Cascade Calculations Research Articles

Expanding quark-gluon plasmas: Transverse flow, chemical equilibration, and electromagnetic radiation

We investigate the chemical equilibration of the parton distributions in collisions of two heavy nuclei. We use initial conditions obtained from a self-screened parton cascade calculation and, for comparison, from the HIJING model. We consider a one-dimensional as well as a three-dimensional expansion of the parton plasma and find that the onset of the transverse expansion impedes the chemical equilibration. At energies of 100 GeV/nucleon, the results for one-dimensional and three-dimensional expansions are quite similar except at large values of the transverse radius. At energies of several TeV/nucleon, the plasma initially approaches chemical equilibrium, but then is driven away from it, when the transverse velocity gradients develop. We find that the total parton multiplicity density remains essentially unaffected by the flow, but the individual concentrations of quarks, antiquarks, and gluons are sensitive to the transverse flow. The consequences of the flow are also discernible in the transverse momenta of the partons and in the lepton pair spectra, where the flow causes a violation of the so-called ${M}_{T}$ scaling.

Many-body cascade calculation for photonuclear reactions

Abstract In the present work we show some results for the pion multiplicity in photon-nucleus reactions at the high energy range (0.5–1.5 GeV). We have noticed that many-body cascade approach introduced here provides a strong change in the pion multiplicity and in the excitation energy of the residual nuclei, as compared with the conventional one-body cascade results for photonuclear reactions. These are the relevant ingredients to the initial configuration of the compound nucleus in the evaporation phase of the reaction. We expect that future experimental data using monochromatic beams in the high energy range will be able to discern the most appropriate model to treat the rapid phase of the photonuclear reaction.

Metastability of the Muonic Boron2SState

The cascade of muonic boron and the two-photon decay $2S\ensuremath{\rightarrow}1S$ have been investigated. The x-ray measurement with Ge and Si(Li) detectors was performed at low target gas pressures of pure ${\mathrm{B}}_{2}{\mathrm{H}}_{6}$ and admixtures with He. The $2S$ population of $\ensuremath{\mu}\mathrm{B}$ is found to be ${\ensuremath{\epsilon}}_{2S}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3.1(2)%$. Cascade calculations indicate that more than half of the $2S$ states are populated with an empty electron shell. Two-photon decays have been observed in mixtures of ${\mathrm{B}}_{2}{\mathrm{H}}_{6}$ in He at partial diborane pressures of 67 Pa and below. The measured fraction of metastable $2S$ states per $\ensuremath{\mu}\mathrm{B}$ atom is 0.58(16)% in an admixture of 1% ${\mathrm{B}}_{2}{\mathrm{H}}_{6}$ in He at 6.7 kPa and is interpreted in terms of pressure dependent quenching.

Attractive interaction potentials and the binary collision approximation

The binary collision approximation (BCA) is applied to interatomic potentials with an attractive region surrounding a repulsive core. The evaluation of the collision apsis is modified and the time integral is reformulated. A new program, TABULA, was developed to study different formulations of the BCA and methods of numerical quadrature and to tabulate the scattering integrals and related quantities. TABULA is illustrated by calculations for Molière and Morse potentials. These show the new time integral equation to be more accurate than the older one. The modifed BCA was installed in a new version of MARLOWE. The increased accuracy reduces the lengths of replacement sequences. Attractive potentials are illustrated by cascade calculations in Au with similar Molière and Morse potentials. The results show systematic differences related to differences in the potentials and in the kinematics of collisions.

Heating nuclei with high-energy antiprotons

The distributions of thermal energy generated in different target nuclei by means of the annihilation of antiprotons onto their surfaces have been investigated. The results confirm that fairly hot nuclei are produced in this approach, as predicted by Intra-Nuclear Cascade calculations. Although the transition towards multifragmentation as the primary decay channel is not observed, these data should allow to pin down the decay patterns of hot nuclei with little excitation of their collective degrees of freedom. In turn this may shed new light on the mechanisms responsible for some events associated with high fragment multiplicities as observed in heavy-ion collisions.

