Showing papers in "Journal of Physics A: General Physics in 1969"
TL;DR: In this paper, the analogue of Van Vleck's theorem on the spectrum of clipped noise was formulated for use in optical spectroscopy, and the analogue was used for optical spectrograms.
Abstract: The analogue of a theorem of Van Vleck on the spectrum of clipped noise is formulated for use in optical spectroscopy.
97 citations
TL;DR: In this article, the entropy of a random-flight polymer confined in a box of volume V is studied and it is shown that when the natural radius of the polymer approaches the linear size of the box, the entropy ceases to have the normal form of a thermodynamic function and the pressure is not a function of the density but takes the form PV= pi 2/3(Ll/R2) kappa T where L is the polymer length, l the step length and R equals V, and the density of the system even though strictly in equilibrium is not uniform.
Abstract: A study is made of the entropy of a random-flight polymer confined in a box of volume V. When the natural radius of the polymer approaches the linear size of the box, the entropy ceases to have the normal form of a thermodynamic function and the pressure is not a function of the density but takes the form PV= pi 2/3(Ll/R2) kappa T where L is the polymer length, l the step length and R equals V, and the density of the system even though strictly in equilibrium is not uniform. The introduction of constraints due to forces, cross linkages and very long-lived quasi-invariants restores the equation of state to a thermodynamic form P=P( rho ) where rho =L/Vl.
91 citations
TL;DR: In this article, the case of randomly excited fluid turbulence is studied and it is argued that there is a strong mathematical analogy between the classical (turbulent) cascade of energy and the quantum field or many-body problem.
Abstract: The statistical mechanics of systems in which the dominant process is a flow of energy through the modes of the system is studied. The case of randomly excited fluid turbulence is studied and it is argued that there is a strong mathematical analogy between the classical (turbulent) cascade of energy and the quantum field or many-body problem. The energy has an analogue in the one-particle Green function, and entropy can be defined, the latter being the information content in the case of the probability distribution function for the turbulence. General operations in Hilbert space can be carried out with at most two functions, and the energy equation and the maximization of the entropy give two equations which determine the two chosen unknown functions. The case of a random long-wave input of energy is studied and shown to lead to the Kolmogoroff spectrum, and the Kolmogoroff constant is evaluated for the approximation system used.
63 citations
TL;DR: In this paper, an analysis of the single-scattering profile S1(x, y, z,...) from the observed spectrum I(x.y, y.z, z....) when the spectrum contains contributions from plural scattering events is given.
Abstract: An analysis is given for the calculation of the single-scattering profile S1(x, y, z, ...) from the observed spectrum I(x, y, z, ...), when I(x, y, z, ...) contains contributions from plural- scattering events. No assumptions are made concerning the line shape for S1(x, y, z, ...), but a value for the unscattered intensity is required. Further, the analysis given requires that all the scattered intensity is collected, so that Poisson statistics are applicable to the scattering processes occurring in the specimen. The solution for S1(x, y, z ...) is then given as a series in I(x, y, z, ...), with appropriate weighting coefficients. The spectrum I(x, y, z, ...) must be corrected for the finite resolution of the spectrometer, before a solution can be obtained for S1(x, y, z, ...). Computational tests and the limitations of the present analysis are given.
49 citations
TL;DR: In this article, a non-trivial approximation procedure was developed for an incompressible fluid, which differs from the theories of Herring and Edwards in that the direct-interaction approximation is obtained in the first non-Trivial approximation.
Abstract: The procedure is developed for an incompressible fluid. It differs from the theories of Herring and Edwards in that the direct-interaction approximation is obtained in the first non-trivial approximation. It provides a simple means of obtaining equations relating the two-velocity correlation function and response function without necessitating the analysis of diagrams, representing terms of a perturbation series, of large order as required in the formalism of Wyld and Lee. The relation to the work of the authors mentioned is briefly discussed.
28 citations
TL;DR: In this article, the generating function, the corresponding integrated intensity distribution, and the photon-counting distribution and its fractional moments are derived for the superposition of coherent and chaotic M-mode fields on the basis of a formalism of arbitrary ordering of field operators.
