Showing papers in "Physical Review in 1957"
TL;DR: In this article, the authors consider statistical mechanics as a form of statistical inference rather than as a physical theory, and show that the usual computational rules, starting with the determination of the partition function, are an immediate consequence of the maximum-entropy principle.
Abstract: Information theory provides a constructive criterion for setting up probability distributions on the basis of partial knowledge, and leads to a type of statistical inference which is called the maximum-entropy estimate. It is the least biased estimate possible on the given information; i.e., it is maximally noncommittal with regard to missing information. If one considers statistical mechanics as a form of statistical inference rather than as a physical theory, it is found that the usual computational rules, starting with the determination of the partition function, are an immediate consequence of the maximum-entropy principle. In the resulting "subjective statistical mechanics," the usual rules are thus justified independently of any physical argument, and in particular independently of experimental verification; whether or not the results agree with experiment, they still represent the best estimates that could have been made on the basis of the information available.It is concluded that statistical mechanics need not be regarded as a physical theory dependent for its validity on the truth of additional assumptions not contained in the laws of mechanics (such as ergodicity, metric transitivity, equal a priori probabilities, etc.). Furthermore, it is possible to maintain a sharp distinction between its physical and statistical aspects. The former consists only of the correct enumeration of the states of a system and their properties; the latter is a straightforward example of statistical inference.
12,099 citations
TL;DR: In this article, a theory of superconductivity is presented, based on the fact that the interaction between electrons resulting from virtual exchange of phonons is attractive when the energy difference between the electrons states involved is less than the phonon energy, and it is favorable to form a superconducting phase when this attractive interaction dominates the repulsive screened Coulomb interaction.
Abstract: A theory of superconductivity is presented, based on the fact that the interaction between electrons resulting from virtual exchange of phonons is attractive when the energy difference between the electrons states involved is less than the phonon energy, $\ensuremath{\hbar}\ensuremath{\omega}$. It is favorable to form a superconducting phase when this attractive interaction dominates the repulsive screened Coulomb interaction. The normal phase is described by the Bloch individual-particle model. The ground state of a superconductor, formed from a linear combination of normal state configurations in which electrons are virtually excited in pairs of opposite spin and momentum, is lower in energy than the normal state by amount proportional to an average ${(\ensuremath{\hbar}\ensuremath{\omega})}^{2}$, consistent with the isotope effect. A mutually orthogonal set of excited states in one-to-one correspondence with those of the normal phase is obtained by specifying occupation of certain Bloch states and by using the rest to form a linear combination of virtual pair configurations. The theory yields a second-order phase transition and a Meissner effect in the form suggested by Pippard. Calculated values of specific heats and penetration depths and their temperature variation are in good agreement with experiment. There is an energy gap for individual-particle excitations which decreases from about $3.5k{T}_{c}$ at $T=0\ifmmode^\circ\else\textdegree\fi{}$K to zero at ${T}_{c}$. Tables of matrix elements of single-particle operators between the excited-state superconducting wave functions, useful for perturbation expansions and calculations of transition probabilities, are given.
9,619 citations
TL;DR: In this paper, the angle energy distribution of a fast electron losing energy to conduction electrons in a thick metallic foil has been derived assuming that the conduction electron constitute a Fermi-Dirac gas and that the fast electron undergoes only small fractional energy and momentum changes.
Abstract: The angle-energy distribution of a fast electron losing energy to the conduction electrons in a thick metallic foil has been derived assuming that the conduction electrons constitute a Fermi-Dirac gas and that the fast electron undergoes only small fractional energy and momentum changes. This distribution exhibits both collective interaction characteristics and individual interaction characteristics, and is more general than the result obtained by other workers. Describing the conduction electrons by the hydro-dynamical equations of Bloch, it has been shown that for very thin idealized foils energy loss may occur at a value which is less than the plasma energy, while as the foil thickness decreases below $\ensuremath{\sim}\frac{v}{{\ensuremath{\omega}}_{p}}$ the loss at the plasma energy becomes less than that predicted by more conventional theories. The net result is an increase in the energy loss per unit thickness as the foil thickness is decreased. It is suggested that the predicted loss at subplasma energies may correspond to some of the low-lying energy losses which have been observed by experimenters using thin foils.