What have we learned from antiproton proton scattering?

From recent charge exchange measurements in the extreme forward direction, an independent and precise determination of the pion nucleon coupling constant is possible. This determination has reopened the debate on the value of this fundamental coupling constant of nuclear physics. Precise measurements of charge exchange observables at forward angles below 900 MeV/c would also give a better understanding of the long range part of the two-pion exchange potential. For example, the confirmation of the coherence of the tensor forces from the pion exchange and the isovector two-pion exchange would be very valuable. With the present data first attempts at an $\NbarN$ partial wave analysis have been made where, as in nucleon nucleon scattering, the antinucleon nucleon high J partial waves are mainly given by one-pion exchange. Finally a recent $\pbarp$ atomic cascade calculation and the fraction of P-state annihilation in gas targets is commented on.

Measurement of Neutron-Production Double-Differential Cross Sections for Nuclear Spallation Reaction Induced by 0.8, 1.5 and 3.0 GeV Protons

Neutron-production double-differential cross sections were measured for the spallation reaction induced by 0.8, 1.5 and 3.0GeV protons on C, Al, Fe, In and Pb targets. The experiments were performed by time-of-flight technique with a typical flight path length of 1 m, and the cross sections were obtained with energy resolutions better than 8% at neutron energies below 100MeV. The experimental data were compared with the results of calculation codes based on an intranuclear-cascade-evaporation model. Adoption of the in-medium effect on nucleon-nucleon cross section in the cascade calculation improves the agreement between the calculated results and experimental data particularly in the case of 0.8-GeV proton incidence. For protons above 1GeV, however, the calculations typically twice overestimate the cross sections in the emitted neutron energy region of 10 to 30MeV.

Effect of multiparticle collisions on pion production in relativistic heavy-ion reactions

In the present work we discuss the effect of N-body processes on pion multiplicity in relativistic heavy-ion reactions. This effect is analyzed in the energy range from the pion threshold up to 2 GeV/nucleon, for several projectile-target systems. The analysis is carried out in the context of intranuclear cascade calculations. It is shown that the inclusion of multibaryonic collisions is a crucial element in the study of the pion production mechanisms, being strongly dependent on the adopted correlation range for the particles involved in the N-body processes. {copyright} {ital 1997} {ital The American Physical Society}

Extended Hauser-Feshbach method for statistical binary decay of light-mass systems

An Extended Hauser-Feshbach Method (EHFM) is developed for light heavy-ion fusion reactions in order to provide a detailed analysis of all the possible decay channels by including explicitly the fusion-fission phase-space in the description of the cascade chain. The mass-asymmetric fission component is considered as a complex-fragment binary-decay which can be treated in the same way as the light-particle evaporation from the compound nucleus in statistical-model calculations. The method of the phase-space integrations for the binary-decay is an extension of the usual Hauser-Feshbach formalism to be applied to the mass-symmetric fission part. The EHFM calculations include ground-state binding energies and discrete levels in the low excitation-energy regions which are essential for an accurate evaluation of the phase-space integrations of the complex-fragment emission (fission). In the present calculations, EHFM is applied to the first-chance binary-decay by assuming that the second-chance fission decay is negligible. In a similar manner to the description of the fusion-evaporation process, the usual cascade calculation of light-particle emission from the highly excited complex fragments is applied. This complete calculation is then defined as EHFM+CASCADE. Calculated quantities such as charge-, mass- and kinetic-energy distributions are compared with inclusive and/or exclusive data for the $^{32}$S+$^{24}$Mg and $^{35}$Cl+$^{12}$C reactions which have been selected as typical examples. Finally, the missing charge distributions extracted from exclusive measurements are also successfully compared with the EHFM+CASCADE predictions.

