Differential cross sections for the ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$(p,n)${}_{}{}^{14}{}_{}{}^{}\mathrm{O}$(g.s.) reaction have been measured at $E_p=35.2\mathrm{}$ MeV with a gas-cell target. Differential cross sections for (p,n) reactions on ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ leading to the first three levels in ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ have been obtained with an isotopically-enriched graphite target for bombarding energies of 25.7, 35, and 45 MeV. The ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$(p,n)${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$(2.31 MeV) cross sections have been analyzed with Lane-model distorted-wave Born approximation calculations to extract energy-dependent well depths for the isovector part of the optical potential. These isovector well depths have been combined with a set of isoscalar optical-potential parameters derived from elastic proton scattering on ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$. The resulting optical potential has been used in microscopic distorted-wave Born approximation analyses of the (p,n) differential cross sections. Strengths for the isovector central $V_{\tau }$ and $V_{\sigma \tau }$ and isovector tensor $V_{T\tau }$ components of the effective interaction have been extracted. A comparison of the isospin-symmetric ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$(p,n)${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$(g.s.), ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$(p,n)${}_{}{}^{14}{}_{}{}^{}\mathrm{O}$(g.s.), and ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$(p,p′)${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$(2.31 MeV) reactions has been made, and unexpected differences among the angular distributions are found.

[NUCLEAR REACTIONS ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$(p,n)${}_{}{}^{14}{}_{}{}^{}\mathrm{O}$(g.s.), $E_{\mathrm{p}}=35.2\mathrm{}$ MeV, measured $\sigma \left(\theta \right)$, $\theta ={10}^{\circ }-{150}^{\circ }$, $\Delta \theta =5^{\circ }$. ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$(p,n)${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$(g.s., 2.31, 3.95 MeV), $E_p=25.7,35,45\mathrm{}$ MeV, measured $\sigma \left(\theta \right)$, $\theta ={10}^{\circ }-{160}^{\circ }$, $\Delta \theta =5^{\circ }$. Gas target, enriched target, Lane-model analysis, microscopic DWBA analysis.]

A sum rule approach is presented to study in detail the role of dynamical correlations in electron scattering reactions. Both the induced nucleon-nucleon repulsive short range and tensor correlations are taken into account in the explicit calculations of energy-weighted and non-energy-weighted sum rules in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. The former are largely affected by tensor correlations in a wide region of momentum transfer, while the latter are mostly model independent. The theoretical results for the longitudinal and transverse integrated response functions of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ are compared with available experimental data.

[NUCLEAR REACTIONS Longitudinal and transverse quasielastic electron scattering sum rules; tensor correlations in finite nuclei; comparison with experimental data in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$.]

Employing the two-body charge effects owing to $\pi$ exchange and the current effects owing to $\pi$-, $\rho$-, and $\omega$-exchange processes, the angular distribution, asymmetry function, and polarization of nucleons from the ${}_{}{}^2{}_{}{}^{}\mathrm{H}{(\gamma ,n)}^1\mathrm{H}$ reaction are investigated. The cross section and polarization parameters are reported for the Paris, Yale, super-soft-core B, and Hamada-Johnston potentials. The changes in the parameters owing to exchange effects are found to be nearly the same for all the potentials, and all the potentials are found to reproduce the low energy angular distribution data provided a suitable normalization factor is chosen.

[NUCLEAR REACTIONS ${}_{}{}^2{}_{}{}^{}\mathrm{H}{(\gamma ,n)}^1\mathrm{H}$. Two-body exchange effects, total and differential cross section, polarization, asymmetry function with realistic nucleon-nucleon interactions.]

