# L. David RoperVirginia Tech (Virginia Polytechnic Institute and State University) | VT · Department of Physics

L. David Roper

PhD MIT theoretical physics 1963

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103

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Introduction

**Skills and Expertise**

## Publications

Publications (103)

The sigmoid and double-sigmoid functions are very useful for representing earth-states transitions in geological models. Simple hyperbolic-tangent versions are given for the functions. An example is given of fitting double-sigmoid functions to the transient state transitions of the Last Major Ice Age.

We present the results of an energy-dependent and set of energy-independent partial-wave analyses of pion-photoproduction data. The analyses extend from threshold to 1.8 GeV in the laboratory photon energy. Resonance photodecay amplitudes are extracted for the 16 baryon resonances found within this energy range. Comparisons are made with previous d...

We have analyzed the available kaon-nucleon elastic-scattering data with laboratory kinetic energies below 2650 MeV. We present the results of an energy-dependent analysis and a set of energy-independent analyses over this energy range. Our isoscalar amplitudes cover the region from threshold to 1100 MeV. The isovector amplitudes extend to 2650 MeV...

An energy-dependent analysis and set of energy-independent analyses are presented for the nucleon-nucleon elastic-scattering data below 1.6 GeV. The database from which the energy-dependent and 25 {ital pp} (18 {ital np}) single-energy solutions are obtained consists of 11 880 {ital pp} and 7572 {ital np} data. A resonancelike structure is found to...

R. A. Arndt et. al. give reply to the comment made by J. Stahov et. al. concerning the determination of the pion-NN coupling constants from elastic pion-nucleon scattering data.(AIP)

The Center for Analysis of Particle Scattering (CAPS) in the Department of Physics at Virginia Polytechnic Institute and State University has analyzed basic two-body hadron reactions below 2 GeV for the last two decades. Reactions studied were nucleon-nucleon, pion-nucleon, K[sup +]-nucleon and pion photoproduction systems. In addition to analyses...

We confirm a recent determination of the pion-nucleon coupling constant. We relate the accuracy of our result to the abundance of low-energy polarization data. Our result has been extracted from a modified dispersion relation and is compared to the Karlsruhe-Helsinki result. The effect of charge-exchange data on this result is also examined.

We have analyzed the available pion-nucleon elastic-scattering data with laboratory kinetic energies below 2 GeV. We present the results of several energy-dependent and energy-independent analyses performed over this energy range. Pole positions and the corresponding residues are reported for resonances. We compare our results to those from our pre...

An energy-dependent partial-wave analysis of pion photoproduction data through the second-resonance region (0--1 GeV laboratory kinetic energy) is presented. A set of energy-independent analyses has also been obtained starting from the energy-dependent solution. The data set contains 9074 data for the reactions {gamma}+{ital p}{r arrow}{ital p}+{pi...

Resonance couplings for the resonant states {ital P}{sub 33}(1232), {ital P}{sub 11}(1440), {ital D}{sub 13}(1520), and {ital S}{sub 11}(1535) are extracted from a recent multipole analysis of pion photoproduction data. We calculate photoproduction residues at the resonance pole in the complex plane for these amplitudes, in addition to the resonanc...

We have analyzed the available pion-nucleon elastic scattering data with laboratory kinetic energy below 2 GeV and have extracted the charged-pion\char21{}nucleon coupling constant. The extracted value of ${\mathit{f}}^{2}$, using fixed-t dispersion relations, is found to be 0.0735\ifmmode\pm\else\textpm\fi{}0.0015, a value in conflict with the res...

Scattering of spinless nucleons in a spherical potential is examined with the use of a computer graphics simulation VSCAT. The potential is defined stepwise and the Schroedinger equation is solved to obtain wavefunctions, scattering phases, partial-wave total cross sections and differential cross sections, which are then displayed graphically. For...

