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Showing papers in "Physical Review in 1946"



Journal ArticleDOI
TL;DR: In this article, the authors present a review of the Physical review, vol. 70, nos. 11 and 12, 965-971, Dec. 1 and 15, 1946.
Abstract: "Reprinted from the Physical review, vol. 70, nos. 11 and 12, 965-971, Dec. 1 and 15, 1946."

1,132 citations


Journal ArticleDOI
TL;DR: The role played by the relaxation time of nuclear induction has been investigated experimentally as discussed by the authors, with the results showing that it varies between about 10 − 5 − 5 seconds and many seconds.
Abstract: The phenomenon of nuclear induction has been studied experimentally. The apparatus used is described, both as to principle and detail. Experiments have been carried out in which the signals from protons contained in a variety of substances were observed. The results show the role played by the relaxation time, which was found to vary between about ${10}^{\ensuremath{-}5}$ second and many seconds.

1,061 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that dipole arrays may be represented as vectors in a many-dimensional vector space and the classical dipole interaction energy is a quadratic form in the components of the dipole moments.
Abstract: It is shown that dipole arrays may be represented as vectors in a many-dimensional vector space. The classical dipole interaction energy is a quadratic form in the components of the dipole moments. Its calculation is reduced to the diagonalization of this form. The characteristic vectors are so called basic arrays. An arbitrary array may be decomposed into a linear combination of basic arrays, the energies are additive and may be obtained from the characteristic values of the quadratic form. The method is demonstrated by the complete solution of the characteristic value problem of a highly symmetric class of cubic arrays. The minimum energy arrays are obtained without and with an external magnetic field for the simple cubic, body-centered cubic, and face-centered cubic lattices. The results are in good qualitative agreement with the experiments of de Haas and Wiersma on Cs Ti alum. Some discrepancies are attributed to quantum effects and to incomplete saturation (entropy $Sg0$). The extension to these more general cases will be considered in a following paper.

499 citations



Journal ArticleDOI
TL;DR: In this paper, the electromagnetic effect of motions in the earth's core, considered as a fluid metallic sphere, is considered, and the behavior of the solutions depends on the symmetry of the "coupling matrix" that arises from the term of the field equations expressing the induction effects.
Abstract: The paper deals with the electromagnetic effect of motions in the earth's core, considered as a fluid metallic sphere. On the basis of simple estimates the electric conductivity of the core is assumed of the same order of magnitude as that of common metals. The mathematical treatment follows Hansen and Stratton: three independent vector solutions of the vectorial wave equation are introduced; two of these have vanishing divergence, and they are designated as toroidal and poloidal vector fields. The vector potential and electric field are toroidal, whereas the magnetic field is poloidal. These vectors, expressed in terms of spherical harmonics and Bessel functions, possess some notable properties of orthogonality which are briefly discussed. The theory of the free, exponentially decaying current modes is then given, leading to decay periods of the order of some tens of thousands of years. Next, the field equations in the presence of mechanical motions of the conducting fluid are set up. The field is developed in a series of the fundamental, orthogonal vectors, and the field equations are transformed into a system of ordinary differential equations for the coefficients of this development. The behavior of the solutions depends on the symmetry of the "coupling matrix" that arises from the term of the field equations expressing the induction effects. In order to evaluate this matrix the velocity field is developed into a series of the fundamental vectors similar to the series for the electromagnetic field. It is then shown that when the velocity is a toroidal vector field the coupling matrix is antisymmetrical. When the velocity field is poloidal, the coupling matrix is neither purely symmetrical nor purely antisymmetrical. For stationary fluid motion the linear differential equations can be integrated in closed form by a transformation to new normal modes, whenever the matrix of the system is either symmetrical or antisymmetrical. In the latter case the eigenvalues are purely imaginary and the coefficients of the new normal modes are harmonic functions of time, representing oscillatory changes in amplitude of the field components. For a symmetrical matrix the eigenvalues are real and the time factors of the new normal modes are real exponentials representing amplification or de-amplification as the case may be, depending on the sign of the velocity. For a matrix without specific symmetry, normal modes do not, as a rule, exist but similar, somewhat less stringent results can be derived in special cases. In the case of toroidal flow, in particular, the oscillatory changes of the field components are superposed upon the slow exponential decay characteristic of the free modes.

