Relative measurements of ${\pi }^0$ photoproduction yields have been performed on hydrogen, deuterium, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, in the region of 1 to 10 MeV above threshold. A simplified distorted-wave impulse approximation model of the four reactions is described; it leads to an overall understanding of the results. Large rescattering effects are brought to evidence in deuterium and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, making the extraction of precise values for the dipole photoproduction amplitudes $E_{0^{+}}$ on nucleons strongly dependent on the theoretical description of the processes.

NUCLEAR REACTIONS ($\gamma$,${\pi }^0$), ${}_{}{}^1{}_{}{}^{}\mathrm{H}$, ${}_{}{}^2{}_{}{}^{}\mathrm{H}$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ targets; measured reaction yields, $E_{{\pi }^0}=1-10\mathrm{}$ MeV.

Relativistic formulas for the deuteron electromagnetic form factors are calculated in the impulse approximation retaining terms to all orders in $\frac{Q^2}{M^2}\cong {\left(\frac{v}{c}\right)}^2$. The formulas are given as double integrals over the deuteron wave functions in momentum space, and hence can be evaluated for any deuteron model. We evaluate these formulas numerically for 9 different deuteron models: Reid soft core, two Lomon-Feshbach models, three Holinde-Machleidt models, and three four-component relativistic models. All of the models give results for the $A$ structure function considerably below the experimental results; the effect of the relativistic treatment is to reduce the size of $A$ by a factor of 2 to 5 at $Q^2$ of 100 ${\mathrm{fm}}^{-2\mathrm{}}$ over what it would be in the nonrelativistic approximation. We discuss briefly the role of exchange currents; the pair terms are included in our calculation in a completely consistent manner, but the explicit $\rho \pi \gamma$ contributions need to be calculated relativistically. We discuss in some detail the sensitivity of our calculation to the almost unknown neutron electric form factor, observing that a $G_{\mathrm{En}}$ roughly twice $G_{\mathrm{Ep}}$ in the region of $Q^2=100\mathrm{}$ ${\mathrm{fm}}^{-2\mathrm{}}$ would enable us to fit the data even without any $\rho \pi \gamma$ contributions. We discuss the high $Q^2$ limits of our formulas, obtaining the result that the form factor falls one power of $Q^2$ faster than that predicted by the dimensional-scaling-quark model. We also study the low $Q^2$ limits and give explicit formulas for the corrections to the deuteron magnetic and quadrupole moments.

NUCLEAR STRUCTURE $d$ calculated relativistic electromagnetic form factors, recoil tensor polarization, and relativistic corrections to ${\mu }_d$ and $Q_d$.

Measurements have been made of the differential cross section $\frac{d^2\sigma }{d\Omega \mathrm{dE}}$ for the scattering of ${\pi }^{\pm }$ from ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{40,44,48}{}_{}{}^{}\mathrm{Ca}$ in the energy region corresponding to quasielastic scattering. Data were taken at incident energies and laboratory angles of 180 MeV, 60°, and 290 MeV, 60° and 120°. The results are compared to a free pion-nucleon cross-section model and to a model based on pion scattering from a Fermi gas of nucleons, which incorporates free pion-nucleon cross sections. Monte Carlo methods were used for the second model, and both single scattering and multiple scattering were allowed. Several qualitative features of the data are explained by the multiple scattering calculation, but not by the free cross-section model or the single scattering model.

NUCLEAR REACTIONS Quasielastic scattering of ${\pi }^{\pm }$ from ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{40,44,48}{}_{}{}^{}\mathrm{Ca}$ at 291 MeV, 60° and 120°, and 180 MeV, 60°. Model of data based on Monte Carlo calculation of scattering from Fermi gas of nucleons, with multiple scattering, using free pion-nucleon cross sections calculated from phase shifts.

