The bound states of ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$ have been studied by the ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}\mathrm{}(d,p)\mathrm{}$ reaction. Absolute differential cross sections were measured at $E_d=3\mathrm{}$ MeV for the 9.05-, 9.152 + 9.155-, 9.22-, 9.76-, and 10.07-MeV states and at $E_d=3.6\mathrm{}$ MeV for the 9.76-, 9.83-, 9.93-, 10.07-, and 10.45-MeV states in ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$. The target was natural nitrogen confined in a differentially pumped gas target. Distorted-wave Born-approximation analysis and Hauser-Feshbach calculations indicate that $l_n=1\mathrm{}$ is involved in the formation of the 9.22-, 9.76-, and probably 10.45-MeV states, whereas $l_n=2\mathrm{}$ transfer is associated with the 9.155-MeV level. An $l_n=0\mathrm{}$ transfer was discerned for the angular distribution associated with the 9.05-MeV state and $l_n=0+2\mathrm{}$ for the angular distribution associated with the 10.07-MeV and probably the 9.93-MeV ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$ state. Spectroscopic factors have been obtained. The correspondence between mirror levels in ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$ and ${}_{}{}^{15}{}_{}{}^{}\mathrm{O}$ and those predicted within the framework of the weak-coupling model is discussed.

Four-particle scattering equations are obtained that are analogous to the Lovelace or Alt-Grassberger-Sandhas equations in the three-particle case: They are equations whose kernel is connected after one iteration, in which the unknown quantities are the transition operators for the various elastic, inelastic, and rearrangement processes. The equations couple together only the transitions to the two-body channels, exactly as in the three-particle analogs, so that there are seven coupled integral equations, corresponding to the seven two-body channels (four of nucleon + triton type, and three of deuteron + deuteron type). Transition operators to the three- and four-body channels appear as integrals over the transition operators to the two-body channels.

Results of calculations on the three-nucleon system are presented for two potentials: a spin-dependent square well potential acting in $s$ waves, and a spin-dependent rank-one separable potential, which gives exactly the same $s$-wave phase shifts and deuteron binding energy as the square well. Significant differences between the $T$ matrices arising from these potentials occur as soon as one goes off the energy shell by 40 or 50 MeV (c.m.). In the three-nucleon system the square well produces a triton binding energy of 9.11 MeV, a doublet scattering length of 0.414 fm, and quartet scattering length of 6.31 fm. The corresponding parameters for the separable potential are 9.92 MeV, -0.165 fm, and 6.33 fm. The results of calculations on the doublet and quartet $s$-wave elastic scattering amplitudes are presented for neutron lab energies up to 14.1 MeV. It is found that the doublet amplitudes are quite sensitive to off-shell effects, while the quartet amplitudes are not. A previously developed off-shell effective range theory for the half-off-shell $T$ matrix is extended to the fully-off-shell case.

We have calculated the cross section for $n+p\to d+2\mathrm{}\gamma$. This process depends critically on the same matrix element that gives the amplitude for singly radiative $\mathrm{np}$ capture from the continuum ${}_{}{}^3{}_{}{}^{}S$ state. It has been suggested that "anomalous" transitions from this continuum ${}_{}{}^3{}_{}{}^{}S$ state may explain a long-standing discrepancy in $\mathrm{np}$ capture (${\sigma }_{\exp }=334.2\mathrm{}\pm 0.5$ mb and ${\sigma }_{\mathrm{th}}=309.5\mathrm{}\pm 5$ mb) by contributing roughly 8% to the total $\mathrm{np}$ capture cross section. If this speculation is correct then the branching ratio of doubly to singly radiative $\mathrm{np}$ capture is 1.4×${10}^{-4\mathrm{}}$. On the other hand a conventional estimate of this amplitude yields a branching ratio of about 3.4×${10}^{-10\mathrm{}}$. An experimental measurement of the doubly radiative cross section in the 10-μb region should therefore settle the question of the importance of the ${}_{}{}^3{}_{}{}^{}S$ initial state in the total radiative $\mathrm{np}$ capture cross section. Such a measurement seems at present to be much easier than similarly motivated polarization measurements.

The analytic continuation of the $S$ matrix into the complex angular momentum plane is performed exactly for the Woods-Saxon-type optical potentials, describing the elastic scattering of spinless but charged particles. The properties of this $S$ matrix, such as the nature of the pole trajectories and the behavior of the background integral, are investigated for several specific cases. Based on these exact calculations, the validity of various approximations made in the Regge theory is assessed. It is found that approximations which retain only the pole terms are generally poor, being quite sensitive to the number and the positions of the poles and converging very slowly with an increasing number of poles. On the other hand, models using a simple analytic background term, in addition to one pole term, are found to reproduce the exact Regge amplitude quite accurately under favorable conditions. Suggestions are made for the possibility of extending this idea into a background-plus-several-pole model, when the background-one-pole model fails.

