Cascade Calculations Research Articles

Moment method in the theory of cascade-process fluctuations

A method for calculating the fluctuations and correlations in cascade processes is outlined, on the basis of deriving random cascade curves from their spatial (longitudinal) moment. The method reduces the problem of calculating cascade fluctuations in a homogeneous medium to calculating the covariational matrix of random moments, depending only on the energy variable. The set of elements of this matrix allows the fluctuations and core correlations of any track characteristics of the cascade to be calculated. The method is intended for calculations of high-energy cascades, when the influence of fluctuations of high-order longitudinal moments (n ≧ 5) may be neglected.

Hadronic Event Generation for Hadron Cascade Calculations and Detector Simulation — Part IV: The Application of the Intranuclear Cascade Model to Reactions of Pions, Nucleons, Kaons, and Their Antiparticles with Nuclei Below 6 GeV/c

An extension of the intranuclear cascade model is described. The primary hadrons may be pions, kaons, nucleons, and their antiparticles. Secondary particles produced include hyperons or anti-hypero...

Production and Interaction of High Energy Neutrinos in Close X-ray Binaries

Reports of air showers with E > 1015 eV from Cygnus X-3, LMC X-4, Vela X-1 and Hercules X-1 have been interpreted as requiring production of neutral secondaries by cosmic rays accelerated by the compact partner in these systems. If neutral pions are the source of photons that produce the observed air showers, then charged pions must also be produced, and they will give rise to neutrinos. We consider limits that may be placed on binary systems like Cygnus X-3 in which a neutron star is a strong source of ultra-high energy (UHE) particles that produce photons, neutrinos and other secondary particles in the companion star through nuclear interactions. The highest energy neutrinos (> 1 TeV), which have the largest interaction cross sections, are absorbed deep in the companion. From a detailed numerical calculation of the hadronic cascade induced in the atmosphere of the companion star, we estimate the neutrino production spectrum from an isotropic flux of monoenergetic 1017 eV protons and we estimate the resulting neutrino absorption in the stellar core. In the case of Cyg X-3 and LMC X-4, the cosmic-ray luminosities required to produce the observed gamma rays would result in energy deposition from neutrino absorption exceeding the intrinsic stellar luminosity of the companion. Over a timescale of 104−105 yr, the star would absorb its own binding energy and be disrupted. On shorter timescales, the energy deposition will cause significant expansion of the star, perhaps leading to quenching of high-energy signals from the source. From these results, we conclude that systems requiring intense UHE proton fluxes are either very young or the companion star is not the site of observed gamma-ray production. Alternatively, if the gamma-ray source is highly variable, the proton flux requirements would be lower, providing some relaxation of the above constraints.[See Gaisser et al. 1986, Ap. J. (Oct. 15), in press].

Double-differential inclusive hydrogen and helium spectra from neutron-induced reactions at 27.4, 39.7, and 60.7 MeV: Oxygen and nitrogen.

Double-differential cross sections for the neutron-induced production of p, d, t, $^{3}\mathrm{He}$, and alpha particles from oxygen and nitrogen have been measured using an unpolarized neutron facility. Neutron beam energies of 27.4, 39.7, and 60.7 MeV were used. The charged particle energy spectra, at six forward laboratory angles, 15, 20, 35, 40, 45, and 65, and, where feasible, at three backward angles, 90, 130, and 150 deg, range up to the kinematic maximum, from a typical low-energy cutoff of 4 MeV for p, d, t, and alpha particles, and 8 MeV for $^{3}\mathrm{He}$. Intranuclear cascade plus deexcitation calculations were carried out. The data are compared with these calculations and with available proton-induced (charge-symmetric) reaction spectra for oxygen.

200-MeV- pi +-induced single-nucleon removal from 24Mg.

Nuclear \ensuremath{\gamma} rays in coincidence with outgoing pions or protons following single-nucleon removal from $^{24}\mathrm{Mg}$ by 200-MeV ${\ensuremath{\pi}}^{+}$ have been detected with Ge(Li) detectors. Differential cross sections are reported for \ensuremath{\gamma} rays from the first excited mirror states of $^{23}\mathrm{Na}$ and $^{23}\mathrm{Mg}$ in coincidence with positive pions or protons detected in particle telescopes at 30\ifmmode^\circ\else\textdegree\fi{}, 60\ifmmode^\circ\else\textdegree\fi{}, 90\ifmmode^\circ\else\textdegree\fi{}, 120\ifmmode^\circ\else\textdegree\fi{}, and 150\ifmmode^\circ\else\textdegree\fi{}; angle-integrated absolute cross sections and cross section ratios \ensuremath{\sigma}${(\mathrm{}}^{23}$Mg)/\ensuremath{\sigma}${(\mathrm{}}^{23}$Na) are calculated. These results are compared with the predictions of a Pauli-blocked plane-wave impulse approximation and the intranuclear cascade and nucleon charge exchange reaction models. The plane-wave impulse approximation and the intranuclear cascade calculations generally agree with the angular dependence of the experimental results but not the absolute magnitude. The nucleon charge exchange calculation does not reproduce the observed cross section charge ratios.