The reaction ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$($\gamma$,${\pi }^{-}$)${}_{}{}^{14}{}_{}{}^{}\mathrm{O}_{\mathrm{g}.\mathrm{s}.\mathrm{}}^{}{}_{}{}^{}$ is calculated within the framework of the distorted wave impulse approximation and the results compared to activation measurements. Investigations are made of the energy dependence of the pion momentum dependent terms in the single particle amplitude and the effects of the nuclear wave function and pion optical potential on total cross sections.

NUCLEAR REACTION ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$($\gamma$,${\pi }^{-}$)${}_{}{}^{14}{}_{}{}^{}\mathrm{O}$. Activation method. $E_0=150-700\mathrm{}$ MeV; measured ${\sigma }_q$, deduced ${\sigma }_k$; calculated ${\sigma }_k$. Ge(Li) detector.

The optical model of antiproton-proton scattering is examined critically. We show that the addition of an attractive real part to the annihilation potential allows one to reduce the imaginary part and to improve the fit to the data. However, the absorptive component must be still rather strong and also have a fairly large range. Such features are difficult to understand in terms of naive direct channel meson exchange processes. We confirm also in the local optical model that no narrow structures can survive annihilation, unless they lie very close to threshold. The optical model we propose, with the realistic Paris potential for the long range $t$-channel part, provides an effective description of background $\overline{N}N$ scattering.

NUCLEAR REACTIONS Analysis of elastic, charge exchange and inelastic $p\overline{p}$ cross sections in optical model; discussion of theoretical and phenomenological annihilation potential.

An ambiguity in the kinematic transformation of the pion-nucleon scattering amplitude from the pion-nucleus center-of-mass frame to the pion-nucleon center-of-mass frame is removed by (1) the requirement of time-reversal invariance and (2) the requirement that the relative momentum be uniquely defined. The first-order optical potential is obtained by an approximate evaluation of the target ground state matrix element of the transformed pion-nucleon amplitude. Our procedure results in elastic differential cross sections that are significantly different from those obtained using previous kinematic transformations. Terms in the transformed two-body amplitudes proportional to the total three momentum squared as prescribed by relativistic potential theory are found to have negligible effects on elastic pion-nucleus scattering.

NUCLEAR REACTIONS Elastic pion-nucleus scattering, kinematics, time-reversal symmetry.

The Feshbach-Villars Hamiltonian formulation of the Klein-Gordon equation is used as the basis for a scattering theory for relativistic, spin-zero, particles. Time dependent and time independent scattering theories are developed. The time independent theory is used as the framework for a separable potential model for $\pi N$ elastic scattering in $P$ waves. This potential leads to a $\pi N$ $T$ matrix which has the right and left hand cuts associated with two-particle unitarity and crossing, respectively, as well as the direct and crossed nucleon poles with the proper residues. The effects of nucleon recoil are included. With a particular choice of the form factors in the potential, the Chew-Low $T$ matrix is reproduced.

NUCLEAR REACTIONS Relativistic scattering theory, pion-nucleon $T$ matrix.

Analyses of 0.8 and 1 GeV $p$+${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ elastic angular distribution data have obtained neutron-proton root-mean-square radius differences ($\Delta r_{\mathrm{np}}$) which are not consistent. Therefore, the 0.8 GeV experiment was repeated using a high resolution spectrometer. The new higher precision data are consistent with the older data, apart from a 15% overall normalization difference. A second order Kerman-McManus-Thaler optical model analysis of the new data, using a model-independent neutron density, yields $\Delta r_{\mathrm{np}}=0.14\mathrm{}\pm 0.04$ fm, in good agreement with the most recent result obtained (0.16±0.05 fm) from a similar analysis of the older 0.8 GeV data. In addition, the elastic angular distribution was extended to 42.5° center of mass in order to explore the momentum transfer region from 3.5 to 5.3 ${\mathrm{fm}}^{-1\mathrm{}}$. Although the familiar diffraction pattern persists to 42.5°, it was not possible within the framework of our application of the Kerman-McManus-Thaler optical model to fit the data even qualitatively at the larger momentum transfers.

