Sum rules for isoscalar transition densities are written down. The sum-rule limits are space-dependent quantities which are shown to be simply related to transition densities previously obtained from models of collective nuclear excitations.

A straightforward procedure is given for determining the independent three-nucleon Faddeev amplitudes for the case of nucleon-nucleon interactions in a given set of partial waves. As an example, the independent positive-parity amplitudes for total trinucleon angular momentum and isospin ½ are given for the case of $J$ and $L$ (nucleon-nucleon) ≤2. It is shown that three of the independent Faddeev amplitudes were neglected by Gignoux and Laverne in their recent paper on the three-nucleon bound state.

The choice of the basis states for the Faddeev amplitude should be dictated by the actual computation for the interaction considered.

Global optical-model parameters describing quasielastic reactions are examined. Such potentials, particularly the absorptive components, do not in general conserve isospin. A prescription is offered in an attempt to provide a guideline for deducing optical parameters which do not violate isospin.

A new interpretation of the experimental results of Gauvin, Le Beyec, Lefort, and Deprun published recently in Phys. Rev. Letters is given. The calculation of effective thresholds in a dynamical classical model for the reactions ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$ on ${}_{}{}^{164}{}_{}{}^{}\mathrm{Dy}$ and ${}_{}{}^{84}{}_{}{}^{}\mathrm{Kr}$ on ${}_{}{}^{72}{}_{}{}^{}\mathrm{Ge}$ and ${}_{}{}^{116}{}_{}{}^{}\mathrm{Cd}$ gives 139, 149.5, and 212 MeV to be compared with the experimental values of 135, 147, and 204 MeV.

A recently published half-life for ${}_{}{}^{10}{}_{}{}^{}\mathrm{Be}$ which differs from older measurements requires modification of several published cross sections using ${}_{}{}^{10}{}_{}{}^{}\mathrm{Be}$ targets.

The parameters of the giant dipole resonance of ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ are calculated from the experimental cross sections of the nuclear Raman effect. It is shown that there is no need to include direct mechanisms to explain the interaction of the $\gamma$ with the nucleus.

Reasons for the success of the particle-hole approach adopted by O'Connell, Donnelly, and Walecka in the unified interpretation of the semileptonic weak and eletromagnetic processes in the ($A=12\mathrm{}$ nuclear system will be examined. The example of the analyses of $0^{+}$0 ↔ $1^{+}$1 transitions in the context of the particle-hole model (PHM) and the intermediate-coupling model (ICM) brings to light two facts: (1) the nuclear matrix elements relevant to the $0^{+}$0 ↔ $1^{+}$1 transitions do not scale in a unique fashion from the PHM to the ICM; (2) the $0^{+}$0 ↔ $1^{+}$1 processes at low momentum transfer are overwhelmingly dominated by the Gamow-Teller matrix element. The dominance of a set of processes by one nuclear transition operator is the key to the success of the one-parameter scaling of the particle-hole amplitudes used by O'Connell, Donnelly, and Walecka.

The ground-state energy of the Lipkin, Meshkov, and Glick many-body Hamiltonian as determined by the Brueckner theory is shown to be an upper bound on the exact value for 2, 3, 4, 6, and 8 particles. Improved upper bounds are obtained for 2, 4, 6, and 8 particles by taking one half of the usually adopted hole-state potential. This latter result lends support to Tobocman's early conjecture about the choice of the self-consistent single-particle potential.

A nonrelativistic calculation of the photodisintegration of the deuteron below pion threshold has been completed in which nucleon polarization effects described by isobar configurations ($N\Delta$ and $\Delta \Delta$) have been included. At lower energies ($E_{\gamma }^{\mathrm{lab}}\le 40$ MeV) the inclusion of these isobar configurations leads to an over-all decrease of the total cross section and the proton angular distribution due to renormalization of the normal deuteron components. At higher energies the total cross section is enhanced (up to 5% at $E_{\gamma }^{\mathrm{lab}}=120\mathrm{}$ MeV) and the proton angular distributions are more forward peaked. These results lead to better agreement with experiment.

