We calculate the total inclusive ($p, {\pi }^{-}\mathrm{xn}$) reaction cross section for 200 MeV protons on ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$ using a simplified intranuclear cascade model in which only one particle at a time is tracked through the nucleus. Computer time is kept to a minimum by multiplying the very small $\mathrm{NN}\to \mathrm{NN}\pi$ probability by a weighting factor. The nucleon and pion charge exchange mechanisms contribute more than half the cross section. The predictions are sensitive to choice of energy in the $\mathrm{NN}\to \mathrm{NN}\pi$ input cross sections, but a reasonable choice gives cross sections in agreement with experiment. The predicted ($p, {\pi }^{-}\mathrm{xn}$) cross section grows rapidly from $T_{\mathrm{lab}}=160\mathrm{}$ MeV (just above threshold) to 220 MeV.

NUCLEAR REACTIONS ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}(p, {\pi }^{-}xn){}_{}{}^{210-x}{}_{}{}^{}\mathrm{At}$, $E$ near 200 MeV, calculated $\sigma \mathrm{}\left(E\right)\mathrm{}$, simplified intranuclear cascade model, nucleon and pion charge exchange.

Differential cross sections for ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}({\pi }^{\pm }, {\pi }^{\pm \prime }){}_{}{}^{13}{}_{}{}^{}\mathrm{C}_{}^{*}{}_{}{}^{}$ were measured at an incident pion energy of 162 MeV. Data were obtained for states or groups of states up to 21.6 MeV in excitation energy. The experimental results are compared with the distorted-wave impulse approximation calculations of Lee and Kurath.

NUCLEAR REACTIONS ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}({\pi }^{\pm }, {\pi }^{\pm \prime })$, $T_{\pi }=162\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$. ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ levels, deduced $L_x$. Comparison with microscopic DWIA calculation.

The inclusion of relativistic kinematics in the theory of elastic scattering of pions from nuclei is examined. The investigation is performed in the context of the first order impulse approximation which incorporates the following features: (1) relative momenta are defined according to relativistic theories consistent with time reversal invariance; (2) the two-nucleon interaction is a new, multichannel, separable potential model consistent with the most recent data derived from a recent nonpotential model of Ernst and Johnson; (3) the recoil of the pion-nucleon interacting pair and its resultant nonlocality are included; (4) the Fermi integral is treated by an optimal factorization approximation. It is shown how a careful definition of an intrinsic target density leads to an unambiguous method for including the recoil of the target. The target recoil corrections are found to be large for elastic scattering from ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and not negligible for scattering from ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. Relativistic potential theory kinematics, kinematics which results from covariant reduction approaches, and kinematics which results from replacing masses by energies in nonrelativistic formulas are compared. The relativistic potential theory kinematics and covariant reduction kinematics are shown to produce different elastic scattering at all pion energies examined ($T_{\pi }<300\mathrm{}$ MeV). Simple extensions of nonrelativistic kinematics are found to be reasonable approximations to relativistic potential theory.

NUCLEAR REACTIONS $\pi$-nucleus elastic scattering, variations of relativistic kinematics and target recoil.

The deuteron spectrum following pion absorption at rest is calculated in a two step model using a "two nucleon" absorption vertex. The deuterons, which are produced in this model by the pickup of a nucleon in the second step, are calculated in the partial wave formalism of the distorted-wave Born approximation. The calculated spectrum with appropriate distortion is found to be in reasonable accord with the experiments.

NUCLEAR REACTIONS Deuteron spectrum following pion absorption at rest. Final state interaction in distorted wave formalism.

Samples of ${}_{}{}^{129}{}_{}{}^{}\mathrm{Sn}$ and ${}_{}{}^{129}{}_{}{}^{}\mathrm{Sb}$ were obtained by on-line mass-separation techniques applied to ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$ thermal-fission products. Half-lives of (6.9±0.1) and (2.5±0.1) min have been measured for the ${}_{}{}^{129}{}_{}{}^{}\mathrm{Sn}$ beta decays. Decay schemes are proposed based on gamma-ray energies and intensities and gamma-gamma coincidence results. A new half-life of (17.7±0.1) min, besides the well known 4.4 h one, was observed in the ${}_{}{}^{129}{}_{}{}^{}\mathrm{Sb}$ decay. A level scheme fed by this decay is proposed taking into account our results and previously reported nuclear reactions data. The ${}_{}{}^{129}{}_{}{}^{}\mathrm{Sb}$ structure is compared with a particle-core coupling calculation.

