Regular Series


Vol. 31 (2000), No. 3, pp. 561 – 752


Remarks on Deformation Quantization on the Cylinder

abstract

Some problems of the deformation quantization for the particle on the circle are considered. It is argued that, from the physical point of view, it seems to be necessary to deal with ”quantized” classical phase space. The compact form of the Moyal \(\ast \)-product is given.


Influence of the Stark Shift and Kerr-Like Medium on the Evolution of Field Entropy and Entanglement in Two-Photon Processes

abstract

We have investigated the evolution of the field quantum entropy and the entanglement of the atom-field in the two-photon process, taking into account the level shifts produced by Stark effect with an additional Kerr-like medium for one mode. The exact results are employed to perform a careful investigation of the temporal evolution of the entropy. A factorization of the initial density operator is assumed, with the privileged field mode being in a coherent state. We invoke the mathematical notion of maximum variation of a function to construct a measure for entropy fluctuations. The effect of both the Stark shift and the presence of a Kerr-like medium on the entropy is analyzed. It is shown that the addition of the Kerr medium and the Stark shift has an important effect on the properties of the entropy and entanglement. The results show that, the effect of the Kerr medium and the Stark shift changes the quasiperiod of the field entropy evolution and entanglement between the atom and the field. The general conclusions reached are illustrated by numerical results.


The Vortex Oscillations in Abelian Higgs Model

abstract

The excitations of the vortex in Abelian Higgs model with small ratio of vector and Higgs particle masses are considered. Three main modes encountered in numerical computations are described in detail. They are also compared to analytic results obtained recently by Arodź and Hadasz in Phys. Rev. D54, 4004 (1996).


Dynamics of a Planar Domain Wall with Oscillating Thickness in \(\lambda {\mit \Phi }^{4}\) Model

abstract

Domain wall-type solution with oscillating thickness in a real, scalar field model is investigated with the help of a polynomial approximation. We propose a simple extension of the polynomial approximation method. In this approach we calculate higher order corrections to the planar domain wall solution and find that the domain wall with oscillating thickness radiates.


Supersymmetry and Bogomol’nyi Equations in the Maxwell Chern-Simons Systems

abstract

We take advantage of the superspace formalism and explicitly find the \(N=2\) supersymmetric extension of the Maxwell Chern–Simons model. In our construction a special form of a potential term and indispensability of an additional neutral scalar field arise naturally. By considering the algebra of supersymmetric charges we find Bogomol’nyi equations for the investigated model.


Determination of Polarised Parton Distributions in the Nucleon — Next to Leading Order QCD Analysis

abstract

We have made next to leading order QCD fit to the deep inelastic spin asymmetries on nucleons and we have determined polarised quark and gluon densities. The functional form for such distributions was inspired by the Martin, Roberts and Stirling fit for unpolarised case. In addition to usually used data points (averaged over \(x\) and \(Q^2\)) we have also considered the sample containing points with similar \(x\) and different \(Q^2\). It seems that splitting of quark densities into valence and sea contribution is strongly model dependent and only their sum (i.e. , \(\Delta u\) and \(\Delta d\)) can be precisely determined from the data. Integrated polarised gluon contribution, contrary to some expectations, is relatively small and the sign of it depends on the fact which sample of data points is used.


Option of Three Pseudo-Dirac Neutrinos

abstract

As an alternative for popular see–saw mechanism, the option of three pseudo-Dirac neutrinos is discussed, where \(\frac {1}{2}(m^{\rm (L)} + m^{\rm (R)}) \ll m^{( D)}\) for their Majorana and Dirac masses. The actual neutrino mass matrix is assumed in the form of tensor product \( M^{(\nu )} \otimes {\left ( \begin {array} {cc} \lambda ^{\rm (L)} & 1 \\ 1 & \lambda ^{\rm (R)} \end {array} \right )}\), where \( M^{( \nu )}\) is a neutrino family mass matrix (\( M^{(\nu )\,\dagger } = M^{(\nu )}\)) and \(\lambda ^{\rm (L,R)} \equiv m^{\rm (L,R)}/m^{\rm (D)}\) with \( m^{\rm (L)}\), \( m^{\rm (R)}\) and \( m^{\rm (D)} \) being taken as universal for three neutrino families. It is shown that three neutrino effects (deficits of solar \(\nu _e \)’s and atmospheric \( \nu _\mu \)’s as well as the possible LSND excess of \(\nu _e \)’s in accelerator \(\nu _\mu \) beam) can be nicely described by the corresponding neutrino oscillations, though the LSND effect may, alternatively, be eliminated (by a parameter choice). Atmospheric \(\nu _\mu \)’s oscillate dominantly into \(\nu _\tau \)’s, while solar \(\nu _e \)’s — into (existing here automatically) Majorana sterile counterparts of \(\nu _e \)’s. A phenomenological texture for neutrinos, compatible with the proposed description, is briefly presented.


