The ($\alpha ,{\alpha }^{\prime }$) reaction on ${\mathrm{Zn}}^{64}$ and ${\mathrm{Zn}}^{66}$ has been studied using the 31-MeV $\alpha$-particle beam from the Massachusetts Institute of Technology cyclotron, with an over-all energy resolution of 80-120 keV. Angular distributions are presented, both for levels with known spin, and for levels whose spin and parity have not been previously determined. New $3^{-}$, $4^{+}$, and $5^{-}$ assignments are made both by comparison with levels of known spin and with the distorted-wave Born approximation. Good angular distributions are presented for the weak states at 1.81 MeV ($2^{+}$) and 2.32 MeV ($4^{+}$) in ${\mathrm{Zn}}^{64}$. They are both out of phase with the $2^{+}$ and $4^{+}$ single-excitation states. The slope of the angular distribution for the 2.32-MeV ($4^{+}$) level is shallower than for the single-excitation $4^{+}$ state, while the slopes are the same for the $2^{+}$ states. Transition strengths in ${\mathrm{Zn}}^{64}$ and ${\mathrm{Zn}}^{66}$ are compared. Fractionation of $3^{-}$ strength in ${\mathrm{Zn}}^{64}$ has been observed, but it is smaller than that found in the calcium isotopes.

The proton transfer reactions on ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$ and ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$ were studied using the reactions ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}({}_{}{}^3{}_{}{}^{}\mathrm{He},d){}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ and ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}({}_{}{}^3{}_{}{}^{}\mathrm{He},d){}_{}{}^{31}{}_{}{}^{}\mathrm{P}$ at 17.85-MeV bombarding energy. Transitions to $T_{>}$ and $T_{<}$ levels were obtained. The spectroscopic factors from distorted-wave Born-approximation analysis were compared with information obtained at lower bombarding energies. The number of $T_{<}$ states is discussed qualitatively in terms of fragmentation caused by core-polarization states. The value for the isovector potential responsible for the splitting of the $T_{>}$ and $T_{<}$ states was determined for several orbits. Charge radii calculated for Coulomb energy differences indicated that ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ requires a larger radius parameter than ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}$.

Interactions of neutrons with silicon have been studied by measuring $\gamma$-ray production cross sections. For incident mean neutron energies $E_n=5.35,5.85,6.4,6.9,7.45,7.95,8.5, \mathrm{and} 9.0$ MeV, spectra were obtained for a natural silicon sample. The $\gamma$ rays were detected using a coaxial Ge(Li) detector of 30-${\mathrm{cm}}^3$ active volume. Data were obtained for $\gamma$-ray scattering angles of 55 and 90° for all $E_n$, of 35° for $E_n=7.45\mathrm{} \mathrm{and} 8.5$ MeV, and of 75° for $E_n=6.4\mathrm{} \mathrm{and} 7.45$ MeV. Time of flight was used with the detector to discriminate against pulses due to neutrons and background radiation. Data were also obtained at $E_n=5.9\mathrm{}$ MeV, ${\theta }_{\gamma }={55}^{\circ }$ for a sample of ${}_{}{}^{29}{}_{}{}^{}\mathrm{SiO}_2^{}{}_{}{}^{}$ enriched to 95% in ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$, and for a similarly enriched sample of ${}_{}{}^{30}{}_{}{}^{}\mathrm{SiO}_2^{}{}_{}{}^{}$. These data have been studied to obtain absolute cross sections for production of $\gamma$ rays for the incident neutron energies quoted above. The cross sections have been compared, where possible, with previously measured values; agreement was fair.

The spectra were studied for $\gamma$ rays which could be associated with deexcitation of nuclear levels having unknown decay modes. For ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$, $\gamma$ rays were found having energies appropriate for decay of levels at excitation energies $E_x=4.736,4.836,4.893, \mathrm{and} 5.249$ MeV. For ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$, $\gamma$ rays were found for decay of levels at excitation energies $E_x>~4.826$ MeV. The spin of the 4.826-MeV state in ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$ is reasonably limited to 2, 3, or 4. No previously unknown transitions were found for ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ or ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}$; for ${}_{}{}^{28}{}_{}{}^{}\mathrm{Al}$, the evidence suggests that the 1.624-MeV level is a doublet of 3-keV separation.

Relativistic nucleon-meson field theory is cast in a form appropriate to the nuclear many-body problem. Martin-Schwinger thermodynamic Green's functions are employed. The $n$-nucleon Green's functions satisfy a set of coupled equations which is formally identical to those of the usual potential many-body problem. Here, however, the two-body potential is replaced by a time-dependent interaction in which the mesons are formally eliminated in favor of higher-order nucleon correlations. A general program of increasing complexity for obtaining approximate solutions to the equations is discussed. It is necessary to solve the "vacuum" (one-, two-, etc., nucleon propagator) first. This has been done in the "Hartree-Fock" approximation which sums all diagrams containing a single continuous nucleon line with all possible uncrossed $\pi$ and $\omega$ meson lines. Peaks in the spectral function are identified with masses of known $N^{*}$ resonances. The appearance of ghost states, which arise in the process of mass and wave-function renormalization, is discussed. The resultant Green's function is used to calculate the magnetic moment of the nucleon, yielding a significantly better isovector component of the magnetic moment than the usual perturbation theory, although the isoscalar component is poor in both cases.

The generalized Hartree-Fock approximation of Kerman and Klein is extended to include continuum states of a collective nature. The equations for scattering in the random-phase approximation are rederived.

The binding energy of ${\mathrm{He}}^4$ and ${\mathrm{O}}^{16}$ was calculated using reaction matrix elements of Tabakin's potential. A separable form of the potential has been used to reduce the basic equation to a simple linear algebraic system. The Pauli operator $Q$ defined in terms of harmonic-oscillator intermediate states permits an easy and accurate calculation. Our numerical results for the binding energies include the first- and second-order contributions. A very resonable agreement between the experimental and theoretical values has been obtained, since the occupied-state energies are made nearly self-consistent and a cancellation of other important higher-order contributions has been achieved by a shift of the entire harmonic-oscillator spectra.

A systematic study of the effective two-body $\Lambda -N$ interaction is made in an exact manner from the binding-energy data of the $p$-shell hypernuclei within the framework of the intermediate-coupling shell model. The binding energy is expressed in terms of the five independent potential integrals of the two-body $\Lambda -N$ interaction, and the latter are determined by a least-squares fit to the experimental data. The energy levels and the $\gamma$ transitions are calculated, and the structures of the $p$-shell hypernuclei are discussed. The potential integrals are then analyzed in terms of phenomenological potentials. A large contribution to the binding energy by noncentral forces, especially the tensor forces, is found. The effect of the existence of a three-body $\Lambda \mathrm{NN}$ force is also discussed.

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 ${}_{}{}^{19}{}_{}{}^{}\mathrm{O}$.