The well-known representation of diffractive-production amplitudes as a difference between elastic amplitudes for the entrance and exit channels is investigated, and found to be generally correct in an appropriate sense, for weakly coupled processes. There is, moreover, complete equivalence at short wavelengths (as one might expect) between diffractive-production models and distorted-wave Born-approximation models. This fact is illustrated explicitly by deriving the former representation from the latter for the cases of deuteron breakup and stripping.

On the example of rotations in a plane, a concise form of expansion for the density matrix of this theory is presented and applied. It is emphasized again that the method is more general than the usual form of time-dependent Hartree-Fock approximation (or self-consistent cranking method) but contains the latter as a well-defined limiting case.

A simple integral expression for the asymptotic normalization coefficient of a bound-state wave function is presented. Correspondingly, a method for correcting wave functions computed by expansion in oscillator wave functions is described.

Levels in ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$ have been studied with the ${}_{}{}^9{}_{}{}^{}\mathrm{Be}\mathrm{}(d,n)\mathrm{}{}_{}{}^{10}{}_{}{}^{}\mathrm{B}$ reaction at 7-, 12-, 15-, and 16-MeV incident energy. Neutron angular distributions for transitions to levels below 7 MeV excitation have been measured with a time-of-flight spectrometer, and they have been compared with distorted-wave Born-approximation (DWBA) calculations. Emphasis has been placed on examining the previously reported discrepancy in the $T=1\mathrm{}$ relative spectroscopic factor ($S_{\mathrm{rel}}$) between ($d,n$) and (${}_{}{}^3{}_{}{}^{}\mathrm{He}$, $d$) reactions. It has been found that the discrepancy still exists though to a lesser degree, and that the $S_{\mathrm{rel}}$ values from ($d,n$) appear to be energy-dependent. Sensitivity of calculations to the choices of deuteron-potential sets as well as of other DWBA parameters has been carefully examined in order to extract reliable spectroscopic factors. It has been found that noncutoff DWBA calculations failed to reproduce the detailed structure of the measured angular distributions beyond stripping peaks when "measured" deuteron-potential parameters were used in the calculations. Also excitation functions have been measured at ${\theta }_{\mathrm{lab}}={15}^{\circ }$ from 14 to 16 MeV in order to check the reaction mechanism for this energy range. The extracted spectroscopic factors compare poorly with the theoretical values of Cohen and Kurath as well as those of Varma and Goldhammer.

We present a practical formalism of low-energy nuclear reactions in which the ground-state correlations are treated in the random-phase approximation. The building blocks of the method are the matrix elements of two weakly energy-dependent effective interactions describing particle-hole pair scattering and pair creation or annnihilation in a correlated system. The corresponding transition operators, which give complete information on any nuclear reaction, are then introduced. We apply the method to a study of nucleon scattering, photonuclear, muonuclear reactions proceeding through the $1^{-}$ states of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$. The single-particle basis states are generated by a local, real Woods-Saxon potential, while the residual interaction has a zero range. In the relatively high excitation energy being studied, the correlations retained in the random-phase approximation affect very little nucleon scattering but reduce transition rates in photonuclear reactions and muon capture by about 8%.

In this paper, a method for projecting the usual BCS states simultaneously onto the eigenstates of particle number and angular momentum is suggested. Fomenko's method of projection in the occupation number space, which leads to rapidly converging series, seems to be very suitable to a subsequent projection onto the eigenstates of angular momentum. For simplicity, the deformation is restricted to be axially symmetric, and general double-projection formulas are established in this case. Simple numerical model calculations, using the adiabatic assumption, show that it is important to project the BCS states onto the particle-number eigenstates before computing the rotational spectrum and the moment of inertia.

The nature of the interaction between two identical nuclei having spins zero is studied based on a microscopic theory of complex collisions. The "internucleus" potential is defined such that it appears consistently in the equation of motion and the $T$ matrix of the elastic scattering channel. It is shown that by a suitable integral transformation a strongly nonlocal potential such as that of the resonating-group method can be transformed into an $l$-dependent local potential with a weak nonlocal residual interaction. An application of the theory is made to a two-$\alpha$ particle system. The theoretical potential shows the similar $l$ dependence to the phenomenological potential. The importance of the $l$ dependence of the real part of the potential is discussed in relation to the elastic scattering phenomena of heavy-ion reactions.

