A set of proton spin observables $D_{\xi }$, $\xi =0, x, y, \mathrm{and} z$, is described which provides selective information on the tensor components of the collision matrix describing the ($p, p^{\prime }$) reaction. These $D_{\xi }$ are related linearly to the experimentally determined components of the depolarization tensor. Simple relations are derived between the $D_{\xi }$ and both the spin components of the nucleon-nucleon amplitudes and the nuclear multipole form factors. For unnatural parity transitions the observable $D_x$ is related to the axial longitudinal form factor which does not enter in the ($e, e^{\prime }$) transition amplitudes for the one photon exchange mechanism.

NUCLEAR REACTIONS New polarization parameters in ($p, p^{\prime }$) reactions.

The results of a radiochemical study of the ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}(p, {\pi }^{-}xn){}_{}{}^{210-x}{}_{}{}^{}\mathrm{At}$ reactions for $x=0\mathrm{} \mathrm{to} 5$ are reported. 200 MeV protons were utilized in an investigation of these pion production reactions as well as secondary processes such as ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}(p, {}_{}{}^{3,4}{}_{}{}^{}\mathrm{He})X$ followed by ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}({}_{}{}^{3,4}{}_{}{}^{}\mathrm{He}, xn){}_{}{}^{213-x}{}_{}{}^{}\mathrm{At}$. The relative importance of such secondary reactions was deduced through variation of the target thickness and from a survey of available data from on-line investigations of ${}_{}{}^{3,4}{}_{}{}^{}\mathrm{He}$ production by other medium energy proton-induced reactions on ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$. An inclusive cross section of 48±13 μb is determined for the ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}(p, {\pi }^{-}xn){}_{}{}^{210-x}{}_{}{}^{}\mathrm{At}$ reactions at 200 MeV. The relative yields of such ($p, {\pi }^{-}\mathrm{xn}$) products are found to be suggestive of a pion production mechanism involving ${\pi }^{-}$ emission through coherent interactions with the target nucleons.

NUCLEAR REACTIONS ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}(p, {\pi }^{-}xn){}_{}{}^{210-x}{}_{}{}^{}\mathrm{At}$, $E_p=200\mathrm{}$ MeV; ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}(p, {}_{}{}^{3,4}{}_{}{}^{}\mathrm{He})X$, ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}({}_{}{}^{3,4}{}_{}{}^{}\mathrm{He}, xn){}_{}{}^{213-x}{}_{}{}^{}\mathrm{At}$; measured $\sigma$, deduced secondary contributions and inclusive ${\pi }^{-}$ production cross section; alpha particle and $\gamma$-ray spectroscopy; Si and Ge(Li) detectors, high purity targets, carrier-free radiochemistry.

The validity of the nucleon charge exchange model for (${\pi }^{\pm }, \pi N$) reactions is tested by comparing cross sections for (${\pi }^{\pm }, \pi N$) reactions near the $\Delta \mathrm{}\left(1232\right)\mathrm{}$ resonance on the odd-$Z$ nuclei ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$, ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$ ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$, and ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}$ that were measured by observing the $\gamma$ decays of the residual nuclei with cross sections calculated from the model. The model reproduces the general trend of the data, but not the detailed features. Comparison of experimental and calculated cross sections indicates that the reactions are largely quasifree, in agreement with our earlier results for self-conjugate nuclei.

NUCLEAR REACTIONS ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$, ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$, ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}$, (${\pi }^{\pm }, \pi N$), $E\simeq 200$ MeV; detected $\gamma \text{'}\mathrm{s}$, Ge(Li); measured $90°\sigma$ for residual levels; deduced $\sigma$ ratios, reaction mechanism; compared results with N-CEX model.

A sensitive test of nuclear charge symmetry has been made by comparing differential cross sections for ${\pi }^{+}$ and ${\pi }^{-}$ elastic scattering from deuterium at 143 MeV. Residual charge symmetry breaking effects in the cross section ratio have been parametrized in terms of mass and width differences among the components of the $\Delta$ isobar. Accurate absolute ${\pi }^{-}d$ differential cross sections were measured for the first time and ${\pi }^{+}d$ differential cross sections agree well with other results and with three-body calculations.

