Scattering from the $M3\mathrm{}$, $M5\mathrm{}$, and $M7\mathrm{}$ moments of the ground state of ${}_{}{}^{51}{}_{}{}^{}\mathrm{V}$ has been observed by a 180° scattering experiment of electrons. The observed $M3\mathrm{}$ and $M5\mathrm{}$ form factors are much smaller than those expected from the single-particle model. The features are reasonably reproduced by the calculation which takes into account the effect of the configuration mixing including the polarization of the ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ core.

NUCLEAR REACTIONS ${}_{}{}^{51}{}_{}{}^{}\mathrm{V}\mathrm{}(e,e)\mathrm{}$ $E=80.84\mathrm{}-229$ MeV, $\theta =180\mathrm{}°$, measured $\sigma (E,180\mathrm{}°)$; deduced magnetic moment form factor.

The problem of a mathematically consistent description of reactions involving composite nuclei is reexamined in the case where the individual nuclear states are given in terms of Slater determinants constructed with single-particle orbitals. The relationship between the single projection method of Peierls and Yoccoz and the double projection method of Peierls and Thouless is clarified. The general scattering functions are then constructed, and a set of scattering equations of the Griffin-Hill-Wheeler type is derived, in which the Hamiltonian and the overlap kernels can be evaluated directly in the independent particle coordinate representation. Proper boundary conditions are specified by the procedure of prediagonalization. To simplify the problem to basic essentials, we consider in this paper the motion of a nucleus in an external potential. The specially simple cases in which the Slater determinants factorize into the internal and external parts are considered as an illustration. The distortion of a nucleus during the scattering process is incorporated here by an explicit dependence of the single-particle orbitals of the Slater determinants on the generator coordinate and momentum. The double projection method is found to be naturally adaptable for this generalization.

NUCLEAR REACTIONS Generator coordinate methods potential scattering; distortion effects.

The generator coordinate formulation of the single nucleus scattering by an external potential presented in the preceding paper is generalized here to the nucleus-nucleus scattering, in which the complete antisymmetrization of all nucleons involved is explicitly carried out and the correct internal states are extracted by the double-projection method of Peierls and Thouless. General distortion effects are incorporated, where the single nucleon orbitals may depend on the relative distance and relative momentum generator coordinates of two nuclei. The special case of nuclear molecular orbitals is also considered. The connection between the distorted orbitals and a restricted time-dependent Hartree-Fock procedure is clarified.

NUCLEAR REACTIONS Generator coordinate methods; nucleus-nucleus scattering; distortion effects.

We investigate a barrier penetration model for the sub-Coulomb fusion of light ion systems and derive an analytic formula for the cross section. The validity of the model is checked against results based on a modified proximity potential which reproduces the fusion cross section at energies above the Coulomb barrier. The meaning of the parameters defining the model as well as the extrapolation of the formula at very low energies are discussed.

NUCLEAR REACTIONS Analytic expression of fusion cross section in a barrier penetration model.

Fragments produced in the interactions of 100 MeV/nucleon ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$ projectiles with a uranium target have been measured at energies from 10 to 130 MeV/nucleon at angles from 10° to 170°. Nuclei with charge $5\le Z\le 10$ were observed. The data can roughly be divided into two groups, corresponding to central and peripheral collisions. The central collision data can be fitted with a thermal model that uses two recoiling sources. The source velocities are consistent with the predictions of the fireball and target explosion models, but the source temperatures inferred from the data are higher than one would expect on the basis of energy and momentum conservation. These results are similar to those obtained in previous studies at beam energies of 400 and 500 MeV/nucleon. The data also follow the pattern of the universal curve of invariant cross section vs momentum observed at higher beam energies by Price et al. The projectile fragmentation data are also fitted by two thermal sources. There are indications that the observed temperatures are higher than one would expect on the basis of other projectile fragmentation studies. From this broad survey we conclude that although much of the spectrum can be described by falling exponentials in energy in the emitting frames, the observed spectrum is due to nonequilibrium sources since the temperatures derived from the slopes of the exponentials are greater than those we predict.

NUCLEAR REACTIONS U(${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$, B), U(${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$, C), U(${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$, N), U(${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$, O), U(${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$, F), U(${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$, Ne), $E=100\mathrm{}$ MeV/nucleon; measured $\frac{d^2\sigma }{d\Omega \mathrm{dE}}(E;\theta )$.