It is shown that the potential obtained by folding a nucleon-nucleon interaction into the ion densities gives a good description of the real part of the optical potential for ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$-${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ scattering between 9- and 16-MeV center of mass. Some evidence is found for an additional repulsive term at lower energies.

Shell-model calculations are performed on the normal parity states of $0p$-shell nuclei with $A=6-14\mathrm{}$. The Hamiltonian is diagonalized in the full $0p$ basis, and the effective two-body interaction is computed from the Sussex relative harmonic-oscillator matrix elements. The second-order corrections to the two-body matrix elements are calculated for all intermediate states up to $2\hslash \omega$ excitation energy. The harmonic-oscillator size parameter is taken to be constant at 1.7 fm for all nuclei, and the $p_{\frac{3}{2}}-p_{\frac{1}{2}}$ single-particle energy splitting is determined for each mass number by a least-squares rms fitting to the experimental spectrum. Static and dynamic properties of the energy levels are calculated and found to be usually in good agreement with experiment.

A prominent peak is observed in the forward-angle spectra of $\alpha$ particles if ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is bombarded by 63.7-, 71.7-, or 81.4-MeV $\alpha$ particles. The energy of the peak is consistent with a sequential decay process involving the 2.18-MeV state of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$. At 71.7 MeV, proton spectra measured at backward angles show that the cross sections for formation of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}_{}^{*}{}_{}{}^{}$ (2.18 MeV) agree with the intensity of the prominent $\alpha$ peak. The peak shape and position imply that the $\alpha$ particles are preferentially emitted forward with respect to the original ${}_{}{}^6{}_{}{}^{}\mathrm{Li}_{}^{*}{}_{}{}^{}$ direction. Two other peaks are observed in some of the $\alpha$ spectra, one of them possibly the result of a sequential decay involving ${}_{}{}^5{}_{}{}^{}\mathrm{Li}$.

[NUCLEAR REACTIONS ${}_{}{}^3{}_{}{}^{}\mathrm{He}(\alpha ,\alpha \text{'})$, ($\alpha ,p$), $E=63.7,71.7,81.4\mathrm{}$ MeV; measured $\sigma (E,\theta )$.]

Measurements have been made of seven polarization transfer coefficients for the ${}_{}{}^3{}_{}{}^{}\mathrm{He}\mathrm{}(d,p)\mathrm{}{}_{}{}^4{}_{}{}^{}\mathrm{He}$ reaction. The experiment used a polarized-deuteron beam from the Los Alamos Scientific Laboratory Lamb-shift polarized-ion source, a liquid-nitrogen cooled ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ gas target, a magnetic quadrupole triplet for focusing the reaction protons, and a helium-filled polarimeter for simultaneously measuring the proton polarization along both transverse axes. Measurements were made of the polarization transfer coefficients $K_y^{y\prime }$ and $K_{yz}^{x\prime }$ at $\theta =0^{\circ }$ for 4- to 14-MeV deuterons. A comparison of the $K_y^{y\prime }$ results with the values reported for the ${}_{}{}^3{}_{}{}^{}\mathrm{H}\mathrm{}(d,n)\mathrm{}{}_{}{}^4{}_{}{}^{}\mathrm{He}$ reaction over the same energy range shows good agreement, as would be expected for the two charge-symmetric reactions. In addition, we have measured the proton polarization $p^{y\prime }$; the vector transfer coefficients $K_y^{y\prime }$, $K_x^{x\prime }$, and $K_z^{x\prime }$; and the tensor transfer coefficients $K_{xx}^{y\prime }$, $K_{yy}^{y\prime }$, $K_{zz}^{y\prime }$, and $K_{xz}^{y\prime }$ at 8.0 MeV for laboratory angles of 15, 30, 45, and 60°. Calculated values for these observables from an $R$ -matrix parametrization of the five-nucleon system are in good agreement with the data.

[NUCLEAR REACTIONS ${}_{}{}^3{}_{}{}^{}\mathrm{He}\mathrm{}(d,p)\mathrm{}$: $E=4-14\mathrm{}$ MeV, $\theta =0^{\circ }$; $E=8\mathrm{}$ MeV, $\theta =15,30,45,{60}^{\circ }$; measured polarization transfer coefficients.]