RADIOACTIVITY ${}_{}{}^{129}{}_{}{}^{}\mathrm{Sn}$ and ${}_{}{}^{129}{}_{}{}^{}\mathrm{Sb}$ decays [from ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}(n_{\mathrm{th}}, f)$]; on-line measured $E_{\gamma }$, $I_{\gamma }$, $\gamma -\gamma$ coincidences, $T_{\frac{1}{2}}$, Ge(Li) detectors; ${}_{}{}^{129}{}_{}{}^{}\mathrm{Sb}$ and ${}_{}{}^{129}{}_{}{}^{}\mathrm{Te}$ deduced levels. Mass-separated ${}_{}{}^{129}{}_{}{}^{}\mathrm{Sn}$ and ${}_{}{}^{129}{}_{}{}^{}\mathrm{Sb}$ activities.

Comparison is made between the mass quadrupole coordinate collective model and an appropriately extended version of the hydrodynamic collective model to ascertain whether or not the former is an exact microscopic formulation of the latter. We find that, while there are strong similarities, it is not.

NUCLEAR STRUCTURE Bohr-Mottelson model, hydrodynamic model, mass quadrupole collective model; comparison, theory.

In an application of the generalized Dyson boson mapping to a shell model Hamiltonian acting in a single $j$ shell, a clear distinction emerges between pair bosons and kinematically determined seniority bosons. As in the Otsuka-Arima-Iachello method it is found that the latter type of boson determines the structure of an interactive boson-model-like Hamiltonian for the single $j$-shell model. It is furthermore shown that the Dyson boson mapping formalism is equally well suited for investigating possible interactive boson-model-like structures in a multishell case, where dynamical considerations are expected to play a much more important role in determining the structure of physical bosons.

NUCLEAR STRUCTURE Boson mapping, interacting boson model, shell model.

The $\Lambda$ well depth is calculated with one- and two-channel potentials, in $s$ and $p$ states, which are phase equivalent. Then the $p$-state contribution to the $\Lambda$ well depth as well as $\Lambda \Sigma$ conversion is estimated.

NUCLEAR STRUCTURE Calculation of $\Lambda$ well depth with two-channel YN potential in $s$ and $p$ states.

We deduce evidence for the existence of a two-body current contribution to $M1\mathrm{}$ transitions and moments in nuclei, based on the application of shell model theory to experimental data. A complete specification of a two-body $M1\mathrm{}$ operator, within a shell-model configuration, can be obtained by combining data from particle-particle and particle-hole nuclei. For this purpose, new particle-hole relations are derived for $M1\mathrm{}$ transitions. The method of analysis is applied to the particle-hole pair ${}_{}{}^{38}{}_{}{}^{}\mathrm{Cl}$-${}_{}{}^{40}{}_{}{}^{}\mathrm{K}$. The two-body current contributions could be effects of either configuration mixing, or mesonic currents, or both.

NUCLEAR STRUCTURE ${}_{}{}^{38}{}_{}{}^{}\mathrm{Cl}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{K}$; shell model analysis of $\mu$ and $B\left(M1\mathrm{}\right)\mathrm{}$ to determine two-body $M1\mathrm{}$ operator.

Second-order perturbation theory is used to examine the effect of excluding the g boson from the model space of the interacting boson model. Perturbative corrections are calculated in a paired fermion space (in a single $j$-shell approximation) and are mapped onto the interacting boson model Hamiltonian using the imaging techniques of Otsuka, Arima, and Iachello. The resulting renormalization of the boson parameters of the Hamiltonian to account for effects of the $g$ boson depends strongly upon the numbers of valence protons and neutrons, and remains significant throughout the half shell.

