The ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$(p,${\mathrm{p}}_0$), (p,${\mathrm{p}}_1$), (p,${\alpha }_0$), and (p,${\alpha }_1$) differential cross sections were measured in the energy range $E_{\mathrm{p}=1.08\mathrm{}–}$4.15 MeV with an overall resolution of 400 eV full width at half maximum. Resonance parameters were obtained for 94 levels with a multilevel, multichannel R-matrix code; parameters include resonance energy, total angular momentum, proton and alpha partial widths, and channel spin and orbital angular momentum mixing ratios. The observed proton and alpha resonance widths provide an upper limit for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$${+}^{12}$C reaction rates for an energy region where there are no direct measurements.

The use of the complex angular momentum plane for describing nuclear resonance reactions is investigated in detail. Many statements, commonly accepted, are critically reconsidered. Particular attention is devoted to the role played by echoes of the resonances and by hard-core potentials. In this way we construct a theory which allows us to connect the resonances belonging to a rotational band. The theory is checked on α-α scattering.

The structure of ${}_{}{}^{111}{}_{}{}^{}\mathrm{Ag}$ was studied using the ${}_{}{}^{110}{}_{}{}^{}\mathrm{Pd}$${(}^3$He, pnγ) ${}_{}{}^{111}{}_{}{}^{}\mathrm{Ag}$ reaction, which has populated an essentially complete set of low-energy states. The proton exit channel was isolated from competing reaction channels by operating γ-ray detectors in coincidence with a large-solid-angle proton detector. The experiments included γ-ray excitation functions, γ-ray angular distributions, and γ-γ coincidences. Four rotational bands have been identified. A symmetric particle-rotor model has been used to interpret these bands, and the model has identified other rotational features as well. A tentative interpretation of several nonrotational states is presented, suggesting that the mixing between rotational and nonrotational states is minimal.

Cross sections for elastic and inelastic scattering of monochromatic photons from ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$ have been measured for excitations between 8.1 and 10.5 MeV. The observed inelastic cross sections ${\sigma }_{\gamma \gamma i}$ correspond to transitions to the $0_2^{+}$, $2_1^{+}$, $2_2^{+}$, and $2_3^{+}$ states. A simple theoretical description using the Brink-Axel hypothesis and estimates of the level density and of the total photon interaction cross section ${\sigma }_{\gamma T}$ gives predictions for the individual cross sections that are in very good agreement with data. The E1 strength corresponding to the inferred ${\sigma }_{\gamma T}$ amounts to about B(E1↑)∼0.5 $e^2$ ${\mathrm{fm}}^2$ for the energy range under consideration.

In the reaction ${}_{}{}^{73}{}_{}{}^{}\mathrm{Ge}$(t,p${)}^{75}$Ge, 30 angular distributions have been measured and compared with distorted-wave predictions to extract L values. Ten L=0 transitions have been identified, leading to $J^{\pi }$${=(9/2\mathrm{}}^{+}$ assignments—most of them new.

We show that the concept of internal and barrier waves based on a semiclassical picture is useful for understanding intuitively the origin of oscillations in fusion excitation functions. The mechanism which causes the oscillations in the excitation function for the α${+\mathrm{}}^{40}$Ca system is investigated by decomposing the S matrix into its internal and barrier components: The S matrices and the fusion cross sections are calculated by using an optical model with a deep real potential which reproduces the fusion data well. It is shown that interference between internal and barrier waves is responsible for the oscillations of the fusion excitation function: The broad peaks are due to destructive interference which satisfies a resonance condition, while the valleys of the oscillations are due to constructive interference. The internal and barrier wave interpretation is fully consistent with the quantum mechanical description which associates the oscillations of the fusion excitation function with broad resonances in the α${+\mathrm{}}^{40}$Ca cluster structure, i.e., with higher nodal states of ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ti}$ at high excitation energy.