The differential cross sections for elastic and inelastic scattering to the first excited ($2^{+}$) states of 100 MeV protons from ${}_{}{}^{46,48,50}{}_{}{}^{}\mathrm{Ti}$ were measured. The angular ranges covered were 9° to 110° for ${}_{}{}^{46,50}{}_{}{}^{}\mathrm{Ti}$ and 9° to 168° for ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ti}$. The elastic scattering data were analyzed with a local optical model potential. The quality of fits to the data covering the smaller angular range (< 110°) is good for all three isotopes, with $\frac{{\chi }^2}{N}\sim 1.5$; whereas the fit to the large angle data of ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ti} (\lesssim {168}^{\circ })$ is not as satisfactory ($\frac{{\chi }^2}{N}\sim 3.75$). Various modifications to the Woods-Saxon shape of the real central potential showed no real improvement. Nevertheless, the large angle data appear to favor a slightly sharper falloff in the real central potential near the surface, such as the Woods-Saxon-squared potential. Systematics of the phenomenological optical model potential of 100 MeV protons were studied. The derived volume integrals and rms radii seem to follow the usual $A$ dependence. The isospin dependence of the real potential was also extracted. The mean free paths computed directly from the imaginary potential strength have large uncertainties due to the insensitivity of the data to the central region of the imaginary potential. Distorted-wave Born approximation and coupled-channels Born approximation calculations for the collective excitation of the target nuclei to the first $2^{+}$ states provided deformation parameters, $B_2$, in agreement with those from other proton and alpha scattering data and electromagnetic measurements.

We have measured (n,2n) and (n,np+n,pn) cross sections for the radioactive nuclides ${}_{}{}^{88}{}_{}{}^{}\mathrm{Y}$ and ${}_{}{}^{88}{}_{}{}^{}\mathrm{Zr}$. The results are, for the (n,2n) reaction on ${}_{}{}^{88}{}_{}{}^{}\mathrm{Y}$ at 14.19±0.04 MeV, 1140±50 mb; and at 14.8±0.1 MeV, 1180±50 mb. The ${}_{}{}^{87}{}_{}{}^{}\mathrm{Y}$ isomer ratios ($\frac{m}{\mathrm{total}}$) are 0.70±0.05 and 0.74±0.05, respectively. For ${}_{}{}^{88}{}_{}{}^{}\mathrm{Zr}$ at 14.8±0.1 MeV, the (n,2n) cross section is 467±23 mb, and the (n,np+n,pn) cross section is 253±25 mb. The ${}_{}{}^{87}{}_{}{}^{}\mathrm{Y}$ isomer ratio for the latter reaction is 0.90±0.06. The results are compared to calculations which are based on a combined statistical-preequilibrium model. Half-lives for ${}_{}{}^{88}{}_{}{}^{}\mathrm{Zr}$, ${}_{}{}^{87}{}_{}{}^{}\mathrm{Zr}$, ${}_{}{}^{87}{}_{}{}^{}\mathrm{Y}_{}^m{}_{}{}^{}$, and ${}_{}{}^{87}{}_{}{}^{}\mathrm{Y}_{}^g{}_{}{}^{}$ are presented. Branching ratios for the decay of ${}_{}{}^{87}{}_{}{}^{}\mathrm{Zr}$ to ${}_{}{}^{87}{}_{}{}^{}\mathrm{Y}_{}^{m,g}{}_{}{}^{}$ were determined and the photon intensity of the 484.9-keV gamma ray from the decay of ${}_{}{}^{87}{}_{}{}^{}\mathrm{Y}_{}^g{}_{}{}^{}$ was measured.

[NUCLEAR REACTIONS ${}_{}{}^{88}{}_{}{}^{}\mathrm{Y}(\mathrm{n},2\mathrm{n}){}_{}{}^{87}{}_{}{}^{}\mathrm{Y}_{}^{m,g}{}_{}{}^{}$, $E=14.2,14.8\mathrm{}$ MeV; ${}_{}{}^{88}{}_{}{}^{}\mathrm{Zr}$(n,2n)${}_{}{}^{87}{}_{}{}^{}\mathrm{Zr}$, $E=14.8\mathrm{}$ MeV; ${}_{}{}^{88}{}_{}{}^{}\mathrm{Zr}(\mathrm{n},2\mathrm{n}+\mathrm{n},\mathrm{n}\mathrm{p}){}_{}{}^{87}{}_{}{}^{}\mathrm{Y}_{}^{m,g}{}_{}{}^{}$, $E=14.8\mathrm{}$ MeV; measured $\sigma \mathrm{}\left(E\right)\mathrm{}$. Comparison with combined statistical and preequilibrium model.