NUCLEAR STRUCTURE Interacting boson model, $g$ boson, microscopic calculation using perturbation theory, renormalization of boson parameters.

A new analytic parametrization of the nuclear form factor is developed using a factorization theorem. We show that the nuclear form factor can be represented in terms of its real zeros and its asymptotic behavior. The parametrization is applied to nuclear form factor data of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. Our results suggest that further diffraction minima can be expected at higher momentum transfer where experiments have not yet been made.

NUCLEAR STRUCTURE Form factor, analyticity, diffraction minima, asymptotic behavior, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^4{}_{}{}^{}\mathrm{He}$.

Theoretical $B\left(E2\mathrm{}\right)\mathrm{}$ values and branching ratios in respect to ${}_{}{}^{150,152,154}{}_{}{}^{}\mathrm{Sm}$ nuclei have been calculated recently using adiabatic time-dependent Hartree-Fock methods which are in poor agreement with experiment. The pairing-plus-quadrupole model of Kumar had already been a failure in describing samarium nuclei. Therefore the asymmetric rotor model has been employed to explain known individual $B\left(E2\mathrm{}\right)\mathrm{}$ values, $B\left(E2\mathrm{}\right)\mathrm{}$ branching ratios, and low lying energy levels. The comparison of phenomenological model results with those of microscopic model calculations has been done only to show the better fit achieved in the present work. The nonaxial parameter ($\gamma$) has been calculated by existing methods, viz., using the energy ratios $\frac{E{2^{+}}^{\prime }}{E{2}^{+}}$, $\frac{E{4}^{+}}{E{2}^{+}}$, and $\frac{E{2^{+}}^{\prime }}{E{6}^{+}}$ or $E{4}^{+}$ and with new approach feeding $E{2}^{+}$ and model dependent intrinsic quadrupole moments ($Q_0$). The asymmetric rotor model estimates are the only ones which stand by the simple test of Kumar (0.5 < enhancement/hindrance factor $F<\mathrm{}2.0\mathrm{}$). It appears that the mass number $A$ and charge number $Z$ play important roles in assigning the shape of the nucleus in terms of the nonaxial parameter $\gamma$.

NUCLEAR STRUCTURE ${}_{}{}^{150,152,154}{}_{}{}^{}\mathrm{Sm}$, rigid rotor model, nonaxial parameter $\gamma$, calculated low lying energy levels, $B\left(E2\mathrm{}\right)\text{'}\mathrm{s}$, branching ratios, compared with experiment and other models.

We report the dependence of trinucleon observables on the strength of two-pion exchange three-body force (Fujita-Miyazawa type). Because of the strong singularity of this force at very short distance, a physical cutoff parameter is introduced in this interaction. The hyperspherical harmonic method is used to handle the solution of this three-body problem. In this method Coulomb and three-body forces are treated nonperturbatively.

NUCLEAR STRUCTURE Trinucleon systems; three-body force; hyperspherical harmonic method.

An investigation is made of the effect of the (central) $\Lambda$-nucleon potential $V_{\Lambda N}$ and of the density distribution $\rho$ of the $\alpha$ particle on the central part of the $V_{\Lambda \alpha }$ interaction, in the framework of the rigid-core model, adopted originally in this context by Dalitz and Downs. Single and double Gaussian shapes for $V_{\Lambda N}$ and $\rho$ are considered, the latter having the advantage that the charge form factor fits rather well the experimental results deduced from the electron scattering experiments including those at high momentum transfers. The differences observed in the values of $V_{\Lambda \alpha }$ depend mainly on the central $\Lambda$-nucleon potential assumed and they are very strong for small values of $r$. Differences also exist in this region because of the various densities used. The double Gaussian density has the effect of lowering the values of $V_{\Lambda \alpha }$ near the center of the $\alpha$ particle in almost all the cases of double Gaussian $\Lambda$-nucleon potentials.