Comprehensive analyses of nucleon-nucleon elastic-scattering data below 1100 MeV laboratory kinetic energy are presented. The data base from which an energy-dependent solution and 22 single-energy solutions are obtained consists of 7223 pp and 5474 np data. A resonancelike structure is found to occur in the /sup 1/D/sub 2/, /sup 3/F/sub 3/, /sup 3/...

Particle scattering patterns were examined for a Coulomb potential, a Yukawa potential, and a short-range attractive well. For the Yukawa potential and short-range well we found structures associated with classical particle resonances. A fortran Tektronix graphics simulation was used to obtain the results presented here.

Comprehensive analyses of pion-nucleon elastic scattering data below 1100-MeV laboratory kinetic energy are presented. The data base from which an energy-dependent solution and 23 single-energy solutions are obtained consists of 3771 ..pi../sup +/p elastic, 4942 ..pi..â»p elastic, and 717 ..pi..â»p charge-exchange data. Partial-wave structure is...

Our K+-proton analysis is extended to 3 GeV/c. Both energy-dependent and energy-band solutions are reported. The P13 resonance is still strongly present, and we find evidence of resonances in the D15 and P11 states. We describe our scattering analyses interactive dial-in (SAID) computing system, which allows other investigators to access the curren...

This review of the properties of leptons, mesons, and baryons is an updating of the Review of Particle Properties, Particle Data Group [Phys. Lett. 111B (1982)]. Data are evaluated, listed, averaged, and summarized in tables. Numerous tables, figures, and formulae of interest to particle physicists are also included. A data booklet is available.

Comprehensive analyses of nucleon-nucleon elastic-scattering data below 1 GeV laboratory kinetic energy are presented. The data base from which an energy-dependent solution and 20 single-energy solutions are obtained consists of 5207 pp data below 1.2 GeV and 5283 np data below 1.1 GeV. The solutions are characterized by tightly constrained "resona...

The motion of a particle in a short-range attractive potential, when treated classically but with quantized angular momentum l, can give rise to a finite series of particle ''resonances.'' When this picture is applied to the ..pi..--N P/sub 33/ resonance it is discovered that a physically reasonable Yukawa potential could produce the effect and tha...

This review of the properties of leptons, mesons, and baryons is an updating of Review of Particle Properties, Particle Data Group [Rev. Mod. Phys. 52 (1980) No. 2, Part II]. Data are evaluated, listed, averaged, and summarized in tables. Numerous tables, figures, and formulae of interest to particle physicists are also included. A data booklet is...

All representations presently being used in analyses of nucleon-nucleon
scattering above the inelastic threshold are flawed by lack of implicit
unitarity, generality, or failure to encode reasonable physical
behavior. We examine unitarity from the point of view of an extended K
matrix, and derive a representation which is unitary, general, and whic...

Recent, precise analyses of p-p and n-p scattering data up to 800 MeV by Arndt et al. have provided the strongest evidence to date for the existence of dibaryon states in the I=1, 1D2 and 3F3 nucleon-nucleon channels. Model fits to their new phases reveal poles located near the "NDelta" threshold (2.15-0.05 i GeV). Because of their strong coupling...

A study of the factors which govern a precise determination of the S- and P-wave pion-nucleon scattering lengths using phenomenological energy-dependent partial-wave analyses is made. The nuclear scattering lengths obtained result from rapidly convergent effective-range expansions and are shown to be insensitive to the energy cutoff. These phenomen...

Energy-dependent and energy-independent partial-wave analyses of the low-energy ..pi../sup + -/p elastic and charge-exchange scattering data are presented. Unique, unitary, energy-dependent solutions giving a chiÂ²/datum of 1 are obtained. The solutions exhibit charge splitting in both the Sââ and Pââ partial waves. The T-matrix pole positions and...

The K+p scattering data up to 2 GeV/c were fitted with a coupled-channel K-matrix parametrization in which inelasticity is represented by a single production channel for each partial wave. Several solutions are possible above laboratory kinetic energies about 1 GeV, but all are essentially the same below this energy. All solutions that we have foun...

