Gauge theoretical realization of the superweak model of CP violation

It is pointed out that the presence in a gauge theory of vector bosons or left-over Higgs bosons with a weak interaction strength of the order of10^?11G_E and which have CPviolating couplings to the strangeness-changing neutral current, will lead to the superweak model of CP violation. An example of such a theory, based on the gauge group SU (2) ?U(1), is given.     

Relationships in infrared intensity theories,in particular the Mayants-Averbukh theory

A brief survey is given of the Mayants-Averbukh infrared intensity theory in relation to the more well-known but equivalent polar tensor theory. In addition, the appearances of the symmetry invariant parameter matrices D_n⁰ of the Mayants-Averbukh theory were derived and tabulated for various symmetries about the midpoint of bond n. The use of these matrices and a single bond coordinate system will offer a convenient alternative to the Mayants-Averbukh treatment of a central, symmetric bond. The rotational mode equations of the Mayants-Averbukh and polar tensor theories have been investigated to elucidate the constrainsts which they impose on infrared intensity theories based on the bond dipole moment model and the atomic point charge model. It was found that the valence-optical theory is in full conformity with the rotational modes only if all electrooptical parameters $\text{?μ}{}_{\mathrm{n}}\text{?γ}{}_{\mathrm{i}}$ are neglected, where γ_i is the ith internal angular coordinate. The constraints imposed on the equilibrium charge-charge flux theory correspond to neglect of all charge flux parameters. The generalized valence-optical theory was found to be incompatible with the rotational mode equations of the Mayants-Averbukh theory. However, its basic dipole moment equation was found useful for suggesting a unique interpretation of a set of d parameters (elements of D_n⁰) in terms of bond dipole moment components.     

Dynamical study of triplet-triplet energy transfer in rigid solution

Triplet-triplet (T-T) energy transfer from acetophenone to naphthalene-d₈ has been studied in EPA rigid-glass solution at 77 K by masuring the decay of donor phosphorescence and the rise of acceptor T-T absorption over a wide range of time. The results were analyzed in terms of the theory proposed by Inokuti and Hirayama on the basis of a point molecular model. Two parameters, R_O and γ, were determined which are involved in their expression for the rate constant of T-T energy transfer, i.e. n(R) = (1/τ_D) exp[γ(1?R/R_O)], where R and τ_D denote the donor-acceptor distance and the lifetime of donor triplet in the absence of acceptor, respectively. It was found that, in contrast to the Inokuti-Hirayama theory in which γ is assumed to have a constant value, γ increases significantly as the time (t) after flash excitation of the donor becomes smaller: γ ≈ 25 for t/τ_D=10^-2?1, ≈ 35 for t/τ_D = 10^-3? 10^-2, and ≈ 45 for t/τ_D = 10^-4?10^-3. This finding suggests that the true rate constant increases with decreasing R value to a greater extent than the n(R) employed by Inokuti and Hirayama.     

EHD-photoluminescence kinetics in doped Ge

Measurements of the LA-phonon assisted line kinetics of the EHD photoluminescence in As- and Sb-doped germanium with impurity concentrations n_D = 10¹⁵ ? 10¹⁷ cm^?3 are presented. These kinetics are found to be strongly dependent on the excitation level at 4.2 K. From the experimental results and a simplified kinetic equation the EHD “diffusion length” in Ge:As sample with n_D = 2 × 10¹⁶ cm^?3 is estimated to be L_D ? 0.34 mm which is consistent with previous results.     

