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Photonic Equations of Motion

Description: Although the concept of the photon as a quantum particle is sharpened by the quantization of the energy of the classical radiation field in a cavity, the photon's spin has remained a classical degree of freedom. The photon is considered a spin-1 particle, although only two classical polarization states transverse to its direction of propagation are allowed. Effectively therefore the photon is a spin-1/2 particle, although it still obeys Bose-Einstein statistics because the photon-photon interaction is zero. Here they show that the two polarization states of the photon can be quantized using Pauli's spin vector, such that a suitable equation of motion for the photon is Dirac's relativistic wave equation for zero mass and zero charge. Maxwell's equations for a free photon are inferred from the Dirac-field formalism and thus provide proof of this claim. For photons in the presence of electronic sources for electromagnetic fields we posit Lorentz-invariant inhomogeneous photonic equations of motion. Electro-dynamic operator equations are inferred from this modified Dirac-field formalism which reduce to Maxwell's equations if spin-dependent terms in the radiation-matter interaction are dropped.
Date: September 17, 2004
Creator: Ritchie, A B & Crenshaw, M E
Partner: UNT Libraries Government Documents Department

Applications of RQMD to Bose-Einstein correlations

Description: Source size parameters measured via two-particle interferometry in experiment NA44 for 200 GeV/nucleon S+Pb collisions are compared to calculations using the RQMD event generator. Reasonable agreement is found in most cases. Based on this agreement, the model is used to study some of the interesting details of the collision dynamics which are not easily measured. 27 refs., 4 figs., 1 tab.
Date: March 1, 1996
Creator: Sullivan, J.P.
Partner: UNT Libraries Government Documents Department

Transverse momentum dependent two-pion Bose-Einstein correlations in Au + Au collisions at 11.6 A {center_dot} GeV/c

Description: Bose-Einstein correlations of {pi}{sup +}{pi}{sup +} and {pi}{sup {minus}}{pi}{sup {minus}} pairs collected by the BNL-E866 Forward Spectrometer in 11.6 A{center_dot}GeV/c Au + Au collisions have been measured. The data were analyzed using three-dimensional correlation functions parameterized by the Yano-Koonin-Potgoretskii and Bertsch-Pratt formalism to study transverse momentum dependent source parameters. Rapid decreases of longitudinal source radii and slower decreases in the transverse parameters with increasing transverse momentum were observed, which suggests a strong longitudinal and some transverse expansion. A freeze-out time {tau}{sub 0} was derived as 4.5--5 fm/c, under the assumption of the freeze-out temperature T = 130 MeV, and the duration of emission was found to be {delta}{tau} {approx} 2--4 fm/c.
Date: December 1998
Creator: Lee, J. H. & Collaboration, E866
Partner: UNT Libraries Government Documents Department

Bose-Einstein final state symmetrization for event generators of heavy ion collisions

Description: The current relativistic heavy ion program at CERN and BNL aims at investigating the equilibration properties of hadronic matter at extreme temperatures and densities where quarks and gluons are expected to be the physically relevant degrees of freedom for particle production processes. The theoretical discussion of these collision systems is complicated by their mesoscopic character. They are not sufficiently small to allow for an analytical description in terms of elementary processes. They are not sufficiently large to take a description in terms of macroscopic observables for granted. Even if simple thermodynamically of hydrodynamically inspired models account for the data, the task remains to understand the microscopic origin of their success, and to establish to what extent such an agreement is necessary or accidental. The authors discuss algorithms which allow to calculate identical two-particle correlations from numerical simulations of relativistic heavy ion collisions. A toy model is used to illustrate their properties.
Date: December 1, 1998
Creator: Wiedemann, U.A.; Heinz, U.; Ellis, J. & Geiger, K.
Partner: UNT Libraries Government Documents Department

Measuring two-particle Bose-Einstein correlations with PHOBOS@RHIC

Description: We present results of a simulation of the measurement of two-particle Bose-Einstein correlations in central Au-Au collisions with the PHOBOS detector at RHIC. This measurement is expected to yield information on the relevant time and distance scales in these collisions. As the space-time scale is directly connected with the equation of state governing the evolution of the particle source, this information will be essential in understanding the physics of nucleus-nucleus collisions at RHIC energies. We demonstrate that the PHOBOS detector has sufficient resolution and acceptance to distinguish a variety of physics scenarios.
Date: December 31, 1995
Creator: Betts, R.; Barton, D. & Carroll, A.
Partner: UNT Libraries Government Documents Department