2,623 citations
TL;DR: In this paper, the polarization of conduction electrons due to the first order perturbed energy corresponding to the Fr\"ohlich-Nabarro and Zener mechanism was investigated and it was shown that the polarization is concentrated in the neighborhood of the Mn ions.
Abstract: The polarization of conduction electrons due to $s\ensuremath{-}d$ interaction in CuMn alloys is investigated. The uniform polarization due to the first order perturbed energy corresponding to the Fr\"ohlich-Nabarro and Zener mechanism is shown to be completely modified by the first order perturbation of the wave functions and the polarization is concentrated in the neighborhood of the Mn ions. At the same time it is shown that the Fr\"ohlich-Nabarro interaction is included in the Ruderman-Kittel result as one component. The electronic $g$-value of Mn ions and the Knight shift of the Cu-nuclei are also discussed from this point of view.
2,274 citations
TL;DR: In this article, it was shown that a Schwarzschild singularity, spherically symmetrical and endowed with mass, will undergo small vibrations about the spherical form and therefore remain stable if subjected to a small nonspherical perturbation.
Abstract: It is shown that a Schwarzschild singularity, spherically symmetrical and endowed with mass, will undergo small vibrations about the spherical form and will therefore remain stable if subjected to a small nonspherical perturbation.
2,105 citations
TL;DR: In this paper, the key steps in the development of the microscopic understanding of superconductivity are discussed, and a detailed review of the main steps in this process is presented. But,
Abstract: Key steps in the development of the microscopic understanding of superconductivity are discussed.
1,969 citations
TL;DR: In this paper, the intensity of optical absorption close to the edge in semiconductors is examined using band theory together with the effective-mass approximation for the excitons, and the experimental results on O and Ge are in good qualitative agreement with direct forbidden and indirect transitions, respectively.
Abstract: The intensity of optical absorption close to the edge in semiconductors is examined using band theory together with the effective-mass approximation for the excitons. Direct transitions which occur when the band extrema on either side of the forbidden gap are at the same K, give a line spectrum and a continuous absorption of characteristically different form and intensity, according as transitions between band states at the extrema are allowed or forbidden. If the extrema are at different K values, indirect transitions involving phonons occur, giving absorption proportional to ${(\ensuremath{\Delta}E)}^{\frac{1}{2}}$ for each exciton band, and to ${(\ensuremath{\Delta}E)}^{2}$ for the continuum. The experimental results on ${\mathrm{Cu}}_{2}$O and Ge are in good qualitative agreement with direct forbidden and indirect transitions, respectively.
1,488 citations
1,283 citations
TL;DR: In this paper, it is shown that, by adding appropriate numbers of particles trapped in the potential energy troughs, essentially arbitrary traveling wave solutions can be constructed, and the possible existence of such waves in an actual plasma will depend on factors ignored in this paper, as in most previous works, namely interparticle collisions and the stability of the solutions against various types of perturbations.
Abstract: The problem of a one-dimensional stationary nonlinear electrostatic wave in a plasma free from interparticle collisions is solved exactly by elementary means. It is demonstrated that, by adding appropriate numbers of particles trapped in the potential-energy troughs, essentially arbitrary traveling wave solutions can be constructed.When one passes to the limit of small-amplitude waves it turns out that the distribution function does not possess an expansion whose first term is linear in the amplitude, as is conventionally assumed. This disparity is associated with the trapped particles. It is possible, however, to salvage the usual linearized theory by admitting singular distribution functions. These, of course, do not exhibit Landau damping, which is associated with the restriction to well-behaved distribution functions.The possible existence of such waves in an actual plasma will depend on factors ignored in this paper, as in most previous works, namely interparticle collisions, and the stability of the solutions against various types of perturbations.
