The decays of the high-spin isomers of ${}_{}{}^{178}{}_{}{}^{}\mathrm{Ta}$ (2.45 h) and ${}_{}{}^{178}{}_{}{}^{}\mathrm{Lu}$ (23.8 min) to the two strongly admixed $K^{\pi }=8^{-}$ states in ${}_{}{}^{178}{}_{}{}^{}\mathrm{Hf}$ were reinvestigated. The main features of the previously reported decay schemes are confirmed and several long-standing ambiguities are resolved. The results of this investigation indicate that the 1147-keV level is largely the two-neutron state and the 1479-keV level is largely the two-proton state in ${}_{}{}^{178}{}_{}{}^{}\mathrm{Hf}$. They are found to be 34% admixed with one another. This mixing value is in good agreement with the value deduced from the $\frac{M1\mathrm{}}{E2\mathrm{}}$ cascade ratios of the 1147-keV band and from the comparison of the $E1\mathrm{}$ ($\nu =7\mathrm{}$) hindrance factors of these two states in this mass region. The band-mixing matrix element for these two states was found to be in agreement with the recent theory which introduces the residual neutron-proton interaction to account for the mixing. The spin-parity of ${}_{}{}^{178}{}_{}{}^{}\mathrm{Lu}_{}^m{}_{}{}^{}$ (23.8 min) was deduced to be $K^{\pi }=9^{-}$ with a possible Nilsson configuration of $\frac{9}{2^{-}}{\mathrm{}\left[514\right]\mathrm{}}_p$, $\frac{9}{2^{+}}{\mathrm{}\left[624\right]\mathrm{}}_n$.

RADIOACTIVITY ${}_{}{}^{178}{}_{}{}^{}\mathrm{Ta}_{}^m{}_{}{}^{}$; from ${}_{}{}^{175}{}_{}{}^{}\mathrm{Lu}(\alpha , n)$, ${}_{}{}^{180}{}_{}{}^{}\mathrm{Hf}(p, 3n)$, and ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}(p, p3n)$; measured $T_{\frac{1}{2}}$, $E_{\gamma }$, $I_{\gamma }$; deduced $log\mathrm{ft}$. ${}_{}{}^{178}{}_{}{}^{}\mathrm{Lu}_{}^m{}_{}{}^{}$; from ${}_{}{}^{176}{}_{}{}^{}\mathrm{Yb}(\alpha , np)$, measured $T_{\frac{1}{2}}$, $E_{\gamma }$, $I_{\gamma }$; deduced $log\mathrm{ft}$, $J$, $\pi$. Ge(Li) detectors, natural and enriched targets, $E_{\alpha }=46\mathrm{}$ MeV and $E_p=33\mathrm{}$ MeV.

The two-center shell model for fission is extended to include the effects of nuclear rotation or angular momentum $J$. The principle of minimization of total nuclear energy with respect to a constraint on $J$ leads to an effective potential energy which depends on $J$ as well as moment of inertia. This effective potential energy is minimized with respect to nuclear shape variables, neutron pairing energy gap, and proton pairing energy gap for each $J$ value. The resulting potential minima, fission barriers, and moments of inertia are quite sensitive to $J$. Results are given for ${}_{82}{}^{208}{}_{}{}^{}\mathrm{Pb}$, ${}_{94}{}^{240}{}_{}{}^{}\mathrm{Pu}$, and for a super-heavy nucleus ${}_{114}{}^{298}{}_{}{}^{}X$. Our microscopic calculations of the critical angular momentum (at which the fission barrier vanishes) are compared with the rotating liquid drop calculations of Cohen, Plasil, and Swiatecki. The influence of these results on the possibility of fusion in heavy-ion reactions is discussed.

NUCLEAR STRUCTURE: Fission and heavy-ion fusion. The two-center shell model calculation of rotational effects in compound nuclei ${}_{82}{}^{208}{}_{}{}^{}\mathrm{Pb}$, ${}_{94}{}^{240}{}_{}{}^{}\mathrm{Pu}$, ${}_{114}{}^{298}{}_{}{}^{}X$.

The method of variation after angular momentum projection is applied to study the recently observed high-spin states and their electromagnetic properties in even-even Dy isotopes. The calculated $B\left(E2\mathrm{}\right)\mathrm{}$ values and the energy spacings are in good agreement with the corresponding experimental results.

NUCLEAR STRUCTURE Dy isotopes; calculated levels, $B\left(E2\mathrm{}\right)\mathrm{}$, $J\le 22$. Variation after projection method. Pairing and quadrupole interaction.

