Mass Operator and Dynamical Implementation of Mass Superselection Rule

We start reviewing Giulini’s dynamical approach to Bargmann superselection rule proposing some improvements. First of all we discuss some general features of the central extensions of the Galilean group used in Giulini’s programme, in particular focussing on the interplay of classical and quantum picture, without making any particular choice for the multipliers. Preserving other features of Giulini’s approach, we modify the mass operator of a Galilei invariant quantum system to obtain a mass spectrum that is (i) positive and (ii) discrete, so giving rise to a standard (non-continuous) superselection rule. The model results to be invariant under time reversal but a further degree of freedom appears that can be interpreted as describing an internal conserved charge of the system (however, adopting a POVM approach, the unobservable degrees of freedom can be pictured as a generalized observable automatically gaining a positive mass operator without assuming the existence of such a charge). The effectiveness of Bargmann rule is shown to be equivalent to an averaging procedure over the unobservable degrees of freedom of the central extension of Galileian group. Moreover, viewing the Galileian invariant quantum mechanics as a non-relativistic limit, we prove that the above-mentioned averaging procedure giving rise to Bargmann superselection rule is nothing but an effective de-coherence phenomenon due to time evolution if assuming that real measurements includes a temporal averaging procedure. It happens when the added term Mc ² is taken in due account in the Hamiltonian operator since, in the dynamical approach, the mass M is an operator and cannot be trivially neglected as in classical mechanics. The presented results are quite general and rely upon the only hypothesis that the mass operator has point spectrum. These results explicitly show the interplay of the period of time of the averaging procedure, the energy content of the considered states, and the minimal difference of the mass operator eigenvalues.     

Optical and scintillation properties of Pr-doped Li-glass for neutron detection in inertial confinement fusion process

Optical and scintillation properties of Pr-doped Li-glass, 20Al(PO₃)₃-80LiF:Pr 3%, have been studied for applications in neutron detection systems. Based on optical transmission and reflectivity, the absorption coefficient and refractive index were calculated from the Beer Lambert law. The absorption edge was apparently shifted to the longer wavelength from 160 nm to 240 nm due to 4f → 5d transitions of Pr ions. The strong absorption peaks of praseodymium 4f → 4f transitions were observed from 420 nm to 500 nm and around 590 nm. The radio-luminescence spectrum excited by ²⁴¹Am 5.5 MeV α source was measured. Strong emission peaks were observed around 250 nm. The α-ray excited pulse height spectrum and decay kinetics were also examined. Light yield was estimated to be 400 ± 40 photons/5.5 MeV α and the main component of the decay time was evaluated to be about 12 ns. Furthermore, the pulse height spectrum of the glass excited by ²⁵²Cf neutrons was also measured, and the light yield was estimated to be 140 ± 10 photons/neutron.     

Why the Logical Hexagon?

The logical hexagon (or hexagon of opposition) is a strange, yet beautiful, highly symmetrical mathematical figure, mysteriously intertwining fundamental logical and geometrical features. It was discovered more or less at the same time (i.e. around 1950), independently, by a few scholars. It is the successor of an equally strange (but mathematically less impressive) structure, the ??logical square?? (or ??square of opposition??), of which it is a much more general and powerful ??relative??. The discovery of the former did not raise interest, neither among logicians, nor among philosophers of logic, whereas the latter played a very important theoretical role (both for logic and philosophy) for nearly two thousand years, before falling in disgrace in the first half of the twentieth century: it was, so to say, ??sentenced to death?? by the so-called analytical philosophers and logicians. Contrary to this, since 2004 a new, unexpected promising branch of mathematics (dealing with ??oppositions??) has appeared, ??oppositional geometry?? (also called ??n-opposition theory??, ??NOT??), inside which the logical hexagon (as well as its predecessor, the logical square) is only one term of an infinite series of ??logical bi-simplexes of dimension m??, itself just one term of the more general infinite series (of series) of the ??logical poly-simplexes of dimension m??. In this paper we recall the main historical and the main theoretical elements of these neglected recent discoveries. After proposing some new results, among which the notion of ??hybrid logical hexagon??, we show which strong reasons, inside oppositional geometry, make understand that the logical hexagon is in fact a very important and profound mathematical structure, destined to many future fruitful developments and probably bearer of a major epistemological paradigm change.     