332 citations


Journal ArticleDOI
TL;DR: In this paper, it is shown that at the temperatures and densities in question (about 1010 ◦ K, and 106 g/cm3) nuclear transformations are mostly caused by the processes of absorption and re-evaporation of free neutrons so that their rates are essentially the same for the light and for the heavy elements.
Abstract: It is generally agreed at present that the relative abundances of various chemical elements were determined by physical conditions existing in the universe during the early stages of its expansion, when the temperature and density were sufficiently high to secure appreciable reaction-rates for the light as well as for the heavy nuclei. In all the so-far published attempts in this direction the observed abundance-curve is supposed to represent some equilibrium state determined by nuclear binding energies at some very high temperature and density [1] [2] [3]. This point of view encounters, however, serious difficulties in the comparison with empirical facts. Indeed, since binding energy is, in a first approximation, a linear function of atomic weight, any such equilibrium theory would necessarily lead to a rapid exponential decrease of abundance through the entire natural sequence of elements. It is known, however, that whereas such a rapid decrease actually takes place for the first half of chemical elements, the abundance of heavier nuclei remains nearly constant [4]. Attempts have been made2 to explain this discrepancy by the assumption that heavy elements were formed at higher temperatures, and that their abundances were already “frozen” when the adjustment of lighter elements was taking place. Such an explanation, however, can be easily ruled out if one remembers that at the temperatures and densities in question (about 1010 ◦ K, and 106 g/cm3) nuclear transformations are mostly caused by the processes of absorption and re-evaporation of free neutrons so that their rates are essentially the same for the light and for the heavy elements. Thus it appears that the only way of explaining the observed abundance-curve

312 citations



Journal ArticleDOI
TL;DR: In this paper, an equation for the energy distribution of electrons in a gas subject to a spatially constant high frequency field is obtained, where the domain of applicability of the equation is limited to situations in which the densities of electrons, ions, and excited molecules are very small compared to the density of normal molecules.
Abstract: In this paper an equation for the energy distribution of electrons in a gas subject to a spatially constant high frequency field is obtained. The domain of applicability of the equation is limited (a) to situations in which the densities of electrons, ions, and excited molecules are very small compared to the density of normal molecules, (b) to electron energies such that the elastic collision cross section for electron-molecule collisions is large compared to the inelastic cross section, (c) to linear dimensions of the discharge region large compared to the mean free path for elastic collision, and (d) to frequencies of the impressed electric field larger than a certain lower limit determined by the pressure, type of gas, and linear dimensions of the discharge region. Methods for the solution of the distribution equation are presented in Section 5; simplified examples illustrating these methods are given in Section 7. The distribution equation for the d.c. case is also derived (Section 6); it agrees with those obtained by other authors. A comparison of the high frequency and d.c. distribution equations suggests a useful correlation between the two cases.

263 citations


Journal ArticleDOI
Walter Gordy1
TL;DR: In this paper, a linear relation between the electronegativity of an atom and the number of electrons in its incompletely filled (valence) shells, and its single bond covalent radius measured in Angstroms has been found valid for all elements having $x$ values available for comparison.
Abstract: The relation, $x=0.31\left(\frac{n+1}{r}\right)+0.50,$ where $x$ represents the electronegativity of an atom according to Pauling's revised scale, $n$ the number of electrons in its incompletely filled (valence) shells, and $r$ its single bond covalent radius measured in Angstroms, has been found valid for all elements having $x$ values available for comparison, except for Ag, Au, and Cu. This equation is used to extend the electronegativity scale to include a total of fifty-two elements. A chart is constructed to demonstrate the systematic relation of the values to the periodic table. Beginning with the definition of the electronegativity of a neutral atom in a stable molecule as the potential at a distance $r$ (covalent radius) from its nucleus which is caused by the nuclear charge effective at that distance, a simple theoretical justification is offered for the existence of a linear relation between $x$ and $\frac{(n+1)}{r}$. This relation, like Mulliken's, provides an "absolute" scale of electronegativity values.

