# William Rory CokerUniversity of Texas at Austin | UT · Department of Physics

William Rory Coker

Ph. D.

## About

111

Publications

893

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

2,050

Citations

Introduction

Additional affiliations

August 1966 - present

## Publications

Publications (111)

Historically, work in medium energy nucleon-nucleus scattering physics started in the 1950s and has continued since. During the past ten years exciting new developments have occurred, and this work reviews these developments. Two distinct theoretical approaches for describing the medium energy scattering process are discussed. The first is nonrelat...

Calculations are presented of the nuclear tensor term in the proton-nucleus optical model potential, generated by the relativistic impulse approximation. We first show that previously published expressions for this term make an unnecessary approximation, and second, clarify its effects in proton-nucleus elastic scattering at intermediate energies....

We compute the analyzing power, Ay, and spin rotation, Q, for proton elastic scattering at 650 and 800 meV from target nuclei 16O, 40Ca, and 208Pb, using both nonrelativistic multiple-scattering theory and a relativistic impulse approximation model. We show that the nonrelativistic theory, based on the Schrödinger equation with relativistic kinemat...

The sensitivity of intermediate energy K/sup +/ meson-induced elastic and inelastic differential cross section predictions to nuclear structure effects in the nuclear interior is examined for â´Â°Ca and Â²Â°â¸Pb targets. The observed sensitivity for K/sup +/ mesons is compared to that obtained with intermediate energy protons. In general, the K/s...

The 500 MeV effective nucleon-nucleon isoscalar interaction is investigated through nonrelativistic folding model analysis of p⃗+nucleus elastic scattering data. Three empirical interactions are deduced. The first, obtained from a relativistic-Schrödinger-equation-equivalent form of a phenomenological Dirac optical potential, contains terms which a...

Excitation curves for the 32S(3He,n0)34Ar reaction at selected angles, and n0 and n1 angular distributions at four energies below the Coulomb barrier were measured. The data were analyzed by considering the interference between direct-reaction and compound-nucleus formation amplitudes.

Excitation curves for the /sup 32/S(/sup 3/He,n/sub 0/) /sup 34/Ar reaction at selected angles, and n/sub 0/ and n/sub 1/ angular distributions at four energies below the Coulomb barrier were measured. The data were analyzed by considering the interference between direct-reaction and compound-nucleus formation amplitudes.

A comparison of the relative sensitivities of 800 MeV proton-nucleus and 444 and 991 MeV K+ meson-nucleus elastic angular distributions to realistic details of neutron density distributions is presented for nuclei 40, 48Ca. The quantitative conclusions agree with qualitative expectations that medium energy K+ mesons are potentially superior at prob...

A previous study of the Coulomb interaction in nonrelativistic multiple-scattering theory is extended to account for relativistic effects. The projectile-nucleus Coulomb potential is computed from the relativistic Møller amplitude for projectile-nucleon scattering at low momentum transfer. The resulting Coulomb potential is reasonably approximated...

New, large-momentum-transfer 0.8 GeV p⃗ + 208Pb elastic analyzing power data are presented and compared to optical model predictions using the Kerman-McManus-Thaler microscopic optical potential. This comparison provides an important test of multiple scattering theories since the predictions are quite sensitive to the assumed nucleon-nucleon scatte...

New, large-momentum-transfer 0.8 GeV p+Â²Â°â¸Pb elastic analyzing power data are presented and compared to optical model predictions using the Kerman-McManus-Thaler microscopic optical potential. This comparison provides an important test of multiple scattering theories since the predictions are quite sensitive to the assumed nucleon-nucleon scatt...

Results are presented of coupled-channels analyses of proton inelastic scattering data for the nucleus 24Mg, in which the 22+, 4.24 MeV, 3+, 5.2 MeV, 42+, 6.01 MeV, and 5+(?), 7.8 MeV states of the γ-vibrational band are excited, at incident proton energies of 20.3, 40, and 800 MeV. Previous coupled-channels analyses of proton and α particle inelas...

Differential cross sections and analyzing powers for the elastic scattering of 800 MeV polarized protons from 40,42,44,48Ca are reported. A first-order, spin-dependent KMT optical potential analysis is presented from which the rms radii of the neutron densities are deduced. A comparison of these results with other determinations and with various th...

