Calculations are carried out for even Ti isotopes using the self-consistent Hartree-Fock-Bogoliubov (HFB) theory, and the results are compared with those obtained from the generalized BCS approximation of Belyaev for axially symmetric deformation. It is found that in most cases the generalized BCS and HFB results agree. However, for isotopes for which the generalized BCS and Hartree-Fock results agree, the HFB approximation may yield a different solution with the same energy minimum having different pairing correlations.

It is demonstrated that the $S$ matrix derived from the Lane-Robson calculable theory of nuclear reactions is independent of the choice of the boundary-condition constants even if a truncated set of the basis states is used.

An experimental test has been made of the validity of the idea that the quasifree scattering of a proton by the moving proton in the deuteron can be described as free proton-proton scattering modified only by an effective momentum distribution of the proton in the deuteron. The measurement confirmed the dependence on the proton momentum and also yielded the effective momentum distribution producing the scattering.

Accurate conversion-electron intensities and $\gamma$-ray intensities were combined to obtain $K$ conversion coefficients for 80 transitions in ${}_{}{}^{156}{}_{}{}^{}\mathrm{Gd}$ from the decay of 5.4-day ${}_{}{}^{156}{}_{}{}^{}\mathrm{Tb}$. These data were used to make spin and parity assignments for the following levels: 1538.90, ${\mathrm{}\left(3\right)\mathrm{}}^{-}$; 1851.84, $3^{-}$; 1948.98, $3^{-}$; 1952.32, $4^{-}$; 2175.08, $3^{-}$, $4^{-}$; and 2232.52 keV, $3^{-}$, $4^{-}$. Levels at 1462.26, 1506.89, and 1538.90 keV are now established on the basis of coincidence data. A complete level scheme is presented that incorporates all of the different features seen in recent studies.

Tests are suggested to verify the hypothesis that thermal $n-p$ capture proceeds via the transition ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\to {}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ and that approximately 10% of the observed capture cross section is due to interaction effects. It is shown that measurements of the "$\gamma$ polarization effect" using polarized neutrons and protons are capable of testing the predictions of the hypothesis to within 1%.

Through a new type of experiment to obtain information on the $K$-shell internal ionization in $\beta$ decay, the summing-energy spectrum of electrons ($\beta$ particles plus emitted $K$-shell electrons) in coincidence with emitted $K$ x rays in the $\beta$ decay of ${}_{}{}^{63}{}_{}{}^{}\mathrm{Ni}$ has been observed directly using two proportional counters. The procedure and results are discussed.

Angular distributions of the polarization and the cross section for $p-{}_{}{}^4{}_{}{}^{}\mathrm{He}$ elastic scattering have been measured in 2-MeV steps between 20 and 45 MeV and in steps of approximately 150 keV across the 23.4-MeV resonance corresponding to the second excited state of ${}_{}{}^5{}_{}{}^{}\mathrm{Li}$ at 16.7 MeV excitation. The relative uncertainties of the polarization measurements are typically less than ±0.01. The normalization uncertainty from energy to energy and relative to the older data below 20 MeV proton energy is approximately 2%. The cross-section angular distributions with a relative uncertainty of 3% have been normalized to previously existing data, since an absolute cross-section measurement was not feasible with our experimental setup. The polarization measurements provide an accurate proton polarization analyzer up to 45 MeV. With the exception of the narrow resonance region around 23.4 MeV, the analyzing power near ${\theta }_{\mathrm{lab}}=125\mathrm{}°$ exceeds 80% at all energies and shows no rapid variations. Around 30 MeV, a very weak and broad anomaly is seen in the polarization, coinciding in ${}_{}{}^5{}_{}{}^{}\mathrm{Li}$ excitation (approximately 22 MeV) with the structure observed in $d-{}_{}{}^3{}_{}{}^{}\mathrm{He}$ elastic scattering.

A phase-shift analysis of recent $p-{}_{}{}^4{}_{}{}^{}\mathrm{He}$ cross-section and polarization data has been performed between 20 and 40 MeV proton laboratory energy. A set of single-energy results is presented, which shows little scatter as a function of energy. The match between our results and existing phase-shift sets below 20 and above 40 MeV is excellent. The most striking feature of the phase shifts above the inelastic threshold at 23.02 MeV is the dominance of absorption in the even partial waves. There is weak evidence in the energy dependence of the phase shifts for levels of ${}_{}{}^5{}_{}{}^{}\mathrm{Li}$ other than the well-known ${\frac{3}{2}}^{+}$ second excited state. Tentative assignments of spin and parity of such levels are discussed. An $R$-matrix parametrization of the ${}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}$ phase shift has been performed over the $p-{}_{}{}^4{}_{}{}^{}\mathrm{He}$ resonance corresponding to the second excited state of ${}_{}{}^5{}_{}{}^{}\mathrm{Li}$, and improved level parameters are presented for this state.

