scholarly journals The orbits of a charged particle round an electric and magnetic nucleus

The following communication is formally a complement to one published in the 'Proceedings' of the Society on "The Effect of the Magneton on the Scattering of α-Rays." In the present paper the more general case of a central positively charged nucleus possessing mass and a magnetic moment is considered. The case is treated as if the mass of the nucleus is so large compared with that of the revolving particle that it may be regarded as fixed. It is, therefore, not directly applicable when the revolving body is an α-particle except in cases where the central mass is large compared with that of the hydrogen atom. It is shown later what modification is needed when the motion of the nucleus is not large enough to affect its magnetic quality. The former paper was suggested by certain theories relating to the scattering of α and β-particles by matter. In the present, however, the chief interest lies in the discussion of the nature and properties of the various orbits, more especially of such as do not extend to infinity, or as they may be called "local orbits." In both cases the motion in the equatorial plane of the magneton alone is considered.

1969 ◽  
Vol 3 (2) ◽  
pp. 255-267 ◽  
Author(s):  
M. P. Srivastava ◽  
P. K. Bhat

We have studied the behaviour of a charged particle in an axially symmetric magnetic field having a neutral point, so as to find a possibility of confining a charged particle in a thermonuclear device. In order to study the motion we have reduced a three-dimensional motion to a two-dimensional one by introducing a fictitious potential. Following Schmidt we have classified the motion, as an ‘off-axis motion’ and ‘encircling motion’ depending on the behaviour of this potential. We see that the particle performs a hybrid type of motion in the negative z-axis, i.e. at some instant it is in ‘off-axis motion’ while at another instant it is in ‘encircling motion’. We have also solved the equation of motion numerically and the graphs of the particle trajectory verify our analysis. We find that in most of the cases the particle is contained. The magnetic moment is found to be moderately adiabatic.


The accurate experiments of Chattock and Bates prove that the angular momentum arising in a ferromagnetic substance from unit change in its magnetic moment is very nearly, if not exactly, one half the value 2 m/e = 1.13 X 10 -7 , which seemed to me the most likely when I first discussed this effect. This conclusion is supported by the fact that the improvements which have been introduced into this subject by successive experimenters in recent years have led to values showing a strong tendency to settle at the same limit m/e = 5.65 X 10 -8 . This value is also in general agreement with that deduced by Barnett from experiments on the converse effect. It seems desirable therefore to reconsider the interpretation of this ratio. The higher value 2 m/e is obtained by making rather definite assumptions, which evidently require modification, as to the nature of the phenomena. These assumptions are that the process of magnetization involves the turning of electron orbits, and that nothing else which may occur has any important influence on the phenomena. The inertia of the electrons is assumed to be entirely of the type which controls the deflection of a beam of cathode rays by a magnetic field, and any change in the motion of the positively charged part of the atom is disregarded. These assumptions are essentially the same as those of the theories of Langevin and Weiss which have been successful in dealing with purely magnetic phenomena.


Introduction .—The conception of the nuclear constitution of atoms arose initially from attempts to account for the scattering of α-particles through large angles in traversing thin sheets of matter. Taking into account the large mass and velocity of the α-particles, these large deflexions were very remarkable, and indicated that very intense electric or magnetic fields exist within the atom. To account for these results, it was found necessary to assume that the atom consists of a charged massive nucleus of dimensions very small compared with the ordinarily accepted magnitude of the diameter of the atom. This positively charged nucleus contains most of the mass of the atom, and is surrounded at a distance by a distribution of negative electrons equal in number to the resultant positive charge on the nucleus. Under these conditions, a very intense electric field exists close to the nucleus, and the large deflexion of the α-particle in an encounter with a single atom happens when the particle passes close to the nucleus. Assuming that the electric forces between the α-particle and the nucleus varied according to an inverse square law in the region close to the nucleus, the writer worked out the relations connecting the number of α-particles scattered through any angle with the charge on the nucleus and the energy of the α-particle. Under the central field of force, the α-particle describes a hyperbolic orbit round the nucleus, and the magnitude of the deflection depends on the closeness of approach to the nucleus. From the data of scattering of α-particles then available, it was deduced that the resultant charge on the nucleus was about ½ A e , where A is the atomic weight and e the fundamental unit of charge. Geiger and Marsden made an elaborate series of experiments to test the correctness of the theory, and confirmed the main conclusions. They found the nucleus charge was about ½ A e , but, from the nature of the experiments, it was difficult to fix the actual value within about 20 per cent. C. G. Darwin worked out completely the deflexion of the α-particle and of the nucleus, taking into account the mass of the latter, and showed that the scattering experiments of Geiger and Marsden could not be reconciled with any law of central force, except the inverse square. The nuclear constitution of the atom was thus very strongly supported by the experiments on scattering of α-rays. Since the atom is electrically neutral, the number of external electrons surrounding the nucleus must be equal to the number of units of resultant charge on the nucleus. It should be noted that, from the consideration of the scattering of X-rays by light elements, Barkla had shown, in 1911, that the number of electrons was equal to about half the atomic weight. This was deduced from the theory of scattering of Sir J. J. Thomson, in which it was assumed that each of the external electrons in an atom acted as an independent scattering unit.


2002 ◽  
Vol 80 (11) ◽  
pp. 1365-1372
Author(s):  
R N Faustov ◽  
A P Martynenko

A quasipotential method is formulated for calculating relativistic and radiative corrections to the magnetic moment of a two-particle bound state in the case of particles with arbitrary spin. It is shown that the g factors of bound particles contain O(α2) terms depending on the particle spin. Numerical values for the g factors of the electron in the hydrogen atom and deuterium are obtained. PACS Nos.: 31.30Jv, 12.20Ds, 32.10Dk


Author(s):  
Gleb L. Kotkin ◽  
Valeriy G. Serbo

This chapter addresses invariance of the Hamiltonian function under a given transformation and the conservation law, the Hamiltonian function for the beam of light, the motion of a charged particle in a nonuniform magnetic field, and the motion of electrons in a metal or semiconductor. The chapter also discusses the Poisson brackets and the model of the electron and nuclear paramagnetic resonances, the Poisson brackets for the components of the particle velocity, and the “hidden symmetry” of the hydrogen atom.


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