The intense peak observed in the spectra of the ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}({}_{}{}^3{}_{}{}^{}\mathrm{He}, d){}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$ reaction at an excitation energy of 4.42 MeV has given rise to two conflicting interpretations, neither of which has satisfactorily explained its intensity. In the present work a resolution of 16 keV was obtained for the (${}_{}{}^3{}_{}{}^{}\mathrm{He}$, $d$) reaction and the peak was resolved and shown to be a doublet with the intensity ratio 3:1. A possible interpretation of this doublet is discussed.

The possibility of $1^{-}$ states above the 9.58- and 7.12-MeV states in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ interfering with these lower states would strongly affect the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(\alpha , \gamma ){}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ capture cross sections near $E_{\alpha }=3.2\mathrm{}$ MeV and the inferred stellar-reaction rate. Cross sections below 3.2 MeV reported earlier have been extended to 4.1 MeV using similar techniques and overlap the previous measurement from ∼2.9 to ∼3.2 MeV.

Allowed $\Delta T=1\mathrm{}$ Gamow-Teller $\beta$ decay from the ${\mathrm{Rb}}^{88}$ $2^{-}$ ground state to the ${\mathrm{Sr}}^{88}$ $3^{-}$ level at 2.73 MeV is calculated. A one-particle-one-hole description of the latter state requires the ${\left[2\mathrm{}{p}_{\frac{1}{2}}^{-1\mathrm{}}\mathrm{}\right(n\left)2d_{\frac{5}{2}}\mathrm{}\right(n\left)\right]}_{T=6\mathrm{}}^{J=3^{-}}$ component in order to predict the observed $log\mathrm{ft}$ value of 6.7. The decay rate is extremely sensitive to the amplitude of this term.

Explicit expressions for the calculation of equivalent local potentials corresponding to given nonlocal separable potentials have been derived. Using these expressions, equivalent local potentials have been calculated for a test case and a self-consistency check of the formulation has been made. An effective-range formalism for nonlocal separable potentials has also been presented following the coordinate representation.

The ${\delta }^{\prime }$ interaction has been used to represent the hard-core potential in variation and Hartree calculations. These calculations were compared with exact calculations for a two-body bound-state problem and a soluble three-body problem. The trial wave function in the variational problem with the ${\delta }^{\prime }$ interaction is shown to approach rapidly its hard-core limit with increasing number of trial parameters. The ${\delta }^{\prime }$ interaction is superior to current soft-core representations of the nucleon-nucleon potential in the Hartree calculations.

The half-lives of several radioactivities induced by Van de Graaff bombardment have been measured using plastic and NaI(Tl) scintillation detectors, together with a time-channel analyzer controlled by a quartz-crystal clock. The half-lives obtained are as follows: ${\mathrm{Be}}^{11}$, 13.81 ± 0.08 sec; ${\mathrm{C}}^{15}$, 2.46 ± 0.01 sec; ${\mathrm{N}}^{16}$, 7.13 ± 0.04 sec; ${\mathrm{O}}^{19}$, 27.1 ± 0.1 sec; and ${\mathrm{Al}}^{28}$, 2.252 ± 0.006 min.

Using the results of a shell-model analysis of the $p$-shell hypernuclei by the authors, the binding energies of the two $\Lambda$ particles in the $p$-shell $\Lambda \Lambda$ hypernuclei are calculated. A consistent account of the binding energies of the two known $\Lambda \Lambda$ hypernuclei, ${}_{\Lambda \Lambda }{}^{ 6}{}_{}{}^{}\mathrm{He}$ and ${}_{\Lambda \Lambda }{}^{10}{}_{}{}^{}\mathrm{Be}$ (or ${}_{\Lambda \Lambda }{}^{11}{}_{}{}^{}\mathrm{Be}$) is obtained. Close agreement with the results of other investigators who used different methods is also pointed out. The effects of the noncentral potentials in the effective two-body $\Lambda -N$ interaction are discussed.

It has been suggested, in effect, that in a deformed nucleus the number of protons (or the amount of charge) which are carried along by the rotational motion may, on the average, be approximated as the product of the atomic number $Z$ and the deformation parameter $\delta$. The theoretical justification of this suggestion is discussed, and a more accurate expression is obtained. Assuming that the interaction of the rotational motion with an external magnetic field is entirely due to the current associated with the amount of charge following the rotational motion, on the average, and also in accordance with the cranking approximation, a macroscopic expression for the rotational gyromagnetic ratio $g_R$ is derived. This expression, supplemented by the usual macroscopic formula for the intrinsic quadrupole moment $Q_0$, may constitute a macroscopic self-consistency relation among the collective parameters in a rotational band, namely, $Q_0$, $g_R$, and the moment of inertia $J$. The values of $g_R$ calculated from the experimental values of $J$ and $Q_0$ are tabulated for the ground-state rotational bands of both even-even and odd-mass nuclei. The aforementioned macroscopic self-consistency is then tested by comparing these calculated values of $g_R$ with both empirical values and previous microscopic calculations. According to the present approach, the well-known lowering of $g_R$ from the usual fluid-model value is mainly due to the limitation on the number of protons which can follow the rotational motion, on the average. It is not clear, however, whether there is any direct connection between this limitation and the pairing interaction which seems to play a rather essential role in the current microscopic calculations. This puzzling situation is further illustrated by considering the moments of inertia of even-even nuclei.

