Pion single and double charge exchange reactions at 50 MeV on ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ are studied using a conventional coupled channels approach. Inclusion of quadrupole transitions through the $2^{+}$ T=1 state in ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ is essential for understanding these reactions. Fitting the single charge exchange data and including quadrupole contributions lead directly to a reasonable description of the double charge exchange data. It is the deep forward minimum of the single charge exchange data, not the forward peaking of the double charge exchange data, that is more likely to have new implications for the pion-nucleus interactions. Investigation of the ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ double charge exchange data supports these conclusions.

An analytical expression for the calculation of the nucleus-nucleus potential has been derived from an empirical formula which describes the fusion excitation function. The nucleus-nucleus potentials calculated for the projectiles ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$, and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ in the interaction region ∼3–6.5 fm by the above procedure agree remarkably well with the real part of the respective optical potentials determined from the analysis of elastic scattering data which exhibit the ‘‘rainbow’’ phenomenon.

The proposed supercoherent elastic neutrino scattering is not compatible with basic assumptions about wave mechanics. The arguments leading to supercoherence would also predict an analogous effect in x ray scattering, contrary to observation.

We have used polycarbonate track-recording films to confirm the rare decay mode of ${}_{}{}^{226}{}_{}{}^{}\mathrm{Ra}$ by ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ emission and to set stringent upper limits on ${}_{}{}^{14}{}_{}{}^{}\mathrm{emission}$ rates of ${}_{}{}^{221}{}_{}{}^{}\mathrm{Fr}$, ${}_{}{}^{221}{}_{}{}^{}\mathrm{Ra}$, and ${}_{}{}^{225}{}_{}{}^{}\mathrm{Ac}$. The ${}_{}{}^{14}{}_{}{}^{}\mathrm{emission}$ rate exhibits a pronounced odd-even effect. For Ra isotopes the hindrance factor for odd-even parents relative to even-even parents is at least 10 times higher for ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ emission than for α emission.

Excitation of isovector giant resonances in ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ was studied by using the ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$${(}^7$Li, ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$${)}^{27}$Mg reaction at incident energies of 100, 150, and 180 MeV. We observed the analog of the giant dipole resonance at $E_x$=14.3 MeV in ${}_{}{}^{27}{}_{}{}^{}\mathrm{Mg}$. From the observed excitation function, we suggest that a peak at $E_x$=9.5 MeV is a resonance with a higher multipolarity than one. In the excitation energy region higher than the giant dipole resonance, no resonance was observed.

The role of elastic and surface effects in the isovector collective excitations is investigated by using a sum rule approach. Simple and accurate relations among the frequencies of different giant resonances are derived. The recently observed M1 rotational state in deformed nuclei is also discussed.

Anomalous absorption of proton partial waves by the nuclear optical potential is investigated for all the stable target nuclei over the range of energy 0–80 MeV and orbital angular momentum 0–13. It occurs with striking regularity very similar to those found for the neutron except that the l=0 anomalies are associated with resonance poles rather than antibound state poles, and the target-nucleus dependence of the anomaly is quite different. The latter is shown to be due to the symmetry term of the optical potential.

The structure of giant resonances in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ has been studied using inelastic scattering of 334-MeV polarized protons. Data were obtained with 70-keV energy resolution over an angular range from 2–13 deg and the spectra were measured over an excitation energy range from 0–25 MeV. The results show that the quadrupole resonance strength is divided into two main components, one centered at 10.6 MeV containing 70% of the energy-weighted sum rule in a 2-MeV wide peak and a second component composed of several discrete peaks located between 7 and 9 MeV which deplete a total of approximately 20% of the energy-weighted sum rule. The giant monopole and dipole resonances as well as a hexadecapole resonance are observed. Measurements of differential cross sections for elastic scattering and inelastic scattering to low-lying $3^{\mathrm{-}}$, $2^{+}$, and $4^{+}$ levels are presented. Comparison of these data with collective model direct reaction calculations shows the calculations to correctly describe the shape and magnitude of the cross sections when normalized to the known transition rates for each level.

