (actually the coefficients of an expansion of the desired eigenfunctions) as one of the electron coordinates (r ₂, the distance of the two fixed Coulomb charges, a parameter of the set of the basic functions) enables us to classify the eigenfunctions of a helium-like ion. This classification resembles the classification scheme for one-electron configurations. The asymptotics forr ₂ indicate bounded, pseudobounded (auto-ionizing) and free states. (Doubly ionized continuum states are not discussed here.) The use of the asymptotic solutions is indicated for the complete solution of the problem which may be either numerical integration or a variational procedure.Neutral muonic helium is included in the discussion.     

Restricted quantum-mechanical three-body problems

The Schrödinger equation is solved if an electron moves in the field of chargesZ ₁ andZ ₂ which are fixed in space. The wave function is expanded in power series, the eigenvalues are given graphically and partly in tabular form. The asymptotic behaviour of the eigenvalues is discussed when the distance of the two fixed charges is small and large. Some consequences are drawn on hydrogen line broadening, shift andgrenzkontinua. Further utilization of the calculations is indicated. The mathematical appendix helps to clarify some technical details of the calculations.     

Restricted quantum-mechanical three-body problems

Eigenvalues and normalized wave functions of an electron are derived in the field of a generalized dipole with chargesZ ₁ andZ ₂ (Z ₁+Z ₂ 0) in the asymptotic region up to the third order (inr ₂) where the distance,r ₂, between the two charges is small. These asymptotic wave functions render it possible to calculate the asymptotic expansion for the coefficients of a coupled infinite system of second order differential equations arising from a perturbative (analytic) solution to the Schrödinger equation of helium-like ions if the nuclear charge is not less than 2.     

Restricted quantum-mechanical three-body problems

A new method is presented in a general form to solve the Schrödinger equation of helium-like ions. The wave function is expanded in terms of the eigenfunctions of a moving electron in the field of two Coulombic ions which are fixed in space. This makes the method similar to the Dirac perturbation theory (perturbation theory for time-dependent problems). In the present method an infinitely coupled system of infinitely many second-order ordinary differential equations must be solved instead of one second-order partial differential equation of three variables. The nature of the singular points and boundary conditions are discussed and some general relations are given which are useful for the numerical treatment.     

Quantum-mechanical cellular methods for investigating the behaviour of materials under pressure

This paper presents the solutions of the Schrödinger equation for hydrogen with the application of various boundary conditions. These solutions have important consequences as regards the high pressure behaviour of the materials, i.e. for the pressure ionization, for the pressure modification of optical features. The results are of some significance in the pressure range of stellar atmospheres or even of laboratory plasmas. The number of bound levels coming into being versus density function has been derived and compared with the Inglis-Teller formula. The modification of some oscillator strengths as a function of density is calculated too.     

Distribution of n-alkanes and PAHs in atmospheric aerosols

The concentrations of n-alkanes and polycyclic aromatic hydrocarbons (PAHs) are determined in atmospheric aerosol samples collected at a rural sampling site in Hungary. For the n-alkanes the chromatographic profiles are established and the average carbon number and carbon preference index (CPI) are calculated. An attempt is made to obtain the origin of n-alkanes found in atmospheric aerosol samples. Based on the results of the measurements the probable importance of a round-the-year biogenic source for the n-alkanes with CPIs close to unity is emphasized.