We review the theoretical background, experimental techniques, and phenomenology of what is known in relativistic heavy ion physics as the Glauber model, which is used to calculate geometric quantities. A brief history of the original Glauber model is presented, with emphasis on its development into the purely classical, geometric picture used for present-day data analyses. Distinctions are made between the optical limit and Monte Carlo approaches, which are often used interchangeably but have some essential differences in particular contexts. The methods used by the four RHIC experiments are compared and contrasted, although the end results are reassuringly similar for the various geometric observables. Finally, several important RHIC measurements are highlighted that rely on geometric quantities, estimated from Glauber calculations, to draw insight from experimental observables. The status and future of Glauber modeling in the next generation of heavy ion physics studies is briefly discussed.

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Glauber Modeling in High Energy Nuclear Collisions

This is a review of the theoretical background, experimental techniques, and phenomenology of what is called the "Glauber Model" in relativistic heavy ion physics. This model is used to calculate "geometric" quantities, which are typically expressed as impact parameter (b), number of participating nucleons (N_part) and number of binary nucleon-nucleon collisions (N_coll). A brief history of the original Glauber model is presented, with emphasis on its development into the purely classical, geometric picture that is used for present-day data analyses. Distinctions are made between the "optical limit" and Monte Carlo approaches, which are often used interchangably but have some essential differences in particular contexts. The methods used by the four RHIC experiments are compared and contrasted, although the end results are reassuringly similar for the various geometric observables. Finally, several important RHIC measurements are highlighted that rely on geometric quantities, estimated from Glauber calculations, to draw insight from experimental observables. The status and future of Glauber modeling in the next generation of heavy ion physics studies is briefly discussed.

Multiplicity distributions in nucleus-nucleus collisions at high energies

A review of the program in space-radiation protection at the Langley Research Center is given. The relevant Boltzmann equations are given with a discussion of approximation procedures for space applications. The interaction coefficients are related to the solution of the many-body Schrodinger equations with nuclear and electromagnetic forces. Various solution techniques are discussed to obtain relevant interaction cross sections with extensive comparison with experiments. Solution techniques for the Boltzmann equations are discussed in detail. Transport computer code validation is discussed through analytical benchmarking, comparison with other codes, comparison with laboratory experiments, and measurements in space. Applications to missions to the Moon and Mars are discussed.

Transport Methods and Interactions for Space Radiations

High-energy, small angle elastic scattering of strongly interacting composite particles

Effect of quadrupole deformation on high-energy scattering by deuterons

The effects of charge exchange in collisions of high-energy particles of isotopic spin \textonehalf{} with deuterons are investigated. The diffraction approximation is used to express the deuteron charge-exchange cross section in terms of the elastic-scattering amplitudes of the neutron and proton and the deuteron ground-state wave function. Examinations are also made of the influence of the charge-exchange mechanism on the total cross section of the deuteron, the elastic differential cross section, and the summed angular distribution of scattering (elastic plus inelastic scattering with initial charges preserved). The important role played by double-scattering processes in shaping the differential cross sections of the deuteron is illustrated in a discussion of proton-deuteron elastic scattering at 2 BeV. Double scattering is shown to be the dominant collision mechanism at scattering angles which are not too close to the forward direction. The effect of the double charge-exchange process on the elastic differential cross section is shown to be small but of some significance in the angular range which is dominated by double scattering. The theory developed for charge-exchange reactions is applied to the ${K}^{0}$ angular distribution which has been observed from ${K}^{+}$-deuteron collisions at 2.27 $\frac{\mathrm{BeV}}{c}$. Estimates are found for the differential and integrated ${K}^{+}$-neutron charge-exchange cross sections, and for some related parameters. The effects of double collisions on these cross sections are relatively small and easily evaluated. The effect of the charge-exchange mechanism on the values of the $\mathrm{pn}$, $\overline{p}n$, and ${K}^{\ifmmode\pm\else\textpm\fi{}}n$ total cross sections which are reached indirectly via measurements on the deuteron is shown to be exceedingly small for momenta above \ensuremath{\sim}2 $\frac{\mathrm{BeV}}{c}$.

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High-Energy Deuteron Cross Sections: Charge-Exchange Effects

Collisions between nuclei are studied by means of a simple extension of the Glauber high energy approximation. An expression for the optical phase shift function, exact within the framework of the Glauber approximation, is expanded in an infinite series and includes the effects of nuclear correlations. The first term corresponds to the standard optical limit result of the Glauber theory, and the higher order corrections arise from the processes in which one or more nucleons of either nucleus can undergo multiple collisions. The center-of-mass correlation is treated consistently so that our results do not exhibit the large-q divergence which characterizes the usual optical limit. It is shown that with realistic constraints on nucleon-nucleon total cross sections, the optical phase shift function does not approach the usual optical limit result when the mass numbers of the colliding nuclei become very large. With a proper treatment of center-of-mass correlations, the optical phase shift series converges rapidly for light nuclei and allows one to perform realistic calculations. The effects of higher order corrections on total and inelastic cross sections and on elastic scattering intensities are examined. The effects of the Coulomb field are included in an average phase approximation and results are comparedmore » with measurements.« less

Collisions Between Composite Particles at Medium and High-Energies

We suggest that the broad shoulder observed in recent measurements of the $\mathrm{pd}$ elastic differential cross section at 2 GeV is a double-scattering effect and propose that further measurements be made to test whether double scattering persists at high energies.

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Double Scattering in High-Energy Elastic Collisions with Deuterons

/pdf/small-angle-high-energy-scattering-by-deuterons-v9jm9voyal.pdf

Victor Franco

Papers

Effect of quadrupole deformation on high-energy scattering by deuterons

High-Energy Deuteron Cross Sections: Charge-Exchange Effects

Collisions Between Composite Particles at Medium and High-Energies

Double Scattering in High-Energy Elastic Collisions with Deuterons

Small-angle high-energy scattering by deuterons