Nuclear reactions between two heavy interacting ions with nucleon transfer have been reconsidered. The direct nuclear reaction mechanism is considered. Different reaction processes are considered for single neutron or proton stripping and pickup reactions. The interacting nuclear potential of the transferred nucleon is taken to have the form of the Skyrme-type potential. With this representation for the nuclear potential of the transferred nucleon, an expression for the differential cross section is obtained by using the distorted-wave Born approximation. This expression is applied and considered for the heavy ion reactions with incident heavy ion projectiles ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$, and ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ bombarding the heavy targets ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$, and ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$. The energies of the incident heavy ions have values in the range between 36.0 and 100.0 MeV. Numerical calculations of the differential cross sections are carried out. The theoretically calculated angular distributions are in good agreements with the experimental measurements. Reasonable spectroscopic factors are extracted from the present calculations.

NUCLEAR REACTIONS Nucleon stripping and nucleon pickup induced by 36.0-100.0 MeV ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$, and ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ on ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$, and ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$; calculated $\sigma \left(\theta \right)$. Finite range DWBA calculations, extracted spectroscopic factors.

For nuclear processes involving pions, such as pion production/absorption or exchange currents, it is shown that a natural organization involves adoption of the $\pi \mathrm{NN}$ vertex function $g_{\pi }\left(q^2\right){\gamma }_5{\tau }_{\alpha }$, where $q$ is the pion four-momentum and $g_{\pi }\left({m_{\pi }}^2\right)\simeq 13.4$ is the renormalized pion-nucleon coupling constant. The result is independent of the form and details of any fundamental interaction Lagrangian. The difference between $g_{\pi }\left(q^2\right){\gamma }_5{\tau }_{\alpha }$ and the fully-dressed $\pi \mathrm{NN}$ vertex function contributes to amplitudes involving more bosons, e.g., scattering amplitudes ($\pi N\to \pi N$), production amplitudes ($\pi N\to \pi \pi N$), etc. Such contributions are mediated through either seagull-like terms or $P11\mathrm{}$ intermediate states. It is pointed out that it is neither necessary nor practical to calculate these partial contributions to scattering and production amplitudes. One can always exploit other approaches, theoretical and phenomenological, to make reasonably good models for the full amplitudes. The usual procedure of including the effects of negative energy parts of the nucleon propagator in interaction potentials, exchange currents, etc., is easily included in the present organization. The result is that from scattering amplitudes, etc; the positive energy nucleon poles are deleted but $Z$ graphs are included.

NUCLEAR REACTIONS Theoretical, organization scheme, pion reactions with nuclei, effective $\pi \mathrm{NN}$ vertex.

We have measured the multiplicities of particles emitted in collisions between $\pi \text{'}\mathrm{s}$ and $p\text{'}\mathrm{s}$ of 1.5 to 2.5 GeV/c momentum with He and Ne nuclei in a streamer chamber. The chamber gas served as the target as well as the detecting medium. Because of the low density and $4\pi$ solid angle of the detector, it was possible to detect nuclear fragments with energies less than 5 MeV, and to essentially count all the particles emitted in a collision. Event distributions as a function of track multiplicity were obtained as well as correlated event distributions.

NUCLEAR REACTIONS He (proton or pion, fragments and pions), Ne (proton or pion, fragments and pions), $E=1.5, 2.0, 2.5$ BeV/c; streamer chamber gas used as target with fragment energies as low as 5 MeV. Measured multiplicities and correlations of produced particle types.

