Mean Impact Parameter Research Articles

Model independent reconstruction of impact parameter distributions for intermediate energy heavy ion collisions

We present a model independent method to reconstruct the impact parameter distributions of experimental data for intermediate energy heavy ion collisions, adapted from a recently proposed approach for ultra-relativistic heavy ion collisions. The method takes into account the fluctuations which are inherent to the relationship between any experimental observable and the impact parameter in this energy range. We apply the method to the very large dataset on heavy ion collisions in the energy range 20--100 MeV/nucleon obtained with the INDRA multidetector since 1993, for two observables which are the most commonly used for the estimation of impact parameters in this energy range. The mean impact parameters deduced with this new method for ``central'' collisions selected using typical observable cuts are shown to be significantly larger than those found when fluctuations are neglected, and as expected the difference increases as bombarding energy decreases. In addition, we will show that this new approach may provide previously inaccessible experimental constraints for transport models, such as an estimation of the extrapolated mean value of experimental observables for $b=0$ collisions. The ability to give more realistic, model independent estimations of the impact parameters associated with different experimental datasets should improve the pertinence of comparisons with transport model calculations which are essential to better constrain the equation of state of nuclear matter.

Glauber model for a small system using the anisotropic and inhomogeneous density profile of a proton

Recent studies reveal that at high energies, collisions of a small system such as $p+p$ gives signatures similar to that widely observed in heavy ion collisions hinting toward the possibility of forming a medium with collective behavior. With this motivation, we have used the Glauber model, which is traditionally applied to heavy ion collisions, in a small system using the anisotropic and inhomogeneous density profile of a proton and found that the proposed model reproduces the charged particle multiplicity distribution of $p+p$ collisions at LHC energies very well. Collision geometric properties such as the mean impact parameter, the mean number of binary collisions ($⟨{N}_{\mathrm{coll}}⟩$), and the mean number of participants ($⟨{N}_{\mathrm{part}}⟩$) at different multiplicities are determined. Having estimated $⟨{N}_{\mathrm{coll}}⟩$, we have calculated the nuclear modificationlike factor (${R}_{\mathrm{HL}}$) in $p+p$ collisions. We also estimated eccentricity and elliptic flow as a function of charged particle multiplicity using the linear response to the initial geometry.

The Proper Motion Field of the Small Magellanic Cloud: Kinematic Evidence for Its Tidal Disruption

Abstract We present a new measurement of the systemic proper motion of the Small Magellanic Cloud (SMC), based on an expanded set of 30 fields containing background quasars and spanning a ∼3 year baseline, using the Hubble Space Telescope (HST) Wide Field Camera 3. Combining this data with our previous five HST fields, and an additional eight measurements from the Gaia-Tycho Astrometric Solution Catalog, brings us to a total of 43 SMC fields. We measure a systemic motion of μ W = −0.82 ± 0.02 (random) ± 0.10 (systematic) mas yr−1 and μ N = −1.21 ± 0.01 (random) ± 0.03 (systematic) mas yr−1. After subtraction of the systemic motion, we find little evidence for rotation, but find an ordered mean motion radially away from the SMC in the outer regions of the galaxy, indicating that the SMC is in the process of tidal disruption. We model the past interactions of the Clouds with each other based on the measured present-day relative velocity between them of 103 ± 26 km s−1. We find that in 97% of our considered cases, the Clouds experienced a direct collision 147 ± 33 Myr ago, with a mean impact parameter of 7.5 ± 2.5 kpc.

CaII Quasar Absorbers: Statistics, Metals, Dust, and Associated Galaxies

AbstractWe summarize results from our recent SDSS survey for CaII quasar absorbers. The survey finds 435 absorbers at z<1.34, which corresponds to ~9 Gyrs of the Universe's history. Two CaII absorber populations are identified, which we call weak and strong. Metal abundance ratios derived from normalized composite spectra show that weak absorbers can be identified with halo-like gas, while strong absorbers are a mix of halo+disk-like gas. Consistent with these abundance ratio results, fluxed composites show that strong absorbers are ~6 times more reddened than weak absorbers (i.e., they contain more dust). Four individual examples of galaxies associated with CaII absorption are found in the SDSS images, and three are star forming galaxies (SFGs). Image composites show that galaxies associated with strong absorbers have mean luminosity-weighted impact parameters, b, which are ~2.4 times smaller than the weak absorbers (bstrong ~ 19 kpc versus bweak 45 kpc). Studies of CaII absorbers suggest links to molecular clouds, SFGs, and circumgalactic gas (CGG).

