Pairs of negative beta particles have been observed originating from a ${}_{}{}^{82}{}_{}{}^{}\mathrm{Se}$ source during a cloud-chamber search for double beta decay. Backgrounds recognized in previous experiments were suppressed to well below the observed event rate, and no other significant backgrounds are apparent. Within the limited statistics of the small data sample, the observed single-electron energy spectrum, the two-electron sum energy spectrum, and the opening angle distribution are consistent with expectation for neutrino-accompanied double beta decay of ${}_{}{}^{82}{}_{}{}^{}\mathrm{Se}$. The tentative assignment of the observed events to double beta decay, results in a ${}_{}{}^{82}{}_{}{}^{}\mathrm{Se}$ half-life of (1.0±0.4)×${10}^{19}$ years, in good agreement with some very recent theoretical predictions. However, the result is in serious disagreement with the much longer half-lives measured in geochemical experiments. A planned follow-up experiment is described.

RADIOACTIVITY $\beta \beta$-decay ${}_{}{}^{82}{}_{}{}^{}\mathrm{Se}$; measured $I_{\beta \beta }$; deduced $T_{\frac{1}{2}}$.

The ${\beta }^{+}$ decay of the new isotope ${}_{}{}^{67}{}_{}{}^{}\mathrm{As}$ to levels in ${}_{}{}^{67}{}_{}{}^{}\mathrm{Ge}$ has been studied via the reaction ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}({}_{}{}^{14}{}_{}{}^{}\mathrm{N}, \alpha n){}_{}{}^{67}{}_{}{}^{}\mathrm{As}_{\to }^{\beta +67\mathrm{}}{}_{}{}^{}\mathrm{Ge}$ using 39- and 41-MeV ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ ions. The ${}_{}{}^{67}{}_{}{}^{}\mathrm{As}$ half-life and total decay energy ($Q_{\mathrm{EC}}$) have been measured to be 42.5 ± 1.2 s and 6.01 ± 0.10 MeV, respectively. The ${\beta }^{+}$ decay scheme to 15 levels up to 2524-keV excitation in ${}_{}{}^{67}{}_{}{}^{}\mathrm{Ge}$ has been determined and, based on measured $log\mathrm{ft}$ values, a spin/parity constraint of $\frac{3}{2^{-}}$ or $\frac{5}{2^{-}}$ for the ground state of ${}_{}{}^{67}{}_{}{}^{}\mathrm{As}$ has been established.

RADIOACTIVITY ${}_{}{}^{67}{}_{}{}^{}\mathrm{As}$ [from ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}({}_{}{}^{14}{}_{}{}^{}\mathrm{N}, \alpha n)$]: measured $T_{\frac{1}{2}}$, $E_{\gamma }$, $I_{\gamma }$, $\gamma -\gamma$ coin, $E_{{\beta }^{+}}$, ${\beta }^{+}-\gamma$ coin; deduced decay scheme, mass excess, $log\mathrm{ft}$ values, $J^{\pi }$ restrictions; ${}_{}{}^{67}{}_{}{}^{}\mathrm{Ge}$ $J^{\pi }$ restrictions. Enriched targets, multiple rabbit, helium jet, Ge(Li) and plastic detectors.

The branching fraction of the ${}_{}{}^{42}{}_{}{}^{}\mathrm{Sc}$ $0^{+}$ ground state to the $0^{+}$ 1837-keV level of ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$ was determined to be (1.03±0.31) × ${10}^{-4\mathrm{}}$ relative to the superallowed decay to the $0^{+}$ ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$ ground state. The experiment was designed to eliminate possible spurious effects and systematic errors. Our result overlaps the larger of two recent measurements which were in rather poor agreement, and is half of that predicted by current microscopic calculations. The importance of this measurement in the extraction of the vector coupling constant $G_V$ is discussed.

RADIOACTIVITY ${}_{}{}^{42}{}_{}{}^{}\mathrm{Sc}$(g.s.); measured ${\beta }^{+}$-decay branch to the ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$ $0^{+}$ 1837-keV level.

A model theory, standard time-independent perturbation theory in a harmonic oscillator shell model basis, is used to investigate various aspects of the center of mass problem. In this model it is shown that the center of mass problem can be solved by projection techniques, but that the way in which one projects is crucial. The apropriate projection functions are found to be $\mathrm{const}\times R^{-\frac{3}{2}}$ for wave function projection and 1 for density projection. The former illustrates, among other things, that the center of mass problem cannot be solved by simply eliminating the spurious components of the wave function. The latter agrees with the Gartenhaus-Schwartz prescription. Also, explicit center of mass corrections are calculated.

NUCLEAR STRUCTURE Methods for treating center of mass effects tested in a model theory.