Abstract: The generating function, the corresponding integrated intensity distribution, and the photon-counting distribution and its fractional moments are derived for the superposition of coherent and chaotic M-mode fields on the basis of a formalism of arbitrary ordering of field operators in quantum optics An alternative description is also given based on a recent analysis of the superposition of coherent and chaotic fields in terms of the correlation functions which makes it possible to derive a number of results valid for arbitrary mean occupation numbers per mode from which the model considered follows as a special case Many earlier results obtained for coherent and chaotic fields and their superposition are included as special cases The present results generally describe a superposition experiment for an N-mode coherent field (eg generated by an N-mode laser operating far above threshold) and an M-mode chaotic field (M>or=N) as well as a field generated by an M-mode laser operating above threshold
26 citations
TL;DR: The angular distribution and vertical intensity of cosmic-ray muons have been measured at depths of 71.6, 734, 1068 and 2235 hg cm-2 of standard rock as discussed by the authors.
Abstract: The angular distribution and vertical intensity of cosmic-ray muons have been measured at depths of 71.6, 734, 1068 and 2235 hg cm-2 of standard rock. The angular distribution was fitted by a law of the form Itheta =Iv cosn theta and values of the exponent n were found to be 1.8+or-0.1, 2.1+or-0.1. 2.3+or-0.1 and 3.6+or-0.2 respectively. The corresponding vertical intensities were found to be (5.00+or-0.17)*10-4, (3.12+or-0.15)*10-6, (1.03+or-0.04)*10-6 and (9.7+or-0.5)*10-8 cm-2 s-1 sr-1 respectively. From a survey of all previous measurements best estimates of the n-depth and intensity-depth curves are derived. The results are explicable entirely in terms of pion and kaon decay for the origin of the muons and do not agree with the direct muon production hypothesis advanced by Bergeson et al. (abstr. A15886 of 1968).
20 citations
TL;DR: In this article, the authors calculated the pressure exerted by an idealized "random-flight" polymer on the walls of a container for the complete range of polymer lengths using a numerical approach based on the method initiated by Edwards and Freed.
Abstract: For Pt. I see preceding abstract. The pressure exerted by an idealized 'random-flight' polymer on the walls of a container is calculated for the complete range of polymer lengths. The calculation uses a numerical approach based on the method initiated by Edwards and Freed.
18 citations
TL;DR: In this paper, it was shown that the binding energy of a molecular fluid is determined by the frequency spectrum of the transverse complex refractive index, and the importance of strictly transverse contributions to binding energy in this approximation was discussed.
Abstract: For Pt I see abstr. 37680 of a1968. Indicates how the microscopic optical scattering theory already reported elsewhere can be developed into a theory of the binding energy of a molecular fluid. The author first reports (k, omega ) dependent dielectric constants for the molecular fluid: these determine the linear response in all processes which depend on virtual optical processes alone. He then briefly describes bulk contributions to the stopping power, to the emission of Cerenkov radiation and to the collective molecular binding in terms of these dielectric constants. Full account is taken of the radiation field at every order in the ensemble averaged polarization diagram approximation and we extend the theory of the non-relativistic Lamb shift. It is shown that, in the continuum approximation which neglects thermal fluctuations, the molecular binding energy is completely determined by the frequency spectrum of the transverse complex refractive index. A numerical estimate is made of the importance of strictly transverse contributions to the binding energy in this approximation.
18 citations
TL;DR: In this paper, complementary variational principles are developed for ground-state wave function corrections which are induced by frequency-dependent perturbations, leading to upper and lower bounds for dynamic polarizabilities which are either measured at real frequencies less in magnitude than the first excitation energy or measured at any imaginary frequencies.
Abstract: Complementary variational principles are developed for ground-state wave function corrections which are induced by frequency-dependent perturbations. These principles lead to upper and lower bounds for dynamic polarizabilities which are either measured at real frequencies less in magnitude than the first excitation energy, or measured at any imaginary frequencies. In the latter case there is a choice of upper bounds, different forms being suited to small and large frequencies. Illustrative results are presented for the hydrogen atom, and reasonable accuracy is obtained with simple one-parameter trial functions.
16 citations
TL;DR: In this paper, complementary variational principles are developed for approximate solutions of the first-order Rayleigh Schrodinger perturbation correction to the wave equation, yielding upper and lower bounds for the second-order energy correction.
Abstract: Complementary variational principles are developed for approximate solutions of the first-order Rayleigh- Schrodinger perturbation correction to the wave equation, yielding upper and lower bounds for the second-order energy correction. The upper bound is the same as Hylleraas's; the complementary lower bound is related to Temple's result for eigenvalues, and (unlike previous lower bounds) is shown to be unconditional. The analysis extends to cover the first-order Brillouin-Wigner correction. As a by-product of the theory it is shown how the Rayleigh-Ritz upper bound and the Temple lower bound for eigenvalues arise in a complementary manner.
