Three pion production on nuclei at 200 GeV

We have carried out a systematic study of the coherent dissociation of pions into 3 pions using nuclear targets. The experiment was performed at Fermilab using a high resolution forward spectrometer. Data were taken with carbon, copper and lead targets at an incident momentum of 202.5 GeV/c. Results are presented on momentum transfers, 3-pion masses, and on the nuclearA-dependence of the production cross section.     

Zwei Bemerkungen über stark summierbare unendliche Reihen

Ohne Zusammenfassung     

Photon propagation in heterogeneous optical media with spatial correlations: enhanced mean-free-paths and wider-than-exponential free-path distributions

Beer's law of exponential decay in direct transmission is well-known but its break-down in spatially variable optical media has been discussed only sporadically in the literature. We document here this break-down in three-dimensional (3D) media with complete generality and explore its ramifications for photon propagation. We show that effective transmission laws and their associated free-path distributions (FPDs) are in fact never exactly exponential in variable media of any kind. Moreover, if spatial correlations in the extinction field extend at least to the scale of the mean-free-path (MFP), FPDs are necessarily wider-than-exponential in the sense that all higher-order moments of the relevant mean-field FPDs exceed those of the exponential FPD, even if it is tuned to yield the proper MFP. The MFP itself is always larger than the inverse of average extinction in a variable medium. In a vast and important class of spatially-correlated random media, the MFP is indeed the average of the inverse of extinction. We translate these theoretical findings into a practical method for deciding a priori when 3D effects become important. Finally, we discuss an obvious but limited analogy between our analysis of spatial variability and the well-known effects of strong spectral variability in gaseous media when observed or modeled at moderate resolution.     

On spectral invariance of single scattering albedo for water droplets and ice crystals at weakly absorbing wavelengths

The single scattering albedo ω_0λ in atmospheric radiative transfer is the ratio of the scattering coefficient to the extinction coefficient. For cloud water droplets both the scattering and absorption coefficients, thus the single scattering albedo, are functions of wavelength λ and droplet size r. This note shows that for water droplets at weakly absorbing wavelengths, the ratio ω_0λ(r)/ω_0λ(r₀) of two single scattering albedo spectra is a linear function of ω_0λ(r). The slope and intercept of the linear function are wavelength independent and sum to unity. This relationship allows for a representation of any single scattering albedo spectrum ω_0λ(r) via one known spectrum ω_0λ(r₀). We provide a simple physical explanation of the discovered relationship. Similar linear relationships were found for the single scattering albedo spectra of non-spherical ice crystals.