NUCLEAR REACTIONS ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$($p$,$p$), $E=0.8\mathrm{}$ GeV, measured $\sigma \left(\theta \right)$; enriched target; resolution ≃ 100 keV, ${\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}=2.5\mathrm{}° \mathrm{to} 42.5°$. Microscopic optical model analysis using KMT potential; deduced $\Delta {\mathcal{r}}_{\mathrm{np}}$; error analysis and comparison with other results.

We have measured the absorption cross section for positive pions in carbon at four incident energies between 91 and 143 MeV. A detector which was sensitive to the total energy deposited in the target was used to identify pion absorption events. The cross section determined from these measurements rises slowly with increasing energy, supporting some of the recent theoretical predictions in this energy region.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$; ${\pi }^{+}$ absorption, measured $\sigma \left(E_{\pi }\right)$.

The asymptotic form of the hadronic mass spectrum, beyond the region where individual resonances can be identified, is a fundamental property of matter, interesting in both particle physics and cosmology. We investigate the possibility of discovering its form through the properties of hot hadronic matter such as might be produced in ultrarelativistic nuclear collisions. We find that at collision energies in the tens of GeV per nucleon in the c.m., a sensitivity of certain measurements to the underlying hadronic spectrum can be expected.

NUCLEAR REACTIONS Hadronic spectrum, theory of very high energy reactions, possible inference for hadronic spectrum.

Low-energy kaon-nucleus interaction has been considered in the framework of multiple scattering theory as formulated by Watson and by Kerman, McManus, and Thaler. A kaon-nucleus optical potential of the shape of nuclear density is shown to follow from theory under the assumption that the nuclear excited states may be neglected and that the range of the underlying microscopic $\overline{K}N$ interaction is small in comparison with the nuclear radius. The depth of the effective potential is a nonlinear function of the $\overline{K}N$ scattering lengths and depends upon a single parameter related to the unknown range of the $\overline{K}N$ interaction. This parameter has been adjusted to the available kaonic atom data. The resulting potential has been used to evaluate the kaonic atom level shifts and widths and the calculated quantities are compared with experiment.

NUCLEAR REACTIONS Optical potential derived and applied to evaluate kaonic atoms level shifts.

We introduce a new formalism for treating the internal bremsstrahlung amplitude, in particular for $\mathrm{ns}$ radiative capture. The formalism is fully relativistic and permits a simple and exact numerical calculation for a large class of potentials. The results for $1s$ and $2s$ radiative capture are presented and compared with earlier results.

RADIOACTIVITY Calculation of IB amplitude in $s$-electron capture.

The directional correlation of coincident $\gamma$ transitions in ${}_{}{}^{84}{}_{}{}^{}\mathrm{Kr}$ have been measured following the decay of 32 min ${}_{}{}^{84}{}_{}{}^{}\mathrm{Br}$ using a Ge(Li)-NaI(Tl) spectrometer. Measurements have been carried out for ten gamma cascades, resulting in the following multipole mixing ratios: $\delta \mathrm{}\left(605\right)=+0.01\mathrm{}\pm 0.01$, $\delta \mathrm{}\left(736\right)=-0.07\mathrm{}\pm 0.01$, $\delta \mathrm{}\left(802\right)=-0.04\mathrm{}\pm 0.01$, $\delta \mathrm{}\left(987\right)=-0.08\mathrm{}\pm 0.01$, $\delta \mathrm{}\left(1016\right)=+0.80\mathrm{}\pm 0.03$, $\delta \mathrm{}\left(1741\right)=-1.05\mathrm{}\pm 0.07$, $\delta \mathrm{}\left(1877\right)=-0.07\mathrm{}\pm 0.03$, and $\delta \mathrm{}\left(2484\right)=+0.01\mathrm{}\pm 0.01$. These data permitted assignments of spins to the levels at 2345 ($4^{+}$), 2623 ($2^{+}$), 2759 ($2^{\pm }$), 3082 ($3^{\pm }$), 3366 keV ($1^{\pm }$) and confirmed previous assignments for the 1898 ($2^{+}$), 2095 ($4^{+}$), and 2700 keV ($3^{-}$) levels. A comparison of some properties of the $2_2^{+}$ and $2_1^{+}$ states in ${}_{}{}^{84,82,80}{}_{}{}^{}\mathrm{Kr}$ and in other even-even nuclei (Ru, Pd, and Cd) is also presented.

