A distorted-wave impulse approximation formalism is developed for the knockout contribution in high energy (> 100 MeV/A) heavy-ion collisions. Computed inclusive proton spectra based on this model, which require only the nuclear densities, nucleon-nucleon scattering amplitude, and proton optical potential as input quantities, agree well in magnitude and shape with the available measured spectra in the forward directions.

NUCLEAR REACTIONS DWIA formalism for the single nucleon knockout in high energy heavy-ion collisions.

Excited levels of ${}_{}{}^{103}{}_{}{}^{}\mathrm{Cd}$ have been investigated in the ${}_{}{}^{94}{}_{}{}^{}\mathrm{Mo}({}_{}{}^{12}{}_{}{}^{}\mathrm{C}, 3n\gamma ){}_{}{}^{103}{}_{}{}^{}\mathrm{Cd}$ reaction and observed up to 4027 keV excitation energy. A decoupled band, based on the 188.1 keV $\frac{7}{2^{+}}$ intrinsic state has been observed up to spin $\frac{19}{2^{+}}$. An interpretation of the experimental results is proposed in the framework of the axial symmetric rotor plus particle model using deformed self-consistent quasiparticle states.

NUCLEAR REACTIONS ${}_{}{}^{94}{}_{}{}^{}\mathrm{Mo}({}_{}{}^{12}{}_{}{}^{}\mathrm{C}, 3n\gamma )$, $E=44-65\mathrm{}$ MeV; measured $E_{\gamma }$, $I_{\gamma }$, $\gamma \left(\theta \right)$, $P_{\gamma }$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$-$\gamma$ delay, $\gamma -\gamma$ coin, ${}_{}{}^{103}{}_{}{}^{}\mathrm{Cd}$ deduced levels and $J^{\pi }$, Ge(Li) detectors, enriched target.

The theoretical spectra of antineutrinos from the beta decays of the products of fissioning ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$, and ${}_{}{}^{239}{}_{}{}^{}\mathrm{Pu}$ were recalculated using recent compilations of the level structure, beta branching ratios, and fission yields. In addition, a very recent semiempirical mass formula, particularly designed to achieve local accuracy on the ($N, Z$) plane, was used to calculate the beta $Q$ values of isotopes of unknown decay schemes. Recent decay systematics, far from the beta stability line, have encouraged us to assume that most of the levels of the isotopes of a given $Z$, differing by $\Delta N=2\mathrm{}$, are very similar in order and in energy. The beta spectrum from equilibrium, thermal fission products of ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$ was calculated and compared with existing experimental data. Theoretical predictions are presented for the inverse beta decay of the proton, the neutral current disintegration of the deuteron, and the excitation of ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ by antineutrinos. Existing data from the elastic scattering of electrons by antineutrinos are reanalyzed with the present antineutrino spectra. The result is that these data agree with the predictions of the Weinberg-Salam model with ($0.24<\mathrm{}{{sin}^2\theta }_W<0.31\mathrm{}$) and do not agree with the predictions of the Feynman-Gell-Mann theory.

RADIOACTIVITY, FISSION ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{239}{}_{}{}^{}\mathrm{Pu}$; antineutrino and beta spectra calculated in secular equilibrium. $\overline{\sigma }$ for ${\overline{\nu }}_e(p, n){\beta }^{+}$, ${\overline{\nu }}_e(d, pn){\overline{\nu }}_e$, ${\overline{\nu }}_e({}_{}{}^7{}_{}{}^{}\mathrm{Li}, {}_{}{}^7{}_{}{}^{}\mathrm{Li}_{}^{*}{}_{}{}^{}){\overline{\nu }}_e$, and ${\overline{\nu }}_e(e^{-}, e^{-}){\overline{\nu }}_e$.

Subbarrier photofission cross sections and the fission half-lives have been calculated for ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ in terms of a suitable double-hump fission barrier model. The competition due to the gamma deexcitation to the shape isomeric state in the second well (and its consequent fission) has been included by introducing an absorptive part in the potential in the second well region. The calculated cross sections reproduce satisfactorily the recently observed "shelf" in the deep-subbarrier energy region and result in a resonance structure in the threshold region consistent with that observed. The calculation also predicts several low energy resonances in the cross sections and a detailed competition of the prompt and the delayed fission contributions suggests that an angular anisotropy measurement might be more sensitive in detecting the relatively small contribution of delayed fission in the energy region 4.5-5.5 MeV.

