Search

Coupled channel calculations for proton-nucleus inelastic scattering are performed using the Dirac formalism. The inelastic scattering of 362, 500, and 800 MeV protons from [sup 40]Ca, [sup 90]Zr, and [sup 208]Pb are considered. Transition potentials for the low-lying collective states are obtained using a simple collective model. Phenomenological as well as parameter-free relativistic impulse approximation (RIA) optical potentials are used for the direct potentials. It is found that reasonable descriptions of both elastic and inelastic observables are obtained. It is shown that the coupling to low-lying states greatly improves the agreement with the large angle data.

Energy-dependent global Dirac optical model potentials are found by fitting proton elastic scattering data in the energy range 20--1040 MeV for $^{12}\mathrm{C}$, $^{16}\mathrm{O}$, $^{40}\mathrm{Ca}$, $^{90}\mathrm{Zr}$, and $^{208}\mathrm{Pb}$. Three different energy- and atomic-mass-number-dependent global Dirac optical potentials are also obtained. A number of characteristic features of the potentials are discussed. In addition, the mean free path, the effective mass ${\mathit{m}}_{\mathit{e}}^{\mathrm{*}}$, the Dirac mass ${\mathit{M}}^{\mathrm{*}}$, and the relativistic energy shift ${\mathit{E}}^{\mathrm{*}}$ are calculated.

In this paper we give the results of a relativistic analysis of elastic and inelastic scattering of 180 MeV antiprotons from {sup 12}C. The calculations are performed within a Dirac coupled-channel framework using a collective model for the transition potentials. While the presence of the inelastic data does seem to remove some of the ambiguity in the Dirac optical model potentials, the largest constraint comes from the elastic analyzing power measurements. In the Dirac approach for proton-nucleus scattering, spin observables are very important; this is also true for the determination of the antiproton-nucleus optical potential.

Various relativistic treatments are applied to deuteron-nucleus elastic scattering at intermediate energies. There are various possibilities for spin-one wave equations. Here we have considered three of them, the Kemmer-Duffin-Petiau, Proca, and Weinberg equations. Second-order equations are obtained from each using a similar set of approximations. Elastic-scattering observables including the differential cross section, and the vector and tensor analyzing powers are calculated using all three equations. The different predictions are compared with each other and with experimental data for 400 MeV $^{58}\mathrm{Ni}$(d,d${)}^{58}$Ni and 700 MeV $^{40}\mathrm{Ca}$(d,d${)}^{40}$Ca. We find that within the approximations made and for the assumed interactions there are no significant differences between the three sets of predicted observables.

The p\ensuremath{\rightarrow}${+}^{13}$C\ensuremath{\rightarrow} (polarized target) elastic-scattering spin observables ${\mathit{A}}_{000\mathit{n}}$ (target analyzing power) and ${\mathit{A}}_{00\mathit{n}\mathit{n}}$ (spin-correlation parameter) were determined at 497.5 MeV over the laboratory angular range 12\ifmmode^\circ\else\textdegree\fi{}--30\ifmmode^\circ\else\textdegree\fi{} with statistical uncertainties typically \ifmmode\pm\else\textpm\fi{}(0.02--0.06). Results of distorted-wave Born approximation calculations, based on either the relativistic or the nonrelativistic impulse approximation, are in reasonable agreement with these new data.

Elastic and inelastic observables for the scattering of 500 MeV protons from $^{40}\mathrm{Ca}$ are calculated using either the first-order relativistic or nonrelativistic impulse approximation for the diagonal potentials and a collective model for the transition potentials. The calculations are done using either Dirac or Schr\"odinger coupled channel programs. The relativistic approach reproduces the inelastic observables better than the first-order nonrelativistic impulse approximation model.