1,171 citations
TL;DR: In this article, a criterion for determining the onset of ferromagnetism in a material as its temperature is lowered from a region in which the linearity of its magnetic moment versus field isotherm gives an indication of paramagnetisms.
Abstract: A criterion is proposed for determining the onset of ferromagnetism in a material as its temperature is lowered from a region in which the linearity of its magnetic moment versus field isotherm gives an indication of paramagnetism. Within the limits of validity of a molecular field treatment, the Curie temperature is shown to be in general indicated by the third power of the magnetization being proportional to the internal magnetic field. The method has been employed to redetermine the Curie point of nickel from the data of Weiss and Forrer, of ${\mathrm{Fe}}_{3}$${\mathrm{O}}_{4}$ from the data of Smith and of some alloys from the data of Kaufmann and his collaborators and the author.
1,068 citations
TL;DR: The contribution of the Fokker-Planck equation for the distribution function for gases, due to particle-particle interactions in which the fundamental two-body force obeys an inverse square law, is investigated in this paper.
Abstract: The contribution to the Fokker-Planck equation for the distribution function for gases, due to particle-particle interactions in which the fundamental two-body force obeys an inverse square law, is investigated. The coefficients in the equation, $〈\ensuremath{\Delta}\mathrm{v}〉$ (the average change in velocity in a short time) and $〈\ensuremath{\Delta}\mathrm{v}\ensuremath{\Delta}\mathrm{v}〉$, are obtained in terms of two fundamental integrals which are dependent on the distribution function itself. The transformation of the equation to polar coordinates in a case of axial symmetry is carried out. By expanding the distribution function in Legendre functions of the angle, the equation is cast into the form of an infinite set of one-dimensional coupled nonlinear integro-differential equations. If the distribution function is approximated by a finite series, the resultant Fokker-Planck equations may be treated numerically using a computing machine. Keeping only one or two terms in the series corresponds to the approximations of Chandrasekhar, and Cohen, Spitzer and McRoutly, respectively.
TL;DR: In this paper, the correlation energy per particle of an electron gas expressed in rydbergs is computed for small values of rs (high density) and found to be given by ec=Alnrs+C+O(rs).
Abstract: The quantity ec is defined as the correlation energy per particle of an electron gas expressed in rydbergs. It is a function of the conventional dimensionless parameter rs, where rs-3 is proportional to the electron density. Here ec is computed for small values of rs (high density) and found to be given by ec=Alnrs+C+O(rs). The value of A is found to be 0.0622, a result that could be deduced from previous work of Wigner, Macke, and Pines. An exact formula for the constant C is given here for the first time; earlier workers had made only approximate calculations of C. Further, it is shown how the next correction in rs can be computed. The method is based on summing the most highly divergent terms of the perturbation series under the integral sign to give a convergent result. The summation is performed by a technique similar to Feynman's methods in field theory.
TL;DR: In this paper, the pseudopotential method was used for an explicit calculation of the first few terms in an expansion in power of the eigenvalues and corresponding eigenfunctions of a system of Bose particles with hard-sphere interaction.
Abstract: It is shown that the pseudopotential method can be used for an explicit calculation of the first few terms in an expansion in power of ${(\ensuremath{\rho}{a}^{3})}^{\frac{1}{2}}$ of the eigenvalues and the corresponding eigenfunctions of a system of Bose particles with hard-sphere interaction. The low-temperature properties of the system are discussed.
TL;DR: In this article, the assumption that the 33 resonance dominates the dispersion integrals leads to detailed predictions about the photomeson amplitude, and an attempt is made to keep first order (in v/c) nucleon recoil effects.
Abstract: Relativistic dispersion relations for photomeson production, analogous to the pion-nucleon scattering dispersion relations, are formulated without proof. The assumption that the 33 resonance dominates the dispersion integrals then leads to detailed predictions about the photomeson amplitude. An attempt is made to keep first order (in v/c) nucleon recoil effects. Except for the latter, the predictions of the cutoff model are generally reproduced.