RADIOACTIVITY ${}_{}{}^{84}{}_{}{}^{}\mathrm{Br}$ from fission of U; measured $\gamma \gamma \left(\theta \right)$. ${}_{}{}^{84}{}_{}{}^{}\mathrm{Kr}$ levels deduced $J$, $\pi$, $\delta$.

The observed inhibition of $M4\mathrm{}$ transitions in $A\sim 90$ nuclei has represented a long standing theoretical problem. In particular by calculating first- and second-order configuration mixing contributions to the inhibited $M4\mathrm{}$ lifetimes of ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$ and ${}_{}{}^{87}{}_{}{}^{}\mathrm{Sr}$, it is found that the first-order perturbative treatment of the residual interaction usually used in shell-model calculations is unjustified in this case. Using random-phase approximation techniques, the renormalization effects of collective ("giant") $M4\mathrm{}$ resonances in ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}$ on the low energy $M4\mathrm{}$ transitions in ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$ and ${}_{}{}^{87}{}_{}{}^{}\mathrm{Sr}$ are investigated. It is concluded that the observed retardation of $M4\mathrm{}$ lifetimes in these nuclei is consistent with the manifestation of nuclear spin polarization.

NUCLEAR STRUCTURE Isomeric states; $M4\mathrm{}$ lifetimes; spin polarization in $A\sim 90$ nuclei.

The dependence upon momentum $k$ and upon energy $E$ of the self-energy of a dilute Fermi gas is studied up to terms of order ${\left(k_{F}c\right)}^2$, where $k_F$ denotes the Fermi momentum and $c$ is the positive scattering length. Algebraic expressions are derived for the imaginary part $W(k;E)\mathrm{}$ of the self-energy in the whole ($k$,$E$) plane. They are compared with a conjecture recently made by Orland and Schaeffer in their analysis of single-particle states in nuclei. The contributions of core polarization and of ground state correlations to the real part $V(k;E)\mathrm{}$ of the self-energy are calculated with the help of subtracted dispersion relations which connect them with $W(k;E^{\prime })$. Algebraic expressions are derived for the momentum distribution in the correlated ground state. It is shown that the effective mass of a quasiparticle with momentum $k$ is equal to the bare particle mass at $k=0\mathrm{}$ and reaches a local maximum for $k$ close to $k_F$. This maximum is ascribed to the dependence of $V(k;E)\mathrm{}$ upon $E$, which is described in terms of an $E$ mass. We compute the contributions of core polarization and of ground state correlations to this $E$ mass. The dependence of $V(k;E)\mathrm{}$ upon $k$ reflects the nonlocality of the self-energy. It is characterized by a $k$ mass that we also calculate. These results shed light on some nuclear matter properties and on the meaningfulness and limitation of nuclear matter calculations that have recently been performed in the framework of the Brueckner-Hartree-Fock approximation.

NUCLEAR STRUCTURE Effective mass near the Fermi surface in dilute Fermi gas model.

A self-consistent approach allowing the introduction of pairing into a comprehensive study of the bulk as well as the structure properties of nuclei is presented. It is emphasized that the density-dependent effective force used in the calculations reported here does permit the extraction of the mean field and the pairing field in the framework of the Bogolyubov theory. First, a brief review of Hartree-Fock-Bogolyubov formalism with density-dependent interactions is presented. Then the derivation of the effective interaction is explained and some details concerning the nuclear matter properties are given. Finally, we report the studies on spherical nuclei with special reference to the pairing properties. In order to demonstrate the versatility of our approach a comprehensive study of various nuclear properties is given. In view of the abundance of results obtained with our approach we plan to report the results on the deformed nuclei in a future publication.