The gauge-invariant periodic quantization method is applied to time-dependent states with definite parities in the Lipkin-Meshkov-Glick model. It is shown that the resulting discrete energy spectrum is free of discontinuity and predicts the correct number of states for all interaction strengths. It offers therefore a qualitative improvement over the gauge-invariant periodic quantized time-dependent Hartree-Fock states of this model.

NUCLEAR STRUCTURE Time-dependent description of many-body bound states, gauge-invariant periodic quantization method, Lipkin-Meshkov-Glick model, good-parity time-dependent states.

The strength of the single particle spin-orbit potential is calculated from the two pion exchange box diagrams involving an intermediate $\Delta \mathrm{}\left(1232\right)\mathrm{}$ resonance excitation by taking account of the exclusion principle for the intermediate nucleon states. The effect of the $\rho$ meson is also considered. The predicted strength is found to account for a substantial part of the empirical spin-orbit splittings.

NUCLEAR STRUCTURE Calculated spin-orbit splittings; effect of an intermediate $\Delta$ excitation.

The positive- and negative-parity states of ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$, ${}_{}{}^{87}{}_{}{}^{}\mathrm{Sr}$, and ${}_{}{}^{89}{}_{}{}^{}\mathrm{Sr}$ are analyzed with the particle-core coupling model which, in the present extension, involves the coupling of a particle (hole) to six core states in ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}$. The calculated energy-level sequences, spectroscopic factors, and the few available electromagnetic properties compare favorably with experiment.

NUCLEAR STRUCTURE ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$, ${}_{}{}^{87}{}_{}{}^{}\mathrm{Sr}$, and ${}_{}{}^{89}{}_{}{}^{}\mathrm{Sr}$: calculated levels, $J$, $\pi$, $S$, $B\left(E2\mathrm{}\right)\mathrm{}$, $q$, and $\mu$. Particle-core coupling model.

It is shown that all absolute calibration data of the analyzing power $T_{20}\left(0\mathrm{}°\right)$ of the ${}_{}{}^3{}_{}{}^{}\mathrm{He}(\overrightarrow{d}, p){}_{}{}^4{}_{}{}^{}\mathrm{He}$ reaction below 6.75 MeV agree well within a 1% uncertainty. This is contrary to the conclusions drawn by Dries et al. The reason for the alleged discrepancy is discussed. An extended $T_{20}\left(0\mathrm{}°\right)$ calibration curve for deuteron energy up to 40 MeV is presented.

NUCLEAR REACTIONS ${}_{}{}^3{}_{}{}^{}\mathrm{He}(\overrightarrow{d}, p){}_{}{}^4{}_{}{}^{}\mathrm{He}$, $E_d=0-40\mathrm{}$ MeV, measured and calibrated $T_{20}\left(0\mathrm{}°\right)$.

The ${}_{}{}^{81}{}_{}{}^{}\mathrm{Kr}_{}^m{}_{}{}^{}$ to ${}_{}{}^{81}{}_{}{}^{}\mathrm{Br}$ electron capture rate has been measured and found to have a $log\mathrm{ft}$ value of 4.58±0.11. This result implies ${}_{}{}^{81}{}_{}{}^{}\mathrm{Br}$ is a feasible target for solar neutrino capture.

RADIOACTIVITY Measured branching ratio ${}_{}{}^{81}{}_{}{}^{}\mathrm{Kr}_{}^m{}_{}{}^{}$ electron capture, deduced $log\mathrm{ft}$ for solar neutrino capture.

The differential cross sections and analyzing powers for the ${}_{}{}^{92}{}_{}{}^{}\mathrm{Zr}(\overrightarrow{p}, \alpha ){}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$ reaction have been measured at $E_p=17\mathrm{}$ MeV. Distorted-wave Born approximation calculations, using both the cluster and three-nucleon microscopic form factors, have been performed for the first four states in ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$. An empirical normalization factor for the ($p, \alpha$) reaction has been obtained from the microscopic calculation of the ground state transition. Using this normalization factor, the spectroscopic factors for the other states have been obtained and these compare well with those obtained in the single proton pickup reactions.

NUCLEAR REACTIONS ${}_{}{}^{92}{}_{}{}^{}\mathrm{Zr}(\overrightarrow{p}, \alpha ){}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$, $E_p=17\mathrm{}$ MeV, measured $\sigma (E_{\alpha }, \theta )$ and $i{T}_{11}(E_{\alpha }, \theta )$, DWBA calculations, spectroscopic factors.