Centrality dependence of the thermal excitation-energy deposition in 8–15 GeV/chadron-Au reactions

The excitation energy per residue nucleon (${E}^{*}/A$) and fast and thermal light particle multiplicities are studied as a function of centrality defined as the number of grey tracks emitted ${N}_{\mathrm{grey}}$ and by the mean number of primary hadron-nucleon scatterings ($\ensuremath{\langle}\ensuremath{\nu}\ensuremath{\rangle}$) and the mean impact parameter ($\ensuremath{\langle}b\ensuremath{\rangle}$) extracted from it. The value of ${E}^{*}/A$ and the multiplicities show an increase with centrality for all systems, 14.6 GeV p-Au and 8.0 GeV \ensuremath{\pi}-Au and $\overline{\mathrm{p}}$-Au collisions, and the excitation energy per residue nucleon exhibits a uniform dependence on ${N}_{\mathrm{grey}}$.

K-band imaging of strong Ca II-absorber host galaxies at z 1

We present K-band imaging of fields around 30 strong Ca ii absorption-line systems, at 0.7 < z < 1.2, three of which are confirmed damped Lyman α systems. A significant excess of galaxies is found within 6.0 arcsec (≃50 kpc) from the absorber line of sight. The excess galaxies are preferentially luminous compared to the population of field galaxies. A model in which field galaxies possess a luminosity-dependent cross-section for Ca ii absorption of the form (L/L*)0.7 reproduces the observations well. The luminosity-dependent cross-section for the Ca ii absorbers appears to be significantly stronger than the established (L/L*)0.4 dependence for Mg ii absorbers. The associated galaxies lie at large physical distances from the Ca ii-absorbing gas; we find a mean impact parameter of 24 kpc (H0= 70 km s−1 Mpc−1). Combined with the observed number density of Ca ii absorbers the large physical separations result in an inferred filling factor of only ∼10 per cent. The physical origin of the strong Ca ii absorption remains unclear, possible explanations vary from very extended discs of the luminous galaxies to associated dwarf galaxy neighbours, remnants of outflows from the luminous galaxies, or tidal debris from cannibalism of smaller galaxies.

Detection of Lyman-α emission from a DLA galaxy: Possible implications for a luminosity-metallicity relation at z = 2–3

In an ongoing programme to identify a sample of high z DLA galaxies we have found the long sought for of aL yα emitter seen in the centre of a broad DLA trough. This is the predicted textbook case of an intervening DLA galaxy if DLA galaxies are small, but would not be expected if intervening high redshift DLA galaxies have large gaseous disks. The Lyα flux is 5.4 +2 −0.8 × 10 −17 erg s −1 cm −2 similar to what has been found in previously known high z DLA galaxies. The impact parameter is found to be 0. �� 3 ± 0. �� 3. This is smaller than what was found in previous cases but still consistent with random sight- lines through absorbers with mean impact parameter ≈1 �� . Of the 24 DLAs targeted in the NICMOS imaging survey five have now been identified as Lyα emitters. The DLA galaxies with detected Lyα emission tend to have higher interstellar metallicities than those with undetected Lyα emission. This is plausibly explained as a consequence of a positive correlation between the Lyα line luminosities of the galaxies and their metallicities, although the present sample is too small for a definitive conclusion. The available observations of high-redshift DLA galaxies are also consistent with a negative correlation between Lyα equiv- alent widths and metallicities, as seen in nearby star-forming galaxies and usually attributed to the preferential absorption of Lyα photons by dust grains.

Collisional Dynamics of Stellar Systems in the Northern and Southern Coalsack Regions

The visual interstellar extinction in the Northern and Southern Coalsack regions is estimated from a photographic survey of proper motion and B, V photometry of 6 × 104 stars as faint as apparent magnitude 14 over a field of view of 6° × 6° in each region. Each cloud is located at a distance of about 160 ± 50 pc from the Sun and exceeds the mean interstellar extinction by more than 0.7 ± 0.1 mag. Galactic plane orbits of 103 stars located at the same distance of 160 ± 50 pc from the Sun in these regions show a semimajor axis of 8.45 ± 0.15 kpc and a mean inclination of 03 ± 02 over the Galactic plane, suggesting a mean impact parameter of 9 ± 3 pc with diffuse clouds of relative velocity on the order of 4 ± 1 km s-1. The weak distant encounter of stars with the cold neutral medium can be explained by a mean mass of about 2500 ± 1250 M⊙ for the gas and dust content in order to account for the diffusion of stellar orbits. A mean displacement of 0012 ± 0001 yr-1 of the western limb of the Southern Coalsack is estimated in the northwest direction and permits a search for strong close stellar encounters. The transfer of angular momentum between the interstellar medium and the scattering of stellar orbits resulting from the encounters suggests a dissipation rate of (2.0 ± 0.7) × 10-4 M⊙ yr-1, leading to an equipartition time of 12 ± 4 Myr. A spin rate of 0.25 ± 0.05 km s-1 pc-1 of the diffuse clouds in the Southern Coalsack is measured and interpreted as the result of the perturbation induced by stellar systems during flyby encounters with a crossing time of 3 Myr, suggesting a cloud core radius of 1 pc.