Excitation functions and thick target recoil ranges for radioactive nuclei produced in ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ bombardment of ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}$ over a 5–50 MeV/nucleon energy range have been measured using the activation technique. At 81 and 118 MeV ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ energy, the angular distributions of the radioactive recoils were also measured. Using the in-beam gamma ray technique, production cross sections for many radioactive as well as stable residual nuclei were measured for the ${}_{}{}^4{}_{}{}^{}$He${+\mathrm{}}^{59}$Co system for a ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ energy range between 30 and 150 MeV. Close to 90% of the reaction cross section was observed over the entire energy range. From the experimental data, information about the energy and linear momentum deposition in the interaction of He projectiles with the Co target was gathered. Two distinct changes in the reaction mechanism are apparent at about 40 and 90 MeV bombarding energies, as manifested by observables related to the energy and momentum deposition. The change of the reaction mechanism at 40 MeV is related to the onset of preequilibrium α-particle and nucleon emission. The nature of the mechanism change which sets in at 90 MeV is less well understood.

The ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$(p,n${)}^{40}$Sc reaction was studied at 134 MeV. Neutron energy spectra were measured by the time-of-flight technique with resolutions of 220 keV at angles from 0° to 41° and 415 keV out to 62°. The $2^{\mathrm{-}}$,$3^{\mathrm{-}}$,$4^{\mathrm{-}}$,$5^{\mathrm{-}}$ band of states based on the ($f_{7/2}$,$d_{3/2}^{\mathrm{-}1}$) 1p1h structure was observed at low excitation energies, in good agreement with known analog states in ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{40}{}_{}{}^{}\mathrm{K}$. The shapes of the cross-section and analyzing-power angular distributions are in good agreement with distorted-wave impulse-approximation calculations using simple 1p1h (Tamm-Dancoff approximation) shell-model wave functions. A relatively strong transition to a state at $E_x$=2.3 MeV with L=3 is identified tentatively as a $4^{\mathrm{-}}$ state with the predominant 1p1h structure (1$f_{7/2}$,2$s_{1/2}^{\mathrm{-}1}$).

The excitation of the (T=1) $6^{\mathrm{-}}$ ($f_{7/2}$,$d_{5/2}^{\mathrm{-}1}$) stretched state is observed near $E_x$=7 MeV, fragmented over approximately 3 MeV. The normalization factor required to make a distorted-wave impulse-approximation calculation agree in magnitude with the $6^{\mathrm{-}}$ excitation is 0.35, which is larger than the normalization factor for this excitation in mass 28, analyzed in a similar manner. The L=1 giant resonance is observed to be centered near $E_x$=10 MeV with a width (full width at half maximum) of about 5 MeV, and a distorted-wave impulse-approximation normalization factor of 0.16. Two $1^{+}$ excitations are observed at $E_x$=2.7 and 4.3 MeV which indicate directly the presence of ground-state correlations in the ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ target. The fact that the analog of the higher $1^{+}$ excitation is not seen in inelastic electron scattering indicates strong interference between spin and orbital current contributions. The effect of ground-state correlations on the 1p1h wave functions was investigated by performing calculations which allowed multiparticle-multihole correlations in the $d_{3/2}$ and $f_{7/2}$ orbitals. The distorted-wave impulse-approximation normalization factors obtained with these wave functions were found to increase by a factor of about 2 relative to those obtained with ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ assumed to be a closed core.

A powerful approximation method based on the separable expansion of the potential has been used to solve the Schrödinger equation for a complex rotated Hamiltonian with nuclear short-ranged and nuclear short-ranged plus Coulomb potentials. It is shown that for potentials analytic in a proper domain of the complex r plane (e.g., the Woods-Saxon potential up to its first pole) solving the rotated Schrödinger equation on the real harmonic oscillator wave function basis is equivalent to solving the original equation on the complex harmonic oscillator wave function basis. For nonanalytic potentials (e.g., the nuclear charged-sphere Coulomb potential which is discontinuous in the complex r plane) the equivalence does not hold and it is the latter version that gives the correct solution. It is demonstrated that the method leads to an accurate determination of the resonance energy and (for not very broad resonances) of the wave function as well.