A derivation of the pairing theory for nuclei is given based on a self-consistent orthonormalization procedure within the context of the equation of motion method. The procedure to minimize the fluctuation effects due to nonconservation of the nucleon number is given. The method is extended for treating the charge independent ($T=1\mathrm{}$) pairing correlations. A new method to deal with the fluctuations due to nucleon number and to isospin simultaneously, is outlined. Numerical computations are performed for the case of $N=Z$ nuclei.

NUCLEAR STRUCTURE ${}_{}{}^{58,60,62,64,66}{}_{}{}^{}\mathrm{Ni}$, calculated ground-state energies, single-particle levels occupation probabilities, pairing interaction. ${}_{}{}^{60,62,64}{}_{}{}^{}\mathrm{A}\mathrm{}(N+Z)\mathrm{}$, calculated $E_0\left(T_{max}\right)$; ${}_{}{}^{60}{}_{}{}^{}\mathrm{A}$ calculated $\Delta E=E_0\mathrm{}(T=2\mathrm{})-E_0\mathrm{}(T=0\mathrm{})\mathrm{}$; charge-independent $T=1\mathrm{}$ pairing interaction. Improved BCS approximation.

In order to investigate some approximations involved in the generalized semimicroscopic model (GSMM), a cluster-phonon model is presented in which a hole or two holes and one particle are coupled between them through $Q-Q$ plus pairing interactions, and to the quadrupole vibrations of a doubly even core having a closed shell. Anharmonicities are also included phenomenologically. Matrix elements are computed using graphical methods and nunumerical calculations are performed for ${}_{}{}^{57}{}_{}{}^{}\mathrm{Co}$ and ${}_{}{}^{115}{}_{}{}^{}\mathrm{In}$, selected as well known examples of odd-mass nuclei in the $1f_{\frac{7}{2}}$ and $1g_{\frac{9}{2}}$ shells, respectively. A good fit to energy levels is achieved through a reasonable variation of the model parameters, and the predictions of the GSMM about the nature of the low-lying levels in both nuclei are confirmed. The calculated electromagnetic properties and spectroscopic factors compare favorably with experiment except for some discrepancies in ${}_{}{}^{115}{}_{}{}^{}\mathrm{In}$.

NUCLEAR STRUCTURE ${}_{}{}^{57}{}_{}{}^{}\mathrm{Co}$, ${}_{}{}^{115}{}_{}{}^{}\mathrm{In}$; calculated levels, $J$, $\pi$, $B\left(E2\mathrm{}\right)\mathrm{}$, $B\left(M1\mathrm{}\right)\mathrm{}$, $q$, $\mu$, $S$, $b$, $\tau$. Cluster-phonon model; 2h-1p excitations, anharmonicities.

The Bansal-French-Zamick model is quite successful in accounting for the Coulomb displacement energies of excited particle-hole states in a variety of light nuclei. Level shifts are typically reproduced to within 50 keV. However, the model fails for certain excited $0^{+}$ states, and this remains a puzzle.

NUCLEAR STRUCTURE Calculated Coulomb energies of particle-hole states $A=13\mathrm{} \mathrm{to} 45$.

Gauvin et al. have suggested that one possible explanation for the high thresholds of the reactions ${}_{}{}^{74}{}_{}{}^{}\mathrm{Ge}({}_{}{}^{84}{}_{}{}^{}\mathrm{Kr}, xn){}_{}{}^{158-x}{}_{}{}^{}\mathrm{Er}$ is the existence of a lower limit to the angular momentum of the compound system formed in the fusion step. We note that such lower limits have, in fact, previously been observed in the collisions of water droplets. Investigation of such lower limits may provide interesting new information on nuclear properties.

NUCLEAR REACTIONS Heavy ion fusion.