Alpha transfer to the ground and first excited $0^{+}$ states of the Ge isotopes has been studied by means of the ${}_{}{}^{64,66,68,70}{}_{}{}^{}\mathrm{Zn}({}_{}{}^6{}_{}{}^{}\mathrm{Li}, d){}_{}{}^{68,70,72,74}{}_{}{}^{}\mathrm{Ge}$ reactions at 34-MeV incident energy. The sharp variation in strength between ${}_{}{}^{72}{}_{}{}^{}\mathrm{Ge}$ and ${}_{}{}^{74}{}_{}{}^{}\mathrm{Ge}$ is shown to result from a change in the proton structure of these two isotopes as the neutron number changes from $N=40\mathrm{} \mathrm{to} 42$.

NUCLEAR REACTIONS ${}_{}{}^{64,66,68,70}{}_{}{}^{}\mathrm{Zn}({}_{}{}^6{}_{}{}^{}\mathrm{Li}, d){}_{}{}^{68,70,72,74}{}_{}{}^{}\mathrm{Ge}$, $E=34\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$ for $0^{+}$ states, DWBA analysis, deduced $S$.

Wave functions calculated with separable potentials in standard nonrelativistic and covariant Faddeev equations were used to estimate relativistic corrections of the overall muon-capture rate in ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. They seem to cancel other relativistic corrections obtained from considering small Dirac wave function components in the effective Hamiltonian for the weak interaction.

NUCLEAR REACTIONS $\mu$ capture in ${}_{}{}^3{}_{}{}^{}\mathrm{He}$; Primakoff equation; relativistic corrections from nuclear wave functions.

Recent experimental data on the structure of the very-neutron-rich isotopes of Na and Mg show sharp departures at $N=20\mathrm{}$ from the predictions of conventional $d_{\frac{5}{2}}-s_{\frac{1}{2}}-d_{\frac{3}{2}}$ shell-model calculations.

NUCLEAR STRUCTURE Isotopes of Na and Mg; calculated ground state energies, magnetic dipole moments, and excitations of $2^{+}$ states; $0d_{\frac{5}{2}}-1\mathrm{}{s}_{\frac{1}{2}}-0\mathrm{}{d}_{\frac{3}{2}}$ shell model, Chung-Wildenthal Hamiltonians.

Starting from the single particle energy level scheme for the Woods-Saxon potential, the systematics of the macroscopic level density parameters of nuclei has been studied. A strong dependence of the level density parameter on the last nucleon separation energy was observed. A simple functional form for this dependence is proposed.

NUCLEAR STRUCTURE Nuclear level densities, semiempirical, macroscopic level density parameter $a$, Woods-Saxon potential, isopin dependence.

Total cross sections of 14.6 MeV neutron induced reactions ($n, n^{\prime }$), ($n, p$), ($n, d$), ($n, \alpha$), ($n, t$), and ($n$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$), on the target nuclei in the mass region $A=27\mathrm{} \mathrm{to} 59$, have been calculated (for the first stage decay) by the Hauser-Feshbach method using a unified set of optical model parameters. The strong reaction channels are described well by the calculations. The ($n, t$) reaction on target nuclei in the ($2s, 1d$) shell seems to proceed predominantly via statistical processes; for heavier nuclei nonstatistical contributions become important. In the case of ($n$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$) reactions, the few experimentally measured cross sections are much higher than those obtained by theoretical calculations.

NUCLEAR REACTIONS ($n, x$) cross sections at 14.6 MeV; Hauser-Feshbach analysis.

Padé approximants to the scattering function $F=kcot\left({\delta }_0\right)$ are studied in terms of the variable $x=k^2$, using four examples of potential models which possess features of the $\mathrm{np}$ ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ state. Strategies are thereby developed for analytically continuing $F$ when only approximate partial knowledge of $F$ is available. Results are characterized by high accuracy of interpolation. It is suggested that a physically realistic inverse scattering problem begins with such an analytically continued $F$. When it exists, the solution of this problem in terms of the Marchenko equation is a local potential of the Bargmann type. Some strategies for carrying out this program lead to a stably defined potential, while others do not. With hard core repulsions present, low order Padé approximants accurately describe $F$ for $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}\le 300$ MeV. However, since the condition $\delta \left(\infty \right)-\delta \mathrm{}\left(0\right)=0\mathrm{}$ is not satisfied in any of our examples containing hard core repulsions, the Marchenko method does not have a solution for them. A possible physical consequence of this result is discussed. Another inverse scattering method is proposed for application to hard core problems.

NUCLEAR REACTIONS Padé approximants used to calculate $kcot\left({\delta }_0\right)$ and to solve inverse scattering problem for models of $\mathrm{np}$ ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ scattering; effects of hard cores.