In this paper, an asymmetric, antisymmetrized optical potential formalism is used to derive the low-order terms in multiple-scattering-type expansions for nonrelativistic proton-nucleus and deuteron-nucleus elastic scattering. In particular, the extended Faddeev theory of N-particle collisions is used to obtain the properly symmetrized, two-particle and three-particle contributions in these two cases, where it has been assumed that all potentials are pair interactions. The main purpose underlying the research reported herein has been to prove that standard results can be obtained from an asymmetric formalism. For the two-particle contributions, the usual $t^A$ρ-type expression is obtained, where $t^A$ is an antisymmetrized, two-particle transition operator. At this level of approximation, the results for the (d,d) case are the same as for the usual folding model. The three-particle contributions in the nucleon-nucleus case are identical to those of Picklesimer and Thaler, thus further demonstrating that standard results are contained in the asymmetric approach. The antisymmetrized, three-particle contributions to the (d,d) optical potential do not seem to have been previously derived; they are the obvious analog of the nucleon-nucleus results, and are physically reasonable in form. However, at this level of approximation, the (d,d) description is no longer found to be that of a folding model.

Standard derivations of the distorted wave Born approximation amplitudes for particle-transfer reactions have always left unanswered two fundamental questions: How can one justify cancellation of the typical, one-body, absorptive-potential counter term, and, which Pauli-principle exchange amplitudes correspond to the standard, nonexchange distorted-wave Born approximation amplitude? This paper provides an answer to these questions. This is accomplished by using a particular type of antisymmetrized, N-particle collision theory to describe the transfer processes. For the reaction (b,a), with the mass of a greater than the mass of b, the extended Faddeev theory of the preceding paper is used, while its time-reversal partner, the precursor form of the Bencze-Redish-Sloan equations, is used for the (a,b) case. They lead to almost identical first-order amplitudes. For all the reactions studied herein, it is found that the form of the nonexchange distorted-wave amplitudes—those that are commonly referred to as distorted-wave Born approximation amplitudes—are essentially the same as are used to fit data. This result is achieved without any need to account for cancellation of a counter term, since none appears, implying an absence of so-called core-excitation effects in first order.

No formalism other than the extended Faddeev–Bencze-Redish-Sloan–type has yet been found to yield such results. In addition, none of the first-order, Pauli-principle exchange amplitudes predicted by the formalism are of the conventional knockon type: all are either heavy-particle type of exchange amplitudes or heavy-particle plus additional, non-knockon types. There is also no need to cancel a counter term in the exchange amplitudes. For the (p,d) reaction, and certain others, the occurrence of a pure heavy-particle pickup amplitude helps to explain why direct reaction data analyses that rely on a distorted-wave Born approximation amplitude alone, i.e., one without an exchange amplitude, have been successful.

The lack of a knockon term also helps to understand the empirical fact that three-particle pickup and not knockon is the mechanism for direct (p,α) reactions. In addition to treating first-order amplitudes, a general expression is given for a two-step correction, and an expression for the nonexchange part of the (p,d)-(d,t) portion of the (p,t) two-step amplitude is derived. It is found to contain the same interactions as occur in a similar amplitude recently derived by Austern and Kawai.

To investigate the role of final state interactions in knockout reactions, we study the transition form factor corresponding to the absorption of a scalar probe in a single particle model description of the nucleus. The numerical aspects of an approximation which treats at the same level initial and final state interactions are discussed. It provides fair agreement with the corresponding exact calculations for momenta of the ejected nucleon larger than 2 ${\mathrm{fm}}^{\mathrm{-}1}$. Comparisons with various other approximations show that a careful treatment of the final state interaction is necessary to obtain a realistic estimate of the form factor.

Deep inelastic scattering cross sections have been measured for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ at electron energies between 100 and 375 MeV at scattering angles of 90° and 140°. Longitudinal and transverse response functions at three-momentum transfers between 250 and 410 MeV/c have been extracted using a Rosenbluth separation. The response functions are compared to calculations modeling the nucleus as a noninteracting relativistic Fermi gas. The model is found to agree with the observed transverse response function in the region of expected quasi-free nucleon knockout, but the model overestimates the observed longitudinal response. Comparisons of the response functions of the two isotopes are made, and differences between ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ are seen.