Thermodynamic q-distributions that aren`t

Description: Bosonic q-oscillators commute with themselves and so their free distribution is Planckian. In a cavity, their emission and absorption rates may grow or shrink-and even diverge-but they nevertheless balance to yield the Planck distribution via Einstein`s equilibrium method, (a careless application of which might produce spurious q-dependent distribution functions). This drives home the point that the black-body energy distribution is not a handle for distinguishing q-excitations from plain oscillators. A maximum cavity size is suggested by the inverse critical frequency of such emission/absorption rates at a given temperature, or a maximum temperature at a given frequency. To remedy fragmentation of opinion on the subject, we provide some discussion, context, and references.
Date: July 1, 1993
Creator: Vokos, S. & Zachos, C.
Partner: UNT Libraries Government Documents Department

Mass identified particle production and Bose Einstein correlations at 1800 GeV

Description: Results were shown on transverse momentum distributions of {pi}, k and p from Fermilab experiment E735. This experiment, related to the search for quark gluon plasma, was run at the Fermilab Tevatron collider with {bar p}p collisions at {radical}s = 1800 GeV. Dependence of particle ratios on transverse momentum and center of mass energies was shown. Results were also shown on Bose Einstein correlations between pairs of identical pions and a measure of size and lifetime of the source.
Date: May 1, 1994
Creator: Alexopoulos, T. & Collaboration, E735
Partner: UNT Libraries Government Documents Department

GGLP effect from 1959 to 1984

Description: The GGLP effect refers to the difference in opening angles of pion pairs for like and unlike pairs. This was found to be the effect of Bose-Einstein statistics for pions. The discovery of the effect in 1959, its interpretation in terms of Bose-Einstein statistics, and the use of the effect in pion interferometry are reviewed. 27 refs. (LEW)
Date: April 1, 1985
Creator: Goldhaber, G.
Partner: UNT Libraries Government Documents Department

Results from E735 at the Tevatron proton-antiproton collider with {radical}s = 1.8 TeV

Description: Experiment E735{dagger} searched for evidence of the transition to quark-gluon plasma in p{bar p} collisions at {radical}{bar s} = 1.8 TeV. Using data from a high statistics run in 1988--1989, results are presented on multiplicity distributions, hyperon and phi production, and Bose-Einstein correlations. Some data was also taken at lower collision energies and results will be compared to previous experiments.
Date: November 1, 1991
Creator: Lindsey, C. & Collaboration, E735
Partner: UNT Libraries Government Documents Department

Meson Interferometry in Relativistic Heavy Ion Collisions

Description: This report contains discussions on the following topics: Recent HBT results form CERN experiment NA44; interferometry results from E802/E859/E866; recent results on two particle correlations from E814; source sizes from CERN data; intermittency and interferometry; Bose-Einstein correlations in 200A GeV S+Au collisions; HBT correlations at STAR; HBT interferometry with PHENIX; HBT calculations from ARC; three pion correlations; and pion correlations in proton-induced reactions.
Date: May 1, 1993
Partner: UNT Libraries Government Documents Department

q-bosons and the q-analogue quantized field

Description: The q-analogue coherent states {vert_bar}z >{sub q} are used to identify physical signatures for the presence of a q-analogue quantized radiation field in the {vert_bar} >{sub q} classical limit where {vert_bar}z{vert_bar} is large. In this quantum-optics-like limit, the fractional uncertainties of most physical quantities (momentum, position, amplitude, phase) which characterize the quantum field are O(1). They only vanish as O(1/{vert_bar}z{vert_bar}) when q = 1. However, for the number operator, N, and the N-Hamiltonian for a free q-boson gas, H{sub N} = {Dirac_h}{omega}(N + 1/2), the fractional uncertainties do still approach zero. A signature for q-boson counting statistics is that ({Delta}N){sup 2}/<N> {yields} 0 as {vert_bar}z{vert_bar} {yields} {infinity}. Except for its O(1) fractional uncertainty, the q-generalization of the Hermitian phase operator of Pegg and Barnett, {phi}{sub q}, still exhibits normal classical behavior. The standard number-phase uncertainty-relation, {Delta}N {Delta}{phi}{sub q} = 1/2, and the approximate commutation relation, [N,{phi}{sub q}] = i, still hold for the single-mode q-analogue quantized field. So, N and {phi}{sub q} are almost canonically conjugate operators in the {vert_bar}z >{sub q} classical limit. The {vert_bar}z >{sub q} CS`s minimize this uncertainty relation for moderate {vert_bar}z{vert_bar}{sup 2}.
Date: December 31, 1994
Creator: Nelson, C. A.
Partner: UNT Libraries Government Documents Department