TL;DR: In this paper, a generalization of Fermi's pseudopotential for the two-body hard-sphere problem is introduced, which leads to an expansion of the energy levels of the system in powers of $a.
Abstract: The system under consideration is an $N$-particle quantum-mechanical system enclosed in a volume $V$, in which the particles interact via two-body hard-sphere potentials, with hard-sphere diameter $a$. The two-body hard-sphere problem is first discussed by a generalization of Fermi's pseudopotential by means of which the problem is formulated entirely in terms of the scattering phase shifts. It is then shown that a pseudopotential for the $N$-body problem can be introduced, and leads to an expansion of the energy levels of the system in powers of $a$. The first order energy levels of a Bose and a Fermi system are calculated. For the Bose system, the first order energy formula exhibits an "energy gap" above the ground state, leading to properties of the system not dissimilar to that of a superfluid. The ground state energy for a Bose system is calculated to order ${a}^{3}$ and that for the Fermi system, to order ${a}^{2}$. The physical interpretation and validity of these results are discussed.
TL;DR: In this paper, the authors present a review of all the present and future experiments anywhere close to reality and discuss how to project into the experimental future, using their own experience of studying the machine-in-the-desert.
Abstract: In order to project into the experimental future, we need some historical perspective. We should be aware of trends (e.g., vectors) so that we can see where a “natural” evolution of HEP will take us and we should be sensitive to problems that, although minor in the 1960s and manageable in the 197Os, have reached near crises states in the 1980s and will become the death knell of the subject in the 1990s. Although I started this review with an idea of seeing how we were doing with our ability to measure in space and time resolution, I became trapped into sociology, so I must then also discuss this as well. My assignment is awkward because all of the present and future experiments anywhere close to reality will be discussed in this program of speakers. What then can I add? Accelerators? About 30 months ago and about five miles from here in Snowmass ’82, I stated my conviction that the scientific need for observing a 1 TeV mass scale was overwhelming, that the technology was in hand, that the cost was moderate, and that we could not afford to dabble in intermediate steps. I would like to claim here that this talk, which coined the name, “Machine-in-the-Desert” or “Desertron,” was the opening shot in what was to become the goal of H E P for the next decade. After an enormous “Sturm und Drang,” we have SSC. It is much too early to say whether or not this was a foolhardy decision, but if we fail, it won’t be because we aren’t unified and convinced that this is the right scientific step. The more we look at the technology, the better it looks. The more we look at the science, the more it is the right step. I think we are committed to SSC, but we must be prepared for some setbacks and disappointments. However, we have a reasonable program to keep us going and if the SSC is under construction by the time LEP and HERA come on (1991-92), we’ll be very busy building the machine and building the detectors that are to use it. Therefore, I want to talk history now and since I’m not a scholar, but a student, I largely will use my own experience. It is also well known that, a t my age, looking back is more pleasant than looking ahead. Let me show you a number of figures, the first of which are pages from some miscellaneous Physical Review papers published in the ancient days when data was recorded by quill pens on fine parchment. FIGURE 1 is from research done on the Nevis cyclotron, which in 1950 was the world’s highest energy machine a t 400 MeV. The device was a Wilson Cloud Chamber working in a magnetic field of 5000 gauss. A total of 4000 photographs yielded the data, which was scanned and analyzed by two students and one assistant professor (me). FIGURE 2 is research done a t BNL, the Cosmotron. Here, 5000 pictures in a “giant” 36” cloud chamber were measured by one
TL;DR: In this article, the effect of free carriers on the optical constants has been determined by using reflectivity and absorption measurements in the region 5 to 35 micron, and the significance of ${m}_{s}$ is considered for four different types of energy band structure.