Based on the ground-state magnetic moments, the magnetic dipole transition probabilities in the ground-state rotational bands of deformed odd-mass nuclei are analyzed assuming that the rotational gyromagnetic ratios are given by a theoretical expression derived previously.

Differential cross sections for the reactions ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}(\alpha ,{}_{}{}^6{}_{}{}^{}\mathrm{Li}){}_{}{}^8{}_{}{}^{}\mathrm{Be}_{\mathrm{g}.\mathrm{s}.\mathrm{}}^{}{}_{}{}^{}$ and ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}(\alpha ,{}_{}{}^6{}_{}{}^{}\mathrm{Li}){}_{}{}^8{}_{}{}^{}\mathrm{Be}_{2.9}^{}{}_{}{}^{}$ have been measured in the angular range from 9 to 25° (lab system) in 1° steps at $E_{\alpha }=46\mathrm{}$ MeV. The shapes of the angular distributions are typical of a direct reaction, and the pickup processes are analyzed in distorted-wave approximations on the basis of an extreme cluster model, i.e., on the assumption that a deuteron is picked up from the target nucleus ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$. Calculations using proper two-particle form factors are also performed, and the results agree with the former method. From the ratio of the experimental to the theoretical cross section, a relative spectroscopic factor (${}_{}{}^8{}_{}{}^{}\mathrm{Be}$-core-plus-deuteron-cluster parentage) is obtained and compared with two-particle fractional-parentage coefficients calculated in intermediate coupling.

Differences in the decay constant of ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ in various states of chemical combination were measured using the differential-ionization-chamber technique. The results are: $\left\{\lambda \right(\mathrm{BeO})-\lambda {\left(\mathrm{Be}{\mathrm{F}}_2\right)}_{\mathrm{amorph}}=(1.130\mathrm{}\pm 0.058)\times {10}^{-3\mathrm{}}\lambda (\mathrm{Be}),\}\left\{\lambda \right(\mathrm{BeO})-\lambda ({\mathrm{Be}}_4\mathrm{O}{\left({\mathrm{CH}}_3\mathrm{COO}\right)}_6)=(-0.724\mathrm{}\pm 0.057)\times {10}^{-3\mathrm{}}\lambda (\mathrm{Be}),\}\left\{\lambda \right(\mathrm{BeO})-\lambda (\mathrm{Be}{\mathrm{Br}}_2)=(1.472\mathrm{}\pm 0.063)\times {10}^{-3\mathrm{}}\lambda (\mathrm{Be}),\}\left\{\lambda \right({\mathrm{Be}}_4\mathrm{O}{\left({\mathrm{CH}}_3\mathrm{COO}\right)}_6)-\lambda {\left(\mathrm{Be}{\mathrm{F}}_2\right)}_{\mathrm{amorph}}=(1.852\mathrm{}\pm 0.082)\times {10}^{-3\mathrm{}}\lambda (\mathrm{Be}),\}\left\{\lambda \right(\mathrm{BeO})-\lambda (\mathrm{Be}{\left({\mathrm{C}}_5{\mathrm{H}}_5\right)}_2)=(0.795\mathrm{}\pm 0.074)\times {10}^{-3\mathrm{}}\lambda (\mathrm{Be}),\}\left\{\lambda \right(\mathrm{BeO})-\lambda ({\mathrm{Be}}^{2+}{\left({\mathrm{OH}}_2\right)}_4)=(-0.374\mathrm{}\pm 0.077)\times {10}^{-3\mathrm{}}\lambda (\mathrm{Be}),\}\left\{\lambda \right(\mathrm{Be}{\left({\mathrm{C}}_5{\mathrm{H}}_5\right)}_2-\lambda \left({\mathrm{Be}}^{2+}{\left({\mathrm{OH}}_2\right)}_4\right)=(-1.169\mathrm{}\pm 0.106)\times {10}^{-3\mathrm{}}\lambda \left(\mathrm{Be}\right).\mathrm{}\}$ The decay constant of ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ is proportional to the electron density at the nucleus. These results can therefore be used to establish a scale for the relative electron density at the Be nucleus in different chemical combinations.

