# Showing papers in "Physical Review in 1941"

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TL;DR: In this article, the Ising model of ferromagnetism is treated by rigorous Boltzmann statistics, and a method is developed which yields the partition function as the largest eigenvalue of some finite matrix, as long as the manifold is only one dimensionally infinite.

Abstract: In an effort to make statistical methods available for the treatment of cooperational phenomena, the Ising model of ferromagnetism is treated by rigorous Boltzmann statistics. A method is developed which yields the partition function as the largest eigenvalue of some finite matrix, as long as the manifold is only one dimensionally infinite. The method is carried out fully for the linear chain of spins which has no ferromagnetic properties. Then a sequence of finite matrices is found whose largest eigenvalue approaches the partition function of the two-dimensional square net as the matrix order gets large. It is shown that these matrices possess a symmetry property which permits location of the Curie temperature if it exists and is unique. It lies at $\frac{J}{k{T}_{c}}=0.8814$ if we denote by $J$ the coupling energy between neighboring spins. The symmetry relation also excludes certain forms of singularities at ${T}_{c}$, as, e.g., a jump in the specific heat. However, the information thus gathered by rigorous analytic methods remains incomplete.

1,455 citations

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TL;DR: In this paper, the authors used the picture of Wigner and Bardeen according to which the work function is a sum of a volume contribution and a contribution due to a double layer on the surface of the metal.

Abstract: Work function is experimentally known to be different for different faces of a crystal by amounts ranging from one-tenth to half a volt. For tungsten the faces can be arranged according to decreasing work function as follows: 110, 211, 100 and finally 111. The explanations so far suggested for the differences of the work function are discussed and shown to give either an incorrect sequence or a wrong order of magnitude of the observed differences. The author uses the picture of Wigner and Bardeen according to which the work function is a sum of a volume contribution and a contribution due to a double layer on the surface of the metal. The origin of the latter can be described in the following manner. With every atom one can associate a polyhedron ("$s$-polyhedron") with the atom at its center, such that it contains all points nearer to the atom under consideration than to any other atom. If the distribution of the electron density within these polyhedra of the surface atoms was the same as for the inside atoms then there would be no double layer on the surface. However, this is not the case since the total energy is lowered by a redistribution of the electron cloud on the surface. There are two effects: the first is a partial spread of the charge out of the $s$-polyhedra and the second is a tendency to smooth out the surface of the polyhedra. In consequence of the second effect the surfaces of equal charge density are more nearly plane than in the original picture. The two effects have opposite influences and since they are comparable in magnitude, it is not possible to predict the sign of the total double layer without numerical computations. Some general formulae for the double layers are derived and discussed more fully in the case of a simple cubic and a body-centered cubic lattice. The minimum problem of the surface energy is solved for four faces of a body-centered crystal and the results are applied to the case of tungsten. One obtains the differences between the work functions for different directions. The results agree satisfactorily with the experimental data: assuming a reasonable density of the free electrons, one obtains the correct sequence of faces and the correct differences of the work function. The surface energies are calculated an d found in agreement with the observed stability of certain crystal faces.

1,117 citations

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TL;DR: In this article, the authors considered random layer lattice structures, which consist of layers arranged parallel and equidistant, but random in translation parallel to the layer, and rotation about the normal.

Abstract: Random layer lattice structures are considered which consist of layers arranged parallel and equidistant, but random in translation parallel to the layer, and rotation about the normal. We call $a$ and $b$ the axes in the layer, and $c$ the axis normal to the layer. In this notation there will be crystalline reflections of type ($00l$), two-dimensional lattice reflections of type ($\mathrm{hk}$), and no general reflections ($\mathrm{hkl}$). Equations are developed for the intensity distribution in a two-dimensional powder reflection, and for the integrated intensity. Equations are also de-developed for the particle size in terms of the peak breadth, and for the displacement of the peak. The powder pattern of a heat treated carbon black is presented as an illustration of two-dimensional lattice reflections.

994 citations

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919 citations

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TL;DR: In this paper, the long wave-length, polar lattice vibrations of alkali halide crystals are discussed without making any specific assumptions about the detailed interactions between the ions, and the ratio of the two frequencies is found to be independent of the effective charge of an ion defined as follows: all of the positive ions in a crystal slab are displaced by an equal amount in a direction perpendicular to the faces of the slab and all of negative ions in the opposite direction.