Abstract: By using reflectivity and absorption measurements in the region 5 to 35 micron, the effect of free carriers on the optical constants has been determined for $n$- and $p$-type germanium, silicon, and indium antimonide, and for $n$-type indium arsenide. The contribution of the free carriers to the electric susceptibility is obtained from the optical constants. A carrier effective mass, ${m}_{s}$, is defined in terms of the susceptibility, and the significance of ${m}_{s}$ is considered for four different types of energy band structure. The experimental values of ${m}_{s}$ are compared with those calculated by using data from other experiments. Good agreement was found for $n$- and $p$-type silicon, $n$-type germanium, and $p$-type indium antimonide. In $p$-type germanium, the susceptibility due to transitions between the overlapping bands in the valence band was taken into account. However, the resulting ${m}_{s}$, for a sample of \ensuremath{\sim}${10}^{19}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ impurity concentration, is larger by a factor of 1.8 than that calculated by using cyclotron resonance data. In $n$-type indium antimonide ${m}_{s}$ increases with carrier concentration. If one assumes ${m}_{s}$ to be energy-dependent, the shape of the conduction band calculated is consistent with previously reported measurements of the shift of the intrinsic absorption edge with electron concentrations. In the case of $n$-type indium arsenide, ${m}_{s}$ differs from the effective mass reported from thermoelectric measurements but gives good agreement with the values determined from the shift of the intrinsic absorption edge for an impure specimen.
TL;DR: A brief review of the physical significance of the paradox of Einstein, Rosen, and Podolsky is given, and it is shown that it involves a kind of correlation of the properties of distant noninteracting systems, which is quite different from previously known kinds of correlation as discussed by the authors.
Abstract: A brief review of the physical significance of the paradox of Einstein, Rosen, and Podolsky is given, and it is shown that it involves a kind of correlation of the properties of distant noninteracting systems, which is quite different from previously known kinds of correlation. An illustrative hypothesis is considered, which would avoid the paradox, and which would still be consistent with all experimental results that have been analyzed to date. It is shown, however, that there already is an experiment whose significance with regard to this problem has not yet been explicitly brought out, but which is able to prove that this suggested resolution of the paradox (as well as a very wide class of such resolutions) is not tenable. Thus, this experiment may be regarded as the first clear empirical proof that the aspects of the quantum theory discussed by Einstein, Rosen, and Podolsky represent real properties of matter.
TL;DR: In this paper, the de Haas-van Alphen effect in the magnetic susceptibility of graphite has been interpreted by applying the susceptibility formula for general bands of Lifschitz and Kosevich to the band model of Slonczewski.
Abstract: The de Haas-van Alphen effect in the magnetic susceptibility of graphite has been interpreted by applying the susceptibility formula for general bands of Lifschitz and Kosevich to the band model of Slonczewski. The majority electrons and holes are responsible for the two periods of oscillation of the susceptibility. The analysis yields information concerning the band structure: (1) the total band overlap is about 0.03 ev, (2) the energy difference between the two doubly degenerate bands at the corner of the Brillouin zone is about 0.025 ev, (3) ${\ensuremath{\gamma}}_{0}$ must be larger than about 1.2 ev, and (4) the relation ${\ensuremath{\gamma}}_{1}=0.04{{\ensuremath{\gamma}}_{0}}^{2}$ holes approximately (where both $\ensuremath{\gamma}'\mathrm{s}$ are in ev and correspond to Wallace's notation). Calculated carrier densities are 2.4\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}5}$ per atom for electrons and 1.8\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}5}$ per atom for holes, in rough agreement with estimates made from galvanomagnetic data. Rough agreement with electron specific-heat data is also obtained.
TL;DR: In this paper, the authors analyzed the absorption spectrum of Si, made with high resolution, near the main absorption edge, at various temperatures between 4.2 and 4.6°C and revealed fine structure in the absorption on the long-wavelength side of this edge.