Using a liquid deuterium target, 800 MeV quasielastic $\overrightarrow{p}+n$ and $\overrightarrow{p}+p$ analyzing powers were measured over the center-of-momentum angular range 14°-75°. Elastic $\overrightarrow{p}+p$ analyzing powers were measured over the center-of-momentum angular range 10°-47° using a liquid hydrogen target, and elastic $p+p$ differential cross sections were obtained over the angular range 6°-90° using CH and C${\mathrm{H}}_2$ targets. The quasielastic $\overrightarrow{p}+p$ data are in good agreement with existing elastic $\overrightarrow{p}+p$ data, suggesting that the effects of final state interactions and Fermi motion averaging are small at this energy for the range of momentum transfer covered by these data. Results of phase shift analyses are reported, and the amplitudes important to microscopic analysis of 800 MeV $\overrightarrow{p}$+nucleus elastic differential cross section and analyzing power data are discussed. Use of these amplitudes to generate the microscopic Kerman-McManus-Thaler optical potential for 800 MeV $\overrightarrow{p}$+${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ elastic scattering does not resolve the problems encountered previously concerning nuclear size information and poor fits to the analyzing power data.

NUCLEAR REACTIONS ${}_{}{}^2{}_{}{}^{}\mathrm{H}(\overrightarrow{p}, pn)p$, ${}_{}{}^2{}_{}{}^{}\mathrm{H}(\overrightarrow{p}, pp)n$, ${}_{}{}^1{}_{}{}^{}\mathrm{H}(\overrightarrow{p}, p)$, ${}_{}{}^1{}_{}{}^{}\mathrm{H}(p, p)$; $E_{p,\mathrm{inc}}=800\mathrm{}$ MeV; measured $p+p$ elastic $\frac{d\sigma }{d\Omega }$ for $6°\le {\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}\le 90°$; measured $\overrightarrow{p}+p$ elastic $A_y\left(\theta \right)$ for $10°\le {\theta }_{\mathrm{c}.\mathrm{m}}\le 47°$; measured $\overrightarrow{p}+p$ and $\overrightarrow{p}+n$ quasielastic $A_y\left(\theta \right)$ for $14°\le {\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}\le 75°$; CH, C${\mathrm{H}}_2$, liquid hydrogen and liquid deuterium targets; two arm coincidence for quasielastic; phase shift analyses; microscopic (KMT) optical model calculations for 800 MeV $\overrightarrow{p}$+${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$.

Measurements have been made of the attenuation cross sections for both ${\pi }^{+}$ and ${\pi }^{-}$ mesons on Al, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, Cu, Sn, Ho, and Pb nuclei. The measurements were made at several energies between 114 and 215 MeV. A new method of data analysis has been used to extract both the real and the imaginary parts of a Coulomb-distorted forward scattering amplitude $f_N\mathrm{}\left(0\right)\mathrm{}$. Insight into the nature of $f_N\mathrm{}\left(0\right)\mathrm{}$ is obtained by the comparison of experimental data with theoretical values calculated from a simple absorption model. This comparison demonstrates that much of the observed rotation of the forward amplitude, when plotted on an Argand diagram, can be attributed to the Coulomb phase contained in $f_N\mathrm{}\left(0\right)\mathrm{}$. Comparison is also made with results of similar experiments. Although the present results are in general agreement with previously published ones, some differences are noted for the heavier elements.

NUCLEAR REACTIONS Measured pion forward scattering amplitudes; Al, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, Cu, Sn, Ho, and Pb; $E=114-215\mathrm{}$ MeV; strong absorption model.

Field theoretic aspects of the pion field interacting with a nucleus are investigated. The quantum field nature of the pion is shown to be most simply and fundamentally incorporated into multiple scattering theory through the Klein-Gordon equation. This is accomplished so that crossing symmetry of the scattering amplitude is manifest and can be maintained without recourse to nonlinear equations. We give specific examples of calculating the first and second order optical potential in the static approximation. Our approach provides a clean separation between the energy and momentum dependence of the pion-nucleon amplitude and does not have the strong momentum cutoffs or the spurious reactive content of other approaches. An off-shell extrapolation of the pion-nucleon amplitude in terms of the four-momenta is required for the evaluation of second and higher order contributions to the optical potential. We discuss the conditions under which our static field theory can be regarded as a limit of a theory which allows for nucleon recoil.

NUCLEAR REACTIONS Pion-nucleus elastic scattering, optical potential, field theoretic effects, crossing symmetry, off-shell behavior of two-body amplitudes.

