The structure of the $\sigma {\tau }_{-}$ strength function is studied with a zero range interaction. The systematics of the giant Gamow-Teller state requires an interaction strength for $V_{\sigma \tau }$ of about 200-240 MeV ${\mathrm{fm}}^3$. While most of the strength goes to a state at high excitation, we find that ∼20-30% of the strength remains at low excitation energy. The $L=1\mathrm{}$ states show considerable $J$ splitting, with a major peak at ≅20 MeV excitation. This peak contains components of $J=0,1, \mathrm{and} 2$. Comparison with the experimental $L=1\mathrm{}$ energy shows that the momentum dependence of the $\sigma \tau$ interaction is small.

[NUCLEAR STRUCTURE. Gamow-Teller states and $L=1\mathrm{}$ states in adjacent odd-odd mass nuclei of double closed shells. TDA and RPA calculation with zero range interaction.]

New, large-momentum-transfer 0.8 GeV $\overrightarrow{p}$ + ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ elastic analyzing power data are presented and compared to optical model predictions using the Kerman-McManus-Thaler microscopic optical potential. This comparison provides an important test of multiple scattering theories since the predictions are quite sensitive to the assumed nucleon-nucleon scattering amplitudes and are not sensitive to the details of the nuclear densities. We show that improvement in the agreement between experiment and a parameter-free theoretical prediction is obtained when the calculation includes the electromagnetic spin-orbit potential which arises from the coupling of the projectile proton's magnetic moment and the Coulomb field of the target nucleus. The sensitivity of the predicted analyzing power to the various ingredients of the theory is also investigated, and the importance of the inclusion of target-nucleon correlations (in the second-order Kerman-McManus-Thaler potential) for proper explanation of the data is discussed.

[NUCLEAR REACTIONS ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}(\overrightarrow{p},p)$, $E=0.8\mathrm{}$ GeV, measured $A_y\left(\theta \right)$; enriched target; resolution $\simeq 100-150$ keV, ${\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}=2^{\circ } \mathrm{to} {32}^{\circ }$. Microscopic optical model analysis using second-order KMT potential; one-photon-exchange magnetic coupling included. Qualitative agreement between experiment and parameter-free calculation.]

Angular distributions for the reaction ${\pi }^{+}+d\to p+p$ have been measured for pion laboratory energies ranging from 20 to 65 MeV. Uncertainties in the total cross sections were less than 6% at all energies studied. The angle integrated cross sections were determined to be 4.31 ± 0.18, 4.84 ± 0.20, 4.26 ± 0.16, 5.19 ± 0.21, 5.30 ± 0.25, 5.20 ± 0.28, and 7.40 ± 0.30 mb for pion laboratory energies of 20, 25, 30, 35, 40, 45, and 65 MeV, respectively. These values confirmed the general trend observed for the total reaction cross section at energies below resonance. The angular distributions and integrated cross sections are compared with recent microscopic calculations. Though qualitative agreement is evident between the models used to describe the process and experimental results, quantitative agreement is still lacking.

[NUCLEAR REACTIONS $d({\pi }^{+},p)p$, $E=20,25,30,35,40,45,65\mathrm{}$ MeV; measured $\frac{d\sigma }{d\Omega }$, deduced total cross section for each energy; obtained fits to $\frac{d\sigma }{d\Omega }$ with polynomials linear and quadratic in ${cos}^2\theta$; compared with microscopic calculations for the reaction.]

The self-consistency requirement is explicitly implemented for the $\pi N$ energy dependent one term separable potential, using the theory of singular integral equations and a dispersion relation involving the real part of the coupling constant. A new definition of the real phase shift will be given and the real part of the coupling constant will be shown to be a constant.

[NUCLEAR REACTIONS Self-consistent $\pi N$ separable model. Singular integral equation method.]

Angular distributions have been measured for the reaction ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$($p,{\pi }^{+}$)${}_{}{}^{13}{}_{}{}^{}\mathrm{C}_{}^{*}{}_{}{}^{}$ at several proton bombarding energies in the range 156-200 MeV. Distinct differences between single-particle and 2p-1h final states are observed in the energy variation of the angular distributions and total cross sections.

[NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(p,{\pi }^{+}){}_{}{}^{13}{}_{}{}^{}\mathrm{C}\mathrm{}\left(\mathrm{Ex}\right)\mathrm{}$, $E_p=156-200\mathrm{}$ MeV, $Ex=0.0,3.09,3.68,3.85,6.86,9.5\mathrm{}$ MeV; measured $\frac{d\sigma }{d\Omega }\left(\theta \right)$, $\theta ={25}^{\circ }-{155}^{\circ }$.]

