Brueckner self-consistent calculations are performed for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^3{}_{}{}^{}\mathrm{H}$, and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ nuclei with various modern hard-core interactions. Elements of the $G$ matrix are calculated by the reference-spectrum method, while $Q-1\mathrm{}$ corrections are made by matrix inversion in the proper single-particle space. Thus, it is not assumed that $Q$ commutes with the center-of-mass motion. The prescription for selecting the appropriate spectrum of single-particle excited states is investigated by comparing results of the Brueckner method with other calculations. These comparisons indicate that the particle spectrum should be left unperturbed. One then finds that the Hamada-Johnston, Yale, and Reid (hard-core) interactions yield about one half the binding energy of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$. The calculated results are dissected into shell-model components. This analysis indicates that the short-range part of the hard-core interaction is too strongly repulsive.

The conventional time-independent perturbation theory and projection-operator techniques are generalized to systems propagating under the influence of an effective non-Hermitian Hamiltonian, e.g., an optical-model potential. The mathematical complications which can arise due to lack of orthogonality and completeness for the eigenstates of such a Hamiltonian are discussed on an elementary level. Examples of the various techniques involved are taken from considerations of models for exotic atoms and cascade processes.

The $\gamma$-ray yield for the reaction ${}_{}{}^9{}_{}{}^{}\mathrm{Be}(p, \gamma ){}_{}{}^{10}{}_{}{}^{}\mathrm{B}$ has been measured over the range of bombarding energies 0.20-0.85 MeV and the radiative decay of the 6.88-MeV resonance level in ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$ studied. A large nonresonant contribution to the reaction cross section has been identified and compared with calculated cross sections based on an extranuclear direct-capture process. The previously measured high isospin impurity of the 6.88-MeV state is consequently significantly reduced; the amplitudes for the $T=0\mathrm{}$ and $T=1\mathrm{}$ parts of the wave function for this state are determined to be 0.92 and 0.39, respectively.

Amplitudes for elastic $s$-wave neutron-deuteron scattering above the breakup threshold are calculated by the method of complex coordinates. The nucleon-nucleon interaction is represented by a local spin-and parity-dependent central Yukawa potential, with parameters chosen to fit low-energy two-nucleon data. Results for inelastic parameters indicate possible errors in a previous phase-shift analysis. Results for the quartet phase shift and quartet and doublet inelastic parameters are consistent with separable potential calculations, but the doublet phase shifts from the two models differ significantly.

Starting from our previous work on the complete angular momentum reduction of the Faddeev equations, general formulas are developed for constructing the bound-state wave function from the Faddeev amplitudes. The $\mathcal{L}-\mathcal{S}$ coupling scheme is used. For trinucleon systems with nucleon-nucleon interactions in the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}D_1^{}{}_{}{}^{}$ states, the complete set of homogeneous Faddeev equations and the formulas for constructing the wave functions are given in detail. The wave function is also given in terms of the Derrick-Blatt classification of states.

Correlated wave functions obtained by solving the Bethe-Goldstone equation with realistic nuclear interactions are employed to calculate Coulomb shifts, isospin mixing, Coulomb energies, and coefficients of the isobaric mass formula in $1p$-shell nuclei. Improved agreement with experiment is obtained, particularly for the Coulomb shifts and isospin mixing which are not sensitive to the size parameter. No evidence is found favoring a charge-dependent component in the nuclear force.