A universal form for the dependence of the second-order pion-nuclear optical potential on the nuclear and pionic isospin and on the densities $\rho$ and $\Delta \rho$ is derived, where $\rho$ is the total density and $\Delta \rho$ is the valence neutron density. The result is characterized by five complex parameters for each partial wave channel contributing to the optical potential. Our result applies to scattering in the vicinity of the (3,3) resonance, and the parameters may be most cleanly determined phenomenologically by applying the theory to elastic, and single- and double-charge-exchange data for medium to heavy weight $J=0\mathrm{}$, spherical nuclei. The relationship between the parameters and a microscopic cluster decomposition of the optical potential is explored. The parameters are calculated theoretically for selected second-order processes to obtian a first orientation to the magnitude of the terms. The results show, in particular, that large contributions to double charge exchange arise from nonanalog intermediate nuclear states and that these contributions have a characteristic isospin dependence which is different from that found in the simple models previously studied.

NUCLEAR REACTIONS Scattering theory for elastic, and single- and double-charge-exchange to IAS in the region of the $p_{33}$ resonance. Second-order effects.

Coherent ${\pi }^0$ photoproduction from nuclei is calculated in the $\Delta$-hole framework. Important background production terms are included, and a comparison with data is presented. Sensitivity to various aspects of the dynamics, such as recoil and the $\Delta$ spreading potential, are examined.

NUCLEAR REACTIONS ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(\gamma , {\pi }^0)$ calculated in $\Delta$-hole formalism and compared with data for $E_{\gamma }=200\mathrm{} \mathrm{to} 400$ MeV.

Taking the meson-nucleon system below threshold as an example, it is shown that it can formally be described by nucleonic degrees of freedom alone. In the Fock space of nucleons one has eigenvalue equations with different optional versions of effective interactions. The Hermitian version explicitly exhibits full relativistic invariance. The non-Hermitian form can be decomposed into one, two, three,..., particle operators. The latter requires the solution of the vacuum, one, two,..., nucleon problems. The techniques proposed are known from coupled cluster many body theory and do not invoke perturbation theory.

NUCLEAR STRUCTURE Nucleon-nucleon interaction, meson exchange.

The pion-induced quasifree nucleon knockout and charge-exchange reactions are shown to have a strong sensitivity to the difference between neutron and proton densities at the nuclear surface. Their possible use as a probe of the neutron densities is discussed.

NUCLEAR REACTIONS $\frac{\sigma {({\pi }^{-}, {\pi }^{-}n)}_{\mathrm{qf}}}{\sigma {({\pi }^{+}, {\pi }^{+}p)}_{\mathrm{qf}}}$, $\frac{\sigma {({\pi }^{+}, {\pi }^{0}p)}_{\mathrm{qf}}}{\sigma {({\pi }^{+}, {\pi }^{+}p)}_{\mathrm{qf}}}$; calculated sensitivity to the neutron density.

The nonresonant interference effects in the (3,3) channel proposed by Olsson are incorporated into a full amplitude that describes photopion production from a single nucleon. The reactions $p(\gamma , {\pi }^{+})n$, $n(\gamma , {\pi }^{-})p$, and $p(\gamma , {\pi }^0)p$ are all well described by this amplitude. The charged pion production cross sections obtained with Olsson's effects are similar to those calculated by Blomqvist and Laget, but the new amplitude has the added feature of also describing neutral pion production. Asymmetry parameters calculated with the new and Blomqvist and Laget amplitudes are compared with experiment for the cases where either the incident photon, the target, or final state baryon are polarized; the new photopion production amplitude provides a good description of these experiments.

NUCLEAR REACTIONS Photopion production amplitude, ($\gamma , \pi$) cross sections, polarization calculations.

The ($p, d$) reaction at intermediate energies is described in terms of the free $\mathrm{pd}$ scattering at backward angles: The formalism is given in the distorted wave approximation. The general features of the cross section, like the angular distribution, the variation with incident energy, and the distribution with respect to momentum transfer, are well accounted for by the predictions of the model.