239 citations


Journal ArticleDOI
TL;DR: In this article, the Fourier integral expression for the intensity distribution in a pressure broadened line is derived from the quantum radiation theory with an adiabatic collision approximation, and the phase shift approximation to the solution is obtained with the actual distribution of phase shifts taken into account.
Abstract: The Fourier integral expression for the intensity distribution in a pressure broadened line is derived from the quantum radiation theory with an adiabatic collision approximation. The phase shift approximation to the solution is obtained with the actual distribution of phase shifts taken into account. It is shown that in general there is a shift in line position as well as a line broadening both proportional to the pressure. The ratio of the shift to the broadening depends only on the power of the intermolecular distance with which the interaction decreases. Experimental values of this ratio in foreign gas broadening are on the average consistent with the inverse sixth power. The predicted line widths are slightly larger than those given by Weisskopf. Good agreement with the observed line width is found for most of the alkali metals absorption lines. Calculated line widths and shifts are given for the vibration-rotation lines of linear polar molecules. A method for treating non-adiabatic collisions is given. The conditions for which the Lorentz line form transforms to the Margenau-type line form are indicated. It is shown that the Jablonski wave mechanical treatment of translational motion leads to the same line forms as the Fourier integral method under the proper physical conditions.

Journal ArticleDOI
TL;DR: In this paper, the distribution in energy of electrons in a high frequency electromagnetic field is derived by kinetic theory methods by using the distribution law, the current density and hence the complex conductivity are calculated as functions of electron density, pressure, and frequency of the field.
Abstract: The distribution in energy of electrons in a high frequency electromagnetic field is derived by kinetic theory methods. By use of the distribution law, the current density and hence the (complex) conductivity are calculated as functions of electron density, pressure, and frequency of the field. The real part of the conductivity has a maximum for gas pressures, or frequencies, such that the mean free time of an electron is approximately equal to the period of the field. From the conductivity, the dielectric constant of the medium, its index of refraction, and its extinction coefficient are deduced. The results are applicable in microwave researches and in ionosphere problems.

Journal ArticleDOI
TL;DR: In this article, the authors give a derivation of the resonance formula for nuclear reactions which is free from artificial assumptions, using a Taylor series development of the wave function with respect to the energy.
Abstract: The purpose of the present paper is to give a derivation of the resonance formula for nuclear reactions which is free from artificial assumptions. Mathematically, the method used amounts to a Taylor series development of the wave function with respect to the energy. It is assumed that the first (energy independent) term in this development is, within a region of configuration space where all particles are close together, the same, no matter in which way the compound state is formed and that this is, in that region of configuration space, already a good approximation. The second term in the development of the wave function with respect to the energy difference from the resonance energy can then be calculated very easily and this calculation is carried out in Section II for resonance scattering, in Sections III and IV for resonance reactions. It is assumed in both calculations that the colliding particles have zero orbital angular momentum around their center of mass. The third term in the same expansion is estimated for resonance scattering in Section VI and it is shown that, if there were no other resonances in the neighborhood, the effect of the third term would be negligible over a very wide energy range (several hundred kilovolt). The formulae for the cross sections, as obtained, are of greater generality than the customary ones inasmuch as they contain extra terms which could be interpreted as potential scattering and potential reaction. The existence of such terms has been noticed already by Bethe. However, as discussed in Section V, the extra terms are, particularly in the neighborhood of the resonance, much smaller than the resonance terms so that one is led back, in practice, to the ordinary resonance formulae, as given, e.g., by Bethe. In particular, the disintegration probability is, as function of energy, proportional to the velocity with which the reaction products separate if the orbital angular momentum of the separating particles vanishes. It may be worth while to remark that the resonance part of the collision matrix has a particularly simple form and is, e.g., of rank 1. The case of orbital angular mementum $1\ensuremath{\hbar}$ is discussed in Section VII. In this case, the disintegration probability of the compound state is proportional to the third power of the velocity of the separating particles so that the scattering is, at very low energies, proportional to the square of the energy. The same holds, in this case, of the "potential scattering" also. Section VII also contains an investigation of the region of validity of the formulae in case of angular momentum $1\ensuremath{\hbar}$ between the colliding particles and shows that this region will extend to the neighboring resonances.