The odd-mass cobalt nuclei from ${}_{}{}^{57}{}_{}{}^{}\mathrm{Co}$ to ${}_{}{}^{63}{}_{}{}^{}\mathrm{Co}$ are described in the framework of the unified model. The vibrational description of even-mass nickel isotopes is discussed and the $1{f_{\frac{7}{2}}}^{-1\mathrm{}}$, $1{f_{\frac{7}{2}}}^{-2\mathrm{}}\mathrm{}\left(0\right)2p_{\frac{3}{2}}$, $1{f_{\frac{7}{2}}}^{-2\mathrm{}}\mathrm{}\left(0\right)1f_{\frac{5}{2}}$, and $1{f_{\frac{7}{2}}}^{-2\mathrm{}}\mathrm{}\left(0\right)2p_{\frac{1}{2}}$ proton configurations are coupled to quadrupole vibrational cores. The spacings among these configurations are determined from stripping reaction data and from and analysis of binding energies, and the collective parameters are determined from experimental data on the Ni cores. Good general agreement of calculated and experimental properties is obtained without free parameters involved. For the best known isotopes, ${}_{}{}^{57}{}_{}{}^{}\mathrm{Co}$ and ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}$, a one-to-one correspondence of the eight or ten first calculated and experimental states is established. Observed spectroscopic factors in pickup and stripping reactions and electromagnetic properties are qualitatively well reproduced for the low-lying levels in general. For the available data most of the calculated values lie within 50% of the experimental values. On the basis of this agreement some spin and parity assignments are proposed among those compatible with experimental data. The results of other models are also discussed.

The singles $\gamma$-ray spectrum of ${}_{}{}^{71}{}_{}{}^{}\mathrm{As}$ was studied using 20- and 40-${\mathrm{cm}}^3$ Ge(Li) detectors. $\gamma -\gamma$ coincidence data were taken using 7-mm and 20-${\mathrm{cm}}^3$ Ge(Li) detectors in conjunction with a 4096 multichannel analyzer with digital gates. Of the 73 $\gamma$ rays observed, 43 are placed in a decay scheme with 14 excited states along with $log\mathrm{ft}$ values for 12 of these.

In-beam $\gamma$-ray measurements of the excited states in ${}_{}{}^{97}{}_{}{}^{}\mathrm{Tc}$ have been made using the reaction ${}_{}{}^{97}{}_{}{}^{}\mathrm{Mo}(p, n\gamma ){}_{}{}^{97}{}_{}{}^{}\mathrm{Tc}$ at incident proton energies between 3.0 and 6.0 MeV. Singles and $\gamma -\gamma$ coincidence measurements were made using Ge(Li) detectors and an on-line two-parameter data-acquisition system. By these methods about 50 $\gamma$ rays associated with the deexcitation of levels in ${}_{}{}^{97}{}_{}{}^{}\mathrm{Tc}$ have been observed. Coincidence spectra produced by gates on 11 of the stronger transitions were used along with the singles measurements to identify 28 levels with energies up to 1580 keV excitation. The states at 807, 896, 1127, 1141, 1173, 1220, and 1311 keV have not been previously reported. Evidence is given for states at 833, 850, 1240, and 1410 keV, of which the 850-keV level is isomeric. Branching ratios are given along with a decay scheme for ${}_{}{}^{97}{}_{}{}^{}\mathrm{Tc}$.

The variational principle in quantum mechanics gives an upper bound on the energy eigenvalue $E_k$ of the $k\mathrm{th}$ state if its trial wave function is orthogonal to the eigenfunctions of all the lower states. A lower bound on $E_k$ has been derived assuming that: (i) its upper bound be less than $E_{k+1\mathrm{}}$, and (ii) the energy fluctuation ${(〈H^2〉-{〈H〉}^2)}^{\frac{1}{2}}$ be less than $\frac{1}{2}(E_{k+1\mathrm{}}-E_k)$. An upper bound on the error in the wave function of the $k\mathrm{th}$ state has also been derived. The formulas for the bounds have been applied to calculate the accuracy of the energies and wave functions of the various $J$ states of the ground and excited $K=0\mathrm{}$ bands in ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$. The intrinsic wave functions of the $K=0\mathrm{}$ bands were taken from the earlier calculations performed by using the deformed Hartree-Fock and Tamm-Dancoff approximations. Techniques for calculating $〈H^2〉$ have also been discussed. Our results show that the energies and wave functions calculated by these approximations are fairly accurate for a number of states. The wave functions of the ground and first excited $J=0\mathrm{}$ states are accurate at least to the order of 92.5 and 87.3%, respectively.