TL;DR: In this paper, it was shown that if the geodesic ray congruence associated with an empty space-time of type N is not hypersurface orthogonal (that is, the Geodesic rays are twisting) then the space time has at most one symmetry.
Abstract: It is shown that if the geodesic ray congruence associated with an empty space-time of type N is not hypersurface orthogonal (that is the geodesic rays are twisting) then the space-time has at most one symmetry.
TL;DR: Canonical formalism, including Hamilton's equations, transformation theory and Poisson brackets for classical field theory with higher time and/or spatial derivatives, is established in this article, including transformation theory.
Abstract: Canonical formalism, including Hamilton's equations, transformation theory and Poisson brackets for classical field theory with higher time and/or spatial derivatives, is established.
TL;DR: The absorption and refractive index increments due to continuous distributions of resonances have been calculated for both Debye-type distributions and for distributions Gaussian in logarithmic frequency.
Abstract: The absorption and refractive index increments due to continuous distributions of resonances have been calculated for both Debye-type distributions and for distributions Gaussian in logarithmic frequency. Comparison of the results with the available experimental data shows that it is not possible to discriminate between the two types of distribution, but suggests that the damping constant of the individual resonances must be of the order of unity.
TL;DR: In this article, it is shown that the rotation operator applied to a wave function can be equivalent to solving Schrodinger's equation if gravitational fields are present, and the specific example of quantum mechanics on a cone is considered in detail.
Abstract: Hegerfeldt and Kraus's criticisms (see abstr. A42300 of 1968) of Aharonov and Susskind's discussion (see abstr. A27919 of 1967) of the above question are investigated. It is shown that the rotation operator applied to a wave function can be equivalent to solving Schrodinger's equation if gravitational fields are present. The specific example of quantum mechanics on a cone is considered in detail.
TL;DR: In this article, it was shown that, to order alpha 2, S-2= Sigma j mod (o mod z mod j) mod 2/Ej-Eo=4.499752 for the dipole sum over Dirac states of the hydrogen atom.
Abstract: It is shown that, to order alpha 2, S-2= Sigma j mod (o mod z mod j) mod 2/Ej- Eo=4.499752 for the dipole sum over Dirac states of the hydrogen atom. This compares with the value 9/2 for the sum over Schrodinger states.
TL;DR: In this paper, the authors derived the N-fold joint photocount distribution of a Gaussian (thermal) radiation field of arbitrary spectral profile, when the counting-time intervals are short compared with the coherence time of the light.
Abstract: Results have been presented by Bedard (see abstr. A33736 of 1967) on the derivation of the N-fold joint photocount distribution of a Gaussian (thermal) radiation field of arbitrary spectral profile, when the counting-time intervals are short compared with the coherence time of the light. In this paper these results are extended for arbitrary counting-time intervals. The authors assume that the fluctuating radiation field has a fixed direction of propagation and that all the photodetector surfaces lie within one coherence area on a plane normal to this direction of propagation. The evaluation of the -fold joint photocount distribution and the photocount moments can be reduced to the solution of either a homogeneous or an inhomogeneous (Fredholm) integral equation of the second kind.
TL;DR: In this article, the effect of varying some of the more important parameters of the high-energy nucleon-air-nucleus collision has been examined, and it is concluded that a multiplicity law of the form Ep1/4 is preferred to an Ep 1/2 law and that there is no evidence for a significantly greater mean transverse momentum than the value of 0.4 Gev/c, which relates to the parents of muons of lower energy.
Abstract: For Pt. III see ibid vol.2, No.3, (1969) 354-64. Studies of muon showers deep underground by the Utah group have stimulated an extension of the previous calculations of the present authors into the region covered by the underground experiment: viz. muon threshold energies of the order of 1000 gev and zenith angles in the region of 60 degrees . The effect of varying some of the more important parameters of the high- energy nucleon-air-nucleus collision has been examined, and it is concluded that a multiplicity law of the form Ep1/4 is preferred to an Ep1/2 law and that there is no evidence for a significantly greater mean transverse momentum than the value of 0.4 Gev/c, which relates to the parents of muons of lower energy. An increase in the fraction of kaons generated with increasing nucleon energy is not favoured. Concerning the mass spectrum of the primary particles, there is some support for the contention that the primaries above 1015 ev are largely protons, but none for the conclusion of Grigorov et al. in 1967 that the proportion of heavy nuclei commences to increase at 1012 ev. However, a problem that affects all the conclusions is that significantly fewer multiple events are observed than expected.