In a distorted-wave type of formalism, two well-behaved integral equations have been obtained for a general three-body rearrangement reaction. The inhomogeneous terms of these equations may be considered to provide mathematically meaningful first approximations (MMFA) to the reaction amplitude. In each of the above mentioned cases, the distorted-wave Born approximation (DWBA) forms an integral part of MMFA. The extra terms in MMFA involve multiple-scattering processes and hence, at least in some casés, their matrix elements may be much smaller than those of DWBA term. This suggests that the success of DWBA may lie in the fact that DWBA is the dominating part of an MMFA. Some of the circumstances under which it can happen are discussed.

The intrinsic states of Cr and Fe isotopes are calculated by solving Hartree-Fock-Bogoliubov equations in the $2p-1f$ shell using a deformed basis and the Rosenfeld-Yukawa potential. The projection of angular momentum states is carried out and the results are compared with the projected Hartree-Fock and experimental spectra.

States in the odd-mass isotopes of tungsten, ${}_{}{}^{183,185,187}{}_{}{}^{}\mathrm{W}$, have been studied by the $\mathrm{W}(\overrightarrow{d},p)$ reaction initiated by polarized deuterons of 12.08- and 15.0-MeV bombarding energy. Vector-analyzing-power angular distributions were obtained for the strongly excited states. The use of measured analyzing powers for states of known $J^{\pi }$ as calibration standards for the assignment of new $J^{\pi }$ values is discussed. This technique is found to be preferable, at the present stage, to a reliance on the distorted-wave Born approximation (DWBA). The phase, but not the magnitude, of the oscillations in the DWBA calculations for the vector-analyzing powers is in qualitative agreement with the data at 12 MeV for spins of $\frac{5}{2}$ or less. At 15 MeV, this is not the case. The dependence of the DWBA calculations on optical-model parameters and $Q$ value is discussed. A number of spin-parity assignments or preferences are made. In particular, candidates for ${\frac{1}{2}}^{-}$ and ${\frac{3}{2}}^{-}$ states are located in each nucleus. The pairs of odd-parity levels are discussed as possible fragments of the first two members of the rotational band built on the $\frac{1}{2}-\left[501\right]\mathrm{}$ Nilsson orbital, but the difficulties associated with this assignment are also pointed out.

Form factors for the excitation of the ${}_{}{}^{51}{}_{}{}^{}\mathrm{V}$ 0.32-, 0.93-, 1.61-, 1.81-, and 2.70-MeV members of the ${\left(1\mathrm{}{f}_{\frac{7}{2}}\right)}^3$ multiplet, and of the 2.40- and 3.91-MeV states have been measured for momentum transfers up to 1.8 ${\mathrm{fm}}^{-1\mathrm{}}$ by using 183- and 250-MeV electrons. Comparisons have been made with form factors calculated by using harmonic-oscillator shell-model wave functions. For the ${\left(1\mathrm{}{f}_{\frac{7}{2}}\right)}^3$ multiplet, effective charges from $1.79e$ to $2.01e$ were obtained for the $E2\mathrm{}$ components of the excitations, and $1.69e$ for the $E4\mathrm{}$ component of the 2.70-MeV excitation. Higher multipole components of each excitation required smaller effective charges in the strict ${\left(1\mathrm{}{f}_{\frac{7}{2}}\right)}^3$ configuration. An analysis of the elastic scattering data using a Fermi charge distribution yielded the parameters $c=3.94\mathrm{}\pm 0.03$ fm, $t=2.22\mathrm{}\pm 0.06$ fm, and 3.58 ± 0.04 fm for the rms radius.

The energy dependence of the neutron asymmetry parameter for nuclear capture of muons has been measured in Si, S, and Ca for neutron energies of 4-53 MeV. Contrary to most recent experiments, the asymmetry parameter is strongly positive over much of the energy range, with values as much as 9 standard deviations from zero. Because of the unusual nature of these results the experiment was performed twice and with excellent agreement between the two sets of data. The integrated asymmetry parameter for $E_n>15.6\mathrm{}$ MeV is +0.316 ± 0.023 for Si and +0.290 ± 0.034 for Ca, values which are in direct conflict with the "standard" $V-A$ theory. Recent theoretical calculations by Bogan and by Piketty and Procureur obtain positive asymmetries, though not yet in good quantitative agreement with these data. The neutron energy spectra from the three targets are all quite similar. They are consistent with a simple exponential falloff in $E_n$ with a decay constant of 7 MeV. The theoretical calculations cited above are in good agreement with higher-energy regions of the spectra.

