Using a decay-in-flight technique, a search for 1-100 nsec $\alpha$ decay has been conducted in a variety of rare earth nuclei made in energetic heavy ion reaction. Assuming spherical rigid rotation and $\alpha$ particle formation factors similar to those of the ground state, this lifetime range corresponds to nuclear spins of $30-50\hslash$ where very high spin isomerism has been predicted theoretically. No evidence for $\alpha$ decay was observed. $\alpha$ decay cross section limits are set for 14 systems in which high spin isomers ($I>\mathrm{}10\mathrm{} \hslash$) are known with lifetimes in the range studied. Comparison to theoretical total cross sections allows $\alpha$-branching ratio estimates to be made.

RADIOACTIVITY Short-lived isomers of Gd, Tb, Dy, Ho, Er; measured limits on $I_{\alpha }$ for $6<\mathrm{}{E}_{\alpha }<16\mathrm{}$ MeV and $1<\mathrm{}{t}_{\frac{1}{2}}<100\mathrm{}$ nsec; deduced limits on $\alpha$-decay branching ratios.

The half-life of ${}_{}{}^{243}{}_{}{}^{}\mathrm{Am}$ was determined by the relative activity method. Synthetic mixtures were prepared by using solutions of ${}_{}{}^{241}{}_{}{}^{}\mathrm{Am}$ and ${}_{}{}^{243}{}_{}{}^{}\mathrm{Am}$ isotopes. The $\alpha$ activity ratios and the atom ratios in these mixtures were kept close to unity by employing the double dilution technique so that these could be measured with high precision and accuracy. The $\alpha$ activity ratios were determined by $\alpha$ spectrometry on electrodeposited sources using a silicon surface barrier detector and the atom ratios were obtained by mass spectrometry. A value of 17.010±0.095 was obtained for the ${}_{}{}^{243}{}_{}{}^{}\mathrm{Am}$/${}_{}{}^{241}{}_{}{}^{}\mathrm{Am}$ half-life ratio which leads to a value of 7358±42 yr for the half-life of ${}_{}{}^{243}{}_{}{}^{}\mathrm{Am}$ using the half-life of ${}_{}{}^{241}{}_{}{}^{}\mathrm{Am}$ as 432.6 yr. The uncertainty specified on the values is a combination of the one standard deviation on the average value and the error evaluated from the estimate on the various error components.

RADIOACTIVITY ${}_{}{}^{243}{}_{}{}^{}\mathrm{Am}$ half-life; measured: ${}_{}{}^{241}{}_{}{}^{}\mathrm{Am}$/${}_{}{}^{243}{}_{}{}^{}\mathrm{Am}$ atom ratios by mass spectrometry, ${}_{}{}^{241}{}_{}{}^{}\mathrm{Am}$/${}_{}{}^{243}{}_{}{}^{}\mathrm{Am}$ $\alpha$ activity ratios by $\alpha$ spectrometry.

Shell-model wave functions for $A=17-39\mathrm{}$ nuclei are used to calculate the one-body densities upon which are based the $M1\mathrm{}$, $E2\mathrm{}$, $M3\mathrm{}$, $E4\mathrm{}$, and $M5\mathrm{}$ moments of stable ground states with $J^{\pi }=\frac{3}{2^{+}} \mathrm{and} \frac{5}{2^{+}}$, Values of the moments are obtained by combining these densities with single-particle matrix elements calculated with both free space and renormalized expressions for the electromagnetic operators. These results extend previous calculations for the $M1\mathrm{}$ and $E2\mathrm{}$ moments. The theoretical values are analyzed in terms of deviations from the predictions of the pure-configuration shell model and compared with available experimental data. While several of these data are well described with the present theory, a few other experimental values differ significantly from the corresponding predicted values.

NUCLEAR STRUCTURE ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}$, ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$, ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{33}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{35}{}_{}{}^{}\mathrm{Cl}$, ${}_{}{}^{37}{}_{}{}^{}\mathrm{Cd}$, ${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$; calculations for the $M1\mathrm{}$, $E2\mathrm{}$, $M3\mathrm{}$, $E4\mathrm{}$, and $M5\mathrm{}$ moments of ground states; complete $0d_{\frac{5}{2}}-1\mathrm{}{s}_{\frac{1}{2}}-0\mathrm{}{d}_{\frac{3}{2}}$ shell-model wave functions; Chung-Wildenthal Hamiltonians.