Abstract: The long wave-length, polar lattice vibrations of alkali halide crystals are discussed without making any specific assumptions about the detailed interactions between the ions. This is made possible by the introduction of the effective charge, ${e}^{*}$, of an ion defined as follows: All of the positive ions in a crystal slab are displaced by an equal amount in a direction perpendicular to the faces of the slab and all of the negative ions in the opposite direction. Then ${e}^{*}$ is the ratio of the dipole moment per ion pair induced in the slab by this displacement to the relative displacement of the positive and the negative ions. Expressions are obtained for the frequency, ${\ensuremath{\omega}}_{l}$, of the longitudinal vibration and the frequency, ${\ensuremath{\omega}}_{t}$, of the transverse vibration in terms of the dielectric constant, $k$, of the crystal, the dielectric constant, ${k}_{0}$, obtained by extrapolating the square of the index of refraction of the crystal from high frequencies to zero frequency, and ${e}^{*}$. The ratio of the two frequencies is found to be independent of ${e}^{*}$ and given by $\frac{{\ensuremath{\omega}}_{l}}{{\ensuremath{\omega}}_{t}}={(\frac{k}{{k}_{0}})}^{\frac{1}{2}}$.

763 citations

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Bell Labs

^{1}TL;DR: The relationship between the true thermal coefficient of expansion and temperature conforms very well to the Grueneisen-Debye theory when values are chosen for the Debye characteristic temperatures as discussed by the authors.

Abstract: Extremely accurate determinations of the linear thermal expansions have been made interferometrically from --- 196\ifmmode^\circ\else\textdegree\fi{}C to temperatures about +400\ifmmode^\circ\else\textdegree\fi{}C for Al and +700\ifmmode^\circ\else\textdegree\fi{}C for Fe, Ni, Cu and Au. The relationship between true thermal coefficient of expansion and temperature conforms very well to the Grueneisen-Debye theory when values are chosen for the Debye characteristic temperatures which turn out to agree well with those chosen to achieve agreement with the Debye theory of specific heats. Our values for these characteristic temperatures are: 410\ifmmode^\circ\else\textdegree\fi{}K for Ni, 420\ifmmode^\circ\else\textdegree\fi{}K for Fe, 400\ifmmode^\circ\else\textdegree\fi{}K for Al, 325\ifmmode^\circ\else\textdegree\fi{}K for Cu, and 190\ifmmode^\circ\else\textdegree\fi{}K for Au. The magnetic Curie temperature for Ni is found to be 352\ifmmode^\circ\else\textdegree\fi{}C. In plotting true coefficient of thermal expansion versus temperature Simon and Bergmann found a horizontal plateau at about 175\ifmmode^\circ\else\textdegree\fi{} to 235\ifmmode^\circ\else\textdegree\fi{}K for Ni and Fe; but we do not confirm this.

541 citations

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TL;DR: In this article, the simplest possible asymmetrical generalization of Riemannian metric is considered, and the physical consequences by application to space-time are obvious, and may be of interest by leading directly to a description of the electromagnetic field.

Abstract: Physical space-time allows of a metric of asymmetrical properties because of the unidirection of time. The simplest possible asymmetrical generalization of Riemannian metric is considered. The study of this metric is here mainly confined to the mathematical aspects. However, the physical consequences by application to space-time are obvious, and may be of interest by leading directly to a description of the electromagnetic field. A close formal connection with five-dimensional Riemannian geometry is shown, which might carry interest for the physical interpretation of five-dimensional relativity.

519 citations

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474 citations

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TL;DR: The velocity of longitudinal waves in cylindrical bars may be expressed as the velocity at infinite wave-length times a function of two variables: Poisson's ratio and the ratio of the diameter of the bar to the wave length as mentioned in this paper.

Abstract: The velocity of longitudinal waves in cylindrical bars may be expressed as the velocity at infinite wave-length times a function of two variables: Poisson's ratio, and the ratio of the diameter of the bar to the wave-length. This function is computed over the domain of the arguments which is of physical interest. Asymptotic values for the velocities at very short wave-lengths are deduced, and the variation of the displacement as a function of the radius is discussed. It is found that a similar analysis can be applied to torsional and flexural waves.

381 citations

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216 citations

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TL;DR: In this article, the elastic properties of polycrystalline specimens were investigated and it was shown that Young's modulus is reduced by 50 percent to 76 percent when no slip at grain boundaries occurs, depending upon Poisson's ratio.

