Elastic and inelastic excitation functions for the systems ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+ ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$+ ${}_{}{}^{28,29,30}{}_{}{}^{}\mathrm{Si}$ have been measured at ${\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}=180\mathrm{}°$ from the Coulomb barrier up to $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=45\mathrm{}$ MeV (${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$), $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=52\mathrm{}$ MeV (${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$+${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$), and $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=32\mathrm{}$ MeV (${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$+${}_{}{}^{29,30}{}_{}{}^{}\mathrm{Si}$). Over the whole energy range they all exhibit pronounced and regular broad oscillations ($0.5\lesssim \theta \lesssim 1.5$ MeV). Elastic and inelastic angular distributions up to ${\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}=180\mathrm{}°$ were taken at five of the maxima and near a minimum of the excitation function for the system ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$+${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$. All angular distributions are oscillatory and exhibit a strong backward rise. The data are discussed in terms of a coherent superposition of a background and a resonant amplitude and in terms of the interference between the internal and barrier wave reflected by a deep optical potential.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$+${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$+${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$+${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$, measured elastic and inelastic $\sigma (\theta ,E)$, $14 \mathrm{MeV}<E_{\mathrm{c}.\mathrm{m}.\mathrm{}}<52\mathrm{} \mathrm{MeV}$, $15°<{\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}<180\mathrm{}°$, resonance and optical potential analysis.

A method is proposed for the exact microscopic computation of the Coulomb exchange interaction in both elastic and inelastic heavy-ion scattering. For comparison with customary Coulomb approximations the method is applied to the elastic scattering of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ on ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and $\alpha$ on ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$. It turns out that bound state and resonance energies are lowered noticeably and resonance widths become correspondingly smaller.

NUCLEAR REACTIONS Scattering theory, exchange Coulomb interaction, effects on elastic $\alpha$-${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$-${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ scattering.

Functional integral formulation of the mean-field approximation for many-body systems is used to study the nuclear partition function. Both static and dynamic mean-field solutions with statistical occupations of the single particle wave functions are discussed. These correspond to different physical processes in the nuclear system. In the static case the effect of mean-field fluctuations on the nuclear level density is exhibited. This effect enters consistently along with the usual effects of temperature and chemical potential fluctuations. Together they account for generalized random phase approximation correlations and produce bosonlike terms in the nuclear entropy. Because of the self-consistency of the approach, no overcounting of the collective and single-particle degrees of freedom occurs. The effects of the single particle continuum are included in the discussion. Consequences of a possible multiplicity of static mean-field configurations are briefly discussed. Dynamical mean-field solutions are considered in relation to compound nucleus fission. They provide the extension of the mean-field description of spontaneous fission given recently. A microscopic expression for the energy dependence of the average fission width is presented. It combines both the dynamical and statistical features of the tunneling mean-field solution in the subbarrier region.

NUCLEAR STRUCTURE, FISSION Static and dynamic mean field with statistical occupations, level density, RPA correlations, bosonlike terms in the nuclear entropy, single-particle continuum, mean-field equations for compound nucleus fission.

The deformation energy surfaces of ${}_{}{}^{205}{}_{}{}^{}\mathrm{At}$ are calculated at high angular momenta and temperatures using a Woods-Saxon potential and the Strutinsky prescription. By this microscopic calculation it is shown that a qualitative explanation of the increasing width of the mass distribution of heavy-ion-induced fission with angular momentum is possible.

NUCLEAR REACTIONS ${}_{}{}^{205}{}_{}{}^{}\mathrm{At}$; studied mass distribution width of fusion-fission events; dependence on angular momentum; Strutinsky prescription for heated rotating nuclei.

We lack an equation relating fission fragment mass before prompt neutron emission to the mass of the resulting fission product. It is shown that by using conveniently defined auxiliary functions and partly neglecting fine structure effects, expressions may be derived for mass number, charge density, and prompt neutron yields of individual fission fragments. All expressions involve parameters which can be evaluated from radiochemical fission product yield data, without recourse to any physical measurement whatsoever. The expressions for neutron yields from individual fragments reproduce the well-known saw-tooth curve. The fragment mass number as a function of charge is composed of two parallel straight lines with a simple discontinuity at symmetric charge division. Similarly, the fragment charge density versus charge has two branches extending in the heavy and light fragment regions, respectively. The corresponding relationship is a homographic function of charge, and is discontinuous at symmetric charge division, where Dirichlet's theorem applies. In the fission of ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$, the two branches come closer together at symmetric charge division as excitation energy of the fissioning nucleus increases. The expressions mentioned above have been applied to nine different low excitation energy (≤14 MeV) fission processes for which selected recommended data are available. Comparison is made with published data wherever available; in general, good agreement is observed. The expression predicted by the liquid drop model for mass asymmetry of fission is shown to be identically valid for charge and neutron asymmetry also. Two new identities are also reported. In addition, two quantities are defined, namely, the inverse charge density with respect to nucleons and that with respect to neutrons. It is shown that the arithmetic mean of either of these quantities for the average light and heavy fragments equals the corresponding quantity for the fissioning nucleus, and that this equality holds true with notable accuracy in all low-energy fission processes considered.