A general formalism is proposed for evaluating the effective interaction between valence nucleons, taking into consideration the low-lying contributions of two-particle two-hole (2p2h), two-particle one-hole (2p1h), three-particle one-hole (3p1h), three-particle two-hole (3p2h), and four-particle two-hole (4p2h) correlations. The formalism consists of solving a hierarchy of multiple scattering type equations with coupling between various correlations and is naturally combined with the $Q$-box approach for folded diagram theory. The energy dependence of the reaction matrix is included in the formalism. The effect of 4p2h correlations is studied for a simple two-level model for mass 42 by solving the hierarchy of coupled equations numerically by neglecting the coupling to 2p1h and 3p1h configurations. The 4p2h correlation with 4p coupled to isospin 0 has dominant contributions as expected. For a reasonable choice of the energy denominator, the 4p2h contribution to the two-body effective interaction is sizably attractive.

NUCLEAR STRUCTURE Shell model, effective interaction between valence nucleons, particle-hole multiple scattering formalism for low-lying states.

Four different methods for handling the retardation of a single meson exchange in the nuclear force have been examined, together with the corresponding contributions to the deuteron charge operator. It is shown that to order ${\left(\frac{v}{c}\right)}^2$ these operators are all part of a single unitarily equivalent family. The Gross quasipotential equation is examined and relativistic corrections to the deuteron charge form factor are shown to be the same as those generated by the author's method, when converted to a common unitary representation. The same result has also been demonstrated for the folded diagram method. The asymmetric terms in Gross's Hamiltonian are shown to take the place of recoil graph contributions to the charge operator. These terms are necessary for Lorentz invariance and the "Gross correction" to the deuteron charge form factor.

NUCLEAR STRUCTURE Deuteron, $\rho$, meson exchange currents, relativistic effects.

The charge form factor of ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ in the $q^2$ range of 0 to 7 ${\mathrm{fm}}^{-2\mathrm{}}$ is calculated with a single-channel $t+\alpha$ resonating-group wave function which is fully antisymmetric and treats correctly the motion of the total center of mass. Both $C0\mathrm{}$ and $C2\mathrm{}$ contributions are taken into account, and proton and neutron distributions are separately considered. With no adjustable parameters in the calculation, the result obtained shows that a good agreement between theory and experiment can be achieved. The calculated rms charge radius and spectroscopic quadrupole moment are equal to 2.44 fm and - 3.70 ${\mathrm{fm}}^2$, respectively, which agree very well with empirically determined values.

NUCLEAR STRUCTURE ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$; charge form factor with resonating-group wave function.

The formulation of Faddeev-type equations in configuration space is discussed. Numerical solutions are obtained using splines and the method of orthogonal collocation. Triton observables and wave-function probabilities are calculated for $s$-wave $\mathrm{NN}$ interaction models of Malfliet and Tjon and the tensor force model of Reid. Comparison with previously published triton results is made; our full five-channel results for the Reid soft-core potential are in excellent agreement with those obtained by Afnan and Birrell using separable expansion methods.

NUCLEAR STRUCTURE ${}_{}{}^3{}_{}{}^{}\mathrm{H}$, Faddeev calculations configuration space.

Coordinate space Faddeev techniques and a variety of potentials are used to calculate energies and wave functions for the trinucleon system, both with and without a static Coulomb interaction between the two protons. The wave functions are used to calculate first- and second-order perturbation theory contributions to the Coulomb energy of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. Because too few partial-wave components of the potential are kept, the energy eigenvalues themselves are an inaccurate gauge of the Coulomb effect. The approximate hyperspherical formula was tested after calculating charge densities and found to be accurate to better than 2 percent. It is demonstrated that when using a phenomenological approach to the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ Coulomb energy, the second-order contribution increases the Coulomb energy by roughly 4 ± 1 keV. Finally, sum rules relating to the $T=\frac{3}{2}$ state probability and the size of the second-order contribution are discussed.

NUCLEAR STRUCTURE ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, Coulomb energy, Faddeev calculation.

Theoretical calculations are presented for the magnetic octupole electromagnetic matrix elements in light nuclei. Shell-model wave functions are used to calculate the $M3\mathrm{}$ matrix elements for the cases ${}_{}{}^{24}{}_{}{}^{}\mathrm{Al}$ $1^{+}$ →$4^{+}$, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Na}$ $1^{+}$ →$4^{+}$, ${}_{}{}^{34}{}_{}{}^{}\mathrm{Cl}$ $3^{+}$ →$0^{+}$, ${}_{}{}^{38}{}_{}{}^{}\mathrm{K}$ $0^{+}$ →$3^{+}$, and ${}_{}{}^{38}{}_{}{}^{}\mathrm{Cl}$ $5^{-}$ →$2^{-}$. The radial matrix elements are calculated with harmonic-oscillator and spherical Hartree-Fock potentials. The comparison of the calculated and experimental matrix elements is expressed in terms of effective spin $g$ factors. Theoretical calculations for the core-polarization corrections are presented and relations between the $E2\mathrm{}$ core-polarization charge and the $M3\mathrm{}$ effective spin $g$ factors are derived.