NUCLEAR REACTIONS ${}_{}{}^2{}_{}{}^{}\mathrm{H}({\pi }^{+}, {\pi }^{+})$, ${}_{}{}^2{}_{}{}^{}\mathrm{H}({\pi }^{-}, {\pi }^{-})$, $E_{\pi }=143\mathrm{}$ MeV, measured $\sigma \left(\theta \right)$. Magnetic spectrograph. Three-body analysis. Charge symmetry breaking parametrized in terms of $\Delta$ isobar mass and width differences.

We have measured the reactions ${}_{}{}^{3,4}{}_{}{}^{}\mathrm{He}({\pi }^{-}, n){}_{}{}^{2,3}{}_{}{}^{}\mathrm{H}$ at $T_{\pi }=285, 428, 525, \mathrm{and} 575$ MeV over an angular range ${\theta }_n=18\mathrm{}°-134\mathrm{}°$ in the center-of-momentum frame, and the reaction ${}_{}{}^3{}_{}{}^{}\mathrm{He}({\pi }^{-}, {\pi }^0){}_{}{}^3{}_{}{}^{}\mathrm{H}$ at $T_{\pi }=285, 428, \mathrm{and} 525$ MeV over an angular range ${\theta }_{{\pi }^0}=60\mathrm{}°-140\mathrm{}°$. The pion absorption is found to proceed by a two-nucleon mechanism, with an energy dependence consistent with the formation of an $I=\frac{1}{2}$ resonance in the intermediate state. The pion single-charge exchange is discussed within the framework of the optical and Glauber models, and the dependence on the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ electromagnetic form factors is discussed. We also examine the isospin dependence of the $\pi$-nuclear Hamiltonian.

NUCLEAR REACTIONS ${}_{}{}^{3,4}{}_{}{}^{}\mathrm{He}({\pi }^{-}, n){}_{}{}^{2,3}{}_{}{}^{}\mathrm{H}$, $T_{\pi }=285-575\mathrm{}$ MeV, ${\theta }_n=18\mathrm{}°-134\mathrm{}°$; and ${}_{}{}^3{}_{}{}^{}\mathrm{He}({\pi }^{-}, {\pi }^0){}_{}{}^3{}_{}{}^{}\mathrm{H}$,, $T_{\pi }=285-525\mathrm{}$ MeV, ${\theta }_{{\pi }^0}=60\mathrm{}°-140\mathrm{}°$; measured $\frac{d\sigma }{d\Omega }$; discussed reaction mechanism, effects of form factors.

Measurements of the spin-flip probability for states in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ excited by 397 MeV protons are presented. These data are compared with distorted-wave Born approximation and plane-wave calculations using Cohen-Kurath wave functions as well as simpler transition densities. The results are discussed in terms of the implications for nuclear structure as well as the nucleon-nucleon effective interaction.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(\overrightarrow{p}, {\overrightarrow{p}}^{\prime })$,, spin-flip probability; DWBA, nucleon-nucleon effective interaction.

The interaction of 175-MeV antiprotons with nuclei is examined within the intranuclear cascade model. The experimental characteristics of nucleon-antinucleon annihilation and scattering are used as input, and the propagation of the resultant pions through the nucleus is treated realistically. The effect of the antiproton-nucleus strong attraction is also included. Overall characteristics of antiproton annihilation within nuclei, particularly the large, well-defined energy deposition, indicate that such collisions constitute a unique laboratory for the study of nuclei at very high excitations. The calculations also identify promising experimental observables and triggers.

NUCLEAR REACTIONS 175 MeV antiproton-nucleus scattering and annihilations. Intranuclear cascade calculations. Nuclei at high excitations.