NUCLEAR REACTIONS Fission calculated subbarrier photofission cross sections and fission half lives using a suitable two-hump fission barrier in ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$. The results reproduce the observed "shelf" in the cross sections in the deep-subbarrier energy region and the observed resonance structure in threshold region.

The relative independent yields of Rb, In, and Cs from the fission of ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$ induced by 20-100 MeV protons have been measured by an on-line mass spectrometer. Total numbers of neutrons emitted per fission event have been deduced from the centroids of these isotopic distributions. The reaction mechanism and charge division process are discussed in terms of equal charge displacement and unchanged charge distribution mechanisms. It is found that the charge division does not depend on the incident proton energy. From a comparison between nearly Gaussian-shaped isotopic distributions of indium, and the asymmetric isotopic distribution of Cs, it is inferred that the total fission cross section includes a significant contribution from low-excitation energy events. This contribution seems to increase with the incident proton energy.

NUCLEAR REACTIONS, FISSION ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}(p, f)$, $E_p=29, 59, 75, 97$ MeV: measured independent relative yields of Rb, In, Cs. Deduced total numbers of neutrons emitted in nearly symmetric (In) and asymmetric (Rb-Cs) fission; charge division mechanism.

Fission fragment angular distributions have been measured for the neutron fission of ${}_{}{}^{230}{}_{}{}^{}\mathrm{Th}$ in the energy range 680-1100 keV with special attention to the region of the large vibrational resonance in the neutron fission cross section near 715 keV. The analysis involved the search for a set of fission barrier parameters which lead to a simultaneous description of the angular distribution data and the existing data for the fission cross section. It was found that the data for the 715 keV resonance could be reproduced only if the $K=\frac{1}{2}$ band responsible for this resonance splits into two separate bands, one of each parity, and if the decoupling parameter has a parity dependent sign. The derived moment of inertia constant $\frac{{\hslash }^2}{2\mathcal{I}}$ has a value of 1.85 keV which suggests that the vibrational resonance occurs within a minimum in the potential energy surface corresponding to a $\beta$ deformation of ${\epsilon }_2=0.85\mathrm{}$. The derived data are all consistent with the predicted triple-humped fission barrier for the thorium nuclei.

NUCLEAR REACTIONS ${}_{}{}^{230}{}_{}{}^{}\mathrm{Th}(n, f)$, $E_n=0.68-1.10\mathrm{}$ MeV, measured $W\left(\theta \right)$, comprehensive statistical model analysis, barrier parameter derived, triple-humped fission barrier for thorium confirmed.

The differential angular distribution of prompt $\gamma$ rays from spontaneous fission of ${}_{}{}^{252}{}_{}{}^{}\mathrm{Cf}$ has been measured. The source was on a thick backing, and the measurements have been performed in forward and backward geometries. An NaI(Tl) crystal was used as a $\gamma$-ray detector, and the prompt neutrons from fission were rejected by time of flight. The total number of $\gamma$ rays emitted within 12 ns after fission with energies greater than 0.114 MeV is 9.7 ± 0.4 per fission, and the total $\gamma$-ray energy released is (7.0±0.3) MeV per fission. Results from earlier experiments that more $\gamma$ rays are emitted from the light than from the heavy fragment group, are substantiated. The anisotropy $A=\frac{I\left(0\mathrm{}°\right)}{I\left(90\mathrm{}°\right)}-1\mathrm{}$ is small and even negative at low energies, reaches a maximum of about 25% at energies of about 0.50-0.65 MeV, and gets gradually smaller at higher energies. No significant difference in the anisotropy as measured with a nonmagnetic (Pt) and a magnetic (Ni) backing has been found. With the assumption that the angular momentum is aligned in a plane perpendicular to the direction of fission, the results can be consistently described within the statistical model in terms of pure dipole and quadrupole radiation with allowance for stretched $E2\mathrm{}$ cascades from even-even fragments. It is concluded that the root mean square value of the primary angular momentum of the fragments is $J_{\mathrm{rms}}=(6.5\mathrm{}\pm 1.0)\hslash$, the average angular momentum is decreasing $1.0\hslash$ per $\gamma$ ray emitted, and the value of the spin cutoff parameter during $\gamma$-ray deexcitation of the fragments is $\sigma ={2.4}_{-0.5\mathrm{}}^{+0.8\mathrm{}}$. The dipole and the quadrupole components are about equally strong at high $\gamma$-ray energies, the dipole component predominates at low energies, and the quadrupole component at intermediate energies. Statistical dipole and quadrupole transitions (stretched for the last ones) account for 38% and 50% of the $\gamma$ rays, respectively, and stretched $E2\mathrm{}$ transitions in cascades from even-even fragments account for the remaining 12% of the $\gamma$ rays. The quadrupole radiation can be assumed to be $E2\mathrm{}$, and the dipole radiation $M1\mathrm{}$ at low energies and $E1\mathrm{}$ at high energies. While the components of the stretched $E2\mathrm{}$ cascades with energies smaller than 0.6 MeV can be accounted for by the transitions in the ground-state rotational bands of even-even fragments, it is indicated that a large part of the components in the energy range 0.6-0.9 MeV can be associated with vibrational transitions in even-even fragments.