NUCLEAR STRUCTURE ${}_{}{}^{24}{}_{}{}^{}\mathrm{Na}$, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{34}{}_{}{}^{}\mathrm{Cl}$, ${}_{}{}^{38}{}_{}{}^{}\mathrm{K}$, ${}_{}{}^{38}{}_{}{}^{}\mathrm{Cl}$; calculations of $M3\mathrm{}$ decay strengths; extraction of effective $M3\mathrm{}$ operator; full $d_{\frac{5}{2}}-s_{\frac{1}{2}}-d_{\frac{3}{2}}$ shell-model calculations with Chung-Wildenthal Hamiltonians.

The negative parity states of ${}_{}{}^{105-109}{}_{}{}^{}\mathrm{Ag}$ are interpreted according to the generalized particle—asymmetric-rotor model. In particular, the influence of the different Nilsson proton orbitals (lying near the Fermi level) on the theoretical level spectra and electromagnetic properties is investigated in detail. Furthermore, the analysis of the wave functions of the theoretical levels, and the contributions of their main components in the $B\left(M1\mathrm{}\right)\mathrm{}$ and $B\left(E2\mathrm{}\right)\mathrm{}$ matrix elements, reveals the single particle or collective character of such levels. The best agreement between the theoretical and experimental results is obtained by coupling four Nilsson proton orbitals (numbers 10-13), with main components on $p_{\frac{1}{2}}$, $p_{\frac{3}{2}}$, $f_{\frac{5}{2}}$ subshells, to an asymmetric rotor ($\epsilon =0.26\mathrm{}$; $\gamma =32\mathrm{}°$).

NUCLEAR STRUCTURE ${}_{}{}^{105-109}{}_{}{}^{}\mathrm{Ag}$ calculated spectra, electromagnetic properties. Generalized particle-asymmetric-rotor model.

The ground state and the first excited states of ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ have been studied within the alpha-cluster model for two standard soft-core forces. We discuss the approximations resulting from variation without projection, variation after parity projection, angular momentum projection after variation, and possible $K$ mixing. In contrast to earlier calculations in lighter nuclei a free variation of all parameters has been performed without forcing the alpha clusters to be arranged in configurations with prescribed symmetry. In all approximations and for both forces the intrinsic ground state turns out to be triaxial with $C_{2v}$ symmetry. The resulting binding and excitation energies, rms radii, and quadrupole moments are given. In comparable cases a close agreement is found with Hartree-Fock results for the same forces.

NUCLEAR STRUCTURE Alpha-cluster structure calculation with $B_1$ and $V_1$ softcore forces for ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$. Calculated energies, densities, quadrupole moments, and rms radii.

The yrast states up to $J={22}^{+}$ of seven even tungsten isotopes ${}_{}{}^{170-182}{}_{}{}^{}\mathrm{W}$ are studied in a microscopic formulation of variation after angular momentum projection with number conservation in each state. The Hamiltonian with quadrupole plus pairing interactions is employed in the calculations of energy spectra, quadrupole moments, and $B\left(E2\mathrm{}\right)\mathrm{}$ values. The results of the calculations are in good agreement with the corresponding experimental data.

NUCLEAR STRUCTURE W isotopes; calculated energy spectra, quadrupole moments, and $B\left(E2\mathrm{}\right)\mathrm{}$ values. Variation with number-conserved projected states.

We give a short derivation of a relativistic two-body bound-state quasipotential integral equation the kernel of which is symmetric, fully continuous, and positive definite. We discuss a numerical solution of the eigenvalue problem based on the analytical structure of the kernel. We have found the first 50 approximate eigenvalues and the corresponding eigenfunctions. We have also estimated the error in the numerical calculation. We give a graphical representation of the first four eigenfunctions.

NUCLEAR STRUCTURE Deuteron bound state. Numerical solution of the relativistic quasipotential equation for a scalar two-body bound state.

We derive an approximate expression for the moment of inertia $\theta$ in the framework of the cranked Hartree-Fock theory. Our method allows for a detailed study of the role of spin-orbit and two-body nuclear potentials. In particular it is shown that in ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ the two-body interaction lowers by 30% the rigid value of $\theta$. The irrotational and rigid values for the moment of inertia are obtained as special cases of the present approach.

NUCLEAR STRUCTURE ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$, calculated moment of inertia, cranked Hartree-Fock method.

We have applied the boson expansion method to describe the low-lying positive parity states of even-even Ru and Pd isotopes. Energy levels, $B\left(E2\mathrm{}\right)\text{'}\mathrm{s}$, branching ratios, and magnetic dipole and electric quadrupole moments have been calculated and are in good agreement with experiment. It is particularly emphasized that our theory describes rather well the properties of the three-phonon-like $3_1^{+}$ state.