Abstract: Measurements of the absorption spectrum of Si, made with high resolution, near the main absorption edge, at various temperatures between 4.2\ifmmode^\circ\else\textdegree\fi{}K and 415\ifmmode^\circ\else\textdegree\fi{}K, have revealed fine structure in the absorption on the long-wavelength side of this edge. This structure has been analyzed and can be interpreted in terms of indirect transitions involving, in general, phonons with energies corresponding to temperatures of 212\ifmmode^\circ\else\textdegree\fi{}K, 670\ifmmode^\circ\else\textdegree\fi{}K, 1050\ifmmode^\circ\else\textdegree\fi{}K, and 1420\ifmmode^\circ\else\textdegree\fi{}K. The form of the absorption associated with each type of phonon indicates that, as well as the formation of free electron-hole pairs taking place, excitons with a binding energy \ensuremath{\sim}0.01 ev are produced in the absorption process. The temperature dependence of the indirect energy band gap has been found and using this along with data on the intrinsic carrier density indicates an increase with temperature of the combined density-of-states effective mass of the electrons and holes. A smoothing out of the basic features of the curves is observed and shown to be consistent with relaxation broadening. A discussion of the significance of the energies of the phonons taking part in the indirect transitions to the lattice vibrational spectrum of Si is given.
TL;DR: In this article, a theory of electrical transport phenomena for a simple quantum-mechanical model was developed, which was based on an expansion in powers of the strength of the scattering mechanism.
Abstract: In a previous paper we have developed a theory of electrical transport phenomena for a simple quantum-mechanical model. That treatment was based on an expansion in powers of the strength of the scattering mechanism. In the present paper we consider the same model, but obtain the transport equation in powers of the density of scatterers without restricting ourselves to weak scattering potentials. The expansion involves scattering operators for single centers, pairs of centers, etc., in a manner in many ways analogous to the virial expansion of equilibrium properties. The lowest order terms yield the usual Boltzmann equation. The first correction, in density, to this equation is explicitly given. For the case of spherically symmetric scatterers the solutions of these equations are also obtained.
TL;DR: In this article, the Peierls-Yoccoz procedure is applied to calculate the effective mass parameter in cases where the forces acting in the system are invariant with respect to translation or rotation.
Abstract: For an $A$-particle system, a trial wave function is constructed of the form $\ensuremath{\Psi}({\mathrm{x}}_{1}, \ensuremath{\cdots}, {\mathrm{x}}_{A})=\ensuremath{\int}\ensuremath{\phi}({\mathrm{x}}_{1}, \ensuremath{\cdots}, {\mathrm{x}}_{A}; \ensuremath{\alpha})f(\ensuremath{\alpha})d\ensuremath{\alpha}.$ The preliminary nucleonic wave function, $\ensuremath{\phi}$, solves the problem in a "construction potential." This potential depends upon a "deformation parameter" or "generator coordinate," $\ensuremath{\alpha}$. The collective wave function, $f(\ensuremath{\alpha})$, or "generator function," is folded into $\ensuremath{\phi}$ to produce a system wave function that depends only upon the coordinates, ${\mathrm{x}}_{i}$, of the particles. In the integration, the deformation parameters dissolve away. They do not appear in the final state function; they only generate it. No collective coordinates ever come into use nor do such coordinates ever have to be defined. In typical cases when the generator function contains one or more nodes, it generates nodes in the system wave function $\ensuremath{\Psi}$ of the kind that describe collective kinetic energy. The energy of the system is extremized with respect to choice of the generator function, $f(\ensuremath{\alpha})$. No Hamiltonian ever appears except the $A$-particle Hamiltonian. All nucleons are treated on the same basis whether in or above closed shells. The appropriate variational calculation leads to an integral equation or "generator wave equation" for $f(\ensuremath{\alpha})$. This equation is solved in two limiting cases: the quadratic approximation, and the $\ensuremath{\delta}$-function approximation. An analysis is made of the Peierls-Yoccoz procedure to calculate the effectivemass parameter in cases where the forces acting in the system are invariant with respect to translation or rotation. There is no external machinery to drive the construction potential. The effective inertia constant does not appear likely to agree in general with that calculated for the essentially different problem of particles in such a machine-driven potential, though the latter value is presumably more nearly correct for physical applications. The trial wave function in the method of generator coordinates is designed for simplicity, not for precision. It is applied in the following paper to the dilatational and shape oscillations of ${\mathrm{O}}^{16}$.