We report on the measurement of lifetimes and magnetic moments of yrast states in ${}_{}{}^{134}{}_{}{}^{}\mathrm{Nd}$ and ${}_{}{}^{136}{}_{}{}^{}\mathrm{Nd}$. Lifetimes in the 10–100 ps range were measured via the recoil distance Doppler shift method applied to the reactions ${}_{}{}^{110}{}_{}{}^{}\mathrm{Pd}$${(}^{28}$,30Si,4n) at 120–125 MeV beam energy. Magnetic moments of the $2_1^{+}$ state in ${}_{}{}^{134}{}_{}{}^{}\mathrm{Nd}$ and the ${10}^{+}$ and ${12}^{+}$ yrast states in ${}_{}{}^{136}{}_{}{}^{}\mathrm{Nd}$ were deduced from the integral Larmor precessions measured after recoil implantation in a magnetized nickel foil, via the reactions ${}_{}{}^{76}{}_{}{}^{}\mathrm{Ge}$${(}^{62}$,64Ni,4n). The ${10}^{+}$ backbending state in ${}_{}{}^{136}{}_{}{}^{}\mathrm{Nd}$ results from $h_{11/2}$ proton (two quasiparticle) alignment. The paramagnetic relaxation time of Nd in nickel was measured by Coulomb excitation and implantation of ${}_{}{}^{148}{}_{}{}^{}\mathrm{Nd}$($2_1^{+}$).

The effects of the Coulomb expansion on the fragment kinetic energy spectrum for a fragmentating hot nuclear system is investigated. In particular, ${}_{}{}^{12}{}_{}{}^{}\mathrm{fragment}$ spectra are calculated and compared with those predicted by the uniform expansion approximation. The results indicate that the energy spectra of fragments are quite sensitive to the details of the Coulomb expansion treatment.

Velocity distributions of mass-resolved evaporation residues from reactions of ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ with ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ have been measured at bombarding energies of 194, 239, and 278 MeV using time-of-flight techniques. In all cases, the observed shifts in the velocity centroids relative to the values expected for complete fusion are consistent with a previously reported parametrization of a threshold for onset of incomplete fusion. Angular distributions were measured and total cross sections extracted for the ${}_{}{}^{32}{}_{}{}^{}\mathrm{Mg}$ system at all three energies. A comparison with existing results for ${}_{}{}^{32}{}_{}{}^{}\mathrm{Mg}$ at lower energies, and with other systems leading to the ${}_{}{}^{56}{}_{}{}^{}\mathrm{Ni}$ compound nucleus, suggests two different types of compound-nuclear limitations to complete fusion at higher energies.

Standard techniques for approximating a given potential with a separable potential are only applicable to energy independent potentials. A method is presented for extending the standard technique to accommodate explicit energy dependence. The approximation leads to a rank N separable t matrix whose on-shell and half-off-shell forms are exact at N selected energies.

A method for solving integral equations is developed and applied to the homogeneous Lippmann-Schwinger equation in momentum space. It has been used with Yukawa-type potentials, V(r)=Σ, and yields solutions that are analytic expressions rational in the variable $k^2$. More specifically, the principal-value form of the homogeneous Lippmann-Schwinger equation is solved by making an analytic series expansion of the integral, which is then summed using Padé approximants. An application to the Malfliet-Tjon potential V in s wave is given. In a finite subspace of rational functions with fixed denominators, the solutions, referred to as Sturmian functions, are obtained corresponding to the energy -0.35 MeV, which is the physical bound state energy for this potential. With these analytic eigenfunctions as form factors and with the associated eigenvalues, a separable expansion, namely, the unitary pole expansion, is constructed for the local potential. The unitary pole expansion is then used for analytic k-matrix calculations. At intermediate energies through $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}$=666 MeV, and at ultrahigh momenta, as the rank of the unitary pole expansion approaches 13, analytic wave functions (or, equivalently, half-shell k matrices) and phase shifts are found that are in good agreement with exact results.