Spin relaxation of conduction electrons in highly-doped n-type germanium at low temperature

We present a theory of the spin relaxation time of the conduction electrons in highly-doped n-type germanium at liquid helium temperature. The theory is compared with some of our measurements and the experimental data available in the literature on As-doped germanium. The observed linewidth at T = 10 K is accounted for in the whole metallic concentration range (N_D > 3 × 10¹⁷cm^?3).In the lower concentration range (3 × 10¹⁷ < N_D < 10¹⁸cm^?3), the relevant mechanism is the random jumping of the g factor upon intervalley scattering. The agreement with experiment is good without any adjustable parameter.In the higher concentration range (N_D > 10¹⁸cm^?3), the dominant process for the linewidth is the spin-flip scattering by ionized donors (Elliott process); the usual theory is shown to be insufficient and the greater effectiveness of scattering by the localized part of the donor potentials is pointed out. The calculated linewidth is related to the intervalley scattering time T_iv. The agreement with experiment is good and predictions are given for the linewidth in the case of other shallow donors in the same concentration range.     

Fluorescence resolue dans le temps des niveax de singulet et d du zinc

The time resolved spectroscopy technique is applied to investigate the (4s, nd) ¹D₂ series of Zn I using a selective stepwise excitation via the resonant 4¹P₁ state. Radiative lifetimes of n¹S₀ (n = 6?8) and n¹D₂ (n = 4,5) levels are measured. Upper limits for transition probabilities 4¹P₁?n¹S₀ (n = 9?12) and 4¹P₁?n¹ (n = 6?10 ) are obtained. Strong configuration interaction effects are observed in the ¹D₂ series and compared with those in Mg I and Cd I.     

On Weinberg's model of CP violation in gauge theories

The consequences of the Weinberg model of CP violation in gauge theories (ref. [1]) are discussed in detail. It is shown (using the valence quark hypothesis) that the contribution of the induced superweak interaction to the experimentally measured quantities η+? and η₀₀ are ≈m_K²/m_π² times larger than that of the direct milliweak decay K₂⁰→2π. The correction to the relation |η+?|/|η₀₀|=1 is also calculated in the model. We estimate the neutron dipole moment $\text{(D}{}_{\mathrm{<mtext>n</mtext>}}\text{??2.8·10}{}^{\mathrm{?25}}\text{e.cm.}\text{)}$ and note that the dipole moments of particles with strange quark constituents should be about three orders of magnitude larger $\text{(}\text{e.g.}\text{D}{}_{\mathrm{\Lambda }}\text{??1.15·10}{}^{\mathrm{?22}}\text{e·}\text{cm}$. The CP violating vertex d?s + gluon is also discussed.All physical quantities appear to depend crucially on the values of quark masses, so that CP violating effects in the models of the type considered may elucidate the nature of quark masses. We argue that the bare (or “mechanical”) values should be used in the calculations and this leads to a considerable difference in the estimates of various effects as compared to those of ref. [1].     

Superstring theory

Dual string theories, initially developed as phenomenological models of hadrons, now appear more promising as candidates for a unified theory of fundamental interactions. Type I superstring theory (SST I), is a ten-dimensional theory of interacting open and closed strings, with one supersymmetry, that is free from ghosts and tachyons. It requires that an SO(n) or Sp(2n) gauge group be used. A light-cone-gauge string action with space-time supersymmetry automatically incorporates the superstring restrictions and leads to the discovery of type II superstring theory (SST II). SST II is an interacting theory of closed strings only, with two D = 10 supersymmetries, that is also free from ghosts and tachyons. By taking six of the spatial dimensions to form a compact space, it becomes possible to reconcile the models with our four-dimensional perception of spacetime and to define low-energy limits in which SST I reduces to N = 4, D = 4 super Yang-Mills theory and SST II reduces to N = 8, D = 4 supergravity theory. The superstring theories can be described by a light-cone-gauge action principle based on fields that are functionals of string coordinates. With this formalism any physical quantity should be calculable. There is some evidence that, unlike any conventional field theory, the superstring theories provide perturbatively renormalizable (SST I) or finite (SST II) unifications of gravity with other interactions.     