Nuclei of ${}_{}{}^{106}{}_{}{}^{}\mathrm{Ag}_{}^m{}_{}{}^{}$ embedded in an iron matrix have been oriented at low temperatures. The decay to ${}_{}{}^{106}{}_{}{}^{}\mathrm{Pd}$ allowed determination of the spin values for the levels at 2366 keV ($J=4\mathrm{}$), 2351 keV ($J=4\mathrm{}$), 2283 keV ($J=4\mathrm{}$), 2077 keV ($J=4\mathrm{}$), and 1932 keV ($J=4\mathrm{}$). The $E2\mathrm{}$ fractions $Q=\frac{{\delta }^2}{(1+{\delta }^2})$ could be deduced for 12 mixed $M1-E2\mathrm{}$ transitions (energies in keV): $Q\left(222\right)=0.017\mathrm{}\pm 0.005$, $\delta <0\mathrm{}$; $Q\left(391\right)={0.996}_{-0.006\mathrm{}}^{+0.004\mathrm{}}$, $\delta <0\mathrm{}$; $Q\left(406\right)=0.91\mathrm{}\pm 0.01$, $\delta <0\mathrm{}$; $Q\left(430\right)=0.982\mathrm{}\pm 0.003$, $\delta <0\mathrm{}$; $Q\left(474\right)=0.01\mathrm{}\pm 0.01$ or $Q\left(474\right)=0.94\mathrm{}\pm 0.02$, $\delta <0\mathrm{}$; $Q\left(601\right)=0.03\mathrm{}\pm 0.03$ or $Q\left(601\right)={0.90}_{-0.06\mathrm{}}^{+0.03\mathrm{}}$, $\delta <0\mathrm{}$; $Q\left(616\right)=0.990\mathrm{}\pm 0.005$, $\delta <0\mathrm{}$; $Q\left(703\right)=0.54\mathrm{}\pm 0.14$, $\delta <0\mathrm{}$ or $Q\left(703\right)=1.00-0.04\mathrm{}$, $\delta >0\mathrm{}$ or $\delta <0\mathrm{}$; $Q\left(793\right)=0.00+0.01\mathrm{}$, $\delta >0\mathrm{}$ or $Q\left(793\right)={0.980}_{-0.020\mathrm{}}^{+0.005\mathrm{}}$, $\delta <0\mathrm{}$; $Q\left(825\right)=0.002\mathrm{}\pm 0.002$ or $Q\left(825\right)=0.97\mathrm{}\pm 0.01$, $\delta <0\mathrm{}$; $Q\left(1046\right)=0.005\mathrm{}\pm 0.003$, $\delta <0\mathrm{}$; $Q\left(1528\right)=0.07\mathrm{}\pm 0.01$ or $Q\left(1528\right)=0.84\mathrm{}\pm 0.02$, $\delta <0\mathrm{}$. In addition, the magnetic moment of $6^{+}$ isomeric state of ${}_{}{}^{106}{}_{}{}^{}\mathrm{Ag}$ was determined to be $\left|\mu \right|=(2.8\mathrm{}\pm 0.2){\mu }_N$.

RADIOACTIVITY ${}_{}{}^{106}{}_{}{}^{}\mathrm{Ag}_{}^m{}_{}{}^{}$; measured $I_{\gamma }\left(\theta \right)$ polarized nuclei, deduced $\mu H$. ${}_{}{}^{106}{}_{}{}^{}\mathrm{Pd}$ deduced $J$, $\pi$, $\delta$. ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ refrigerator, Ge(Li) detectors.

The effect of nuclear deformation on the isospin mixing matrix elements has been investigated for deformed configurations in ${}_{}{}^{18}{}_{}{}^{}\mathrm{F}$. An enhancement of the mixing with deformation is found.

NUCLEAR STRUCTURE Isospin mixing.

The equivalence of Harris model equations with those of the generalized variable-moment-of-inertia (GVMI) model given by Das et al. is examined in the light of the backbending feature of the rotational states. It is shown that this feature is absent in the Harris model taken to any order. The GVMI model equations are found to be consistent and in one-to-one correspondence with an expansion of the square of the angular velocity in terms of a polynomial in the moment of inertia rather than with the Harris expansion and may give a backbending feature in some cases depending on the relative values of the parameters appearing in the potential energy term.

NUCLEAR STRUCTURE Variable moment of inertia, angular velocity, cranking model, backbending, high spin rotational states.

The half-lives of ${}_{}{}^{18}{}_{}{}^{}\mathrm{Ne}$ and ${}_{}{}^{20}{}_{}{}^{}\mathrm{F}$ have been measured by multiscaling $\beta$ rays detected in a plastic scintillator. ${}_{}{}^{18}{}_{}{}^{}\mathrm{Ne}$ was formed in the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}({}_{}{}^3{}_{}{}^{}\mathrm{He}, n){}_{}{}^{18}{}_{}{}^{}\mathrm{Ne}$ reaction at $E_{{}_{}{}^3{}_{}{}^{}\mathrm{He}}=5.7\mathrm{}$ MeV using a ${\mathrm{Ta}}_2$ ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}_5^{}{}_{}{}^{}$ target depleted in ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$. ${}_{}{}^{20}{}_{}{}^{}\mathrm{F}$ was produced in the ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}(d, p){}_{}{}^{20}{}_{}{}^{}\mathrm{F}$ reaction with 2.0-MeV deuterons on a Ba${\mathrm{F}}_2$ target. Half-life values of 1.669±0.004 sec for ${}_{}{}^{18}{}_{}{}^{}\mathrm{Ne}$ and 10.996±0.020 sec for ${}_{}{}^{20}{}_{}{}^{}\mathrm{F}$ were obtained. Using the present and other recent results the $A=18\mathrm{}$ $\beta$ decay mirror asymmetry is found to be -0.86±0.80%.