NUCLEAR REACTIONS Quasideuteron, ($p, d$) reaction, intermediate energies, distorted waves.

The total $K$-shell ionization probability accompanying the ${\beta }^{-}$ decay of ${}_{}{}^{60}{}_{}{}^{}\mathrm{Co}$, $P_K\left({\beta }^{-}\right)$, was determined from singles and coincidence $K$ x-ray spectra of Ni to be (14.2±1.4)×${10}^{-4\mathrm{}}$ using a high resolution Si(Li) photon Spectrometer. This result is in good agreement with the recent theoretical work of Law and Suzuki.

RADIOACTIVITY Measured Ni $K$ x rays in singles and coin in ${\beta }^{-}$ decay of ${}_{}{}^{60}{}_{}{}^{}\mathrm{Co}$; deduced $K$-ionization probability.

Self-consistent random-phase approximation calculations with SIII, SkM*, and Sks forces are performed in ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. Collective compression modes with ${\lambda }^{\pi }=1^{-} \mathrm{and} 2^{+}$ are identified in the response function. Their energies are studied in connection with the compressibility properties of the effective interactions. The selectivity of various probes in exciting compression modes is discussed, as well as the sum rules associated with these probes.

NUCLEAR STRUCTURE ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$, ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$; calculated energies, strengths, transition densities for ${\lambda }^{\pi }=1^{-}, 2^{+}$ compression modes. RPA method, Skyrme-type forces. Sum rules.

Muonic x-ray spectra have been measured for ${}_{}{}^{199}{}_{}{}^{}\mathrm{Hg}$ and ${}_{}{}^{200}{}_{}{}^{}\mathrm{Hg}$. From the data we have determined model-independent charge radii and isomer shifts of certain excited nuclear states and have inferred spectroscopic quadrupole moments of excited states for both isotopes. The quadrupole moment of the lowest $\frac{5}{2^{-}}$ state in ${}_{}{}^{199}{}_{}{}^{}\mathrm{Hg}$ is found to be positive, in agreement with previous muonic-atom data but in disagreement with a recent Mössbauer study. $B\left(E2\mathrm{}\right)\mathrm{}$ values of low-lying excited states have been determined for ${}_{}{}^{199}{}_{}{}^{}\mathrm{Hg}$. An $E1\mathrm{}$ muonic-nuclear resonance has been discovered in ${}_{}{}^{200}{}_{}{}^{}\mathrm{Hg}$.

NUCLEAR STRUCTURE ${}_{}{}^{199,200}{}_{}{}^{}\mathrm{Hg}$; measured muonic x-ray spectra; deduced monopole and quadrupole charge parameters, isomer shifts.

We explore the dependence of the magnetic and charge form factors of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ on nucleon structure models and $\mathrm{NN}$ interaction models within the traditional framework of nucleons, isobars, and mesons. We utilize wave functions which incorporate the effect of a genuine three-body force, and include contributions to the nuclear current from a variety of mesonic exchange and isobaric processes. The importance of the high momentum transfer region as a source of information on short-range processes in the nuclear medium is reiterated by our results.

NUCLEAR STRUCTURE Trinucleon systems; electromagnetic form factors; three-body force and mesonic exchange currents.

Partial decay widths of the lowest $T=2\mathrm{}$ state of ${}_{}{}^8{}_{}{}^{}\mathrm{Be}$ are calculated using ${\mathrm{}\left(1p\right)\mathrm{}}^4$ shell-model wave functions. Agreement with experiment is improved if there is, in addition to the Coulomb force, a charge-dependent component of the nuclear force with magnitude close to that suggested by nucleon-nucleon scattering data. The calculations are able to account for the empirical values of the isobaric multiplet mass equation $b$ and $c$ coefficients for $A=8\mathrm{}$, $T=2\mathrm{}$, and provide an explanation of why the quadratic form of the isobaric multiplet mass equation is inadequate for this multiplet.

NUCLEAR STRUCTURE Isospin mixing in mass 8, charge-dependent forces, IMME coefficients.

