The method of Garside and MacDonald is used to treat the single-particle resonances in the renormalized random-phase-approximation treatment of scattering. The resonances are shifted by an additional potential to single-particle bound states, which can be handled in the usual manner. The coupling to the continuum is done analytically using separable matrix elements.

The Hartree-Fock-Bogoliubov (HFB) equations with generalized isospin pairing are numerically solved without any approximations, except imposing certain self-consistent symmetries. Realistic forces are used to make definite conclusions concerning the shapes of nuclei and the existence of isospin pairing. Comparison with previous approximations shows that in the $s-d$ shell the HFB equations may not be quantitatively approximated by HF+BCS, HB-BCS, or by iterating between HF and BCS. Isospin pairing offers an explanation for axial symmetry in ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ and ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ and for the existence of low-lying vibrational states in ${}_{}{}^{36}{}_{}{}^{}\mathrm{Ar}$.

The reactions ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}({}_{}{}^7{}_{}{}^{}\mathrm{Li},t){}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}({}_{}{}^6{}_{}{}^{}\mathrm{Li},d){}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ have been studied at 17 and 18 MeV, respectively. Both reactions are selective in the states they populate, although this is more evident in the (${}_{}{}^7{}_{}{}^{}\mathrm{Li}$, $t$) case. Angular distributions were extracted for 15 levels below 8.5-MeV excitation. These exhibit pronounced structures and are generally indicative of direct-reaction mechanisms. Transitions to the negative-parity states at 3.06, 3.85, and 4.55 MeV are the strongest observed below 7-MeV excitation. These levels are discussed within the framework of the weak-coupling model and the transitions compared with those from the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^7{}_{}{}^{}\mathrm{Li},t)$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^6{}_{}{}^{}\mathrm{Li},d)$ reactions leading to the first $K=0\mathrm{}$ rotational band in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$. Strong transitions are also observed to levels at 7.38, (8.46, 8.49), (8.87, 8.95), and (9.14, 9.20) MeV.

A simple three-part density-dependent effective interaction is used to calculate several general properties of the semiinfinite nuclear surface. This interaction, which is referred to here as the modified $\delta$ interaction (MDI), is quite similar to one introduced by Skyrme. The three parameters of the MDI are fixed by fitting the binding energy and density of infinite nuclear matter with $N=Z$ and also the ground-state energy of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, all in first-order perturbation theory.

The nuclear surface properties are calculated in several different ways. First, they are extracted directly from the single-particle wave functions of a one-dimensional static Woods-Saxon potential. The diffuseness and depth of the potential are obtained by minimizing the surface energy. This procedure is called the independent particle model (IPM). The resulting surface thickness of 2.2 fm and surface energy of 19.3 MeV and the approximately Fermi shape of the density distribution are in good agreement with empirical results.

The calculations were then repeated using the Thomas-Fermi approximation to obtain the density. The resultant surface thickness and surface energy, 2.0 fm and 16.0 MeV, are considerably smaller than the IPM results. Furthermore, the calculated density distribution has a longer "shoulder" inside the nucleus and a shorter "tail" outside than the IPM distribution.

The theory of two-nucleon transfer reactions is extended to include higher-order transitions going through intermediate nuclear states produced by inelastic scattering of the ingoing or outgoing particle. The reaction, as is usual, is treated to first order, but the inelastic processes are treated to all orders among the retained channels. The theory is formulated so that it is very easily applied to any microscopic structure calculation, since the relevant content of such calculations appear in the theory only through the values of the matrix elements of the pair-creation ${\left[d^{†}{d}^{†}\right]}_J$ and scattering ${\left[d^{†}\tilde{d}\right]}_J$ operators.

Different methods of calculating the number of degrees of freedom $N_{\mathrm{eff}}$ in statistical cross-section fluctuations are compared. The underlying physical assumptions of the methods are discussed critically, and numerical examples for $N_{\mathrm{eff}}$ are given.

