The electromagnetic form factors and radii of ${\mathrm{He}}^3$ have been evaluated using the three-body wave function obtained from a perturbational solution of the trinucleon system with the Eikemeier-Hackenbroich potential. The effect of $S^{\prime }$-state admixture and magnetic-exchange interactions are included in the calculation. Satisfactory fits to the form factors to large momentum transfer, including the correct prediction of the location of the diffraction minimum in the charge form factor, are found. Our calculations are in agreement with the latest Stanford $e-{\mathrm{He}}^3$ results in suggesting that the magnetic radius is larger than the charge radius if suitable magnetic-exchange effects are considered.

A high-resolution Coulomb-excitation study of ${\mathrm{Ir}}^{193}$ has failed to show any evidence of a 142-keV $\gamma$ ray attributed to a ground-state transition in two recent papers.

The $\gamma$ rays following the decay of 6.9-h ${}_{}{}^{93}{}_{}{}^{}\mathrm{Mo}$ have been examined with Ge(Li) and NaI detectors, and improved measurements of energies and intensities have been made.

New measurements of the energies and the intensity ratio of the two $\gamma$ rays which are emitted following the $\beta$ decay of ${}_{}{}^{37}{}_{}{}^{}\mathrm{S}$ to ${}_{}{}^{37}{}_{}{}^{}\mathrm{Cl}$ are reported. The more accurate energies are 3102.7 (±0.3) keV and 3706(±2) keV, and the revised intensity of the 3706-keV radiation relative to the 3102.7-keV radiation is 0.012(±0.003). The revised $log\mathrm{ft}$ value for the $\beta$ transition to the 3706-keV level of ${}_{}{}^{37}{}_{}{}^{}\mathrm{Cl}$ is now in better agreement with a recent shell-model calculation.

The results of a complete calculation of the binding energy $D$ of a $\Lambda$ particle in nuclear matter using the method of the independent-pair approximation, which systematically take into account the second- and third-order Born corrections, are presented. It is found that these corrections are small and that the Born series converges rapidly. A comparison of our results with those obtained using other methods based on the Brueckner theory shows that they are identical.

A new derivation of the quasispin groups used in nuclear spectroscopy is given. It is shown that these groups arise as the maximum commuting subgroups of the Flowers symplectic groups inside groups of generalized Bogoliubov transformations. These transformations are defined to be the most general transformations which conserve the anticommutation relations of the fermion operators of a nuclear shell.

A number of results on the boundary-condition-model (BCM) $T$ matrix are developed. It is shown that the half-off shell $T$ matrix is unique, but the fully off-shell $T$ matrix is not. Further, it is shown that the ambiguity in the $T$ matrix resides in that part of the complete $T$ matrix which is identifiable as the $T$ matrix for the pure BCM, where by pure BCM is meant no forces outside the boundary-condition radius. Three different formulas for the pure BCM $T$ matrix are presented. The first is derived by using the relations that exist between the half-off-shell $T$ matrix and the fully off-shell $T$ matrix for well-behaved potentials, and is found to be separable. The second is taken from the work of Kim and Tubis. The third is derived from a pseudopotential constructed by Hoenig and Lomon. All three agree exactly half off shell, and satisfy the off-shell unitarity relation. Numerical comparisons are given which show that significant differences can occur in the fully off-shell $T$ matrices. An integral- as well as a differential-equation approach are given for finding the contribution to the BCM $T$ matrix from the forces outside the boundary-condition radius. Separable representations for the BCM $T$ matrix are developed, and their usefulness in carrying out calculations on the three-nucleon system is discussed.

The $d(p,pn)p$ reaction has been studied to determine the $d(p,đ)p$ angular distribution and excitation function for the proton bombarding energy range 7 to 17 MeV. Protons and neutrons were detected in coincidence at the same angle to enhance the detection of $d(p,đ)p$ events. The spectra were fitted using the density-of-states function of Phillips, Griffy, and Biedenharn for the singlet deuteron, and a flat background arising from reactions other than $d(p,đ)p$. Angular distributions were taken at 7, 8, 10, 12, 13.5, 15, and 17 MeV. There was forward peaking at all energies, contrary to calculations on the doublet state in $n-d$ scattering by Aaron, Amado, and Yam. The excitation function shows little structure between 7 and 17 MeV.

Calculations are performed, in the one-particle-hole and projected Hartree-Fock (PHF) approximations, for the low-lying $2^{+}$ and $3^{-}$ excitations in ${\mathrm{C}}^{12}$ and ${\mathrm{O}}^{16}$, respectively. A new expression is derived for static moments of excited states in the random-phase approximation (RPA) and general one-particle-hole approximations. The purpose of this study was to investigate: the practical usefulness of the above approximations for nontrivial realistic problems; the validity of the one-particle-hole and PHF approximations for positive- as well as negative-parity excitations; the ability of the equations of motion and PHF methods to predict static moments of excited states; the magnitude of corrections to the RPA with explicit inclusion of ground-state correlations; and the validity of the inconsistent RPA procedure of including backward amplitudes at the expense of violating the Pauli principle. We conclude that the one-particle-hole approximation is particularly appropriate for negative-parity excitations and that the PHF approximation is appropriate for positive-parity excitations.

