Using two models for the antinucleon-nucleon ($\overline{\mathrm{N}}\mathrm{N}$) interaction, we obtain complex, energy dependent $\overline{\mathrm{N}}\mathrm{N}$ transition operators $t$ appropriate for ($\overline{\mathrm{N}}, {\overline{\mathrm{N}}}^{\prime }$) inelastic scattering studies on complex nuclei. It is shown that the spin-isospin dependence of the $\overline{\mathrm{N}}\mathrm{N}$ annihilation potential plays an important role in determining the dominant spin-isospin modes in the nuclear response. In particular, for the most realistic of our $\overline{\mathrm{N}}\mathrm{N}$ models, a large spin dependent component $t_{\sigma }$ is obtained, leading to the strong excitation of isoscalar spin-flip states; this term is suppressed in the corresponding NN $t$ matrix. The central spin and isospin independent term, $t_0^c$, is large for $\overline{\mathrm{N}}\mathrm{N}$, at all relevant momentum transfers $q$. At high $q$ the isoscalar spin-orbit ($t_0^{\mathrm{LS}}$) and isovector tensor ($t_{\tau }^T$) components are important. Cross section and analyzing power predictions for $\overline{\mathrm{N}}$ inelastic scattering as well as corrections due to energy and density dependence are discussed.

The $2p-1s$ atomic transition in pionic hydrogen has been studied with the help of a point-focusing graphite diffraction spectrometer. The transition energy was measured to be $E(2p-1s)=2433.5\mathrm{}\pm 1.7$ eV. From this result a strong interaction shift of -3.9±1.7 eV was derived. The $K\alpha$ x-ray yield in the 2.7 atm hydrogen target at 40 K was found to be 0.025±0.013 per stopped pion.

The energy spectra of deuterons recoiling from a deuterium gas target bombarded by transversely polarized 796-MeV protons have been measured to obtain the differential cross sections, $\frac{d\sigma }{\mathrm{dt}}$, and analyzing powers, $A_y\mathrm{}\left(t\right)\mathrm{}$, for $\overrightarrow{\mathrm{p}}$-d elastic scattering over a range of laboratory angles from 4.53° to 13.02°, corresponding to a range of four-momentum transfer squared, $\mathrm{}\left|t\right|\mathrm{}$, from 0.013 to 0.108 Ge${\mathrm{V}}^2$/${\mathit{c}}^2$. Employing several sets of nucleon-nucleon, N-N, amplitudes obtained from N-N phase shift analyses, comparisons are made between the experimental data and the predictions of a multiple scattering theory. In this region of four-momentum transfer, $A_y$ is shown to depend almost entirely on the spin-independent and spin-orbit N-N amplitudes.

NUCLEAR REACTIONS $\mathrm{d}(\overrightarrow{\mathrm{p}}, \mathrm{p})\mathrm{d}$, $E=796\mathrm{}$ MeV; measured $\frac{d\sigma }{dt\left(\theta \right)}$ and $A_y\left(\theta \right)$; comparison with multiple-scattering theory using free N-N amplitudes, $-t=0.013-0.108\mathrm{}$ Ge${\mathrm{V}}^2$/${\mathit{c}}^2$, $\Delta t=1.88\mathrm{}\times {10}^{-3\mathrm{}}$ Ge${\mathrm{V}}^2$/${\mathit{c}}^2$.

A $\pi \mathrm{N}$ $S$-wave separable model is developed by implementing most of the field theoretically required analytic properties of the scattering amplitude. In order to improve the low energy behavior of the solution, the $S$-wave interaction model of Drell et al. is incorporated. The resultant dispersion relation is solved using a technique of singular integral equations. Also proposed is an iterative procedure for solving singular integral equations.

NUCLEAR REACTIONS $\pi \mathrm{N}$ $S$-wave separable model. Field theoretical properties with Drell et al. interaction model. Singular equations by Omnès's method.