Carbon + carbon fusion-evaporation reactions have been studied in two series of measurements: (i) The system ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ has been studied for laboratoryy bombarding energies betwen 30 and 60 MeV in 5-MeV steps. Angular distributions for all residual nuclei have been measured and the corresponding yields versus bombarding energy are compared to a fusion-evaporation calculation. It is also shown that, at least at one bombarding energy, the fusion evaporation residue yields for the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ systems are almost the same, confirming the independence of the way in which the compound nucleus ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$ is formed. (ii) The systems ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, and ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ have been studied at $E_{\mathrm{lab}}=40\mathrm{}$ MeV. This energy corresponds approximately to the maxima of the fusion evaporation cross sections for all these systems. The yields to final residual nuclei show that the additional neutrons strongly affect mainly the $\alpha \mathrm{xn}$ and $2\alpha \mathrm{xn}$ channels and this is well reproduced by the Hauser-Feshbach statistical model. The results are compared to those obtained for neighboring fusion-evaporation systems.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ beams on ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, and ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ targets; natural and enriched targets; $30<~E \left(\mathrm{lab}\right)<~60$ MeV; time of flight with $Z$ identification technique; fusion-evaporation yields; comparison with statistical particle evaporation calculations.

A characteristic pattern frequently observed in the angular distribution of heavy-ion elastic scattering at moderate energies above the Coulomb barrier has been attributed either to a Fresnel diffraction or to a rainbow effect. We propose a comparison between the strong absorption radius $R_{\mathrm{sa}}$ and the rainbow radius $R_r$ at different energies, which may have some relevance on deciding whether the absorptive or the refractive interpretation is to be preferred. Despite the difficulties in the exact determination of these two distances, an analytical expression for their energy dependence is found empirically by analyzing data of fifteen pairs of heavy ions. According to this criterion the center-of-mass energy, above which refraction prevails over absorption, is proportional to $Z_1{Z}_2$.

NUCLEAR SCATTERING Optical and diffraction models, rainbow refraction of heavy ions.

We study phenomenologically the inclusive fragmentation cross section data of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ at 2.1 GeV/nucleon, and ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$ at 1.88 GeV/nucleon upon collisions with a ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ target. The main assumptions on the fragmentation mechanism are the diffractive excitation of the high energy beam nucleus into the state of virtual dissociation and its direct decay into two fragments as was previously proposed by the authors. Starting from Izosimova et al.'s formula for the same problem, we derive a phenomenological inclusive cross section formula for fragment production, which is applicable to both ordinary and very light fragments. We find that the data can be understood if we assume that the fragments are being produced not only in their ground states but also in the low lying excited states. Our formula relates the inclusive cross section of light fragment (cluster) to the effective number of the same cluster in the low lying excited states of the beam nucleus.

NUCLEAR REACTIONS High energy fragmentations of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$, and ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$, inclusive cross section formula, diffractive excitation, two body decays, spin effects, effective numbers of clusters.

The nuclear structure of high-spin states in ${}_{}{}^{46}{}_{}{}^{}\mathrm{Ti}$ and ${}_{}{}^{46}{}_{}{}^{}\mathrm{V}$ has been investigated using the ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}({}_{}{}^9{}_{}{}^{}\mathrm{Be},2pn){}_{}{}^{46}{}_{}{}^{}\mathrm{Ti}$ and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}({}_{}{}^9{}_{}{}^{}\mathrm{Be},p2n){}_{}{}^{46}{}_{}{}^{}\mathrm{V}$ reactions. Excitation function, angular distribution, recoil distance, Doppler shift attentuation, and $\gamma -\gamma$ coincidence measurements were undertaken. Some additional data on ${}_{}{}^{46}{}_{}{}^{}\mathrm{Ti}$ from the ${}_{}{}^{35}{}_{}{}^{}\mathrm{Cl}({}_{}{}^{16}{}_{}{}^{}\mathrm{O},\alpha p){}_{}{}^{46}{}_{}{}^{}\mathrm{Ti}$ reaction are included.

