${}_{}{}^{87}{}_{}{}^{}\mathrm{Y}_{}^m{}_{}{}^{}$ produced by the $\mathrm{Rb}(\alpha ,2n)$ reaction and implanted into cubic Al and Au hosts has been oriented with 2-6 T external magnetic fields at low temperature. The nuclear magnetic moment of the 9/$2^{+}$ isomeric state is $\mu =6.10\left(\{+32\mathrm{}\}\{-15\mathrm{}\}\right){\mu }_N$, which inserts well in the systematics of 1 $g_{\frac{9}{2}}$ nuclear moments. Attenuation of the orientation has been observed after heat treatment of samples, attributed to oxygen trapping by yttrium atoms.

[RADIOACTIVITY ${}_{}{}^{87}{}_{}{}^{}\mathrm{Y}_{}^m{}_{}{}^{}$, measured $I_{\gamma }\left(\Theta \right)$ from polarized nuclei, deduced $\mu \left({}_{}{}^{87}{}_{}{}^{}\mathrm{Y}_{}^m{}_{}{}^{}\right)$. ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ dilution refrigerator, Ge(Li) detectors.]

The combined interaction of a static electric field gradient and a static magnetic field with the electromagnetic moments of a nucleus is considered for the case of nuclear orientation at low temperature. The general expression of the angular directional distribution of radiation emitted by the oriented state is developed for polycrystalline samples, where the principal axes of the electric field gradients are randomly distributed with respect to a fixed magnetic field direction. Due to axial symmetry of the ensemble the effect of the quadrupole interaction is reduced to an attenuation factor on the usual $B_K$ coefficients. Numerical calculations of these attenuation factors for $K=1, 2, \mathrm{and} 4$ have been performed in the case of the symmetric electric field gradient for a wide range of electric to magnetic interaction ratios and spin values $I=1,\frac{3}{2},\dots 8$. Typical attenuation curves for spin 5/2 and 9/2 are presented. Comparing the experimental anisotropies with the tabulated values, one can extract the quadrupole interaction value $\hslash {\omega }_Q$.

[RADIOACTIVITY Attenuation by random and symmetric electric quadrupole interaction of the low temperature nuclear orientation coefficient due to a polarizing magnetic field are computed for multipole order 1, 2, and 4 of the emitted radiation angular distribution.]

We discuss two simple effective interactions which fit selected empirical ${\left(j^2\right)}_{T=1\mathrm{}}$ matrix elements. One important property of both interactions is the presence of a long range repulsion in odd states, as was already pointed out previously by others. We then discuss the role of configuration mixing in both the weak coupling and strong coupling limits to show qualitatively that the repulsion can arise naturally from truncation of the model space used to define the interaction. Presumably with a sufficiently larger model space no long range repulsion is needed. We also remark on the difference between yrast state energies and centroids of the single particle transfer strength. It is the latter which are based in the empirical matrix elements. Finally we briefly discuss a semiclassical model for calculating matrix elements for a finite range interaction.

[NUCLEAR STRUCTURE Effective interactions, ${\left(j^2\right)}_{T=1\mathrm{}}$ configurations, configuration mixing.]

A microscopic method for determining the coefficients of a fourth-order boson expansion of the Hamiltonian is used to obtain angular momentum projected states, their energies, and electric quadrupole properties. A Tabakin potential is used in applying the method to the even-even Ba isotopes, $A=130-138\mathrm{}$.

[NUCLEAR STRUCTURE Angular momentum projected quasiboson formalism, ${}_{}{}^{130,132,134,136,138}{}_{}{}^{}\mathrm{Ba}$, calculated levels, $J$, $\pi$, $B \mathrm{}\left(E2\mathrm{}\right)\mathrm{}$, quadrupole moments. Tabakin interaction.]

Calculated energy levels arising from specific particle-hole configurations relative to ${}_{}{}^{56}{}_{}{}^{}\mathrm{Ni}$ are in good agreement with the observed spectra of $A=53-58\mathrm{}$ Fe isotopes. The energies of intruder states are closely reproduced, and spin assignments can be proposed for several known high-spin states. The energies of yrast levels, which to date have not been isolated, are predicted.

[NUCLEAR STRUCTURE ${}_{}{}^{53,54,55,56,57,58}{}_{}{}^{}\mathrm{Fe}$; calculated levels, deduced particle-hole structure. Shell model with fitted effective interaction.]