Abstract: Previous experiments have shown that in annealed polycrystalline specimens, the grain boundaries are much more susceptible to plastic shear than are the interiors of the grains. This paper investigates the elastic properties of a specimen in which the grain boundaries are incapable of supporting shearing stresses. In such a specimen Young's modulus is found to be from 50 percent to 76 percent of its value when no slip at grain boundaries occurs, depending upon Poisson's ratio. This reduction of Young's modulus by slipping at grain boundaries should be observable by comparing values measured statically at elevated temperatures with those measured dynamically.

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TL;DR: The possible existence of a second rare-earth-like group of elements, beginning with uranium and extending to the transuranic elements, was discussed in this article by a calculation of the atomic eigenfunctions of the $4f$ and $5f$ electrons.

Abstract: The possible existence of a second rare-earth-like group of elements beginning with uranium and extending to the transuranic elements, is discussed by a calculation of the atomic eigen-functions of the $4f$ and $5f$ electrons. Energy and spatial extension of the $4f$ eigenfunctions drop suddenly at the beginning of the rare-earth group; the binding energy is calculated to be 0.95 ev in lanthanum, $Z=57$, and 5 ev in neodymium, $Z=60$. The $5f$ eigenfunctions undergo the same type of change around $Z=92$. The binding energies were calculated to be 1.35 ev for $Z=86$, 8.5 ev for $Z=91$ and 14 ev for $Z=93$.

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TL;DR: In this paper, it was shown that the effect of the diamagnetic field on an orbital electron on an atomic electron is equivalent to a reduction in the value of an outer $s$ electron by an amount of just the same order of magnitude as the relativistic correction calculated by Margenau.

Abstract: In the precise molecular beam experiments of Rabi and his collaborators, it is necessary to know the value at the nucleus of the magnetic field produced by the diamagnetism of the atomic electrons. This has been calculated on the basis of the Fermi-Thomas model, and checked for a number of atoms by use of the available Hartree calculations. The statistical treatment gives for ratio of induced to external field $0.319\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}{Z}^{\frac{4}{3}}$, while the numerical coefficient on the basis of the Hartree model is lower by 19 percent at $Z=19$ and by 12 percent at $Z=80$. The effect is equivalent to a reduction of the nuclear $g$ value by a factor of ($1\ensuremath{-}0.319\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}{Z}^{\frac{4}{3}}$), and in this form, the correction may be applied in the calculation of hyperfine structure of heavy atoms. The influence of the diamagnetic fields on an orbital electron has also been considered, and it is shown that it is equivalent to a reduction in the $g$ value of an outer $s$ electron by an amount of just the same order of magnitude as the relativistic correction calculated by Margenau.

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TL;DR: In this paper, a treatment of various phenomena occurring in the passage of neutrons through domains which are regularly or irregularly magnetized is presented, and a modified theory of the well-known neutron polarization experiments is presented.

Abstract: The paper contains a treatment of various phenomena occurring in the passage of neutrons through domains which are regularly or irregularly magnetized. After setting up general equations for the behavior of the neutron spin in different types of magnetic fields which correspond approximately to various stages of magnetization in ferromagnets we obtain very general results for the depolarization of an originally polarized beam. These results can be easily extended to arbitrarily constituted beams. We report next, briefly, on current views concerning the domain structure of ferromagnets and discuss in detail the possibilities of investigating this structure by means of experiments with partially polarized neutron beams. The discussion divides itself naturally into the treatment of single crystals, macroscopically unmagnetized polycrystals and of polycrystals near magnetic saturation. Revising previous unsatisfactory treatments we derive in a very general manner formulae for the change of intensity and polarization of a neutron beam traversing a saturated or quasisaturated ferromagnetic medium. The formulae obtained constitute the basis for a modified theory of the well-known neutron polarization experiments. A closing paragraph contains a brief comparison between theory and experiment as far as it can be carried out without evaluating certain phenomenological constants, a task reserved for the following paper.

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TL;DR: An extension of the mass spectrometric method of study of ionization and dissociation processes occurring in diatomic molecules under electron impact and the results of further investigation of the molecules were discussed in this paper.

