Half-life limits $T_{\frac{1}{2}}\left({\beta }^{-}\right)>\mathrm{}7.0\mathrm{}\times {10}^{17}$ yr and $T_{\frac{1}{2}}\left(\mathrm{EC}\right)>\mathrm{}8.8\mathrm{}\times {10}^{17}$ yr have been deduced for ${}_{}{}^{50}{}_{}{}^{}\mathrm{V}$ from Ge(Li) spectra.

RADIOACTIVITY ${}_{}{}^{50}{}_{}{}^{}\mathrm{V}$, deduced ${\beta }^{-}$, EC half-life limits, Ge(Li) detector.

We calculated pion-deuteron elastic scattering in the impulse approximation, using Wick's three-body helicity formalism, and compared it with data at energies around the 3,3 resonance. We used a separable form for the off-shell $\pi N$ $T$ matrix, which avoids the problems of other forms that have been used previously, and found good agreement with experimental data.

NUCLEAR REACTIONS $d(\pi , \pi )d$, $E=142, 182, 256$ MeV; calculated $\frac{d\sigma }{d\Omega }$.

The $Q$ values for the (${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^8{}_{}{}^{}\mathrm{Li}$) reaction on ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ and ${}_{}{}^{36}{}_{}{}^{}\mathrm{Ar}$ have been measured. The resulting masses for the new nuclei ${}_{}{}^{27}{}_{}{}^{}\mathrm{P}$ and ${}_{}{}^{31}{}_{}{}^{}\mathrm{Cl}$ are compared with the predictions of various models. The lowest $T=\frac{3}{2}$ state in ${}_{}{}^{27}{}_{}{}^{}\mathrm{Si}$ was also observed in the ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}(p, t){}_{}{}^{27}{}_{}{}^{}\mathrm{Si}$ reaction, and its excitation energy and mass excess were determined.

NUCLEAR REACTIONS ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{36}{}_{}{}^{}\mathrm{Ar}$(${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^8{}_{}{}^{}\mathrm{Li}$) measured $Q$. Deduced mass ${}_{}{}^{27}{}_{}{}^{}\mathrm{P}$, ${}_{}{}^{31}{}_{}{}^{}\mathrm{Cl}$. ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}(p, t)$ measured $Q$ lowest, $T=\frac{3}{2}$ level.

Exchange effects in the $\alpha$+${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ + ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, and $p$+${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ systems are examined by studying the behavior of phase shifts and cross sections calculated with the resonating-group method. The result shows that these effects can be approximately represented by an exchange potential $V_{\mathrm{ex}}=V_a+{\mathrm{}(-1\mathrm{})\mathrm{}}^l{V}_b$. The term $V_a$, representing mainly the knockout process, is found to have an appreciable magnitude and to have a range shorter than that of the direct nuclear potential. The term ${\mathrm{}(-1\mathrm{})\mathrm{}}^l{V}_b$, representing mainly the heavy-particle pickup process, is, on the other hand, rather small in all these three systems. Based on the findings obtained from this and previous investigations, an empirical rule is given which indicates the situation under which the heavy-particle pickup process is expected to be important.

NUCLEAR REACTIONS ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(\alpha , \alpha )$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$(${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$), ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(p, p)$. Potential-model analysis of resonating-group results.

The ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^3{}_{}{}^{}\mathrm{He}, p){}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ reaction mechanism has been studied by measuring the alignment of ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ excited states using a particle-$\gamma$ angular correlation technique. A collinear geometry has been used with simultaneous particle detection at 0° and 180°. Strong fluctuations of the nuclear alignments, observed between 11 and 20 MeV bombarding energy, reflect a complex reaction mechanism similar to that observed previously at lower energies.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^3{}_{}{}^{}\mathrm{He}, p\gamma )$, $11\le E\le 20$ MeV; measured $p-\gamma$ angular correlations. Deduced nuclear alignments. Comparison with direct interaction and Hauser-Feshbach theories.

Elastic electron scattering cross sections for ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ were measured relative to those of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ in the range of momentum transfer squared between 0.032 and 0.34 ${\mathrm{fm}}^{-2\mathrm{}}$. The ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ rms charge radius was determined from the data to be 1.89 ± 0.05 fm.

NUCLEAR REACTIONS ${}_{}{}^3{}_{}{}^{}\mathrm{He}(e, e)$, $E=28.8-95.0\mathrm{}$ MeV; measured $\sigma \mathrm{}\left(E\right)\mathrm{}$ at $\theta =75\mathrm{}°$; deduced rms charge radius.