The isospin-nonconserving ($d,\alpha$) reactions on ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ leading to the $0^{+}$, $T=1\mathrm{}$ states at $E_x=2.31\mathrm{}$ MeV in ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ and $E_x=1.74\mathrm{}$ MeV in ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$ have been studied in the energy intervals of $E_d=14.0\mathrm{} \mathrm{to} 18.1$ MeV and 26.2 to 29.5 MeV, respectively. Two resonances were observed in the excitation function for the reaction on ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ at $E_d=14.4\mathrm{} \mathrm{and} 15.0$ MeV followed by a weak tail with little energy dependence. This behavior is similar to that observed earlier for the reaction on ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ in the same energy region. The results for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ at the higher bombarding energies, in conjunction with arguments related to the properties of highly excited states, appear to favor a direct- or semidirect-reaction mechanism. Consistent with the observed facts are virtual $E1\mathrm{}$ Coulomb excitation of the deuteron or the preferential spin-flip process suggested by Noble. No evidence was found for the two-step process involving isospin-mixed intermediate states, which was also suggested by Noble.

The two-body shell-model matrix elements for central and tensor forces can be expanded as linear combinations of Talmi integrals. A closed form, which does not involve vector-coupling coefficients or transformation brackets, is obtained for the coefficients appearing in this expansion. For the case that all the oscillator constants are the same, the result is simple enough to allow tabulation. A table of these coefficients for matrix elements involving the shell-model states $0s$, $0p$, and $0d$ is included. The main advantage of this method over the Talmi-Brody-Moshinsky method is discussed.

Given a finite many-particle vector space, which may be of large dimensionality, and a Hamiltonian which operates inside it, we may investigate the general properties of the system by a method of expanding preselected basis states in terms of the Hamiltonian eigenfunctions. The corresponding intensity, considered as a function of the Hamiltonian eigenvalues, is a spectral distribution which may be studied via its energy moments; we consider such distributions averaged over subsets of basis states. The properties of these averaged distributions are discussed, as well as methods for applying them in general studies of complicated systems; methods are given for evaluating the moments in some significant cases. Detailed formal results are given for configuration distributions in the spherical shell model.

Thermonuclear-reaction rates have been calculated over the temperature range $2<~\left(\frac{T}{{10}^9}\right)°\mathrm{K}<~6$ for some cases of particular interest in nucleosynthesis during silicon burning (Michaud and Fowler). We explicitly relate our calculations to the evaporation theory and the optical model for particle channels. For $\gamma$-ray channels we develop an approximate formula fitted to the experimental results of Macklin and Gibbons on radiative capture reactions for neutrons. We compare our calculated rates with available data and discuss the effect of excited states.

The quasifree scattering process (QFS) has been studied in the reaction $\mathrm{D}(p, 2p)n$ at incident energies of 14, 17, 20, 23, 33, 38, 45, and 57 MeV at ${\theta }_{\mathrm{L}}={\theta }_{\mathrm{R}}=43\mathrm{}°$ (left and right) to the incident beam and ${\theta }_{\mathrm{LR}}=180\mathrm{}°$. The QFS peak cross section remains almost constant from 20 to 100 MeV and begins to drop at lower energies. The magnitude of the cross section, as well as the shape of the QFS peak, is compared with predictions of a modified-simple-impulse-approximation calculation including a cutoff radius. The energy dependence of the QFS peak cross section is compared with the corresponding cross sections of the reaction $\mathrm{D}(p, pn)p$ and to the free nucleon-nucleon elastic scattering cross sections.

Cross sections of elastic and inelastic electron scattering at incident electron energies of 250 and 400 MeV are presented. Data are given for elastic and inelastic scattering from ${\mathrm{N}}^{15}$ and elastic scattering from ${\mathrm{N}}^{14}$. The data are analyzed with the use of the shell model, in Born approximation. The rms radius of ${\mathrm{N}}^{14}$ is found to be 2.64 F at 400 MeV. The rms radius of ${\mathrm{N}}^{15}$ at 250 and 400 MeV is 2.65 and 2.63 F, respectively. Excited levels in ${\mathrm{N}}^{15}$ at 5.3, 6.3, and 7.3 MeV are studied. Values of the nuclear transition probabilities are presented for these levels. The spin and parity assignments made are $J^{\pi }={\frac{5}{2}}^{+}$ and $J^{\pi }={\frac{1}{2}}^{+}$ for the doublet at 5.3 MeV. The 6.3-MeV level is assigned $J^{\pi }={\frac{3}{2}}^{-}$. Of the triplet of levels at 7.3 MeV, only the 7.3- and 7.5-MeV levels are strongly excited. These agree with $J^{\pi }={\frac{3}{2}}^{+}$ and $J^{\pi }={\frac{7}{2}}^{+}$, respectively.