NUCLEAR REACTIONS ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}({}_{}{}^9{}_{}{}^{}\mathrm{Be},2pn){}_{}{}^{46}{}_{}{}^{}\mathrm{Ti}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}({}_{}{}^9{}_{}{}^{}\mathrm{Be},p2n){}_{}{}^{46}{}_{}{}^{}\mathrm{Ti}$, $E=20\mathrm{}-45$ MeV; measured $\sigma (E,E_{\gamma })$ and coin; deduced levels; measured $\sigma (E_{\gamma },\theta )$; deduced $J^{\pi }$ for high spin levels; measured RDM and DSA; deduced $\tau$, ${\mathrm{}\left|M\right(E1\mathrm{}\left)\right|}^2$, ${\mathrm{}\left|M\right(M1\mathrm{}\left)\right|}^2$, ${\mathrm{}\left|M\right(E2\mathrm{}\left)\right|}^2$. Natural targets Ge(Li) detectors.

Both in-plane and out-of-plane angular correlations of coincident C and $\alpha$ particles have been measured for 65 MeV ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ bombardment of a ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ target. Exploitation of the time-of-flight method enabled the measurement of very low energy alpha particles at back angles. Results from the present experiment show that evaporation from an intermediate nucleus ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}$* accounts for the majority of the $\mathrm{C}-\alpha$ coincidence events observed. A small number of alpha particles from the breakup of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$* were detected at angles around that of the carbon detector. Less than 10% of the alpha particles detected are of pre-equilibrium origin. This is in sharp contrast to earlier results.

NUCLEAR REACTIONS ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$+ ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$. $E_{\mathrm{lab}}=65\mathrm{}$ MeV; measured $\frac{d^2\sigma }{d{\Omega }_{c}d{\Omega }_{\alpha }}$, $\mathrm{C}-\alpha$ coin, ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ target.

The lifetimes of the $J^{\pi }=0^{+} 6590$-keV and $J^{\pi }=3^{-} 6728$-keV states in ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ and the $J^{\pi }=3^{-} 5834$-keV state in ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ were measured using the recoil distance method. Gamma rays following the $\mathrm{pn}$ and $2n$ evaporation channels from ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ + ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ reactions were detected at ${\theta }_{\gamma }=0\mathrm{}°$. The experimental results are ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$(${6590,0}^{+}$), $\tau =3.7\mathrm{}\pm 0.9$ ps; ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$(${6728,3}^{-}$), $\tau =96\mathrm{}\pm 15$ ps; ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$(${5834,3}^{-}$), $\tau =12.9\mathrm{}\pm 1.9$ ps. Extensive shell-model calculations for both ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ have been performed using an SU(3) basis and are compared to these and other experimental results.

NUCLEAR REACTIONS ${}_{}{}^7{}_{}{}^{}\mathrm{Li}({}_{}{}^9{}_{}{}^{}\mathrm{Be},pn\gamma )$ $E_{\mathrm{Be}}=5.5\mathrm{}$ MeV; ${}_{}{}^9{}_{}{}^{}\mathrm{Be}({}_{}{}^7{}_{}{}^{}\mathrm{Li},pn\gamma )$ and ${}_{}{}^9{}_{}{}^{}\mathrm{Be}({}_{}{}^7{}_{}{}^{}\mathrm{Li},2n\gamma )$ $E_{\mathrm{Li}}=3.8\mathrm{}-7.8$ MeV; measured $E_{\gamma }$,$I_{\gamma }$ (recoil distance method); calculated $\tau$ from theory and compared with experiment.

Differential cross sections for evaporation residue formation following the complete fusion of ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$ with 187.6 to 220 MeV ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$ ions were measured with high precision using a velocity selector together with a counter telescope. The resulting cross sections for complete fusion ranged in magnitude from 50 μb at 93.3 MeV to 230 mb at 108.9 MeV (c.m.). The cross sections for complete fusion at sub-barrier energies were shown to be far greater than those predicted by standard barrier penetration models.

NUCLEAR REACTIONS Complete fusion, ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$ + ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$, $E=187.6\mathrm{} \mathrm{to} 220$ MeV lab, measured $\sigma (E,\theta )$ for evaporation residues.

A nonperturbative method is developed for calculating the excitation of a many-body system by a time-dependent Hamiltonian. The stationary-phase approximation to a functional-integral representation of the interaction-picture many-body evolution operator results in a mean-field approximation to the $S$ matrix which is asymptotically time independent. A one-body temporally nonlocal evolution equation defines the stationary mean-field configurations. The general method and character of the stationary solutions are illustrated by application to the forced harmonic oscillator and forced Lipkin model. Potential applications to realistic nuclear and atomic scattering situations are discussed.

NUCLEAR REACTIONS Mean-field approximation, many-body $S$ matrix, time-dependent Hartree Fock.