We calculate the corrections due to pion production, Fermi motion, and the Pauli principle on the ratio of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({\pi }^{\pm },\pi N){}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ total cross sections for particle-stable final states. These corrections are important above 400 MeV. When they are combined with those estimated earlier for final state nucleon charge exchange interactions, good agreement is obtained with the data, which cover the energy region from 40 to 550 MeV.

[NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({\pi }^{\pm },\pi N){}_{}{}^{11}{}_{}{}^{}\mathrm{C}$, calculated ratio of knockout cross sections 40 - 1000 MeV, impulse approximation, nucleon final state charge exchange interactions, pion production corrections, Pauli principle and Fermi motion effects.]

The first correction terms to the eikonal phases are evaluated in closed form for the case of scattering from a potential with a spin-orbit component. It is shown that the size of such effects is significant for the measurement of the polarization parameters in medium energy proton-nucleus scattering.

[NUCLEAR REACTIONS $\mathrm{S}\mathrm{p}\mathrm{i}\mathrm{n}-\frac{1}{2}$ elastic scattering; eikonal corrections to polarization parameters.]

The excitation function for the combined ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}(p,\gamma ){}_{}{}^{210}{}_{}{}^{}\mathrm{Po}$ and ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}(p,{\pi }^0){}_{}{}^{210}{}_{}{}^{}\mathrm{Po}$ reactions was measured for proton energies from 62 to 480 MeV. The measurements were made using standard radiochemical and residual $\alpha$-counting techniques. Below pion-production threshold the radiative proton-capture cross section was observed to decrease with increasing proton energy. Above threshold the combined cross section increases to about 10 μb at 170 MeV. From a smooth extrapolation of the ($p,\gamma$) cross section to energies above pion-production threshold, an estimate of a cross section for the ($p,{\pi }^0$) process is obtained. A theoretical fit of the summed total cross section into all particle bound states was made using a density of states factor, a two nucleon $t$ matrix, and by taking into account the initial state (proton) and final state (pion) distortions using optical potentials.

[NUCLEAR REACTIONS ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}(p,\gamma ){}_{}{}^{210}{}_{}{}^{}\mathrm{Po}+{}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}(p,{\pi }^0){}_{}{}^{210}{}_{}{}^{}\mathrm{Po}$, ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}\mathrm{}(p,2n)\mathrm{}{}_{}{}^{208}{}_{}{}^{}\mathrm{Po}$, ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}\mathrm{}(p,4n)\mathrm{}{}_{}{}^{206}{}_{}{}^{}\mathrm{Po}$, $E_p=62-480\mathrm{}$ MeV, measured polonium-production cross section, thin targets, radiochemical method, $\alpha$ counting, theoretical fit to the ($p,{\pi }^0$) data using two-nucleon model.]

A distorted-wave impulse-approximation analysis of 180-MeV ${\pi }^{\pm }$ inelastic-scattering data to the $2_1^{+}$ and $3_1^{-}$ states in ${}_{}{}^{42,44,48}{}_{}{}^{}\mathrm{Ca}$ is used to extract the neutron and proton (alternatively, isovector and isoscalar) multipole matrix elements for exciting these states. Model-dependent errors are examined by comparing results of calculations using collective-model form factors with those using form factors fitted to electron inelastic-scattering data.

[NUCLEAR REACTIONS ${}_{}{}^{42,44,48}{}_{}{}^{}\mathrm{Ca}({\pi }^{\pm },{\pi }^{\pm })$; measured $\sigma \left(\theta \right)$; DWIA analysis; deduced neutron and proton multipole matrix elements.]

A simple model is used to reproduce modern $\pi N$ phase shifts in the $S$, $P$, $D$, and $F$ waves for $T_{\pi }<2\mathrm{}$ GeV (except $P_{11}$). In these channels a rank one, two-channel separable potential model is used and the inverse scattering problem is solved directly. In the $P_{11}$ channel the phase shifts are fit with a separable $t$ matrix which contains a pole at the nucleon mass and an explicit sign change in the phase shift. This model is intended for use in theories of the low and medium energy pion-nucleus interaction where it supersedes the obsolete LT and LMM potentials. The explicit pole in the $P_{11}$ channel should facilitate the inclusion of pion annihilation into the many body problem.

[NUCLEAR REACTIONS ${\pi }^{\pm }N$; 0-2 GeV phase shifts reproduced; $S$, $P$, $D$, $F$ waves; separable potential with inverse scattering problem; nucleon pole and sign change in $P_{11}$.]

The solution of the inverse scattering problem for a separable model of the pion-nucleon $T$ matrix is obtained. The model is based on the Feshbach-Villars Hamiltonian formulation of the Klein-Gordon equation, and includes the left hand cut in the complex energy plane associated with crossing, as well as the direct and crossed nucleon poles. Numerical results are given for the four $P$-wave channels.

[NUCLEAR REACTIONS Pion-nucleon elastic scattering; inversion procedure for separable $T$ matrix; contains nucleon poles and crossing cut.]

