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Cross section parameterizations for cosmic-ray nuclei. I. Single nucleon removal.

Parameterizations of single nucleon removal from the electromagnetic and strong interactions of cosmic rays with nuclei are presented. These parameterizations are based upon the theoretical models developed by Baur, Bertulani, Benesh, Cook, Vary, Norbury, and Townsend. They should be very suitable for use in cosmic-ray propagation through interstellar space, Earth's atmosphere, lunar samples, meteorites, spacecraft walls, and lunar and martian habitats.

Cosmic Radiation↗

Parameterization of spectral distributions for pion and kaon production in proton-proton collisions.

Accurate semi-empirical parameterizations of the energy-differential cross sections for charged pion and kaon production from proton-proton collisions are presented at energies relevant to cosmic rays. The parameterizations depend on the outgoing meson momentum and also the proton energy, and are able to be reduced to very simple analytical formulas suitable for cosmic-ray transport.

Cosmic Radiation↗

Moments of dipole oscillator-strength distribution for the helium sequence.

The moments S(mu) for -6 < or = mu < or = 2 and L(mu) for mu = 0, 1 and 2 are calculated for the helium sequence for atomic numbers Z up to 30 under a screened hydrogenic model. In this model, one describes the atom by single-particle hydrogenic wavefunctions and treats the initial and the final state as characterised by two different effective charge parameters Zi and Zf, respectively. An asymptotic expansion is made of the differential oscillator strength of the screened hydrogenic model. Assuming the value 287.6 for the coefficient of the term epsilon -7/2 for helium atom as given by Salpeter and Zaidi, the parameter Zf is determined for the helium sequence. This approach has resulted in values which are in reasonable agreement with the various moment values of other authors.

Helium↗

Inclusive inelastic scattering of heavy ions in the independent particle model.

We consider the inclusive inelastic scattering of heavy ions using the Glauber model and the independent particle approximation. Inclusive inelastic distributions for projectile excitation of the target and total inelastic scattering, where all projectile and target excited states are summed, are discussed using closure. The total inelastic distribution when integrated is shown to be equivalent to the absorption cross section found from applying the optical theorem to the elastic scattering amplitude in the coherent approximation. Calculations are presented for several heavy-ion pairs using realistic nuclear densities in a large mass number approximation.

Elementary Particles↗

Dose equivalent near the bone-soft tissue interface from nuclear fragments produced by high-energy protons.

During manned space missions, high-energy nucleons of cosmic and solar origin collide with atomic nuclei of the human body and produce a broad linear energy transfer spectrum of secondary particles, called target fragments. These nuclear fragments are often more biologically harmful than the direct ionization of the incident nucleon. That these secondary particles increase tissue absorbed dose in regions adjacent to the bone-soft tissue interface was demonstrated in a previous publication. To assess radiological risks to tissue near the bone-soft tissue interface, a computer transport model for nuclear fragments produced by high energy nucleons was used in this study to calculate integral linear energy transfer spectra and dose equivalents resulting from nuclear collisions of 1-GeV protons transversing bone and red bone marrow. In terms of dose equivalent averaged over trabecular bone marrow, target fragments emitted from interactions in both tissues are predicted to be at least as important as the direct ionization of the primary protons-twice as important, if recently recommended radiation weighting factors and "worst-case" geometry are used. The use of conventional dosimetry (absorbed dose weighted by aa linear energy transfer-dependent quality factor) as an appropriate framework for predicting risk from low fluences of high-linear energy transfer target fragments is discussed.

Bone Marrow↗

Single nucleon emission in relativistic nucleus-nucleus reactions.

Significant discrepancies between theory and experiment have previously been noted for nucleon emission via electromagnetic processes in relativistic nucleus-nucleus collisions. The present work investigates the hypothesis that these discrepancies have arisen due to uncertainties about how to deduce the experimental electromagnetic cross section from the total measured cross section. An optical-model calculation of single neutron removal is added to electromagnetic cross sections and compared to the total experimental cross sections. Good agreement is found thereby resolving some of the earlier noted discrepancies. A detailed comparison to the recent work of Benesh, Cook, and Vary is made for both the impact parameter and the nuclear cross section. Good agreement is obtained giving an independent confirmation of the parametrized formulas developed by those authors.

Electromagnetic Phenomena↗

Charge dependence and electric quadrupole effects on single-nucleon removal in relativistic and intermediate energy nuclear collisions.

Single-nucleon removal in relativistic and intermediate energy nucleus-nucleus collisions is studied using a generalization of Weizsäcker-Williams theory that treats each electromagnetic multipole separately. Calculations are presented for electric dipole and quadrupole excitations and incorporate a realistic minimum impact parameter, Coulomb recoil corrections, and the uncertainties in the input photonuclear data. Discrepancies are discussed. The maximum quadrupole effect to be observed in future experiments is estimated and also an analysis of the charge dependence of the electromagnetic cross sections down to energies as low as 100 MeV/nucleon is made.

Electromagnetic Fields↗

Electric quadrupole excitations in relativistic nucleus-nucleus collisions.

Calculations are presented for electric quadrupole excitations in relativistic nucleus-nucleus collisions. The theoretical results are compared to an extensive data set and it is found that electric quadrupole effects provide substantial corrections to cross sections, especially for heavier nuclei.