Chemical equilibration of an expanding quark-gluon plasma

The chemical equilibration of the parton distribution in collisions of two heavy nuclei at the CERN large Hadron Collider is investigated. Initial conditions are obtained from a self-screened parton cascade calculation. The onset of transverse expansion of the system is found to impede the chemical equilibration. The system initially approaches chemical equilibrium, but then is driven away from it, when the transverse velocity becomes large.

Measurement of Neutron-Production Double-Differential Cross Sections for Nuclear Spallation Reaction Induced by 0.8, 1.5 and 3.0 GeV Protons.

Neutron-production double-differential cross sections were measured for the spallation reaction induced by 0.8, 1.5 and 3.0GeV protons on C, Al, Fe, In and Pb targets. The experiments were performed by time-of-flight technique with a typical flight path length of 1 m, and the cross sections were obtained with energy resolutions better than 8% at neutron energies below 100MeV. The experimental data were compared with the results of calculation codes based on an intranuclear-cascade-evaporation model. Adoption of the in-medium effect on nucleon-nucleon cross section in the cascade calculation improves the agreement between the calculated results and experimental data particularly in the case of 0.8-GeV proton incidence. For protons above 1GeV, however, the calculations typically twice overestimate the cross sections in the emitted neutron energy region of 10 to 30MeV.

Cascade calculation of hadronic hydrogen atoms

Cascade calculations of hadronic hydrogen atoms are performed to obtain the x-ray yields as a function of the target density. An extension of Leon-Bethe's Stark mixing rates to $m\ensuremath{\ne}0$ states is made without the introduction of the parameter ${k}_{\mathrm{STK}},$ which is necessary in the Borie-Leon model to enhance the Stark mixing rates. Although the energies of their L x rays are too low to observe, we can roughly estimate the 2p absorption width of pionic and kaonic hydrogen atoms from the measured K x-ray yields.

Computer simulation of the sputtering of polyatomic multilayered materials with consideration of the spatial overlapping of the collision cascades

The special dynamic computer code DYTRIRS for the simulation of the sputtering and modification phenomena in multilayered compound materials under high-fluence ion irradiation was developed on the basis of the Monte Carlo computer code TRIRS for the collision cascade calculation. In the computer simulation technique, the spatial overlap of ion-induced atomic collision cascades in a modified material are taken into account. This simulation technique was tried out on the specially grown multilayered structures. the results of the simulation of the sputtering phenomena of the Fe and Cu targets protected by carbon layer under high fluence ion irradiation are demonstrated.

Determination of nuclear friction in strongly damped reactions from prescission neutron multiplicities.

Nonfusion, fissionlike reactions in collisions of four heavy systems (well below the fusion extra-push energy threshold), for which Hinde and co-workers had measured the prescission neutron multiplicities, have been analyzed in terms of the deterministic dynamic model of Feldmeier coupled to a time-dependent statistical cascade calculation. In order to reproduce the measured prescission multiplicities and the observed (nearly symmetric) mass divisions, the energy dissipation must be dramatically changed with regard to the standard one-body dissipation: In the entrance channel, in the process of forming a composite system, the energy dissipation has to be reduced to at least half of the one-body dissipation strength (${\mathit{k}}_{\mathit{s}}^{\mathrm{in}}$\ensuremath{\le}0.5), and in the exit channel (from a mononucleus shape to scission) it must be increased by a factor ranging for the studied reactions from ${\mathit{k}}_{\mathit{s}}^{\mathrm{out}}$=4 to ${\mathit{k}}_{\mathit{s}}^{\mathrm{out}}$=12. These results are compared with the temperature dependence of the friction coefficient, recently deduced by Hofman, Back, and Paul from data on the prescission giant dipole resonance emission in fusion-fission reactions. The combined picture of the temperature dependence of the friction coefficient, for both fusion-fission and nonfusion reactions, may indicate the onset of strong two-body dissipation already at a nuclear temperature of about 2 MeV. \textcopyright{} 1996 The American Physical Society.