We report measurements of the 4 analyzing tensors and of up to 14 polarization-transfer coefficients, at each energy and angle studied, for ${}_{}{}^4{}_{}{}^{}\mathrm{He}\mathrm{}(d,d)\mathrm{}{}_{}{}^4{}_{}{}^{}\mathrm{He}$ elastic scattering. This number of observables greatly overdetermines the scattering matrix, and many consistency checks are therefore available. These data represent the first measurements of polarization-transfer phenomena in which both the incident and outgoing polarized particles have spin 1. Bombarding energies were in the range 4.8 to 9.0 MeV.

The deuteron specific distortion effect in the $d+\alpha$ problem is considered with a microscopic procedure. This procedure consists in the addition of square-integrable or distortion functions into the usual no-distortion resonating-group wave function. The result shows that with the consideration of this effect, a nucleon-nucleon potential which fits the low-energy two-nucleon scattering data and which yields a satisfactory agreement with the empirical $\alpha +\alpha$ phase shifts can be used to describe quite well the $d+\alpha$ experimental data. Also, it is shown that the specific distortion effect has an odd-even character; it has significant effects in even-$l$ states, but not in odd-$l$ states. Resonance structures are found in the partial-wave scattering amplitudes. These structures arise as a consequence of the coupling of the compound-nucleus states with the elastic scattering channel.

It is shown that the Kowalski formulation of the Sasakawa approach to potential scattering can be used as the basis for a momentum-space formulation of the theory of the Jost function. Two examples are presented for which the Kowalski equations can be solved in closed form. One example is a separable potential, and the other is the exponential potential. The separable potential illustrates the fact that the series obtained by iterating Kowalski's equations does not always converge. The exponential potential provides a verification of Coester's proof that the iteration series does converge for a certain class of local potentials of arbitrary strength. The practicality of Kowalski's equations are demonstrated by using them to calculate the phase shifts and half-off-shell $T$ matrix that are produced by the Reid potential in some of the uncoupled states of the two-nucleon system.

The scattering amplitude at high energy is calculated in various approximations, explicitly incorporating both the single and double hard collisions. For the purpose of improving the large-angle behavior of the amplitude, approximations are introduced directly to the full Green's function rather than to the scattering function, thus avoiding the usual assumption of a straight-line trajectory. The previous study using the semiclassical Green's function gave very accurate amplitude up to a moderately large angle, and we have further examined its applicability to more general forms of potentials. Some of the practical difficulties in carrying out the amplitude integrals are pointed out, and the problem is simplified by introducing an angle-averaging procedure and also by an eikonal approximation to the semiclassical Green's function. These procedures are then tested using Gaussian and Yukawa forms of the potential; they are relatively simple to apply and the over-all accuracy is improved.

14 deuteron groups populating levels to 10.26 MeV excitation in ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ have been measured with the ${}_{}{}^{19}{}_{}{}^{}\mathrm{F} ({}_{}{}^3{}_{}{}^{}\mathrm{He},d){}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ reaction. Excitation functions measured at ${\theta }_{\mathrm{lab}}=25\mathrm{} \mathrm{and} {45}^{\circ }$ from 20.0 to 21.2 MeV reveal little structure, and therefore probably little compound-nuclear contribution to the observed cross sections for the deuteron groups. In particular, the $2^{-}$ level at 4.97 MeV excitation, strongly populated at $E_{3_{\mathrm{He}}}=10\mathrm{}$ MeV, is weakly populated in the present energy range. The "$j$-forbidden" $4^{+}$ level at 4.25 MeV excitation, on the other hand, is strongly populated in the present energy range. A collective-model coupled-channel Born-approximation analysis of angular distributions measured at $E_{3_{\mathrm{He}}}=21\mathrm{} \mathrm{and} 23$ MeV is better able to explain the data than distorted-wave Born-approximation analysis for the positive-parity states. The negative-parity states are poorly described by both theories.

[NUCLEAR REACTIONS ${}_{}{}^{19}{}_{}{}^{}\mathrm{F} ({}_{}{}^3{}_{}{}^{}\mathrm{He},d)$, $E=20-23\mathrm{}$ MeV; measured $\sigma (E,\theta )$, deduced $S$. DWBA and CCBA analysis; $\theta =20-{150}^{\circ }$, $\Delta \theta =5^{\circ }$.]

