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The 16O(e,e'p) reaction in the quasi-elastic region has been studied in several experiments to determine spectroscopic factors, hence, the degree to which $^{16}$O looks like a closed shell. By varying the kinematics, experimentalists are able to extract response functions which comprise the cross section. However, analysis of the response functions separately produces very different spectroscopic factors. Two calculations led to different conclusions as to whether exchange currents can eliminate the discrepancies. Neither calculation considered relativistic corrections. The purpose of the article is to investigate the disagreement as to whether exchange currents are the solution to obtaining consistent spectroscopic factors, and to show that relativistic corrections have a much greater influence on providing this consistency. This calculation employs the recoil corrected continuum shell model, a model that uses a realistic interaction, and produces non-spurious scatterings states that are solutions to the coupled channels problems. Pionic and pair contributions to the exchange currents were calculated as developed by Dubach, Koch, and Donnelly. Relativistic effects are included by use of the direct Pauli reduction. Contributions of the exchange currents are shown to be insufficient to provide consistent spectroscopic factors. However, the inclusion of relativistic corrections, that can be large, lead to more consistent spectroscopic factors and cross sections. The influence of channel coupling is also shown to be significant. Tests of current conservation show that inclusion of the direct Pauli reduction produces small increases in its violation. Response functions which depend on the transverse current are sensitive to the lower component of relativistic wave functions, and hence, would provide a measure of the appropriateness of any relativistic model.

A brief history of the continuum shell model with full correction for target recoil is provided. Past applications to nucleon induced reactions, nucleon capture, knockout reactions by pions and electrons, and strangeness exchange reactions are provided. Recent progress of the model is reviewed. Examples of continuum states for p-shell nuclei, derived from both two and three-body interactions, are given. Finally, the general model is presented in which any core states and any states of the composite system may be incorporated in a calculation.

A continuum shell model is now available for p -shell nuclei with exactly the same important properties as a bound-state p -shell model calculation. This means that one can obtain all solutions that correspond to coupling one nucleon to the possible p -shell states of a bound-state calculation. The resulting coupled-channels solutions are antisymmetric and contain no spurious components. This model can be used to describe a very broad range of nuclear phenomena, from capture reactions at astrophysical energies, to knockout reactions at low energies, to nucleon scattering and charge exchange at intermediate energies. Example calculations are shown for the compound systems 7 Be and 7 Li. Here it is demonstrated that agreement between theoretical and experimentally determined elastic and inelastic cross sections and analyzing power values can be improved by coupling to all open channels.

A procedure is suggested for calculating electroexcitation multipoles to order 1/${M}_{N}$${}^{2}$ with only the operators required in the calculations to order 1/${M}_{N}$. It is also shown that calculations to order 1/${M}_{N}$${}^{2}$ cannot account for the contributions of a fully relativistic calculation of the transverse response.

Background: The $R$ matrix formalism of Lane and Thomas has proven to be a convenient reaction theory for solving many-coupled channel systems. The theory provides solutions to bound states, scattering states, and resonances for microscopic models in one formalism. Purpose: The first purpose is to extend this formalism to the relativistic case so that the many-coupled channels problem may be solved for systems in which binary breakup channels satisfy a relative Dirac equation. The second purpose is to employ this formalism in a relativistic continuum shell model. Methods: Expressions for the collision matrix and the scattering amplitude, from which observables may be calculated, are derived. The formalism is applied to the 1p-1h relativistic continuum shell model with an interaction extracted from relativistic mean-field theory. Results: The simplest of the $\sigma +\omega +\rho$ exchange interactions produces a good description of the single-particle energies in $^{16}$O and $^{90}$Zr and a reasonable description of proton scattering from $^{15}$N. Conclusions: The development of a calculable, relativistic $R$ matrix and its implementation in a $1p-1h$ relativistic continuum shell model provide a simple relatively self-consist, physically justifiable model for use in knockout reactions.