The distribution of the single-neutron strength up to an excitation energy Ex = 7.0 MeV in 11Be was investigated with the 10Be(d, p)11Be reaction at Ed = 25 MeV. The states are found to be excited with significant strength. The angular distribution for the 1.785 MeV state is typified by an orbital angular momentum transfer ln = 2. This together wit...

New differential cross section and analyzing-power data for 800-MeV ppol+12C,116, 124Sn inelastic scattering to the first 2+ states are presented. A distorted-wave Born-approximation analysis which utilizes collective form factors and includes deformation of the spin-orbit potential is shown to provide a reasonable description of the analyzing-powe...

Elastic scattering analyzing powers and differential cross sections for 800 MeV + 54Fe, 58,64Ni are reported. An approximately mode-independent technique is used to extract information concerning the neutron density distributions of these nuclei.

The first order, spin-dependent microscopic proton-nucleus optical potential of Kerman, McManus, and Thaler is used to analyze 800 MeV polarized proton elastic differential cross section and analyzing power data for target nuclei 58Ni, 90Zr, 116,124Sn, and 208Pb. Approximately model-independent target neutron density distributions are constructed i...

Distorted-wave Born-approximation calculations for medium-energy proton inelastic scattering to collective states, which use microscopic, spin-dependent optical potentials that properly describe proton elastic analyzing powers, show that inclusion of the deformation or collectivity of the spin-orbit term in the inelastic transition matrix element h...

Differential cross section and analyzing power data for elastic
scattering of 0.8-GeV polarized protons from 12C,
58Ni, 90Zr, and 208Pb have been
analyzed in terms of the Kerman-McManus-Thaler formalism using
spin-dependent nucleon-nucleon scattering amplitudes. The derived
results for nuclear matter densities are in good agreement with
theoretical...

Angular distributions for the elastic and inelastic scattering of 0.8 GeV protons from /sup 12/C, /sup 13/C, and /sup 208/Pb have been measured. Reported are data for the ground, 4.4 MeV 2/sup +/, 7.6 MeV 0/sup +/, 9.6 MeV 3/sup -/, and 14.1 MeV 4/sup +/ states of /sup 12/C; the ground, 3.1 MeV 1/2/sup +/, 3.7 MeV 3/2/sup -/, 6.9 MeV 5/2/sup +/, 7....

Angular distributions for the elastic and inelastic scattering of 0.8
GeV protons from 12C, 13C, and 208Pb
have been measured. Reported are data for the ground, 4.4 MeV 2+, 7.6
MeV 0+, 9.6 MeV 3-, and 14.1 MeV 4+ states of 12C;
the ground, 3.1 MeV 12+, 3.7 MeV 32-, 6.9 MeV
52+, 7.6 MeV 52-, and 11.9 MeV (?) states of
13C; and the ground, 2.6 MeV 3-...

Differential cross section and analyzing power data for elastic scattering of 0.8 GeV polarized protons from 116Sn and 124Sn are analyzed in terms of a spin-dependent Kerman-McManus-Thaler formalism. Neutron matter densities and rms radii are deduced with careful attention to sources of error, and found to be in good agreement with Hartree-Fock pre...

We present an analysis of new data for 0.8-GeV inelastic proton scattering to the ${2}^{+}$ (4.4 MeV) and ${4}^{+}$ (14.1 MeV) states of $^{12}\mathrm{C}$, using both distorted-wave Born-approximation and coupled-channels calculations with empirical, spherical, and deformed optical potentials. Both the deformation of the optical potential and the t...

The first elastic-scattering analyzing-power (${A}_{y}$) data at 0.8 GeV are presented and discussed. Angular distributions of ${A}_{y}$ over the range 2\ifmmode^\circ\else\textdegree\fi{} to 20\ifmmode^\circ\else\textdegree\fi{} (30\ifmmode^\circ\else\textdegree\fi{} for $^{12}\mathrm{C}$) have been obtained for $^{12}\mathrm{C}$, $^{58}\mathrm{Ni...

Differential cross sections for elastic scattering of 0.8-GeV protons from 12C, 58Ni, and 208Pb have been measured. Preliminary analysis of the data in terms of the Kerman-McManus-Thaler formalism with spin-dependent nucleon-nucleon amplitudes shows sensitivity to details of proton and neutron matter distributions.