Abstract: An extension of the mass spectrometric method of study of ionization and dissociation processes occurring in diatomic molecules under electron impact and the results of further investigation of the molecules ${\mathrm{H}}_{2}$, CO, NO, ${\mathrm{N}}_{2}$, and ${\mathrm{O}}_{2}$ are discussed The shapes of the peaks which appear in the graph of resolved ion current as a function of ion accelerating potential are analyzed and accounted for in terms of the wave-mechanical theory of the diatomic molecule and the characteristics of the mass spectrometer It is indicated how the study of the peak shape coupled with appearance potential measurements has made possible conclusions concerning the nature of the dissociation process and the structure of the molecule Differences between previous mass spectrometric data and those from other sources have been clarified either by obtaining better data with the mass spectrometer or by formulation of a satisfactory interpretation of the difference based on conclusions of an analysis of the ion peak shape Values of dissociation energies, ionization potentials and interpretations of the processes that occur are given

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TL;DR: In this paper, the effect of dislocations on the magnetization curve at high fields is calculated by direct use of dislocation theory, where the deviation from saturation is assumed to be due to magnetostrictive forces, localized in the stress field about the dislocations rather than at the dislocation itself; their effect is more complicated than that of the simple "line concentrations of force" considered in an earlier article.

Abstract: The effect of dislocations on the magnetization curve at high fields is calculated by direct use of dislocation theory. The deviation from saturation is assumed to be due to magnetostrictive forces, localized in the stress field about the dislocation rather than at the dislocation itself; their effect is more complicated than that of the simple "line concentrations of force" considered in an earlier article. Pairs of dislocations of opposite sign, separated by a short distance, contribute a term $\frac{a}{H}$ to the deviation from saturation; in this respect they resemble line concentrations. Pairs separated by a long distance and surplus dislocations of one sign contribute a term $\frac{b}{{H}^{2}}$, with $b$ theoretically not a constant but a logarithmically varying function of $H$. From data on the variation of the empirical $a$ and $b$ with plastic strain, it is possible to calculate the density of dislocations and the "block" length if a value is assumed for the distance $Y$ between the members of a dislocation pair. The orders of magnitude obtained agree with those obtained in the theory of hardening if $Y$ is taken $\ensuremath{\cong}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ cm. It appears that all but about 1 percent of the dislocations are members of such pairs.

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TL;DR: In this article, a new value of the proper lifetime of mesotrons of (2.4 + 2.3 + 3.6 + 1.3 ) was derived, based upon measurements with particles with momentum of approximately 5.

Abstract: In order to determine the dependence of the probability of decay on momentum, mesotrons with range between 196 and 311 g/${\mathrm{cm}}^{2}$ of lead and mesotrons with range larger than 311 g/${\mathrm{cm}}^{2}$ of lead were investigated separately. The softer group of mesotrons was found to disintegrate at a rate about three times faster than the more penetrating group, in agreement with the theoretical predictions based on the relativity change in rate of a moving clock. A new value of the proper lifetime of mesotrons of (2.4\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ sec. is determined, based upon measurements with particles with momentum of approximately 5\ifmmode\times\else\texttimes\fi{}${10}^{8}$ ev/c.

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TL;DR: In this article, it was shown that energy losses through the neutrinos produced in reactions between free electrons and oxygen nuclei can cause a complete collapse of the star within the time period of half an hour.

Abstract: At the very high temperatures and densities which must exist in the interior of contracting stars during the later stages of their evolution, one must expect a special type of nuclear processes accompanied by the emission of a large number of neutrinos. These neutrinos penetrating almost without difficulty the body of the star, must carry away very large amounts of energy and prevent the central temperature from rising above a certain limit. This must cause a rapid contraction of the stellar body ultimately resulting in a catastrophic collapse. It is shown that energy losses through the neutrinos produced in reactions between free electrons and oxygen nuclei can cause a complete collapse of the star within the time period of half an hour. Although the main energy losses in such collapses are due to neutrino emission which escapes direct observation. the heating of the body of a collapsing star must necessarily lead to the rapid expansion of the outer layers and the tremendous increase of luminosity. It is suggested that stellar collapses of this kind are responsible for the phenomena of novae and supernovae, the difference between the two being probably due to the difference of their masses.

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TL;DR: A mass spectrographic measurement of the relative abundances of the isotopes in eight samples of radiogenic lead and thirteen samples of common lead has been made as discussed by the authors, and three independent determinations of the age could be made.

Abstract: A mass spectrographic measurement of the relative abundances of the isotopes in eight samples of radiogenic lead and thirteen samples of common lead has been made. As five of the radiogenic lead samples originated from minerals containing both uranium and thorium, three independent determinations of the age could be made. One of the samples was the oldest so far studied and appears to have an age close to two billion years. The common lead samples were found to have large variations in the relative abundances of the same sort as were reported in a previous investigation of twelve other samples.

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TL;DR: In this article, a detailed study has been made of the lattice imperfections which are assumed to account for plastic deformation, and it is shown that about twice as much energy is required to produce a certain amount of slip inside a solid as is required at the surface.