Multiplicities in84Kr interactions in emulsion at 800–950 MeV/nucleon

Inelastic interactions induced by84Kr nuclei at 800–950 MeV/nucleon have been studied using a high angular resolution emulsion detector. Data on multiplicities of the produced particles, projectile and target fragments are shown. Comparisons with cascade calculations have been performed.

S- and P-state annihilation in p interactions at rest

Two body branching ratios for pp annihilation at rest are used to calculate the fraction of P-state annihilation as a function of target density. In the presence of Stark mixing it is necessary to take into account an enhancement of annihilations from fine structure states over that expected from a statistical population. The enhancement factors are obtained using an atomic cascade calculation which fits available pp atom X-ray measurements.

Reaction mechanisms in 12C( gamma,pp) near 200 MeV.

Inclusive $^{12}\mathrm{C}(\ensuremath{\gamma}, pp)$ cross sections have been measured with tagged photons in the range ${E}_{\ensuremath{\gamma}}=187\ensuremath{-}227$ MeV using the Saskatchewan-Alberta Large Acceptance Detector (SALAD). The large angular acceptance allowed the measurement of noncoplanar $\mathrm{pp}$ emission. The cross sections were compared to a Monte Carlo intranuclear cascade calculation. Agreement was reasonable for the shapes of the cross sections but the calculated total cross section was 3.9 times larger than the data.

Negative-pion capture process and its chemical effects in some hydrocarbons.

A negative-pion capture process for several kinds of hydrocarbons was studied by the simultaneous observation of low-energy pionic x rays and ${\mathrm{\ensuremath{\pi}}}^{0}$ decays following the nuclear capture of pions by hydrogen. We measured the pionic x-ray intensity pattern and the pion-capture probabilities of constituent carbon and hydrogen. The x-ray intensity pattern depends on the chemical environment; a cascade calculation showed that this can be qualitatively attributed to the effects of a pion transfer from hydrogen. The pion-capture probabilities on hydrogen could be explained by a combined model involving a modified large mesomolecular model and an external transfer process. The external transfer parameter of the pion from a pionic hydrogen atom to carbon atoms was deduced to be ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{C}}$=1.7\ifmmode\pm\else\textpm\fi{}0.2 based on the results for a series of alkanes in the condensed phase. The large difference between the pion-capture probabilities on hydrogen observed in alkanes and that in benzene can be well understood based on the proposed model. \textcopyright{} 1996 The American Physical Society.

On the Optimal Control Method for Airfoil and Cascade Analysis

In solving the full potential equation, the least-squares technique proposed by Glowinski, Periaux, and Pironneau [in Finite Elements in Fluids, Vol. 3, R. Gallagher, ed., John Wiley and Sons, 1976] provides a robust and efficient approach. In this paper, this approach is investigated and a new algorithm is proposed. In particular, the upwind density technique is used instead and a very effective way of handling the circulation is proposed. The whole approach is then extended for cascade calculations.

Photon splitting in soft gamma repeaters

The exotic quantum process of photon splittingϒ →ϒϒ has great potential to explain the softness of emission in soft gamma repeaters (SGRs) if they originate in neutron stars with surface fields above the quantum critical fieldB cr = 4.413×1013 Gauss. Splitting becomes prolific at such field strengths: its principal effect is to degrade photon energies, initiating a cascade that softens gamma-ray spectra. Uniform field cascade calculations have demonstrated that emission could be softened to the observed SGR energies for fields exceeding about 1014 Gauss. Recently, we have determined splitting attenuation lengths and maximum energies for photon escape in neutron star environments including the effects of magnetospheric dipole field geometry. Such escape energies εesc suitably approximate the peak energy of the emergent spectrum, and in this paper we present results forε esc as a function of photon emission angles for polar cap and equatorial emission regions. The escape energy is extremely insensitive to viewing perspective for equatorial emission, arguing in favour of such a site for the origin of SGR activity.