New prescriptions are presented for the single scattering approximations for the optical potential and distorted-wave impulse approximation transition amplitudes. They are based on the application of systematics observed in the behavior of off-shell T matrices calculated from realistic potential models.

A low-energy scattering theory is developed for long-range potentials which cannot be handled by the usual Coulomb modified effective range theory. A long-range modified scattering length is introduced which may be calculated either by extrapolation to zero energy or by the direct solution of the zero-energy Schrödinger equation. The theory is illustrated by numerical calculations for a model system.

Inelastic proton scattering at forward angles has been carried out on ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ at a bombarding energy of 201 MeV. The (p,p’) spin-flip transitions to $1^{+}$ and $2^{\mathrm{-}}$ states are compared with (e,e’), (p,γ), and charge exchange data, and with microscopic distorted-wave Born approximation calculations using shell model wave functions. The ratios of orbital to spin contributions are deduced for the known $1^{+}$ states in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$.

The ratio of the flux of 15.10-MeV gamma rays to the flux of 4.438-MeV gamma rays resulting from excitation of the corresponding states in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ is a sensitive measure of the spectrum of the exciting particles produced in solar flares and other cosmic sources. These gamma rays are produced predominantly by interactions with ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, both of which are relatively abundant in the solar photosphere. Gamma-ray production cross sections for proton interactions have been reported previously for all important channels except for the production of 15.10-MeV gamma rays from ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$. The first reported measurement of the 15.10-MeV gamma-ray production cross section from p${+\mathrm{}}^{16}$O is presented here. A cyclotron was employed to produce 40-, 65-, and 85-MeV protons which interacted with ${\mathrm{CH}}_2$ and BeO targets. The resultant gamma-ray spectra were measured with a high-purity germanium semiconductor detector at 70, 90, 110, 125, and 140 deg relative to the direction of the incident beam for each proton energy. Other gamma-ray lines resulting from direct excitation and spallation reactions with ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ were observed as well, and their gamma-ray production cross sections, several of which have not been reported previously, are presented. The results are compared with previously reported measurements, as available.

A theory of compound-nucleus reactions is formulated which is valid for most of the physical situations—from the domain of isolated to the domain of overlapping resonances. We allow for a more general than Gaussian statistics of the resonance decay amplitudes. The energy spectrum is parametrized in terms of a variable ${\sigma }_p$ that measures its stiffness. The following results are obtained: We formulate a condition under which Hauser-Feshbach expressions emerge. They include an elastic enhancement factor W. This factor essentially depends on the fourth moment of the decay amplitudes and the stiffness parameter ${\sigma }_p$. Within our model, ${\sigma }_p$ is given by requiring Wigner’s level repulsion. If, in addition, one specializes to the Gaussian statistics of the decay amplitudes, the present results yield the analytical solution to the earlier Monte Carlo simulations. In the same limit, we find agreement with experimental results on W that are available for the regimes of well-isolated and of strongly overlapping resonances.

A theoretical investigation of the angular distribution and polarization of outgoing nucleons in photodisintegration of the deuteron for elliptically polarized gamma rays has been carried out. The results have been expressed in terms of those obtained with linearly polarized gamma rays plus terms which depend upon a parameter χ which can be varied to yield results for circularly or elliptically polarized gamma rays. Numerical results for the Paris potential for low-energy gamma rays are presented. Considerable differences in polarization of the outgoing nucleons for circularly polarized and linearly polarized gamma rays are found.

A beam of polarized neutrons has been used to measure the analyzing power for n-p radiative capture at a lab angle of 90° and neutron energies of 6.0 and 13.43 MeV. Both reaction products were detected with good energy resolution, and time-of-flight techniques were used to remove unwanted background. The measured analyzing powers are consistent with the results of deuteron photodisintegration experiments in which the polarization of the outgoing neutron is measured. The results are somewhat less negative than currently available theoretical calculations which include meson-exchange currents.

The T matrix is more easily calculated when the initial and final channels are described in terms of a basis of wave packets for the relative motion. Usual channels, however, describe relative motion in terms of pure plane waves. We give a fast and practical connection between the latter and the former representations.

The level structure of the low-energy octupole resonance in ${}_{}{}^{46}{}_{}{}^{}\mathrm{Ti}$ has been studied by inelastic scattering using a 65 MeV polarized proton beam. The excitation strength and distribution of the $2^{+}$, $3^{\mathrm{-}}$, and $4^{+}$ states below $E_x$∼8.0 MeV have been determined. The energy weighted sum rule fractions of 10.8%, 11.7%, and 1.98% are found to be exhausted for the quadrupole, octupole, and hexadecapole transitions, respectively. No clear bump of the low-energy octupole resonance strength isolated from the first $3^{\mathrm{-}}$ states has been observed. All the $3^{\mathrm{-}}$ states dispersed in the region of $E_x$=3–8 MeV seem to form one bump in ${}_{}{}^{46}{}_{}{}^{}\mathrm{Ti}$. It is suggested that the fragmentation of a collective $3^{\mathrm{-}}$ state is due to the coupling effect of the octupole excitation with the static deformation of the ${}_{}{}^{46}{}_{}{}^{}\mathrm{Ti}$ ground state, being in qualitative agreement with a random phase approximation calculation.