Nuclear properties of the excited states of ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ar}$ were measured by using the ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}(t,p\gamma ){}_{}{}^{42}{}_{}{}^{}\mathrm{Ar}$ reaction at a bombarding energy of 2.9 MeV. Angular correlations of $\gamma$ rays were measured using a spectrometer consisting of five NaI(T1) counters in time coincidence with an annular particle detector positioned about 180°. The analysis of these correlations yielded multipole-mixing and branching-ratio information for the electromagnetic deexcitations of ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ar}$ states, as well as spin assignments for some of the excited states. Coincident $\gamma$-ray spectra were also obtained using a Ge(Li) detector. Some of the measured excitations and spin assignments [$E_x$ (kev); $J$] are: [1207±1.5; 2], [2414±5], [2485±3; 2], [2510±3], [3012±3; 1,2,3], [3092 ±3; 4], [3555±3; 2], [4004±5], [4123±4;≤2], [4285±5, 1,2,3], and [4629±5;≥1]. The results of this experiment are compared with recent shell-model calculations.

The mean lifetimes of levels in ${}_{}{}^{26}{}_{}{}^{}\mathrm{Al}$ below 4 MeV have been investigated with the Doppler-shift attenuation method and the ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}({}_{}{}^3{}_{}{}^{}\mathrm{He},p){}_{}{}^{26}{}_{}{}^{}\mathrm{Al}$ reaction at 6 MeV. The outgoing protons have been detected at angles of ±60° with respect to the beam axis, in coincidence with $\gamma$ rays detected at 90° in an 80-${\mathrm{cm}}^3$ Ge(Li) detector. The results for levels below 3 MeV are generally in agreement with earlier lifetime studies. New information is reported for the following levels (energy in keV, lifetime in fsec): 2741 (54±8), 3074 (290±70), 3161 (36±10), 3597 (44±17), 3680 (27±12), 3721 (<23), 3750 (43±9), 3754 (27±11), and 3962 (68±14). The 3074-keV level is assigned positive parity on the basis of the present lifetime results. Experimental transition strengths are extracted and discussed in terms of isospin selection rules in electromagnetic transitions.

Elastic and inelastic differential cross sections for neutron scattering from Si and S have been measured at an incident neutron energy of 9.8 MeV, using the high-energy neutron group from the ${}_{}{}^9{}_{}{}^{}\mathrm{Be}(\alpha ,n){}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ source reaction. Due to the presence of the 4.439-MeV first-excited-state group from the ${}_{}{}^9{}_{}{}^{}\mathrm{Be}(\alpha ,n){}_{}{}^{12}{}_{}{}^{}\mathrm{C}_{}^{*}{}_{}{}^{}$ reaction only the scattering from the ground and first excited states in Si and S could be observed. Measurements were made on both elements by the time-of-flight technique in the angular region ${20}^{\circ }\le {\theta }_{\mathrm{lab}}\le {150}^{\circ }$ with an average neutron energy spread of 600 keV. The measured yields were corrected for flux attenuation, angular resolution, and multiple scattering. The cross sections were fitted by incoherently adding a compound-nuclear contribution to a direct-reaction contribution calculated by the optical-model-plus-distorted-wave-Born-approximation method and also by the coupled-channel method. Collective-model fits to S using oblate and prolate deformed rotational-model and vibrational-model form factors were all reasonably good. The fits to Si are not as good, possibly for reasons related to the large fluctuations in the neutron total and differential cross sections for Si in this energy region. The values of $\beta$ obtained from these fits are, for the most part, consistent with those obtained from other measurements.

Differential elastic cross sections for the scattering of high-energy electrons from ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}$ have been measured. The data have been analyzed in terms of phenomenological charge distributions at two values of the incident electron energy. Comparison was made between the empirical distributions and those predicted by a state-independent shell-model description of the nucleus.

[NUCLEAR REACTIONS ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}\mathrm{}(e,e)\mathrm{}$, $E=200,400\mathrm{}$ MeV; measured $\sigma (E,\theta )$; Deduced nuclear charge distributions; Enriched target.]