A study of the ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}({}_{}{}^3{}_{}{}^{}\mathrm{He},d){}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^3{}_{}{}^{}\mathrm{He},\alpha ){}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ reactions leading to the 8.11-MeV state in ${}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ yields an unambiguous assignment of $J^{\pi }={\frac{3}{2}}^{-}$ for that state.

The $4f\to 3d$ pionic x rays in ${\mathrm{Ba}}^{138}$, ${\mathrm{Ce}}^{140}$, and ${\mathrm{Ce}}^{142}$ have been observed in order to measure the effect of the nuclear interaction on a pion in a $3d$ atomic level. The results are used to look for differences in the pion interaction with these nuclei. Within experimental error, we could not detect an isotope shift in the ${\mathrm{Ce}}^{142}$-${\mathrm{Ce}}^{140}$ results. The nuclear isotone shift in the x-ray energy and width for ${\mathrm{Ce}}^{140}$-${\mathrm{Ba}}^{138}$ of 1.59 ± 0.30 and 1.3 ± 1.3 keV agrees with the values of 1.31 and 2.0 keV predicted from an optical-model calculation.

The polarization analyzing power for the elastic scattering of 7.80- and 3.38-MeV neutrons from ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ has been measured at laboratory angles ranging from 40 to 140°. Polarized neutrons were produced in the ${}_{}{}^9{}_{}{}^{}\mathrm{Be}(\alpha ,n){}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ reaction at 45° (lab) with a mean $\alpha$ energy of 2.55 MeV. Results of a phase-shift analysis are given and are found to agree with optical-model calculations reported by Satchler et al.

The feasibility of using the reactions $\{e+N({\epsilon }_i,J_i)\to e^{\prime }+,N({\epsilon }_f,J_f\left)\right\}\left\{\searrow N\right({\epsilon }_{\mathrm{ff}},J_{\mathrm{ff}})+\gamma \}$ to investigate low-lying states of heavy nuclei is discussed. By detecting the decay photon, the problem of poor energy resolution for high-energy electrons can be circumvented. The formalism for the $e^{\prime }-\gamma$ coincidence cross section is given. The Coulomb distortion of the electron wave functions, which is important for heavy nuclei, is taken into account. Results for the $e^{\prime }-\gamma$ coincidence cross section and the $\gamma$-detection cross section for several nuclei are given. The $e-\gamma$ coincidence cross section appears to be feasible when superconducting accelerators became operational. The $\gamma$-detection cross section offers a method for investigating low-lying states with present-day accelerators.

The intensity of the unique first-forbidden 4.708-MeV outer branch of the ${}_{}{}^{19}{}_{}{}^{}\mathrm{O}$ $\beta$ spectrum, leading to the 110-keV ${\mathrm{½}}^{-}$ hole state in ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$, has been determined as $\left({4.8}_{-3.3\mathrm{}}^{+1.2\mathrm{}}\right)\times {10}^{-4\mathrm{}}$ per ${}_{}{}^{19}{}_{}{}^{}\mathrm{O}$ decay. Consequently, the comparative half-life is $f_{1}t=\left({1.5}_{-0.3\mathrm{}}^{+3.1\mathrm{}}\right)\times {10}^{10}$ sec, and the strength of the transition is ${〈G_1〉}^2={0.13}_{-0.09\mathrm{}}^{+0.03\mathrm{}} {\mathrm{F}}^2$. This result was found from the analysis of $\beta -\gamma$ coincidence spectra obtained from reactor-irradiated water samples that had been enriched in ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$. An upper limit of 6 × ${10}^{-4\mathrm{}}$ is set on the branching of the 197-keV level decay in ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ through the 110-keV state. The results can be used to infer the extent of wave-function admixture (core excitation) in the ground state of ${}_{}{}^{19}{}_{}{}^{}\mathrm{O}$.