The proton${\mathrm{-}}^{90}$Zr interaction at sub-Coulomb energies has been investigated in the context of the Lane model, with isospin coupling included, and with alternate decay modes represented with the Hauser-Feshbach model. Scattering and reaction cross sections were accurately measured in order to obtain enough information to constrain the real and absorptive parts of the proton potential. Differential elastic scattering excitation functions were measured at back angles of 135° and 165° from 2 to 7 MeV, with cross section accuracies of 3%. The energy range was sufficient to go from a region where the backscattering was predominantly Coulomb, enabling additional checks on the cross section accuracies, to a region where the gross structure of the cross sections deviated significantly from Rutherford scattering. Radiative capture cross sections were measured from 1.9 to 5.7 MeV proton energies. The capture cross sections were obtained by summing the measured cross sections for the first two primary gamma rays in addition to some 34 other transitions which terminated on the ground and first excited state. The total inelastic scattering cross section to all ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$ excited states (except the first excited state which has been previously measured) was measured at several energies between 3.9 and 5.7 MeV by observing the radiative decay of the residual, excited ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$ nuclei. The analysis yielded several model parameters suggestive of large nuclear structure effects. The depth of the absorptive potential was found to vary as $W_D$=2.73+0.70 $E_{\mathrm{p}}$ in the 2 to 7 MeV proton energy range studied. A real diffuseness of 0.54 fm, significantly smaller than that obtained in neighboring nuclei, was obtained.

The masses of ${}_{}{}^{77}{}_{}{}^{}\mathrm{Kr}$ and ${}_{}{}^{75}{}_{}{}^{}\mathrm{Kr}$ were determined by measuring the Q values of the ${}_{}{}^{80}{}_{}{}^{}\mathrm{Kr}$${(}^3$He${,}^6$He${)}^{77}$Kr, ${}_{}{}^{78}{}_{}{}^{}\mathrm{Kr}$(d,t${)}^{77}$Kr, and ${}_{}{}^{78}{}_{}{}^{}\mathrm{Kr}$${(}^3$He${,}^6$He${)}^{75}$Kr reactions. We find that the ${}_{}{}^{77}{}_{}{}^{}\mathrm{Kr}$ and ${}_{}{}^{75}{}_{}{}^{}\mathrm{Kr}$ mass excesses are -70.160(10) and -64.231(16) MeV, respectively. These new results are integrated into the total scheme of mass measurements in the light rubidium and krypton isotopes. Comparisons with several mass formulae are presented.

Transverse polarization transfer coefficients for the (p,n) reaction on ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$ and ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$ targets have been measured at $E_{\mathrm{p}=80\mathrm{}}$ MeV and theta=0°. Observed values for the Gamow-Teller giant resonance region are $D_{\mathrm{NN}}$=-0.36±0.07 and -0.18±0.05 for ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$ and ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$ targets, respectively, consistent with predominantly spin-flip transitions. Those for the dipole resonance are $D_{\mathrm{NN}}$=0.14±0.03 and 0.11±0.03, indicating the coexistence of the spin-flip resonance with a non-spin-flip resonance. Finite positive $D_{\mathrm{NN}}$ values are observed up to an excitation energy of 30 MeV on both targets, showing the importance of the single step process. The obtained results are interpreted in terms of a plane-wave impulse approximation. In conjunction with the higher energy $D_{\mathrm{NN}}$ data, the transition strength ratios of non-spin-flip to spin-flip, and the $D_{\mathrm{NN}}$ values pertinent to spin-flip transitions, have been deduced empirically for the Gamow-Teller resonance, the dipole resonance, and $E_x$=28 MeV, regions in the ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$(p,n) reaction.

Differential cross sections for ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$(p,p’) and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$(d,d’) excitation of the $1^{+}$ state at $E_x$=5.846 MeV were measured at $E_{\mathrm{inc}=45\mathrm{}}$ MeV. The fact that the measured strengths of both reactions are very similar supports the isoscalar nature of the $1^{+}$ state. The comparison of the experimental proton angular distribution to microscopic distorted-wave calculations using random phase approximation wave functions with and without tensor correlations suggests that the isoscalar tensor part of the (π+ρ)-exchange potential is too strong.