TL;DR: In this paper, the authors defined the critical size for single-domain behavior, defined as the largest size at which magnetization reversal proceeds by rotation in unison, for the prolate ellipsoid and was found to be practically independent of magnetocrystalline anisotropy and elongation.
Abstract: The field at which the spins of a previously saturated ideal ferromagnetic particle cease to be aligned is defined as the nucleation field. This field is calculated, using calculus of variation, for an infinite cylinder and a sphere, assuming three mechanisms of magnetization reversal: spin rotation in unison, magnetization curling, and magnetization buckling. Theoretical treatment shows that, in fact, only curling and rotation in unison need be considered.The critical size for single-domain behavior, defined as the largest size at which magnetization reversal proceeds by rotation in unison, is calculated for the prolate ellipsoid and is found to be practically independent of magnetocrystalline anisotropy and elongation and approximately equal to $\frac{{A}^{\frac{1}{2}}}{{I}_{s}}$. Here $A$ is the exchange constant and ${I}_{s}$ is the saturation magnetization.For cylinders larger than the critical size, the coercive force, for a field applied in the direction of the long axis, is found to be equal to the nucleation field, when magnetocrystalline anisotropy is neglected. The coercive force thus calculated decreases with the radius of the cylinder, $R$, according to ${H}_{c}=\frac{6.78A}{{I}_{s}{R}^{2}}$.Available experimental data are discussed and are generally found to be in a better agreement with this than with previous theory.
TL;DR: In this paper, the authors examined the mode spectrum of spheroids for the case, which may often hold in practice, where exchange and electromagnetic propagation can be ignored simultaneously, where the spheroid was found to have longwavelength modes of oscillation of the ferromagnetic sample.
Abstract: It has been found recently that in ferromagnetic resonance experiments performed in inhomogeneous rf exciting fields at a fixed frequency, absorption of power takes place at a number of distinct magnetic fields. This is ascribed to the existence of long-wavelength modes of oscillation of the ferromagnetic sample. The mode spectrum of spheroids is examined for the case, which may often hold in practice, where exchange and electromagnetic propagation can be ignored simultaneously.
TL;DR: In this article, the authors analyzed the physical mechanism of secondary electron emission under the impact of high-speed heavy particles and showed that the yield is proportional to the rate of energy loss of the incident particles.
Abstract: The physical mechanism of secondary electron emission under the impact of high-speed heavy particles is analyzed. The treatment is based on the formation of secondaries according to the Bohr-Bethe theory of ionization, the diffusion of the slow secondaries to the surface, and their subsequent escape in the vacuum. The yield is found to be proportional to the rate of energy loss of the incident particles, and it is shown to be essentially the same for all metals, independent of their work function, conductivity, and other bulk properties. The observed energy distribution of the secondaries, the effect of adsorbed layers and the dependence of the yield on temperature, particle charge, and velocity are found to be explained in terms of this mechanism. The application to the general problem of the escape of electrons from metals and to the study of electron capture and loss by ions passing through solids is discussed.
TL;DR: In this paper, a photographic technique is used to measure velocities associated with the 24ST aluminum shock wave and with the shock wave in each specimen, which are transformed, using the conservation relations, to pressure-compression points.