NUCLEAR STRUCTURE Density-dependent Hartree-Fock-Bogolyubov (DDHFB) approximation applied to the calculations of the structure of spherical nuclei: binding energies, pairing correlations, density distributions, magnetic form factors, and quasiparticle spectra.

A general method for a microscopic description of nuclear dynamical problems is discussed. The method is based on a functional integral representation for the many-body time evolution operator $U(t_f,t_i)$. In the stationary phase limit, a time-dependent mean-field approximation for the matrix elements of $U$ is obtained. Using standard procedures this allows for extraction of quantum mechanical information about bound states, tunneling, or scattering phenomena in a many-nucleon system. The approximation represents a natural generalization of the time-dependent Hartree-Fock method.

NUCLEAR STRUCTURE, NUCLEAR REACTIONS derived mean-field approximation for matrix elements of $\exp \mathrm{}(-iHt)\mathrm{}$ from exact functional integral; discussed relation to static HF, TDHF, and scattering calculations.

A theory is presented in which approximations to quantum observables are obtained by applying the stationary-phase approximation to an exact functional integral representation of the many-body evolution operator. The requirement that the leading correction to the stationary-phase approximation vanish leads to a time-dependent Hartree-Fock mean field. Application of the theory to the Fourier transform of the trace of the evolution operator and the study of its poles yields quantized bound states with large amplitude. The theory is shown to reproduce the familiar static Hartree-Fock and random-phase approximations in the appropriate limits and yields an excellent approximation to the entire spectrum of the exactly solvable Lipkin model.

NUCLEAR STRUCTURE Derivation of time-dependent mean-field theory from functional integral representation. Quantum theory of large amplitude collective motion. Application to Lipkin model.

We develop a systematic approach to the calculation of self-consistency effects in core plus valence nucleon systems. A detailed calculation of the effective one-body Hamiltonian for $A=17\mathrm{}$ in an $11\hslash \Omega$ model space is readily extrapolated to a $20\hslash \Omega$ model space which is sufficient to develop accurate tails for the single-particle wave functions. The effective one-body interaction is found using a Brillouin-Wigner type perturbation theory which eliminates folded diagrams and leads to a manifestly Hermitian interaction. A renormalized Brueckner calculation is performed for $A=16\mathrm{}$ and the results are employed in a shell-model study of $A=17\mathrm{}$. The self-consistent results still have a weak dependence on the initial unperturbed Hamiltonian. However, we find a single unperturbed Hamiltonian which yields a reasonable binding energy for $A=16\mathrm{}$ and, except for a weak spin-orbit splitting, reasonable results for the lowest states in the $A=17\mathrm{}$ system. This agreement is important for continued valence $s-d$ shell studies.

NUCLEAR STRUCTURE Brueckner theory, self-consistency effects, ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ spectra and wave functions, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ properties.

We report here the results of the calculation of total muon capture rates (${\Lambda }_{\mu \mathrm{c}}$) in Ne isotopes using Hartree-Fock wave functions. These wave functions are generated from (a) a phenomenological set of interaction matrix elements and (b) a microscopic set derived from the Reid soft core potential. Satisfactory agreement with the experiment both for the spectra of and the ${\Lambda }_{\mu \mathrm{c}}$ in ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ is obtained. The trend of the variation of ${\Lambda }_{\mu \mathrm{c}}$ in Ne isotopes as predicted by the empirical formulas is explained by incorporating the oblate admixture in the ground states of ${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}$ and ${}_{}{}^{24}{}_{}{}^{}\mathrm{Ne}$.

NUCLEAR STRUCTURE Hartree-Fock (HF), projected HF, energy spectra, total muon capture rates, Ne isotopes.