The Garvey-Kelson mass sum rule is known to be violated when $Z=N=\mathrm{odd}$, $Z=N+1=\mathrm{even}$, or $Z=N+1=\mathrm{odd}$ nuclei are considered. This violation is a result of the lack of cancellation of certain two-body matrix elements. These matrix elements can be calculated assuming various models of the nuclei involved, e.g., deformation, level orderding, etc., and the amount by which the sum rule is violated empirically can then be used to distinguish the most appropriate model. The results of this empirical determination of nuclear characteristics agree quite well with the results of more involved calculations and conform to the generally accepted picture of nuclei in the $s-d$ shell.

A semiclassical Monte Carlo calculation has been performed which indicates that Coulomb forces among the final-state particles may significantly affect the angular distributions and directional-correlation functions for sequential reactions with three bodies in the final state.

We investigate the effects of taking the two-nucleon scattering matrices off energy shell in the first term of the nucleon-nucleus optical potential. In order to avoid Coulomb interference, only neutron-nucleus elastic scattering is considered. We look both for the possibility of improving the fit to the elastic nucleon-nucleus scattering observables by varying off-shell parametrization, as well as the possibility of extracting off-shell information on the nucleon-nucleon force.

We study with sum-rule techniques nuclear neutrino-induced reactions in the limit in which these reactions involve mainly giant-resonance excitation (i.e., at small angles). Resonant excitation is particularly important because simple shell-model and Fermi-gas calculations appear to give results which are too low relative to experiment for the differential cross section at small angles. Furthermore, in the strictly forward scattering region, we find an interesting interplay between nonrelativistic first-forbidden and allowed relativistic terms.

Direct numerical calculations in $K^{-}$-mesonic atoms have shown that the perturbation theory commonly used is inadequate. The theory fails to describe the very strong repulsive (level-shift) effect due to the absorptive part of the optical potential. Because of this large repulsive effect, the optical potentials best fitted to the recent level-shift and width data are found to be attractive. The potential may be very attractive, but not enough to produce a $K^{-}$-nucleus bound state by the strong interaction against the strong repulsive effect of the large imaginary part: The latter works as if it were a hard core. Taking the $3d$ state of the $K^{-}-{\mathrm{S}}^{32}$ atom as a model, we also examine how well we can determine the nuclear-density parameters from the $K^{-}$-mesonic-atom spectra within the optical-potential model.

A convenient parametrization of experiments in which a polarized spin-1 particle bombards a target and a polarized spin-1 particle emerges is given. The parameters defined are a generalization of the "Wolfenstein parameters" long used in the description of spin-$\frac{1}{2}$ polarization-transfer experiments. A specific $M$ matrix for a spin-0 target is used to find the relations between the various observables in several coordinate systems. The formalism is valid for the general 1 + 0 → 1′ + 0′ problem, where 1 and 1′ may indicate different spin-1 particles and 0 and 0′ may indicate different spin-0 particles, but where the product of initial channel and final channel parities is unchanged. The constraints imposed by time-reversal invariance when the reaction is specialized to elastic scattering are discussed. The prospects for a complete determination of the $M$ matrix and for possible time-reversal tests are briefly touched upon.

Hartree-Fock calculations with two-body forces are presented in several nuclei, taken as spherical, from ${\mathrm{He}}^4$ to ${\mathrm{Pb}}^{208}$. We first present the results obtained with the best (SP1 and SP2) of the recent smooth semirealistic interactions of Saunier and Pearson. These yield good binding energies and radii except in the vicinity of ${\mathrm{Ni}}^{56}$. However, the spectra in nuclei with spin-unsaturated shells are poor: The spin-orbit splittings in such nuclei are very small (if not negative), and, in particular, in ${\mathrm{Pb}}^{208}$ the level ordering near the top of the Fermi sea is incorrect. This feature does not allow meaningful extrapolation to the superheavy region with these potentials.

In an attempt to find a two-body interaction allowing such an extrapolation, we modify SP1 and find that with a very strong positive triplet-even phenomenological tensor force the ${\mathrm{Pb}}^{208}$ spectrum is very much improved, and the level ordering and density of uppermost occupied states are comparable to the experimental ones. As a result, ${\mathrm{Pb}}^{208}$ is now found doubly magic, together with a good binding energy and radius. The magic nature of ${\mathrm{O}}^{16}$, ${\mathrm{Ca}}^{40}$, ${\mathrm{Ca}}^{48}$, ${\mathrm{Ni}}^{56}$, and ${\mathrm{Zr}}^{90}$ is also reproduced by the modified SP1. Consequently this interaction provides new possibilities for valuable extrapolation to the superheavy region with a two-body force.

We develop a consistent procedure for introducing an external single-particle potential into the cluster expansion of the energy expectation value with respect to a correlated wave function. It is shown that the usual Brueckner reaction-matrix approximation may be extracted from the correlated-basis-functions theory by a special treatment of the external potential and an associated special choice of two-body correlation factor.