RADIOACTIVITY, FISSION ${}_{}{}^{252}{}_{}{}^{}\mathrm{Cf}$ (sf); measured $\sigma (E_{\gamma }, \theta )$ of $\gamma$ from fragments, $N_{\gamma ,\mathrm{tot}}$, $E_{\gamma ,\mathrm{tot}}$, $N_{\gamma H}$, $N_{\gamma L}$; deduced $\overline{J}$, yield of various multipolarities.

A nonstatic model for elastic pion-nucleon scattering is developed using knowledge of the analytic structure of the scattering amplitude and partial wave $\frac{N}{D}$ dispersion techniques. In $S$, $D$, and $F$ partial wave channels the model is equivalent to a separable potential model which includes the coupling to inelastic channels. In $P$-wave channels the nucleon pole which arises from absorption and emission of the pion is included. A more general model which incorporates both a nucleon pole term and a separable potential term is developed for the $P_{11}$ channel. This model is capable of reproducing the change of sign which is present in the $P_{11}$ phase shifts. The necessary information concerning the coupling of the inelastic scattering to the elastic scattering is taken from the experimentally determined phase shifts as input. If simple kinematic factors are included explicitly, quite simple analytic functions for the form factors in the model are able to reproduce the experimental phase shifts for pion laboratory kinetic energies up to 1.2 GeV. The model produces off-shell behavior which is different from previous models. In particular, the inclusion of the nucleon pole alters substantially the range of the interaction in all $P$-wave channels.

NUCLEAR REACTIONS Pion-nucleon elastic scattering; separable potential and Chew-Low models extended; $S$-, $P$-, $D$-, and $F$-wave phase shifts for $E<~1.2$ GeV.

This paper derives a unitary model for the coupled $\pi NN-NN$ problem. Starting from the integral equations obtained by Avishai and Mizutani we introduce an extension of Karlsson's procedure to restate the scattering problem in terms of on-shell transition amplitudes. We obtain a soluble system of Heitler-type integral equations, which unitarize the scattering problem. The model enables the construction of the approximate on-shell transition amplitudes which satisfy both two- and three-particle unitarity constraints.

NUCLEAR REACTIONS The coupled $\pi NN-NN$ problem. Unitary model. Approximation schemes.

Differential ranges of ${}_{}{}^{44}{}_{}{}^{}\mathrm{Sc}_{}^m{}_{}{}^{}$, ${}_{}{}^{46}{}_{}{}^{}\mathrm{Sc}$, ${}_{}{}^{47}{}_{}{}^{}\mathrm{Sc}$, and ${}_{}{}^{48}{}_{}{}^{}\mathrm{Sc}$ emitted at 17° and 163° to the beam in the interaction of ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ with 400 GeV protons have been measured. The mean kinetic energies of the fragments decrease from 54.2±1.0 MeV at 17° to 42.0±0.7 MeV at 163°. From this shift, the mean velocity of the emitting nucleus $〈v_{\parallel }〉$ is obtained as 0.10 ${(\mathrm{M}\mathrm{e}\mathrm{V}/\mathit{A})}^{\mathrm{½}}$. The angular distribution of Sc fragments in a system moving with this velocity is found to be asymmetric about 90° with more fragments emitted at backward than at forward angles ($\frac{F}{B}\sim 0.8$). The implications of this result for the reaction mechanism are considered.