The technique of hyperspherical harmonics is used in the calculation of elastic scattering of three nucleons, $N+N+N\to N+N+N$. The calculation is done within the context of rigorous treatment of spin-isospin variables involved in the system and standard three-body theory. We obtain formulas for the differential cross section and total cross section for the scattering channel characterized by total orbital angular momentum unity, negatve parity, total spin ½, and total isospin $\frac{3}{2}$. The calculation of this specific scattering channel is investigated by analyzing the uncoupled channel, grand orbital $L=1\mathrm{}$ and the coupled channel, grand orbital $L=1.3\mathrm{}$ Two model calculations for spin-independent and spin-dependent two-body potentials of the total cross section are presented for both uncoupled and coupled channels. The convergence of the hyperspherical harmonic expansion of the wave function is discussed.

NUCLEAR REACTIONS Three-body to three-body elastic scattering; uncoupled and coupled channels; partial wave analysis; phase shift; total cross section.

We use expansions in hyperspherical harmonics to calculate electric dipole transitions in the triton photoeffect. Gunn's ground state wave function is used with a Born approximation; the resulting cross section is compared with sum-rule calculations. We also use Ballot's ground state wave function for the spin-independent Volkov potential, in Born approximation, and combined with a continuum wave function for grand orbital one for the Volkov potential assumed to have Wigner character. The latter assumption gives an integrated cross section only 6% larger than the Thomas-Reiche-Kuhn sum rule; i.e., the severe truncation has only a small effect.

NUCLEAR REACTIONS Triton; calculated photoeffect; hyperspherical harmonics; sum rules.

We have put very tight upper and lower bounds on the effect of vacuum polarization on the proton-proton scattering wave function, in the region where the nuclear potential is known, but have not succeeded in doing the same at very small distances. Simply making a smooth extrapolation of the bounds leads to the expectation that vacuum polarization reduces the proton-proton reaction rate by between 0.8% and 1.2% assuming the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ potential is known beyond 2 fm. An independent argument following the work of Picker and Haftel leads to the conclusion that $1.7<\mathrm{}{\Lambda }^2<7.2\mathrm{}$ with vacuum polarization included, assuming the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}D_1^{}{}_{}{}^{}$ potentials are known beyond 3 fm.

NUCLEAR REACTIONS Effect of vacuum polarization on scattering length, wave function. Bounds on $\mathrm{pp}\to {\mathrm{de}}^{+}\nu$ reaction rate.

A lower limit for the spreading width of doorway resonances is derived as a function of absorption coefficients and of the branching ratio of the doorway to channels that are not directly coupled to it. Equations are obtained that provide a means of experimental determination of the fluctuating part of the cross sections without measurement of the fine structure.

NUCLEAR REACTIONS Doorway states, fluctuation cross section, spreading width, and branching ratios discussed.

We calculated the differential cross section and polarization ($I_0, p_y, C_{\mathrm{yy}}, \mathrm{and} K_z^x$) for ($n, p$) scattering at energies between 20 and 140 MeV with a separable potential model. It is shown that (a) the potentials fitted to the results of an unconstrained phase shift analysis cannot reproduce the experimental data and (b) the mixing parameter ${\epsilon }_1$ is most probably positive at all energies and a smoothly varying function of the energy. More polarization experiments are needed to settle these questions unambiguously.

NUCLEAR REACTIONS ($n, p$) scattering observables, 20-140 MeV calculated with separable $R$ matrix.

The distorted-wave Born approximation is used in the case of the stripping reaction ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}(d, p){}_{}{}^{33}{}_{}{}^{}\mathrm{S}_{}^{*}{}_{}{}^{}$ leading to decaying states in order to explain the strong dependence of the ratio of the energy differential ($d, p$) stripping cross section to the total neutron elastic scattering cross section on the same target, on transferred angular momentum ($l$) The necessity of using a distorted-waves approximation instead of a plane-waves approximation, which is much simpler to calculate and which also shows " $l$ dependence," is discussed in the context of identification of levels. The slowly converging overlap integral appearing in the distorted-wave Born approximation is treated by employing a Gaussian convergence factor. It is also found that in the plane-wave calculation, the inclusion of the unscattered part in the neutron form factor affects only the $l=0\mathrm{}$ resonances. The desirability of including the effect of the nuclear interior is discussed. The angular distribution for the reaction ${}_{}{}^6{}_{}{}^{}\mathrm{O}(d, p){}_{}{}^{17}{}_{}{}^{}\mathrm{O}_{}^{*}{}_{}{}^{}$ has been obtained employing the distorted-wave Born approximation method. The spectroscopic factor for this reaction is obtained and compared with that reported previously.