Electromagnetic Phenomena↗

Optical model description of momentum transfer in relativistic heavy ion collisions.

An optical model description of momentum transfer in relativistic heavy ion collisions, based upon composite particle multiple-scattering theory, is presented. The imaginary component of the complex momentum transfer, which comes from the absorptive part of the optical potential, is shown to be the main contributor to the momentum loss of the projectile. Within the context of the Goldhaber formalism, predictions of fragment momentum distribution observables are made and compared with experimental data. Use of the model as a tool for estimating collision impact parameters is also discussed.

Ions↗

Calculations of hadronic dissociation of 28Si projectiles at 14.6A GeV by nucleon emission.

An optical potential abrasion-ablation collision model is used to calculate hadronic dissociation cross sections for one, two, and three nucleon removal for the first time for a 14.6A GeV 28Si beam fragmenting in aluminum, tin, and lead targets. These estimates are compared with recent semi-inclusive measurements. Significant differences between some calculated and measured semi-inclusive cross sections exist which cannot be resolved without measurements of the exclusive channel hadronic cross sections. Calculations for each exclusive reaction channel contributing to the semi-inclusive cross sections are presented and discussed.

Aluminum↗

Momentum transfer in relativistic heavy ion charge-exchange reactions.

Relativistic heavy ion charge-exchange reactions yield fragments (delta Z = +1) whose longitudinal momentum distributions are downshifted by larger values than those associated with the remaining fragments (delta Z = -1, -2, ...). Kinematics alone cannot account for the observed downshifts; therefore, an additional contribution from collision dynamics must be included. In this work, an optical model description of collision momentum transfer is used to estimate the additional dynamical momentum downshift. Good agreement between theoretical estimates and experimental data is obtained.

Ions↗

Multiple-scattering effects in quasielastic alpha-4He scattering.

A multiple-scattering series for describing the quasielastic peak in nucleus-nucleus collisions is derived using the high-energy optical model. The effects of multiple knockout of target nucleons and internal excitation of the projectile are studied and found to be important for large energy loss and momentum transfers in inclusive alpha-4He scattering at 7 GeV/c. An approximate evaluation of higher-order inelastic collision terms is considered for forward-peaked wave functions and is demonstrated to be accurate.

Helium↗

Optical model analyses of 1.65 A GeV argon fragmentation: cross sections and momentum distributions.

An optical potential fragmentation model capable of predicting fragmentation cross sections and fragment momentum distributions is used to analyze recent measurements of 1.65 A GeV argon projectiles fragmenting in carbon and potassium-chloride targets obtained with the Heavy Ion Spectrometer System (HISS) at the Lawrence Berkeley Laboratory Bevalac. The theoretical model uses an abrasion-ablation-FSI (frictional spectator interaction) collision formalism to estimate elemental and isotopic production cross sections for comparison with the measured values. The collision momentum transfer model is incorporated into a Goldhaber formalism to analyze measured transverse and longitudinal distributions of the projectile fragments. Good agreement between theory and experiment is obtained for all observables.

Argon↗

Geometric model for nuclear absorption from microscopic theory.

A parameter-free geometric model for nuclear absorption is derived from microscopic theory. The expression for the absorption cross section in the eikonal approximation taken in integral form is separated into a geometric contribution, described by an energy-dependent effective radius, and two surface terms which are shown to cancel in an asymptotic series expansion. For collisions of light nuclei, an expression for the effective radius is derived using harmonic-oscillator nuclear density functions. A direct extension to heavy nuclei with Woods-Saxon densities is made by identifying the equivalent half density radius for the harmonic-oscillator functions. Coulomb corrections are incorporated and a simplified geometric form of the Bradt-Peters type obtained. Results spanning the energy range of 1 MeV/nucleon to 1 GeV/nucleon are presented. Good agreement with experimental results are obtained.

Elementary Particles↗

Universal characteristics of transverse momentum transfer in intermediate energy heavy ion collisions.

A microscopic optical model formalism for estimating momentum transfer in intermediate energy heavy ion collisions predicts universal behavior of the transverse component. In particular, for symmetric systems (Ap = AT) heavier than niobium, it appears that values of P perpendicular/A are independent of the mass and charge of the colliding nuclei and vary only with impact parameter and incident beam energy. This suggests that momentum transfer per nucleon saturates to some limiting value with increasing mass.

Calcium↗

Widths of transverse momentum distributions in intermediate-energy heavy-ion collisions.

The need to include dynamical collision momentum transfer contributions, arising from interacting nuclear and Coulomb fields, to estimates of fragment momentum distributions is discussed. Methods based upon an optical potential model are presented. Comparisons with recent experimental data of the Siegen group for variances of transverse momentum distributions for gold nuclei at 980 A MeV fragmenting on silver foil and plastic nuclear track detector targets are made. The agreement between theory and experiment is good.

Gold↗

Optical model analyses of heavy ion fragmentation in hydrogen targets.

Quantum-mechanical optical-model methods for calculating cross sections for the fragmentation of high-energy heavy ions by hydrogen targets are presented. The cross sections are calculated with a knockout-ablation collision formalism which has no arbitrary fitting parameters. Predictions of elemental production cross sections from the fragmentation of 1.2A GeV 139La nuclei and of isotope production cross sections from the fragmentation of 400A MeV 32S nuclei are in good agreement with recently reported experimental measurements.

Cosmic Radiation↗