Scitation is the online home of leading journals and conference proceedings from AIP Publishing and AIP Member Societies

The production-history projection method of the authors is refined to determine the earliest date at which reasonably well determined depletion parameters can be ascertained. The method is applied to the United States production data for silver, crude oil, natural gas, coal, iron ore and uranium ore.

Optional videotaped lectures have been developed for use with a senior
level PSI quantum mechanics course. Details of the course and the
videocassette system are given. A summary of a comprehensive evaluation
of the course and optional lectures is presented.

The first paper of this series reported on energy-dependent and energy-independent phase-shift analyses of proton-proton elastic scattering data between 1 and 500 MeV. The present paper extends the analysis to include neutron-proton elastic scattering data between 0 and 425 MeV. Although this analysis is similar to those of the Livermore series, it...

Recent comprehensive analyses of n-p data near 50 and 325 MeV reveal a
complex χ2 hypersurface with nonquadratic behavior at 50
MeV and multiple minima at 325 MeV. We present the "most reasonable"
solutions at these energies and present graphically some of the complex
χ2 structure which invalidates the conventional measure
of error on the resultant...

The conductance of oxidized cholesterol membranes modified with excitability-inducing material was observed in membranes containing either single conductance channels or 100-1000 channels. Membranes containing single channels have several conductance states for each voltage polarity, and the current through membranes containing manychannels decays...

A simple physical-mathematical model is developed for an excitable artificial membrane consisting of a non-amphipathic lipid matrix spanned by protein channels having three conductance states. Although the model shows some of the features of squid axon data, the appropriate artificial membrane data are not available to these authors. A plea is made...

The recent data for K→2π, Ξ→Λπ, and Λ→Nπ decays are used to extract solutions for the parameters of these decays. The available K→3π, Σ→Nπ, and Ω→Ξπ data are not sufficient to determine the parameters of these decays. No preference is found for a ΔI=1/2 solution in any of the three analyzed decays. It may be possible to distinguish between ΔI=1/2 a...

It is demonstrated that the Hodgkin-Huxley voltage-clamp currents can be fitted with a Hodgkin-Huxley-type parametrization that involves about half as many parameters as did the original Hodgkin-Huxley fits and uses lower powers of the n and m function. A good fit to the Hodgkin-Huxley data is also obtained when the ion current densities are expres...

Energy-dependent partial-wave amplitudes based on a coupled-channel (K+p, KDelta) K- matrix formalism are obtained for elastic K+p scattering up to Plab=2 GeV/c. The data used include new high-precision differential cross sections. A total of 42 parameters describing the l

A recent phase-shift analysis of p-p scattering from 0-500 MeV has been used to calculate the average Coulomb rotation of the forward nuclear p-p amplitude in this energy range. We find that the rotated amplitude is well represented over this energy range by the unrotated amplitude (the imaginary part of which is related to the total cross section)...

Energy-independent and energy-dependent analyses are given for the proton-proton scattering data from 1 to 500 MeV. These analyses are similar to those of the Livermore series, but a number of modifications have been made, particularly in the low-energy representation. First, the range of the analyses has been extended by 50 MeV (i.e., from 450 to...

The accelerated-convergence expansion has generated some controversy in applications to single-energy analyses of kaon-nucleon scattering. We have applied this expansion to pion-nucleon scattering at 490 MeV as the first test of the method in a region where strong s-channel effects are in evidence. The χ2 values obtained from the accelerated-conver...

A description is given of an introductory biophysics PSI (Personalized System of Instruction) course which utilizes tutors selected from the students themselves (bootstrap tutors). In the author's opinion such tutors, while obviously easier to obtain, are as good as or better than tutors selected from a previous class.

Energy-dependent phase-shift analyses of low-energy n-α and p-α elastic scattering data were performed. Effective range parameters were obtained using the least number of parameters, and data up to the lowest energy necessary to give good fits. Fits to data up to 5 MeV for p-α scattering and up to 3 MeV for n-α scattering, with 7 parameters used in...