RADIOACTIVITY ${}_{}{}^{18}{}_{}{}^{}\mathrm{Ne}$, ${}_{}{}^{20}{}_{}{}^{}\mathrm{F}$: measured $T_{\frac{1}{2}}$; deduced $\beta$ decay mirror asymmetry.

We investigate the effects which the experimental uncertainty of the neutron charge form factor can have on the charge form factors of ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$.

NUCLEAR REACTIONS Elastic electron scattering, charge form factors, three-nucleon systems.

The reactions ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}(\alpha , p){}_{}{}^{34}{}_{}{}^{}\mathrm{S}$ and ${}_{}{}^{35}{}_{}{}^{}\mathrm{Cl}(\alpha , p){}_{}{}^{38}{}_{}{}^{}\mathrm{Ar}$ have been used to study the $E0\mathrm{}$ $\pi$ decays of the ${}_{}{}^{34}{}_{}{}^{}\mathrm{S}$(3.91 MeV, $0^{+}$) and ${}_{}{}^{38}{}_{}{}^{}\mathrm{Ar}$(3.38 MeV, $0^{+}$) states to the ground state. The $E0\mathrm{}$ branching ratios $\frac{{\Gamma }_{\pi }}{\Gamma }$ were measured to be (0.38 ± 0.06) × ${10}^{-3\mathrm{}}$ and (6.6 ± 1.0) × ${10}^{-3\mathrm{}}$, respectively. When these values are combined with the available lifetime of these states, $E0\mathrm{}$ matrix elements ${〈M〉}_{\pi }=(1.55\mathrm{}\pm 0.15)$ ${\mathrm{fm}}^2$ (${}_{}{}^{34}{}_{}{}^{}\mathrm{S}$) and (2.26 ± 0.21) ${\mathrm{fm}}^2$ (${}_{}{}^{38}{}_{}{}^{}\mathrm{Ar}$) are obtained.

NUCLEAR REACTIONS ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}(\alpha , p)$, $E=7.60\mathrm{}$ MeV; ${}_{}{}^{35}{}_{}{}^{}\mathrm{Cl}(\alpha , p)$, $E=7.67\mathrm{}$ MeV; ${}_{}{}^{34}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{38}{}_{}{}^{}\mathrm{Ar}$ measured $E0\mathrm{}$ branching ratios. Deduced $E0\mathrm{}$ matrix elements. Natural targets.

Angular distributions of the ${}_{}{}^{37}{}_{}{}^{}\mathrm{Cl}(p, {}_{}{}^3{}_{}{}^{}\mathrm{He}){}_{}{}^{35}{}_{}{}^{}\mathrm{S}$ reaction at 40.2 MeV bombarding energy have been measured for states in ${}_{}{}^{35}{}_{}{}^{}\mathrm{S}$ up to 9.16 MeV energy excitation. These data have been analyzed with the distorted-wave Born approximation, and values of the angular momentum $L$ transferred to several states have been deduced. A shell-model analysis of the transitions to the low-lying levels has been performed, and the new information gained about the structure of ${}_{}{}^{35}{}_{}{}^{}\mathrm{S}$ is discussed.

NUCLEAR REACTIONS ${}_{}{}^{37}{}_{}{}^{}\mathrm{Cl}(p, {}_{}{}^3{}_{}{}^{}\mathrm{He})$, $E_p=40.2\mathrm{}$ MeV; measured ($E_{{}_{}{}^3{}_{}{}^{}\mathrm{He}}, \theta$); enriched target. ${}_{}{}^{35}{}_{}{}^{}\mathrm{S}$ deduced levels, $L$ values.