Proton-proton bremsstrahlung in principle provides information about the off-shell nucleon-nucleon force, but first the dominant on-shell contribution must be understood. Comparisons of purely on-shell soft photon calculations with 200 and 730 MeV data have already been made. In this paper similar comparisons are made for the remaining two modern experiments, those at 42 and at 156 MeV. For 42 MeV soft photon and standard potential model calculations differ by amounts comparable to, or somewhat larger than, the errors in the data which tend to fall in between the theoretical curves, which thus fit the data equally well. For the 156 MeV data the soft photon results are a slight improvement over potential models, but neither fit the data very well.

NUCLEAR REACTIONS $p+p\to p+p+\gamma$ $E=42, 156$ MeV; comparison of soft photon approximation calculations with $\sigma \left({\theta }_{\gamma }\right)$ data.

The ($p, p\alpha$) and ($p, d{}_{}{}^3{}_{}{}^{}\mathrm{He}$) reactions on ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ have been investigated at a bombarding energy of 101.5 MeV in a non-coplanar geometry. Coincident data were obtained for coplanar angles ${\theta }_{p,d}=81.2\mathrm{}°$ and ${\theta }_{\alpha ,{}_{}{}^3{}_{}{}^{}\mathrm{He}}=-41.0\mathrm{}°$, and the $\alpha \left({}_{}{}^3{}_{}{}^{}\mathrm{He}\right)$ detector ranging from $\beta =0\mathrm{}° \mathrm{to} 20°$ out of the plane. These data show a smooth reduction in cross section with increasing $\beta$. Comparisons with distorted-wave impulse approximation calculations show that the reactions are dominated by quasifree processes, and that the $D$-state component of the ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ wave function dominates for large $\beta$. Absolute spectroscopic factors for the $S$- and $D$-state terms extracted from the two different reactions are consistent and in excellent agreement with theoretical predictions.

NUCLEAR REACTIONS ${}_{}{}^9{}_{}{}^{}\mathrm{Be}(p, p\alpha )$ and ${}_{}{}^9{}_{}{}^{}\mathrm{Be}(p, d{}_{}{}^3{}_{}{}^{}\mathrm{He})$, $E_{\mathrm{lab}}=101.5\mathrm{}$ MeV; measured $\frac{d^3\sigma }{d{\Omega }_{1}d{\Omega }_{2}d{E}_1}$ ($E_1, E_2, {\theta }_1, {\theta }_2, {\beta }_2$); Non-coplanar geometry; DWIA analysis; deduced alpha particle spectroscopic factors.

Within the framework of the post form distorted-wave Born-approximation theory of breakup reactions, we study the elastic and inelastic breakup of the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ particle. With the standard set of parameters for the optical model potential we are able to understand coincidence and inclusive data for this process, which were recently measured by Matsuoka et al. at the incident ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ energy of 90.0 MeV. The elastic breakup accounts only for about 20% of the total inclusive (${}_{}{}^3{}_{}{}^{}\mathrm{He}$, $d$) yield. With our theory we are able to understand quantitatively the breakup process, a dominant peripheral reaction mechanism.

NUCLEAR REACTIONS $A({}_{}{}^3{}_{}{}^{}\mathrm{He}, d)$ breakup at $E_{{}_{}{}^3{}_{}{}^{}\mathrm{He}}=90.0\mathrm{}$ MeV, $A={}_{}{}^{51}{}_{}{}^{}\mathrm{V}, {}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$; calculated elastic and inelastic breakup cross sections; post form DWBA theory of breakup.

Absolute cross sections for the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}({}_{}{}^3{}_{}{}^{}\mathrm{He}, p)$ reaction to the ground, 2.94-, 16.63-, and 16.92-MeV states in ${}_{}{}^8{}_{}{}^{}\mathrm{Be}$, as well as for the total underlying proton continuum, have been obtained for incident ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ energies between ∼0.5 and 1.85 MeV. Differential and total (integrated) reaction cross sections with accuracies of 10-20% are presented. Thermonuclear reaction-rate parameters are calculated. Interpretation of the observed proton and alpha particle continuous spectra is discussed.

NUCLEAR REACTIONS ${}_{}{}^6{}_{}{}^{}\mathrm{Li}({}_{}{}^3{}_{}{}^{}\mathrm{He}, p){}_{}{}^8{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^6{}_{}{}^{}\mathrm{Li}({}_{}{}^3{}_{}{}^{}\mathrm{He}, p)2\mathrm{}\alpha$, $E_{{}_{}{}^3{}_{}{}^{}\mathrm{He}}=\sim 0.5-1.85$ MeV; enriched LiF target; measured $\sigma (E_{{}_{}{}^3{}_{}{}^{}\mathrm{He}}, \theta )$, $\sigma \left(E_{{}_{}{}^3{}_{}{}^{}\mathrm{He}}\right)$; calculated $〈\sigma v〉$.