Results of recoil-corrected continuum shell model calculations are presented for {sup 4}He({pi},{pi}{sup {prime}}p){sup 3}H. The extremely large values of {sigma}({pi}{sup +},{pi}{sup +{prime}}p)/{sigma}({pi}{sup {minus}},{pi}{sup {minus}{prime}}p) are shown to be a result of neutron excitations which couple to outgoing proton channels. The large ratio will occur in regions where neutron excitations increase rapidly in a particular channel and, therefore, may be a signal for giant resonances. {copyright} {ital 1997} {ital The American Physical Society}

Background: The recoil-corrected continuum shell model provides coupled-channels solutions for bound and unbound wave functions from realistic effective interactions. The wave functions are antisymmetric and contain no spurious components because the calculations are performed in the center-of-mass system.Purpose: This model has now been extended to include 1$\ensuremath{\hbar}\ensuremath{\omega}$ excitations in the structure of $p$-shell target (residual) nuclei, hence allowing 0$s$-shell knockout processes. Several reactions involving the ${}^{12}$C compound system are investigated to demonstrate the utility of the model.Methods: The states of ${}^{11}$B and ${}^{11}$C are constructed in the nonspurious 0$\ensuremath{\hbar}\ensuremath{\omega}$ plus 1$\ensuremath{\hbar}\ensuremath{\omega}$ model space. An interaction, fitted to Cohen and Kurath (8-16) plus Reid soft core $g$-matrix elements, is employed. One nucleon is coupled to these states to create a basis for the bound and scattering states for ${}^{12}$C.Results: Calculated elastic and inelastic cross sections agree well with available data. The calculated transverse response at high momentum transfer is lower than that extracted from data. Although significant, meson exchange currents are not sufficient to give agreement with data. Likewise inclusion of 0$s$-shell knockout is not sufficient to provide agreement. The high-energy octupole resonance appears at low momentum transfer and an energy of 106/${A}^{1/3}$.Conclusions: The model should provide meaningful predictions for states near the proton drip line via the ($p$,$n$) reaction. Coupled-channels solutions are necessary for describing ${}^{12}$C($e$,${e}^{\ensuremath{'}}x$) at low momentum transfer. Lack of strength at low energy and momentum transfer in optical model calculations of ${}^{12}$C($e$,${e}^{\ensuremath{'}}x$) is at least partly attributable to the omission of giant resonances. Data for (${\ensuremath{\pi}}^{+}$,${\ensuremath{\pi}}^{+\ensuremath{'}}p$)/(${\ensuremath{\pi}}^{\ensuremath{-}}$,${\ensuremath{\pi}}^{\ensuremath{-}\ensuremath{'}}p$) could verify this conclusion. Lack of strength in the transverse response may be attributable to recoil terms which are omitted in most calculations.

Calculations have been performed for inelastic electron scattering from {sup 4}He within the framework of the recoil-corrected continuum shell model. Comparisons are made to data ranging from {ital q} near zero to {ital q}=650 MeV/{ital c}. Both inclusive and exclusive processes have been investigated. The effect of meson exchange currents, spin-channel coupling, {ital p}-{ital n} channel coupling, relativistic corrections, and final state interactions are investigated. Agreement with data is generally good; however, the calculated inclusive transverse response is too small in the region of low energy transfer. This reduced strength is related to the lack of current conservation in the model. {copyright} {ital 1996 The American Physical Society.}

Inelastic electron scattering cross sections for {sup 4}He have been calculated at 180{degree}. The wave functions employed are those generated in the recoil-corrected continuum shell-model framework with the M3Y {ital g}-matrix interaction. The calculations include the complete, translationally invariant transition operator and pion-exchange current contributions. Good agreement is obtained with data at {ital E}{sub 0}=60.6, 130, and 200 MeV. Approximations to the full operator and their implications for single-particle models of nucleon knockout are discussed.

The Dirac oscillators are shown to be an excellent expansion basis for solutions of the Dirac equation by $R$-matrix techniques. The combination of the Dirac oscillator and the $R$-matrix approach provides a convenient formalism for reactions as well as bound state problems. The utility of the $R$-matrix approach is demonstrated in relativistic impulse approximation calculations where exchange terms can be calculated exactly, and scattering waves made orthogonal to bound state wave functions.

