It is shown that each Yakubovski component of the totally antisymmetric four-body wave function satisfies the same equation as the unantisymmetric wave function. In the antisymmetric total wave function, the wave functions belonging to the same kind of partition are totally antisymmetric among themselves. This leads to the coexistence of cluster models, including the single particle model as a special case of the cluster model, as a sum.

NUCLEAR STRUCTURE Four-body problem. Antisymmetrization. Decoupled Yakubovski equation. Cluster models. Coexistence with single particle model.

The masses of neutron-deficient and neutron-rich isotopes of rubidium (${}_{}{}^{74-79}{}_{}{}^{}\mathrm{Rb}$, ${}_{}{}^{90-99}{}_{}{}^{}\mathrm{Rb}$) and of cesium (${}_{}{}^{117-124,126}{}_{}{}^{}\mathrm{Cs}$, ${}_{}{}^{138,140-147}{}_{}{}^{}\mathrm{Cs}$) have been determined by direct on-line mass spectrometry. The measured masses are compared to current mass predictions. From the trend of neutron separation energies, experimental neutron pairing energies are deduced and evidence is found for the onset of a deformation at $N=60\mathrm{}$ in the neutronrich rubidium isotopes.

NUCLEAR STRUCTURE ${}_{}{}^{74-79}{}_{}{}^{}\mathrm{Rb}$, ${}_{}{}^{90-99}{}_{}{}^{}\mathrm{Rb}$, ${}_{}{}^{117-124,126}{}_{}{}^{}\mathrm{Cs}$, ${}_{}{}^{138,140-147}{}_{}{}^{}\mathrm{Cs}$; measured masses, on-line mass spectrometry. $S_{2n}$ deduced; evidence for deformation at $N=60\mathrm{}$. Comparison with mass predictions.

We study the effect of configuration mixing on the well known linear relations between the energy spectra of $j^2$ and $j^n$ configurations. We show that both single-particle excitations and third-order corrections lead to breakdown of these relations. Contributions from the former tend to cancel when many high-lying orbits contribute simultaneously.

NUCLEAR STRUCTURE Linear relations between leads, configuration mixing effects.

The Lipkin-Nogami version of the spherical BCS method is extended to study the effects of pairing correlations on the ground-state properties of nuclei with permanent deformation. The Kuo-Brown effective interaction is used to study the even-even nuclei in the $2p-1f$ shell. Considerable changes in the pairing energies compared with the deformed BCS and full Hartree-Fock-Bogoliubov methods are obtained. The neutron-pair separation energies and the projected spectra show improved agreement with the data.

NUCLEAR STRUCTURE Lipkin-Nogami method with deformed basis applied to even Ti isotopes. Effective Kuo-Brown Interaction; projected spectra.

The low-lying positive-parity states of doubly even titanium isotopes are analyzed with the classical semimicroscopic model which involves the coupling of a two-proton cluster to the corresponding vibrational cores. The calculated energy-level sequence and electromagnetic properties compare favorably with experiment although no attempt to the best fit to individual properties was pursued. Comparison with calculated values with other models is also performed.

NUCLEAR STRUCTURE ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ti}$, ${}_{}{}^{46}{}_{}{}^{}\mathrm{Ti}$, ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ti}$, and ${}_{}{}^{52}{}_{}{}^{}\mathrm{Ti}$; calculated levels, $J$, $\pi$, $B\left(E2\mathrm{}\right)\mathrm{}$, $B\left(M1\mathrm{}\right)\mathrm{}$, $q$, $\mu$, $\delta$, $\tau$, $b$. Classical semimicroscopic model.

An inconsistency is pointed out between a recent "elementary particle" treatment of Coulomb corrections to weak transitions due to Armstrong and Kim, and a previous analysis of the problem by Stech and Schulke. The correct procedure is derived and demonstrated.

RADIOACTIVITY Coulomb correction to weak decays.

Difficulties in the proposed formulation by Wu and Chang for emission rates of complex particles in the pre-equilibrium exciton model are discussed. Formal problems result in their derivation and in the equilibrium limit. Practical problems result from the neglecting of known direct reaction mechanisms.

NUCLEAR REACTIONS Pre-equilibrium exciton model formalism, complex-particle emission.

Comparison is made between the predictions of the rotation-vibration description of ${}_{}{}^{196}{}_{}{}^{}\mathrm{Pt}$ and that afforded by the O(6) limit of the interacting boson approximation.

NUCLEAR STRUCTURE ${}_{}{}^{196}{}_{}{}^{}\mathrm{Pt}$; calculated energy levels, $J$, $\pi$, $B\left(E2\mathrm{}\right)\mathrm{}$ ratios. Interacting rotation-vibration model.