We obtain the relativistic distorted wave impulse approximation amplitude for nucleon-nucleus collective transitions using an eikonal formalism. The effect of the Darwin term is to suppress the upper-to-upper contribution and enhance the lower-to-lower compared with a nonrelativistic treatment. In collective transitions these combine in a way that results in a transition density proportional to the derivative of the total Dirac distortion including quadratic and spin-orbit pieces. This leads to the same phenomenologically successful relations between elastic and inelastic amplitudes as in the Schrödinger description for collective transitions and promises a better treatment of non-collective transitions. We comment on the vanishing of $P-A$ in this treatment.

The magnetic dipole moments of states in mirror pairs of the $\mathrm{sd}$-shell nuclei and the strengths of the Gamow-Teller beta decays which connect them are compared with predictions based on mixed-configuration shell-model wave functions. From this analysis we extract the average effective values of the single-particle matrix elements of the $l$, $s$, and ${[Y^{\mathrm{}\left(2\right)\mathrm{}}\otimes s]}^{\mathrm{}\left(1\right)\mathrm{}}$ components of the $M1\mathrm{}$ and Gamow-Teller operators acting on nucleons in the $0d_{\frac{5}{2}}$, $1s_{\frac{1}{2}}$, and $0d_{\frac{3}{2}}$ orbits. These results are compared with the recent calculations by Towner and Khanna of the corrections to the free-nucleon values of these matrix elements which arise from the effects of isobar currents, mesonic-exchange currents, and mixing with configurations outside the $\mathrm{sd}$ shell.

RADIOACTIVITY $A=17-39\mathrm{}$ nuclei, magnetic dipole moments and Gamow-Teller beta-decay strengths; shell-model wave functions, complete $0\hslash \omega$ $0d_{\frac{5}{2}}-1\mathrm{}{s}_{\frac{1}{2}}-0\mathrm{}{d}_{\frac{3}{2}}$ basis space, empirical Hamiltonian; extraction of empirical normalizations of the $l$, $s$, and ${[Y^{\mathrm{}\left(2\right)\mathrm{}}\otimes s]}^{\mathrm{}\left(1\right)\mathrm{}}$ single-particle operators.

Anisotropic angular correlation between gamma rays and the $K$ x rays following the $K$ conversion from nuclei with large static deformations has been studied. A complete theoretical expression for ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}$, the second known case of this phenomenon, is presented. This case involves several mixed nuclear transitions which result in 62% of the x rays arising from magnetic dipole internal-conversion processes and 38% arising from electric-quadrupole internal-conversion processes.

We have measured the branching ratio for beta decay of the $J^{\pi }=0^{-}$ state at 120 keV in ${}_{}{}^{16}{}_{}{}^{}\mathrm{N}$ allowing us to infer a beta decay probability of ${\Lambda }_{\beta }=(0.45\mathrm{}\pm 0.05)$ ${\sec }^{-1\mathrm{}}$, in excellent agreement with recent calculations which include pion exchange corrections to the axial vector time component as an essential feature. When combined with the muon capture rate for the inverse reaction, our result implies $\frac{g_p}{g_A}=11\mathrm{}\pm 2$.

RADIOACTIVITY ${}_{}{}^{16}{}_{}{}^{}\mathrm{N}$(${\mathrm{O}}^{-}$, 120 keV) beta decay, meson exchange currents, weak axial vector current.

We compute the effect of radiative corrections on the shape of the end point in tritium beta decay. In order to obtain a correction which is finite relative to the uncorrected spectrum, it is necessary to sum the contribution of soft real photons to all orders. A technique for performing this sum taking into account the constraints of energy conservation is presented. While radiative effects make a relatively small change in the electron spectrum, they could prove important in precise end point measurements designed to determine the neutrino mass.

RADIOACTIVITY Calculation of radiative corrections to the ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ $\beta$ spectrum.