Multiple particle production processes in the light'' of quantum optics

Description: Ever since the observation that high-energy nuclear active'' cosmic-ray particles create bunches of penetrating particles upon hitting targets, a controversy has raged about whether these secondaries are created in a single act'' or whether many hadrons are just the result of an intra-nuclear cascade, yielding one meson in every step. I cannot escape the impression that: the latter kind of model appeals naturally as a consequence of an innate bio-morphism in our way of thinking and that in one guise or another it has tenaciously survived to this day, also for hadron-hadron collisions, via multi-peripheral models to the modern parton shower approach. Indeed, from the very beginning of theoretical consideration of multiparticle production, the possibility of many particles arising from a single hot'' system has been explored, with many fruitful results, not the least of which are the s{sup 1/4} dependence of the mean produced particle multiplicity and the thermal'' shape of the P{sub T} spectra. An important consequence of the thermodynamical-hydrodynamical models is that particle emission is treated in analogy to black-body radiation, implying for the secondaries a set of specific Quantum-Statistical properties, very similar to those observed in quantum optics. From here on I shall try to review a number of implications and applications of this QS analogy in the study of multiplicity distributions of the produced secondaries. I will touch only in passing another very important topic of this class, the Bose-Einstein two-particle correlations.
Date: September 1, 1990
Creator: Friedlander, E.M.
Partner: UNT Libraries Government Documents Department

Bose-Einstein correlation of positive kaon pairs in E859--Extended results and model comparisons

Description: Results are presented for multidimensional Bose-Einstein Correlation analyses of {pi}{sup +} and K{sup +} mid-rapidity pairs collected by BNL-AGS experiment E859 in 14.6 A{center_dot}GeV/c Si + Au central collisions. Comparisons are made to the cascade codes ARC (v. 1.9.5) and RQMD (v. 1.08). 14 refs., 2 figs., 3 tabs.
Date: December 31, 1995
Creator: Cianciolo, V.
Partner: UNT Libraries Government Documents Department

Meson and baryon correlation studies using the PEP-TPC/2. gamma. Facility

Description: Results on vector meson, and strange and charmed-baryon production are presented for data taken during the period 1982--1986 using the TPC/2{gamma} detector at PEP. Vector mesons ({rho}{sup 0}, K{sup *} and {phi}) with 0, 1 and 2 strange quarks are used to obtain redundant measures of strange-quark suppression and of the vector to pseudoscalar ratio in hadronization. Measurements of the production rates of {Lambda}, {Xi}{sup {minus}}, {Omega} and {Xi}{sup *0} hyperons and for the {Lambda}{sub c} and of rapidity correlations between {Lambda}{bar {Lambda}} pairs provide sensitive tests of baryon production in fragmentation models. In addition, two- and three-particle correlations between like sign pions provide further evidence for the Bose-Einstein effect in e{sup +}e{sup {minus}} interactions including the relativistic motion of particle sources. 9 refs., 7 figs.
Date: March 1, 1991
Creator: Ronan, M.T.
Partner: UNT Libraries Government Documents Department

Log(s) physics results from CDF

Description: The Collider Detector at Fermilab (CDF) is a large, azimuthally symmetric detector designed to study {bar p}p interactions at the Fermilab Tevatron Collider. Results are presented from data taken with a minimum bias trigger at {radical}s = 630 and 1800 GeV during the 1987 run. The topics include the current analysis of dn/d{eta} and some very preliminary results on short range pseudorapidity correlations and Bose-Einstein correlations. 7 refs., 5 figs., 2 tabs.
Date: November 8, 1989
Partner: UNT Libraries Government Documents Department