RADIOACTIVITY ${}_{}{}^{87}{}_{}{}^{}\mathrm{Y}_{}^m{}_{}{}^{}$, ${}_{}{}^{87}{}_{}{}^{}\mathrm{Y}_{}^g{}_{}{}^{}$, ${}_{}{}^{88}{}_{}{}^{}\mathrm{Zr}$; measured half-life. ${}_{}{}^{87}{}_{}{}^{}\mathrm{Zr}$, measured branching decay. ${}_{}{}^{87}{}_{}{}^{}\mathrm{Y}_{}^g{}_{}{}^{}$, measured $I_{\gamma }$.]

Semiclassical methods are used to analyze the second-order processes—the direct-one step process and the two-step process—in heavy ion collisions. Our main results are the following: (i) In the strong absorption limit, the direct one-step and two-step form factors are equally important and interfere destructively near the grazing angular momentum. The Austern-Blair theory gives satisfactory results for well-matched reactions. The angular distributions of mutual and double excitations are out of phase compared with that of the single excitation. (ii) For the weak to moderate absorption case, the internal part of the two-step process is enhanced. The angular distribution shows the refractive effect of overlapping resonances. Applications have been made to inelastic ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$-${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ reactions.

A new cascade model has been constructed and applied to high-energy heavy-ion collisions, where the emphasis is placed on a systematic study of nuclear collective motion. The model provides a time-dependent microscopic description of nuclear cascade collisions which takes into account some important aspects of the colliding system. The calculated results agree consistently with the experimental data, which otherwise have been interpreted as evidence for collective motion.

The behavior of ${}_{}{}^{176}{}_{}{}^{}\mathrm{W}$ at high angular momentum was investigated through both spectroscopy of the discrete and correlation measurements of the continuum $\gamma$ rays. The $\gamma -\gamma$ coincidence data were taken with a detection system consisting of two Compton-suppressed Ge(Li) counters. First and second moments of inertia were derived from the data.

In the wake of the statistical theory for angular momentum in binary (deep inelastic) processes, a statistical theory for the distribution of angular momentum between the fragments has been developed for the case of multifragmentation (three or more fragments). From the generalized partition function, the average energy and angular momentum of each fragment are derived as well as the corresponding variances. The first moments in the two quantities suggest a "rigid rotation" limit analogous to the binary case. The components of the polarization tensor are calculated for each fragment. The role of thermally generated angular momentum versus that arising from rigid rotation is discussed. Comments are offered on the applicability of the theory to various reactions.

A series of experiments was carried out on the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^{16}{}_{}{}^{}\mathrm{O},\alpha )$ reaction to search for the population of molecular resonances as final state interactions. Contrary to our expectation, no positive evidence was found in $\alpha -{}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ coincidence measurements for molecular states. The experimental configuration was arranged to selectively observe events corresponding to decays into the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ resonance channel. A study of the incident energy dependence of the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^{16}{}_{}{}^{}\mathrm{O},\alpha )$ reaction clearly indicates the importance of sequential processes in the $\alpha$-particle yield. In particular, the process where the incident ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ picks up an $\alpha$ forming ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}_{}^{*}{}_{}{}^{}$ resonances and then decays back to $\alpha +{}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ can reasonably explain most of observed structures in the inclusive $\alpha$ spectra. The sequential process caused by the inelastic excitation of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ to ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}_{}^{*}{}_{}{}^{}\to \alpha +{}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ can also contribute to the broad peaks observed in the inclusive spectra, but only in the high excitation region.

Energy spectra for p, d, t, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, and ${}_{}{}^6{}_{}{}^{}\mathrm{He}$ from the reaction ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$ at 35 MeV/nucleon are presented. A common intermediate rapidity source is identified using a moving source fit to the spectra that yields cross sections which are compared to analogous data at other bombarding energies and to several different models. The excitation function of the composite to proton ratios is compared with quantum statistical, hydrodynamic, and thermal models.