The possibility of computing the three-body correlation energy in nuclear matter by direct solution of integral equations in momentum space is studied. An important feature of the procedure is that the off-energy-shell reaction matrix, which comes from an arbitrary two-body potential, is approximated by a sum of separable terms. Detailed numerical calculations are made for an $S$-wave force consisting of the Reid ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ potential acting in both singlet and triplet states. The main results are as follows: (1) The Reid ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ reaction matrix can be accurately represented by two or three separable terms for all relative momenta $k$ in the region $0<k<\mathrm{}8\mathrm{}$ ${\mathrm{fm}}^{-1\mathrm{}}$. This is the relevant region for the calculations. (2) Integrals over momenta can be adequately approximated by finite sums over only 6 or 8 Gauss points. (3) Many three-body states can be adequately treated in lowest order and therefore do not appear in the integral equations. On the basis of these results, it is estimated that a calculation using the full nuclear force would require the solution of systems of 100-200 linear equations. Solving such systems is perfectly feasible with present-day computers. The three-body correlation energy has been calculated at three different densities for the assumed two-body force.

The results of an investigation of the elastic $\mathrm{pd}$ differential cross section for center-of-mass angles between 91 and 164° at energies of 316, 364, 470, and 590 MeV are presented. For center-of-mass scattering angles larger than 130°, the cross sections at any given angle are within 10% of each other for the three largest energies. The extrapolated 180° differential cross section observed in this experiment remains nearly constant from 316 to 590 MeV. This is in marked contrast to the rapid decrease in cross section with increasing energy observed by other investigators for both larger and smaller energies. Possible theoretical explanations of this behavior are mentioned.

The radioactivities ${}_{}{}^{17}{}_{}{}^{}\mathrm{N}$ and ${}_{}{}^{17}{}_{}{}^{}\mathrm{F}$ have been produced in the reactions ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}\mathrm{}(t,p)\mathrm{}{}_{}{}^{17}{}_{}{}^{}\mathrm{N}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}\mathrm{}(d,n)\mathrm{}{}_{}{}^{17}{}_{}{}^{}\mathrm{F}$, respectively, and their half-lives have been measured by observing the decay of neutrons from ${}_{}{}^{17}{}_{}{}^{}\mathrm{N}$ and 0.51-MeV $\gamma$ rays from ${}_{}{}^{17}{}_{}{}^{}\mathrm{F}$. The half-life obtained for ${}_{}{}^{17}{}_{}{}^{}\mathrm{N}$ is 4.169±0.008 sec in agreement with earlier measurements. Our value for ${}_{}{}^{17}{}_{}{}^{}\mathrm{F}$, $T_{\frac{1}{2}}=64.50\mathrm{}\pm 0.25$ sec, is considerably lower than previous measurements. The relevance of the ${}_{}{}^{17}{}_{}{}^{}\mathrm{N}$ result to the question of mirror symmetry in the $\beta$ decay of the $A=17\mathrm{}$ system is discussed.

Quasifree proton scattering from ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is examined on the basis of available data. Cross sections are given in the pole-dominance approximation for either two protons or a proton and deuteron detected in coincidence. The cross sections are evaluated for a constant ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ vertex and a separable-potential model of the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ vertex amplitude. Both two- and three-body breakup of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ are considered, with final-state rescattering included between the spectator nucleons in three-body breakup. It is shown that the asymptotic form of the coordinate-space ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ wave function governs the shape of these low-momentum-transfer cross sections and that final-state rescattering between the spectator pair in ${}_{}{}^3{}_{}{}^{}\mathrm{He}\mathrm{}(p,2p)\mathrm{pn}$ mainly affects the magnitude of this cross section.

The absolute cross section and angular distribution for the ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}(\gamma ,p_0)$ process have been measured, in the giant-resonance energy range from 17 to 25 MeV. Between 17 and 21 MeV, the large angular anisotropy requires mixing of at least two dominant $E1\mathrm{}$ reaction channels. Above 22 MeV, $d$-wave emission from $2^{-}$ states appears to dominate. Admixture of about 5-10% of $E2\mathrm{}$ and/or $M1\mathrm{}$ strength is observed at all energies. The observations are qualitatively consistent with the shell-model predictions of Cooper and Eisenberg.