The formalism for photoproduction of pions from nuclei has been developed in the distorted-wave impulse approximation, taking into account the effect of the change in pion momentum in nuclear medium. Detailed calculations have been done for the reaction ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(\gamma , {\pi }^{+}){}_{}{}^{16}{}_{}{}^{}\mathrm{N}$ for photon energies from 170 to 380 MeV, with a view to investigate the effect due to the gradient operator ${\overrightarrow{\nabla }}_{\pi }$ for momentum of the pion and test the sensitivity of the photopion cross sections to the details of the pion-nucleus optical potential. The results clearly establish that the gradient operator increases the cross sections throughout the energy region considered, the increase being small at lower energies. Also with ${\overrightarrow{\nabla }}_{\pi }$, the cross sections are rendered less sensitive to the optical potential. The calculated differential cross sections agree very well with the recent experimental data of Shoda et al. for $\gamma$-ray energy of 200 MeV. However, the cross sections obtained at medium energies are higher when compared to the available experimental data.

NUCLEAR REACTIONS ${\pi }^{+}$ photoproduction from ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$; distorted wave impulse approximation; pion-nucleus optical potentials; gradient operator for the pion momentum.

Beta-ray end-point energies for Rb and La fission products were measured on an on-line mass separator using a hyperpure Ge $\beta$ spectrometer. Coincidence measurements were used to establish feeding relationships and to verfy level schemes in daughter nuclides. $Q_{\beta }$ values are reported for ${}_{}{}^{88,94,96,98}{}_{}{}^{}\mathrm{Rb}$ and ${}_{}{}^{146,148}{}_{}{}^{}\mathrm{La}$. Our results are compared with those from other experiments and with predictions of mass formulae.

RADIOACTIVITY ${}_{}{}^{88,94,96,98}{}_{}{}^{}\mathrm{Rb}$, ${}_{}{}^{146,148}{}_{}{}^{}\mathrm{La}$ [from ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}(n, f)$]; measured $E_{\beta }$, $E_{\gamma }$, $\beta \gamma$, $\gamma \gamma$ coin; deduced $Q_{\beta }$ mass excess. On-line mass separation, HpGe, Ge(Li) detectors.

A nuclear spectroscopic study of the high-spin ground state of ${}_{}{}^{240}{}_{}{}^{}\mathrm{Np}$ ($I^{\pi }=5^{+}$) showed substantial differences from earlier work. The sources, prepared by the ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}(\alpha , pn)$ and ${}_{}{}^{244}{}_{}{}^{}\mathrm{Pu}(n, p4n)$ reactions, were chemically separated and purified. A total of 34 $\gamma$ rays (139.9-1167.1 keV) were observed of which 13 are new; nine others which were reported previously are not confirmed. Absolute intensities of the $\gamma$ rays were determined with the aid of $4\pi$ beta measurements. A modified decay scheme is proposed and discussed; six levels in ${}_{}{}^{240}{}_{}{}^{}\mathrm{Pu}$ with $I^{\pi }=1^{-}, 2^{-}, 3^{-}, \dots , 6^{-}$ are assigned to a $K^{\pi }=1^{-}$ octupole vibrational band. The half-life measured with high purity sources is 61.9±0.2 min.

RADIOACTIVITY 61.9-min ${}_{}{}^{240}{}_{}{}^{}\mathrm{Np}_{}^g{}_{}{}^{}$ from ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}(\alpha , pn)$ and ${}_{}{}^{244}{}_{}{}^{}\mathrm{Pu}(n, p4n)$; radiochemistry, Ge(Li), and $4\pi \beta$ detectors. Measured $E_{\gamma }$, $I_{\gamma }$, $T_{\frac{1}{2}}$; deduced $E_{{\beta }^{-}}$, $log\mathrm{ft}$, ${}_{}{}^{240}{}_{}{}^{}\mathrm{Pu}$ level assignments and decay scheme.

The double beta decay process for ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{76}{}_{}{}^{}\mathrm{Ge}$ is considered. The inhibition of the process for ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$, previously considered by Khodel, is discussed in terms of a $K$ selection rule. The large value found for the ${}_{}{}^{76}{}_{}{}^{}\mathrm{Ge}$ transition to ${}_{}{}^{76}{}_{}{}^{}\mathrm{Se}$, by Haxton, Stephenson, and Strottman, is here illustrated by a pairing calculation using asymptotic Nilsson wave functions. The coherence of the process is clearly shown in this model. The contribution of high lying intermediate states, especially due to delta particle-nucleon hole states, is discussed.

RADIOACTIVITY Double beta decay, pairing correlations, delta admixtures.