For a system of fermions interacting via a pure pairing force, exact level densities are obtained in a semirealistic model space. The results are transmitted through graphs and tables so that they are readily available for comparison with various approximate methods. A fairly detailed comparison with a particular approximate method using the grand partition function is also made. The consequences of adding the quadrupole force to the Hamiltonian are discussed. Variational calculations done in the specific case of Sn isotopes suggest that although these nuclei are spherical in the ground state (zero temperature), it is possible that they prefer deformation at finite but low temperature. This can lead to very large changes in the calculated values of level densities.

[NUCLEAR STRUCTURE ${}_{}{}^{116}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{117}{}_{}{}^{}\mathrm{Sn}$; calculated level density using quasispin formalism, grand partition method, and pairing-plus-quadrupole model at finite temperature.]

The binding energy of ${}_{}{}^3{}_{}{}^{}\mathrm{H}$, percentage $S$-, $S^{\prime }$-, and $D$-state probabilities and charge form factor of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ are calculated using the Adhikari-Sloan separable expansion to the Holinde and Machleidt one-boson-exchange potential. The results show that the Adhikari-Sloan expansion has good convergence for the binding energy, and the lowest order Adhikari-Sloan expansion considered gives excellent results for the form factor.

[NUCLEAR STRUCTURE ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ binding energy, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ charge form factor, Faddeev approach, separable expansion to realistic $N-N$ interaction.]

For very rapidly rotating nuclei, the moment of inertia can be readily increased if the mass is distributed in the form of a torus. Thus, a rotating toroid can be a figure of equilibrium when the angular momentum exceeds a certain limit. The angular momentum thresholds for the onset of toroidal figures of equilibrium are evaluated and found to be greater than the limits at which the fission barriers vanish for nuclei with the topology of a sphere. Stability against sausage deformation, in which the toroid becomes thicker in some sections but thinner in some other, is examined. We obtain two different results on the question of stability, depending on the flow pattern in the presence of these axially asymmetric deformations which, in turn, is greatly affected by the dissipative mechanism.

[NUCLEAR STRUCTURE Rotating toroidal nuclei. Nuclei with very large angular momentum. Sausage stability. Regions of stable rotating toroidal nuclei.]

A new method for analyzing $\alpha$-nucleus optical potentials is presented. It consists of adding to the conventional Woods-Saxon real potential an extra potential given by a Fourier-Bessel series. The coefficients of the series are determined by least-squares fit to experimental cross sections for elastic scattering. A detailed discussion of the uncertainties in the derived parameters is presented, both for the real potential as a function of radius and for integral quantities such as the volume integral and the root-mean-square radius. The method is illustrated using existing data over wide angular range for the elastic scattering of 139 MeV $\alpha$ particles by ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$ and of 104 MeV $\alpha$ by ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, where with the new method ${\chi }^2$ per degree of freedom is reduced by a factor of between 5 and 7 to a value of almost 1. The method is also used for the analysis of data for 104 MeV $\alpha$ particles scattered by ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$, which is restricted to the diffraction region of the angular distribution. In that case the new method is capable of uniquely specifying the region where the real potential is well determined. Evidence is presented for saturation effects in the folding model.

[NUCLEAR REACTIONS $\alpha$-nucleus optical potentials; modifications to Woods-Saxon form using Fourier-Bessel series. ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}(\alpha ,\alpha )$, ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}(\alpha ,\alpha )$, $E_{\alpha }=104\mathrm{}$ MeV. ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}(\alpha ,\alpha )$, $E_{\alpha }=139\mathrm{}$ MeV.]

The structure of light nuclei is considered using the $\alpha$ cluster model. On the basis of $\alpha$ clusters, the model structures of the nuclei ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ are proposed as composed of three particles. The bound state problems for these nuclei are solved using separable potentials, where the Faddeev equations are given. Three different types of the nonlocal separable potentials are used, i.e., potentials of the Yamaguchi, Gaussian, and Tabakin forms. The Gaussian and Tabakin potentials contain both attraction and repulsion. Solving the Faddeev equations, numerical calculations are performed for the resulting integral equations. The present theoretically calculated values of binding energies for these nuclei are in good agreement with the experimental data. The very close agreement between theoretical and experimental values of the binding energies indicates that the repulsive forces of the nuclear potential are very important and should be taken into account.

[NUCLEAR STRUCTURE ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$; three-body model. Calculated binding energies.]

By assuming a two-range central-plus-tensor potential, the effective residual interaction is determined by a least-squares fit with the low-lying energy spectra of $N=29\mathrm{}$, $21\le Z\le 28$ nuclei. All the strengths are found to be almost the same for the proton-neutron and proton-proton interactions. The strengths are compared with Schiffer's results. The two-body matrix elements are in good agreement with the previous results carried out with a nonlocal potential and the Hamada-Johnston potential. The importance of these potentials seems to be overestimated.