Differential cross sections for elastic and inelastic scattering of electrons by ${}_{}{}^{154}{}_{}{}^{}\mathrm{Gd}$ have been measured for states below 1 MeV of excitation. Levels of three major collective bands are studied: the $0^{+}$, $2^{+}$, $4^{+}$, and $6^{+}$ rotational states; the $2^{+}$ gamma vibration; and the $0^{+}$ and $2^{+}$ beta vibrational levels. This study includes the first electron scattering measurements of a beta vibration. Extraction of these small inelastic cross sections required improvements in momentum resolution and detector response uniformity. Data from the rotational band are compared with axially symmetric Hartree-Fock predictions. Disagreement between the measurements and Legendre projections of the calculated density, particularly for higher multipolarity states, indicates a breakdown in the Hartree-Fock approximation or the rotational model. Small amplitude vibrations of the nuclear shape derived from the measured rotational densities agree well in shape when independently normalized to the cross section strength for both the beta and gamma $2^{+}$ vibrations, substantiating their geometrical interpretations. Once transition strength of the beta band is set, however, the strength and shape of the $0^{+}$ beta is not correctly predicted, indicating a more complicated configuration.

Giant multipole resonances in ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$ were investigated by inelastic electron scattering. From a model-dependent analysis assuming resonant parts expressed as a sum of Breit-Wigner shapes and a smooth background, the centroid excitation energies, the widths, and the sum rule depletions were deduced and compared with the results on neighboring isotones. Our results were in excellent agreement with photoreaction data.

Measured and calculated transverse polarization coefficients are compared at 0° for the reactions ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$(p→,n→), ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$(p→,n→), and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$(p→,n→) at intermediate incident energies and at negative Q values up to ∼50 MeV in an attempt to better understand the spin-parity composition of the charge-exchange continuum. Even at 0° the data indicate a significant amount of natural parity spin-flip strength, and this is supported by our calculations. We also present the predicted polarization transfer coefficient spectrum for the (p,n) reaction on ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$ at 500 Mev, whose measurement is anticipated in the near future.

We have measured charged particle spectra from 100 MeV α-induced reactions on targets of ${}_{}{}^{24}{}_{}{}^{}$,25,26Mg, ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$, and ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$. The charged particles are protons, deuterons, tritons, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, and α particles. The cross sections were analyzed in the framework of the exciton coalescence model. The data suggest complex particle formation to be independent of individual nuclear structure. The deduced single-particle state densities show strong odd-even effects.

The giant resonance region in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ has been studied using inelastic scattering of 200-MeV polarized and unpolarized protons. Both differential cross sections σ(theta) and analyzing power $A_y$(theta) measurements were made. The isoscalar giant quadrupole resonance at 10.6±0.5 MeV, and the combined isovector giant dipole resonance and isoscalar giant monopole resonance at 14.0±0.6 MeV are clearly observed. Within uncertainties all three giant resonances are in accord with full energy-weighted sum rule depletions, based on comparisons with macroscopic distorted wave Born approximation calculations. Data for a peak at 20.9±1.0 MeV are found to be consistent with an isoscalar giant octupole resonance exhausting 36±12 % of the energy-weighted sum rule strength. A peak located at an excitation energy of 12.0±0.7 MeV is shown to be a 2ħω, L=4 transition depleting 8±3 % of the hexadecapole energy-weighted sum rule strength. The measured reduced transition probability for the $3^{\mathrm{-}}$ state at 2.614 MeV is consistent both with the accepted value and with results measured at 334 and 800 MeV. Our results for the $3^{\mathrm{-}}$ state at 2.614 MeV and for the giant quadrupole resonance do not support the anomalous behavior found in earlier studies at 104, 156, and 201 MeV. This shows that the macroscopic distorted wave Born approximation can be used to extract deformation lengths providing meaningful comparison with electromagnetic energy-weighted sum rules for proton inelastic scattering to at least 800 MeV incident proton energy.