We present global Dirac optical model fits to elastic proton scattering data from heavy nuclear targets at energies between 65 and 1040 MeV. Such optical potentials provide critical input for a wide variety of nuclear reactions. The energy and mass number dependence of the parameters in the Lorentz four-vector and scalar potentials of Dirac phenomenology are given. The characteristic features of the potentials are discussed and the predictive power of the global approach presented here is tested for both interpolation and extrapolation.

We report precision measurements of the polarization transfer parameter ${\mathit{D}}_{\mathit{NN}}$ for 500 MeV polarized proton elastic scattering from $^{12,13}\mathrm{C}$ at the first diffractive minima in the differential cross sections. The ratio ${\mathit{D}}_{\mathit{NN}}$${(}^{13}$C)/${\mathit{D}}_{\mathit{NN}}$${(}^{12}$C) (1.000\ifmmode\pm\else\textpm\fi{}0.028) is consistent with zero spin-flip probability (S) for $^{13}\mathrm{C}$, where S (1-${\mathit{D}}_{\mathit{NN}}$). Comparisons are made with results of theoretical calculations reported in the literature. \textcopyright{} 1996 The American Physical Society.

The elastic scattering observables for 400 MeV [pi][sup [plus minus]] on [sup 28]Si are calculated using a relativistic impulse approximation Kemmer-Duffin-Petiau formalism to calculate the [pi][sup [plus minus]] nucleus optical potential, and the Kemmer-Duffin-Petiau wave equation of motion with the aforementioned potential. The results are compared with recent experiments and with the results of nonrelativistic impulse approximation treatments.

It has been shown that there exist transformations that can be used to change the Lorentz transformation character of potentials, which appear in the Dirac equation for elastic scattering. We consider the situation for inelastic scattering described by coupled channel Dirac equations. We examine a two-level problem where both the ground and excited states are assumed to have zero spin. Even in this simple case we have not found an appropriate transformation. However, if the excited state has zero excitation energy it is possible to find a transformation.

Differential cross sections for proton elastic scattering from $^{42}$,44,48Ca have been measured at seven energies in the laboratory energy range from 21.0 to 48.4 MeV, and for $^{40}\mathrm{Ca}$ at six energies between 25.0 and 45.0 MeV. Measurements were made at 2.5\ifmmode^\circ\else\textdegree\fi{} intervals from 10\ifmmode^\circ\else\textdegree\fi{} to 90\ifmmode^\circ\else\textdegree\fi{} (laboratory angles), and at 5.0\ifmmode^\circ\else\textdegree\fi{} intervals between 90\ifmmode^\circ\else\textdegree\fi{} and 170\ifmmode^\circ\else\textdegree\fi{}. Relative errors in the data are typically between 3% and 4%; the scale errors are also 3%. The data have been analyzed by both nonrelativistic and relativistic optical models. The optical potential parameters were used to calculate nuclear matter radius information for the calcium isotopic series, which is compared to previous results.

The results of an optical model analysis of medium energy p-/sup 4/He elastic scattering cross section and analyzing power measurements are reported. The analysis is based on the use of the Dirac equation with a mixture of a Lorentz scalar potential and the timelike component of a four-vector potential.

In this application of Dirac phenomenology a relativistic impulse approximation is used to describe proton-nucleus elastic scattering at intermediate energies. The results demonstrate the superiority of this relativistic treatment over the nonrelativistic impulse approximation, especially with regard to spin observables. The method has important implications with respect to the extraction of neutron distributions.

Discrepancies among experiments and theory on electron scattering from oriented holmium are partially resolved. An estimate is presented which suggests that the distorted-wave Born-approximation orientation effect calculated by Wright is too large by about a factor of 2. Distorted-wave Born approximation calculations (made with a coupled-channel program) are presented which confirm this suggestion. They agree well with the Stanford data for orientation perpendicular to the scattering plane. The previous discrepancy for orientation along the recoil-momentum direction is reduced, but is not removed. The sensitivity of these results to the charge shape is examined although a fit to the data is not made. Results are given of a complete coupled-channel calculation for the first three nuclear states. Suggestions are made for future work, and cross sections and orientation effects for energy-resolved scattering from holmium at 200 MeV are given. (AIP)

The energy dependence of a relativistic optical model potential consisting of a mixture of Lorentz scalar and Lorentz vector components is determined from the analysis of p-/sup 40/Ca elastic scattering experiments from 26 to 1040 MeV.

