Electromagnetic radiation from nuclear collisions at RHIC energies

The hot and dense strongly interacting matter created in collisions of heavy nuclei at RHIC energies is modeled with relativistic hydrodynamics, and the spectra of real and virtual photons produced at mid-rapidity in these events are calculated. Several different sources are considered, and their relative importance is compared. Specifically, we include jet fragmentation, jet-plasma interactions, the emission of radiation from the thermal medium and from primordial hard collisions. Our calculations consistently take into account jet energy loss, as evaluated in the AMY formalism. We obtain results for the spectra, the nuclear modification factor (R_AA), and the azimuthal anisotropy (v_2) that agree with the photon measurements performed by the PHENIX collaboration at RHIC

Elliptic flow of thermal photons in relativistic nuclear collisions

We predict the transverse momentum (pT) dependence of elliptic flow of thermal photons for Au+Au collisions at the Relativistic Heavy Ion Collider. We model the system hydrodynamically, assuming formation of a thermalized quark-gluon plasma at some early time, followed by cooling through expansion, hadronization and decoupling. Photons are emitted throughout the expansion history. Contrary to hadron elliptic flow, which hydrodynamics predicts to increase monotonically with pT, the elliptic flow of thermal photons is predicted to first rise and then fall again as pT increases. Photon elliptic flow at high pT is shown to reflect the quark momentum anisotropy at early times when it is small, whereas at low pT it is controlled by the much larger pion momentum anisotropy during the late hadronic emission stage. An interesting structure is predicted at intermediate pT ~ 0.4 GeV/c where photon elliptic flow reflects the momenta and the (compared to pions) reduced v2 of heavy vector mesons in the late hadronic phase.Comment: 4 pages, 4 figures. Amended Fig. 3 and corresponding discussion, with complete explanation of the low-pT structure of photon elliptic flow around pT=400 MeV/

Fitted HBT radii versus space-time variances in flow-dominated models

The inability of otherwise successful dynamical models to reproduce the ``HBT radii'' extracted from two-particle correlations measured at the Relativistic Heavy Ion Collider (RHIC) is known as the ``RHIC HBT Puzzle.'' Most comparisons between models and experiment exploit the fact that for Gaussian sources the HBT radii agree with certain combinations of the space-time widths of the source which can be directly computed from the emission function, without having to evaluate, at significant expense, the two-particle correlation function. We here study the validity of this approach for realistic emission function models some of which exhibit significant deviations from simple Gaussian behaviour. By Fourier transforming the emission function we compute the 2-particle correlation function and fit it with a Gaussian to partially mimic the procedure used for measured correlation functions. We describe a novel algorithm to perform this Gaussian fit analytically. We find that for realistic hydrodynamic models the HBT radii extracted from this procedure agree better with the data than the values previously extracted from the space-time widths of the emission function. Although serious discrepancies between the calculated and measured HBT radii remain, we show that a more ``apples-to-apples'' comparison of models with data can play an important role in any eventually successful theoretical description of RHIC HBT data.Comment: 12 pages, 16 color figure

Evolution of pion HBT radii from RHIC to LHC -- Predictions from ideal hydrodynamics

We present hydrodynamic predictions for the charged pion HBT radii for a range of initial conditions covering those presumably reached in Pb+Pb collisions at the LHC. We study central (b=0) and semi-central (b=7fm) collisions and show the expected increase of the HBT radii and their azimuthal oscillations. The predicted trends in the oscillation amplitudes reflect a change of the final source shape from out-of-plane to in-plane deformation as the initial entropy density is increased.Comment: 6 pages, incl. 5 figures. Contribution to the CERN Theory Institute Workshop "Heavy Ion Collisions at the LHC -- Last Call for Predictions", CERN, 14 May - 8 June 2007, to appear in J. Phys.