The continuum spectra of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ have been measured up to excitation energies of 40 MeV by means of inelastic electron scattering. Incident electron beam energies between 60 and 120 MeV were used, corresponding to a momentum transfer range of 0.3 ${\mathrm{fm}}^{-1\mathrm{}}$ to 1.1 ${\mathrm{fm}}^{-1\mathrm{}}$. Scattered electrons were observed at two angles, 92.6° and 127.7°. The radiation corrected spectra and the form factors are presented, and compared with calculations based on a zero-range approximation. In this model, the sharp rise from the $p+d$ threshold previously reported may be identified as a ${}_{}{}^2{}_{}{}^{}S\to {}_{}{}^2{}_{}{}^{}S$ Coulomb monopole transition.

NUCLEAR REACTIONS ${}_{}{}^3{}_{}{}^{}\mathrm{He}(e, e^{\prime })$, $E_x=0-40\mathrm{}$ MeV; measured $\sigma (E; \theta )$; $\theta =92.6\mathrm{}° \mathrm{and} 127.7°$. Comparison between radiation-corrected spectra and zero-range model calculations; multipole decomposition.

The ${}_{}{}^{33}{}_{}{}^{}\mathrm{S}(n, {\alpha }_0)$ and ${}_{}{}^{33}{}_{}{}^{}\mathrm{S}(n, \gamma )$ cross sections have been measured from ∼10 to ∼700 keV. Resonance parameters are given for 39 resonances. The level spacing is determined to be 9.1±0.9 keV. The $\sigma (n, {\alpha }_0)$ and $\sigma (n, \gamma )$ cross sections are averaged over a Maxwellian distribution for values of $\mathrm{kT}$ from 25 to 275 keV. When these cross sections are used in a nucleosynthesis calculation of the rare isotope ${}_{}{}^{36}{}_{}{}^{}\mathrm{S}$, the overproduction of this isotope, relative to the other nuclei formed in the universe, is reduced from a factor of 10 to 2.5.

NUCLEAR REACTIONS ${}_{}{}^{33}{}_{}{}^{}\mathrm{S}(n, {\alpha }_0)$, ${}_{}{}^{33}{}_{}{}^{}\mathrm{S}(n, \gamma )$, $10<\mathrm{}{E}_n<700\mathrm{}$ keV; deduced $A_{\gamma }$, $\frac{{\Gamma }_{\alpha }}{{\Gamma }_{\gamma }}$, $〈D〉$; Maxwellian averaged $\sigma (n, {\alpha }_0)$ and $\sigma (n, \gamma )$ for $\mathrm{kT}<\mathrm{}275\mathrm{}$ keV.

We compare numerical solution of the "minimal" three-body equations obtained from unitarity and analyticity with the full Schrödinger solution in a simple three-boson model. We find that for short-range forces the minimal equations give the correct shape, but not magnitude, for the three-body amplitudes. This is true even for a singular form with no mathematical credentials.

NUCLEAR REACTIONS Numerical investigation of unitarity and analyticity constraints in a three-boson model.

The single-channel resonating-group method with a central nucleon-nucleon potential is used to study the $n$ + ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ system up to a c.m. energy of about 17 MeV. The specific distortion of the triton in this system is investigated, and it is found that its effect on the $n$ + ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ phase shifts is small. A phenomenological imaginary potential is included in the calculation in order to account approximately for the effects of reactions on the elastic channel. The strength of this potential is chosen to reproduce measured total reaction cross sections for the charge-conjugate system $p$ + ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. The results of the calculation are in satisfactory agreement with measured $n$ + ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ elastic differential cross sections.

NUCLEAR REACTIONS ${}_{}{}^3{}_{}{}^{}\mathrm{H}(n, n)$, $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=4.5-17.25\mathrm{}$ MeV; calculated phase shifts and $\sigma \left(\theta \right)$; studied specific distortion. Resonating-group method with imaginary potential.

Exchange symmetry is used to eliminate reference to physically indistinguishable channels in the coupled-equations nuclear-reaction formalism. The resulting equations are similar in structure to the original ones except that they are far fewer in number and the interactions contain exchange operators.

NUCLEAR REACTIONS Coupled-equations nuclear-reaction formalism of Kouri, Levin, Hahn, and Tobocman is explicitly antisymmetrized.

A recently proposed degenerate-kernel scheme for solving Fredholm integral equations of the second kind gave very good results for Lippmann-Schwinger equations. The method is here extended to give a very simple and practical method for the three-body equations with separable two-body interactions. Numerical calculations of the three-body amplitudes are carried out at positive energies for two simple models. In spite of the more complicated singularities in the kernel as well as in the solutions of the equation, satisfactory convergence is achieved.

NUCLEAR REACTIONS Faddeev equation solved. Degenerate kernel scheme used.