The π+ d → pp reaction at intermediate energies

Conclusion The joint efforts of the laboratories with intermediate energies accelerators at ANL, KEK, LANL, LNPI, Saclay, SIN and TRIUMF produced a rather definite picture of the ⁺pp reaction in the isobar region. However the problem of anomalies for the square-root branch point due to the production of isobar in the intermediate state have not been resolved so far. The poles obtained in different phenomenological analyses could be just the effective parametrization of these cuts (see e.g. [13]). Anyway, some singularities are definitely necessary to describe the data.The experimental data in regions s < 2·05 GeV and s < 2·25 GeV are clearly insufficient. Further accumulation of the data in these regions is necessary. Polarized deuteron data are badly needed in the whole kinematical range [13]. Besides as it was mentioned before it is necessary to measure accurately cross sections of other inelastic reactions which are important for the investigation (observation?) of dibaryonsNN N, NN andd N, NN [21]. It would be of interest also to measure cross sections of non quasi two-particle channels likeNN N, 2N andd N, 2N [22]. (In the case ofNN scattering quasi two-particle channels are known to dominate in a wide energy range.)Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.I am grateful to L. A. Kondratyuk, M. G. Ryskin and M. I. Strikman for valuable discussions of the considered problems.     

Ferretti-Rajeev term and homotopy theory

We reduce Ferretti-Rajeev models to the usual sigma models with Chern-Simons terms (-terms), and show that whether is quantized or not corresponds to the fact ₄(G _j,n )₃(U(j))= or 0 of the topology in the process of our reduction. We also reconsider the topological invariance of the Chern classes in the language of the field theory.Partially supported by the Grant-in-Aid for Scientific Research, No. 04640088     

Semiclassical theory of the scattering of π-mesons by nucleons in the case of strong coupling. Part I

The scattering cross section of the reaction + N N + , + N N + is calculated by the semiclassical method. It is predicted that the latter reaction occurs through N** resonance. The mass of this resonance, the spin, and isospin are found. The zero approximation with respect to the coupling constant between the - and -mesons is considered.     

Vibronic properties of 2-azaanthracene and its derivatives

We report an experimental and theoretical (PPP method) study of the UV absorption spectra of 2-azaanthracene and four of its methyl-substituted derivatives. We find that the p bands of these compounds consist of two different vibronic ^* bands. Our experimental and theoretical results suggest a rule for evaluating the effect of methyl groups on ^* transition energies as a function of the charge on the atoms. We interpret the reasons for the different effects of a polar solvent and hydrogen bonding on the ^* bands of these compounds.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 7–15, June, 1977.     

Wedge-screw dispiration in smectic liquid crystals with antiferroelectric order

Using the approximative expression for the elastic energy density of the antiferroelectric (AF) liquid crystal the elastic self-energy of (, b)-wedge-screw dispiration is estimated. Then the elastic interaction between (, b)-wedge-screw dispiration and (2)-wedge dischnation in AF liquid crystals is investigated. The attraction of dislocation part of dispiration with (2)-wedge disclination can lead to the formation of (3)-wedge-screw dispiration. When (2)-wedge disclination is trapped by (2d)-screw dislocation the resulting (2, 2d)-dispiration can dissociate into a pair of two (, d)-dispirations.The authors express their thanks to Professors A. Fukuda, H. Takezoe, Dr. Y. Takanishi and to Dr. K. Miyachi for discussions concerning their experimental observations of (3, d)-wedge-screw dispirations and (, d)-twist-edge dispirations in AF structures. This work was supported by the grant No. 19062 from Acad. Sci. Cz. R. and also benefited by the grant No.: 202/93/155 from the Grant Agency of the Czech Republic.     

On the implementability of automorphism groups

LetA be aC*-algebra andG be a locally compact group acting as strongly continuous automorphisms onA. Let be a representation ofA then we say is a covariant representation if there exists a strongly continuous unitary representation of the group acting onH which implements the automorphisms. We give necessary and sufficient conditions on a representation ofA such that a) is subrepresentation of a covariant representation and b) is subrepresentation of a covariant representation quasi-equivalent to .     

Weakly model dependent pion form factor with physically interpretable parameters

Conclusion We have constructed the pion form factor model satisfying fundamental principles, providing some freedom for the asymptotic behaviour and depending only on the adjustable parameters with a definite physical interpretation. The explicit incorporation of the pion form factor left-hand cut from the second Riemann sheet into a model was carried out for the first time. As a result we have described (contrary to the previous attempts [18, 19]) the pion form factor data from the range of momenta –9·770 GeV² t 9·579 GeV² and data on theP-wave isovector phase shift in the elastic region simultaneously with the adjustable parameters acquiring very reasonable values. The asymptotic behaviour was enforced by the data to be consistent with the naive quark model prediction. The calculated values of the pion charge radius as well as theP-wave isovector scattering length coincide with the world averaged values. With regard to these positive features of our pion form factor model it can be employed for the reliable calculation (via unitarity) of theP-wave isovector scattering partial amplitude outside the physical region, which could be useful in a saturation of various sum rules in scattering physics.     