The ($p,2p$) and the ($p,d$) reaction cross sections for a ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ target have been calculated using a three-body theory that avoids making the Born approximation. Real separable potentials were used to describe all interactions. The general shape and magnitude of the reaction cross section agree with the experimental data. Fine structure details of the experimental cross sections are not reproduced. Modifications to distorted-wave Born-approximation calculations are suggested.

A procedure is presented which leads to a well-defined, convergent method for extending ordinary distorted-wave Born-approximation (DWBA) analysis to the calculation of scattering to long-lived resonant states. This method is based upon the use of a normalized wave function for the resonant state. The cross section calculated with this wave function is correct to terms of the order of $\frac{\Gamma }{E_0}$, the ratio of the resonance width to its energy. To illustrate this technique the cross section for the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}\mathrm{}(d,p)\mathrm{}{}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ transfer reaction to the resonant 5.08-MeV state of ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ is calculated. The results are compared to those obtained by other methods and are found to agree to order $\frac{\Gamma }{E_0}$.

The suggestion that nonlocal terms arising from the effects of antisymmetrization in light systems should be present in heavier systems, is examined. The introduction of one such term into the optical potential for proton-nucleus scattering produces significant effects at backward angles. It is shown that these nonlocal effects can be represented almost exactly by the introduction of a Majorana component into the real central potential. The results are applied in an analysis of 30-MeV proton elastic scattering data from ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$.

Nuclear properties of the excited states of ${}_{}{}^{32}{}_{}{}^{}\mathrm{Si}$ were measured using the ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}(t,p\gamma )$ reaction at bombarding energies of $E_t=2.7\mathrm{} \mathrm{and} 2.8$ MeV. Angular correlations of $\gamma$ rays were obtained using a spectrometer consisting of five NaI(Tl) counters in time coincidence with an annular particle detector positioned near 180°. Unique spin assignments for some of the excited states were obtained in addition to multipole-mixing-ratio and branching-ratio information. Nuclear lifetimes were measured using the Doppler-shift attenuation method. Some of the measured excitation energies, spins, and mean lifetimes [$E_x$ (keV), $J$, and $\tau$ (psec), respectively] are as follows: 1942.5 ± 2.0, 2, 0.92 ± 0.30; 4985 ± 4, ≤2, ≤0.44; 5290 ± 3, 3, 0.27 ± 0.10; 5413 ± 3, 1, ≤0.074; 5956 ± 3, 2, ≤0.08; 6196 ± 5, 1, ≤0.055; 6385 ± 5, 2, ≤0.072. A hitherto unreported state at 4234 ± 4 keV was found to have a spin $J=2\mathrm{}$ and mean lifetime of $\tau =0.38\mathrm{}\pm 0.12$ psec. The reported spectroscopic data are compared to the predictions of recent shell-model calculations.

The levels of ${}_{}{}^{86}{}_{}{}^{}\mathrm{Kr}$ have been investigated by the ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}(t,\alpha )$ reaction with 15-MeV tritons. $\alpha$-particle spectra were recorded with a semiconductor counter telescope at c.m. angles between 13° and 73°, and excited states were observed up to 4.3 MeV. Differential cross sections for 13 levels were compared with distorted-wave Born-approximation calculations, giving $l_p$ values and spectroscopic factors. The predominant $l_p=1\mathrm{}$ and $l_p=3\mathrm{}$ reaction amplitudes, which are assumed to represent $2p_{\frac{3}{2}}$ and $1f_{\frac{5}{2}}$ proton pickup, are essentially exhausted by 4 MeV excitation. All of the experimental angular distributions are best fitted with a single value of $l_p$, although $l_p=1, 3$ mixtures would be expected for population of $2^{+}$ levels. One definite $l_p=4\mathrm{}$ angular distribution was observed, indicating a small $1g_{\frac{9}{2}}$ proton component in the ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$ ground state. Results of this experiment are compared with recently reported ${}_{}{}^{86}{}_{}{}^{}\mathrm{Kr}(p,p^{\prime })$ and ${}_{}{}^{86}{}_{}{}^{}\mathrm{Br}$ decay data.