Correction terms and approximations for atom location by channelling enhanced microanalysis

A theory for X-ray emission from crystals, when subjected to electron beam irradiation under dynamical electron diffraction conditions, is used to derive correction terms which account for differences in measured responses from atoms due to variations in delocalization and X-ray absorption. The (e,2e) interaction kernel, involving ionization of target atoms within the lattice, is modelled using Hartree–Fock atomic bound-state wavefunctions. Incoherent channelling patterns are calculated for Al K-shell as well as Co K- and L-shell emissions from beta phase AlCo for a 250 keV electron beam and compared with experiment. This theory enables a correction factor G s to be defined for each orientation s, facilitating an exact implementation of statistical ALCHEMI (atom location by channelling enhanced microanalysis), referred to as Model A. Various levels of approximation are then applied to this exact model and compared with previous implementations of ALCHEMI analysis. In a first approximation (Model B), an averaged correction factor G is used to calculate an offset constant C for the overall fit between dopant and host atom responses, and G is used to extract relative partitioning from the fitted parameters. The next approximation, Model C, allows the offset constant to be determined from the fitting procedure itself. The last Model D has no correction terms in the fitting procedures. Experimental data were found to have sufficient systematic error that it was not useful to assess accurately the differences between these models. Thus pseudodata were used to investigate both precision and goodness of fit parameter for these models for ALCHEMI. The effect of increasing X-ray detection times (and hence decreasing relative levels of statistical noise) was considered. The theory also yields a measure of ionization delocalization from first principles, and we find the mean impact parameter for Co L-shell ionization to be about twice that derived from the previous semiclassical estimates.

Are Pressure-Confined Clouds in Galactic Halos Possible Models of Lyman Alpha Clouds?

Our understanding of the Lyα forest has changed considerably following observations by HST and Keck. Lyα clouds at low redshifts (z &lt; 1.7) observed by HST showed two unexpected features: Lanzetta et al. (1995) found that most luminous galaxies at such redshifts produce Lyα absorptions at mean impact parameter ~160h−1kpc, and established the association between Lyα clouds and galaxies. Ulmer (1996) pointed out the strong clustering of Lyα clouds in this redshift range. Motivated by the above, we propose a two-component protogalaxy model for the Lyα clouds based upon our previous work (Miyahata &amp; Ikeuchi 1995). In our model, the Lyα clouds are stable cold clouds confined by the pressure of ambient hot gas in a galactic halo. We determine the properties of these cold clouds and hot gas on the basis of theoretical and observational constraints. We take into account the stability of a cold cloud in the galactic halo in addition to the general stability conditions in a two-component medium (e.g. Ikeuchi &amp; Ostriker 1986), and compare the derived quantities of Lyα clouds in the galactic halo and in the intergalactic medium at both high and low redshifts. We conclude that the ciondition that a cloud is stable against both evaporation and tidal disruption by a hot galactic halo is very restrictive. In the most noteworthy example at z ~ 0.5, a pressure-confined, stable spherical Lyα cloud with NHI = 1014cm−2 cannot survive in the galactic halo, although much higher column density clouds of NHI = 1017cm−2 can. Miyahata &amp; Ikeuchi (1997) discuss how these results constrain an alternative model for Lyα clouds associated with the galaxies observed by Lanzetta et al. (1995).

Nucleus-nucleus collision as superposition of nucleon-nucleus collisions

Angular distributions of charged particles produced in 16O and 32S collisions with nuclear track emulsion were studied at momenta 4.5 and 200 A GeV/c. Comparison with the angular distributions of charged particles produced in proton-nucleus collisions at the same momentum allows to draw the conclusion, that the angular distributions in nucleus-nucleus collisions can be seen as superposition of the angular distributions in nucleon-nucleus collisions taken at the same impact parameter b NA , that is mean impact parameter between the participating projectile nucleons and the center of the target nucleus

Shape of collective flow in highly central Au(150 A MeV)+Au collisions

Using the FOPI facility at GSI, charged particles (1 ≤Z≤6) produced in the Au(150 A MeV)+Au reaction have been measured at laboratory angles 1.20 < Θlab < 300. Highly central collisions have been selected with two criteria, both dealing with the longitudinal and transverse degrees of freedom of the reaction. The relevance of this selection method is supported by QMD calculations which indicate that such criteria are able to select mean impact parameters less than 2 fm. Bias effects introduced by the criteria have been evaluated. The centre-of-mass polar angle distributions of low energy clusters emitted in these central collisions, have been extracted: the intensity ratio deduced for a transverse to longitudinal emission is found to be R= 1.4 −0.4 +0.2 . Model comparisons using QMD are presented. The value of R appears to depend sensitively on the nucleon-nucleon cross section, σnn. Within this model, a value of σ=25+ - 5 mb is derived.