The cross section for the reaction ${}_{}{}^6{}_{}{}^{}\mathrm{Li}(p, pd){}_{}{}^4{}_{}{}^{}\mathrm{He}(\mathrm{g}.\mathrm{s}.\mathrm{})$ has been measured in a kinematically complete experiment with 590-MeV protons. Reactions with recoil momenta of the residual ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ nucleus up to 120 MeV/c have been detected. The results are interpreted in terms of the plane-wave impulse approximation and the $\alpha -d$ cluster model. It is found that the reaction occurs with a cross section 0.8 times as large as the free elastic $\mathrm{pd}$ cross section at the same average c.m. scattering angle. The width of the momentum distribution for the motion of a deuteron in ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ is observed to be 124±4 MeV/c (full width at half maximum), a value considerably larger than had been observed before in similar experiments at lower energies.

The structure of the low-lying levels in odd-mass gallium isotopes is investigated within the framework of the semimicroscopic model, assuming three protons coupled to a quadrupole vibrator. A detailed comparison with experiments is performed for ${}_{}{}^{69}{}_{}{}^{}\mathrm{Ga}$.

The Doppler-shift-attenuation method has been used to investigate the lifetimes of states in ${\mathrm{Ar}}^{37}$ below 3.603-MeV excitation energy. Energies (in keV) and mean lifetimes (in psec) were determined as follows: 1409.8±0.1 (1.22±0.15); 1611.3±0.1 (>5); 2217.1±0.4 (0.91±0.18); 2490.0±0.4 (1.04±0.19); 2795.5±0.6 (<0.04); 3169.7±0.8 (0.10±0.02); 3184.9±1.0 (0.30±0.06); 3271.6±1.0 (0.06±0.02); 3515.9±1.0 (<0.05); 3525.7±2.0 (0.60±0.30); 3603.0±2.0 (<0.08).

The recoil-distance method was used to measure electromagnetic transition probabilities in ${\mathrm{Na}}^{22}$, ${\mathrm{Ne}}^{22}$, and ${\mathrm{P}}^{30}$. ${\mathrm{Na}}^{22}$ and ${\mathrm{Ne}}^{22}$ were produced from the 6.4-MeV ${\mathrm{He}}^4$-on-${\mathrm{F}}^{19}$ reaction. ${\mathrm{P}}^{30}$ was produced from the 6.4-MeV ${\mathrm{He}}^4$-on-${\mathrm{Al}}^{27}$ reaction. The mean lives in psec were: ${\mathrm{Ne}}_{1.275\to 0}^{22}$, 5.9±1.1; ${\mathrm{Na}}_{0.891\to 0}^{22}$, 16.1±3.0; ${\mathrm{Na}}_{1.528\to 0}^{22}$, 4.5±0.8; ${\mathrm{P}}_{0.709\to 0}^{30}$, 53±10.

The reaction ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}(d, p){}_{}{}^{20}{}_{}{}^{}\mathrm{F}$ has been studied with 16-MeV deuterons. Outgoing protons were detected in photographic emulsions in a magnetic spectrograph. Spectroscopic factors were extracted and combined with previous information and compared with results of shell-model calculations performed in a complete $\mathrm{sd}$-shell basis. Of the previously known 25 states below $E_x=4.5\mathrm{}$ MeV, angular distributions measured at 14 angles were obtained for all but the 5 at $E_x=1.824, 2.871, 3.761, 4.20, \mathrm{and} 4.21$ MeV. Strong stripping angular distributions were observed for 10 states-6 dominated by $l=2, \mathrm{and} 4$ by $l=0\mathrm{}$. These 10 states agree reasonably well in position and strength with the 10 lowest shell-model states predicted to have appreciable amounts of the configuration [${}_{}{}^{19}{}_{}{}^{}\mathrm{F}(\mathrm{g}.\mathrm{s}.\mathrm{})\otimes 1d_{\frac{5}{2}} or 2s_{\frac{1}{2}}$ neutron)].