The observed forward-peaked angular distributions and polarization at 90° of photonucleons from ${\mathrm{O}}^{16}$ are ascribed to the interference of $E1\mathrm{}$ and ($E2+M1\mathrm{}$) transitions within the context of a direct-reaction model, using wave functions computed in a Woods-Saxon potential.

The following reactions were studied. At $E_h=6.2\mathrm{}$ MeV: ${\mathrm{B}}^{10}(h, n){\mathrm{N}}^{12}$. At $E_h=10\mathrm{} \mathrm{and} 11$ MeV: ${\mathrm{B}}^{10}(h, n){\mathrm{N}}^{12}\mathrm{}\left(p\right)\mathrm{}{\mathrm{C}}^{11}$, ${\mathrm{B}}^{10}(h, p){\mathrm{C}}^{12}\mathrm{}\left(n\right)\mathrm{}{\mathrm{C}}^{11}$, ${\mathrm{B}}^{10}(h, p){\mathrm{C}}^{12}\mathrm{}\left(p\right)\mathrm{}{\mathrm{B}}^{11}$, ${\mathrm{B}}^{10}(h, p){\mathrm{C}}^{12}\left(\alpha \right){\mathrm{Be}}^8$, ${\mathrm{B}}^{10}(h, p){\mathrm{C}}^{12}\mathrm{}\left(d\right)\mathrm{}{\mathrm{B}}^{10}$. States at 5.3 MeV in ${\mathrm{N}}^{12}$ and 20.5 MeV in ${\mathrm{C}}^{12}$ were identified as members of an isobaric triad, with $J^{\pi }$, $T=3^{+}, 1$ having a pronounced two-particle structure. Angular correlations support this assignment. For these and other states, branching ratios of the emitted particles are measured, and conclusions on isospin purities and other properties are drawn.

The contribution of the two-pion-exchange three-nucleon force to the binding energy of nuclear matter is evaluated using the modified pion-mass method of Brown and Green and by the conventional potential approach. Using nonrelativistic formulas, the relation between the two methods is clarified. It is shown that the Brown-Green prescription, as given in their paper, is incorrect when a cutoff in the $\mathrm{NN}$ distance is applied and the modified pion mass is momentum dependent. When the correct prescription is used, the first-order contribution becomes sensitive to the pionic form factor chosen. Using the same form factor as used by Brown and Green, the contribution with an $\mathrm{NN}$ cutoff of 1 F is only about 0.1 MeV instead of 1.25-MeV repulsion per particle as quoted by them. Another form factor leads to about 0.5-MeV repulsion. The second-order contribution, including the cross terms involving the two-body one-pion-exchange potential and three-body forces, has been recalculated in the Brown-Green spirit after correcting for their earlier error. It is attractive, much larger than the first-order term, and is about the same for the two form factors used. The net effect of the two-pion-exchange three-body force is rather sensitive to the $\mathrm{NN}$ cutoff and is about a 4- to 8-MeV per particle attraction in nuclear matter, depending on the cutoff.

The reduced matrix elements for the $l$-forbidden $M1\mathrm{}$ transitions are calculated in the frame-work of the pairing model. Three quasiparticle states are admixed to the seniority-one state by perturbation due to the short range $\delta$ force and the tensor force. It is shown that the mixing of the tensor force is essential to explain the observed values of the reduced matrix elements.

The polarization $P\left(\theta \right)$ and differential cross section $\sigma \left(\theta \right)$ for the scattering of neutrons by ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$ have been measured for $0.075<~E_n<~2.2$ MeV. Both $\sigma \left(\theta \right)$ and $P\left(\theta \right)$ are simultaneously fitted reasonably well by $R$-matrix parameters for broad states in ${}_{}{}^{12}{}_{}{}^{}\mathrm{B}$ with assignments $2^{-}$ ($l=0\mathrm{}$) and $4^{-}$ ($l=2\mathrm{}$) at excitation energies $E_x=4.37\mathrm{} \mathrm{and} 4.54$ MeV, respectively. The $2^{-}$ level has not previously been observed, while the $4^{-}$ level has previously been assigned to be $3^{-}$. These results, together with a previous $3^{-}$ assignment for a state at $E_x=3.39\mathrm{}$ MeV, give experimental evidence for proton-hole-neutron-particle shell-model configurations ${\left(1\mathrm{}{p}_{\frac{3}{2}}\right)}^{-1\mathrm{}}\left(1\mathrm{}{d}_{\frac{5}{2}}\right)$ and ${\left(1\mathrm{}{p}_{\frac{3}{2}}\right)}^{-1\mathrm{}}\left(2\mathrm{}{s}_{\frac{1}{2}}\right)$ in ${}_{}{}^{12}{}_{}{}^{}\mathrm{B}$. Shell-model calculations were made with $\delta$-function residual interactions and include configuration mixing of the resulting $2^{-}$ states. Work on $T=1\mathrm{}$ states in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}_{}^{*}{}_{}{}^{}$ has been compared with the present work.