NUCLEAR REACTIONS, FISSION ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$, ${}_{}{}^{233}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{239}{}_{}{}^{}\mathrm{Pu}$, ${}_{}{}^{252}{}_{}{}^{}\mathrm{Cf}$. Expressions for fragment mass, charge density, and neutron yields versus charge involving parameters determinable from radiochemical yields.

The energy loss and deflection function in the strongly damped collision of heavy ions is analyzed in the nucleon exchange model as a function of the nuclear response time. Nucleus velocity changes and the rapid transfer of the relative angular momentum to internal spin are evaluated at each point on a trajectory which is determined by the effective interionic potential. Comparison of the position of the strongly damped peak with experimental data determines the nuclear response time to be around ${10}^{-21\mathrm{}}$ s, larger than the transit time. This strengthens our belief that deformations do not affect strongly damped collisions profoundly.

NUCLEAR REACTIONS ${}_{}{}^{139}{}_{}{}^{}\mathrm{La}$(${}_{}{}^{86}{}_{}{}^{}\mathrm{Kr}$,$X$), $E=505, 610, \mathrm{and} 710$ MeV; calculated energy losses, deflection functions, $\sigma \left(\theta \right)$, total mass exchanged, and total $l$ transfers using nucleon exchange model for strongly damped collision. Deduced nuclear response times.

A local representation of the free nucleon-nucleon $t$ matrix has been determined for several projectile bombarding energies between 100 and 800 MeV/nucleon and is presented in tabular form. The form of the interaction has been tailored for use in calculations of elastic and inelastic proton scattering in this energy range. The technique used to derive the interaction is outlined and some of the resulting uncertainties are discussed. A number of the most important properties of the interaction and their roles in the calculation of nucleon-nucleus scattering observables are discussed. A few applications of the interaction are made to a variety of ($p$,$p^{\prime }$) transitions within a single-scattering context.

NUCLEAR REACTIONS An energy-dependent multiple Yukawa representation of the on-shell nucleon-nucleon $t$ matrix between 100 and 800 MeV.

Pion inelastic scattering calculations, exciting the stretched state configurations of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, have been performed in the context of the impulse approximation, but with excited states generated from the recoil corrected continuum shell model. The calculation, therefore, allows for the subsequent decay of excited states via particle emission. The unbound nature of these states is shown to greatly effect their structure and isospin mixing, and therefore the pion cross sections. The calculated cross sections are consistent with observed ${\sigma }_{{\pi }^{+}}$, ${\sigma }_{{\pi }^{-}}$ differences.

NUCLEAR REACTIONS Pion scatteirng, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$($\pi$,${\pi }^{\prime }$) ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$($4^{-}$), continuum shell model, isospin mixing.

The cross section of ${\pi }^{-}+{}_{}{}^3{}_{}{}^{}\mathrm{He}\to d+n$ and ${\pi }^{-}+{}_{}{}^4{}_{}{}^{}\mathrm{He}\to t+n$ has been measured at energies between $T=50\mathrm{} \mathrm{and} 295$ MeV and angles between ${\theta }_n\approx 20° \mathrm{and} 150°$ covering the momentum transfer range $q\approx 0.4-1.0$ GeV/c. A phenomenological analysis of the data is attempted to identify the characteristic $T$, $\theta$, and $q$ dependences of the ($\pi$,$n$) reaction dynamics. Most conspicuous is the angular dependence of the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$(${\pi }^{-}$,$n$)${}_{}{}^3{}_{}{}^{}\mathrm{He}$ which mirrors characteristic features of $\pi$ + He elastic scattering. The $T$ dependence of ($\pi$,$n$) in ${}_{}{}^{3,4}{}_{}{}^{}\mathrm{He}$ (for $\theta <70\mathrm{}°$) is similar to $\pi +N$ or $\pi$ + He elastic scattering. The clear dependence of $T$ and $\theta$ is indicative of $\pi +N$ (off-shell) scattering in the basic pion-absorption process. The nuclear form factor $q$ dependence is most pronounced for forward angles, and the largely exponential falloff with $q$ is similar to that of analogous nuclear reactions. Comparisons with theoretical calculations show that crucial ingredients are missing in currently used models and general directions of needed refinements are indicated.