An Unorthodox Alternative for Righthanded Neutrinos: Lefthanded See–Saw

abstract

A new lefthanded see–saw mechanism is constructed, implying both the smallness of active-neutrino masses and decoupling of heavy passive neutrinos, similarly to the situation in the case of conventional see–saw. But now, in place of the conventional righthanded neutrinos, the lefthanded sterile neutrinos play the role of heavy passive neutrinos, the righthanded neutrinos and righthanded sterile neutrinos being absent. Here, the lefthanded sterile neutrinos are different from charge conjugates of conventional righthanded neutrinos because their lepton numbers differ. In this case, the neutrino mass term is necessarily of pure Majorana type.


Entropy in Cluster Analysis of Single Events in Heavy Ion Collisions

abstract

We analyse the cluster structure of the final multihadron states resulting from heavy ion collisions using the concept of Jaynes–Shannon entropy. Further evidence for an interesting differentiation of events is provided.


Measurement of Entropy of a Multiparticle System: a “Do-List”

abstract

An algorithm for measurement of entropy in multiparticle systems, based on the recently published proposal of the present authors is given. Dependence on discretization of the system and effects of multiparticle correlations are discussed in some detail.


all authors

S. Chojnacki, J. Kownacki, P. Lubiński, J. Tys, D. Brzozowiec, M. Kapusta

An Estimation of the Production Yield of \(^{111}\)In and \(^{123}\)I Isotopes Using the \(^{16}\)O Induced Reaction on \(^{\rm nat}\)Ag

abstract

The production of \(^{111}\)In and \(^{123}\)I isotopes has been studied, using \(^{16}\)O induced reaction. The maximal cross section for the production of these isotopes was measured to be 168 \(\mu \)b and 187 \(\mu \)b for \(^{111}\)In and \(^{123}\)I, respectively, for a beam energy of about 70 MeV.


A Study for the Nucleus-Nucleus Differential Cross-Section

abstract

The near-side and the far-side decomposition following Fuller formalism have been calculated for the interaction of \(^{12}\)C–\(^{12}\)C system at energies 1016, 1449 and 2400 MeV and for \(^{16}\)O–\(^{12}\)C system at energy 1503 MeV. Fraunhofer oscillations observed at forward angles in the total differential cross-section are due to the strong interference between the near-side and the far-side contributions. The exponential fall off following the interference pattern is due to the dominance at large angles of the far-side amplitude and should thus be referred to as a far-side tail rather than a nuclear rainbow effect.


First and Second-Order Corrections to the Eikonal Phase Shifts for the Interactions of Two Deformed Nuclei

abstract

We present first and second-order corrections to the eikonal phase shifts for the interactions of two deformed nuclei. The elastic scattering differential cross-section has been calculated for the interactions of \(^{12} \)C–\(^{12}\)C system at energy 1016, 1449 and 2400 MeV. The two results calculated from the first and second-order corrections do not give substantial improvement between the experimental data and the theoretical calculations for the elastic scattering. The deflection function and the \(S\)-matrix have been calculated including the first and second-order corrections to the eikonal phase shift. Also, the near-side and the far-side decompositions of the scattering amplitude have been calculated including the first and second-order corrections to the eikonal phase shifts.


Energy Dependence of the Fragmentation of the Au Projectile in Au-Emulsion Interactions

abstract

The fragmentation of gold nuclei interacting in nuclear emulsions is studied over the energy range of 0.1 to 10.6 GeV/nucleon. Different fragmentation processes are selected and investigated. The probability of fission of the gold nucleus strongly decreases with increasing beam energy. On the other hand, spallation processes do not show a significant energy dependence. At low incident energies nuclear multifragmentation only occurs in rather central Au-Emulsion interactions, while at 10.6 GeV/nucleon it is also observed in more peripheral collisions. The statistical properties of the multifragmentation events are studied. It is found that the mechanism responsible for gold multifragmentation is different than for other fragmentation processes, although no evidence suggesting the presence of a liquid-gas phase transition is found. Among Au-Emulsion interactions at 10.6 GeV/nucleon we also observe a small fraction of events in which the projectile gold nucleus is completely broken into singly charged fragments. Such events are not seen at lower energies. These interactions are the most central collisions and are accompanied by a considerable production of secondary particles.


Quartet \(n\)–\(d\) Scattering Lengths

abstract

Quartet \(n\)–\(d\) scattering lengths are calculated using second-generation nucleon-nucleon potential models. These results are compared to the corresponding quantity recently calculated using chiral perturbation theory.


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