Total binding energies for systems of $N$ neutrons and $Z$ protons near $N=Z=8\mathrm{}$ are obtained for the harmonic oscillator Hamiltonian via moment methods and are compared with the exact results. We examine the accuracy of employing only the few lowest moments of the eigenvalue density to predict the ground state (g.s.) energy as a function of several ingredients in the method. We find systematic errors are strongly dependent on the scheme chosen for truncating the single particle space and rather weakly dependent on the size of the model space in many cases of interest. Two functional forms approximating the exact eigenvalue distribution, the Gram-Charlier series and the Weibull distribution, give results of comparable accuracy in cases where three moments are employed. Best overall accuracy is obtained using the traditional truncation scheme where all single particle states below a fixed energy are retained. For this truncation scheme, the distribution of energy eigenvalues is significantly skewed. However, the Gaussian approximation, which requires only the two lowest moments, yields one of the better estimates of the g.s. energy. This is true for both the total distribution of eigenvalues and for the distribution restricted to states of specific total angular momentum. The absolute error in the g.s. energy estimate is generally found to grow with increasing model space size; however, most of the error is systematic, and the relative binding energies of adjacent nuclei are found to be predicted with considerably greater accuracy. Isolation of these systematic errors plus demonstration of small errors in relative energies enhances the prospects for obtaining reliable total nuclear binding energies from realistic (no-core) Hamiltonians using moment methods.

NUCLEAR STRUCTURE Binding energies from moment methods; spectral properties of harmonic oscillator Hamiltonian; efficacy of moment methods versus truncation scheme and model space size.

We present a formal derivation of the exact dynamics of the one-body density matrix. Its essential ingredients are shown to be the following: (a) a mean field unitary time evolution; (b) irreducible nonunitary corrections to the unitary evolution (collision effects); and (c) effects due to the time evolution of initial state correlation [which contribute to both (a) and (b)]. In the weak coupling limit the collision effects give rise to a term of Boltzmann form. A qualitative discussion of the importance of collision effects for the expectation values of one-body operators and a quantitative illustration in the framework of an exactly soluble model are given. In this case one finds large nonunitary contributions.

NUCLEAR STRUCTURE Exact microscopic description of the time evolution of the one body density matrix.

A three-band-mixing rotation-vibration description of Faessler et al., corrected to include anharmonicity of the classical beta and gamma vibrations of the nuclear core by assuming different mass parameters for the ground, beta, and gamma vibrational states, has been applied to the ${}_{}{}^{150,152,154}{}_{}{}^{}\mathrm{Sm}$, ${}_{}{}^{154}{}_{}{}^{}\mathrm{Gd}$, ${}_{}{}^{156}{}_{}{}^{}\mathrm{Dy}$, and ${}_{}{}^{194}{}_{}{}^{}\mathrm{Pt}$ nuclei. A comparison of the present results with older three-band mixing calculations using three parameter and five parameter descriptions has been made. Contrary to the older predictions, an excellent reproduction of the observed energy levels below back bending is obtained for all three bands. The agreement between the theoretical and experimental $B\left(E2\mathrm{}\right)\mathrm{}$ values and branching ratios improves remarkably, especially in ${}_{}{}^{150}{}_{}{}^{}\mathrm{Sm}$ and ${}_{}{}^{194}{}_{}{}^{}\mathrm{Pt}$ where the mass parameters for beta and gamma vibrations are nearly double their rotation counterparts. A discussion has been made.

NUCLEAR STRUCTURE ${}_{}{}^{150,152,154}{}_{}{}^{}\mathrm{Sm}$, ${}_{}{}^{154}{}_{}{}^{}\mathrm{Gd}$, ${}_{}{}^{156}{}_{}{}^{}\mathrm{Dy}$, ${}_{}{}^{194}{}_{}{}^{}\mathrm{Pt}$; calculated energy levels $B\left(E2\mathrm{}\right)\mathrm{}$ and branching ratios, rotation vibration description anharmonicity, mass parameters.