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We analyzed the numerical values of half-lifes of excited electronic states of the H, He and Li atom, as well as the [Li.sup.+] ion. By means of a fractal scaling model originally published by Muller in this journal, we interprete these half-lifes as proton resonance periods. On the logarithmic scale, the half-lifes were expressed by short continued fractions, where all numerators are Euler's number. From this representation it was concluded that the half-lifes are heavily located in nodes or sub-nodes of the spectrum of proton resonance periods., 1 Introduction The model of a chain of similar harmonic oscillators was proposed by Muller [1-3] as a phenomenological theory describing physical quantities as proton resonance oscillation modes. In the [...]

A numerical analysis revealed that masses, radii, distances from the sun, orbital periods and rotation periods of celestial bodies can be expressed on the logarithmic scale though a systematic set of numbers: 4e, 2e, e, |, | and 16. We analyzed these data with a fractal scaling model originally published by Muller in this journal, interpreting physical quantities as proton resonances. The data were expressed in continued fraction form, where all numerators are Euler's number. From these continued fractions, we explain the volcanic activity on Venus, the absence of infrared emission of Uranus and why Jupiter and Saturn emit more infrared radiation than they receive as total radiation energy from the Sun. We also claim that the Kuiper cliff was not caused by a still unknown planet. It can be understood why some planets have an atmosphere and others not, as well as why the ice on dwarf planet Ceres does not evaporate into space through solar radiation. The results also suggest that Jupiter and Saturn have the principal function to capture asteroids and comets, thus protecting the Earth, a fact which is well-reflected in the high number of their irregular satellites., 1 Introduction Recently in three papers of this journal, Muller [1-3] suggested a chain of similar harmonic oscillators as a general model to describe physical quantities as proton resonance oscillation [...]

A numerical analysis of elementary particle masses on the logarithmic number line revealed systematic mass gaps of 2e, e, e/2, e/4, e/8 and e/16. Also in abundance data of the chemical elements, a repeated abundance gap of e/2 could be detected. This lead us to modify a fractal scaling model originally published by Muller in this journal, interpreting elementary particles as proton resonances. We express a set of 78 accurately determined particle masses on the logarithmic scale in a continued fraction form where all numerators are Euler's number., 1 Introduction Recently in three papers of this journal, Muller [1-3] has proposed a chain of similar harmonic oscillators as a new model to describe the fractal properties of nature. [...]