Quadrupole coupling constants of the ${}_{}{}^{43}{}_{}{}^{}\mathrm{Sc}$(19/$2^{-}$) and the ${}_{}{}^{43}{}_{}{}^{}\mathrm{Ti}$(19/$2^{-}$) mirror isomers, implanted into hexagonal Ti, have been measured with the time differential perturbed angular distribution method. Values of $\frac{e^2\mathrm{qQ}}{h}=8.5\mathrm{}\left(19\right)\mathrm{}$ MHz and 8.0(16) MHz are found at room temperature, corresponding to $eQ=19.9\mathrm{}\left(14\right)\mathrm{}e{\mathrm{fm}}^2 \mathrm{and} 30\left(7\right)\mathrm{}e{\mathrm{fm}}^2$ for the ${}_{}{}^{43}{}_{}{}^{}\mathrm{Sc}$(19/$2^{-}$) and the ${}_{}{}^{43}{}_{}{}^{}\mathrm{Ti}$(19/$2^{-}$) states, respectively. The isomeric lifetimes were remeasured as $T_{\frac{1}{2}}=469\mathrm{}\left(4\right)\mathrm{}$ nsec and 553(21) nsec for the two states. These values, along with transition rates of high spin states in $A=42\mathrm{}$ nuclei were analyzed in terms of effective charges, and were found to be consistent with $e_n=0.56\mathrm{}\left(7\right)\mathrm{}$ and $e_p=1.26\mathrm{}\left(9\right)\mathrm{}$ for the quadrupole moments, $e_n=0.65\mathrm{}\left(3\right)\mathrm{}$ and $e_p=1.35\mathrm{}\left(5\right)\mathrm{}$ for the $B\left(E2\mathrm{}\right)\mathrm{}$ values. The slight increase in the effective charges for the nondiagonal compared to the diagonal $E2\mathrm{}$ matrix elements is understood as the effect of an increased core deformation in the lower spin partner of the transition.

NUCLEAR REACTIONS ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}[{}_{}{}^{19}{}_{}{}^{}\mathrm{F},p2n]{}_{}{}^{43}{}_{}{}^{}\mathrm{Sc}\left({\frac{19}{2}}^{-}\right)$, $E\left({}_{}{}^{19}{}_{}{}^{}\mathrm{F}\right)=45.5\mathrm{}$ MeV; ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}[\alpha ,p]{}_{}{}^{43}{}_{}{}^{}\mathrm{Sc}\left({\frac{19}{2}}^{-}\right)$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}[\alpha ,n]{}_{}{}^{43}{}_{}{}^{}\mathrm{Ti}\left({\frac{19}{2}}^{-}\right)$, $E_{\alpha }=21\mathrm{}$ MeV; pulsed beam, measured $T_{\frac{1}{2}}$, deduced $B\left(E2\mathrm{}\right)\mathrm{}$, measured $\gamma (\theta ,t)$ in Ti metal, deduced $Q$.

The velocity dependence of the transient hyperfine magnetic field manifest at nuclei of ${}_{}{}^{108}{}_{}{}^{}\mathrm{Pd}$ ions recoiling through magnetized Fe was investigated to a velocity higher than previously examined for the heavier nuclides. The state of interest ($2_1^{+}$) was populated by Coulomb excitation using beams of 80-MeV ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ and 180-MeV ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$ ions and precessed $\gamma$-ray angular distribution measurements were carried out in coincidence with backscattered projectiles. These results, when combined with prior lower-velocity measurements for ${}_{}{}^{106}{}_{}{}^{}\mathrm{Pd}$, yield a transient field velocity dependence $v^p$, $p=0.41\mathrm{}\pm 0.15$, for Pd isotopes over the extended velocity range $1.74\le 〈\frac{v}{v_0}〉\le 7.02 (v_0=\frac{c}{137})$ a result incompatible with a linear velocity dependence.

NUCLEAR REACTIONS ${}_{}{}^{108}{}_{}{}^{}\mathrm{Pd}$ (${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}\prime$) ${}_{}{}^{108}{}_{}{}^{}\mathrm{Pd}$($2_1^{+}$), ${}_{}{}^{108}{}_{}{}^{}\mathrm{Pd}$ (${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}\prime$) ${}_{}{}^{108}{}_{}{}^{}\mathrm{Pd}$($2_1^{+}$), $E_S=80\mathrm{}$ MeV, $E_{\mathrm{Ni}}=180\mathrm{}$ MeV, enriched target; measured $W(\theta ,H,\infty )$ in polarized Fe. Deduced transient field and velocity dependence of PdFe for $\frac{v}{c}<~0.054$.