Effects of high-energy neutrino production and interactions on stars in close X-ray binaries

Limits are discussed that may be placed on binary systems in which a compact partner is a strong source of high-energy particles that produce photons, neutrinos, and other secondary particles in the companion star. The highest energy neutrinos are absorbed deep in the companion and the associated energy deposition may be large enough to affect its structure or lead to its ultimate disruption. This neutrino heating is evaluated, starting with a detailed numerical calculation of the hadronic cascade induced in the atmosphere of the companion star. For some theoretical models, the resulting energy deposition from neutrino absorption may be so great as to disrupt the companion star over a time scale of 10,000-100,000 yr. Even if the energy deposition is smaller, it may still be high enough to alter the system substantially.

A Method for Transonic Inverse Cascade Design With a Stream Function Equation

A new profile design method is developed on the basis of [1–3] for transonic flow. The rotational dynamic stream function equation, which is expressed in functional form using calculated coordinates, is deduced. This method can be used for the calculation of cascade and S1 stream surface of a transonic flow with a local shock wave on the blade suction surface. This method consists of two parts: an inverse method with a given velocity distribution along the suction surface and a given thickness distribution; and an inverse method with given velocity distributions on suction and pressure surfaces. Using this method it is easy to obtain a blade profile with prescribed velocity and thickness distributions. The design of optimal profile may then be done with the calculated optimal velocity distribution on the blade surface. The rotational condition is satisfied when the stream function equation is adopted with the entropy term. If the compatibility condition can be fulfilled between the S1 and S2 equations, the iterative calculations of two kinds of stream surfaces in three-dimensional flow will be convergent. In this paper a unique value of density can be determined from the known stream function value. The computational program is written with this method and several transonic examples have been calculated. These results are quite good.

Target residue cross sections and recoil energies from the reaction of 1760 MeV 40Ar with medium and heavy targets

Cross sections and recoil range measurements of the rare-earth isotones ( N = 84–85) formed in 40Ar induced reactions at E lab = 1.76 GeV have been performed. An electrostatic collection method associated to a gas flow transport was used. The various experimental results plead in favor of an origin of these residues in the decay of highly excited precursors. Such excited precursors can be explained by an incomplete fusion mechanism. Comparisons with existing theoretical models (an extended abrasion-ablation model and intranuclear cascade calculations) have been performed.

Modelling ion-assisted deposition of CeO2 films

The theory presented explains quantitatively the experimentally observed increase in film density of a vapor-deposited CeO2 film when bombarded during growth with low-energy O 2 + ions. The density enhancement is expressed in terms of the yields for recoil implantation of surface atoms, ion incorporation and sputtering, which have been determined by employing a three-dimensional Monte Carlo cascade calculation. Ion-to-vapor flux ratios between 0 and 1.4 and O+ ion energies between 25 and 600 eV have been examined. The density shows an almost linear increase with the ratio of ion-to-vapor fluxes. An optimum O+ ion energy for densification is found at about 200 eV which is in agreement with experiment.

A short review of Monte Carlo hadronic cascade calculations in the multi-TeV energy region

Studies of a number of design problems of high energy proton accelerators are often carried out using Monte Carlo simulations of hadronic and electromagnetic cascades. This paper reviews results obtained using three computer programs which are compatible with the design problems of multi-TeV accelerators. Comparisons of the results obtained using these codes are made with each other and, where possible, with existing experimental data. Rather good agreement is typically found.

Subthreshold negative pions and energetic protons produced at θcm = 90° in 246 MeV/nucleon 139La+ 139La collisions

The inclusive cross section for subthreshold negative pions and high energy protons produced at θ cm = 90° has been measured for 139La+ 139La at 246 MeV/nucleon. The spectrum of negative pions exhibits no bump or sharp break as has been suggested by theoretical speculation on the formation of a pionic instability in central nucleus-nucleus collisions. The measured spectra for both pions and protons are compared with results of a phase space model and an intranuclear cascade calculation.

Pion absorption on nuclei at 65 MeV.

Proton-proton and proton-neutron angular correlations as well as proton and deuteron inclusive spectra from pion absorption on C, Al, Cu, and Ta were measured at ${T}_{\ensuremath{\pi}}$=65 MeV. We compared the results with the prediction of the intranuclear cascade model, assuming that pion absorption proceeds only through two-nucleon absorption processes. The differential cross sections of the (${\ensuremath{\pi}}^{+}$,p) and (${\ensuremath{\pi}}^{+}$,pp) reactions were fairly well reproduced by the calculation in a wide angular range. Ratios R of the pion absorption cross section on a pn pair to that on a pp or nn pair, were in agreement between the inclusive and exclusive measurements for C and Al, but for Cu, the inclusive measurement gave a smaller R value. The internuclear cascade calculations for the (${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$,pn) and (${\ensuremath{\pi}}^{\mathrm{\ensuremath{-}}}$,pp) reactions revealed the importance of the pion charge exchange process before absorption, even at ${T}_{\ensuremath{\pi}}$=65 MeV.

