scholarly journals The compton scattering and the new statistics

1929 ◽  
Vol 125 (796) ◽  
pp. 231-237 ◽  
Keyword(s):  
Compton Scattering ◽  
Electron Gas ◽  
Compton Effect ◽  
Maxwellian Distribution ◽  
Great Success ◽  
Free Electrons ◽  
Electron Theory ◽  
Conservation Of Momentum ◽  
New Statistics ◽  
Energy Principles

Great success has been achieved by Sommerfeld in the electron theory of metals by assuming that there are free electrons in them which obey the Fermi-Dirac statistics. It has been assumed in the case of univalent metals that on the average one electron per atom is free. In general, however, the valency electrons can be considered as free. These free electrons will take part in the Compton scattering. The analysis of such a Compton effect reduces to the analysis of the collisions between radiation quanta and an electron gas. The general features of such a scattering was first considered by Dirac. But he has assumed a Maxwellian distribution for the electrons which will not be applicable to the case under consideration, because the electrons in a conductor being degenerate do not obey the Maxwell's law, but the Fermian distribution. In considering such a process we take it that the conservation of momentum and energy principles are satisfied for each particular collision just as in Compton's theory—only we are here dealing with moving electrons instead of stationary electrons which Compton considers. Thus electrons of different momenta components will produce different Compton shifts, and the intensity of any particular shift will depend on the number of electrons in that state. Thus we have to average for the radiation falling on an assembly of electrons whose momenta are distributed according to the Fermi-Dirac law.

Thermal Properties of an Incompletely Degenerate Fermi Gas

1936 ◽  
Vol 32 (1) ◽  
pp. 108-111 ◽  
Author(s):  
N. F. Mott
Keyword(s):  
Thermal Properties ◽  
Specific Heat ◽  
Electron Gas ◽  
Electronic States ◽  
Fermi Gas ◽  
Paramagnetic Susceptibility ◽  
Free Electrons ◽  
Periodic Field ◽  
Degenerate Fermi Gas ◽  
Image Position

The purpose of this note is to calculate the specific heat and paramagnetic susceptibility of an electron gas obeying the Fermi-Dirac statistics for all temperatures, including those temperatures for which the gas is partially degenerate. The results are applicable to the electrons in a metal, whether free or moving in a periodic field, provided only that the number of electronic states per gram atom with energy between E and E + dE can be expressed in the formas for free electrons.

Compton scattering in a degenerate electron gas

2009 ◽  
Vol 10 (S10) ◽  
pp. 277-282
Author(s):  
Jean-Robert Buchler ◽  
William R. Yueh
Keyword(s):  
Compton Scattering ◽  
Electron Gas ◽  
Degenerate Electron ◽  
Degenerate Electron Gas

scholarly journals The distribution of electrons in a metal

1928 ◽  
Vol 120 (786) ◽  
pp. 727-735 ◽  
Keyword(s):  
Phase Space ◽  
Potential Field ◽  
Nuclear Charge ◽  
Electron Gas ◽  
Interesting Application ◽  
Heavy Atoms ◽  
Upper Limit ◽  
Dimensional Phase Space ◽  
New Statistics ◽  
Number Of Cells

1. The Statistics of a Degenerate Gas . An interesting application of the new statistics of Fermi and Dirac has been made by Thomas (and also independently by Fermi) to the distribution of electrons in heavy atoms. The basic idea of these researches is that the “electron gas” surrounding a nuclues “degenerate,” so that every cell of extension h 3 of a six dimensional phase space contains two electrons, one electron spinning in one direction and another in the opposite direction. An upper limit to the possible translational energies of the electrons is imposed by the condition that electrons shall not have enough energy to escape from the field of the nucleus, viz:— ϵ≼ e . V, (1) where ϵ and e represent the energy and charge of the electron and V is the potential field. The possible range of momentum co-ordinates (neglecting relativity considerations) is then limited by p ≼(2 me V) ½ (2) and the total number of cells of extension h 3 in the phase space is given by 4π(2 me V) 3/2 /3 h 3 (3) for every unit of ordinary (co-ordinate) space available. If every cell contains two electrons, the density is given by ρ = —8π e (2 me V) 3/2 /3 h 3 . (4) Since, however, the potential V is determined by the nuclear charge and the distribution of electrons, we have ∇ 2 = —4πρ = (32π 2 e (2 me V) 3/2 /3 h 3 ,(5) an equation to determine V, subject to V → 0 as r → ∞ V r as r → 0}, (6) where E is the charge on the nucleus.

