The Magnetism from the Movement of Electron in Hydrogen Atom

In this work we calculated the magnetism from the movement of electron in hydrogen atom and found that the contributions from the electron in the same main quantum levels to the magnetism of the hydrogen atom are the same; but the contributions from the electron in different main quantum levels to the magnetism of the hydrogen atom are the eigenvalue dependent instead. These facts tell us that the concepts about “intrinsic property” and “relativity effect” of electron spin should be discarded, and accordingly, the quantum mechanics should be rebuilt.

COLLECTIVE POTENTIAL FOR HEAVY ION NUCLEAR REACTIONS

It is shown that the nuclear charge polarisation during heavy ion nuclear reactions enhances the secondary maximum of the collective energy surface and produces a secondary minimum in the deformation energy near R ~ Rmin + 2fm. The potential energy and mass formulas are given as a function of A and Z. It has been shown that charge polarisation without shape deformation and indeed of the prolate type does not produce any secondary minimum. It is also seen that the relativity effect consists in shifting the secondary minimum towards higher rest excentricities. For deformation of the oblate type the collective potential has a similar form like that in the spherical case. Entry and exit channel collective potentials are also given for the case of strong nucléon transfer. The mass for the two-body interacting system has been calculated and for large distances it tends to the corresponding reduced mass. The present theory is based on a particular form of the single particle potential following from the scalar π-meson classical field theory.

Extreme secular excitation of eccentricity inside mean motion resonance

Context. It is well known that asteroids and comets fall into the Sun. Metal pollution of white dwarfs and transient spectroscopic signatures of young stars like β-Pic provide growing evidence that extra solar planetesimals can attain extreme orbital eccentricities and fall into their parent stars. Aims. We aim to develop a general, implementable, semi-analytical theory of secular eccentricity excitation of small bodies (planetesimals) in mean motion resonances with an eccentric planet valid for arbitrary values of the eccentricities and including the short-range force due to General Relativity. Methods. Our semi-analytic model for the restricted planar three-body problem does not make use of series expansion and therefore is valid for any eccentricity value and semi-major axis ratio. The model is based on the application of the adiabatic principle, which is valid when the precession period of the longitude of pericentre of the planetesimal is much longer than the libration period in the mean motion resonance. In resonances of order larger than 1 this is true except for vanishingly small eccentricities. We provide prospective users with a Mathematica notebook with implementation of the model allowing direct use. Results. We confirm that the 4:1 mean motion resonance with a moderately eccentric (e′ ≲ 0.1) planet is the most powerful one to lift the eccentricity of planetesimals from nearly circular orbits to star-grazing ones. However, if the planet is too eccentric, we find that this resonance is unable to pump the planetesimal’s eccentricity to a very high value. The inclusion of the General Relativity effect imposes a condition on the mass of the planet to drive the planetesimals into star-grazing orbits. For a planetesimal at ~ 1 AU around a solar mass star (or white dwarf), we find a threshold planetary mass of about 17 Earth masses. We finally derive an analytical formula for this critical mass. Conclusions. Planetesimals can easily fall into the central star even in the presence of a single moderately eccentric planet, but only from the vicinity of the 4:1 mean motion resonance. For sufficiently high planetary masses the General Relativity effect does not prevent the achievement of star-grazing orbits.

Determinations of the Rydberg constants, e / m , and the fine structures of H α and D α by means of a reflexion echelon

During the last few years many investigations have been carried out with the object of determining the fine structure of the red Balmer line of Hydrogen, H α , and its corresponding analogue, D α , in the heavier isotope Deuterium. It is only in these cases that the positions and relative intensities of the components can be accurately calculated in terms of the fundamental constants e, h, c , etc. The results are thus of considerable importance as affording a direct check on the fundamental basis of the quantum theory. When account is taken of the effects of electron spin and the relativity variation of mass with velocity, the wave mechanical equations of Dirac give a result for the structure and intensity ratios identical with that given by the “Sommerfeld formula” which was an earlier attempt to make allowance for the relativity effect.

Applications of the method of impact parameter in collisions

In the application of quantum mechanics to collisions the method of impact parameter has been largely neglected in favour of the more statistical method put forward by Born in 1926. This is mainly because the method of impact parameter is not applicable to all kinds of collisions. It affords, however, a valid treatment of light collisions in which the momentum transfer is small compared with the momentum of the primary particle, and its application in these cases proves very fruitful. We shall deal, in this paper, mostly with the problems which eminently lend themselves to treatment by this method and which have not been previously considered. One of these is the spatial distribution with respect to the path of the particle of the atoms ionised and excited by it. The results obtained in this respect show the existence of a radius of action characteristic of the velocity of the particle. Another problem field of a moving particle and the perturbation of distant atoms by the field of a moving particle and the perturbation of atoms by radiation—one which bears intimately on the theory of the loss of energy by electric particles put forward by Fermi in 1924. The problem of the relativity effect in light collisions is also fully discussed, the quantum-mechanical relativity corrections to the primary ionisation and loss of energy in light collisions being deduced. These corrections were put forward by the writer some time ago, and compared with experiment. Very recently, however, the problem was considered by Bethe, and M ϕ ller, on the basis of Born's theory, and they arrive at the same results. A feature of the use of the method of impact parameter in this problem, as indeed in others, is that the general physical reasons for the results obtained are readily apparent.