906 research outputs found
The Influence of High Multiplicities at RHIC on the Gamov Factor
The corrections for two-pion correlations due to electromagnetic final-state
interactions at high secondary multiplicities are investigated. The analysis is
performed by solving the Schr\"odinger equation with a potential which is
dictated by the multi-particle environment. Two different post-freeze-out
scenarios are examined. First, for a uniformly spread environment of secondary
particles, a screened Coulomb potential is exploited. It is shown that the
presence of a static and uniform post-freeze-out medium results in a noticeable
deviation from the standard Gamov factor. However, after going to a more
realistic model of an expanding pion system, this conclusion changes
drastically. We argue that the density of the secondary pions n_\pi(t,R), where
R is a distance from the fireball, is bounded from above by n_\pi(t,R)\le
const/R^2 for all times t. Then, a two-particle scalar potential which is found
as a solution of the Maxwell equation for non-uniform medium replaces the
screened one. Even this upper limit does not result in an essential deviation
from the Gamov correction.Comment: 11 pages, 7 figures, minor text corrections are mad
Some forgotten features of the Bose Einstein Correlations
Notwithstanding the visible maturity of the subject of Bose-Einstein
Correlations (BEC), as witnessed nowadays, we would like to bring to ones
attention two points, which apparently did not received attention they deserve:
the problem of the choice of the form of correlation function when
effects of partial coherence of the hadronizing source are to be included and
the feasibility to model effects of Bose-Einstein statistics, in particular the
BEC, by direct numerical simulations.Comment: Talk delivered by G.Wilk at the International Workshop {\it
Relativistic Nuclear Physics: from Nuclotron to LHC energies}, Kiev, June
18-22, 2007, Ukraine; misprints correcte
On kinematics and dynamics of independent pion emission
Multiparticle boson states, proposed recently for 'independently' emitted
pions in heavy ion collisions, are reconsidered in standard second quantized
formalism and shown to emerge from a simplistic chaotic current dynamics.
Compact equations relate the density operator, the generating functional of
multiparticle counts, and the correlator of the external current to each other.
'Bose-Einstein-condensation' is related to the external pulse. A quantum master
equation is advocated for future Monte-Carlo simulations.Comment: 10 pages LaTeX, Sec.7 adde
Bose-Einstein Correlations of Pion Wavepackets
A wavepacket model for a system of free pions, which takes into account the
full permutation symmetry of the wavefunction and which is suitable for any
phase space parametrization is developed. The properties of the resulting mixed
ensembles and the two-particle correlation function are discussed. A physical
interpretation of the chaoticity lambda as localizat of the pions in the source
is presented.
Two techniques to generate test-particles, which satisfy the probability
densities of the wavepacket state, are studied:
1. A Monte Carlo procedure in momentum space based on the standard Metropolis
technique.
2. A molecular dynamic procedure using Bohm's quantum theory of motion.
In order to reduce the numerical complexity, the separation of the
wavefunction into momentum space clusters is discussed. In this context th
influence of an unauthorized factorization of the state, i. e. the omissio of
interference terms, is investigated. It is shown that the correlation radius
remains almost uneffected, but the chaoticity parameter decreases
substantially. A similar effect is observed in systems with high multiplic
where the omission of higher order corrections in the analysis of two-part
correlations causes a reduction of the chaoticity and the radius.
The approximative treatment of the Coulomb interaction between pions and
source is investigated. The results suggest that Coulomb effects on the co
radii are not symmetric for pion pairs of different charges. For negative the
radius, integrated over the whole momentum spectrum, increases substan while
for positive pions the radius remains almost unchanged.Comment: 15 pages, 8 figures, 0.8 Mb, uses ljour2-macro, Submitted to Z. Phys.
A (1997
Hanbury-Brown--Twiss Analysis in a Solvable Model
The analysis of meson correlations by Hanbury-Brown--Twiss interferometry is
tested with a simple model of meson production by resonance decay. We derive
conditions which should be satisfied in order to relate the measured momentum
correlation to the classical source size. The Bose correlation effects are
apparent in both the ratio of meson pairs to singles and in the ratio of like
to unlike pairs. With our parameter values, we find that the single particle
distribution is too distorted by the correlation to allow a straightforward
analysis using pair correlation normalized by the singles rates. An analysis
comparing symmetrized to unsymmetrized pairs is more robust, but nonclassical
off-shell effects are important at realistic temperatures.Comment: 21 pages + 9 figures (tarred etc. using uufiles, submitted
separately), REVTeX 3.0, preprint number: DOE/ER/40561-112/INT93-00-3
Hbt Analysis of Anisotropic Transverse Flow
The effects of anisotropic transverse collective flow on the HBT correlation
function is studied. There exist three different physics contributions related
to flow which affect the correlation function: anisotropic source shape,
anisotropic space-momentum correlations in pion emission, and the effects
related to the HBT measurement of the size of a moving source in different
reference frames. Resolution of these contributions experimentally can lead to
a detailed understanding of both collective flow in nucleus-nucleus collisions
and the HBT technique itself. A method is presented which permits the
derivation of model independent relations between the radius of a source
measured in a frame in which it is moving and in its rest frame.Comment: latex, 16 pages, 1 figur
Testing the Resolving Power of 2-D K^+ K^+ Interferometry
Adopting a procedure previously proposed to quantitatively study
two-dimensional pion interferometry, an equivalent 2-D chi^2 analysis was
performed to test the resolving power of that method when applied to less
favorable conditions, i.e., if no significant contribution from long lived
resonances is expected, as in kaon interferometry. For that purpose, use is
made of the preliminary E859 K^+ K^+ interferometry data from Si+Au collisions
at 14.6 AGeV/c. As expected, less sensitivity is achieved in the present case,
although it still is possible to distinguish two distinct decoupling
geometries. The present analysis seems to favor scenarios with no resonance
formation at the AGS energy range, if the preliminary K^+ K^+ data are
confirmed. The possible compatibility of data with zero decoupling proper time
interval, conjectured by the 3-D experimental analysis, is also investigated
and is ruled out when considering more realistic dynamical models with
expanding sources. These results, however, clearly evidence the important
influence of the time emission interval on the source effective transverse
dimensions. Furthermore, they strongly emphasize that the static Gaussian
parameterization, commonly used to fit data, cannot be trusted under more
realistic conditions, leading to distorted or even wrong interpretation of the
source parameters!Comment: 11 pages, RevTeX, 4 Postscript figures include
Multi-boson effects and the normalization of the two-pion correlation function
The two-pion correlation function can be defined as a ratio of either the
measured momentum distributions or the normalized momentum space probabilities.
We show that the first alternative avoids certain ambiguities since then the
normalization of the two-pion correlator contains important information on the
multiplicity distribution of the event ensemble which is lost in the second
alternative. We illustrate this explicitly for specific classes of event
ensembles.Comment: 6 pages, three figures,submit to PR
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