We have looked for the $J^P=0^{+}$ nuclear excitation of ${\mathrm{Zn}}^{68}$ in muonic atoms as suggested by Henley and Wilets. ${\mathrm{Zn}}^{68}$ was chosen because the energy of the $0^{+}$ excitation is close to the energy difference of the $2s-1s$ muonic levels, thus allowing a dynamic interaction between a muon in a $2s$ state and the nucleus in the ground state. We find that the $2s-1s$ level difference is 20 keV less than the nuclear excitation energy and, as a result, the dynamic interaction is too small for us to observe. We measure the ${\mathrm{Zn}}^{66}$-${\mathrm{Zn}}^{68}$ isotope shift to be $\frac{\delta R}{\delta R_{\mathrm{std}}}=0.47\mathrm{}\pm 0.11$.

A search for double $\gamma$ emission from the first excited ${\mathrm{O}}^{+}$ states in ${\mathrm{Ca}}^{40}$ and ${\mathrm{Zr}}^{90}$ has been carried out using a NaI(Tl) scintillation spectrometer and a sum-coincidence technique. No definite evidence for double $\gamma$ emission is found in either case. In the 3.35-MeV, ${\mathrm{O}}^{+}$-to-ground-state transition in ${\mathrm{Ca}}^{40}$, an upper limit of 4 × ${10}^{-4\mathrm{}}$ has been established for the branching ratio of double $\gamma$ emission with respect to internal pair emission. For the 1.75-MeV ${\mathrm{O}}^{+}$-to-ground-state transition in ${\mathrm{Zr}}^{90}$, an upper limit of 1.8 × ${10}^{-4\mathrm{}}$ has been obtained for the branching ratio of double $\gamma$ emission with respect to the sum of internal-conversion electrons and internal pairs. The significance of these results in the light of existing theories is discussed.

The analysis of inelastic scattering of 11-MeV protons from quadrupole and octupole collective levels of 14 even-even nuclei between ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ti}$ and ${}_{}{}^{76}{}_{}{}^{}\mathrm{Ge}$ is reported. The distorted-wave Born approximation is used to calculate the cross sections using the collective-model generalization of the optical model for inelastic scattering. The analysis is performed using both real and complex form factors for the model. A satisfactory description of all the data is obtained when a contribution due to compound-nucleus decay for most of the octupole levels and a few of the quadrupole levels is included.

Angular distributions have been measured for 15 levels observed in the ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}({}_{}{}^3{}_{}{}^{}\mathrm{He},d){}_{}{}^{41}{}_{}{}^{}\mathrm{Sc}$ reaction at 40-MeV bombarding energy. Distorted-wave Born-approximation calculations for the proton unstable excited states quasibound by the Coulomb and centrifugal barrier were performed using a form factor corresponding to an unbound (resonance) level in a Woods-Saxon well. The resulting spectroscopic factors are found to be insensitive to the scattering phase shifts, and in agreement with those obtained by elastic scattering. Most of the available $1f_{\frac{7}{2}}$, $2p_{\frac{3}{2}}$, and $2p_{\frac{1}{2}}$ strength and a large portion of the $1f_{\frac{5}{2}}$ strength is observed below 6-MeV excitation. Little $1g_{\frac{9}{2}}$ or $2d_{\frac{5}{2}}$ strength is observed.

Total reaction cross sections for protons on ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ have been measured at 15 energies between 10.3 and 21.6 MeV by the beam-attenuation method. The total reaction cross section for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ rises sharply at low energies, reaches a maximum value around 13 MeV, and reaches a minimum value around 16 MeV. The rise at the lower energies is a result of the Coulomb barrier. The dip at 16 MeV is probably associated with the ($p,n$) threshold for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$. A comparison is made between the present experimental values and preliminary optical-model predictions based on available elastic-scattering data and polarization data. The variation in the reaction cross section is also compared with the integrated partial cross sections for elastic scattering. Total reaction cross sections for protons on carbon have been measured at ten energies between 9.88 and 19.48 MeV. Resonances in the total reaction cross section are observed in the neighborhood of 10.4 and 13.8 MeV. Variations of 200 mb are seen in the cross sections with changes in energy of the incident protons of about 200 keV. A comparison is made of the present total reaction cross sections and the integrated partial cross sections for elastic scattering and inelastic scattering to the first excited state of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$.