Abstract: A detailed study has been made of the lattice imperfections which are assumed to account for plastic deformation. Calculations of the strain energy associated with these dislocations have been made in the following cases: a dislocation in a uniform shear stress, two dislocations in an infinite medium, and a dislocation near a surface. The force acting on a dislocation is found by taking the gradient of the strain energy. A force is found which tends to attract dislocations toward the surface of a specimen. It is shown that about twice as much energy is required to produce a certain amount of slip inside a solid as is required to produce the same amount of slip at the surface. The energy required to produce a dislocation is found to be several electron volts per atomic plane, the exact amount depending on where it is located and how it was produced. Finally the energy stored in a material during work hardening is calculated by assuming that the dislocations are arranged in a regular two-dimensional lattice in the material. The density of dislocations found for severely work hardened material agrees with the predictions of other investigators. Numerical values found for the energy stored during work hardening are in agreement with experiment.

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TL;DR: In this article, Fermi's original "polar vector" form of the theory was extended to first and second forbidden transitions for arbitrarily charged nuclei and the final results were given in the form of a "correction factor" $C, by which the allowed distribution must be multiplied to give a forbidden spectrum.

Abstract: Fermi's theory of the energy distribution of $\ensuremath{\beta}$-particles is extended to first and second forbidden transitions for arbitrarily charged nuclei. The calculations are done not only for Fermi's original "polar vector" form of the theory but also for the scalar, tensor, axial vector and pseudoscalar forms. Selection rules appropriate for these are given in Table I. The final results are given in the form of a "correction factor" $C$, by which the allowed distribution must be multiplied to give a forbidden spectrum. They are listed in \textsection{}4. The energy dependence of the correction factors was found to be completely independent of knowledge concerning the details of the nuclear states only for the scalar and pseudo-scalar interactions (which give identical results) and for certain special selection rules in the other interactions. Comparison with experimental data on ${\mathrm{Na}}^{24}$, ${\mathrm{P}}^{32}$ and RaE seems to eliminate the scalar, pseudo-scalar and axial vector possibilities, all of which yield results independent of detailed knowledge concerning the nuclear states involved in these cases. The polar vector and tensor results depend on the unknown ratio of the magnitudes of certain nuclear matrix elements. Arbitrary adjustment of the unknown ratios allows fairly good fitting of the data. Especially striking is the reproduction of a "K-U type" shape for the RaE spectrum. Although the tensor and polar vector theories are equally favored by the evidence of the energy distributions, the fact that the tensor theory leads to Gamow-Teller selection rules perhaps make it preferable.

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TL;DR: In this article, it was shown that the conventional models of paramagnetic relaxation cannot be used at helium temperatures, because the lattice vibrations cannot possibly serve as a thermostat in the way ordinarily supposed.

Abstract: The present paper is rather negative in character. Its aim is to show that the conventional models of paramagnetic relaxation cannot be used at helium temperatures, because the lattice vibrations cannot possibly serve as a thermostat in the way ordinarily supposed. Namely, if the quanta exchanged between the spin system and the lattice oscillators are of the order 0.2 ${\mathrm{cm}}^{\ensuremath{-}1}$ characteristic of the usual Stark splittings in chrome or iron alum, the spins will be in thermal contact only with oscillators at the extreme low frequency end of the lattice spectrum which are too few in number to conduct away the surplus spin energy. It is found that this limited band of oscillators is interrupted much more frequently by interactions with the spins than by (a) collisions with the walls or (b) interplay with other oscillators due to anharmonic terms (calculated in the next paper). Consequently the lattice vibrations in thermal contact with the spin system will be at nearly the spin temperature, and not at that of the helium container as ordinarily supposed. Impurities with abnormally large Stark splittings, of the order 2.0 ${\mathrm{cm}}^{\ensuremath{-}1}$, would make a wider band of lattice oscillators available and so would avoid the difficulty of insufficient lattice conductivity, but it is very doubtful whether the impurities could be in thermal equilibrium with the great bulk of the paramagnetic ions. By thus showing that conventional hypotheses will not work, we aim to pave the way for a future paper proposing a rather unusual substitute conduction mechanism which is, however, compatible with the thermodynamic formulae of Casimir and du Pr\'e.

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TL;DR: In this paper, the authors give a general account of the principles of operation of the electron induction accelerator and more detailed analysis of the orbits of the electrons which was undertaken to serve as a guide in the design of the accelerator.