NUCLEAR REACTIONS ${\pi }^{-}+{}_{}{}^3{}_{}{}^{}\mathrm{He}\to d+n$ and ${\pi }^{-}+{}_{}{}^4{}_{}{}^{}\mathrm{He}\to t+n$, $T_{\pi }=50-295\mathrm{}$ MeV, ${\theta }_n=20\mathrm{}°-150\mathrm{}°$; measured $\sigma ({\theta }_d,T_{\pi })$ and $\sigma ({\theta }_t,T_{\pi })$, discussed reaction mechanisms; the energy and nuclear form factor dependence of the reaction dynamics.

The elastic scattering of positive kaons from ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^3{}_{}{}^{}\mathrm{H}$, and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ is calculated with a theoretical momentum space optical potential. The theory includes nuclear spin, nucleon recoil and binding, a Lorentz invariant angle transformation, realistic nuclear form factors for the proton and neutron matter and spin distributions, and a kaon-nucleon $T$ matrix with off-shell behavior based on a separable potential model. Differential and total cross sections, polarizations, and isotopic ratios are examined for kaon energies from 0.4 to 1 GeV and compared with results from pion and electron scattering.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$($K^{+}$,$K^{+}$), ${}_{}{}^4{}_{}{}^{}\mathrm{He}$($K^{+}$,$K^{+}$), ${}_{}{}^3{}_{}{}^{}\mathrm{He}$($K^{+}$,$K^{+}$), ${}_{}{}^3{}_{}{}^{}\mathrm{H}$($K^{+}$,$K^{+}$), ${}_{}{}^3{}_{}{}^{}\mathrm{He}$($K^0$,$K^0$); $E=39-804\mathrm{}$ MeV; $\sigma \left(\theta \right)$ and ${\sigma }_{\mathrm{tot}}$; theoretical calculation, momentum space optical potential; spin effects, binding, recoil, angle transformation; compare with ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ data.

Differential cross sections and analyzing powers for the ($\overrightarrow{p}$,${\pi }^{+}$) reaction have been measured with 147- to 159-MeV polarized protons. Transitions to the ground, 2.12-, and 4.45-MeV states in ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$, the ground, 3.09-, and (3.68-3.85)-MeV doublet in ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, the ground and 0.87-MeV state in ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$, and the ground state in ${}_{}{}^{14}{}_{}{}^{}\mathrm{Ca}$ are studied. Pion center-of-mass energies range from 5 to 11 MeV. The results show distinct differences of the ($\overrightarrow{p}$,${\pi }^{+}$) analyzing power for the various transitions.

NUCLEAR REACTIONS ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$($\overrightarrow{p}$,${\pi }^{+}$), polarized protons, $E_p=147-159\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$, $A\left(\theta \right)$.

The fourth-order noniterative $2\pi$-exchange diagrams involving double-isobar intermediate states are evaluated in momentum space, in the framework of noncovariant perturbation theory. The role of these diagrams is studied by making a detailed comparison with (i) the corresponding iterative diagrams and (ii) diagrams involving $\mathrm{NN}$ or $N\Delta$ intermediate states. Current prescriptions for replacing all time-orderings of those diagrams by (simple) pion-range transition potentials are tested.

NUCLEAR REACTIONS Nucleon-nucleon interaction, noniterative $2\pi$ exchange, intermediate $\Delta \Delta$ states, transition potentials.

The sums in the potential scattering series are carried out by permitting only one large angle scattering. An early result of Schiff is thus rederived and in the process the connection between it and the recent successful work of Chen is made clear. The amplitudes are convenient to use. The results are applied to the local Laplacian optical potential used in pion-nucleus scattering. The large angle amplitude is very sensitive to three different treatments of the coordinate systems transformation of the $\pi N$ amplitude that have been proposed.

NUCLEAR REACTIONS Large angle potential scattering theory; $\pi$-nucleus optical potentials, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$($\pi$,$\pi$) calculated $\sigma \left(\theta \right)$.

The fourth-order noniterative diagrams involving nucleon-isobar intermediate states and including $\pi$ exchange are calculated in momentum space in the framework of noncovariant perturbation theory. A potential model is presented which includes, apart from these diagrams, suitable one-boson-exchange terms and iterative isobar diagrams involving $N\Delta$- and $\Delta \Delta$-intermediate states, considering $\pi$ and $\rho$ exchange for the transition potentials. Finally, noniterative two-$\pi$-exchange diagrams involving two-nucleon intermediate states are also taken into account. Such a model is able to describe $\mathrm{NN}$ scattering phase shifts satisfactorily. The role of the different parts of the potential model in $\mathrm{NN}$ scattering is studied.

NUCLEAR STRUCTURE Nucleon-nucleon interaction, noniterative $\pi$ exchange, intermediate $N\Delta$ states, crossed-box diagrams, $\mathrm{NN}$ phase shifts.