Multiplicity distributions in e+e− annihilations at petra energies

Measurements of the charged multiplicities for hadron production in e⁺e^? annihilation in the center of mass energy range 9–32 GeV have been made. The average charged multiplicity has an energy dependence much stronger than ln s and similar to that reported for pp collisions. Quantitative differences are observed in the magnitude of both the average multiplicity 〈n_ch〉 and the dispersion D_ch for e⁺e^? and pp interactions at the same center of mass energy. 〈n_ch〉 and the ratio 〈n_ch/D_ch in e⁺e^? annihilations are significantly larger than in pp collisions and are found to be in overall agreement with QCD predictions. KNO scaling is seen to be satisfied.     

Helium emission spectra—II. Pressures to 0.91 torr

Electron impact excitation is employed to study the pressure variation of the steady state luminescence from 27 levels of helium. Apparent cross sections are determined for these levels over the pressure range 0.025–0.91 torr, a much broader pressure range for observing collisional excitation transfer processes than has been previously investigated. Model calculations are carried out in which the data is fit to a set of coupled steady state equations. Primary and secondary electron excitation, radiative transfer, and bimolecular and termolecular collisional processes are accounted for in the analysis. We find that n¹P→n¹D collisional excitation transfer is much more important as a populating mechanism for n¹D levels than has been previously believed. The cross section for 4¹P→4¹D collisional transfer is estimated to be (1.3±0.3)×10^?14 cm². A termolecular process, believed to involve formation of He₂⁺, becomes an important loss mechanism for the 3¹P and 4¹P levels at pressures above 0.5 torr. Rate constants for this process are estimated to be (6.6±1.0)×10^?27 cm⁶/sec and (1.9±0.4)×10^?26 cm⁶/sec for 3¹P and 4¹P, respectively. The magnitude of the 3³D and 4³D apparent cross sections require a large 4³F population, a result which leads us to conclude that the 4F level is singlet-triplet mixed. There is evidence that collision induced transitions between all sublevels do not occur with equal probability. The most internally consistent results are arrived at by assuming ΔJ=0 to be a favored collisional transfer process.     

Relationships in Raman intensity theories,in particular the Mayants-Averbukh theory

Brief surveys are given of the Mayants-Averbukh Raman intensity theory, and of the polar tensor Raman intensity theory recently presented by Bogaard and Haines. It was found that these intensity theories in essence are equivalent. In addition, the appearances of the symmetry invariant parameter matrices F_n⁰ of the Mayants-Averbukh theory were derived and tabulated for various symmetries of bond n. These matrices, and a single bond coordinate system, can be used as a convenient alternative to the Mayants-Averbukh treatment of bonds which have some kind of symmetry with respect to the midpoint of the bond. A modification of the Mayants-Averbukh treatment is also suggested. The rotational mode equations of the Mayants-Averbukh theory have been investigated to elecudate the constraints which they impose on Raman intensity theories based on the bond polarizability model. It was found that the valenceoptical theory is in conformity with the rotational modes only if all electrooptical parameters $\text{?α}{}_{\mathrm{ii}}{}^{\mathrm{(n)}}\text{?γ}{}_{\mathrm{p}}$ are neglected, where α_ii⁽ⁿ⁾ (i = 1, 2, 3) are the diagonal components of the polarizability α⁽ⁿ⁾ of bond n, and γ_p is the pth internal angular coordinate. Furthermore, the valence-optical theory was found to be strictly applicable only for cylindrical bond symmetry, C_mv (m ≥ 4). A generalized valence-optical Raman intensity theory, allowing also for non-zero off-diagonal components α_ij⁽ⁿ⁾, was found to be incompatible with the rotational mode equations of the Mayants-Averbukh theory. However, its basic polarizability equation was useful for suggesting a unique interpretation of a set of f parameters (elements of F_n⁰) in terms of components of the anisotropic part of a symmetric bond polarizability.     