Photon HBT interferometry for non-central heavy-ion collisions

Currently, the only known way to obtain experimental information about the space-time structure of a heavy-ion collision is through 2-particle momentum correlations. Azimuthally sensitive HBT interferometry (Hanbury Brown-Twiss intensity interferometry) can complement elliptic flow measurements by constraining the spatial deformation of the source and its time evolution. Performing these measurements on photons allows us to access the fireball evolution at earlier times than with hadrons. Using ideal hydrodynamics to model the space-time evolution of the collision fireball, we explore theoretically various aspects of 2-photon intensity interferometry with transverse momenta up to 2 GeV, in particular the azimuthal angle dependence of the HBT radii in non-central collisions. We highlight the dual nature of thermal photon emission, in both central and non-central collisions, resulting from the superposition of QGP and hadron resonance gas photon production. This signature is present in both the thermal photon source function and the HBT radii extracted from Gaussian fits of the 2-photon correlation function.Comment: 18 pages, 12 figure

Computer problem-solving coaches for introductory physics: Design and usability studies

The combination of modern computing power, the interactivity of web applications, and the flexibility of object-oriented programming may finally be sufficient to create computer coaches that can help students develop metacognitive problem-solving skills, an important competence in our rapidly changing technological society. However, no matter how effective such coaches might be, they will only be useful if they are attractive to students. We describe the design and testing of a set of web-based computer programs that act as personal coaches to students while they practice solving problems from introductory physics. The coaches are designed to supplement regular human instruction, giving students access to effective forms of practice outside class. We present results from large-scale usability tests of the computer coaches and discuss their implications for future versions of the coaches

Computer problem-solving coaches for introductory physics: Design and usability studies

The combination of modern computing power, the interactivity of web applications, and the flexibility of object-oriented programming may finally be sufficient to create computer coaches that can help students develop metacognitive problem-solving skills, an important competence in our rapidly changing technological society. However, no matter how effective such coaches might be, they will only be useful if they are attractive to students. We describe the design and testing of a set of web-based computer programs that act as personal coaches to students while they practice solving problems from introductory physics. The coaches are designed to supplement regular human instruction, giving students access to effective forms of practice outside class. We present results from large-scale usability tests of the computer coaches and discuss their implications for future versions of the coaches

Assessing student written problem solutions: A problem-solving rubric with application to introductory physics

Problem solving is a complex process valuable in everyday life and crucial for learning in the STEM fields. To support the development of problem-solving skills it is important for researchers and curriculum developers to have practical tools that can measure the difference between novice and expert problem-solving performance in authentic classroom work. It is also useful if such tools can be employed by instructors to guide their pedagogy. We describe the design, development, and testing of a simple rubric to assess written solutions to problems given in undergraduate introductory physics courses. In particular, we present evidence for the validity, reliability, and utility of the instrument. The rubric identifies five general problem-solving processes and defines the criteria to attain a score in each: organizing problem information into a Useful Description, selecting appropriate principles (Physics Approach), applying those principles to the specific conditions in the problem (Specific Application of Physics), using Mathematical Procedures appropriately, and displaying evidence of an organized reasoning pattern (Logical Progression)

Assessing student written problem solutions: A problem-solving rubric with application to introductory physics

Problem solving is a complex process valuable in everyday life and crucial for learning in the STEM fields. To support the development of problem-solving skills it is important for researchers and curriculum developers to have practical tools that can measure the difference between novice and expert problem-solving performance in authentic classroom work. It is also useful if such tools can be employed by instructors to guide their pedagogy. We describe the design, development, and testing of a simple rubric to assess written solutions to problems given in undergraduate introductory physics courses. In particular, we present evidence for the validity, reliability, and utility of the instrument. The rubric identifies five general problem-solving processes and defines the criteria to attain a score in each: organizing problem information into a Useful Description, selecting appropriate principles (Physics Approach), applying those principles to the specific conditions in the problem (Specific Application of Physics), using Mathematical Procedures appropriately, and displaying evidence of an organized reasoning pattern (Logical Progression)