Isotope shifts and hyperfine structure splittings of the CaI resonance line ($4s^2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}-4s4p{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$, $\lambda =422.7\mathrm{}$ nm) have been measured for all calcium isotopes between ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$, including the short-lived isotope ${}_{}{}^{47}{}_{}{}^{}\mathrm{Ca}$ ($T_{\frac{1}{2}}=4.54\mathrm{}$ d). Resonance fluorescence was observed in a well-collimated atomic beam of calcium excited by a narrow band tunable continuous-wave dye laser. Combining the result with muonic x-ray data for the stable isotopes, accurate values for the changes of mean square charge radii of the Ca nuclei are obtained, in addition to information on electromagnetic moments from the measured hyperfine structure constants. The influence of ground state correlations (represented by quadrupole and octupole mean square deformations) on the observed peculiar variation of the Ca charge radii is discussed as well as the relation to the droplet model and to a mixed ${\left(f_{\frac{7}{2}}\right)}^n$ model.

NUCLEAR STRUCTURE Isotope shifts and hyperfine structure of Ca isotopes, $A=40\mathrm{} \mathrm{to} 48$, measured by laser spectroscopy, deduced $\delta 〈r^2〉$ and nuclear moments.

This paper begins with an explanation of the implications of the requirement that a two-body relativistic equation should approach a one-body equation when one of the masses becomes very large. It is found that the Bethe-Salpeter equation does not satisfy this requirement. An infinite family of three-dimensional equations depending on a parameter $-1\mathrm{}\le \nu \le 1$ is constructed, all of which do satisfy this limit. When $\left|\nu \right|=1\mathrm{}$ one of the particles is on its mass shell; when $\nu =0\mathrm{}$ both particles are equally off mass shell. The fourth order irreducible kernel for this family is studied in the expanded static limit for all $\nu$. It is found, both for scalar theories and for a realistic chiral theory of spin ½ nucleons interacting with isovector pions, that the leading order terms in the static limit cancel for any $\nu$, and that the nonleading terms are independent of energy only for the $\left|\nu \right|=1\mathrm{}$ equation. Other criteria for the selection of a relativistic two-body equation and implications for the form of the two-pion exchange potential are briefly discussed.

NUCLEAR STRUCTURE Family of two body equations. One body limit. Energy independence of fourth order kernel. Chiral symmetry and nuclear forces.

Examination of the sum of all ladder and crossed ladder exchanges between three particles leads to a set of relativistic three-body equations of the Faddeev type in which two of the three particles are restricted to their mass shell. The choice of which two particles are on shell at a given instant is uniquely determined by the requirement that they be spectators either before or after the interaction. It is shown that these equations satisfy the cluster property, and the two-body amplitudes which drive the equations are known in principle. Three-body unitarity is proved. Three-body forces which arise from the underlying dynamics are discussed, classified, and estimated numerically for a spinless example. It is found that the three-body forces tend to cancel to some extent, are sensitive to the details of the dynamics, and that contributions to such forces, primarily of relativistic origin, can be important.

NUCLEAR STRUCTURE Relativistic Faddeev equations from ladder and crossed ladder exchanges. Unitarity, cluster property, and three-body forces.

The decay of the 2648- and the 803-keV excited states in muonic ${}_{}{}^{206}{}_{}{}^{}\mathrm{Pb}$ has been observed and the isomer shifts of these states have been measured. The isomer shift of the nuclear $2^{+}$ state at 803 keV is -1.45±0.31 keV; the isomer shift of the nuclear $3^{-}$ state at 2648 keV is +6.81±0.46 keV. The measured shifts in ${}_{}{}^{206}{}_{}{}^{}\mathrm{Pb}$ are similar to those measured in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ and support the suggestion that the corresponding states in those nuclei have similar origin.

NUCLEAR STRUCTURE ${}_{}{}^{206}{}_{}{}^{}\mathrm{Pb}$; measured isomer shifts of 803-keV $2^{+}$ and 2648-keV $3^{-}$ nuclear states.