An experiment has been performed to test the time-reversal symmetry in the emission of the mixed $E2$ and $M1$ 129 keV $\gamma$ transition in ${}_{}{}^{191}{}_{}{}^{}\mathrm{Ir}$. The phase angle associated with the imaginary part of the ratio of multipole transition amplitudes was measured through observation of the angular distribution of the linear polarization of the $\gamma$ rays from a ${}_{}{}^{191}{}_{}{}^{}\mathrm{Os}$ source polarized at low temperature (20 to 30 mK obtained with a dilution refrigerator). A Compton polarimeter was used to measure linear polarization. Interaction of the $\gamma$ ray with the surrounding atomic electrons is expected to give rise to a phase shift $\xi$ indistinguishable from the time-reversal phase $\eta$. In the present experiment we have observed a phase angle $(\eta +\xi )=(-4.8\mathrm{}\pm 0.2)\times {10}^{-3\mathrm{}}$ for the 129 keV $\gamma$ ray. This value is in good agreement with the most recent calculations of the atomic final state interaction $\xi =(-4.3\mathrm{}\pm 0.4)\times {10}^{-3\mathrm{}}$. Assuming the validity of the calculated $\xi$, a limit $\left|\eta \right|<\mathrm{}{10}^{-3\mathrm{}}$ is inferred, consistent with time-reversal invariance.

[RADIOACTIVITY ${}_{}{}^{191}{}_{}{}^{}\mathrm{Os}$; measured linear polarization of 129 keV from polarized nuclei, time-reversal test. Deduced relative phase of $E2$, $M1$. Relate to atomic final state effect.]

Using the technique of nuclear magnetic resonance on oriented nuclei, the magnetic hyperfine splitting frequencies ${\nu }_M=\frac{g{\mu }_N{B}_{\mathrm{HF}}}{h}$ of the 11/$2^{-}$ state in ${}_{}{}^{195}{}_{}{}^{}\mathrm{Au}$ ($T_{\frac{1}{2}}=31\mathrm{}$ sec; $E=319\mathrm{}$ keV) in Fe and Ni have been determined as ${\nu }_M\left({}_{}{}^{195}{}_{}{}^{}\mathrm{Au}_{}^m{}_{}{}^{}Fe\right)=979.8\mathrm{}\left(4\right)\mathrm{}$ MHz and ${\nu }_M\left({}_{}{}^{195}{}_{}{}^{}\mathrm{Au}_{}^m{}_{}{}^{}Ni\right)=226.3\mathrm{}\left(2\right)\mathrm{}$ MHz. Taking the known hyperfine fields of ${}_{}{}^{197,198}{}_{}{}^{}\mathrm{Au}$ in Fe and Ni and correcting for hyperfine anomalies a value of $\mathrm{}\left|g\right|=1.123\mathrm{}\left(17\right)\mathrm{}$ is derived for the nuclear $g$ factor of ${}_{}{}^{195}{}_{}{}^{}\mathrm{Au}_{}^m{}_{}{}^{}$.

[RADIOACTIVITY ${}_{}{}^{195}{}_{}{}^{}\mathrm{Au}_{}^m{}_{}{}^{}$ daughter of ${}_{}{}^{195}{}_{}{}^{}\mathrm{Hg}_{}^m{}_{}{}^{}$ [from ${}_{}{}^{194}{}_{}{}^{}\mathrm{Pt}(\alpha ,3n)$]; measured $I_{\gamma }(\theta ,T,\nu )$ of oriented states; NMR on oriented nuclei. ${}_{}{}^{195}{}_{}{}^{}\mathrm{Au}_{}^m{}_{}{}^{}$ deduced $g$, $\mu$.]

The neutrinoless lepton violating double $\beta$ decay is investigated in the context of modern gauge theories, whereby it is mediated by a Majorana neutrino. Transition operators appropriate for calculations of the relevant nuclear matrix elements are constructed. In addition, some of the approximations of the pregauge theories of double $\beta$ decay are investigated. Explicit shell model calculations are performed in the case of the $A=48\mathrm{}$ system.

[RADIOACTIVITY Double $\beta$ decay. Gauge theories. Majorana neutrinos. Lepton nonconservation. Shell model calculations.]

Angular distributions have been measured for 25 gamma rays emitted in the decay of ${}_{}{}^{166}{}_{}{}^{}\mathrm{Ho}_{}^m{}_{}{}^{}$ oriented at low temperatures in paramagnetic neodymium ethyl sulfate and in ferromagnetic Ho metal. The hyperfine Hamiltonians are discussed and parameters describing the strength of the hyperfine interactions are deduced. The reduction of anisotropy in polycrystalline Ho metal is analyzed in detail, with reference to application to nuclear reaction studies using polarized nuclear targets. Spin assignments and multipole mixing ratios are deduced for the levels and transitions in ${}_{}{}^{166}{}_{}{}^{}\mathrm{Er}$.