Journal ArticleDOI
TL;DR: In this article, the water vapor absorption line resulting from the rotational transition was investigated experimentally, and the wave-length range between 0.7 cm and 1.34$ cm was explored.
Abstract: The water vapor absorption line resulting from the rotational transition ${5}_{\ensuremath{-}1}$-${6}_{\ensuremath{-}5}$ has been investigated experimentally. Radiation is fed into an air-filled cubical copper cavity 8 ft. on an edge. Strings of thermocouples with alternate junctions coated with a "lossy" material are placed at random in the cavity. The e.m.f. of these thermocouples is proportional to the $Q$ of the cavity and its contents. With the total pressure inside the cavity at one atmosphere, the partial pressure of the water vapor is varied from 1 mm to 55 mm of Hg. A measurement of the change in e.m.f. with humidity yields a value for the losses in the water vapor, provided the $Q$ of the cavity is known. This quantity may be determined from additional measurements taken with an aperture opened in the side of the cavity. The wave-length range between 0.7 cm and 1.7 cm has been explored. Results indicate a peak at $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{ u}}=0.744\ifmmode\pm\else\textpm\fi{}0.005$ ${\mathrm{cm}}^{\ensuremath{-}1}$, corresponding to a wave-length $\ensuremath{\lambda}=1.34$ cm. The absorption line is broadened as the water vapor density is increased. At very low density, the half-width of the curve (half-width at half-height) is 0.087\ifmmode\pm\else\textpm\fi{}0.01 ${\mathrm{cm}}^{\ensuremath{-}1}$, while the corresponding value for a density of 50 gram/${\mathrm{meter}}^{3}$ is 0.107\ifmmode\pm\else\textpm\fi{}0.01 ${\mathrm{cm}}^{\ensuremath{-}1}$. The cross section for a water-water collision must be nearly 5 times that for a water-air collision to account for this change in half-width with vapor density. The attenuation at the peak is 0.025 db per kilometer for 1 gram of water vapor per cubic meter.

Journal ArticleDOI
TL;DR: In this article, the absorption of microwave radiation in traversing the earth's atmosphere has been measured at three wave-lengths (1.00 cm, 1.25 cm, and 1.50 cm) in the region of a water-vapor absorption line.
Abstract: The absorption of microwave radiation in traversing the earth's atmosphere has been measured at three wave-lengths (1.00 cm, 1.25 cm, and 1.50 cm) in the region of a water-vapor absorption line. The measurement employs a sensitive radiometer to detect thermal radiation from the absorbing atmosphere. The theory of such measurements and the connection between absorption and thermal radiation are presented. The measured absorption together with water-vapor soundings of the atmosphere permits the calculation of the absorption coefficients at standard conditions (293\ifmmode^\circ\else\textdegree\fi{}K, 1015 millibar). These are 0.011, 0.026, and 0.014 db/km/g ${\mathrm{H}}_{2}$O/${\mathrm{m}}^{3}$ for the wave-lengths 1.00 cm, 1.25 cm, and 1.50 cm, respectively. These values are (50 percent) greater than those given by the theory of Van Vleck. The collision width of the line and its location are in better agreement with the theory and infra-red absorption measurement. It is also found that there is very little (20\ifmmode^\circ\else\textdegree\fi{}K) radiation from cosmic matter at the radiometer wave-lengths.

Journal ArticleDOI
TL;DR: In this article, it was shown that the ionization potential of a substance has little influence upon the amount of energy that must be absorbed by that substance per each pair of ions actually produced.
Abstract: The energy absorbed by a substance exposed to an ionizing radiation is used partly in ionization, partly in optical excitation. Arguments based on atomic mechanics are presented, to show that, the greater the ionization potential, the greater is the share of the absorbed energy which is actually spent in ionization. This explains why the ionization potential of a substance has little influence upon the amount of energy that must be absorbed by that substance per each pair of ions actually produced.