NUCLEAR STRUCTURE ${}_{}{}^{98-104}{}_{}{}^{}\mathrm{Ru}$, ${}_{}{}^{102-110}{}_{}{}^{}\mathrm{Pd}$, energy levels, $B\left(E2\mathrm{}\right)\text{'}\mathrm{s}$, branching ratios, magnetic moments, static quadrupole moments, boson expansion.

The recently suggested $A$ dependence of the sub-Coulomb proton optical model potential in the mass region $89\le A\le 130$ is here discussed. Optical model parameters are deduced for ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$, ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}$, and ${}_{}{}^{103}{}_{}{}^{}\mathrm{Rh}$ from neutron and proton scattering data. Comparisons are made with previous analyses of proton strength functions.

NUCLEAR REACTIONS spherical optical model calculations, nucleon strength functions: $A=89, 93, 103$, shell effect, ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}$ ($p, p$) $E_p=22.2\mathrm{}$ MeV, ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}(p, n)$ ${}_{}{}^{93}{}_{}{}^{}\mathrm{Zr}$ $E_p=18.7\mathrm{}$ MeV.

Lagrange's optical model analysis, which includes not only sub-Coulomb proton absorption cross sections but also neutron data and other proton data, adds insight into the anomalous behavior of the sub-Coulomb protons but does not explain all of the anomaly.

NUCLEAR REACTIONS $\sigma (p, n)$, $89<~A<~130$, optical model.

Another look is taken at the transition amplitude for radiative muon capture. We conclude that the standard, or diagrammatic, amplitude first given by Opat for hydrogen is a good approximation to the systematic expansion of Adler and Dothan, and use it to calculate the angle-integrated photon spectrum in ${}_{}{}^3{}_{}{}^{}\mathrm{He}{\mu }^{-}\to {}_{}{}^3{}_{}{}^{}\mathrm{H}\gamma \nu$. The result is in fair agreement with Beder and Fearing. Also, the "soft-pion" prediction for ${}_{}{}^3{}_{}{}^{}\mathrm{He}{\pi }^{-}\to {}_{}{}^3{}_{}{}^{}\mathrm{H}\gamma$ is compared with experimental data.

RADIOACTIVITY ${\mu }^{-}{}_{}{}^3{}_{}{}^{}\mathrm{He}\to {\nu }_{\mu }{}_{}{}^3{}_{}{}^{}\mathrm{H}\gamma$, ${\pi }^{-}{}_{}{}^3{}_{}{}^{}\mathrm{H}\to {}_{}{}^3{}_{}{}^{}\mathrm{He}\gamma$; theories of radiative muon capture; tests of PCAC and soft-pion predictions.

We have measured the cross sections of the reaction ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({\pi }^{+}, {\pi }^{+}p){}_{}{}^{11}{}_{}{}^{}\mathrm{B}$ in a coincidence experiment at 100 and 130 MeV and compare our results with the cross sections calculated in the plane-wave impulse approximation.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({\pi }^{+}, {\pi }^{+}p){}_{}{}^{11}{}_{}{}^{}\mathrm{B}$, $e=100\mathrm{} \mathrm{and} 130$ MeV; measured $\sigma (E, E_{\pi }, E_p, {\theta }_{\pi }, {\theta }_p)$ in coincidence; compared with plane wave impulse approximation.

The virtual photon spectrum shape and intensity within several MeV of the kinematic limit was measured for ${}_{}{}^9{}_{}{}^{}\mathrm{Be}(e, {\pi }^{+}){}_{}{}^9{}_{}{}^{}\mathrm{Li}, e^{\prime }$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(e, {\pi }^{+}){}_{}{}^{16}{}_{}{}^{}\mathrm{N}, e^{\prime }(T_{\pi }=28\mathrm{} \mathrm{MeV}, {\theta }_{\pi }=90\mathrm{}°)$. The intensity over this interval is 1.25±0.10 times plane-wave virtual photon theory predictions; the shape agrees with theory within errors. Measurements on the proton 30 to 55 MeV below the end point agree with the intensity predictions of virtual photon theory within the errors (±8%).

NUCLEAR REACTIONS ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(e, {\pi }^{+})$, $E=180.4\mathrm{}$ MeV; ${}_{}{}^9{}_{}{}^{}\mathrm{Be}(e, {\pi }^{+})$, $E=184.8\mathrm{}$ MeV; measured $\sigma (E_{\pi }, {90°}_{\mathrm{lab}})$ relative to ($\gamma , {\pi }^{+}$), near $E_{\pi }=28\mathrm{}$ MeV. ${}_{}{}^1{}_{}{}^{}\mathrm{H}(e, {\pi }^{+})$, $E=230\mathrm{}$ MeV; measured $\sigma (E_{\pi }, {90°}_{\mathrm{lab}})$ relative to ($\gamma , {\pi }^{+}$), near $E_{\pi }=18, 30$ MeV. Compared to PWBA virtual photon theory.