The spectra of seven p-shell {lambda} hypernuclei are calculated with effective interactions derived from the new Nijmegen ESC04 baryon-baryon interaction. The results of interactions ESC04A and ESC04B compare well with the known experimental levels, whereas those of ESC04C and ESC04D do not. The primary difference between the two pairs of potentials is the ratio of triplet to singlet strength in the central potential. The {sub {lambda}}{sup 16}O results indicate that the tensor interaction is too weak and/or the spin-orbit odd interaction is too strong for all potentials. In addition the {lambda}N-{sigma}N coupling potentials have an unusual radial behavior. The calculations provide a natural explanation for the reduction of the spin-spin interaction of phenomenological interactions from the beginning to the end of the shell.

$\ensuremath{\Lambda}$-hypernuclei single-particle energies are calculated for the new Nijmegen ESC04 baryon-baryon interaction. A Brueckner-Hartree approach is employed. Whereas good agreement with experimental results is obtained for the $A=3,4$, and 5 systems, the heavier systems are considerably overbound. A possible source for some of the overbinding is the spin-orbit odd interaction and its effect on the ${}^{3}{\mathrm{P}}_{2}$ channel.

Calculations are reported for reactions in the {sup 8}B and {sup 8}Li compound systems with the recoil corrected continuum shell model. Comparison with observed structure indicates that the spin-orbit component of the M3Y interaction must be modified near the middle of the p shell. Calculations are performed with three spin-orbit strengths. The prediction for {sup 7}Be(p,{gamma}){sup 8}B, based on this model and available data, is that S{sub 17}(0) equals 21.63 eV b and S{sub 17}(20) 21.02 eV b. Calculations for {sup 7}Li(n,{gamma}){sup 8}Li indicate that the {sup 8}Li, 1{sub 2}{sup +} state is nearly degenerate with the 3{sup +} state. It is shown that a measurement of {sup 7}Li(n,{gamma}){sup 8}Li(1{sub 1}{sup +}) can locate the 0{sup +} state. It is also shown that {sup 7}Be(p,p{sup '}){sup 7}Be(1/2{sup -}) can locate the 1{sup +} and 0{sup +} strength in {sup 8}B.

Two recent experiments yield conflicting results on the possibility of a low-lying 1/2{sup -} state in {sup 7}He at E{sub n}{sup c.m.}{approx}1 MeV. A calculation with the recoil corrected continuum shell model reproduces this state as well as results that are compatible with the data from both reports, but only with the conclusion of one.

A continuum shell model has been constructed which allows inclusion of any nonspurious states of the core nuclei and any nonspurious states of the composite system. The resulting coupled-channels solutions are antisymmetric and translationally invariant. These wave functions can be used to calculate many nuclear phenomena, from capture reactions at astrophysical energies, to knockout reactions at low energies, to nucleon scattering and charge exchange at intermediate energies. The model is used to investigate the {sup 4}He({gamma},p){sup 3}H, {sup 4}He({gamma},n){sup 3}He, and, {sup 3}He(p,p){sup 3}He reactions.

[ital g]-matrix calculations have been performed for [sub [Lambda]][sup 5]He, [sub [Lambda]][sup 17]O, and [sub [Lambda]][sup 41]Ca by solving the [Lambda]-[Sigma] coupled channels Bethe-Goldstone equation. The potentials employed were the Nijmegen model D and Nijmegen soft core. Calculations were performed with various choices for the Pauli-forbidden space and the energy denominator. The Nijmegen model D does a reasonable job of reproducing most experimental single-particle energies, but the calculated ground-state binding energies vary smoothly from being underbound in the [sub [Lambda]][sup 5]He to overbound in [sub [Lambda]][sup 41]Ca. The Nijmegen soft core underbinds all single [Lambda] states, but gives level spacings which agree with experimental values.

Calculations are reported for low energy, proton capture by 14N with the recoil corrected continuum shell model. An interaction from a fit to Cohen and Kurath (6–16) p-shell matrix elements and Reid soft-core g-matrix elements is employed. The prediction for 14N(p, γ)15O, based on this model and available data, is that S(0) equals 1.676 and S(30) is 1.666 keV b. Good agreement with available cross section data support this result. No evidence is found for significant contributions from the subthreshold resonance.