The angular distribution of the $K$ electrons ejected during allowed $K$-capture transitions in polarized nuclei is calculated using a formalism previously developed by the author. It is shown that a result having a relative accuracy of order $Z\alpha$ may be obtained through the use of nonrelativistic electronic wave functions and a "semirelativistic" Coulomb Green's function due to Glauber and Martin. The result shows that, contrary to the predictions of previous theories, there is a noticeable asymmetry in the angular distribution of the ejected electrons, the asymmetry parameter being approximately a linear function of the electron's momentum. Possible experimental tests of the theory are described.

Properties of double-closed-shell nuclei are calculated using the Hartree-Fock method. The effective nucleon-nucleon interaction is taken to be the density-dependent "modified $\delta$ interaction," which is closely related to the Skyrme interaction, but with only three free parameters. These parameters were chosen so as to reproduce, as well as possible, the binding energy and rms charge radii of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. This interaction leads to a binding energy 16.5 MeV/A and Fermi momentum 1.33 ${\mathrm{fm}}^{-1\mathrm{}}$ of nuclear matter. Good agreement is found with the empirical rms charge radii of the other double-closed-shell nuclei, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$, and ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$. The same holds for the single-particle removal energies, especially those from $1s$ levels. The Hartree-Fock calculations with the present spin-independent and $s$-state interaction leads to as good agreement with experiment as those made by others, in particular, those made by Vautherin and Brink, who used a Skyrme interaction with five parameters.

The differences between the Skyrme and modified $\delta$ interaction are discussed. It is pointed out that the effective mass of a nucleon depends strongly on the odd-state part of the interaction, while the asymmetry potential is also sensitive to its spin dependence.

Using an implanted source of ${}_{}{}^{127m}{}_{}{}^{}\mathrm{Te}$ in iron in a Mössbauer experiment, the magnetic moment of the 57.6-keV state in ${}_{}{}^{127}{}_{}{}^{}\mathrm{I}$ is measured to be $(2.54\mathrm{}\pm 0.05){\mu }_N$ and the hyperfine field of iodine in iron 1.172±0.016 MG at 4.2°K. The measured magnetic moment continues the regular trend of the magnetic moments of the $\frac{7}{2}$+ states of other iodine isotopes. Its value is in good agreement with the calculations of Kisslinger and Sorensen and of Castel.

The uniqueness and energy dependence of optical-model parameters which describe the ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}(p, p){}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ scattering reaction have been studied in the bombarding range 8 to 14 MeV. In the analysis of data with a 3% error two discretely ambiguous well depths with mean values of 35 and 55 MeV are found which yield comparably good fits. The imaginary well depth is approximately 4 MeV for both. To select one well depth, a 1% measurement was made at the energy ($E_p=7.6\mathrm{}$ MeV) at which the difference between the two computed cross sections at backward angles is maximized, a difference of approximately 3%. These measurements select the 55-MeV well depth consistent with the number of occupied states in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. The spin-orbit term is undetermined in this study, since the values of the imaginary potential render the analysis insensitive to it.

Neutron spectra from the reactions ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}(p, n){}_{}{}^{197}{}_{}{}^{}\mathrm{Hg}$, ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}(p, n){}_{}{}^{209}{}_{}{}^{}\mathrm{Po}$, ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}(\alpha , n){}_{}{}^{184}{}_{}{}^{}\mathrm{Re}$, and ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}(\alpha , n){}_{}{}^{200}{}_{}{}^{}\mathrm{Tl}$ have been analyzed to extract the level-density parameters for the appropriate residual nuclei. Comparisons with constant-temperature and Fermi-gas forms indicate that both forms describe the data over a limited energy range. A recent calculation of the magnitude of shell effects by Gadioli et al. is compared with the experimentally determined values; this approach provides a better estimate of the level density of ${}_{}{}^{209}{}_{}{}^{}\mathrm{Po}$ than does the standard Fermi-gas model in which shell effects are included in the level-density parameter $a$.