This is in accord with our observation that separable expansions should not be regarded as low energy approximations, but instead are finite l approximations, for the following reason. For the class of potentials we consider, the partial wave two-body operators $V_l$(p,q), $t_l$(p,q,E), and $k_l$(p,q,E) are compact even though V(r), T(p,q,E), and K(p,q,E) are not compact. Therefore, in principle, these partial wave operators can be approximated by sequences of separable expansions which converge to them in norm. We show that the unitary pole expansion may be such a sequence. There is a practical need for analytic separable expansions that converge more rapidly. In this light we illustrate how our solutions can be used with the Ernst-Shakin-Thaler formulation of separable expansions, and we also discuss the application of our method to the calculation of Gamow states.

Form factors for transverse electron scattering from ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ have been determined for momentum transfers as high as q=4.6 ${\mathrm{fm}}^{\mathrm{-}1}$. Data are presented for the elastic (M1), 3.088 MeV (E1), and 9.50 MeV (M4) transitions in ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, and for the 15.11 MeV (M1), 16.11 MeV (E2), and 16.58 MeV (M2) transitions in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. It is found that calculations in the lowest-order shell-model space fail to account for the measured q dependences of E1, M1, and E2 form factors beyond q=2 ${\mathrm{fm}}^{\mathrm{-}1}$. On the other hand, form factor shapes observed for M2 and M4 multipoles are satisfactorily described to q=4 ${\mathrm{fm}}^{\mathrm{-}1}$ within the minimal 1ħω configuration space.

The minimal substitution, p→p-qA, in the Hamiltonian operator of a nuclear system is a familiar method of introducing electromagnetic interactions in a gauge invariant way. The procedure does not work, however, when isospin dependent forces are present. In this work, the procedure is extended to isospin dependent potentials in a model-independent way. The ambiguity inherent in the minimal substitution is avoided by making a simple choice. The result is generally not expected to coincide with the predictions of a fundamental theory, if any, that may underlie the phenomenological nuclear potential, nor is it expected to resolve the present discrepancies between theory and experiment. Yet it is thought to be an improvement over treatments that ignore the so-called exchange and interaction currents altogether or treat them in an inconsistent or non-gauge-invariant manner. More general formulas containing arbitrary paths or functions are also given, as is a generalization that allows non-point-like nucleons. An application of the method to the photodisintegration of the deuteron is under way.

Differential cross sections and analyzing powers for the (p→,n) reaction on carbon isotopes have been measured for angles up to ${\theta }_{\mathrm{lab}=50\mathrm{}}$° using 160 MeV protons. The angular distributions for the stronger transitions are compared with the results of distorted-wave impulse approximation calculations which utilize transition densities from existing shell model calculations. The total observed Gamow-Teller strength is also compared with the shell model predictions. In addition, the shapes of these angular distributions are discussed emphasizing decomposition into longitudinal, transverse, and non-normal-parity-transfer components. Some comparisons of the present (p,n) data with corresponding (p,p’) data and with other relevant (p,n) data are also made.

The behavior of the fully-off-the-energy-shell T matrices for the Reid-soft-core and Paris-80 potentials are studied for a variety of partial waves, both uncoupled and coupled. Although the potentials have qualitatively different structures in both coordinate space and momentum space, the resulting off-energy-shell behavior is very similar in the range of energy and momentum relevant to low and medium energy nuclear physics.