[RADIOACTIVITY ${}_{}{}^{166}{}_{}{}^{}\mathrm{Ho}_{}^m{}_{}{}^{}$ [from Ho ($n,\gamma$)]; measured $I_{\gamma }\left(\theta \right)$ from oriented nuclei. ${}_{}{}^{166}{}_{}{}^{}\mathrm{Ho}_{}^m{}_{}{}^{}$ deduced magnetic dipole moment, hyperfine interaction parameters; ${}_{}{}^{166}{}_{}{}^{}\mathrm{Er}$ deduced $J^{\pi }$, $\frac{E2\mathrm{}}{M1\mathrm{}}$ and $\frac{M2\mathrm{}}{E1\mathrm{}}$ mixing ratios.]

The charge densities of ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ are computed for several potential models. These densities are further broken down into isospin components and into components from the $S$, $S^{\prime }$, and $D$ states. Wave functions for these states are plotted in order to illustrate the structure seen in the densities. Inclusion of nucleon finite size eliminates the fine structure seen in the point nucleon cases. Form factors corresponding to those densities are also calculated. The inclusion of a Coulomb interaction between the two protons in ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is seen to produce a small but nonnegligible change in the density. The theoretical ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ densities for the Reid soft core model are compared to the "experimental" one obtained by fitting the experimental form factor data after having approximately removed the effect of nucleon finite size. The central depression seen in the experimental density is not present in the theoretical ones, and we speculate on this and other discrepancies.

[NUCLEAR STRUCTURE Trinucleon system, charge density, wave function components, Coulomb interaction.]

The standard partial wave (channel) representation for the Faddeev solution to the Schrödinger equation for the ground state of 3 nucleons is written in terms of functions which couple the interacting pair and spectator angular momenta to give $S$, $P$, and $D$ waves. For each such coupling there are three terms, one for each of the three cyclic permutations of the nucleon coordinates. A series of spherical harmonic identities is developed which allows writing the Faddeev solution in terms of a basis set of 5 bipolar harmonics: 1 for $S$ waves; 1 for $P$ waves; and 3 for $D$ waves. The choice of a $D$-wave basis is largely arbitrary, and specific choices correspond to the decomposition schemes of Derrick and Blatt, Sachs, Gibson and Schiff, and Bolsterli and Jezak. The bipolar harmonic form greatly simplifies applications which utilize the wave function, and we specifically discuss the isoscalar charge (or mass) density and the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ Coulomb energy.

[NUCLEAR STRUCTURE Three-body problem, classification of states.]

We present a simple method for the derivation of the classical limit of the most general interacting boson model Hamiltonian as well as the Hamiltonians in the three limits of the interacting boson model. Also the problem of higher order terms is considered.

[NUCLEAR STRUCTURE Classical limit of the interacting boson model.]

Using a very simple type of wave packet, which is obtained by letting unitary displacement operators having as generators canonical operators $\hat{Q}$ and $\hat{P}$ in the many-body Hilbert space act on a reference state, we investigate the relationship between the semiclassical and the generator coordinate methods. The semiclassical method is based on the time-dependent variational principle, whereas in the generator coordinate method the wave packets are taken as generator states. To establish the equivalence of the two methods, we examine in detail, using tools developed in previous works, the concept of redundancy of the wave packet and the importance of the zero-point energy effects. We make a numerical application to the case of the Goldhaber-Teller mode in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$.

[NUCLEAR STRUCTURE Relationship between the semiclassical and the generator coordinate methods. Redundancy and zero-point energy effects. Numerical application to the Goldhaber-Teller mode in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$.]

The coupling of the solutions to the random phase approximation pairing vibration and the collective quadrupole oscillation, obtained from a boson expansion approach, is used to describe simultaneously many properties of the even-even isotopes of Ge. Low lying energies, $E0\mathrm{}$ and $E2\mathrm{}$ transitions, two nucleon transfer amplitudes, and quadrupole moments are calculated and fairly good agreement is obtained compared to experiment. In particular the behavior of the ${\mathrm{O}}_2^{+}$ state energy as a function of mass is accurately described including the prediction of its being the lowest energy excited state of ${}_{}{}^{72}{}_{}{}^{}\mathrm{Ge}$. The shape of the nucleus is concluded to be in a transitional region between prolate and oblate.

[NUCLEAR STRUCTURE ${}_{}{}^{68-76}{}_{}{}^{}\mathrm{Ge}$ boson expansion and RPA calculations. Quadrupole moments, $B\left(E2\mathrm{}\right)\mathrm{}$; ($p,t$) and ($t,p$) spectroscopic amplitudes and $E0\mathrm{}$ transitions.]