A Ge(Li) detector was used to measure $\gamma$-ray transitions in ${}_{}{}^{36}{}_{}{}^{}\mathrm{S}$ via $p-\gamma$ coincidence studies in the ${}_{}{}^{34}{}_{}{}^{}\mathrm{S}(t,p\gamma ){}_{}{}^{36}{}_{}{}^{}\mathrm{S}$ reaction at $E_t=3.1\mathrm{}$ MeV. Measurements were carried out in Method II geometry at $\gamma$-ray detection angles of 0, 45, and 90°. Analyses of the Doppler-shift attenuations evident in the primary $\gamma$-ray transitions were used to determine mean lives of ${}_{}{}^{36}{}_{}{}^{}\mathrm{S}$ states. Angular-correlation analysis confirms previous spin-parity assignments of $2^{+}$, $3^{-}$, $1^{+}$, and $2^{+}$ for the states at 3.29, 4.19, 4.52, and 4.57 MeV, respectively. The "level" previously reported at 6.20 MeV was found to be a doublet of ∼38-keV separation: In other respects the present work largely confirms previous conclusions on the $\gamma$-ray branching of states of ${}_{}{}^{36}{}_{}{}^{}\mathrm{S}$. The excitation energies, given in keV, together with the mean lifetimes (in psec) deduced from these measurements are as follows: 3291 (0.11 ± 0.03); 4192 (${1.1}_{-0.3\mathrm{}}^{+0.6\mathrm{}}$); 4523 (0.025 ± 0.012); 4575 (0.080 ± 0.015); 5251 (0.10 ± 0.04); 5391 (···) 5509 (0.27 ± 0.06); 5573 (<0.2); 6187 (0.08 ± 0.03); and 6225 (<0.03). The energy uncertainties are ≤1 keV. No evidence was seen for $\gamma$ decays to the $0^{+}$ level at 3346 ± 4 keV.

The differential ranges of ${}_{}{}^{64}{}_{}{}^{}\mathrm{Cu}$ recoils emitted at 0-12° and 35-46° to the beam were measured for the ${}_{}{}^{65}{}_{}{}^{}\mathrm{Cu}({}_{}{}^3{}_{}{}^{}\mathrm{He},\alpha )$ reaction at 32 MeV by means of the electrostatic-collection technique. The results have been compared with a Monte Carlo evaporation calculation, as well as with a kinematic calculation for $\alpha$-particle emission ascribable to a pickup process. The range at 0-12° is consistent with the evaporation of four single nucleons, and the contribution from pickup is less than 2%. The differential range at 35-46° consists of two well-resolved peaks whose positions are in accord with the expectations for these two mechanisms. The pickup process is found to account for (12±2)% of the recoils emitted at this angle.

${}_{}{}^{33}{}_{}{}^{}\mathrm{Si}$ has been produced via the ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}+{}_{}{}^{18}{}_{}{}^{}\mathrm{O}\to {}_{}{}^{33}{}_{}{}^{}\mathrm{Si}+2p+n$ reaction using 23-40-MeV ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ ions. Identification is made from the observed $\gamma$ rays of 1431.3 ± 0.5, 1847.69 ± 0.25, and 2538 ± 2 keV which agree with the first three excited states of ${}_{}{}^{33}{}_{}{}^{}\mathrm{P}$. By means of the reaction ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}\mathrm{}(t,p)\mathrm{}{}_{}{}^{33}{}_{}{}^{}\mathrm{P}$, $\gamma$ rays from the first two excited states of ${}_{}{}^{33}{}_{}{}^{}\mathrm{P}$ have been measured as 1431.4 ± 0.3 and 1847.60 ± 0.15 keV. The three ${}_{}{}^{33}{}_{}{}^{}\mathrm{Si}$ $\gamma$ rays decay together and a value of $T_{\frac{1}{2}}=6.3\mathrm{}\pm 0.3$ sec is obtained from the 1848-keV line. Relative $\gamma$ intensities correspond to ${}_{}{}^{33}{}_{}{}^{}\mathrm{Si}$ $\beta$ branches to the 1431-, 1848-, and 2539-keV states of ${}_{}{}^{33}{}_{}{}^{}\mathrm{P}$ in the ratios 0.06 ± 0.06: 1: 0.10 ± 0.02. No information was obtained on a possible ${}_{}{}^{33}{}_{}{}^{}\mathrm{Si}$ ground-state $\beta$ branch. The results are consistent with the expected mass and spin-parity ($J^{\pi }={\frac{3}{2}}^{+}$) of the ${}_{}{}^{33}{}_{}{}^{}\mathrm{Si}$ ground state.

Excitation functions have been measured at laboratory angles of 60, 80, and 120° in 50-100-keV steps for proton scattering from the $0^{+}$, $2^{+}$, and $4^{+}$ members of the ground-state rotational band in ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$. Prominent structure of width 300 keV is seen in both the $2^{+}$ and $4^{+}$ cross sections at all three angles and throughout the entire energy range from 16 to 18.2 MeV. At 60°, there is a 30% change in the $2^{+}$ and $4^{+}$ cross sections over the resonance at 17.7 MeV. The presence of this structure makes very dubious the quadrupole and hexadecapole deformations extracted from direct-reaction analyses of proton scattering below 18 MeV.