Levels of ${}_{}{}^{238}{}_{}{}^{}\mathrm{Pu}$ were studied in the ${\beta }^{-}$ decay of ${}_{}{}^{238}{}_{}{}^{}\mathrm{Np}$ and the $\alpha$ decay of ${}_{}{}^{242}{}_{}{}^{}\mathrm{Cm}$. Thirteen $\gamma$-ray transitions were observed for the first time, and additional information about multipolarities and mixing ratios was obtained. An analysis of the $\gamma$-ray branching ratios gives a measure of the $E1\mathrm{}$ transition probabilities between octupolevibrational states and the ground-state band, corresponding to $F_W=4.3\mathrm{}\times {10}^4$ for $\Delta K=1\mathrm{}$ transitions and $F_W=1.5\mathrm{}\times {10}^4$ for $\Delta K=0\mathrm{}$. The latter transitions are three orders of magnitude faster than those that occur in the isotone ${}_{}{}^{236}{}_{}{}^{}\mathrm{U}$, for which $F_W(\Delta K=0)=2.2\mathrm{}\times {10}^7$, from a direct measurement of the half-life of the 0,$1^{-}$ state. Estimates of the hindrance factors for $E1\mathrm{}$ transitions from octupole states in other heavy nuclei are given, and the validity of the calculations on which they are based is discussed.

RADIOACTIVITY ${}_{}{}^{238}{}_{}{}^{}\mathrm{Np}$ [from ${}_{}{}^{237}{}_{}{}^{}\mathrm{Np}$($n$,$\gamma$)] measured $E_{\gamma }$, $I_{\gamma }$, $I_{\mathrm{ce}}$, ICC. ${}_{}{}^{242}{}_{}{}^{}\mathrm{Cm}$ [from ${}_{}{}^{214}{}_{}{}^{}\mathrm{Am}$($n$,$\gamma$)${}_{}{}^{242}{}_{}{}^{}\mathrm{Am}$(${\beta }^{-}$)] measured $E_{\gamma }$,$I_{\gamma }$. ${}_{}{}^{238}{}_{}{}^{}\mathrm{Pu}$ deduced levels, $J^{\pi }$, $t_{\frac{1}{2}}$ (levels). Ge(Li) and Si(Li) detectors.

A method is proposed for solving bound-state equations in the momentum space, which are homogeneous Fredholm integral equations of the second kind. We rewrite such equations in the form of equivalent inhomogeneous Fredhold integral equations of the second kind with "weaker" kernels. Then the usual techniques for solving inhomogeneous integral equations can be used in the present case. A recently proposed method for an iterative Neumann series solution of inhomogeneous equations appears to be natural and very suitable for our purpose. The method is illustrated numerically in the case of the two nucleon bound state with the Yukawa and the Malfliet-Tjon potential and in the case of the $s$-wave three nucleon bound state in the Mitra-Amado model.

NUCLEAR STRUCTURE Bound state equations, equivalent inhomogeneous integrals equations, iterative solution, two-nucleon system with Yukawa-type potential, three-nucleon system in the Mitra-Amado model, wave function calculated in the momentum space.

The properties of hot, dense stellar matter are investigated with a finite temperature nuclear Thomas-Fermi model.

NUCLEAR STRUCTURE Hot stellar matter, equation of state, finite temperature nuclear Thomas-Fermi model.

A momentum-space method is developed for the calculation of three-body terms in the Brueckner-Bethe method for nuclear matter. The method is similar to one used earlier for central $S$-wave potentials. Here we extend it to the full nuclear force, including tensor forces, spin-orbit forces, etc. Furthermore, we show how the method can be used to investigate the possibility of long-range correlations in nuclear matter by summing the generalized ring series. The numerical accuracy obtainable with various mesh parameters and cut-offs in momentum space, and with various truncations of partial-wave expansions, is thoroughly explored. Several angle-average approximations are used, and the estimated numerical accuracy in the three-body cluster energy is 10-15%. The method is applied to a central potential $v_2$, a semirealistic potential $v_6$ (Reid), which has a tensor force, and to the Reid potential, augmented by an interaction that is consistent with empirical scattering phase shifts in two-body partial waves with $j\ge 3$. In all cases the three-body contribution to the energy is correctly given in order of magnitude by ${\kappa }_2{D}_2$, where $D_2$ is the two-body contribution and ${\kappa }_2$ is the usual convergence parameter of the Brueckner-Bethe method. The generalized ring series is found to converge rapidly, indicating that long-range correlations are not very important for the binding energy of nuclear matter. The Reid potential is found to saturate at the right energy but at too high a density.

NUCLEAR STRUCTURE Method for solving Brueckner-Bethe three-body equations in nuclear matter developed and applied to the Reid potential.