Employing an extended version of the Boltzmann-Uehling-Uhlenbeck equation, we present simulations of the reaction 800 MeV/nucleon Ca+Ca. Deuteron spectra are calculated from the model without ad hoc assumptions. Absolute values of the proton and deuteron spectra are in good agreement with experiment. The dependence of the total deuteron yield on the nuclear equation of state is investigated and found to be weak. Both entropy and freeze-out density are strongly dependent on impact parameter. This suggests, in particular, that the freeze-out density has no physical meaning. Methods for calculating entropy are discussed and numerically compared.

The final states of central Ca + Ca and Nb + Nb collisions at 400 and 1050 MeV/nucleon and at 400 and 650 MeV/nucleon, respectively, are studied with two independently developed statistical models, namely the classical microcanonical model and the quantum-statistical grand canonical model. It is shown that these models are in agreement with each other for these systems. Furthermore, it is demonstrated that there is essentially a one-to-one relationship between the observed relative abundances of the light fragments p, d, t, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, and α and the entropy per nucleon, for breakup temperatures greater than 30 MeV. Entropy values of 3.5–4 are deduced from high-multiplicity selected fragment yield data.

An excitation function for the 40Ca${(}^{16}$O${,}^{28}$${\mathrm{Si}}^{\mathrm{*}}$${)}^{28}$${\mathrm{Si}}^{\mathrm{*}}$ reaction has been measured between 74.925≤$E_{\mathrm{lab}\mathrm{\le }}$77.25 MeV in 75-keV steps for 30°≤${\mathrm{theta}}_{\mathrm{lab}\mathrm{\le }60\mathrm{°}}$. $Q—-value and angular distributions were measured at each beam energy. Intermediate width (Γ≃200 keV) structures are present in the excitation function at the 3–5 % level of the cross section. An analysis of the present excitation function, together with one previously obtained for the inclusive elastic and inelastic ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ scattering yields, indicates that the structures in the two excitation functions are correlated at an 80% confidence level. This suggests that the process responsible for the resonances is of compound-nuclear origin.

The recent attempts to extract the temperature in the late stage of medium energy (20–60 MeV/nucleon) heavy ion collisions from the yields of γ- and particle-instable fragments are discussed. The quantum statistical model is employed to demonstrate that feeding from instable states distorts the yields used for the temperature determination severely. Some particle instable fragments are only moderately affected by feeding. These selected species can still be useful for determining the temperature. The breakup temperatures of the fragment conglomerate extracted with this method are T≃4–8 MeV, much smaller than the corresponding slope factors, which indicate T∼15 MeV.

The ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$${(}^{20}$Ne,α ${}^{16}$$O_{g.s.\mathrm{}}^{12}$$C_{g.s}$., ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$${(}^{20}$Ne,α ${\mathrm{}}^{20}$Ne${)}^8$${\mathrm{Be}}_{\mathrm{g}.\mathrm{s}.\mathrm{}}$, and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$${(}^{20}$Ne,α ${\mathrm{}}^{12}$C${)}^{16}$${\mathrm{O}}^{\mathrm{*}}$ reactions at E${(\mathrm{}}^{20}$Ne)=157 MeV were studied by using position-sensitive telescopes. It was established that α${\mathrm{-}}^{16}$O coincidences in the first reaction result not only from sequential breakup of the projectile, but also from the transfer-reemission process ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}_{\mathrm{g}.\mathrm{s}.\mathrm{}}^{}{}_{}{}^{}$C${(}^{20}$Be${,}^{16}$${\mathrm{O}}_{\mathrm{g}.\mathrm{s}.\mathrm{}}$${)}^{16}$${\mathrm{O}}^{\mathrm{*}}$→α+${\mathrm{}}^{12}$ Distributions of the excitation energy in the primary reaction products were deduced by calculating respective branching ratios with a Hauser-Feshbach statistical-decay code. It was found that excitation energy is generated in mass transfer reactions quite asymmetrically: it is mostly concentrated in the nucleus that acquires mass, while the ‘‘donor’’ nucleus, on the average, remains cold. These results clearly support the basic concept of ‘‘spectator’’ models of heavy-ion reactions.

Coupled-channels effects occurring in fusion ${(}^{23}$Na→${+\mathrm{}}^{48}$Ti) and elastic scattering ${(}^7$Li→${+\mathrm{}}^{120}$Sn) of aligned deformed heavy ions are treated on the same footing in a semiquantal decoupling approximation which holds for large angular momenta. Numerical results obtained are compared to those of the exact quantum mechanical formalism by invoking recent experimental data.

We present a simple quark model for nucleus-nucleus collisions which employs the Glauber multiple scattering theory. The model is first used to fit a quark-quark scattering amplitude to high energy nucleon-nucleon elastic scattering data. This amplitude is then used to calculate high energy αp and αα elastic scattering cross sections. The nucleus-nucleus calculations are performed using both a simple first-order optical phase shift function (essentially a tρ approximation) and an optical phase shift function calculated through fifth order. We also calculate the same cross sections using a conventional nuclear model together with Glauber theory. Comparisons of the results of the different theoretical approaches and the data are presented.