The ground-state nuclear pair decay branch from the 7.65-MeV $0^{+}$ level in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ has been measured using the reaction ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(p,p^{\prime }){}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ on a 3.5-mg/${\mathrm{cm}}^2$ thick carbon target at $E_p=10.5\mathrm{}$ MeV together with a magnetic pair spectrometer. For normalization the internal pair line due to the 4.44-MeV $E2$ transition from the first-excited state of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ was used. In separate measurements the corresponding relative populations of the 7.65- and 4.44-MeV states were determined. The angular distribution of the 4.44-MeV $\gamma$ rays was also measured in order to obtain the correction to the spectrometer efficiency due to nuclear alignment. A pair decay branch of (7.1 ± 0.8) × ${10}^{-6\mathrm{}}$ was obtained for the 7.65-MeV level in agreement with, but somewhat more accurate than previous measurements.

NUCLEAR STRUCTURE ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, 7.65-MeV state; measured $\frac{{\Gamma }_{\pi }}{\Gamma }$; deduced ${\Gamma }_{\mathrm{rad}}$.

A method is presented for the expansion of properly antisymmetrized cluster model (or resonating group method) wave functions in terms of translationally invariant shell-model wave functions. By coupling the relative motion (harmonic oscillator) wave functions and the internal cluster functions to resultant ${\mathrm{SU}}_3$,${\mathrm{SU}}_4$ strong coupled functions, the cluster model wave functions can be expanded in terms of standard shell-model wave functions by ${\mathrm{SU}}_3$, ${\mathrm{SU}}_4$ recoupling techniques, using readily available recoupling coefficients. As a specific example, the full shell-model expansions are given for ($\alpha +{}_{}{}^{12}{}_{}{}^{}\mathrm{C}_{}^{\mathrm{}\left(04\right)\mathrm{}}{}_{}{}^{}$) cluster functions for all possible ${\mathrm{SU}}_3$ symmetries and $\alpha -{}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ relative motion wave functions carrying from 4 to 8 oscillator quanta, hence ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ core excitations up to $4\hslash \omega$.

NUCLEAR STRUCTURE Shell-model expansions of cluster functions; $\alpha +{}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ representations of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$.

An equations-of-motion method is proposed for treating neutron-proton pairing correlations conserving both nucleon number $N$ and isospin $T$. This method makes it possible to find approximate solutions to the charge-independent pairing Hamiltonian by a step-by-step procedure. It is shown that for the degenerate model the exact results are obtained.

NUCLEAR STRUCTURE Charge-independent treatment of pairing correlations.

The equivalence of effective two-body and two-body plus three-body forces for the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ system is investigated. Sussex matrix elements are modified to bind the $A=3\mathrm{}$ and $A=4\mathrm{}$ systems in both a two-body as well as three-body approach. Both approaches predict reasonably accurate binding energies and rms radii for the ground states of light systems although these methods do not accurately predict the first excited state in the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ system.

NUCLEAR STRUCTURE Three-body forces in the $A=3\mathrm{}$ and $A=4\mathrm{}$ systems.

A recent high resolution study of ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}({}_{}{}^3{}_{}{}^{}\mathrm{He},t)$ found that the cross section to a presumed single $1^{+}$ state of ${}_{}{}^{24}{}_{}{}^{}\mathrm{Al}$ at 1.12 MeV is in fact a doublet. This peak in the spectra was successfully separated into two peaks in a reanalysis of our previous data, and the new results were compared with the earlier discussion of the reaction mechanism. It is found that a new state of spin ${\mathrm{}(1,2,3)\mathrm{}}^{+}$ exists near 1.12 MeV in ${}_{}{}^{24}{}_{}{}^{}\mathrm{Al}$.

NUCLEAR REACTIONS ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}({}_{}{}^3{}_{}{}^{}\mathrm{He},t)$ to 1.12 MeV doublet in ${}_{}{}^{24}{}_{}{}^{}\mathrm{Al}$. Comparison to earlier CCBA analysis.