All available $B\left(E2\mathrm{}\right)\mathrm{}$ values in the mass region $8\le Z$, $N\le 20$ relevant to the isovector electric quadrupole operator are compared to the theoretical $B\left(E2\mathrm{}\right)\mathrm{}$ values based on Chung-Wildenthal $0d_{\frac{5}{2}}-1\mathrm{}{s}_{\frac{1}{2}}-0\mathrm{}{d}_{\frac{3}{2}}$ shell-model wave functions with harmonic oscillator radial wave functions, and some selected cases are compared with local and energy dependent Woods-Saxon potential wave functions. The empirical effective charges deduced from these comparisons are insensitive to differences in mass, state, and dominant single-nucleon orbit. The value for the effective charge parameter $e_p-e_n$ extracted in the harmonic oscillator approximation is consistent with $1.0e$. The values extracted with local and energy-dependent Woods-Saxon potentials, which are more meaningfully related to the underlying structure of the isovector polarizability, are consistent with $0.7e$ and $0.6e$, respectively. Some inadequacies in the experimental data and theoretical models are discussed and improvements are suggested.

NUCLEAR STRUCTURE $17\le A\le 39$ nuclei: comparison of experimental $E2\mathrm{}$ isovector matrix elements with shell-model predictions; extraction of the isovector effective charge; full basis $0d_{\frac{5}{2}}-1\mathrm{}{s}_{\frac{1}{2}}-0\mathrm{}{d}_{\frac{3}{2}}$ shell-model wave functions; Chung-Wildenthal Hamiltonians.

We have measured the spectrum of $\gamma$ rays following the decay of 6.55±0.03-h ${}_{}{}^{135}{}_{}{}^{}\mathrm{I}$ to levels of ${}_{}{}^{135}{}_{}{}^{}\mathrm{Xe}$. These $\gamma \gamma$-coincidence measurements have enabled us to construct a level scheme with 31 levels below 2700 keV and make a number of spin and parity assignments. The levels and their deexcitation properties are used to test a large-scale shell model calculation. In general, good agreement is found for this limiting case of the large-scale shell model code. Precise energy values and absolute intensities for the $\gamma$ rays were determined for use in reactor effluent metrology.

NUCLEAR STRUCTURE Shell model calculations five exciton test case.

RADIOACTIVITY ${}_{}{}^{135}{}_{}{}^{}\mathrm{I}$ fission product, radiochemical separation. Determined $t_{\frac{1}{2}}$, $E_{\gamma }$, and $I_{\gamma }$. ${}_{}{}^{135}{}_{}{}^{}\mathrm{Xe}$ deduced levels and $J^{\pi }$ values.

The accuracy of the uncoupled adiabatic approximation is investigated for bound trinucleon systems. The quality of this approximation is related to the strength of the repulsive core of the nuclear potential.

NUCLEAR STRUCTURE Quantum few-body problem.

The hyperspherical harmonic method has been used to calculate the effect of two-pion exchange three-body force (Fujita-Miyazawa type) on trinucleon systems, with the $N-N$ Afnan- Tang S3 potential. The Coulomb force and three-body force have been taken into account nonperturbatively. Simplification in the numerical calculation has been achieved through the use of an adiabatic approximation in order to decouple the system of differential equations. Binding energy, charge form factor, and pointlike proton density of both ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ have been calculated for various values of the cutoff parameter in the three-body force. Results indicate that the inclusion of the three-body force improves agreement with experiment. An interesting feature is the possible appearance of nodes near origin in the hyper-radial wave function.

NUCLEAR STRUCTURE Trinucleon systems; three-body force; bound states of ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ using hyperspherical harmonic method; adiabatic approximation; charge form factors.

In the framework of the hyperspherical formalism, we present a study of the coupled adiabatic approximation for the case of three nucleons interacting via central spindependent two-body potentials. We analyze the convergence of the ground state eigenvalues versus the grand orbital quantum number ($2K$) and compare the results to that of the coupled equations. We also compare with two simpler but less accurate approximations: the uncoupled adiabatic approximation and the extreme adiabatic approximation. The former provides an upper and the latter provides a lower bound to the ground state energy.

NUCLEAR STRUCTURE Few body bound states, reduction of hyperspherical equations applied to triton, quantum few-body problem.