Calculations have been performed for the photoproduction of eta mesons on nuclear targets to selected discrete states. A recent fit to the {sup 1}H({gamma},{eta}){sup 1}H elementary amplitude was employed in an impulse approximation. Transition densities were determined by comparison with inelastic electron scattering data. Stretched state excitations yield cross sections on the order of tenths of microbarns in the region of the {ital S}{sub 11}(1535). Calculations for photoproduction to selected states demonstrate how experiments can provide the isospin structure of the elementary amplitude. The same experiments can also test models of the {eta}{ital N} interaction by comparing measured and calculated distortion effects.

Pion inelastic scattering calculations, exciting the stretched state configuration of /sup 12/C, have been performed in the context of the impulse approximation, but the excited states generated from the recoil corrected continuum shell model. The calculation, therefore, allows for the subsequent decay of excited states via particle emission. The unbound nature of these states is shown to greatly effect their structure and isospin mixing, and therefore the pion cross sections. The calculated cross sections are consistent with observed sigma..pi..+, sigma..pi..- differences.

The /sup 4/He giant dipole resonance is calculated with a continuum shell model which treates the center of mass correctly and includes possible noncentral components of the nucleon-nucleon interaction. The (..pi..,p) and (..pi..,n) cross sections and asymmetry coefficients agree well with the experiment. The b/sub 2/ asymmetry coefficients is shown to depend on the spin-orbit odd component of the effective nuclear force. The 1/sup -/ level positions and channel mixing are in best agreement with ''solution II'' of the R-matrix fit of Werntz and Meyerhof.

Cross sections are calculated for the reaction 2H(γ, η)2H. The calculation includes an impulse term and rescattering terms which are obtained by a reduction of a covariant formalism. Modern vertex functions and a realistic deuteron wave function are employed. Calculated 90° cross sections are at least a factor of two smaller than the existing data. The calculated angular distributions indicate that future experiments can determine the reaction mechanism and isolate the cause for the disagreement with theory.

Calculations for the in-flight production of {Sigma} hypernuclei with the reactions {sup 12}C({ital K}{sup {minus}},{pi}{sup {minus}}){sub {Sigma}}{sup 12}C, {sup 12}C({ital K}{sup {minus}},{pi}{sup +}){sub {Sigma}}{sup 12}B, {sup 16}O({ital K}{sup {minus}},{pi}{sup +}){sub {Sigma}}{sup 16}C, and {sup 9}Be({ital K}{sup {minus}},{pi}{sup {minus}}){sub {Sigma}}{sup 9}Be are presented. The framework of the recoil corrected continuum shell model is employed. The calculations can account for the major feature of the data with a modification of the {Sigma}{ital N} interaction of Yamamoto and Bando. This provides information on the strength of the central part of the {Sigma}{ital N} interaction and on the {Sigma}{ital N}{r arrow}{Lambda}{ital N} conversion strength. However, detailed information on the spin components of the {Sigma}{ital N} force will be difficult to obtain.

The procedure for calculating strangeness exchange cross sections in the recoil corrected continuum shell model formalism is developed. Cross sections are compared with existing 12 Λ C, 16 Λ O and 40 Λ Ca data and agreement is good. The calculated 16 Λ O, 4° spectrum demonstrated the ability of the RCCSM to calculated bound states, resonances, and quasi-free scattering in one formalism. A search for collective states was performed. After proper removal of center-of-mass excitations, no substantial collectivity was found. A survey of stretched excitations was performed. The 16 Λ O(3 + ) and 28 Λ Si(5 + ) states were found to be narrow and contain more than 85% of the 1p Λ 1h n strength. They are therefore, good candidates for initial (γ, K + ) studies. In contrast, only 50% of the 1p Λ 1h n strength for 12 Λ C(3 + ) will be observed in one state, with the remaining strength spread over several MeV with weak structure.

Particle capture calculations to 4 He have been performed within the framework of the continuum shell model with full correction for target recoil and with non-central forces. Differential cross section and polarization results are presented for both neutron and proton capture. The calculations include E1, E2 and M2 contributions. The calculated ratio of total cross sections, σ(γ, p)/σ(γ, n) is close to one above E p = 4 MeV. Possible corrections to this ratio are discussed. The calculated E2 strength is very broad and structureless. The maximum E2 strength is near 63 A − 1 3 MeV excitation. Of this E2 strength virtually all is 1 D 2 .