A model for the deuteron optical potential which folds the optical potentials of the nucleons with their internal motion in the deuteron is discussed. Effects due to spin dependence, deuteron electric and nuclear breakup, and higher-order effects are incorporated more carefully than in previous articles. Approximations are used which reduce the nonlocal potential to a local potential and single-channel approach. The cross section and four analyzing tensors are calculated without any adjustment of free parameters. Good agreement is obtained in comparisons with data for 15-MeV polarized deuterons elastically scattered from ${}_{}{}^{52}{}_{}{}^{}\mathrm{Cr}$, ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$, ${}_{}{}^{122}{}_{}{}^{}\mathrm{Sn}$, and ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$.

A previously presented perturbative calculation of elastic nucleon-deuteron scattering is compared with the exact calculation of Doleschall. It is found that the nucleon polarization in $N-d$ scattering is not accurately predicted by the perturbation theory but that the vector and tensor deuteron polarizations are in satisfactory agreement with the exact calculation. It is suggested that considerably more complicated potentials than those now in use will have to be employed to predict the nucleon polarization data at energies above 14 MeV. Some calculations of recently measured spin-transfer coefficients are presented and compared with the available data.

A prescription for including exchange effects in neutron-proton bremsstrahlung ($\mathrm{np}\gamma$) by requiring gauge invariance of the complete $\mathrm{np}\gamma$ amplitude is given entirely within a potential framework. To lowest order in the photon momentum ($K^0$) this prescription is unambiguous and it includes, as well as exchange effects, any other nonlocal effects in the nuclear potential. The lowest-order contribution is written, with the use of the Schrödinger equation, so as to eliminate the necessity of intergrating over the nuclear potential. The higher-order exchange contributions are treated through order $K^2$ using the one-pion exchange (OPE) only. (Because the effective expansion is $\frac{K}{\mu }$, where $\mu$ is the mass of the exchanged meson, the pion is expected to dominate.) These higher-order terms are the same as the Feynman-diagram prescription would give for $\mathrm{np}\gamma$ due to OPE. Calculations with the Hamada-Johnston (HJ) and Bryan-Scott III (BS) potentials are compared to the experimental results at 208 MeV by Brady et al. and at 130 MeV by Edgington et al. This inclusion of the exchange bremsstrahlung (order $K^0$) increases the cross section by roughly a factor of 2, providing generally good agreement with both experiments. An estimate of the order-$K^2$ terms indicates that they contribute < 2%; possible implications of this result on order-$K$ contributions are discussed. Contributions arising from nonlocal terms other than exchange such as momentum-dependent and spin-orbit effects amount to about 1%. There is little difference between the $\mathrm{np}\gamma$ predictions for the HJ and BS potentials. Our $\mathrm{np}\gamma$ coplanar results for the HJ potential are compared to those obtained in a calculation, which uses the low-energy theorem for internal radiation, by Celenza et al.

[NUCLEAR REACTIONS Neutron-proton bremsstrahlung ($\mathrm{np}\gamma$), $E=130,200\mathrm{}$ MeV; calculated coplanar $\sigma ({\theta }_n,{\theta }_p,{\theta }_{\gamma })$, $\sigma ({\theta }_n,{\theta }_p)$ including meson-exchange contributions, comparison to experiment. Developed higher-order corrections arising from OPE.]

Reaction products from compound-nucleus formation via the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ + Mg and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ reactions have been identified by means of $\gamma$-ray—$\gamma$-ray coincidence techniques. For bombarding energies in the ranges $24 \mathrm{MeV}\le E_c\le 26 \mathrm{MeV}$ and $30 \mathrm{MeV}\le E_0\le 40 \mathrm{MeV}$, the light-particle emission consists largely of the ($2p$), ($\mathrm{pn}$), and ($\alpha p$) modes. The data also suggest that single-proton and single-neutron emissions take place. The relative cross sections for certain of the $\gamma$ rays associated with the ($2p$) and ($\mathrm{pn}$) processes imply a steadily increasing fusion cross section over the 30-40-MeV range.