TL;DR: In this article, a generalized Prufer transformation is used to derive comparison and oscillation theorems for the matrix Sturm-Liouville eigenvalue problem, and it is shown in particular that if the eigenvectors are required to vanish at one (at least) of the end points, then the Eigenvalues are uniquely characterized by the number of points (termed focal points) at which a certain determinant (of linearly independent solutions each satisfying the other boundary condition) vanishes.
Abstract: A generalized Prufer transformation is used to derive comparison and oscillation theorems for the matrix Sturm-Liouville eigenvalue problem. It is shown in particular that if the eigenvectors are required to vanish at one (at least) of the end points, then the eigenvalues are uniquely characterized by the number of points (termed focal points) at which a certain determinant (of linearly independent solutions each satisfying the other boundary condition) vanishes. Simple but effective computational procedures based on this analysis are suggested, and their use is illustrated by a single-centre calculation on the 3s sigma state of the hydrogen molecular ion.
TL;DR: In this article, the authors used the data gathered with the University of Utah neutrino detector during late spring and summer of 1967 to study penetrating muon showers, which contained two or more nearly parallel muons incident in a range of zenith angles between 30 degrees and 75 having penetrated from 1500 to 6000 hg cm-2 of rock overburden.
Abstract: Data gathered with the University of Utah neutrino detector during late spring and summer of 1967 were used to study penetrating muon showers. These downward-going events contained two or more nearly parallel muons incident in a range of zenith angles between 30 degrees and 75 having penetrated from 1500 to 6000 hg cm-2 of rock overburden. Studies were made to determine the radial extent of the showers, the frequency of occurrences of showers of each multiplicity, and the degree of isotropy of the arrival directions of shower events was plotted in celestial coordinates, with the result that these shower events could be characterized by a radius of 6 to 10 m, a multiplicity spectrum which is a power law in multiplicity having an exponent between -3.4 and -4.0 and no observable anisotropy. These shower data, together with measurements of events containing a single penetrating muon, were used to derive an empirical shower density function that accounts for the energy and angular dependence of the events of multiplicity 1, 2 and 3, as well as the absolute numbers of these events observed.
TL;DR: In this article, a theoretical analysis has been made of the muon component of extensive air showers incident at large angles to the vertical, using the model described previously, and the expected numbers of muons reaching ground level as a function of threshold energy and zenith angle for primary particles of various energies.
Abstract: For Pt. II see abstr. A15896 of 1968. A theoretical analysis has been made of the muon component of extensive air showers incident at large angles to the vertical. Using the model described previously, calculations have been made of the expected numbers of muons reaching ground level as a function of threshold energy and zenith angle for primary particles of various energies. The data have been combined with alternative primary spectra of cosmic rays, with and without an enhanced contribution from heavy nuclei, to give the expected muon density spectra. It is found that the density spectrum is sensitive to the distribution of transverse momentum among the parents of the muons and to a lesser extent to the mass composition of the primaries. There is thus the possibility of deriving information about the mean transverse momentum, and perhaps setting limits on the mass composition, from a comparison with experiment.
TL;DR: By using atomic beam magnetic resonance techniques, it has been shown that the nuclear spin of 206Tl (half-life 4.2 min) is either zero, or the nuclear magnetic moment mu I <10-5 nuclear magnetons as mentioned in this paper.
Abstract: By using atomic beam magnetic resonance techniques it has been shown that the nuclear spin of 206Tl (half-life 4.2 min) is either zero, or else the nuclear magnetic moment mu I<10-5 nuclear magnetons. Measurements on isotopes of copper and silver have yielded the values for their nuclear spins I and hyperfine interaction constants A, from which their nuclear magnetic moments have been deduced using the Fermi-Segre relation. No diamagnetic correction has been applied.
TL;DR: In this paper, the exact static exterior and interior solution of Einstein's equations for a plane-thick disk is obtained, and it has been shown that the corresponding energy-momentum tensor fulfils the generalized O'Brien-Synge junction conditions.
Abstract: The exact static exterior and interior solution of Einstein's equations for a plane thick disk is obtained. It has been shown that the corresponding energy-momentum tensor fulfils the generalized O'Brien-Synge junction conditions. The correspondence of this tensor to the surface energy-momentum tensor of a thin plane plate is demonstrated. The disk being neither very thick nor very dense, a connection with the Newtonian theory has been obtained.
TL;DR: In this paper, a large array of muon detectors has been used to measure the frequency of multiple muons from extensive air showers as a function of zenith angle over the range 30 degrees -85 degrees.