A quasi three‐dimensional inverse design method using source and vortex integral equations

AbstractAn integral equation method is presented for the quasi three‐dimensional inverse aerofoil and cascade design. Fluid compressibility and vorticity diffusion are introduced by means of sources resp. distribution functions for the boundary vortices. Application of a Taylor development to the kinematical condition, enlarged by an additional source term, leads to a linear equation system for the profile shape and the channel height. Thus, both the velocity distribution and the profile thickness can be prescribed. Several calculations of aerofoil sections and cascades are presented, which illustrate the accuracy and possibilities of the method.

Calculations of Two and Three-Dimensional Transonic Cascade Flow Fields Using the Navier-Stokes Equations

The multidimensional, ensemble-averaged, compressible, time-dependent Navier-Stokes equations have been used to study the turbulent flow field in two and three-dimensional turbine cascades. The viscous regions of the flow were resolved and no-slip boundary conditions were utilized on solid surfaces. The calculations were performed in a constructive ‘O’-type grid which allows representation of the blade rounded trailing edge. Converged solutions were obtained in relatively few time steps (∼ 80–150) and comparisons for both surface pressure and heat transfer showed good agreement with data. The three-dimensional turbine cascade calculation showed many of the expected flow-field features.

Antiproton annihilations in nuclei may not produce high nuclear temperatures

Detailed intranuclear cascade calculations are presented which indicate that significant thermalization of the energy released during antiproton annihilations in nuclei does not occur. The exponential tails of the nucleon kinetic energy distributions, dentified by some authors as corresponding to high nuclear temperatures, are shown to be the direct result of the dynamics of the pion-nucleon cascade subsequent to the annihilation, and do not imply a substantial of a large fraction of the nuclear medium.

Intensity patterns of pionic X-rays emitted from simple molecules

Intensity patterns in the Balmer series of pionic X-rays emitted from carbon and oxygen in simple molecules are reported and analysed using a cascade code. It is shown that modifications are needed in the angular momentum distribution at the beginning of the cascade calculation in order to fit the data.

Linear momentum transfer in 40-150 MeV proton-induced reactions with 238U.

Angular correlations between coincident fission fragments have been measured for 40-, 90-, and 150-MeV proton-induced reactions on a /sup 238/U target. From these data linear momentum transfer distributions have been derived, which are then compared with other results for protons and more complex projectiles. On a per nucleon basis, protons exhibit the largest average linear momentum transfer values of any projectile over the energy range from E/A = 40 to 1000 MeV. This can be understood in terms of fundamental scattering cross sections, and is qualitatively demonstrated by intranuclear cascade calculations. Both cascade and precompound decay calculations reproduce the linear momentum transfer distributions with moderate success.

Entropy evolution in heavy ion collision.

The entropy evolution in heavy ion collisions is investigated by means of a cascade model study. The method for calculating the entropy is based on a smoothing over the momentum space by introducing a local temperature field. It is shown that the resulting specific entropy is rather sensitive to the proper choice of the phase space subdivision at the disassembly stage of the collision. Compared to recent results for specific entropy values inferred from the composite particle yield of 4..pi.. measurements, it is found that the cascade calculations do not favor other model treatments, but as a trend we obtain smaller entropy values than following from conventional considerations within equilibrium statistics.

Calculation of the displacement peaks in the continuum approximation

A method of numerical modeling of displacement peaks (DP) in the gas-dynamic approach is described and results are presented. It is assumed in the calculation that the radiation damage is completely localized in the DP, and the losses in electronic excitation are extremely small. Modeling of DP evolution in a solid with the Gruneisen parameter characteristic of copper and aluminum is taken as the basic calculation. Density, temperature and pressure distributions are analyzed. The great economy of computational work in comparison with atomistic calculations of cascades by the method presented here is a definite advantage of the model. It opens up prospects for the development of a universal DP catalogue convenient for practical use.

Capture of negative muons in chromium oxides

Muonic X-ray intensities for the Lyman series in oxygen and of the Lyman and Balmer series in chromium have been measured in CrO3 and in crystalline and amorphous Cr2O3. By means of muon cascade calculations which reproduce the measured intensities, angular momentum distributions of the captured muons have been determined for oxygen in a mu atomic level n=14 and for chromium in n=17. The Cr/O capture ratios per atom have been found to be 3.23 in CrO3 and 2.64 in both structures of Cr2O3. This difference is due to the electronic bond structures. The capture probability in chromium is larger in the higher oxidation state which is in contrast to observations in some other elements.