The random-phase approximation has been treated in two steps: (a) First, we solve the so-called nuclear structure problem in which the single particle continuum states are excluded. (b) In the second part, we include the continuum utilizing a reformulated version of the random-phase approximation which uses the outcome of the nuclear structure method as an input. Thus the effect of the continuum is directly estimated. Below threshold the excitation energies are shifted; above threshold they obtain additionally a width. Numerical results are presented for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{N}$.

NUCLEAR STRUCTURE RPA calculations for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{N}$ including continuum.

The $\alpha$ particle angular distributions measured on and off the 12.8 MeV resonance in the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ system have been used to deduce spin and parity values of $7^{-}$ for the resonance. These results are in disagreement with all existing theoretical predictions.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$,$\alpha$)${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=12.80\mathrm{} \mathrm{and} 13.01$ MeV; measured $\sigma \left(\theta \right)$ for $\alpha$ particles. Deduced $J^{\pi }$ for the 12.8 MeV resonance.

Energy spectra and spectroscopic factors of negative-parity states in ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ge}$ are calculated within the framework of the quasiparticle-vibration coupling approach in the unified nuclear model. The calculated results are in very good agreement with the experimental data.

NUCLEAR STRUCTURE ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ge}$; calculated levels, $J$, $\pi$, and spectroscopic factors. Compared with experiments.

The $K$-electron capture probability ($P_k$) in the decay of ${}_{}{}^{108}{}_{}{}^{}\mathrm{Ag}_{}^m{}_{}{}^{}$ (127 yr) has been determined from a measurement of the Pd $K$ x-ray intensities as well as from the analysis of the $K$ x-ray gamma-ray sum peak. From the measured value of $P_k (0.85\mathrm{}\pm 0.04)$ the ground-state mass difference between ${}_{}{}^{108}{}_{}{}^{}\mathrm{Ag}$ and ${}_{}{}^{108}{}_{}{}^{}\mathrm{Pd}$ is estimated as $Q^{+}={1926}_{-169\mathrm{}}^{+\infty }$ keV.

RADIOACTIVITY ${}_{}{}^{108}{}_{}{}^{}\mathrm{Ag}_{}^m{}_{}{}^{}$: measured $I_{\gamma }$, $I_{\mathrm{Kx}}$, sum peak area; deduced $P_K$, $Q^{+}$.

The recrossing of the ground state band with the superband as an explanation for the second anomaly in ${}_{}{}^{158}{}_{}{}^{}\mathrm{Er}$ is examined in terms of the moment of inertia. A two band mixing calculation does not reproduce the experimental moment of inertia curve.

NUCLEAR STRUCTURE ${}_{}{}^{158}{}_{}{}^{}\mathrm{Er}$ second anomaly, moment of inertia in two band mixing calculation.

Detailed results of the investigation of the in-beam $\gamma$ rays from 140 MeV $\alpha$ particles incident on the deformed nucleus ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ are presented. They are supplemented by experimental evidence obtained from the observed differential cross section measurements for $p$, $d$, $t$, $h$, and $\alpha$ particles in the discrete portion of the energy spectra. Striking spectroscopic similarities are observed for the strongly excited states in residual nuclei both near and considerably removed in $N$ and $Z$ from the target nucleus. Some of these involve related collective states exhibiting strong quadrupole excitations.

NUCLEAR REACTIONS ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$($\alpha$,$p$), ($\alpha$,$d$), ($\alpha$,$t$), ($\alpha$,$h$), ($\alpha$,${\alpha }^{\prime }$), ($\alpha$,$x-\gamma$), $E_{\alpha }=140\mathrm{}$ MeV; measured $E_{\gamma }$, ${\sigma }_{\gamma }$, cross sections for producing specific levels in residual nuclei, Doppler broadening, $\sigma (\theta ,E)$ for discrete energy groups $p$, $d$, $t$, $h$, $\alpha$; deduce reaction channel characteristics. Ge(Li) detector.

Both light and heavy mass fragments are observed giving angular distribution, energy, and particle identification information. Total cross section yields are compared to $\gamma$-ray-based values reported in the preceding paper. The mass fragment data are supportive of the $\gamma$-ray data particularly the observed Doppler broadening of the $\gamma$-ray lines. Comparison of the mass fragment and $\gamma$-ray data with both pre-equilibrium-evaporation and intranuclear cascade code predictions is discussed. Possible reaction mechanism models are discussed. Approximately 30% of the reaction cross section is assigned to direct processes, some involving collective surface excitations that appear to be memory conserving. Various possible direct pre-equilibrium processes are discussed.

NUCLEAR REACTIONS ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$($\alpha$,$x$), $E=140\mathrm{}$ MeV; measured mass fragment $\frac{d^2\sigma }{\mathrm{dEd}\Omega }$, deduce fragment velocities, Monte Carlo and exciton model calculations, deduce reaction mechanism model characteristics.