A simple semiclassical picture of the rotating spatial density distribution for spin-aligned high-$j$ quasiparticles emerges from the cranking model. Evidence for the physical relevance of this picture can be sought in the signature splitting of rotational bands in $\gamma$-soft nuclei. The cerium region is a suitable testing ground, and model calculations are presented for bands which might be observed experimentally.

NUCLEAR STRUCTURE Cranking model. Triaxiality of rotating quasiparticle orbitals. Calculated effect on signature splitting in high spin bands of ${}_{}{}^{129-133}{}_{}{}^{}\mathrm{La}$, ${}_{}{}^{129-135}{}_{}{}^{}\mathrm{Ce}$, ${}_{}{}^{131-135}{}_{}{}^{}\mathrm{Pr}$.

We combine the spectral distribution method and the SU(4) algebra to evaluate the Gamow-Teller strengths to low-lying states in the $\mathrm{ds}$ shell. The spectral distribution method is used to calculate the mixing of the SU(4) $\mathrm{ST}$ representations, and the SU(4) algebra gives us the matrix elements of the Gamow-Teller operator between two different SU(4) $\mathrm{ST}$ representations.

NUCLEAR STRUCTURE SU(4) spin-isospin spaces, spectral distribution method, Gamow-Teller $log\mathrm{ft}$ values, applications to nuclei in the $\mathrm{ds}$ shell.

We have introduced a new "hole" formulation by using two rules for deriving the generator coordinate method kernels of the multicluster system with any cluster partitions. The uniform formulae for the overlap kernel, kinetic energy kernel, and potential energy kernel given in this paper can be used easily and are available for computing codes without any further treatment. We have used them to calculate the binding energies of $1p$ shell nuclei and $1p$ shell $\Lambda$ hypernuclei.

NUCLEAR STRUCTURE Derived formulae of kernels. Calculated binding energies of $1p$ shell nuclei, $\Lambda$ hypernuclei.

The transition density between parent and analog states is studied with an eye on its role in charge-exchange nuclear reactions. The structure of the target nucleus is described in a perturbative approach, in which the Coulomb and asymmetry potentials mix the eigenstates of a chargeindependent single-particle Hamiltonian. In this model formulae are derived for the transition density, the Coulomb displacement energy, and the neutron-proton density difference, and their relationship is used to estimate the transition density. This estimate shows that (i) the largest contribution comes from the density of the excess neutrons; (ii) the weight of the Coulomb-mixing effect is small up to excess neutron number 10, and grows rapidly beyond; (iii) the weight of the core polarization term induced by the excess neutrons is modest and is the same for all nuclei. It is indicated that the Coulomb effect may explain the departure from the Lane model of nucleon charge-exchange scattering found for heavy nuclei, whereas the core polarization may account for the observed anomalous dependence of the 0° pion charge-exchange cross section on the number of excess neutrons.

NUCLEAR STRUCTURE Transition densities for charge exchange to IAS; Coulomb and core-polarization effects.

A time-dependent variational procedure is proposed that possesses the same constants of the motion as the exact many-body Schrödinger dynamics. The class of trial wave functions is larger than the manifold of Slater determinants that supports the time-dependent Hartree-Fock dynamics. These wave functions can be regarded as superpositions of the eigenfunctions of the conserved observable of interest and the variational equations display the usual parametric structure, with properly admixed energy gradients and the symplectic metric tensor. In an application to the Lipkin-Meshkov-Glick model, significant improvements over the usual mean-field or determinantal dynamics can be achieved.

NUCLEAR STRUCTURE Mean field symmetry breaking; symmetry restoration; nondeterminantal wave function; time-dependent variational principle; parametric equations of motion; mean energy metric tensor; canonical coordinates; quasispin models; comparison with time-dependent Hartree-Fock dynamics.

Techniques, recently renovated to use for constructing the Hermitian form of the boson expansion theories, are used to reformulate the non-Hermitian boson expansion theory of Dyson. It is shown, in particular, that a combined use of the Usui operator method and the term-by-term bosonization method leads to a very natural rederivation of the Dyson expansions. The eigenvalue problem, including the derivation of separately normalized eigenbra and eigenket vectors, is also discussed. The results obtained here can be used to analyze both even-$A$ and odd-$A$ nuclei.