Phase transitions in an exactly soluble one-dimensional exclusion process

We consider an exclusion process with particles injected with rate at the origin and removed with rate at the right boundary of a one-dimensional chain of sites. The particles are allowed to hop onto unoccupied sites, to the right only. For the special case of = = 1 the model was solved previously by Derridaet al. Here we extend the solution to general , . The phase diagram obtained from our exact solution differs from the one predicted by the mean-field approximation.     

Adiabatic Models of the Cosmological Radiative Era

We consider a generalization of the Lemaitre-Tolman-Bondi (LTB) solutions by keeping the LTB metric but replacing its dust matter source by an imperfect fluid with anisotropic pressure _ab . Assuming that total matter-energy density is the sum of a rest mass term, ^(m), plus a radiation ^(r) = 3p density where p is the isotropic pressure, Einstein's equations are fully integrated without having to place any previous assumption on the form of _ab . Three particular cases of interest are contained: the usual LTB dust solutions (the dust limit), a class of FLRW cosmologies (the homogeneous limit) and of the Vaydia solution (the vacuum limit). Initial conditions are provided in terms of suitable averages and contrast functions of the initial densities of ^(m), ^(r) and the 3-dimensional Ricci scalar along an arbitrary initial surface t = t _i . We consider the source of the models as an interactive radiation-matter mixture in local thermal equilibrium that must be consistent with causal Extended Irreversible Thermodynamics (hence _ab is shear viscosity). Assuming near equilibrium conditions associated with small initial density and curvature contrasts, the evolution of the models is qualitatively similar to that of adiabatic perturbations on a matter plus radiation FLRW background. We show that initial conditions exist that lead to thermodynamically consistent models, but only for the full transport equation of Extended Irreversible Thermodynamics. These interactive mixtures provide a reasonable approximation to a dissipative tight coupling characteristic of radiation-matter mixtures in the radiative pre-decoupling era.     

Scalar mesons in ππ and K¯K scattering

The s-wave pion scattering amplitude is analysed with the aim to clarify the mass spectrum of scalar mesons and to find evidence of lightest glueball. The S-matrix and K¯K coupled channel formalism is used. The existence of scalar mesons S^* and is implied by the data. The production K¯K and the elastic K¯KK¯K coupled amplitudes are predicted from the scattering data. The couplings c f S^* to and K¯K states are determined.     

Asymptotically abelian systems

We study pairs { , } for which is aC*-algebra and is a homomorphism of a locally compact, non-compact groupG into the group of *-automorphisms of . We examine, especially, those systems { , } which are (weakly) asymptotically abelian with respect to their invariant states (i.e. |A _g (B) — _g (B)A 0 asg for those states such that ( _g (A)) = (A) for allg inG andA in ). For concrete systems (those with -acting on a Hilbert space andg _g implemented by a unitary representationg U _g on this space) we prove, among other results, that the operators commuting with and {U _g } form a commuting family when there is a vector cyclic under and invariant under {U _g }. We characterize the extremal invariant states, in this case, in terms of weak clustering properties and also in terms of factor and irreducibility properties of { ,U _g }. Specializing to amenable groups, we describe operator means arising from invariant group means; and we study systems which are asymptotically abelian in mean. Our interest in these structures resides in their appearance in the infinite system approach to quantum statistical mechanics.     

π-Meson production by photons at He3 in current-algebra model

In an analysis of the photoproduction of-mesons at He³ in the current-algebra model with hard-mesons, the amplitude for the process is derived with the help of the Ward identity, which follows from the hypothesis of the partial conservation of axial-vector current and current algebra. Only the-meson and the He³ and H³ nuclei are taken into account in the sums over intermediate states. The contact terms are important for an explanation of the experimental data. The differential cross sections are calculated for the photoproduction of ⁺-mesons at He³; they agree satisfactorily with the experimental data for low energies (E<240 MeV) and for low-momentum transfer (¦t¦<2.5 F^–2).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizikii, No. 7, pp.96–102, July, 1975.In conclusion the authors thank G. M. Radutskii for discussion of these results.     

From monotonic to oscillatory decay of correlations: Analytical approximation for the two-dimensional,one-component plasma

An approximate evaluation of the pair distribution and the structure factor is performed analytically for the two-dimensional, one-component plasma at any value of the coupling constant. The approximate distribution remains positive and satisfies three sum rules, including the compressibility one. When 0 or 2, exact results are found. At=2 the transition from monotonie (<2) to oscillatory (>2) decay of correlations takes place. Comparison with the Monte Carlo simulations shows good agreement for 0<<4.     