An energy-dependent phase-shift analysis of 0–21 MeV n-α scattering is presented and compared to the previous 0–23 MeV p-α analysis. The error matrix and inverse error matrix for both the n-α and the p-α analyses are given.

A technique is given for obtaining numerical solutions to the time-dependent electrodiffusion equations for a simple membrane. Voltage-clamp current densities are given as functions of time for several membrane boundary conditions and ion mobilities.

The use of partial-wave representations of existing scattering data in the planning of future measurements is described. A procedure is described for determining those measurements which are within the realm of experimental feasability and which will produce the best definition of the scattering matrix. The procedure is then applied to 330 MeV np s...

1 Physics and Biology.- Physics and Life.- Molecular Physics.- Molecular Biophysics.- Thermodynamics and Biology.- Information Theory.- 2 Cells, Viruses, and Heredity.- The Living Cell.- Cell Division.- Viruses and Bacteriophages.- Basic Laws of Genetics.- Mutations and Mutability.- Genetics of Bacteria and Phages.- 3 Biological Molecules.- Amino A...

The dipole models for steady-state currents in excitable membranes of Arndt, Bond and Roper and of Hamel and Zimmerman are
compared by fitting the equations to the data of Gilbert and Ehrenstein. The more complex Hammel and Zimmerman model does
not fit the data as well as does the simpler Arndt, Bond and Reper model. When fitting the data, the Hamm...

Following Wei's suggestion that nerve stimulation and conduction properties are due to dipole layers at the two membrane surfaces
(Wei, 1969), we have done steady-state electro-diffusion calculations in the constant field approximation for a simple double-dipole-layer
model. We are thereby able to quantitatively fit the recent potassium iso-osmotic...

Electroneutral approximate solutions for steady-state electrodiffusion of ions across a simple membrane are derived for general bionic environments and a restricted class of ion environments with more than two ion types, and a criterion is given for the electroneutral solution to be a good approximate solution.

Measurements of the polarization function P(θ) in n-4He scattering have been made at neutron energies of 11.0, 17.7, 23.8, 25.7, 27.3, and 30.3 MeV with the aim of improving upon previous descriptions of the interaction, especially as regards the analyzing power. Significant differences were found at the higher energies between experimental values...

Herein we show that the voltage-clamp current density at zero time calculated from electrodiffusion equations is linear in
the clamping voltage for a simple membrane (no charge structure) and for a membrae with fixed charges. Such membranes are
nonexcitable. Excitable membranes can be represented by a homogeneous membrane with dipole layers at the...

A comprehensive comparative study of the available K̄N partial wave analyses is made with a view to bring out their similarities and disagreements and to point towards those momentum regions that require particular attention in all future analyses. The multichannel nature of the K̄N scattering is discussed along with the presently available scatter...

The theoretical expressions for experimentally determined quantities in K→2π decays and leptonic kaon decays are used to determine solutions for various theoretical parameters. Two solutions are found: one for which the |ΔI|=1/2 dominance rule is valid, and another for which it is not. Both solutions yield ε≅η+-≅η00. Even precise measurements of φ0...

Starting from reported single-energy analyses of p-α elastic
scattering we obtain an energy-dependent solution to p-α
scattering between 0 and 23 MeV. We also did single-energy analyses at
energies where both differential-cross-section and polarization data are
available starting from the energy-dependent solution. The single-energy
results are rat...

Recent Princeton-Pennsylvania n-p differential cross sections are combined with existing n-p data at 210 and 330 MeV in order to obtain partial-wave representations of the T=0 N-N scattering matrix. The new data differ significantly from the existing large-angle cross sections at these energies, being more sharply peaked at the back angle and diffe...

A technique is given for obtaining numerical solutions to the steady-state electrodiffusion equations for a simple membrane. Solutions are given for several membrane boundary conditions in terms of ratios of current density to mobility for each ion type.

The available partial-wave analyses on the KN scattering data, the majority of which are single-channel analyses over limited momentum ranges, are studied with a view to facilitate a multichannel partial wave analysis over an extended momentum range (0-1400 MeV/c). The high-energy behaviour of the KN scattering amplitudes is examined by making ener...