Compton effect in and power absorption by an electron gas

1970 ◽  
Vol 13 (9) ◽  
pp. 1199-1202
Author(s):  
O. G. Bokov ◽  
M. V. Yudovich
Keyword(s):  
Electron Gas ◽  
Compton Effect ◽  
Power Absorption

scholarly journals The theory of electronic semi-conductors

1931 ◽  
Vol 133 (822) ◽  
pp. 458-491 ◽  
Keyword(s):  
Classical Theory ◽  
Energy Levels ◽  
Electron Gas ◽  
Mean Free Path ◽  
Pauli Principle ◽  
Critical Energy ◽  
Free Electrons ◽  
Conduction Electrons ◽  
Metallic Conduction ◽  
Direct Proportionality

The application of quantum mechanics to the problem of metallic conduction has cleared up many of the difficulties which were so apparent in the free electron theories of Drude and Lorentz. Sommerfeld* assumed that the valency electrons of the metallic atoms formed an electron gas which obeyed the FermiDirac statistics, instead of Maxwellian statistics, and, using in the main classical ideas, showed how the difficulty of the specific heat would be removed. He was, however, unable to determine the temperature dependence of the resistance, as his formulae contained a mean free path about which little could be said. F. Bloch took up the question of the mechanics of electrons in a metallic lattice, and showed that if the lattice is perfect an electron can travel quite freely through it. Therefore so long as the lattice is perfect the conductivity is infinite, and it is only when we take into account the thermal motion and the impurities that we obtain a finite value for the conductivity. On this view all the electrons in a metal are free, and we cannot assume, as we do in the classical theory, that only the valency electrons are free. This does not give rise to any difficulty in the theory of metallic conduction, as the direct proportionality between the conductivity and the number of free electrons no longer holds when the Pauli principle is taken into account. If there is no external electric field, the number of electrons moving in any direction is equal to the number moving in the opposite direction. The action of a field is to accelerate or retard the electrons, causing them to make transitions from one set of energy levels to another. This can only happen if the final energy levels are already unoccupied, and therefore only those electrons whose energies are near the critical energy of the Fermi distribution can make transitions and take part in conduction, as it is only in the neighbourhood of the critical energy that the energy levels are partly filled and partly empty. These electrons are few in number compared with the valency electrons, and are what should be called the conduction electrons. On the classical theory alone are the valency electrons, the free electrons and the conduction electrons the same.

scholarly journals Diamagnetism of cadmium

1938 ◽  
Vol 166 (926) ◽  
pp. 325-341 ◽  
Keyword(s):  
Single Crystals ◽  
Cold Working ◽  
Electron Gas ◽  
Hexagonal Structure ◽  
Magnetic Data ◽  
Free Electrons ◽  
Foreign Matter ◽  
Zinc Cadmium ◽  
Points Of View ◽  
Theoretical Side

The study of the susceptibility of metal crystals has received some attention in recent years both from theoretical and experimental points of view. The careful and thorough investigations of Goetz and Focke (1934) on single crystals of bismuth have greatly extended our knowledge regarding the properties of the crystalline state. McLennan, Ruedy and Cohen (1928) and McLennan and Cohen (1929) have determined the principal suscepti­bilities of a number of metals, including zinc, cadmium, antimony and tin. Hoge (1935) investigated tin crystals and showed the existence of a feeble anisotropy. Rao and Subramaniam (1936) studied thallium and showed from magnetic data the existence of a transformation point (235° C.), at which temperature its ordinary hexagonal structure passes over into the cubic type. Rao (1936 a , b ) has examined the influence of cold-working on single crystals of bismuth, zinc and tin and arrived at important conclusions based on the observed variations of the principal susceptibilities. An extension of this study to other metals and a careful repetition of some of the earlier investigations on the lines of more recent work seem essential. In this paper cadmium has been taken up for special study. We have indeed the values of McLennan and others (1928) for the principal susceptibilities of cadmium, but it is proposed here to study carefully the influence of cold­ working and of foreign matter on its diamagnetism. On the theoretical side a large amount of interesting work has been accomplished. Pauli (1926) applied the Fermi-Dirac statistics to the calculation of the paramagnetism of a free electron gas. If ( χ A ) е is the gram-atomic susceptibility due to the free electrons, q the number of free electrons per atom, and V 0 the width of the occupied energy range in the completely degenerate state in volts, for ordinary temperatures, ( χ A ) e × 10 6 = 48·17( q / V 0 ) {1 ‒ 6·11 × 10 -9 ( T / V 0 ) 2 }. (1)

scholarly journals Calculation of the ionization state for LTE plasmas using a new relativistic-screened hydrogenic model based on analytical potentials

2002 ◽  
Vol 20 (1) ◽  
pp. 145-151 ◽  
Author(s):  
J.G. RUBIANO ◽  
R. RODRÍGUEZ ◽  
J.M. GIL ◽  
P. MARTEL ◽  
E. MÍNGUEZ
Keyword(s):  
Atomic Structure ◽  
Maxwellian Distribution ◽  
Atomic Data ◽  
Ionization State ◽  
Free Electrons ◽  
Saha Equation ◽  
Model Based ◽  
Plasma Effects ◽  
Self Consistent ◽  
Hydrogenic Model

In this work, the Saha equation is solved using atomic data provided by means of a new relativistic-screened hydrogenic model based on analytical potentials to calculate the ionization state and ion abundance for LTE iron plasmas. The plasma effects on the atomic structure are taken into account by including the classical continuum lowering correction of Stewart and Pyatt. For high density, the Saha equation is modified to consider the degeneration of free electrons using the Fermi–Dirac statistics instead of the Maxwellian distribution commonly used. The results are compared with more sophisticated self-consistent codes.

Bipartition Angles for Compton Scattering by Free Electrons

1955 ◽  
Vol 99 (2) ◽  
pp. 343-345 ◽  
Author(s):  
H. M. Childers ◽  
J. D. Graves
Keyword(s):  
Compton Scattering ◽  
Free Electrons
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