Test problems in radiative transfer calculations

Description: Several test problems are presented for evaluating the radiation diffusion equations. For spatial transport schemes, 1-D problems with known analytic solutions are tested on 2-D domains with non-orthogonal meshes. It is shown that a scheme based on the Finite Element Method is insensitive to grid distortions when the diffusion term is dominant. Other test problems deal with Compton scattering, specifically the 1-D Fokker-Planck equation coupled to an equation describing the change in electron temperature. The test problems model the evolution of a Planckian radiation field as it equilibrates with the electrons. In all cases, the numerical results are compared with the analytic ones. 15 refs., 9 figs., 7 tabs.
Date: January 12, 1989
Creator: Shestakov, A. I.; Kershaw, D. S. & Zimmerman, G. B.
Partner: UNT Libraries Government Documents Department

Analysis of multiparticle Bose-Einstein correlations in ultra-relativistic heavy ion collisions

Description: We introduce the coalescence variables, a set of three boost-invariant kinematic quantities which may be used in analyzing n-particle correlations. These variables characterize the invariant mass of an n-particle and in three directions and separate the timelike and spacelike characteristics of the source. The analytic Kolehmanien-Gyulassy model is generalized to give two, three, and four-particle correlation functions, with coherence and Coulomb corrections applied to the basic formalism. We demonstrate the relation of the coalescence variables to be radius and duration of the source, and find that for sufficiently large transverse radii, Coulomb effects can suppress the structure of the Hanbury-Brown-Twiss correlations so that no significant information on source size can be obtained. 11 refs., 10 figs.
Date: October 19, 1990
Creator: Cramer, J.G.
Partner: UNT Libraries Government Documents Department

Bose-Einstein correlations of pions in e/sup +/e/sup minus/ annihilation at 29 GeV center-of-mass energy

Description: Measurements of two- and three-particle correlations between like-sign pions produced in e/sup +/e/sup minus/ annihilation at 29 GeV center-of-mass energy are presented. The analysis is based on data taken during the period 1982--1986 using the TPC/2..gamma.. detector at PEP. Two-particle correlations are studied as a function of Q, the momentum difference as measured in the rest frame of the pion pair, and as a function of q/sub 0/, the energy difference as measured in the lab frame. The Bose-Einstein enhancement is observed when Q is small even when the energy difference, q/sub 0/, is substantial. This observation provides evidence that the Bose-Einstein correlations are best described by a model that correctly accounts for the relativistic motion of the particle sources. Three-pion correlations are measured both by using a standard three-pion correlation function, and also by using a correlation function for which the correlations between the pairs of pions within the triplet have been subtracted. The observation of three-pion correlations after pair correlations have been subtracted supports the interpretation that the observed correlations are due to Bose-Einstein interference. 56 refs.
Date: January 13, 1989
Creator: Avery, R.E.
Partner: UNT Libraries Government Documents Department

Kaon correlation systematics in E859

Description: Bose-Einstein correlations between K{sup +}`s and between {pi}{sup +}`s produced in collisions of 14.6 A{center_dot}GeV/c {sup 28}Si ions and {sup 197}Au nuclei have been measured using the E859 spectrometer. Parameters obtained from fits to correlation functions in relative momentum describe a K{sup +} source that is slightly smaller than the {pi}{sup +} source and comparable in size to the {sup 28}Si projectile. Correlation functions were also formed for {pi}K{sup +} and pK{sup +} pairs extracted from the data set. Bose-Einstein correlations are expected to be absent here. The observed correlations can be understood as being the result primarily of the two-particle Coulomb interaction. For the pK{sup +} pairs, an adequate description is obtained only when taking into account the finite sizes of the p K{sup +} sources. The space-time coordinate distributions of pions and kaons produced by the event generator ARC for the 14.6 A{center_dot}GeV/c {sup 28}Si on {sup 197}Au collision yield source sizes that are larger than those observed in the experiment. Much closer agreement is seen when viewing the distributions through a simulated version of the detector.
Date: December 31, 1993
Creator: Vossnack, O. E. & Collaboration, E802
Partner: UNT Libraries Government Documents Department