NUCLEAR STRUCTURE Hypernuclei; ${}_{\Lambda }{}^5{}_{}{}^{}\mathrm{He}$; $\Lambda -\alpha$ interaction; $\Lambda -N$ interaction, density of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$.

Five form factor values for the 0.478 MeV transition in ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ have been measured at $\theta =180\mathrm{}°$ in the momentum-transfer range, $0.4<q<\mathrm{}0.75\mathrm{}$ ${\mathrm{fm}}^{-1\mathrm{}}$, using a ${\mathrm{Li}}_2$S target. These data will complement measurements recently taken on this transition at $q>\mathrm{}0.8\mathrm{}$ ${\mathrm{fm}}^{-1\mathrm{}}$ by other investigators. Comparison is made with theoretical calculations. A value of the ground-state transition width ${\Gamma }_0\mathrm{}\left(M1\mathrm{}\right)=(7.5\mathrm{}\pm 1.7)\times {10}^{-3\mathrm{}}$ eV is found for this transition in agreement with earlier measurements of other workers.

NUCLEAR REACTIONS ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ ($e, e^{\prime }$), $E_0=40-74\mathrm{}$ MeV; measured $\frac{d\sigma }{d\Omega }$ at $\theta =180\mathrm{}°$; deduced form factors and transition width ${\Gamma }_0$.

Recoil distance lifetime measurements have been performed for high spin states in ${}_{}{}^{55}{}_{}{}^{}\mathrm{Fe}$ excited in the reaction ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ti}({}_{}{}^{12}{}_{}{}^{}\mathrm{C}, \alpha n)$ at 39 MeV beam energy. The experimental $E2\mathrm{}$ and $M1\mathrm{}$ transition strengths are found to support recent shell model calculations by Vennink and Glaudemans.

NUCLEAR REACTIONS ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ti}({}_{}{}^{12}{}_{}{}^{}\mathrm{C}, \alpha n){}_{}{}^{55}{}_{}{}^{}\mathrm{Fe}$ $E=39\mathrm{}$ MeV; measured recoil distance; deduced $T_{\frac{1}{2}}$, $B\left(E2\mathrm{}\right)\mathrm{}$ $B\left(M1\mathrm{}\right)\mathrm{}$; natural target, Ge(Li) detectors.

Differential cross sections at $15°<~{\theta }_L<~30°$ of the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(d, {}_{}{}^2{}_{}{}^{}\mathrm{He}){}_{}{}^{12}{}_{}{}^{}\mathrm{B}$ reaction were measured at a bombarding energy of $E_d=99.2\mathrm{}$ MeV.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(d, {}_{}{}^2{}_{}{}^{}\mathrm{He})$, $E_d=99.2\mathrm{}$ MeV; measured $\sigma (E_f, \theta )$.

Nuclear time delays of the order of ${10}^{-20\mathrm{}}$ sec as a function of photon energy have been extracted from the experimental $p{}_{}{}^{12}{}_{}{}^{}\mathrm{C}\gamma$ cross sections near the 1.7-MeV scattering resonance. Our extraction is based upon the Feshbach-Yennie approximation which includes both the principal term and the correction term.

NUCLEAR REACTIONS Proton-carbon bremsstrahlung, extract nuclear reaction time delays from the experimental data.

Using the plane-wave impulse approximation we have derived simple expressions for the triple scattering parameters in inelastic proton transitions characterized by a single $\mathrm{lsj}$ value. The plane-wave impulse approximation gives an excellent account of the results of distorted-wave impulse approximation calculations leading to $1^{+}$, $T=1\mathrm{} \mathrm{and} 2^{-}$, $T=0\mathrm{}$ states in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ at $E_p=500\mathrm{}$ MeV.

NUCLEAR REACTIONS Scattering theory, polarization transfer observables.

Separable potentials reproducing the $K^{+}p$ scattering data at energies up to the pion production threshold are presented. They are rank-one and energy dependent. Their interest lies mainly in their usefulness in a Faddeev treatment of the $K^{+}d$ system.

NUCLEAR REACTIONS $K^{+}p$; low-energy scattering; energy-dependent separable potentials.