NUCLEAR STRUCTURE Boson expansion theories, Hermitian, non-Hermitian, particle-pair representation, Tamm-Dancoff representation, Marumori-Yamamura-Tokunaga method, term-by-term bosonization method, even-$A$ nuclei, odd-$A$ nuclei, infinite expansions, finite expansions, minimal truncation, maximal truncation, nonorthonormal basis, Dyson theory, spin wave, kinematic origin of unharmonicity.

We calculate the second-order static physical nucleon-nucleon potential resulting from applying a unitary dressing transformation to the trilinear pion-nucleon interaction with cloudy bag model vertex functions. We find that for two physical nucleons separated by any distance greater than twice the bag radius this potential is exactly the usual one-pion exchange potential modified in strength by a factor 1.05 for a bag of radius 0.7 fm.

NUCLEAR STRUCTURE Dressing transformation, cloudy bag model, calculated second-order nucleon-nucleon potential.

We develop a method for treating the $N$-fermion problem as a system of correlated pairs of particles. Coherent pair states are introduced and a variational as well as a secular method are discussed for providing upper bounds to the exact ground state and approximations to the low lying spectra. Specific applications to two soluble models are presented. For these models the coherent correlated pair method is superior to the Bardeen-Cooper-Schrieffer approximation and to the Hartree-Fock approximation and in fact yields the exact solutions for all particle numbers and sufficiently large coupling constants.

NUCLEAR STRUCTURE Correlated pairs; coherent states; upper bound to ground state energy; applications to soluble $N$-fermion models.

We test the coherent correlated pair method with the soluble SU(3) Hamiltonian of Li, Klein, and Dreizler. We compare the results for the ground state energy with the exact solution and with the Hartree-Fock results as a function of coupling parameters and number of particles. For all cases the coherent correlated pair method yields the better upper bound to the ground state energy.

NUCLEAR STRUCTURE Correlated pairs; coherent states; upper bounds to ground state energies; applications to exactly soluble SU(3) $N$-fermion model.

The cross sections of the electroexcitation of the giant electric-dipole resonances in ${}_{}{}^{42,44}{}_{}{}^{}\mathrm{Ca}$ have been measured for low-momentum transfers $0.3<~q<~0.4$ ${\mathrm{fm}}^{-1\mathrm{}}$, where the quadrupole transition is as small as 10-20% of the total spectra. The dipole resonances were observed to be broadened with some structure in both nuclei, supporting the previous analysis for the measurement at high-momentum transfer.

NUCLEAR REACTIONS ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$(e, e′) and ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ca}$(e, e′), $E=62.5\mathrm{} \mathrm{and} 75.0$ MeV, $q=0.3-0.4\mathrm{}$ ${\mathrm{fm}}^{-1\mathrm{}}$, enriched targets, measured $\sigma (E^{\prime }, \theta )$ up to 30 MeV in excitation energy; deduced giant electric-dipole cross sections.

Accurate differential cross sections for elastic and inelastic ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ scattering by ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ and ${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}$ have been measured at up to 15 angles and in laboratory energy steps of ∼ 100 keV for $20<~E_{\mathrm{C}}^{\mathrm{lab}}<~34$ MeV ($12.5<\mathrm{}{E}_{\mathrm{c}.\mathrm{m}.\mathrm{}}<21.5\mathrm{}$ MeV). Several broad maxima appear in elastic scattering by ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ but not by ${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}$. The cross section for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$) ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ was negligible in this energy range.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{20,22}{}_{}{}^{}\mathrm{Ne}$ elastic and inelastic scattering, $20<~E_{\mathrm{C}}<~34.4$ MeV; measured $\sigma (E, \theta )$ at 15 angles, $\Delta E_{\mathrm{C}}=100\mathrm{}$ keV; absence of yield to ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ exit channel.