The Brueckner-Bethe-Goldstone-Faddeev formalism is employed to calculate the binding energy of /sup 4/He with the Reid soft-core potential. The propagator in the reaction matrix is modified to account for translational invariance, and antisymmetrization of the wave function. Convergence of the method is tested by introducing a variable energy shift in the excited-state spectrum. (AIP)

The influence of spin-unsaturated subshells on the coupling between hadronic probes and the target nucleons is studied for the case of elastic scattering. Particular attention is focused on the case of pion scattering from nuclei where the sigma-arrow-rightxn term in the pion-nucleon t matrix gives rise to a surface correction term to the ..pi..-nucleus optical potential. A closed form expression for this term is given and its effects on a few cases of ..pi..-nucleus scattering are estimated. Similar estimates are made for proton-nucleus scattering at 800 MeV bombarding energy.

Calculations for $^{4}\mathrm{He}(\ensuremath{\gamma}, \mathrm{p})^{3}\mathrm{H}$ and $^{4}\mathrm{He}(\ensuremath{\gamma}, \mathrm{n})^{3}\mathrm{He}$ have been performed with the recoil-corrected continuum shell model. A charge-symmetry breaking interaction has been introduced in an effort to explain the large value (\ensuremath{\sim}2) observed in recent experiments for the cross section ratio $R=\frac{\ensuremath{\sigma}(\ensuremath{\gamma}, \mathrm{p})}{\ensuremath{\sigma}(\ensuremath{\gamma}, \mathrm{n})}$. The calculations indicate that it is highly unlikely that such a large value of the cross section ratio can be obtained within standard theoretical assumptions.NUCLEAR REACTIONS $^{4}\mathrm{He}(\ensuremath{\gamma}, \mathrm{p})$, ($\ensuremath{\gamma}, \mathrm{n}$), ${E}_{x}=20\ensuremath{-}36$ MeV; calculated $\ensuremath{\sigma}(E)$, expansion coefficients ${a}_{k}(E)$, ${B}_{k}(E)$ for $\ensuremath{\sigma}(E, \ensuremath{\theta})$, $P(E, \ensuremath{\theta})$. $^{3}\mathrm{H}$(p,n); calculated $A(E)$, $P(E)$. Studied influence of charge symmetry breaking interaction.

The continuum shell model with full correction for target recoil is extended to 1p-1h configurations. The procedure is discussed in a framework which allows generalization to more complicated configurations. An application is made to nucleon reaction channels in 4 He using the g -matrix interaction of Bertsch et al . Excellent agreement with the data is obtained.

A simple procedure is described for determining the structure of hypernuclei. This procedure allows for complete flexibility in the hyperon wave function, while eliminating spurious center of mass components. The method is applied to /sub ..lambda..//sup 6/Li, /sub ..lambda..//sup 7/L, and 1 /sub ..lambda..//sup 6/O. Center of mass corrections are large for the /sub ..lambda..//sup 6/Li and /sub ..lambda..//sup 7/Li p states and still substantial for 1 /sub ..lambda..//sup 6/O. Spectra and selected transition and formation rates are calculated. Comparison is made with the recently measured (5/2)/sup +/..-->..(1/2)/sup +/ gamma-ray energy in /sub ..lambda..//sup 7/Li. Large changes are seen in the l/sub ..lambda../ = 1 wave functions between /sub ..lambda..//sup 6/Li and 1 /sub ..lambda..//sup 6/O. The l/sub ..lambda../ = 1 levels inferred from (K/sup -/,..pi../sup -/) are well reproduced. The ground state 1 /sub ..lambda..//sup 6/O is overbound, suggesting that a two-body ..lambda..N interaction must be modified in the nuclear interior.

The continuum shell-model with full correction for target recoil and including non-central forces is applied to the A = 12 and A = 16 systems. A modification of the g -matrix interaction of Bertsch et al . is employed. A comprehensive study of particle channels has been made in the 1p–1h approximation. Calculated level diagrams and cross sections compare favorably with experiment.

Inelastic electron scattering cross sections for /sup 4/He have been measured at 180/sup 0/ for incident electron energies of 130 and 200 MeV. Spectra measured up to excitation energies of 54 MeV are relatively featureless and show no evidence for resolvable excitations. The data are compared with continuum shell-model calculations which include all one-body breakup channels.