Particle correlations in p- anti p interactions at radical s = 1800 and 630 GeV

Description: Preliminary results on Bose-Einstein correlations and two particle pseudorapidity correlations in p{bar p} interactions at {radical}s = 1800 and 630 GeV are presented. Data were collected with a minimum- bias'' trigger with the Collider Detector at Fermilab. The size of the particle emitting source, measured via Bose-Einstein interference at {radical}s =1800 GeV, is of the order of 1 fm. The observed short-range pseudorapidity correlations, compared to lower energy data, do not show any significant energy dependence. 10 refs., 5 figs.
Date: January 1, 1990
Partner: UNT Libraries Government Documents Department

Transverse momentum dependence of Bose-Einstein correlations in S+nucleus collisions at 200 GeV/nucleon

Description: The NA35 experiment has collected a high statistics set of momentum analyzed negative hadrons near and forward of mid-rapidity for central collisions of 200 GeV/Nucleon {sup 32}S projectiles incident on S, Ag and Au targets. Using two pion momentum space correlations in order to study the size of the source of particle production, small dependences upon transverse momentum are found for the transverse source dimensions; however for the heaviest system, R{sub long} decreases by about 40% as transverse momentum is increased over the interval 50 < P{sub T} < 600 MeV/c. Preliminary model calculations using a microscopic phase space approach (RQMD) appear to reproduce the observed characteristics of the data.
Date: July 1, 1994
Creator: Morse, R. J. & Collaboration, NA35
Partner: UNT Libraries Government Documents Department

Bose-Einstein correlations in e/sup +/e/sup -/ collisions

Description: The MARK II detector is used to study the Bose-Einstein correlation between pairs and triplets of charged pions produced in hadronic decays of the J)psi), the ..sqrt..s = 4 to 7 GeV continuum above the J)psi), two photon events at ..sqrt..s = 29 GeV, and e/sup )plus/)e/sup )minus/) annihilation events at ..sqrt..s = 29 GeV as a function of Q/sup 2/, the four-momentum transfer squared. After corrections for Coulomb effects and pion misidentification, we find a nearly full Bose-Einstein enhancement ..cap alpha.. in the J)psi) and the two photon data and about half the maximum value in the other two data sets. The radius parameter )tau)(an average over space and time) given by pion pair analyses lies within a band of +-0.10 fm around 0.73 fm and is the same, within errors, for all four data sets. Pion triplet analyses also give a consistent radius of approx. 0.54 fm. fits to two-dimensional distributions R(q/sub T//sup 2/, q/sub C//sup 2/) of invariant components of Q/sup 2/ = q/sub T//sup 2/ )plus) q/sub C//sup 2/ give )tau)/sub T/ approx. )tau)C approx. )tau), where q/sub T/ is the transverse three-momentum difference calculated with respect to the net pair three-momentum, and q/sub C/ is in effect the longitudinal three-momentum difference in the pion pair rest frame. When q/sub T/ is calculated with respect to the jet axis for two-jet events in the e/sup )plus/)e/sup )minus/) annihilation data at ..sqrt..s = 29 GeV, a fit to R(q/sub T//sup 2/, q/sub C//sup 2/) also gives )tau)/sub T/ approx. )tau)/sub C/ approx. )tau). Noting that q/sub L/ and q/sub 0/ are not invariant, we make fits to R(/sub T//sup T/, q/sub L//sup 2/) and to R(q/sub T//sup 2/, q/sub 0//sup 2/) (Kopylov formulation), and we find )tau)/sub 0/ approx. )tau)/sub L/ approx. )23))tau)/sub T/ to )12))tau)/sub T/. ...
Date: December 1, 1987
Creator: Juricic, I.
Partner: UNT Libraries Government Documents Department

Results from E735 at the Tevatron proton-antiproton collider with radical s = 1. 8 TeV

Description: Experiment E735{dagger} searched for evidence of the transition to quark-gluon plasma in p{bar p} collisions at {radical}{bar s} = 1.8 TeV. Using data from a high statistics run in 1988--1989, results are presented on multiplicity distributions, hyperon and phi production, and Bose-Einstein correlations. Some data was also taken at lower collision energies and results will be compared to previous experiments.
Date: November 1, 1991
Creator: Lindsey, C.
Partner: UNT Libraries Government Documents Department