Periodate salts as pyrotechnic oxidizers: development of barium- and perchlorate-free incendiary formulations

In a flash: pyrotechnic incendiary formulations with good stabilities toward various ignition stimuli have been developed without the need for barium or perchlorate oxidizers. KIO(4) and NaIO(4) were introduced as pyrotechnic oxidizers and exhibited excellent pyrotechnic performance. The periodate salts may garner widespread use in military and civilian fireworks because of their low hygroscopicities and high chemical reactivities.     

Prediction of theoretical plate number in isothermal gas chromatographic analysis on capillary columns

A method for the prediction of the efficiency of gas chromatographic analysis in isothermal conditions by using experimental data of 1-alcohols and n-alkanes measured on capillary columns filled with polar and non-polar stationary phases in isothermal and isobaric conditions is described. The theoretical plate height trend indicates the change of separation efficiency as a function of inlet pressure and column temperature. By evaluating the variation of the diffusion coefficients of the analysed compounds into the mobile and stationary phase it is possible to predict the column efficiency and the number of theoretical plates at any temperature.     

Effect of Eu and Pb doping on the dosimetric properties of LiCAF

LiCaAlF₆ (LiCAF) crystals doped with two different ions (europium and lead) have been investigated as potential new dosimetric materials. The stability of thermally stimulated luminescence (TSL) glow peaks in LiCAF:Eu was evaluated by means of the initial rise technique. The decay times at room temperature of the traps related to the dosimetric glow peaks were found to range between 40 and 2 × 10⁴ years confirming the good dosimetric characteristics of this crystal. The glow curve of LiCAF:Pb is dominated by a peak at approximately 300 °C emitting in the UV region (³P_0,1–¹S₀ transition of Pb²⁺) superimposed to a very broad structure at lower temperature (20–200 °C) featuring recombination at an intrinsic defect centre. The anomalous behavior of the low temperature structure during thermal cleaning procedures prevented any reliable numerical analysis of the TSL glow peak at 300 °C.     

FIR Laser Lines from CH3OD: A Review

The methanol isotopic species CH₃OD has also proved to be an efficient and powerful medium to generate radiation in the far infrared (FIR) region. After the critical review of 1994, six papers have been published dealing with new FIR laser lines from this molecule. As a consequence of the use of wide tunability waveguide CO₂ lasers as well as a new pulsed CO₂ laser operating at hot and sequential bands, as of optical pumping sources, the total number of the FIR laser lines increased from 122 in 1994 to 227 today. In this communication we present an updated and complete catalogue of FIR laser lines generated from CH₃OD. Information on wavelength, offset, relative polarization, intensity, and optimum operation pressure is generally available.     

A trust region method for minimization of nonsmooth functions with linear constraints

We introduce a trust region algorithm for minimization of nonsmooth functions with linear constraints. At each iteration, the objective function is approximated by a model function that satisfies a set of assumptions stated recently by Qi and Sun in the context of unconstrained nonsmooth optimization. The trust region iteration begins with the resolution of an “easy problem”, as in recent works of Martínez and Santos and Friedlander, Martínez and Santos, for smooth constrained optimization. In practical implementations we use the infinity norm for defining the trust region, which fits well with the domain of the problem. We prove global convergence and report numerical experiments related to a parameter estimation problem. Supported by FAPESP (Grant 90/3724-6), FINEP and FAEP-UNICAMP. Supported by FAPESP (Grant 90/3724-6 and grant 93/1515-9).     

Six-fermion calculation of intermediate-mass Higgs boson production at future {e^+ e^-} colliders

The production of an intermediate-mass Higgs boson in processes of the kind fermions at the energies of future linear colliders is studied. The recently developed and fully automatic algorithm/code ALPHA is used to compute the tree-level scattering amplitudes for the reactions . The code has been interfaced with the Monte Carlo program HIGGSPV/WWGENPV, properly adapted to 6-fermion production, in order to provide realistic results, both in the form of cross sections and event samples at the partonic level. Phenomenological results, that incorporate the effects of initial-state radiation and beamstrahlung, are shown and commented, emphasizing the potentials of full six-fermion calculations for precise background evaluation as well as for detailed studies of the fundamental properties of the Higgs particle. Received: 22 May 1997 / Published online: 20 February 1998