[NUCLEAR STRUCTURE Calculated energy levels and effective interaction, shell model.]

Matrix elements of a general Hamiltonian $H$ in a subspace spanned by collective $K^{\pi }=0^{+}$ deformed phonons are derived with the help of recursion formulas. Various approximations are discussed both in the fermion space and in the boson space. Careful comparisons are made in the framework of a simple solvable model.

[NUCLEAR STRUCTURE Multiphonon $K^{\pi }=0^{+}$ states in deformed nuclei. Exact and approximate relations for matrix elements of a general Hamiltonian. Application to a solvable model.]

A $\gamma$-ray cascade with side chains previously assigned to ${}_{}{}^{99}{}_{}{}^{}\mathrm{Pd}$ and recently shown to occur in a nuclide with $Z\le 45$, is unambiguously assigned to ${}_{45}{}^{}{}_{}{}^{}\mathrm{Rh}$. Particle-$\gamma$ coincidence measurements on the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$ and ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$ + ${}_{}{}^{91}{}_{}{}^{}\mathrm{Zr}$ reactions at 56 and 40 MeV, respectively, identify transitions in coincidence with charged particles to allow the elemental assignment. Systematics indicate the probable isotope is ${}_{}{}^{99}{}_{}{}^{}\mathrm{Rh}$.

[NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$, $E_{\mathrm{lab}}=56\mathrm{}$ MeV; measured $E_{\gamma }$, particle-$\gamma$ coin.; ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$ + ${}_{}{}^{91}{}_{}{}^{}\mathrm{Zr}$, $E_{\mathrm{lab}}=40\mathrm{}$ MeV; measured $E_{\gamma }$, particle-$\gamma$ coin. ${}_{}{}^{99}{}_{}{}^{}\mathrm{Pd}$, ${}_{}{}^{99}{}_{}{}^{}\mathrm{Rh}$, enriched targets, Ge(Li), Si detectors.]

High resolution intensity studies have been made of the 115, 239, and 300 keV transitions in ${}_{}{}^{212}{}_{}{}^{}\mathrm{Bi}$, the 252, 277, 511, 583, 722, 763, and 860 keV transitions in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$, the 288, and 453 keV transitions in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Tl}$, and the 727 and 785 keV transitions in ${}_{}{}^{212}{}_{}{}^{}\mathrm{Po}$, using carefully intensity-calibrated Ge(Li) and Si(Li) detectors. Twenty-four $K$-, $L$-, and $M$-shell internal-conversion coefficients were derived from the data and multipole mixing parameters $\left|\delta \right|$ and mixing percentages were deduced.

[RADIOACTIVITY ${}_{}{}^{228}{}_{}{}^{}\mathrm{Th}$; Measured $I_{\gamma }$, $I_e$; deduced ${\alpha }_{K,L,M}$ and $\left|\delta \right|$ for transitions in ${}_{}{}^{212}{}_{}{}^{}\mathrm{Bi}$, ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$, ${}_{}{}^{208}{}_{}{}^{}\mathrm{Tl}$, and ${}_{}{}^{212}{}_{}{}^{}\mathrm{Po}$.]

The average number of prompt neutrons per fission has been measured for ${}_{}{}^{237}{}_{}{}^{}\mathrm{Np}$ using a scintillator tank that has a neutron detection efficiency of about 70%. The measurements at six energies between 1.0 and 14.7 MeV have an accuracy of ±2%. A least squares fit to the results gives ${\overline{\nu }}_p=2.605+0.153\mathrm{}{E}_n$ (MeV).

[NUCLEAR REACTIONS, FISSION ${}_{}{}^{237}{}_{}{}^{}\mathrm{Np}\mathrm{}(n,f)\mathrm{}$, $E=1.0-14.7\mathrm{}$ MeV; measured ${\overline{\nu }}_p\mathrm{}\left(E\right)\mathrm{}$.]