The results of a Dirac equation optical model analysis of p- 4 He elastic scattering data are reported. The optical potential obtained at 1029 MeV reproduces the systematics of p- 4 He data over the energy range from 560 to 1730 MeV.

A Dirac equation optical model calculation with the real part of the optical potential constrained by relativistic model considerations is used to represent 180 MeV p-/sup 40/Ca elastic scattering data. The Dirac equation optical potential consists of a mixture of Lorentz scalar and Lorentz vector potentials. Features of an effective Schroedinger equation optical potential constructed from these two potentials are deduced and compared with results from the standard optical model.

Results of relativistic and nonrelativistic impulse approximation calculations are compared for p+/sup 40/Ca elastic scattering observables between 181 and 1040 MeV. At 400 MeV and above the relativistic approach is superior, especially with regard to spin observables. Below 400 MeV neither calculation agrees well with experiment.

Large angle elastic differential cross section and analyzing power data are reported for 497.5 MeV p-arrow-right+/sup 40/Ca. The characteristic diffraction pattern extends to the largest momentum transfer, 5.3 fm/sup -1/. Theoretical models which incorporate either relativistic or nonrelativistic dynamics do not quantitatively describe the data for q>3.5 fm/sup -1/. Possible explanations for the discrepancy are suggested

An effective Coulomb correction term arising from the second order Dirac equation is calculated for /sup 40/Ca. The optical potential used consists of a mixture of a Lorentz scalar potential and the timelike component of a Lorentz four-vector potential. These calculations show that the real Coulomb correction term resulting naturally from the Dirac equation is in agreement with empirics.

Lorentz vector and scalar, isovector and isoscalar proton-nucleus optical potentials are obtained from invariant nucleon-nucleon amplitudes using a relativistic impulse approximation. Cross sections, analyzing powers, and spin rotation functions for $^{90}\mathrm{Zr}$(p,p) and the $^{90}\mathrm{Zr}$(p,n)$^{90}\mathrm{Nb}$ (isobaric analog state) reaction at 160 and 500 MeV are calculated using a relativistic generalization of the Lane equations. These predictions are compared to nonrelativistic impulse approximation results and to experimental data at 160 MeV.

A Dirac equation optical model calculation with a relativistic Majorana exchange potential is used to represent the large angle diffraction structure observed in the 788 MeV p-/sup 4/He cross section data.

We present a global relativistic optical model for p+40Ca consisting of Lorentz scalar and vector potentials parametrized as a function of energy. The shapes chosen are Woods-Saxons for the real potentials, and a linear combination of Woods-Saxons and derivative Woods-Saxons for the imaginary potentials.

We have performed optical-model calculations using the Klein-Gordon and the Dirac equations for the 600 MeV p-/sup 4/He scattering experiments of Boschitz et al., and the 1050 MeV p-/sup 4/He scattering experiments of Baker et al. We have compared these analyses with our previous analysis of the 1000 MeV p-/sup 4/He experiment of Palevsky et al. In comparing the results at the three energies we find that the experiments require a slightly energy-dependent optical potential rms radius. The average value is in good agreement with the /sup 4/He matter radius obtained from electron scattering, and substantially smaller than the low energy /sup 4/He optical potential rms radius. On the other hand, the experiments require quite different values for the optical potential strength parameters. (AIP)

We obtain a solution of the Dirac equation in the presence of the electromagnetic field of a complex nucleus by means of coupled-channel partial wave analysis using a new method in which the asymptotic solutions of the coupled radial wave equations include all electromagnetic couplings. A computer program employing this method is used to determine the importance of dispersion effects in the scattering of 250 MeV electrons from /sup 40/Ca and /sup 44/Ca. We find the dispersion effects to be less than 1% for angles below 90degree (i.e., considerably less than experimental error over the range investigated experimentally), thus supporting the view that the difference in the differential cross sections from /sup 40/Ca and /sup 44/Ca arises primarily from a difference in the ground state charge distributions of the two isotopes.