The relationship between chemical and tracer diffusion coefficients of aliovalent ions in an ionic lattice

The theoretical model developed by Lidiard was extended to describe the relationship between the chemical and tracer diffusion coefficients of aliovalent ions in an ionic lattice.It is shown that the relationship between the chemical diffusion coefficient, D, and the tracer diffusion coefficient, D¹, is D = 2D¹ if the migration of dimers is the principal mechanism of transport and for the migration of trimers D = 3D¹ if the concentration of impurity ion is relatively small. These relationships are valid regardless of the charge of the aliovalent or lattice ions.The chemical diffusion coefficients of Cr³⁺ in Cr-doped MgO were determined for three different temperatures, 1656, 1717 and 1768K, and for the concentration region 2.5×10^?2?2.8×10^?1 mole% Cr₂O₃. Using previously determined values for the tracer diffusion coefficient of ⁵¹Cr in Cr-doped MgO it was found that for the temperature and concentration region investigated D = (2.00±0.17)D¹ which indicates that diffusion proceeds primarily by the migration of dimers.     

Superconductivity in thin tin films: Fluctuation effects

The excess electrical conductivity in thin tin films due to thermodynamic fluctuations above T_c has been measured as a function of temperature and sheet resistance R_ns of films which varied from 0.2 Ω/? to 120 Ω/?. Results have been compared with the Aslamazov-Larkin, Maki-Thompson and Patton theories. It is found that among three the Maki-Thompson theory gives a better fit to experimental data. The pair breaking parameter a fitting parameter in the M-T theory, is found to behave linearly with R_ns of films and is given by ? ? 9x10^?3 + 1.02x10^?2R_ns for R_ns ≤ 12 Ω/?.     

Approximation of the electron excitation cross sections for triplet states excited from the 23 S 1 metastable state in helium

The method of approximated four-parameter representation of the electron-impact cross sections for a helium atom excited from the 2³ S ₁ metastable state into higher triplet states is applied and discussed. The approximation consists in interpolation over the whole set of the cross section values for each helium atomic level measured in our experiments and reported by other researchers. The approximation parameters and the cross sections calculated using these parameters for the maxima of the corresponding excitation functions are presented for 19 triplet levels of the S, P, and D HeI series with n=2–10. The interpolated values are compared to the theoretical cross sections. The serial regularities were investigated for the S, P, and D levels studied and a decrease in the cross sections for excitation from the given metastable state within each series, described by the approximate law Q=Cn ^?5, was revealed. Validity of the similarity relationship and the Bethe approximation for cross sections in the 2³ S?n ³ P series was verified. It is shown that the cross sections for a triplet level excitation from the 2³ S ₁ metastable state exceed the corresponding values for excitation from the ground state of helium by a factor of approximately 10³ for n=2 and 3 and 10 2 for the higher levels. It is concluded that the proposed method of representation of the cross sections for the electron-impact excitation of triplet levels from the metastable state increases accuracy and more importantly, reliability of the final results.     

Attainable superheat of ethane-methane solutions

Methods of measuring lifetime and continuous pressure decrease were used to study kinetics of spontaneous boiling-up of superheated ethane-methane solutions. The attainable superheats of solutions at two pressure values (1.0 and 1.6 MPa) and two concentrations of methane (2.1 and 6.0 mole %) were determined experimentally in the range of nucleation rate J = 1·10⁴–3·10⁸ s^?1m^?3. At temperatures 266.5, 270.0, and 273.15 K, the attainable stretching of the studied solutions was measured. The experimental results were compared with the theory of homogeneous nucleation. At nucleation rates J ≥ 2.5·10⁶ s^?1m^?3, there is a fair agreement of the theory and experiment. The discrepancy in attainable superheat temperatures T _n does not exceed 0.8 K. It is shown that significant underheating of solution to theoretical values T _n at J < 2.5·10⁶ s^?1m^?3 cannot be bound only with heterogeneous nucleation but is conditioned by other factors as well.     

Study of the relaxation of metastable 6p 3 2 D 3 2/0 states of bismuth atoms in a bismuth-vapor laser

A universal absorption technique for studying the kinetics of relaxation of atomic states in the afterglow of a repetitively pulsed discharge in metal vapor lasers is proposed. It uses the measurement of the absorption of narrowband emission of a tunable dye laser and numerical simulation of absorption. The relaxation of metastable 6p ^{3 2} D ₃ ^2/0 states of Bi atoms in the afterglow of a 472.2-nm bismuth vapor laser was studied. The prepulse values of the concentration of metastable atoms n _m were not higher than 10¹¹ cm^?3 and did not impede the improvement of laser characteristics. The afterpulse values of n ^m were ～10¹³ cm^{? 3}.     