The energy and angular distribution of $\alpha$ particles inelastically scattered from Al have been measured from 30 to 170° for 20.0- and 27.5-MeV bombarding energies. Angular distributions of the inelastic $\alpha$ particles corresponding to residual nuclei excited to the continuum are found to be symmetric around 90°. For a number of angular distributions, the magnitude of the anisotropy is large; i.e., the ratio of differential cross sections at 170 to 90° is greater than 2.5. In the interpretation of the experimental results, the nuclear-level-density parameter and the spin cutoff parameter are derived by application of the semiclassical compound-nucleus theory of Ericson and Strutinski. This cutoff parameter is consistent with the rigid-rotor model of the nucleus. In order to obtain agreement between the magnitudes of the calculated and the experimentally measured cross sections, it was necessary to incorporate nuclear shell effects into the statistical-theory calculations.

Experimental energies, spectroscopic factors, and electromagnetic data associated with the low-lying levels of ${\mathrm{Cr}}^{53}$ are fitted by means of a model in which the basis states are taken to be single-particle orbits vector-coupled to states of the ${\mathrm{Cr}}^{52}$ core. Unknown properties of the core states are treated as parameters. A least-squares minimization procedure is used to determine optimum fits to the data. Although most of the low-energy data can be fitted quite successfully, the spectroscopic factors and quadrupole moment are not well reproduced. The observed levels appear to be more highly mixed than is suggested by the model. It is also found to be necessary to introduce an effective charge in order to reproduce the $B\left(E2\mathrm{}\right)\mathrm{}$ data.

Levels are calculated for the $N=29\mathrm{}$ and $Z=29\mathrm{}$ nuclei, ${\mathrm{Ti}}^{51}$, ${\mathrm{Cr}}^{53}$, ${\mathrm{Fe}}^{55}$, ${\mathrm{Cu}}^{61,63,65}$. The model used is the intermediate-coupling model with quasivibrational core, as developed by True and Thankappan. A pattern search routine is used to fit the five parameters to the levels and stripping strengths. Except for the case of ${\mathrm{Cr}}^{53}$, levels and strengths are fitted fairly well. In particular, in ${\mathrm{Fe}}^{55}$ we identify the states at 1.917 and 2.051 MeV as ${\frac{3}{2}}^{-}$ and ${\mathrm{½}}^{-}$ states, respectively. $B\left(E2\mathrm{}\right)\mathrm{}$ values for transitions to the ground state are calculated, and the comparison with data for ${\mathrm{Cu}}^{63}$ and ${\mathrm{Cu}}^{65}$ shows good agreement. However, there are no experimental $B\left(E2\mathrm{}\right)\mathrm{}$ data available for the other nuclei.

The even selenium isotopes ${}_{}{}^{72}{}_{}{}^{}\mathrm{Se}$, ${}_{}{}^{74}{}_{}{}^{}\mathrm{Se}$, ${}_{}{}^{76}{}_{}{}^{}\mathrm{Se}$, and ${}_{}{}^{78}{}_{}{}^{}\mathrm{Se}$ have been investigated by means of the $\mathrm{Ge}(\alpha ,2n\gamma )\mathrm{Se}$ and $\mathrm{Ge}(\alpha ,4n\gamma )\mathrm{Se}$ reactions. The $\gamma$ radiation from these nuclei was studied during the irradiation using techniques of in-beam spectroscopy. The energies of the $\gamma$ rays, their relative intensities, their angular distributions, and their time distributions relative to the 2-nsec beam bunch have been measured. Quasirotational ground-state bands were observed up to 10+ for ${}_{}{}^{76}{}_{}{}^{}\mathrm{Se}$, up to 8+ for ${}_{}{}^{74}{}_{}{}^{}\mathrm{Se}$ and ${}_{}{}^{78}{}_{}{}^{}\mathrm{Se}$, and up to 6+ for ${}_{}{}^{72}{}_{}{}^{}\mathrm{Se}$. The level energies are compared to a semiempirical formula.