Abstract: An explosive system is used to drive a strong shock wave into a plate of 24ST aluminum. This shock wave propagates through the 24ST aluminum into small test specimens which are in contact with the front surface of the plate. A photographic technique is used to measure velocities associated with the 24ST aluminum shock wave and with the shock wave in each specimen.The measured velocities are transformed, using the conservation relations, to pressure-compression points. Resulting pressure-compression curves are given for 27 metals. The range of data is different for each material but typically covers the pressure interval 150 to 400 kilobars; probable errors in reported experimental pressure-compression curves are 1 or 2% in compression for a given pressure.The experimental curves, which consist thermodynamically of a known $P$, $V$, $E$ locus for each material, are used to calculate a more complete high-pressure equation of state. This is done by means of a theoretical estimate of the volume variation of the Gr\"uneisen ratio $\ensuremath{\gamma}(V)=V{(\frac{\ensuremath{\partial}P}{\ensuremath{\partial}E})}_{V}$. Calculated $P$, $V$, $T$ states are listed for the various materials. For 24ST aluminum, quantities of application in shock-wave hydrodynamics are also tabulated.
TL;DR: In this article, the authors discuss several possible tests for the validity of the symmetry operation of allowed beta decay under time reversal, including the detection of terms which are not invariant under time reversals, and the determination of the ten complex coupling constants which now characterize beta decay.
Abstract: Noninvariance under space reflection and charge conjugation has now been established for beta decay processes. Invariance under time reversal remains an open question, however. We discuss here several possible tests for the validity of this symmetry operation. General expressions are given for the distribution function in three experimental situations, which have the possibility of detecting terms in allowed beta decay that are not invariant under time reversal: (a) experiments in which the nuclei are oriented and electron and neutrino momenta are measured; (b) experiments in which the nuclei are not oriented, but the recoil momentum and electron momentum and polarization are observed; (c) experiments in which the nuclei are oriented and the electron momentum and polarization are measured. The distribution functions obtained omit Coulomb distortion effects and relativistic corrections for the nucleons, but are othewise complete. Such experiments should permit, in addition to the detection of terms which are not invariant under time reversal, the beginnings of a determination of the ten complex coupling constants which now characterize beta decay. An additional, somewhat surprising, result is found. If the two-component neutrino theory of Lee and Yang is correct, and if certain perhaps reasonable assumptions concerning the relative magnitudes of the various coupling constants are valid, then the longitudinal polarization of electrons in allowed beta decay even from unoriented nuclei should be almost complete (specifically, equal to $\frac{v}{c}$).
TL;DR: In this article, the phase diagram in the region about the cleavage planes was clarified and the lattice conductivity was attributed to transport of energy by ambipolar diffusion of electrons and holes.
Abstract: Samples of both $n$-type and $p$-type ${\mathrm{Bi}}_{2}$${\mathrm{Te}}_{3}$ containing from 3\ifmmode\times\else\texttimes\fi{}${10}^{17}$ to 5\ifmmode\times\else\texttimes\fi{}${10}^{19}$ extrinsic carriers were prepared and the phase diagram in the region about ${\mathrm{Bi}}_{2}$${\mathrm{Te}}_{3}$ has been clarified. The Hall mobility parallel to the cleavage planes varies as ${T}^{\ensuremath{-}1.5}$ for holes and ${T}^{\ensuremath{-}2.7}$ for electrons. Room temperature values are ${\ensuremath{\mu}}_{p}=420$ ${\mathrm{cm}}^{2}$ ${\mathrm{v}}^{\ensuremath{-}1}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ and ${\ensuremath{\mu}}_{n}=270$ ${\mathrm{cm}}^{2}$ ${\mathrm{v}}^{\ensuremath{-}1}$ ${\mathrm{sec}}^{\ensuremath{-}1}$. The energy gap is ${E}_{g}=0.20$ electron volts. From thermal conductivity measurements over the temperature range from 77\ifmmode^\circ\else\textdegree\fi{}K to 380\ifmmode^\circ\else\textdegree\fi{}K the lattice conductivity was found to be ${\ensuremath{\kappa}}_{L}=5.10\ifmmode\times\else\texttimes\fi{}\frac{{10}^{\ensuremath{-}2}}{T}$ watt-${\mathrm{deg}}^{\ensuremath{-}1}$ ${\mathrm{cm}}^{\ensuremath{-}1}$. The sharp rise in the thermal conductivity in the vicinity of room temperature was attributed to transport of energy by ambipolar diffusion of electrons and holes.