The cross sections for the binary and ternary fission of U, Th, Bi, Pb, and Au induced by 300 GeV protons have been measured with Makrofol polycarbonate detectors. We deduce that the ternary events and most of the binary events with a projected angle ${\alpha }_{12}<170\mathrm{}°$ in the plane perpendicular to the beam direction proceed by the same mechanism which characterizes fission induced by very high energy protons.

NUCLEAR REACTIONS Binary and ternary fission of U, Th, Bi, Pb, and Au; $E_p=200\mathrm{}$ GeV, 300 GeV; measured cross sections ${\sigma }_B$, ${\sigma }_{\overline{\pi }}$, ${\sigma }_T$.

The cross section for delayed fission for the ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}(n,n^{\prime }){}_{}{}^{238}{}_{}{}^{}\mathrm{U}_{}^m{}_{}{}^{}$ reaction at 14.5 MeV neutron energy has been measured using an annular plastic track detector in a recoil geometry. Seven runs each of 50 hours neutron bombardment were made on a ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ target and each run was followed by a similar irradiation of a ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$ target to determine the background. A statistical model calculation for the isomer excitation function has been made and compared with the present measurement at 14.5 MeV and reported data near the threshold of the reaction.

NUCLEAR REACTIONS ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}(n,n^{\prime })$, $E_n=14.5\mathrm{}$ MeV; measured $\sigma$ (delayed fission). Calculated $\frac{\sigma \left(\mathrm{isomer}\right)}{\sigma \left(\mathrm{prompt}\right)}$.

Angular distributions for elastic and inelastic scattering of ${\pi }^{+}$ projectiles from natural carbon and silicon targets at energies of ∼35 and 68 MeV are reported. The elastic data, along with other reported low energy pion scattering data for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, is fitted using the zero-range four-parameter ($b_0,b_1$) Kisslinger optical potential. The best-fit potential is found to be nearly independent of energy between 30 and 68 MeV, the largest energy dependence being in $\mathrm{Re}\left(b_0\right)$ which changes by 30%. Simple distorted-wave impulse approximation calculations which succeed in describing the $2^{+}$ 4.4 MeV cross section at 48.5 MeV do much worse at 67.5 MeV for angles where the $2^{+}$ cross section is comparable to or larger than the elastic cross section. This suggests that a coupled channels calculation is needed. The poor agreement between data and theory for the $0^{+}$ (7.6 MeV) and $3^{-}$ (9.6 MeV) ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ transitions found earlier at 48.5 MeV persists at 67.5 MeV. The shape of the pion energy spectra and the energy integrated inelastic angular distribution at 67.5 MeV is poorly described by a quasifree pion-nucleon scattering process.

NUCLEAR REACTIONS Elastic and inelastic scattering of 35 and 68 MeV ${\pi }^{+}$ from ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$. Angular distributions: $25°<~\theta <~150°$. Optical model and DWIA analysis of cross-section data.

An estimate is made of the effect of expanding about the full nucleon and meson propagators as well as the mean meson fields in certain model renormalizable relativistic field theories of nuclear matter. Meson masses are determined self-consistently by satisfying, at zero momentum only, the Schwinger-Dyson equations which result when the energy functional is truncated at the two-loop level. The tachyonic pion problem of the standard mean field expansion is eliminated but the opposite problem of a far too massive pion in normal nuclear matter arises.

NUCLEAR STRUCTURE Relativistic mean field theories of nuclear matter, tachyonic pions. Approximate solutions of Schwinger-Dyson equations.

The angular distribution of the $\mathrm{pd}\to {}_{}{}^3{}_{}{}^{}\mathrm{He}{\pi }^0$ reaction at 800 MeV was measured and compared to a common ($p,\pi$) model. The data are consistent with other data in this energy region and are in qualitative agreement with predictions of the model. There are quantitive differences between data and theory.

NUCLEAR REACTIONS ${}_{}{}^2{}_{}{}^{}\mathrm{H}(p,{}_{}{}^3{}_{}{}^{}\mathrm{He}){\pi }^0$, $T_p=800\mathrm{}$ MeV, measured $\frac{d\sigma }{d\Omega }$, compared with Ruderman model.