An attempt to survey all of the topics traditionally covered in
undergraduate physics courses in one semester, with strong emphasis on
everyday phenomena of nature, is described. In order to compress a
survey course in physics into one semester, a number of unusual
techniques were used and are described. A point was also made, during
the course, to...

Differential cross sections for elastic scattering of 0.8-GeV protons from C12, Ni58, and Pb208 have been measured. Preliminary analysis of the data in terms of the Kerman-McManus-Thaler formalism with spin-dependent nucleon-nucleon amplitudes shows sensitivity to details of proton and neutron matter distributions.

We present and discuss here the results of a calculation of the real part of the potential energy of a proton within nuclear matter, making use of the realistic Reid soft-core nucleon-nucleon interaction, which we justify in the intermediate-energy range. The problem of evaluating the volume of the real part of the proton-nucleus optical-model pote...

Medium energy proton elastic and inelastic scattering to states of 58Ni and 208Pb, and 4He elastic and inelastic scattering to states of 40Ca, are analyzed using the partial wave approach, by solving the Schrödinger equation with relativistic kinematics and using the distorted wave Born approximation. Our results can be compared with results of sev...

We present results of a phenomenological analysis of recently obtained data for 4He + 4He elastic scattering at 0.65 and 0.85 GeV incident laboratory energies. We find that the observed angular distributions cannot be fit unless the nuclear potential has a strong, short-range repulsive contribution, in agreement with the results of microscopic and...

Elastic scattering of α-particles from helium has been measured at bombarding energies of 0.85 and 0.65 GeV over the range of four momentum transfer from 0.9 to 3.8 (GeV/c)2. The results are compared with the predictions of an α-α potential obtained by a folding procedure using a p-4He potential and 4He charge distribution.

An analysis is given of the stripping reaction $sup 28$Si($sup 3$He,
d)$sup 29$P at an incident $sup 3$He energy of 35.3 MeV, considering seven
residual states. These extend in excitation energy to 4.8 MeV with the highest
four being unbound to proton emission and described via complex energy
eigenstates. The results of a distorted-wave Born-ap...

We analyze the stripping reaction 28Si(3He,
d)29P at an incident 3He energy of 35.3 MeV,
considering seven residual states. These extend in excitation energy to
4.8 MeV with the highest four being unbound to proton emission and
described via complex energy eigenstates. The results of a
distorted-wave Born-approximation analysis are rather disappoin...

Recently obtained data for elastic scattering of 12,13C from 14N, 16O, 28Si and 32S are analyzed by a variety of methods, including the conventional six-parameter optical model, Ericson's parameterization of the strong-absorption S-matrix, the Glauber formalism, and a simple single-folding model. It is shown that earlier analyses of similar data, i...

An assertion made in a recent paper dealing with the28Si(3He,d) reaction to the 1/2+ ground state of29P, namely that the spectroscopic factor extracted in the conventional way using DWBA analyses has a strong energy dependence, is shown to be due to a complication of inconsistent DWBA analyses by various authors, rather than being due to any intrin...

A total of 21 states of 33S in the region of excitation from about 8.6 to 9.5 MeV have been studied using the reaction 32S(d, p) at 12 MeV incident deuteron energy and a biased quadrupole spectrometer. Fractionated single-particle states are identified via their forward-angle cross sections, using distorted-wave Born-approximation predictions with...

We show that when one considers heavy-ion-induced direct nuclear reactions, the narrowly localized reaction surface makes a traditional approximation used in analysis of light-ion reactions to particle-unbound states a very poor one. Even for unbound states having single-particle widths 10-5 of their resonance energies, quite different heavy-ion an...

We discuss macroscopic form factors generated using the Lane equations, and microscopic form factors generated using a complex effective nucleon-nucleon interaction, in terms of their similarities, differences, and relative successes in describing experimental data for90Zr(p, n)90NbA and91Zr(p, n)91NbA from 22 to 40 MeV. Our conclusions are that th...

We discuss the general problem of j dependence in nuclear reactions, and evidence that l=2j dependence seen in (d,p) reactions is, at least in many cases, connected with the collective character of the target and residual nuclei in the reaction. To test this idea, we present analyses of three sets of data for 28Si(d,p)29Si, at 10, 13, and 18 MeV in...

