Phase transition in a four-dimensional random walk with application to medical statistics

A random walk in a piecewise homogeneous medium can exhibit a variety of asymptotic behaviors. In particular, it may lodge strictly in one region or divide in probability among several. This will depend upon the parameters describing (a) the walk, (b) the interregion boundary, and (c) the initial location of the walk. We analyze from this point of view a special four-dimensional walk on an integer lattice with two homogeneous regions separated by a hyperplane of codimension 1. The walk represents a continuing sequence of clinical trials of two drugs of unknown success probabilities and the two regions represent the Bayes-derived criterion as to which drug to try next. The demarcation in the parameter space of success probabilities and initial coordinates between one- and two-region asymptotics is mapped out analytically in several special cases and supporting numerical evidence given in the general case.     

Interaction of relativistic alpha particles in emulsion at 2.1 GeV/c/nucleon

An analysis for 2,000 events produced by 2.1 GeV/c/n alpha particles in nuclear emulsion has been carried out. Multiplicity and angular distributions of charged secondaries have been measured and correlation among them are discussed. The presented data are compared with relevant values from proton and¹⁴N interactions with nuclei. The multiplicity distribution of showers has been tested by a modified independent nucleon-nucleus multiple scattering model (INAM) of reference [8], and by the model of reference [12].     

Positive pion photoproduction from hydrogen at photon energies between 500 MeV and 1,400 MeV in forward direction

The differential cross section of the reactionγ+p→π ⁺ was measured at pion CM-angles of 20° and 30° for photon energies between 500 MeV and 1,400 MeV. The pions were detected in a magnetic spectrometer. By measuring each pion trajectory and by offline calculation of the initial pion parameters an energy resolution of about 2.5% FWHM was achieved. The results complete a set of data which were measured in recent years at the Bonn 2.5 GeV synchrotron. In comparison to photoproduction analyses two effects were revealed: The η cusp appears in the energy dependence of the cross section as a sharp drop atK _γ=710 MeV. In the region of the third resonance the data show a greater enhancement than predicted by most of the analyses.     

Diffractive proteon fragmentation in 16, 32, and 110 GeV/cK − p interactions and the diffractive production of heavy quarks(s\bar s,c\bar c)

The inclusive proton diffraction dissociation cross sections in 16, 32, and 110 GeV/cK ^? p interactions are determined from the spike nearx=1 in the inclusive negative particle spectra and are compared to those obtained inK?p interactions using other selection methods at various energies. The same procedure is applied to events containing aV ⁰ in order to obtain the cross section for diffractive \(s\bar s\) production. While the total cross section for proton diffraction is found to be approximately constant in the energy range studied here, proton diffraction yielding an \(s\bar s - pair\) is found to increase significantly. In particular it is almost constant at 85 μb forΛ ⁰ and Σ production but for \(NK\bar K\) it rises from zero at 16 GeV.c to about 200 μb at 110 GeV/c. From the result for \(s\bar s\) diffractive production an estimate for the \(c\bar c\) diffractive production cross section of approximately 1–10 μb at 110 GeV/c is obtained.     

Potential scattering in the generator Coordinate method

The generator coordinate formulation of the quantum-mechanical scattering problem transforms the solution of a problem in Hilbert space into an equivalent problem in Banach space. The structure of this problem is, however, that of an ill-posed problem. In order to shed some light onto the numerical intricacies, we investigate a number of potential scattering systems. One finds that, notwithstanding the numerical uncertainties of the weight function, excellent results for phase shifts (and scattering solutions) can be obtained.     

High-resolution laser excitation spectra of linear triatomic molecules: Analysis of the B2Σ+-X2Σ+ system of SrOH and SrOD

Single-mode cw dye laser excitation spectra of the (0, 0⁰, 0)-(0, 0⁰, 0), (1, 0⁰, 0)-(1, 0⁰, 0), (0, 1¹, 0)-(0, 1¹, 0) bands of the 611- to 607-nm system of SrOH and SrOD were observed and assigned. The spectrum is consistent with a ²Σ-²Σ system where the molecule is linear in both electronic states. The rotational analysis is obtained by measuring P-R separations in the excitation spectrum. A technique which greatly aided in the spectral assignment that utilizes a monochromator as a bandpass filter in obtaining excitation spectra is described. A new spin-rotation constant, γ⁽⁺⁾ - γ^(?), was found necessary to fit the l-type doubling of the (0, 1¹, 0) mode in B²Σ⁺ of SrOH. This new constant is assumed to arise from two ${}^2\text{Σ}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ vibronic states, split by Renner-Teller interaction, of the (0, 1¹, 0) mode of A²Π. From a perturbation treatment of this electronic interaction, ?ω₂ of the (0, 1¹, 0) mode of A²Π was found to be 14 cm^?1. The linear structure of SrOH and SrOD in both electronic states is consistent with the model, in the one-electron approximation, in that the transition involves the promotion of the unpaired 5s to the 5p orbital localized on the strontium.