The absolute differential cross sections of the (${}_{}{}^3{}_{}{}^{}\mathrm{He},p$) reactions on ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$, and ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ have been measured at $E_{\mathrm{He}}=10\mathrm{}$ MeV. The cross sections to various excited states are in reasonable agreement with rotational-model calculations except for a normalization factor which is different for each target nucleus. The evidence for rotational motion in ${}_{}{}^{26,28}{}_{}{}^{}\mathrm{A}1\mathrm{}$ and ${}_{}{}^{30}{}_{}{}^{}\mathrm{P}$ is reviewed, and the differences in normalization factors are attributed to core overlap differences. In particular, the reduced yield in the ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}({}_{}{}^3{}_{}{}^{}\mathrm{He},p){}_{}{}^{28}{}_{}{}^{}\mathrm{Al}$ reaction reflects a large change in deformation between ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$ and ${}_{}{}^{28}{}_{}{}^{}\mathrm{A}1\mathrm{}$. In order to determine $J^{\pi }$ values in ${}_{}{}^{28}{}_{}{}^{}\mathrm{A}1\mathrm{}$, $\gamma$-ray spectra were measured in coincidence with proton groups leading the certain high-lying states in ${}_{}{}^{28}{}_{}{}^{}\mathrm{A}1\mathrm{}$. A spin of $J^{\pi }=1^{+}$ was established for a state at 3.105 MeV in ${}_{}{}^{28}{}_{}{}^{}\mathrm{A}1\mathrm{}$.

60-point angular distributions have been measured in 200-keV steps for ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}(\alpha ,{\alpha }_0){}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ in the energy range 21-28 MeV. At an incident energy of 23.9 MeV an anomalous structure of full width at half maximum ∼300 keV is seen for angles greater than 90°, but above 25 MeV no correlated structure is seen. The data above 25 MeV have been analyzed in terms of the optical model, and discrete potential ambiguities, as well as a radius ambiguity, have been found. These potential parameter sets were able to give qualitative fits to the data throughout the angular range 25-150° (c.m.) at the energies 24.9, 25.9, and 27.5 MeV, and at the lower energies 22.3 and 23.3 MeV the general trend of the data was reproduced.

In the case of angular-momentum-mismatch conventional distorted-wave Born-approximation (DWBA) calculations tend to give results which are strongly dependent on the opticalmodel parameters chosen and, to a lesser degree, on finite-range and nonlocality effects. We discuss reasons for this sensitivity and present systematic calculations for ($d,\alpha$) reactions on nondeformed targets ranging from ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ti}$ to ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. Satisfactory DWBA results could be obtained for the entire range of targets, provided that all potentials for the generation of scattered and bound wave functions were restrained to have nearly identical physically meaningful real well geometries and real depths of $V\approx n{V}_0$, where $V_0$ is the proton scattering potential and $n$ is the number of nucleons in the projectile. The use of well geometries with $r_0=1.2\mathrm{}$ fm, $a=0.75\mathrm{}$ fm, and retention of the basic DWBA requirement that the optical potentials should also correctly fit elastic scattering removes the familiar ambiguities for deuteron and $\alpha$ potentials. It is shown that with these parameter restrictions finite range effects are expected to be small so that a first-order correction procedure is adequate. Explicit calculations are compared with over 30 ($d,\alpha$) angular distributions of known angular momentum transfer for experimental bombarding energies ranging from 12 to 17 MeV. Consistent agreement with experiment was obtained.

Lifetimes of excited states in ${}_{}{}^{26}{}_{}{}^{}\mathrm{Al}$ have been investigated by the recoil-distance method using the ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}(\alpha ,n\gamma ){}_{}{}^{26}{}_{}{}^{}\mathrm{Al}$ reaction. To obtain information on the population of states in ${}_{}{}^{26}{}_{}{}^{}\mathrm{Al}$ by this reaction, a Ge(Li) $\gamma$-ray spectrum was measured in coincidence with neutrons. A mean life $\tau =5.7\mathrm{}\pm 1.1$ psec.was obtained for the $2^{+}$ 1759-keV state in ${}_{}{}^{26}{}_{}{}^{}\mathrm{Al}$.

High-resolution excitation functions were measured in the energy range $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=19\mathrm{}-25$ MeV for the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^{16}{}_{}{}^{}\mathrm{O},\alpha )$ reaction to highly excited states in ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ ($E_{\mathrm{exc}}\approx 13.5-17.5$ MeV). The strong, rapid observed fluctuations suggest a predominately compound-nucleus reaction mechanism. The selective population of high-spin states in ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ by the present reaction in contrast to the lack of such selectivity in the ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}({}_{}{}^{14}{}_{}{}^{}\mathrm{N},\alpha )$ reaction can readily be explained by Hauser-Feshbach statistical-model calculations. A fluctuation analysis indicates coherence widths of 90-150 keV, and cross correlations were found to be small and thus compatible with a purely statistical compound-nucleus process.