Abstract: A large vertical array of muon detectors has been used to measure the frequency of multiple muons from extensive air showers as a function of zenith angle over the range 30 degrees -85 degrees . The experimental data have been compared with the predictions of the theory developed by de Beer et al. (see preceding abstract); accepting the values of the parameters used in this theory it is concluded that there is no evidence for a large increase in the relative flux of heavy nuclei in the energy range 1015l1017 eV. If all the other parameters but the mean transverse momentum (pT) are assumed to be known, the data suggest a mean value of (pT) increasing from 0.37 GeV/c to 0.44 GeV/c as the interaction energy increases from 200 to 3000 GeV.
TL;DR: In this paper, the zero-frequency component of the correlation function J(0), its calculation from thermal Green functions and its physical interpretation are studied, which is not directly obtainable from the Green function, and a new method proposed.
Abstract: Some problems associated with the zero-frequency component of the correlation function J(0), its calculation from thermal Green functions and its physical interpretation are studied. Various proposals for determining J(0), which are not directly obtainable from the Green function, are examined and a new method proposed. The related question of the zero-frequency limit of J( omega ) is also considered.
TL;DR: In this article, three-dimensional Monte Carlo calculations have been performed on the development of the hadronic component of extensive air showers using a semi-empirical model of high-energy nuclear interactions.
Abstract: Three-dimensional Monte Carlo calculations have been performed on the development of the hadronic component of extensive air showers using a semi-empirical model of high-energy nuclear interactions. Results include integral energy spectra and lateral distribution of nuclear active particles as well as total hadronic energy flux. The probability of multi-core showers is discussed. The contribution of pionization tends to mask the dependence of this probability on primary atomic number. Fluctuations of total and central hadronic energy flux are investigated. Maps of hadronic energy flux in the core region of individual showers are presented.
TL;DR: In this article, the rate of energy loss is deduced from the observed mean pulse height of a scintillation counter operated underground, which requires a knowledge of the intensity depth curve but not of the muon momentum spectrum.
Abstract: The usual method of determining the rate of energy loss of muons by comparison of the sea-level spectrum with the intensity underground is shown to be inadequate to determine the energy-dependent term because of the impression of the spectrograph results. An alternative method has now been developed in which the rate of energy loss is deduced from the observed mean pulse height of a scintillation counter operated underground. This method requires a knowledge of the intensity depth curve but not of the muon momentum spectrum. The various corrections necessary to apply the method to the results of the Tilmanstone Colliery experiment, described in the preceding paper are considered and shown to be small. The energy loss by direct pair production is found to be 1.05+or-0.20 times the value predicted by Kobayakawa (abstr. A19217 of 1967).
TL;DR: In this paper, the magnetic moments of the lowest rotational states of even-even nuclei and the probabilities of magnetic dipole transitions between these states are calculated on the basis of the model suggested by Krutov in 1968.
Abstract: See also preceding abstract. The magnetic moments of the lowest rotational states of even-even nuclei and the probabilities of magnetic dipole transitions between these states are calculated on the basis of the model suggested by Krutov in 1968 the non-axiality of the nuclear equilibrium shape and the difference between the mass and charge distributions being taken into account. The results of calculations are compared with the available experimental results, the agreement being reasonably satisfactory.
TL;DR: In this article, the intensity and degree of coherence in a field due to a slit illuminated by a line source were studied and the propagation of the mutual coherence of a polychromatic light beam was used to obtain the intensity.
Abstract: The intensity and degree of coherence in a field due to a slit illuminated by a line source are studied. The propagation of the mutual coherence of a polychromatic light beam is used to obtain the intensity and the degree of coherence due to the slit at points distant from those at the slit. The variations of the intensity and of the degree of coherence with different variables are studied.
TL;DR: In this article, the flow rates of hydrogen, helium, air, carbon dioxide and water vapour between two parallel optically flat glass surfaces have been measured and the distance between the two surfaces was of the order of 10 mu m and the flow experiments were carried out with pressures in front of and behind the channels of 10 torr and 0.1 torr respectively.
Abstract: The flow rates of hydrogen, helium, air, carbon dioxide and water vapour between two parallel optically flat glass surfaces have been measured. The distance between the two surfaces was of the order of 10 mu m and the flow experiments were carried out with pressures in front of and behind the channels of the order of 10 torr and 0.1 torr respectively. A flow equation is presented which describes the flow of the gases and the vapour through the channels.