The linear polarization of the resonantly produced 4843 keV radiation from ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ has been remeasured, and the results are inconsistent with either a pure E1 or M1 transition. A comparison of self-absorption and scattering results suggests two levels with widths of about 2.5 eV. It is proposed that one has as $1^{-}$ and the other a $1^{+}$ character.

NUCLEAR REACTIONS ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}(\gamma ,\gamma )$, bremsstrahlung $E_e=4.95\mathrm{}$ MeV; measured LP, $\sigma \left(126\mathrm{}°\right)$; deduced $\pi$, $\Gamma$. Enriched and natural targets.

Evidence for cusps is presented for the cross sections of inelastic proton scattering from ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ti}$, ${}_{}{}^{52}{}_{}{}^{}\mathrm{Cr}$, and ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$ as well as for the ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ti}(p,n){}_{}{}^{48}{}_{}{}^{}\mathrm{V}$ reaction. Detailed statistical model calculations are compared with the experimental absolute cross sections.

NUCLEAR REACTIONS ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ti}(p,n)$, measured $\sigma (E,0)$, $E_p=4.7\mathrm{}-5.4$ MeV. Compared data with statistical model calculations. Presents evidence for cusps in cross sections.

The ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}({}_{}{}^3{}_{}{}^{}\mathrm{He},t){}_{}{}^{56}{}_{}{}^{}\mathrm{Co}$ reaction has been studied at 38.2 MeV incident beam energy. Angular distributions have been obtained for 20 levels ranging in energy up to the isobaric analog states at 3511 and 3577 keV. Spins and parities have been assigned for most of the levels based on a comparison with distorted-wave Born approximation calculations.

NUCLEAR REACTIONS ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}({}_{}{}^3{}_{}{}^{}\mathrm{He},t)$, $E_{{}_{}{}^3{}_{}{}^{}\mathrm{He}}=38.2\mathrm{}$ MeV, measured $\sigma \left(\theta E_t\right)$, spectrograph and DWBA analysis; deduced $E_x$ and $J^{\pi }$ of ${}_{}{}^{56}{}_{}{}^{}\mathrm{Co}$ levels.

The heavy odd-mass ${}_{}{}^{129-133}{}_{}{}^{}\mathrm{Sb}$ isotopes have been studied. Partial level schemes are constructed and $\mu \mathrm{s}$ isomeric states are observed and located as follows: $3 \mu \mathrm{s} \left({}_{}{}^{129}{}_{}{}^{}\mathrm{Sb}\right)$, $50 \mu \mathrm{s} \left({}_{}{}^{131}{}_{}{}^{}\mathrm{Sb}\right)$, and $17 \mu \mathrm{s} \left({}_{}{}^{133}{}_{}{}^{}\mathrm{Sb}\right)$. By means of particle-core coupling as well as one-proton two-neutron-hole (1p-2h) shell-model calculations, many of the observed properties such as energy spectra, branching ratios, and isomeric states can be reproduced qualitatively and even quantitatively.

NUCLEAR STRUCTURE ${}_{}{}^{127,131}{}_{}{}^{}\mathrm{Sb}$ levels and lifetimes. Unified model and shell-model calculations.

The ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}(\alpha ,{}_{}{}^2{}_{}{}^{}\mathrm{He}){}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$ reaction is found to be highly selective in the population of high-spin states. Under the assumption of (simple) shell-model wave functions the angular distributions can be well described by distorted-wave Born approximation calculations with an optical-model parameter set identical to that used in the analysis of the ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}(\alpha ,d){}_{}{}^{30}{}_{}{}^{}\mathrm{P}$ reacti at $E_{\alpha }=50\mathrm{}$ MeV. Two previously unobserved states at $E_x=8.93\mathrm{} \mathrm{and} 10.64$ MeV are suggested to both have $J^{\pi }=6^{+}$.

NUCLEAR REACTIONS ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}(\alpha ,{}_{}{}^2{}_{}{}^{}\mathrm{He})$, $E=65\mathrm{}$ MeV: measured $\sigma (E,\theta )$. Natural target; $\theta =11\mathrm{}°-37°$ calculated $\sigma \left(\theta \right)$.