Determination of mean energies and impact parameters characteristic of charge-changing reactions.

Measurements are reported of mean energies of argon recoil ions produced by beams of 23-MeV ${\mathrm{Cl}}^{5+,8+,10+}$ or 19-MeV ${\mathrm{F}}^{9+}$, and of neon recoil ions produced by beams of 22-MeV ${\mathrm{Cl}}^{4+}$, detected in coincidence with the charge-changed outgoing projectile. A screened-elastic-Coulomb-scattering calculation permits estimation of impact parameters characteristic of each pair (q,r) of final projectile- (q) and recoil- (r) ion charge states. The results are found to be in good agreement with impact parameters deduced from measured cross sections and do not require measurement of projectile scattering angle.

New connections between increasing and fluctuating mean transverse momentum and impact parameter at the CERN collider and ISR

The new observations of increasing mean transverse momentum for the bulk of produced particles with increasing multiplicity, and of nonstatistical fluctuations in the mean transverse momentum per event, are related through the mean squared impact parameter as a function of the number of produced particles, and its fluctuations.

Study of the 2p 1/2 ? excitation probability in collision systems withZ 1+Z 2&gt;150 using line width analysis

The 90°-line width ofK x-ray lines induced in heavy ion collisions is mainly determined by the kinematical broadening. Its conversion into mean impact parameters together with total excitation cross section allows to obtain mean excitation probabilities. Within the energy range (1.4–5.9) MeV/u mean excitation probabilities for 2p1/2σ-excitation are deduced. Collision systems in theZ-range (150–180) are investigated. A very poor agreement between experiment and theoretical predictions has been found. The excitation probabilities are larger than predicted and are nearly independent of the atomic numberZ of the united atom. The collision energy dependence is much weaker than predicted. Even a decrease of the mean excitation probabilities at high collision energies has been found.

Classical relativistic trajectory method and application to the K-shell ionisation in U-U collisions

The classical trajectory method of Abrines and Percival (1966) has been extended to relativistic velocities of the charged particles. The method is based on the solution of the classical relativistic Hamilton equations of motion for a three-body system consisting of a target nucleus, a charged projectile and a single electron. The electromagnetic fields are taken to be of Lienard-Wiechert type with extended charges of the nuclei. The theory has been applied to calculate the cross section, mean impact parameter and angular distribution for the ionisation of a singly occupied K shell in U-U collisions at Elab=1 and 10 GeV/n.

A tool for spectroscopy of super-heavy quasimolecules (Z 1+Z 2&gt;137) the Bang-Hansteen scaling rule

From 90° line width analysis ofKα1 lines excited in very heavy ion-atom collisions (Z1 +Z2>137) mean impact parameters for the ionization probability are derived. The experimental mean impact parameters are shown to obey the Bang-Hansteen scaling rule¯bE(R)=C · ħv correlating the minimum momentum transferE(R)/v and the mean impact parameterb. Theoretical values of the constantC are (0.8±0.1) for 2p1/2σ excitation and (1.0±0.1) for 1sσ excitation in the rangeZ1+Z2=140–160. It is proposed to apply the scaling rule as a spectroscopic tool to study the 1sσ and 2p1/2σ levels in superheavy quasimolecules. The need of a sound theoretical base justifying the application of the scaling rule is emphasized.

Probability of forming 1s σ vacancies in 625 MeV Xe + Au, Pb, Bi, and Th collisions at small impact parameters

Probabilities of forming 1sσ vavancies in 625 MeV 136Xe + Au, Pb, Bi, and Th encounters were measured at mean impact parameters of 15–20 fm and found to be (3–4) × 10 −2. This is of the same order of magnitude as computed by Soff et al.

Spin effects in overlap calculations

The influence of the spins of produced particles on estimates of the mean impact parameter of multiparticle production is studied. First we present a simple model yielding strong effects, comparable to the ones in typical inelastic two-body reactions. After this we ask whether, as in the two-body case, exact non-trivial estimates using experimental data are possible. It is argued that this is very unlikely, even with perfect data.

Corrections for Small Values of the Logarithm Term in the Electrical Conductivity of a Fully Ionized Plasma

Correction factors which extend the range of validity of expressions for the electrical conductivity of a fully ionized gas to small values of the logarithm of the ratio of the Debye length to the mean impact parameter for a 90° deflection are developed and compared.