We present results of calculations which suggest that several of the spin observables for elastic scattering of 500-MeV polarized protons from a polarized /sup 13/C target are sensitive to relativistic aspects of nuclear structure.

High-quality fits to 497 MeV p− 40 Ca cross sections and analyzing powers are obtained using a Dirac equation optical model treatment. The predicted spin-rotation function Q ( θ ) agrees well with experiment. The spin rotation observable provides almost no new information about the real part of the Dirac optical potential but may provide some information about the imaginary part.

The first calculations of p-bar-nucleus elastic scattering using the relativistic impulse approximation are presented and compared with the recent 46.8-MeV p-bar-/sup 12/C elastic scattering data. The calculated cross sections agree well with the data. The differences between relativistic and nonrelativistic impulse approximation calculations using the same input are small.

The subject of the adsorption of atoms on surfaces is of considerable theoretical and technical importance. A knowledge of the processes involved is essential, for example, before we can understand many industrial applications which depend for their success upon the catalytic activity of metallic oxides. It is of great advantage in making experiments in this field if the adsorbed atoms or molecules can be detected by electrical methods, and TAYLOR and LANGMUIR have shown recently that these methods allow us to make an extremely accurate and detailed study of the adsorption of caesium atoms on a tungsten surface. The object of the experiments described in this paper was to examine the extent to which the adsorption of atoms on the surface of a metallic oxide can be described in terms similar to those developed by TAYLOR and LANGMUIR in their work with metallic tungsten. There is a marked contrast between the behaviour of metal atoms adsorbed (a) on the surface of a metal, and (b) on the surface of a dielectric like glass, and this difference is to be associated with the difference in the electrical properties of the two types of materials.

A transformation is used to obtain sets of equivalent Lorentz scalar, Lorentz four-vector, and tensor optical potentials. These potentials are used in the Dirac equation for describing elastic scattering observables.

Elastic and inelastic $p+^{40}\mathrm{Ca}$ observables are calculated using a relativistic impulse approximation model for the diagonal optical potential and a simple collective ansatz for the transition potentials. The calculations were performed using Dirac coupled channel codes. Agreement with large angle elastic-scattering data is greatly improved by the inclusion of strongly coupled, lowlying collective states.

We present the first global relativistic optical-model treatment of proton-nucleus elastic scattering. Energy-dependent optical potential parameters for the Lorentz vector and scalar potentials of Dirac phenomenology are given. Several different assumptions regarding the optical-model energy dependence are considered. Constraints from relativistic mean-field theory are presented.

The first application of the Kemmer-Duffin-Petiau wave equation for spin-0 particles to meson-nucleus scattering is given. A relativistic impulse approximation using the Kemmer-Duffin-Petiau formalism is used to calculate meson-nucleus optical potentials. Comparison with the nonrelativistic impulse approximation is given.

Lorentz scalar and four-vector optical potentials are obtained for protons elastically scattered from /sup 16/O, /sup 40/Ca, /sup 48/Ca, /sup 90/Zr, and /sup 208/Pb. It is demonstrated that Dirac optical potentials constrained by relativistic Hartree theory are capable of producing good agreement with experiment

We present a description of the spin-one Kemmer-Duffin-Petiau equations. An effective second-order equation is obtained for various types of interactions. An argument is given for the use of one particular form of interaction for deuteron-nucleus scattering. This provides the basis for a generalization of the standard Watanabe model in which Dirac scalar and vector nucleon-nucleus potentials are used as input. Parameter-free calculations are performed using both phenomenological and microscopic nucleon-nucleus potentials, and results are compared with deuteron-nucleus elastic scattering data at 400 and 700 MeV. Qualitative agreement is generally obtained. A good description of the forward-angle vector analyzing power data is achieved.