We have analyzed the available data on the primary $E1\mathrm{}$ transitions in the thermal-neutron capture by even isotopes of calcium with the aim of determining the relative importance of direct and compound-nucleus mechanisms of capture in these nuclides. In some of these cases, the thermal-neutron scattering length, as well as the spectroscopic factors of the final states, is known, and an absolute estimate of the direct capture cross sections can be made. In these cases (${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ca}$) the estimates made from a specialized optical model (which reproduces the scattering length precisely) and a global optical model with a valency contribution from a local level are in agreement and are also generally close in absolute value to the experimental cross sections. The detailed deviations can be accounted for as a compound-nucleus contribution to the transitions, which fluctuates, but has an overall magnitude in agreement with Cameron's semiempirical relationship for this mechanism. In both nuclides the compound-nucleus contribution to the capture can plausibly be attributed to a bound local level. For ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ there is some indirect evidence for the value of the thermal-neutron scattering length, and the use of this value in the calculations of direct capture leads to agreement with the data. There is no evidence for an important compound-nucleus contribution in this magic number nucleus. In ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{46}{}_{}{}^{}\mathrm{Ca}$ the thermal-neutron scattering length can be adjusted to "best fit" the calculation of direct capture from the optical model to the experimental data. After this adjustment the detailed agreement between theory and data is very good, indicating the major predominance of the direct mechanism in capture at thermal-neutron energies by these nuclides.

The neutron energy spectra from the (p,n) reaction on ${}_{}{}^{90}{}_{}{}^{}$,91,92,94Zr, ${}_{}{}^{92}{}_{}{}^{}$,94,95,96,97,98,100Mo, and ${}_{}{}^{110}{}_{}{}^{}\mathrm{Pd}$ with 25 MeV protons and ${}_{}{}^{90}{}_{}{}^{}$,91,92,94Zr with 18 MeV protons are analyzed in terms of the preequilibrium exciton model introducing effective Q values, the pairing correlation, and the modified uniform spacing model in which the uniform spacing model is modified so as to have a wide spacing at the magic number. For all these targets, the calculated spectra using the above model for 25 MeV protons show good agreement with the experimental ones not only on the absolute cross sections in the neutron energy region of 12–18 MeV, but also on the observed spectra with pronounced structures in the neutron energy region higher than 18 MeV.

The mechanism of the backward-angle anomaly in α${+\mathrm{}}^{40}$Ca scattering is studied from the α-cluster viewpoint with a deep potential which fits the α-cluster structure of ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ti}$ at low excitation energy, fusion data, and elastic scattering. It is found that the backward-angle anomaly is due to the persistent existence of the three molecular vibrational bands with the α${+\mathrm{}}^{40}$Ca cluster structure in ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ti}$ whose relative motions are excited.

Inelastic electron scattering form factors of the $J^{\pi }$${=1\mathrm{}}^{+}$ states at excitation energies $E_x$=5.800 and 5.846 MeV in ${}_{}{}^{206}{}_{}{}^{}\mathrm{Pb}$ and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$, respectively, are discussed in terms of a simple model of isoscalar-isovector mixing. It is known that for these states, which are often called loosely ‘‘isoscalar’’ $1^{+}$ states, about half of the transition strength is accounted for by this mixing. It is demonstrated here that the isoscalar-isovector mixing is also crucial for explaining the momentum dependence and the absolute magnitude of the form factor. The relative importance of the convection current contribution to the form factor with respect to the spin one is also studied. Finally, the isovector M1 strength distribution in ${}_{}{}^{206}{}_{}{}^{}\mathrm{Pb}$ between $E_x$=6.7–8.2 MeV derived from high resolution inelastic electron scattering is shown to agree in shape and magnitude with the one measured recently in an experiment with tagged polarized photons.

We present new techniques for calculating electron-positron pair production in the field of a fixed point charge in distorted-wave Born approximation which permits the evaluation of the Dirac-Coulomb radial matrix elements for lepton energies much greater than the electron rest mass, and for large angular momenta. Using these techniques, the pair production cross sections for 10 and 20 MeV photons on uranium (Z=92) are evaluated and compared to the so-called ‘‘bridging formulae’’ which connect the low energy (ω<5 MeV) distorted-wave Born approximation results to the approximate results for high energy (ω>50 MeV) obtained with the Sommerfeld-Maue approximation and to the experimental results.