We have used the crystal blocking technique to measure the lifetimes of ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ compound states excited by the ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ ($p$,$\alpha$) reaction at $E_p=937\mathrm{} \mathrm{and} 885$ keV. Axial blocking on the $〈110〉$ axis of thick Al crystals and Kodak LR 115 plastic detectors are used. Measurements have been made at a 0.2 μm depth. A study is made of the yields of some ($p$,$\alpha$) resonances on Al and of the depth dependence of blocking dips. The data are analyzed by comparison with a realistic Monte Carlo model. The resulting lifetime, ${\tau }_{937}<17\mathrm{}$ as (as = ${10}^{-18\mathrm{}}$ s) and ${\tau }_{885}={38}_{-9\mathrm{}}^{+10\mathrm{}}$ as are compared with previous work.

NUCLEAR REACTIONS ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$($p$,$\alpha$)${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, $E=0.731-1.183\mathrm{}$ MeV; measured yields in thin targets. LR 115 cellulose nitrate detectors. $E=0.885, 0.937$ MeV; measured blocking effect. ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ deduced mean lifetime. Single crystal thick Al targets.

Levels below 10 MeV in ${}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}$ have been investigated with the ${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}$(${}_{}{}^3{}_{}{}^{}\mathrm{He}$,$\alpha$) reaction at a bombarding energy of 15 MeV, with an enriched gas target. Angular distributions were extracted for twenty-six levels (or groups of levels). Only two levels of each $J^{\pi }=\frac{1}{2^{+}}, \frac{3}{2^{+}}, \mathrm{and} \frac{5}{2^{+}}$ have spectroscopic factors larger than 0.03. Results for positive-parity states are in good agreement with shell-model calculations in an ${\mathrm{}\left(\mathrm{sd}\right)\mathrm{}}^5$ basis. But the presence of additional levels above 6 MeV, not present in the shell-model calculation, suggests core excitation is important for the positive-parity states above that energy. The $\frac{1}{2^{-}}$ state at 2.79 MeV has only about half the strength expected for a pure 6p-1h state, with $T_p=1\mathrm{}$. Very little $1p_{\frac{3}{2}}$ pickup is observed below 10 MeV excitation.

NUCLEAR REACTIONS ${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}$(${}_{}{}^3{}_{}{}^{}\mathrm{He}$,$\alpha$), $E=15.0\mathrm{}$ MeV; measured $\sigma (E_{\alpha },\theta )$. ${}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}$ deduced levels, $l$, $J$, $\Pi$. DWBA analysis. Enriched gas target.

The states of ${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}$ below 8.6 MeV excitation energy have been studied using the technique of inelastic electron scattering. Ratios of inelastic to elastic scattering cross sections were measured with incident electron energies between 60 and 110 MeV and scattering angles of 110° and 128°. Form factors for 14 inelastic transitions were measured for the momentum transfer range 0.4 to 1.0 ${\mathrm{fm}}^{-1\mathrm{}}$. Reduced transition probabilities for these states have been deduced and assignments of spin and parity have been made.

NUCLEAR REACTIONS ${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}$($e$,$e^{\prime }$), $E=60\mathrm{} \mathrm{to} 110$ MeV; measured $\sigma \mathrm{}\left(E\right)\mathrm{}$ at 110° and 128° up to 8.6 MeV in excitation energy; deduced $J$, $\pi$, $B\left(\mathrm{CL}\right)\mathrm{}$. Enriched ${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}$ target.

The method of hyperspherical harmonics is used to calculate ($\alpha \mathrm{np}$) three-body elastic scattering, $\alpha +n+p\to \alpha +n+p$. Two scattering channels, $J^{\pi }=1^{+}$, isospin zero, and $J^{\pi }=0^{+}$, isospin 1, are studied. Formulas for the differential cross section and total cross section are given for the uncoupled channel case. Only the grand orbital $L=0\mathrm{}$ term is used. Numerical computations of the phase shift and the total cross section are done by employing three sets of potential parameters for each scattering channel. A brief discussion of the $S$-matrix is made by means of the hyperspherical method. Finally the applicability of our results in regard to the truncation of the wave function is examined.

NUCLEAR REACTIONS Elastic scattering, uncoupled channel, three-body to three-body phase shift, cross section.

It is shown that the optical model potential with central, spin-orbit, and exchange terms can provide reasonably good fits to the cross section, polarization, and the polarization transfer coefficients $K_x^{x^{\prime }}$ and $K_z^{x^{\prime }}$ for $p$+${}_{}{}^3{}_{}{}^{}\mathrm{He}$ elastic scattering in the energy range 6.8-16.2 MeV. The measured values of the polarization transfer coefficient $K_y^{y^{\prime }}$ are compared with those calculated by adding a spherical spin-spin interaction term to the potential. Both phenomenological and folding-model spin-spin terms are considered. Good agreement is obtained for the 16.2 MeV data but not for the data at lower energies. The effects of including a tensor spin-spin interaction are also studied.

NUCLEAR REACTIONS $p$+${}_{}{}^3{}_{}{}^{}\mathrm{He}$ elastic scattering; optical model calculations.