A total of 40 states of 31Si in the region of excitation from about 5 to 9 MeV have been studied using the reaction 30Si(d,p) at 10 MeV incident deuteron energy, and a biased quadrupole spectrometer. Fractionated single-particle states are identified via their forward-angle cross sections, using distorted-wave Born-approximation predictions with bo...

The mechanism for ((d,α)) reactions is discussed, with special attention given to the 98Mo(d,α)96Nb reaction leading to the presumed [(g9/2)p(d5/2)-1n] multiplet in 96Nb. The analysis relies on the coupled-reaction-channel approach for including contributions from the successive pickup processes (d,t)-(t,α) and (d,3He)-(3He,α). An excellent descrip...

A charged-particle energy-mass identification system is described which uses an offset, slightly rotated, magnetic quadrupole doublet in conjunction with a single lithium-drifted silicon detector. Perfect particle identification is achieved while maintaining the high resolution of the single charged-particle detector. The versatility, low cost, and...

We have obtained statistically accurate angular distribution data at extreme forward angles (theta=2°-40°) for 30Si(d,p)31Si leading to the 2.32 MeV (3/2+) and 2.79 MeV (5/2+) states, at Ed=10 MeV, We show that the extreme difference in the angular distributions for these two states can be explained by coupled-channel Born approximation calculation...

Distorted-wave Born-approximation (DWBA) calculations are performed for 54Fe(d,n) angular distributions at 10 MeV populating five proton resonances in 55Co, at 5.17, 5.54, 5.74, 5.86, and 6.07 MeV excitation, using Gamow states as form factors. Results of the calculations are compared with previous DWBA analyses in which bound-state functions were...

It is demonstrated that nonorthogonality effects can play a very important role in multistep processes involving successive particle-transfer reactions. This is shown for the particular example of the (3He, d)-(d, t) process, where nonorthogonality terms can be included as a renormalization of the effective interaction for the direct (3He t) charge...

A simple recipe for generating a complex effective interaction for distorted wave Born approximation calculations from a real, microscopic charge-exchange form factor is investigated. The recipe is tested against angular distribution data for 208Pb(p, n) and 209Bi(p, n) from 25 to 50 MeV incident proton energy. The form factor resulting from the re...

Using a coupled-reaction-channels (CRC) description of nuclear reactions, we have studied the reaction 88Sr(h, t) 88Y to 4-, 5-, and 2+, 3+ doublet states. The data, taken at 23 MeV, show angular distributions with anomalous shapes, which cannot be explained by simple distorted-wave Born approximation calculations; our calculations, including (h, a...

The88Sr(d, n∼p)88Sr cross section has been measured at 170 ° for deuteron energies from 7.5 to 10.0 MeV, and the total88Sr(d, n∼p) cross section obtained. The total cross section is compared with results of coupled-channel Born approximation calculations using both empirical and shell-model-reaction-theory form factors to describe the decaying isob...

Various improvements to the usual distorted-wave Born approximation description of direct reactions on light nuclei are investigated, using 11B(h, alpha)10B as an example, and including finite-range effects, compound nuclear contributions, and deformation as well as inelastic process in the entrance and exit channels. It is found that only the inel...

36,38Ar(d, p) angular distributions at 9- and 10-MeV incident energy, for 13 neutron-unbound states in 37,39Ar, are described in terms of conventional distorted-wave Born-approximation theory using complex-energy eigenstates as form factors, and spectroscopic information is extracted which is consistent with previous studies of the bound neutron st...

We have developed a formulation of the theory of multichannel nuclear reactons which permits practical and realistic numerical calculations in which a number of different reaction channels are coupled, assuming a zero-range approximation for the effective coupling and neglecting effects arising from the non-orthogonality of different reaction chann...

Excitation functions of the (p,np̃) reaction on 91Zr, 119Sn, 208Pb, and 209Bi are compared with the predictions of exact solutions of the coupled Lane equations, and it is found that the distorted-wave Born-approximation and coupled-channel predictions have essentially the same overall shape if the same optical and symmetry potentials are used. A l...