For the scattering of ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ on ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ coupled channel calculations of the elastic scattering and inelastic single excitation of the first $2^{+}$ state of ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ are carried out. The real coupling potentials are calculated in the framework of an adiabatic model. The resulting cross sections reveal structures in agreement with the observed ones and support their interpretation as nuclear molecular resonances.

We calculate the Wigner function of the one-body density of a system of 32 independent particles moving in two adjacent cubic boxes communicating through a window. We discuss the applicability of the currently used definition of the classical analog of the one-sided flux obtained from the Wigner function.

[NUCLEAR REACTIONS Wigner function for a simple quantum mechanical model, nucleon exchange, static one-sided flux.]

Two recent studies of high-spin fission from compound nuclei near ${}_{}{}^{200}{}_{}{}^{}\mathrm{Pb}$, formed in three different entrance channels (${}_{}{}^6{}_{}{}^{}\mathrm{Li}$+${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$, ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$+${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}$, and ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$+${}_{}{}^{170}{}_{}{}^{}\mathrm{Er}$), have led to differing conclusions concerning the need to modify rotating liquid-drop model fission barrier heights to reproduce observed decay properties. In order to investigate possible origins of the differences, we have performed consistent statistical model calculations for all three systems. We obtain satisfactory agreement with the measured fission cross sections for the three systems with a level density treatment incorporating collective enhancements which fade with increasing temperature, and input structure parameters fixed to predictions of the rotating liquid-drop model and the noninteracting Fermi-gas model. We thus find no evidence for any significant inadequacy of the rotating-liquid-drop-noninteracting-Fermi-gas structure predictions for high excitation and $A\simeq 200$.

Using a Fokker-Planck equation, we consider induced nuclear fission for large values of the friction constant. Then, the equation simplifies to the Smoluchowski equation which we solve using a method of van Kampen. We find that the fission rate obeys a scaling law. From our numerical results and those obtained previously, we estimate the transient time $\tau$ for fission. For small nuclear temperature, $\tau$ is defined as the time delay between the onset of a nuclear reaction and the attainment of the quasistationary probability flow over the fission barrier. For nuclear temperatures large compared to the fission barrier, the entire fission process is governed by transients, and $\tau$ essentially yields the fission lifetime. We speculate on the significance of our results for recent experimental observations.

We report on a complete ($2E,2v$) experiment for fast neutron induced fission on ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$. The energy dependence of fragment properties so far known only for thermal neutron induced fission is studied. Experimental problems as well as difficulties in data analysis are considered in detail in order to obtain clean and unbiased results. In particular, a self-consistent determination of the fragment total kinetic energy ($E_{K,\mathrm{tot}}$) was achieved by comparing the results obtained via the respective velocities and pulse heights. We find systematic discrepancies of 2 MeV if $E_{K,\mathrm{tot}}$ is determined from the observed pulse heights with the calibration scheme of Schmitt et al. Therefore, refined calibration constants were deduced by comparison with accurate radiochemical mass yields. Measurements were performed at neutron energies of 0.50 and 5.55 MeV. Our results include mean values of fragment properties before and after neutron evaporation, e.g., of fragment velocities and masses, total kinetic energies, and the respective variances. We also show the distributions of fragment mass, of $E_{K,\mathrm{tot}}$, and of the variance of $E_{K,\mathrm{tot}}$. In addition, the number of prompt fission neutrons $\nu$ is given as a function of fragment mass. Our resolution of 2.1 mass units reveals fine structure not only in the fragment mass distribution but also in $E_{K,\mathrm{tot}}\left(A^{*}\right)$ and $\nu \left(A^{*}\right)$. For the lower neutron energy of 0.50 MeV the present results compare reasonably well with similar measurements performed with thermal neutrons. Apparently the 0.5 MeV increase in saddle point excitation does not alter the results significantly. The improved accuracy of this measurement is demonstrated by comparison of our neutron emission data with direct measurements of fission neutrons. At the higher neutron energy of 5.55 MeV we observe the expected decrease of shell and pairing effects which indicates an increase in nuclear temperature. These results are in qualitative agreement with the model of Wilkins, Chasman, and Steinberg. However, a striking discrepancy exists for the number of fission neutrons, where we find that the increase in the total number of fission neutrons is totally accounted for by heavy fragments alone.