Integral representations for the $s$-wave, off-shell Jost function and half-off-shell $T$ matrix for a superposition of Yukawa potentials are derived. A representation for the form factor or vertex function associated with a bound state or resonance produced by such a potential is also derived. The analytic structure of the various functions is discussed. The applicability of the form factor result to the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ virtual bound state of the two-nucleon system is pointed out, and a calculation of the form factor for the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ Reid potential is presented.

NUCLEAR REACTIONS Off-shell Jost function, $T$ matrix, and form factor for a superposition of Yukawa potentials; application to ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ Reid potential.

It is shown that asymmetric couplings among the rearrangement channels in the reduced matrix equations for many-particle scattering do not necessarily imply an asymmetric amplitude. An approximation procedure is formulated which can always provide a symmetric solution.

NUCLEAR REACTIONS Multichannel scattering, particle rearrangements; asymmetric coupling and symmetric solutions.

We have calculated the photoabsorption cross sections due to electric dipole transitions from the ground state of ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$ to excited states in the giant-resonance region using a two-hole, one-particle shell model with zero-range Soper and with separable Tabakin residual interactions. The calculated results are compared with available experimental data and the need for further experimental work is suggested.

PHOTONUCLEAR REACTIONS Calculated total cross sections for ${}_{}{}^{15}{}_{}{}^{}\mathrm{N} (\gamma ,p)+(\gamma ,n)+(\gamma ,d)$.

The validity of the broken-pair approximation as an approximation to the seniority shell model is investigated. The results of the broken-pair approximation and the seniority shell model, obtained by employing identical input information (single-particle levels and their energies, effective two-body matrix elements, ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}$ inert core) for $N=50\mathrm{}$, even-$A$ nuclei are compared. A close agreement obtained between the calculated broken-pair approximation and the seniority shell model energies for ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$, ${}_{}{}^{92}{}_{}{}^{}\mathrm{Mo}$, ${}_{}{}^{94}{}_{}{}^{}\mathrm{Ru}$, and ${}_{}{}^{96}{}_{}{}^{}\mathrm{Pd}$ nuclei and large (95-100%) overlaps between the broken-pair approximation and the senority shell model wave functions for ${}_{}{}^{92}{}_{}{}^{}\mathrm{Mo}$, demonstrates the validity of the broken-pair approximation in this region and in general its usefulness as a good approximation to the seniority shell model.

NUCLEAR STRUCTURE Shell model, seniority shell model, broken-pair approximation, quasiparticle Tamm-Dancoff (QTD), projected QTD; ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$, ${}_{}{}^{92}{}_{}{}^{}\mathrm{Mo}$, ${}_{}{}^{94}{}_{}{}^{}\mathrm{Ru}$, ${}_{}{}^{96}{}_{}{}^{}\mathrm{Pd}$.

The ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}\mathrm{}(d,p)\mathrm{}{}_{}{}^{20}{}_{}{}^{}\mathrm{F}$ reaction has been used to investigate the 4-6 MeV region of excitation of ${}_{}{}^{20}{}_{}{}^{}\mathrm{F}$. Excitation energies were obtained for 26 levels and angular distributions for 23. A distorted-wave Born-approximation analysis yielded $l$ values and spectroscopic strengths for several of these.

NUCLEAR REACTIONS ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}\mathrm{}(d,p)\mathrm{}$, $E=12.0\mathrm{}$ MeV, $E_x=4\mathrm{}-6$ MeV, measured $E_x$, $\sigma \left(\theta \right)$, DWBA analysis.

Elastic electron scattering cross sections of ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}$ were measured over a momentum transfer range from 0.19 to 2.56 ${\mathrm{fm}}^{-1\mathrm{}}$ at both forward and backward angles. Information on all of the ground state multipole moments of both Coulomb and magnetic character has been obtained.

NUCLEAR REACTIONS ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}\mathrm{}(e,e)\mathrm{}$, $E=40.0\mathrm{}-260$ MeV, $\theta =28\mathrm{}°-180°$; measured $\sigma (E,\theta )$; deduced C0, C2, C4, M1, M3, and M5 moments.