NUCLEAR REACTIONS ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}(p, x){}_{}{}^{44}{}_{}{}^{}\mathrm{Sc}_{}^m{}_{}{}^{}$, ${}_{}{}^{46}{}_{}{}^{}\mathrm{Sc}$, ${}_{}{}^{47}{}_{}{}^{}\mathrm{Sc}$, ${}_{}{}^{48}{}_{}{}^{}\mathrm{Sc}$; $T_p=400\mathrm{}$ GeV. Measured differential ranges at 17° and 163°; deduced two-step model parameters.

Evidence of the excitation of the 899-keV $2^{+}$ state in muonic ${}_{}{}^{204}{}_{}{}^{}\mathrm{Pb}$ has been obtained. The isomer shift of the nuclear $E2\mathrm{}$ ground-state transition is found to be - 1.98 ± 0.16 keV, a value that is in disagreement with interpretation of the first excited state as a volume-conserving one-phonon quadrupole vibration.

NUCLEAR STRUCTURE ${}_{}{}^{204}{}_{}{}^{}\mathrm{Pb}$; measured isomer shift of $2^{+}$ nuclear state.

The role of nuclear $A^{*}$ excitations for a unified description of pion induced reactions on nuclei in the medium energy range is discussed. As specific examples we treat the excitation of the $1^{+}$, $T=1\mathrm{}$ (15.11 MeV) state in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ by inelastic pion scattering and compare it with the single charge exchange reaction and the radiative capture of pions in flight into the corresponding ground states of the residual nuclei. It is shown that those reactions provide further useful tools to investigate the multipole distribution of the $A^{*}$ excitation strength and thus complement elastic pion scattering data.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(\pi , {\pi }^{\prime }){}_{}{}^{12}{}_{}{}^{}\mathrm{C}(1^{+}, 15.11 \mathrm{MeV})$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({\pi }^{+}, {\pi }^0){}_{}{}^{12}{}_{}{}^{}\mathrm{N}(\mathrm{g}.\mathrm{s}.\mathrm{})$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({\pi }^{+}, \gamma ){}_{}{}^{12}{}_{}{}^{}\mathrm{N}(\mathrm{g}.\mathrm{s}.\mathrm{})$, $\Delta (3, 3)$ energy region, $A^{*}$ reaction mechanism.

The results of new proton-proton bremsstrahlung differential cross section measurements at $T_p=730\mathrm{}$ MeV are presented. The experiment was designed to measure photons of 40-300 MeV at forward angles in coincidence with the scattered and recoil protons. The cross sections rise rapidly when $E_{\gamma }>100\mathrm{}$ MeV, in sharp disagreement with external-emission dominance calculations which predict a smooth and nearly flat spectrum. The model calculations of Tiator et al., which consider the $\Delta \mathrm{}\left(1232\right)\mathrm{}$ resonance in the intermediate state, agree with our results, as does an adjusted soft-photon approximation calculation.

NUCLEAR REACTIONS Proton-proton bremsstrahlung, $T=730\mathrm{}$ MeV; measured $\sigma (\theta , E_{\gamma })$, 40-300 MeV; compared with soft-photon and isobar calculations.

Measurements of the invariant cross sections for the reaction $p\left(400\mathrm{} \mathrm{GeV}\right)+({}_{}{}^6{}_{}{}^{}\mathrm{Li}, \mathrm{B}\mathrm{e},\mathrm{C},\mathrm{A}\mathrm{l},\mathrm{C}\mathrm{u},\mathrm{T}\mathrm{a})\to ({\pi }^{\pm }, K^{\pm })+X$ at laboratory angles from 70° to 160° are reported. Upper limits for $\overline{p}$ production are given. Comparisons of the data are made using several scaling variables.

NUCLEAR REACTIONS Inclusive cross section; 400 GeV incident protons; ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, Be, C, Al, Cu, Ta targets; production of $\pi$, $K$, and $\overline{p}$; lab angles 70° to 160°.

Recent kaon-nucleon phase shift parametrizations are used to investigate the energy dependence of kaon-nucleus scattering. When nucleon motion is included the differential and total cross sections are found to vary smoothly with energy. The consequences for isobar dynamics are discussed.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(K^{\pm }, K^{\pm }){}_{}{}^{12}{}_{}{}^{}\mathrm{C}_{}^{\mathrm{}(0.0,4.4)\mathrm{}}{}_{}{}^{}$, $E_K=100-1000\mathrm{}$ MeV; role of nucleon motion and kaon distortions; $\sigma \left(\theta \right)$ for various $\mathrm{KN}$ amplitudes.