The effect of $\Lambda N$ tensor forces on the $\Lambda$-particle binding in nuclear matter is studied with the use of second-order perturbation theory and the Brueckner-Bethe reaction-matrix approach in the $g$-matrix approximation. The $g$ matrix is calculated self-consistently by use of the Kallio-Day version of the reference-spectrum method. The free kinetic energies are assumed for the unoccupied states. One-boson-exchange (OBE) models indicate that the $\Lambda N$ tensor force is expected to be of short range and moderate strength. For short-range tensor forces the dominant momentum components are very large, and the effects of such forces are only slightly modified by the nuclear medium. On the other hand, if the $\Lambda N$ tensor forces were of rather long range, they would be quite strongly suppressed in nuclear matter. These features are very clearly exhibited by consideration of the effective nonlocal central potentials that represent the ($s$-state) effect of tensor forces for nuclear matter and for scattering. The ratio of the (nuclear-matter) expectation values of these two effective potentials is a good measure of the suppression. The expectation value of the effective potential for nuclear matter is just the second-order perturbation-theory energy. Reaction-matrix calculations show that higher-order effects may become quite important for shorter ranges. Such calculations have, in particular, been made for various mixtures of central and tensor forces chosen to give a constant $s$-wave scattering length. Yukawa shapes corresponding to the kaon and one- and two-pion masses were used, as well as "realistic" OBE potentials with a hard core and a tensor component due to kaon exchange (and also approximately due to $\eta$ exchange). For a particular mixture, the suppression is measured by the reduction in the well depth relative to the depth for a purely central potential which has the same hard core and the same scattering length and effective range as the mixture. For the short-range tensor forces there is rather little suppression even for very strong tensor forces which account for all the triplet scattering. Different assumptions about the $d$-state interaction have an almost negligible effect on the $s$-state well depth if the same assumption is made for both scattering and nuclear matter. Similar considerations are made for the effect of tensor forces in the $p$ wave, for which we find very little suppression ($\lesssim 1$ MeV). We conclude that if central and short-range tensor forces are chosen to compensate each other for low-energy scattering, they will also compensate each other quite closely for nuclear matter. In particular, for the OBE potentials with strengths consistent with the phenomenological values of the $\Lambda N\overline{K}$ coupling constants, the reduction in the well depth is at most about 4 MeV. The conclusions about the $\Lambda N$ interaction obtained from a comparison of the calculated and phenomenological well depths are, therefore, effectively unchanged by the presence of a $\Lambda N$ tensor force. Consequently, in order to bring the two numbers into agreement, it is necessary to invoke a substantial short-range repulsion, a rather weak $p$-state interaction, and suppression of the $\Lambda N-\Sigma N$ coupling and/or repulsive $\Lambda \mathrm{NN}$ three-body forces.

We derive expressions for the $K$ matrix for the general case where the Hamiltonian is separated as $H=H_0+V$, and $H_0$ can have discrete as well as continuum states. It is shown that the correct handling of the bound states in the continuum eliminates one of the correction terms proposed by Tobocman and Nagarajan. In addition, some of the properties of the $K$ matrix evaluated at complex energies are discussed.

The photoneutron cross section of ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ is calculated using the Dirac model: It is found to have a form that differs somewhat from the standard Breit-Wigner form near threshold. A good fit to the data is obtained.

Cross sections for the ${}_{}{}^7{}_{}{}^{}\mathrm{Be}(p,\gamma ){}_{}{}^8{}_{}{}^{}\mathrm{B}$ reaction have been measured at 20 proton energies ranging from 0.953 to 3.281 MeV. Measurements were made relative to the cross section for the ${}_{}{}^7{}_{}{}^{}\mathrm{Li}\mathrm{}(d,p)\mathrm{}{}_{}{}^8{}_{}{}^{}\mathrm{Li}$ reaction at the 0.770-MeV resonance peak. The results were analyzed in two ways to obtain values for $S\left(0\right)\mathrm{}$, the zero-energy cross-section factor. The first type of analysis, based on the assumption that the observed cross section was composed of a nonresonant part and resonant contributions from the first two excited states of ${}_{}{}^8{}_{}{}^{}\mathrm{B}$, gave an $S\left(0\right)\mathrm{}$ of 0.0263 ± 0.0027 keVb. The second type of analysis assumed an additional resonance contribution from a higher-lying state and led to an $S\left(0\right)\mathrm{}$ of 0.0226 ± 0.0043 keVb. The result obtained from the second analysis represents our best estimate for the value of $S\left(0\right)\mathrm{}$ obtainable from the present measurements.

The amplitude for a knockout reaction in the plane-wave impulse approximation is derived from the Faddeev equations. It factorizes into the product of an off-shell two-body $t$ matrix times the bound-state wave function in momentum space. In this paper results are derived for the ($p,2p$) experiment from a realistic potential and compared with those arising from some current approximations. Distortion effects are ignored in order to isolate the off-shell effects. We find that for incident protons with lab energy below 200 MeV using an off-shell amplitude can change the cross section significantly as compared with the on-shell approximations in current use. The effect increases with the binding energy of the struck proton and with the recoil momentum. This indicates that ($p,2p$) reactions below 200 MeV are sensitive to the off-shell behavior of the two-body amplitude and that they should not be used to obtain nuclear information using on-shell approximations.

Scattering asymmetries in the angular range ${78}^{\circ }<~{\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}<~{127}^{\circ }$ have been measured for 9.9- and 11.9-MeV (lab energy) unpolarized deuterons incident on a polarized ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ gas target.

Angular asymmetries have been measured for the reaction protons, using a polarized ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ gas target and an unpolarized deuteron beam. Deuteron (lab) energies were 6, 8, and 10 MeV. Observations were made in the angular range ${57}^{\circ }<~{\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}<~{137}^{\circ }$. Present and earlier data are compared with Plattner and Keller's data using vector-polarized deuterons.