Dielectric relaxation of KBr doped with KOH and KOD

The complex dielectric constant of KBr single crystals doped with KOH and with KOD has been measured in the temperature range from 0.32°K to 300°K using a small a. c. signal. A relaxation timeτ ₀ was determined by means of Cole-Cole plots. ForT<4°K the temperature dependence ofτ ₀ can be approximated byAT ^?n , wheren is between 1.2 and 1.3 for the dilute samples, and between 0.8 and 1.0 for two samples with large hydroxyl concentrations.n has the same value for OH^? and OD^? dipoles. The constantA roughly doubles upon substitution ofH byD. The relaxation behavior was found to be independent of concentration in the range between 3×10¹⁸ cm^?3 dipoles and 10¹⁹ dipoles cm^?3.     

Chiral anomalies and constraints on the gauge group in higher-dimensional supersymmetric Yang-Mills theories

Chiral anomalies for gauge theories in any even dimension are computed and the results applied to supersymmetric theories in D = 6, 8 and 10. For D = 8 there is an anomalous chiral U(1) invariance, just as in D = 4, except for certain special groups. For D = 6 and D = 10 there is no anomalous chiral U(1) symmetry, but the gauge current is anomalous except for certain “anomaly-free” groups. For D = 6 the group is thereby constrained to be one of {SU(2), SU(3), exceptional}, while for D = 10 it is constrained to be one of {SU(n) n ≤ 5, USp(4), E₈}.     

Rydberg states in the D layer of the atmosphere and the GPS positioning errors

The noncoherent radiation in the frequency range 0.8–8.0 (GHz) formed in the D layer of the ionosphere at high solar activity due to transitions between Rydberg states is considered. The emitting layer thickness located 80–110 km above ground surface is estimated. A complicated irregular behavior of the frequency dependence of the radiation intensity for different values of å electron concentration n _e and temperature T _e due to different characteristics of electron scattering on the nitrogen and oxygen molecules is revealed. The dependences of the flux power of UHF radiation from the D layer in the indicated frequency range on the concentration and temperature of free electrons are calculated. It is shown that, at a frequency of ν = 1.44 GHz, the UHF radiation spectrum features a characteristic waist point, the position of which is almost independent of the electron temperature T _e ; i.e., a one-parameter dependence of the power flux on the electron n _e density takes place. In the frequency range of 4.0–8.0 GHz, the radiation spectrum exhibits a family of curves that, for each value of n _e and a wide range of T _e , give rise to a relationship known as the “bottleneck.” It was found that, with increasing frequency, the bottleneck moves upwards along a curve described by a quadratic dependence on the radiation frequency. For a frequency of ～5 GHz, and a certain range of temperature T _e and electron concentration within 5 · 10³ cm^?3 < n _e < 2 · 10⁴ cm^?3, an almost linear dependence of the UHF radiation power on n _e is observed. A comparative analysis of GPS signal delays at frequencies ν _f ⁽¹⁾ = 1.57 and ν _f ⁽²⁾ ≈ 5 GHz for various states of the ionosphere is performed. It is shown that, under the same condition, the use of the second frequency is more advantageous and informative. The ways of further development of the theory and experiment in studying the role of quantum resonant properties in the distortion of global satellite positioning system signals and in solving the fundamental problem of their elimination are discussed.     

Photoluminescent studies of the condensed phase in phosphorus-doped silicon

Photoluminescent studies give evidence for the existence of the electron—hole droplet in phosphorus-doped silicon in the impurity concentration range 9.0 × 10¹⁵cm^?3 ? N_D ? 4.3 × 10¹⁹cm^?3.