An analysis is presented of 30.2 MeV92Mo(, d)93Tc
A
angular distributions for seven isobaric analog resonances in93Tc
A
, using complex energy eigenstates to provide single-particle resonance state functions as form factors for the DWBA calculations. Details of the computation and use of complex energy eigenstates or Gamov functions are given, and...

Excitation functions for proton elastic and inelastic scattering to several low-lying states of 96Mo have been measured in the energy range from 5.2 to 8.0 MeV. Isobaric analog resonances have been used to deduce the structure of parent states in 97Mo. In particular, the ground state of 97Mo was found to have parentage in four excited states of 96M...

An analysis of the 40Ar(tau,t)40K reactions populating the 0+ analog state at 4.38 MeV and the 0+ antianalog state at 1.65 MeV with incident 3He energies of 35 and 18 MeV is made, including contributions from a pickup-stripping reaction mechanism as well as a conventional direct reaction mechanism. Agreement in magnitude and shape between calculate...

An in-beam electron spectrometer was used to identify internal-conversion transitions resulting from proton bombardment of 92Mo at 8.0 and 11.0 MeV.

Differential and total cross sections for 88Sr(d, np~)88Sr have been obtained and compared with the results of coupled-channel Born approximation calculations, which also are in agreement with earlier data for 88Sr(d, p)89Sr(d5/2 g.s.) excitation functions at 170°. Present address: Richard Laboratory, Kansas State University, Manhattan, Kansas 6650...

Excitation functions for the quasi-elastic (p, np̃) reaction are presented 91Zr, 119Sn, 208Pb and 209Bi from threshold to 45 MeV. Attempts to fit the data with conventional macroscopic DWBA calculations, using the Becchetti-Greenless (BG) optical model parameters, show that for all four nuclei considered an extremely unrealistic but consistent ener...

In-beam γ-ray measurements of the excited states in 97Tc have been made using the reaction 97Mo(p, nγ)97Tc at incident proton energies between 3.0 and 6.0 MeV. Singles and γ-γ coincidence measurements were made using Ge(Li) detectors and an on-line two-parameter data-acquisition system. By these methods about 50 γ rays associated with the deexcitat...

Using proton form factors computed with a simple theory of analog resonances, recent data for 92Mo(3He, d)93TcA to three prominent isobaric analog resonances, the d at 8.39 MeV excitation, the triplet at 9.90 MeV, and the (?) at 10.72 MeV, are fitted wi Spectfroscopic factors resulting from the analysis are in reasonable agreement with those obtain...

The reactions93Nb(p, p)93Nb,93Nb(p, n)93Mo, and93Nb(p, p) through isobaric analog resonances in94Mo have been used to study the structure of low-lying93Nb states, specifically the degree to which these states can be described as single protons coupled to the core states of92Zr. Excitation curves were obtained from 5.8 to 7.6 MeV incident proton ene...

Total and partial widths and resonance mixing phases for analog resonances in 87Rb, 89Y, 91,93Nb, 93,97Tc are calculated in the framework of a nonorthogonal, optical-model basis in a shell-model theory of reactions. The proton optical potential used is identical to that with which the experimental resonance parameters were extracted, for 89Y and 91...

It is shown that, although final nuclear states populated in charge exchange reactions on most nuclei with A>60 are proton unbound, there is at most a 10% enhancement of the microscopic charge-exchange from factor when the decay of the final state is taken into account.

A simple method for computation of semi-microscopic, zero-range three-nucleon transfer form factors for use in DWBA calculations is proposed and applied in two examples: 92Zr(p,alpha)89Y(1/2- g.s. and 3/2-, 1.51 MeV) and 90Zr(p, alpha)87Y(1/2- g.s. and 3/2- 0.38 MeV). Research supported in part by the US Atomic Energy Commission.

The (p, ) reaction was studied on a208Pb target at 16.475 MeV. Nineteen states were observed in205Tl, up to 3.6 MeV in excitation. Angular distributions were obtained for five strong proton-hole transitions, and DWBA fits made to determinelj values. Results are compared with previous206Pb(t, )205Tl,206Pb(d,3He)205Tl,205Tl(p, p), and205Tl(n, n) work...

The 86Kr(d,p)87Kr reaction leading to three strong low-lying states in 87Kr(d5/2g.s., 0.53 MeVs1/2, and 1.47 MeVd3/2) has been studied as a function of energy from 5.0 to 10.5 MeV at 100, 120, 140, and 160° laboratory angles. The strong, unusually shaped threshold cusp observed in the 86Kr(d,p)87Kr(d5/2 g.s.) excitation curve near 7.56 MeV, thresho...