Journal ArticleDOI
TL;DR: In this paper, it is shown that a zonal fluid motion (zonal toroidal flow in the terminology adopted here) produces rotation of the tesseral magnetic dipole terms and also oscillatory changes in amplitude of these terms.
Abstract: In Part I a method has been developed for the integration of the electromagnetic field equations in the presence of fluid motions in a spherical conductor. This analysis is here applied to an interpretation of the secular geomagnetic variations. A very brief survey of some of the observed features of the secular variation is first given. It is pointed out that not only the phases but also the magnitudes of the harmonic components, including the main dipole, are subject to large changes at the present time. There follows a brief study of the skin effect which indicates that the observed variations of the dipole terms originate in a layer adjacent to the core's boundary several hundred kilometers deep; those of the higher terms originate in a layer no more than 200 km deep. Next, the "coupling matrix" introduced in Part I is evaluated in form of a table of all matrix elements that contain vectors of dipole and quadrupole type but no higher harmonics. It is shown that a zonal fluid motion (zonal toroidal flow in the terminology adopted here) produces rotation of the tesseral magnetic dipole terms and also oscillatory changes in amplitude of these terms. There is one and only one type of matrix element that represents an interaction of the main magnetic dipole with itself; the corresponding fluid motion is a meridional flow (poloidal flow) of quadrupole symmetry. With this term amplification or de-amplification occurs, depending on the sign of the velocity. The theory thus can account for all the observed components of the secular variation.


Journal ArticleDOI
TL;DR: In this article, an energy analysis of the non-integral masses in n-butane, butadiene, and ethane has been made and the values obtained agree with those predicted on the basis that they arise from metastable ions.
Abstract: It has been recently reported that the non-integral masses appearing in the mass spectra of various hydrocarbons may be explained by the spontaneous dissociation of some of the ions into fragments of lighter mass after they have been accelerated and emerge from the ion gun. By means of an energy filter, an energy analysis of the non-integral masses in n-butane, butadiene, and ethane has been made and the values obtained agree with those predicted on the basis that they arise from metastable ions. Variation of the pressure and electrode potentials confirms that the dissociation is spontaneous. The formation of metastable ions appears to be a general occurrence in the ionization and dissociation of hydrocarbons and is shown here to occur in ethane, propane, 1, 3-butadiene, butene-1, cis-butene-2, isobutylene, normal butane, iso-butane, pentene-2, normal pentane, iso-pentane, and methyl-cyclo-pentane.

Journal ArticleDOI
Warren P. Mason1
TL;DR: In this article, the elastic, piezoelectric, and dielectric constants of KDP and ADP were measured through temperature ranges down to the Curie temperatures.
Abstract: Measurements have been made of all the elastic, piezoelectric, and dielectric constants of KDP and ADP crystals through temperature ranges down to the Curie temperatures. The piezoelectric properties agree well with Mueller's phenomenological theory of piezoelectricity provided the fundamental piezoelectric constant is taken as the ratio of the piezoelectric stress to that part of the polarization due to the hydrogen bonds. It is found that the dielectric properties of KDP agree well with the theory presented by Slater based on the interaction of the hydrogen bonds with the ${\mathrm{PO}}_{4}$ ions. ADP undergoes a transition at -125\ifmmode^\circ\else\textdegree\fi{}C which results in fracturing the crystal. This transition cannot be connected with the ${\mathrm{H}}_{2}$P${\mathrm{O}}_{4}$ hydrogen bond system which controls the dielectric and piezoelectric properties, for these lie on smooth curves that do not change slope as the transition temperature is approached. It is suggested that two separate and independent hydrogen bond systems are involved in ADP. The transition temperature and specific heat anomaly appear to be connected with hydrogen bonds between the nitrogens and the oxygens of the ${\mathrm{PO}}_{4}$ ions, while the dielectric and piezoelectric properties are controlled by the ${\mathrm{H}}_{2}$P${\mathrm{O}}_{4}$ hydrogen bonds.