Abstract: The first section gives a general account of the principles of operation of the electron induction accelerator The second section gives the more detailed analysis of the orbits of the electrons which was undertaken to serve as a guide in the design of the accelerator

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TL;DR: In this article, a new method for treating the most important eigenvalue problems in quantum mechanics is developed, which can be found immediately once the equations are factorized by means of linear operators.

Abstract: A new method for treating the most important eigenvalue problems in quantum mechanics is developed. The solutions can be found immediately once the equations are factorized by means of linear operators. These operators acting on a normalized eigenfunction change it into a new normalized eigenfunction and all solutions can be found once the basic eigenfunction is known. This basic eigenfunction is a solution of a simple differential equation of the first order. The underlying theory is explained more fully on a special case (Section 1) and then the rules of procedure are formulated explicitly (Section 2). The rest of the paper contains applications including the Kepler problem treated according to Dirac's theory.

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TL;DR: In this paper, a theoretical and experimental investigation of the amplification properties of proportional counters has been made with the following primary assumptions: (1) All secondaries are produced by electron impact with no photon emission in the counter gas and thus no photoelectric emission at the cathode; (2) fluctuations in energy loss and specific ionization are neglected; and (3) the analysis involves the determination of the average number of ionizing collisions per unit distance (average energy) as a function of position in a counter, and the spatial extent of the ionization region near the wire an

Abstract: A theoretical and experimental investigation of the amplification properties of proportional counters has been made. On the basis of a discharge mechanism in which the amplification is due to electron avalanches the theory has been developed with the following primary assumptions: (1) All secondaries are produced by electron impact with no photon emission in the counter gas and thus no photoelectric emission at the cathode; (2) fluctuations in energy loss and specific ionization are neglected. The analysis involves the determination of the average number of ionizing collisions per unit distance (average energy) as a function of position in the counter, and the spatial extent of the ionization region near the wire anode. The former quantity is calculated explicitly in terms of the constants of the counter and the latter is shown to be simply related to the threshold voltage for proportional amplification, and is most suitably determined from the measurements. The gas fillers used in the measurements of the amplification factor were, for the most part, methane-argon mixtures of various relative concentrations and total pressures. In addition, other polyatomic mixtures, illuminating gas, B${\mathrm{F}}_{3}$-A and ether-A were used. Comparison of theory and experiment gives quite satisfactory agreement in all cases but two: large A concentration (50 percent or more at a total pressure of 10 cm Hg) and low total pressure (5 cm, or less, with a mixture containing 90 percent C${\mathrm{H}}_{4}$). In the anomalous cases the measured amplification factor rises extremely rapidly and such mixtures are therefore somewhat undesirable for stability reasons. This unstable behavior is characteristic of gas mixtures of the monatomic and/or diatomic type. An explanation of the difference in amplification properties of the polyatomic and simpler type gases is proposed. It is shown that while photon emission in the ultraviolet and subsequent contributions to the avalanche by photoelectric emission at the cathode is to be expected for the simpler gases, polyatomic gases should effectively quench such photon emission by virtue of greater energy loss of the slower electrons in exciting molecular vibrations and rotations. Moreover, appreciable emission of ultraviolet light by polyatomic molecules under electron bombardment is not to be expected. This explanation receives confirmation from cathode tests which were performed: measurements of pulse size, or amplification factor, for solid and perforated, oxidized and non-oxidized Cu cathodes. Further support of these arguments is found in experiments of other investigators: energy loss and mean free path measurements, electron bombardment of gases in a photo-cell. Finally, specific recommendations as to desirable pressure and concentration in the C${\mathrm{H}}_{4}$-A mixture are given.

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TL;DR: In this paper, the vertical intensity was obtained with lead thicknesses of 4, 6, 8, 10, 12, and 18 cm interposed between the counter tubes and it was shown that the intensity of the hard component increased continuously to the highest altitudes reached.

Abstract: This chapter focuses on the nature of the primary cosmic radiation and the origin of the mesotron. The chapter describes certain measurements of the vertical intensity and the production of mesotrons at high altitudes in which various arrangements of counters in three-, four-, or fivefold coincidences were used. The vertical intensity was obtained with lead thicknesses of 4, 6, 8, 10, 12, and 18 cm interposed between the counter tubes. The chapter illustrates the combined results of these experiments. It was seen from these measurements that the intensity of the hard component increased continuously to the highest altitudes reached. It was also found that measurements of the hard component made at very high altitudes with lead thicknesses even as small as 4 cm were not appreciably affected by electrons.