Proton form factors for isobaric analog resonances populated directly as residual states in (d,n) and (3He,d) reactions are discussed and computed explicitly using a Lane-model Hamiltonian and the formalism of Feshbach's unified reaction theory. The resonance form factors thus obtained are compared in specific cases with equivalent parent bound-sta...

Angular distributions for 14C(τ, α)13C leading to the ground state of 13C were obtained at incident 3He energies of 5.98, 8.0 and 10.0 MeV. 14C(τ, τ)14C angular distributions were obtained at the same energies and used to obtain optical potentials for the entrance channel of (τ, α). Exit channel optical potentials were extracted from 13C(α, α)13C a...

Not Available Present address: Temple University, Philadelphia, Pennsylvania 19122.

A charge-exchange threshold cusp is observed in the summed 160° excitation curve for 93Nb(d,p)94Nb(6+,g.s.- 2+,0.31 MeV) at ~7.1 MeV, the threshold of the analogous 93Nb(d,n)94MoA(6+,13.2 MeV-2+,13.5 MeV) reaction. As predicted by theory, it is essentially identical in shape to the excitation curve previously measured for 90Zr(d,p)91Zr(d52,g.s.) in...

An extensive study of 90,91Zr(d,p) excitation functions has been carried out for deuteron energies from 5 to 11 MeV, in order to investigate the extent and systematic behavior of charge-exchange contributions to the (d,p) process. Nine residual states in 91Zr, up to excitations of 3.7 MeV, were involved, as well as three residual states of 92Zr, up...

Excitation functions for the 92Zr(d,p)93Zr reaction to eight low-lying states in 93Zr were measured from 4.2- to 11.2-MeV incident deuteron energy, a region including the (d,n) thresholds to the analogs of the observed states. Charge-exchange effects were observed for at least the d52 ground state in 93Zr. Also, 92Zr(d,d) angular distributions were...

Internal conversion electrons were detected using cooled Si(Li) detectors. No effort was made to separate the scattered electrons and the scattered protons prior to detection. The resolution obtained was typically 4 keV or better.

States of 87Kr have been investigated via the
86Kr(d, p)87Kr reaction, with 11-MeV deuterons and
an over-all energy resolution of 30 keV. Proton groups leading to 23
states in 87Kr have been identified. The angular-distribution
data have been analyzed using finite-range distorted-wave
Born-approximation (DWBA) calculations to extract spectroscopic...

States of $^{87}\mathrm{Kr}$ have been investigated via the $^{86}\mathrm{Kr}(d, p)^{87}\mathrm{Kr}$ reaction, with 11-MeV deuterons and an over-all energy resolution of 30 keV. Proton groups leading to 23 states in $^{87}\mathrm{Kr}$ have been identified. The angular-distribution data have been analyzed using finite-range distorted-wave Born-appro...

Angular distributions for the (d,..cap alpha..) reactions on Â¹Â³C, Â¹â´N, and Â³Â¹P targets have been measured in the 10 to 12 MeV incident deuteron energy range. The Â³Â¹P(d,..cap alpha..)Â²â¹Si measurements have been repeated at a deuteron energy of 33.7 MeV. The experimental angular distributions for the first three alpha groups in each react...

Angular distributions for the elastic and inelastic scattering of 0.8 GeV protons from Â¹Â²C, Â¹Â³C, and Â²Â°â¸Pb have been measured. Reported are data for the ground, 4.4 MeV 2/sup +/, 7.6 MeV 0/sup +/, 9.6 MeV 3â», and 14.1 MeV 4/sup +/ states of Â¹Â²C; the ground, 3.1 MeV 1/2/sup +/, 3.7 MeV 3/2â», 6.9 MeV 5/2/sup +/, 7.6 MeV 5/2â», and 11.9...

Excitation curves for the Â³Â²S(Â³He,nâ) Â³â´Ar reaction at selected angles, and nâ and nâ angular distributions at four energies below the Coulomb barrier were measured. The data were analyzed by considering the interference between direct-reaction and compound-nucleus formation amplitudes.