The cross section for true absorption of positive pions in carbon was obtained from experiments at 85, 125, 165, 205, and 245 MeV. The results are compared with theoretical calculations. The total ${\pi }^{+}$-carbon cross section is decomposed into its major channels: elastic scattering, inclusive inelastic scattering, true absorption, and single charge exchange, as a function of pion energy. The inclusive ${\pi }^{+}$ angular distribution was also measured and the results suggest that quasifree processes play an important role for backword scattering.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({\pi }^{+}, {{\pi }^{+}}^{\prime })$, (${\pi }^{+}$, absorption) $E=85-245\mathrm{}$ MeV, measured $\sigma (E, \theta )$, deduced decomposition ${\sigma }_{\mathrm{react}}$.

We analyze the role of the $n-n$ final state interaction in $\gamma d\to {\pi }^{+}$ $\mathrm{nn}$ at threshold energies by taking the $n-n$ amplitude which includes the hard core term. The effect of the two-body off-c.m. correction to the amplitude in the final three particle phase space is studied. A simple analytic expression for the cross section, which depicts the correct energy dependence, is obtained.

NUCLEAR REACTIONS Photopion production, final state interaction, impulse approximation, off-c.m. correction, deuteron wave function.

We derive a new approach to the proton-nucleus large angle scattering which accounts in a systematic way for Pauli, binding, and Fermi motion effects. We concentrate here on $\mathrm{pd}$ scattering. After antisymmetrization of incident and target protons, the $\mathrm{pd}$ amplitude can be separated into (1) the standard multiple scattering series with the last $\mathrm{pp}$ amplitude antisymmetrized and (2) a neutron exchange amplitude which includes rescattering terms. The optimal approximation designed to minimize corrections is derived for the antisymmetrized $\mathrm{pd}$ amplitude. The single scattering amplitude is factorized into an on-shell (antisymmetrized) $\mathrm{pN}$ amplitude and the deuteron form factor, and it is found to play a main role in the large angle $\mathrm{pd}$ scattering at sufficiently high energy. The results are applied to analysis of $\mathrm{pd}$ elastic scattering data ($T_p\gtrsim 300$ MeV) which are well reproduced by the calculations. This analysis also permits an extraction of the deuteron body form factor for values of $q^2$ which far exceed those measured in $\mathrm{ed}$ elastic data.

NUCLEAR REACTIONS Proton-nucleus scattering. Pauli, binding, and Fermi motion effects. Antisymmetrization. Minimization of corrections. $\mathrm{pd}$ large angle scattering. Comparison with data. Deuteron form factor.

A detailed study of the ${\beta }^{\mp }-\alpha$ angular correlations in the ${}_{}{}^8{}_{}{}^{}\mathrm{Li}\left({\beta }^{-}\right)$ and ${}_{}{}^8{}_{}{}^{}\mathrm{B}\left({\beta }^{+}\right)$ decays was performed. Since these decays proceed to the $2\alpha$ continuum, detection of both alpha particles enabled determination of various correlations as functions of the final-state energy. The experimental results show a small (≈ 15% of weak magnetism) deviation from the conserved vector current prediction which is dependent on the final-state energy. An effect of this size cannot be interpreted as convincing evidence for the presence of second-class currents or a breakdown of conserved vector current theory. However, the inclusion of the vector second-forbidden terms in the nuclear weak current as predicted by the conserved vector current theory is crucial to obtain even approximate agreement with the experimental results.

RADIOACTIVITY ${}_{}{}^8{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^8{}_{}{}^{}\mathrm{B}$; measured $\beta \alpha$ angular correlation, final-state energy dependence. Model independent test of CVC and second-class currents.

The half-life of ${}_{}{}^{230}{}_{}{}^{}\mathrm{Th}$ was measured by the specific activity method. Alpha counting was done in a low geometry counter whose geometry factor was calculated from its dimensions. Sample weights were determined by isotopic dilution. Measurements were made on four isotopic mixtures ranging from 0.383 to 99.52% ${}_{}{}^{230}{}_{}{}^{}\mathrm{Th}$. The half-life is 75381±295 years.

RADIOACTIVITY ${}_{}{}^{230}{}_{}{}^{}\mathrm{Th}$ half-life, specific activity; measured: $\alpha$ activity by low geometry counter, thorium mass by mass spectrometric isotopic dilution.