We show that the exact steady-state solution to the electrodiffusion equations for a simple membrane is the constant electric field solution when the ion environment is electroneutral on both sides of the membrane and the total numbers of ions of the same valence on both sides are equal.

An energy-dependent phase-shift analysis of 0-20-MeV n-α scattering is attempted. Reasonable fits to the 0-16.4 data are obtained, but the rest of the data up to 20 MeV elude good fits. Single-energy analyses at energies where polarization data are available corroborate the energy-dependent analysis. Our results differe from the Hoop-Barschall phas...

A determination is made of the constraints which are imposed upon the low-energy 3S1-3D1 scattering parameters in order that the S matrix may satisfy the known static deuteron properties. A multichannel effective-range representation is used to derive a relationship between the phase parameters δS, δD, and ε1 at "low" energies. The relationship is...

Progress and proposals for future work are given in the partial wave analysis of nucleon-nucleon elastic scattering, kaon plus-nucleon elastic scattering, and pion-nucleon elastic and inelastic scattering. Activities are also required with respect to the Scattering Analysis Interactive Dial-in (SAID) facility. (LEW)

It is proposed to continue efforts on the analysis of the reactions; NN ..-->.. NN; PI N ..-->.. PI N, K/sup +/p ..-->.. K/sup +/p and PI N ..-->.. PI PI N below 2 GeV. The continuation of development of computer programs and data bases at VPI and SU is further proposed which can be accessed through telephone lines from anywhere and which will disp...

The Center for Analysis of Particle Scattering (CAPS) in the Department of Physics at Virginia Polytechnic Institute and State University has analyzed basic two-body hadron reactions below 2 GeV for the last two decades. Reactions studied were nucleon-nucleon, pion-nucleon, K{sup +}-nucleon and pion photoproduction systems. In addition to analyses...

Analysis of the United States minerals production data shows that at least fifteen metals have already peaked in production. The mineral fuels crude oil and natural gas are very near their peaks. The fact that most metals have peaked in production is consistent with the fact that most metals are more than fifty percent imported. Chapter One discuss...

Activities are reported with respect to the Scattering Analyses Interactive Dial-in (SAID) Facility. The facility provides scattering analysis solutions for nucleon-nucleon scattering, pion-nucleon scattering, and kaon plus-nucleon scattering. Data base management, partial wave analysis, modeling, and calculation of reaction cross sections are repo...

Progress is reported in the areas of nucleon-nucleon scattering analysis, pion production via isobar channels, theoretical questions concerning partial wave analysis, analysis of kaon plus-proton scattering. 8 refs., 17 figs. (LEW)

The Center for Analysis of Particle Scattering (CAPS) in the Department of Physics at VPI and SU has concentrated on analyses of basic several two-body hadron reactions below 2 GeV for the last two decades. Basic reactions under investigation are nucleon-nucleon, pion-nucleon, and K(+)-nucleon elastic systems. In addition to analysis of these syste...

The principle focus of study for the Center for Analysis of Particle Scattering (CAPS) in the Department of Physics at VPI and SU continues to be analyses of basic two-body reactions below 2 GeV. In addition to the nucleon-nucleon, pion-nucleon, and K/sup +/-nucleon elastic systems, we have performed an extensive isobar analysis of the pion product...

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 1963. Vita. Includes bibliographical references.

The theoretical expressions for experimentally determined parameters for K-->2pi decays are used to determine solutions for various theoretical parameters. This is accomplished by first assuming CP conservation and then treating the CP-nonconserving parts of the theoretical expressions as small corrections. We find two types of solutions: one type...

It is shown that there are three phase-shift ambiguities that can occur when not all possible observables are available for the phase-shift analysis at a given energy in spin-0-spin- 1/2 scattering. Two of the ambiguities, change of sign of the phases and exchange of opposite-parity phases, have been recognized for some time. The third ambiguity, w...

## Projects

Project (1)