Journal ArticleDOI
John P. Blewett1
TL;DR: In this paper, the effects of radiation losses on the electron orbits are calculated, and it is shown that not only should the orbit shift pulse necessary to bring electrons to a target inside the equilibrium orbit fall below the value expected in the absence of radiation, but also electrons should eventually arrive at the target with no orbit shift pulses whatever, at a phase of the field wave predictable from the theory.
Abstract: This paper discusses the possibility that radiation losses because of the high radial accelerations experienced by the electrons in an induction electron accelerator may introduce limitations in the design of accelerators for energies above 100 million electron volts. The effects of radiation losses on the electron orbits are calculated, and it is shown that not only should the orbit shift pulse necessary to bring electrons to a target inside the equilibrium orbit fall below the value expected in the absence of radiation, but also electrons should eventually arrive at the target with no orbit shift pulse whatever, at a phase of the field wave predictable from the theory. Both effects have been observed in the General Electric 100-Mev unit in a manner consistent with the predictions of the theory. The radiation itself has not yet been detected.

Journal ArticleDOI
Abstract: The dependence of the velocity of thermal repulsion of tricresyl phosphate droplets suspended in air on temperature gradient, pressure, and particle radius, $a$, was measured and compared with the velocities calculated from radiometer theory. Thermal repulsion is shown to be a radiometer effect. The velocity of thermal repulsion is directly proportional to the temperature gradient. The velocity of thermal repulsion at constant pressure increases with decreasing particle radius to a maximum when the mean free path, $L$, is about 1.5 times the radius, and then decreases. The velocity of thermal repulsion is approximately proportional to $\frac{1}{P}$ when $\frac{L}{a}l0.5$. The dependence of the force of thermal repulsion on temperature gradient, pressure, and particle radius are in agreement with the requirements of radiometer theory at high pressures. The resistance of air to the motion of tricresyl phosphate droplets is accurately given by Millikan's equation. The coefficient of slip on these droplets is 8.25\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ cm at 76-cm pressure and 30\ifmmode^\circ\else\textdegree\fi{}C. The measured velocities of thermal repulsion have been compared with the theoretical values calculated from the resistance of the medium and the radiometer forces as given by Albert Einstein and by Paul S. Epstein. The numerical agreement is satisfactory in view of the approximations in the theoretical derivations and the uncertainty in the heat conductivity of the tricresyl phosphate. Thermal repulsion can be used to determine the radius of particles too small to be measured by sedimentation velocity.

Journal ArticleDOI
TL;DR: In this article, the effect of radiation losses on the damping of synchrotron oscillations is discussed. And the transition from a betatron to a Synchro-Cyclotron was discussed.
Abstract: In accelerators of the type discussed by Veksler and McMillan (e.g., the synchrotron and synchro-cyclotron) the motion of particles can be described in terms of stable oscillations about a synchronous orbit. Expressions are worked out for the frequencies of these oscillations, and for the way in which their amplitudes are damped as the energy is increased. The effect of radiation losses on the damping is discussed. It is shown that the synchrotron can advantageously be operated as a betatron until the electron velocity is close to that of light; the dee voltage is then turned on and the machine works as a synchrotron for the remainder of the acceleration. The transition from betatron to synchrotron operation proved to be quite efficient. Formulae are given for the distortions of the orbits by azimuthal asymmetries of the magnetic field. The results are illustrated in terms of the California synchrotron.

Journal ArticleDOI
Peter G. Bergmann1
TL;DR: In this paper, the statistical properties of the inhomogeneities of the transmitting medium with the fluctuations to be expected in the signal level of radiative energy were derived by means of the methods of geometrical optics.
Abstract: By means of the methods of geometrical optics, approximate formulae are being derived which correlate the statistical properties of the inhomogeneities of the transmitting medium with the fluctuations to be expected in the signal level of radiative energy. Through a further simplification of the formulae obtained, it is possible to predict the dependence of signal fluctuation on range without detailed knowledge of the statistical parameters of the "micro-structure" of the transmitting medium.