The elastic scattering of a pion from quark bag models of the nucleon, the $\Delta \mathrm{}\left(1232\right)\mathrm{}$, and the ${\mathrm{N}}^{*}$ (1470) is investigated. A rank two $\frac{N}{D}$ dispersion theory is used to derive a dynamic equation for pion-nucleon elastic scattering which includes the effect of coupling the pion production channels to the elastic channel. In the limit of no coupling to production channels, the model reduces to the cloudy bag model. In the $P_{11}$ channel, the model is quantitatively in agreement with the experimental phase shifts for pion laboratory kinetic energies below 1 GeV with reasonable parameters. In the $P_{33}$ channel, we find similar quantitative agreement. In this channel, the data allow for any mass of the delta bag greater than about 1290 MeV with the model going over continuously to the Chew-Low model as the mass of the delta bag state is increased. The physical resonance is found to be a mixture of a pion-nucleon Chew-Low—type resonance with the delta state of the bag. A bag radius of approximately 1.1 fm is found but several corrections to the model which would alter this radius are noted.

[NUCLEAR REACTIONS Pion-nucleon elastic scattering, coupling of pion production channels to elastic channel; $P_{33}$ and $P_{11}$ channels.]

We treat the response in a finite nucleus to longitudinal spin-isospin probes. Since linear momentum is here not a good quantum number, we adopt a formalism suggested by Toki and Weise, which incorporates an expansion in partial waves of good nuclear total angular momentum. The basic quantity involved is the pion self-energy II, which is nonlocal in momentum space. This quantity peaks at diagonal momentum distribution only for momentum $q\approx k_c$, where $k_c$ is the critical momentum for pion condensation precursor features, $k_c\sim 2-3m_{\pi }$. To solve for the response function $\mathcal{R}$, we iterate II by solving an integral equation exactly (using numerical methods). The response $\mathcal{R}$ is singular for criticality (Migdal parameter $g^{\prime }\approx 0.4$ and momentum $q\approx k_c$). We use $\mathcal{R}$ to renormalize the matrix element of a longitudinal spin-isospin probe and find, as expected, a large effect near criticality as well as a very significant effect of nonlocality in general. We apply our formalism to levels with $J^P=0^{-},T=1\mathrm{}$ in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and $J^P=1^{+},T=1\mathrm{}$ in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. The results are compared with currently used approximations. The local density approximation employed in this context gives semiquantitative agreement only. Using infinite nuclear matter, we find the best agreement for the equivalent constant density $\rho =0.12\mathrm{}$ ${\mathrm{fm}}^{-3\mathrm{}}$ for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$; this agreement remains only qualitative, however. We give a detailed test of the model interactions suggested by Meyer-ter-Vehn in which it emerges that the value of $k_c$ is not correctly produced. The approximations of Toki and Weise are satisfactory for $g^{\prime }\gtrsim 0.6$ and $k\approx k_c$. Approximations cannot be reliably used, however, for small $g^{\prime }$ or far from the critical momentum transfer. This is especially the case for the description of the nonlocality of II in momentum space through the use of a Bessel-function distribution, which is unreliable throughout the relevant range of parameters.

[NUCLEAR REACTIONS Pionlike discrete nuclear excitations in finite nuclei; spin-isospin strength distribution effects; pion self-energy and response function; ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}_{}^{*}{}_{}{}^{}(J^P=0^{-},T=1)$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}_{}^{*}{}_{}{}^{}(J^P=1^{+},T=1)$; comparison with various approximations.]

The importance of inelastic channels in proton-nucleus scattering grows with momentum transfer, $q$, so that for large $q$ coupled channels are required. This happens when the elastic and inelastic cross sections become comparable. We incorporate these ideas in a simple analytic framework to explain the large angle p-${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ elastic scattering data at 800 MeV for which standard optical model calculations have failed completely.

We extend earlier work on analytic evaluations of nucleon scattering amplitudes to the Dirac treatment. The resulting closed form expressions are accurate and show how the two-body and target input influence scattering observables. The insight available should be quite useful as the Dirac equation description of proton-nucleus scattering becomes the standard approach.