The isospin violating reaction ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^6{}_{}{}^{}\mathrm{Li},\alpha ){}_{}{}^{14}{}_{}{}^{}\mathrm{N}\left(2.31\mathrm{} \mathrm{MeV}\right)$ was investigated in the range of beam energies from 9.0 to 14.0 MeV. Excitation functions were measured for the ground state, 2.31-MeV state and 3.95-MeV state of ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ at 15°, 20°, 60°, and 160°. Excitation functions were taken at 40° for the ground state and 3.95-MeV states. Angular distributions were obtained at 10.5-, 11.25-, 12.5-, 13.75-, and 20.0-MeV beam energies. The cross section for the isospin forbidden reaction to the 2.31-MeV state is 0.4 to 1.8% of that to the allowed ground state and 3.95-MeV state in the beam energy range 9 to 14 MeV. At 20.0 MeV the yield to the forbidden state is only 0.02% of the allowed yield. Isospin mixing by the Coulomb force is believed responsible for the forbidden yield observed between 9-14 MeV.

[NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^6{}_{}{}^{}\mathrm{Li},{\alpha }_0,{\alpha }_1,{\alpha }_2)$, $E=9-14\mathrm{}$, 20 MeV; measured $\sigma (\theta ,E_{{}_{}{}^6{}_{}{}^{}\mathrm{Li}})$. Enriched target. Deduced isobaric spin violation.]

Cross sections for proton-induced reactions on ${}_{}{}^{65}{}_{}{}^{}\mathrm{Cu}$ are presented for the c.m. energy range 1.1 to 3.6 MeV. As the ($p,n$) threshold at 2.13 MeV is crossed, the cross sections for the competing ($p,\gamma$) and ($p,{\alpha }_0$) reactions fall quickly. These features are identified as Wigner cusps. Statistical model calculations successfully account for the observations.

[NUCLEAR REACTIONS ${}_{}{}^{65}{}_{}{}^{}\mathrm{Cu}(p,\gamma )$, ($p,{\alpha }_0$), $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=1.1-3.6\mathrm{}$ MeV; measured $\sigma \mathrm{}\left(E\right)\mathrm{}$; found Wigner cusp. Hauser-Feshbach model calculations.]

A single shell model component with SU(3) quantum numbers $\left(\lambda \mu \right)=(16,2)\mathrm{}$ is identified as the primary parent for the decay into ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}\left(2_1^{+}\right)+{}_{}{}^{16}{}_{}{}^{}\mathrm{O}\left(0_1^{+}\right)$ fragments of the $E2$ resonance recently observed in ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$.

[NUCLEAR STRUCTURE ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$; SU(3) shell model parentage of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}\left(2_1^{+}\right)+{}_{}{}^{16}{}_{}{}^{}\mathrm{O}\left(0_1^{+}\right)$ fission.]

A precise value for the ${}_{}{}^6{}_{}{}^{}\mathrm{He}$ mass excess has been obtained by comparison of the $Q$ values for the ${}_{}{}^7{}_{}{}^{}\mathrm{Li}(d,{}_{}{}^3{}_{}{}^{}\mathrm{He}){}_{}{}^6{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}(d,{}_{}{}^3{}_{}{}^{}\mathrm{He}){}_{}{}^{18}{}_{}{}^{}\mathrm{O}_{}^{*}{}_{}{}^{}$ reactions, the latter populating the first excited state of ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$. The measurements were performed at 0° in a magnetic spectrograph. The result for the ${}_{}{}^6{}_{}{}^{}\mathrm{He}$ mass excess is (17593.7 ± 1.1) keV, about 3 keV less than the previous value, and 3 times more accurate. The effect on the $A=8\mathrm{}$ isobaric quintet and on the $\beta$ decay of ${}_{}{}^6{}_{}{}^{}\mathrm{He}$ is discussed.

[NUCLEAR REACTIONS ${}_{}{}^7{}_{}{}^{}\mathrm{Li}(d,{}_{}{}^3{}_{}{}^{}\mathrm{He}){}_{}{}^6{}_{}{}^{}\mathrm{He}$, ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}(d,{}_{}{}^3{}_{}{}^{}\mathrm{He}){}_{}{}^{18}{}_{}{}^{}\mathrm{O}$. $E_d=20.8\mathrm{}$ MeV, $\theta =0^{\circ }$, magnetic spectrograph. ${}_{}{}^6{}_{}{}^{}\mathrm{He}$, measured mass excess.]

Core-excited states that were selectively excited in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^{12}{}_{}{}^{}\mathrm{C},\alpha ){}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ are found to be also selectively excited in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^{10}{}_{}{}^{}\mathrm{B},d){}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$, though perhaps to a lesser extent.

[NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^{10}{}_{}{}^{}\mathrm{B},d)$, $E=20.0\mathrm{} \mathrm{and} 20.5$ MeV, measured $\sigma \left(\theta \right)$; compared $\sigma$ for 7.42- and 7.83-MeV states.]