Levinson's Theorem for the Schrödinger Equation in One Dimension

Levinson's theorem for the one-dimensional Schrödinger equation with asymmetric potential which decays at infinity faster thanx ^–2 is established by theSturm-Liouville theorem. The critical case where the Schrödinger equation hasa finite zero-energy solution is also analyzed. It is demonstrated that the numberof bound states with even (odd) parityn ₊(n _–) is related to the phase shift ₊ (0)[_– (0)] of the scattering states with the same parity at zero momentum as ₊ (0)+ /2 =n ₊ and _– (0) =n _– for the noncritical case, and ₊ (0) =n ₊ and_– (0) – /2 =n _– for the critical case.     

Laser collimation of an Fe atomic beam on a leaky transition

We report results of the first laser collimation of a thermal beam of Fe atoms on the leaky ⁵D₄ ⁵F₅ transition, with both parallel linear ^xx and crossed linear ^xy laser polarization configurations. The measured atomic beam divergence is compared to a rate-equation model and a quantum Monte Carlo model. The experimental values for the divergence are limited by the finite laser line width, which is comparable to the natural line width of the Fe atom. In general, flux decreases with higher intensities, showing the effect of the leaky transition. At the best beam collimation _RMS = 0.17 mrad, which is for a detuning of = – and a saturation parameter of s = 6, the flux decreased to approximately 70%. Highest flux was measured for a detuning of = –2 and s = 4, reaching 135% of the uncooled value. From our measurements we estimate the total leak rate to be 1/(240 ± 40), which is in good agreement with the literature value of 1/244. The crossed linear polarization configuration is the better choice, with a slightly better collimation but the same atomic beam flux. Plugging of the largest leak would increase the flux to at least 80% of the closed transition value, resulting in better contrast for atom lithography.     

Radiative photoproduction of pions and pion compton scattering

The cross section for the radiative photoproduction of ⁺ mesons on hydrogenp ⁺ n in dependence on the momentum transfer squared has been measured at the 1·2 GeV electron synchrotron PACHRA. Using extrapolation of the data to pion pole the differential cross section for the pion Compton scattering ^{+ +} has been obtained, and the electric polarizability of the ⁺ meson has been estimated to be =(20±12) x 10^-43cm³.Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.The authors thank P. A. Cherenkov for his constant attention to this work and helpful discussions at all stages of the work.     

Relation between Higgs and Weinberg angles in minimal SUSY from diophantine analysis

Diophantine quantization is applied to neutral Higgs and gauge bosons in minimal SUSY, with the additional requirement that , like _w , be a rational angle. One finds for the Higgs mixing angles that =–/4 and that = _w or /2– _w . TheCP-odd HiggsA turns out to be degenerate in mass with the Z, and the two neutralCP-even Higgs bosons have masses of about 123 and 37.5 GeV, respectively. The charged Higgs has a mass of about 121.5 GeV. Further, if >/4, the infrared quasi-fixed-point solution yields at-quark mass in the neighborhood of 170 GeV, in agreement with recent data.Deceased. Submitted by the estate of the author.     

Ergodic states in a non commutative ergodic theory

Using the Godement mean of positive-type functions over a groupG, we study -abelian systems { , } of aC*-algebra and a homomorphic mapping of a groupG into the homomorphism group of . Consideration of the Godement mean off(g)U _g withf a positive-type function overG andU a unitary representation ofG first yields a generalized mean-ergodic theorem. We then define the Godement mean off(g) ( _g (A)) withA and a covariant representation of the system { , } for which theG-invariant Hilbert space vectors are cyclic and study its properties, notably in relation with ergodic and weakly mixing states over . Finally we investigate the discrete spectrum of covariant representations of { , } (i.e. the direct sum of the finite-dimensional subrepresentations of the associated representations ofG).On leave of absence from Istituto di Fisica G. Marconi Piazzale delle Scienze 5 — Roma.     

General tachyon absorption by Kerr-Newman black holes: Thermodynamic consequences

Following the analyses of B. Carter and J. V. Narlikar, the nature of the incomplete, spacelike trajectories about a charged, rotating black hole is described. The study concentrates on those paths which a charged tachyon would follow, incident from off the equatorial plane (on which=/2). The effect of the absorption upon the black hole is calculated and it is concluded that for _i /2 only certain charged tachyons will reduce its entropy. However, a sustained bombardment by such particles could cause the singularity to be exposed.     

An approximation method to solve Einstein's field equations on a curved background metric

An approximation method is developed to calculate the gravitational field of a matter sourceT moving on a curved background metric that is an exact solution of the field equations and deviates only weakly from flat space-time. The fieldh of the sourceT is supposed to be much smaller than the curved part of the background, so that in the series expansion ofh each order can be expanded in powers of the background.