There is increasing evidence that relativistic effects play an important role in the description of nuclear structure and reactions. The development of a relativistic impulse approximation (RIA) and its success at intermediate energies is a case in point. Although the RIA cannot be used to describe proton scattering at low energies it successfully describes recent p–12C data at 46.8 MeV. We discuss a phenomenological nuclear optical model approach based on the Dirac equation containing large cancelling Lorentz scalar and Lorentz vector potentials. The model is used to describe proton and neutron scattering at low energy (T

A Dirac equation based optical model treatment of proton‐nucleus scattering is discussed. Results obtained using a relativistic optical model consisting of Lorentz scalar and Lorentz four‐vector components are given. The parameters in the model have been varied to obtain high quality fits to elastic differential cross section, analyzing power, and spin rotation function measurements. Features of these Dirac optical model potentials are compared with various theoretical relativistic calculations.

Since 1972, the Speech Recognition Group at IBM's Thomas J. Watson Research Center has worked on a system for the automatic recognition of natural continuous speech. The goal of our research is to produce a voice-activated text-processing system. We have recently worked on a 5,000-word isolated-speech system for recognition of business correspondence and interoffice memoranda.Although speech recognition is performed with beguiling ease by human beings, the task of transferring this ability to computers has proven quite difficult. Our approach to the problem has been to develop general statistical techniques that allow the recognition system to organize itself when presented with a large sample of speech called training data. In essence, our system refines itself from some crudely specified initial configuration so as to take advantage of regularities present in a speech sample.Suppose that a talker wishes to convey to a listener the string of words W1, W2, ..., Wn. Each of the words has a pronunciation, in accordance with which the talker will guide his/her speech apparatus through an intricate cascade of gestures, with the result that a series of sound pressure waves will emanate. A microphone placed within the influence of these waves will respond to them in a fashion that is characteristic of the word sequence W1, W2, ..., Wn.Let the response of the microphone be denoted by the sequence A1, ..., Am. We can regard A1, ..., Am as a garbled version of the intended message W1, ..., Wn. The problem of recovering a message from a garbled transmission is the province of communication theory. The problem may be stated as follows: for a garbled transmission A (=A1, ...Am), determine the message W (=W1, ..., Wn) that is most probable given A. That is, find W such that Pr(W|A) is as large as possible.From Bayes's rule, we have Pr(W|A) = {Pr(W|A)}Pr(W)}Pr(A). Since we are interested in maximizing this for a particular fixed A, we can ignore the denominator on the right. The first term in the numerator constitutes a probabilistic characterization of the transmission channel. It tells us what A's to expect when the talker intends a particular word string W. The second term in the numerator is a probabilistic characterization of the word strings that the talker desires to convey. Pr(W) embodies all rules of grammar (ungrammatical word strings are less probable than grammatical ones) as well as all semantic constraints (meaningless word strings are less probable than meaningful ones).It is, of course, impossible to compute these probabilities exactly. We have, however, developed methods for obtaining useful approximations to them. We refer to the approximation of Pr(A|W) as a statistical model for the speech production process and to the approximation of Pr(W) as a statistical model for the language. A discussion of these models constitutes the body of the talk.

We present a description of the spin-1 Kemmer-Duffin-Petiau equations and make an application to deuteron-nucleus scattering. Comparison with d${+}^{58}$Ni elastic scattering data at 400 MeV shows that the Kemmer-Duffin-Petiau model reproduces experimental spin observables quite well.

The differential cross sections and analyzing power are calculated for p+/sup 40/Ca and p+/sup 208/Pb elastic scattering with a tensor term included in the relativistic impulse approximation optical potential.(AIP)