Differential cross sections for the ${}_{}{}^4{}_{}{}^{}\mathrm{He}(\alpha ,p)$ reaction leading to the ground and 478-keV states of ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ have been measured at 11 energies between 39.0 and 49.5 MeV and used to determine integral cross sections for ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ production in ${}_{}{}^4{}_{}{}^{}\mathrm{He}(\alpha ,p)$. Comparison of the ground state cross sections with ${}_{}{}^7{}_{}{}^{}\mathrm{Li}(p,\alpha )$ data using the principle of detailed balance indicates good agreement with the most recent ${}_{}{}^7{}_{}{}^{}\mathrm{Li}(p,\alpha )$ measurements but not with some older results. Cross sections for ${}_{}{}^4{}_{}{}^{}\mathrm{He}(\alpha ,d){}_{}{}^6{}_{}{}^{}\mathrm{Li}$ (ground state), extracted at three energies, are consistent with the most recent ${}_{}{}^6{}_{}{}^{}\mathrm{Li}(d,\alpha )$ measurements. Cross sections for ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ production via ${}_{}{}^4{}_{}{}^{}\mathrm{He}(\alpha ,n){}_{}{}^7{}_{}{}^{}\mathrm{Be}$ were determined at nine energies between 39.4 and 47.4 MeV by direct collection of the ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ and detection of the $\gamma$ rays following its decay. These cross sections are essentially identical to the ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ production cross sections above 43 MeV but are smaller below this energy because of threshold effects. The ${}_{}{}^4{}_{}{}^{}\mathrm{He}(\alpha ,p)$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}(\alpha ,n)$ reactions are involved in several mechanisms which have been proposed to explain the universal abundance of ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$, and calculations of these processes have assumed cross sections larger than our data. We therefore confirm earlier conclusions that ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ is unlikely to be produced by galactic cosmic-ray spallation alone, but the status of the other mechanisms remains unclear. Peaks in the ${}_{}{}^4{}_{}{}^{}\mathrm{He}(\alpha ,p)$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}(\alpha ,n)$ excitation functions are discussed in terms of resonances in ${}_{}{}^8{}_{}{}^{}\mathrm{Be}$. Parameters determined by Kumar and Barker in a fit to ${}_{}{}^7{}_{}{}^{}\mathrm{Li}(p,\alpha )$ data are inadequate to explain our ${}_{}{}^4{}_{}{}^{}\mathrm{He}(\alpha ,p){}_{}{}^7{}_{}{}^{}\mathrm{Li}$ (478 keV) cross sections.

NUCLEAR REACTIONS ${}_{}{}^4{}_{}{}^{}\mathrm{He}(\alpha ,p)$, $E=39.0\mathrm{}-49.5$ MeV; measured $\sigma (E;\theta ,E_p)$, $\sigma \mathrm{}\left(E\right)\mathrm{}$. ${}_{}{}^4{}_{}{}^{}\mathrm{He}(\alpha ,n)$, $E=39.4\mathrm{}-47.4$ MeV; measured $\sigma \mathrm{}\left(E\right)\mathrm{}$. ${}_{}{}^4{}_{}{}^{}\mathrm{He}(\alpha ,d)$, $E=46.7\mathrm{}-49.5$ MeV; measured $\sigma (E;\theta )$, $\sigma \mathrm{}\left(E\right)\mathrm{}$. Astrophysical implications for ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ production considered. Discussion of ${}_{}{}^8{}_{}{}^{}\mathrm{Be}$ levels in $R$-matrix formalism.

We generalize the probability current and boundary conditions for wave functions appropriate to a parity-violating interaction of the type $F\left(\overrightarrow{\mathrm{r}}\right)\overrightarrow{\sigma }·\overrightarrow{\mathrm{p}}$.

NUCLEAR REACTIONS Scattering theory, parity violation.

General features for the scattering of fermions (neutrons) from parity-violating potentials are discussed. A bound for the rotatory power $\Phi$ is derived. A simple model is solved exactly and the parity violation is evaluated at threshold and at energies corresponding to $S_{\frac{1}{2}}$ and $P_{\frac{1}{2}}$ resonances. Experimental consequences of this model are explored. Large enhancements of the rotatory power $\Phi$ are found at resonance.

NUCLEAR REACTIONS Scattering theory, parity violation.