Recent measurements of the 54Fe(p, γ)55Co cross section indicate the existence of a splitting between the T components of the giant dipole resonance. We have calculated the (p, γ) cross section in the shell-model formalism. The bound-state interaction was determined by a fit to fp and sd shell nuclei. The calculation predicts the isospin splitting of ≈ 2.4 MeV and is consistent with all data in the energy region Ep = 9–15 MeV as well as the low-lying 55Co spectrum.

Coupled-channels calculations were performed for /sup 54/Fe(..cap alpha..,..cap alpha../sub 0/)/sup 54/Fe and /sup 54/Fe(..cap alpha..,..cap alpha../sub 1/)/sup 54/Fe* in the region of the giant quadrupole resonance. Reasonable agreement with the data was obtained. The wave functions were then employed to calculate the ..cap alpha.. capture cross section. This calculation suggests that the capture cross section is nonresonant. The implications for decay modes of the giant quadrupole resonance are discussed.

R-matrix techniques are shown to be applicable to the Dirac equation. The Bloch operator is derived and the resulting R-matrix equations are developed for a calculable theory. An example is presented in which the results of the R-matrix procedure agree with those of standard numerical integration techniques.

The $p$-wave form of the spin-orbit operator provides the basis for a single scattering model for the excitation of unnatural parity levels in pion-nucleus scattering in the region of the $\ensuremath{\Delta}$ resonance. The model is found to give a reasonable description of the ${\ensuremath{\pi}}^{+}$ and ${\ensuremath{\pi}}^{\ensuremath{-}}$ experimental cross sections for the excitation of stretched ${4}^{\ensuremath{-}}$ and ${6}^{\ensuremath{-}}$ states in $^{16}\mathrm{O}$ and $^{28}\mathrm{Si}$. In the calculations the interaction strength was fixed from the free pion-nucleon data and the spin transition densities were determined from recent ($e, {e}^{\ensuremath{'}}$) and ($p, {p}^{\ensuremath{'}}$) data. A schematic discussion of possible corrections to the model is also presented.

Observations of intermediate-energy proton capture populating unbound states are analyzed in terms of the bremsstrahlung emitted during single-particle transitions. The model accounts for the major features of the data. The present results suggest that these experiments can yield information on the structure of highly excited states.

A formalism is developed for treating the single-particle description of continuum to continuum electromagnetic transitions. Convenient formulae are given for the measured observables and for the single-particle matrix elements of the transition operators. Target recoil is taken explicitly into account. The long-wavelength approximation is not made. Convergence is demonstrated both for the radial integrals and with respect to partial waves and transition multipoles. The model is compared with available experimental data. Many of the observed features are reproduced.

Calculations have been performed for the 12 Λ C and 16 Λ O states above Λ-threshold. It is demonstrated that continuum coupling reduces ( K − , π − strength assigned to a specific level. Natural parity states which begin to show some degree of collectivity are broad and become part of the quasi-elastic bump. The stretched states which appear in conventional nuclei also become broad and difficult to be identified experimentally.

The results of comprehensive distorted-wave impulse-approximation calculations are presented for the reaction /sup 12/C(..pi../sup +/,K/sup +/) /sub //sub

Polarization-analyzing power differences in /sup 11/B(p,n)/sup 11/C are predicted to be observable at selected energies below E/sub p/ approx. 10 MeV at the level of vertical-bar P-A vertical-bar> or approx. =0.1. This result is derived from recoil corrected continuum shell model calculations in the lp-lh approximation, using a realistic g-matrix interaction.

The width of the 6/sup -/, T = 1, E/sub x/ = 14.36 MeV state in /sup 28/Si has been measured via the /sup 27/Al( p,p)/sup 27/Al reaction. The value of GAMMA = 3.7 +- 0.4 keV yields a single particle fraction ..beta../sub 1//sup ts2/ = 0.68 +- 0.07 which is shown to be consistent with the combined results for the inelastic excitation of this state by ..pi../sup + -/, p, and e/sup -/ and the /sup 27/Al(/sup 3/He,d)/sup 28/Si(g.s.) reaction.