NUCLEAR REACTIONS ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}(d, p)$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(d, p)$ reactions, unbound states, calculated $\frac{\left[d^2\sigma \right(d, p\left)\right]}{d\Omega \mathrm{dE}}$, $\frac{\left[d\sigma \right(d, p\left)\right]}{d\Omega }$, $E_D=12-13.3\mathrm{}$ MeV, DWBA analysis.

The total elastic cross section, ${}_{}{}^6{}_{}{}^{}\mathrm{Li}(n, \alpha ){}_{}{}^3{}_{}{}^{}\mathrm{H}$ cross section, differential cross section, and polarization are calculated for the $n$-${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ system in the energy range 0-5 MeV by using general $R$-matrix theory and taking into account various coupled channels in addition to the direct channels. The results are compared with the experimental results and earlier calculations. Our calculations are helpful in estimating the contribution of dominant coupled channels to the cross sections in 0-5 MeV energy range.

NUCLEAR REACTIONS $R$-matrix theory, $n$-${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ system, cross sections, polarization.

A wave function method for computing off-shell $K$ matrix elements is presented. Certain computational advantages are derived thereby. The formalism developed is used to relate the $K$ matrix elements for the exponential potential to tabulated functions.

NUCLEAR REACTIONS Scattering theory, a wave function approach to $K$ matrix theory.

The wave function approach to reaction matrix theory has been adapted to the $K$ matrix calculation for potentials which behave like $K$ near the origin. The results are used to obtain the Hultheń $r^{-1\mathrm{}}$ matrix in terms of tabulated transcendental functions.

NUCLEAR REACTIONS Scattering theory, $K$ matrix for singular potentials, Hulthén $K$ matrix obtained in closed form.

Microscopic distorted-wave calculations for the ${}_{}{}^{112,116,124}{}_{}{}^{}\mathrm{Sn}(p, n)$ reactions to the isobaric analog states have been made using a $G$-matrix interaction, supplemented by a phenomenological imaginary isovector potential. A reasonable description of the magnitudes and shapes of the angular distributions is obtained for a proton bombarding energy of 22.8 MeV. The same interaction provides a reasonable description of the asymmetry induced in the ${}_{}{}^{120}{}_{}{}^{}\mathrm{Sn}(\overrightarrow{p}, n)$, reaction at $E_p=24.5\mathrm{}$ MeV when the two-body spin-orbit interaction is included.

NUCLEAR REACTIONS ${}_{}{}^{112,116,124}{}_{}{}^{}\mathrm{Sn}(p, n)$, $E=22.8\mathrm{}$ MeV, calculated $\sigma \left(\theta \right)$; ${}_{}{}^{120}{}_{}{}^{}\mathrm{Sn}(\overrightarrow{p}, n)$, $E=24.5\mathrm{}$ MeV, calculated asymmetry.

${}_{}{}^{68}{}_{}{}^{}\mathrm{Ga}$ has been studied with the ${}_{}{}^{69}{}_{}{}^{}\mathrm{Ga}(d, t)$ and ${}_{}{}^{70}{}_{}{}^{}\mathrm{Ge}(d, \alpha )$ reactions at 17.0 and 14.5 MeV, respectively. Magnetic spectrograph analysis yielded resolutions of 7-10 keV. 20 of 45 states resolved below 2.2 MeV excitation were previously unknown. ${}_{}{}^{69}{}_{}{}^{}\mathrm{Ga}(d, t){}_{}{}^{68}{}_{}{}^{}\mathrm{Ga}$ angular distributions were taken in 4°-5° steps from 8° to 60°. $l_n$ transfers, spectroscopic factors, and $J^{\pi }$ limits for levels below 1.4 MeV were deduced from comparison with zero range distorted-wave Born approximation calculations. $J^{\pi }$ values and dominant configurations for some low-lying states could be assigned.

NUCLEAR REACTIONS ${}_{}{}^{69}{}_{}{}^{}\mathrm{Ga}(d, t)$, $E_d=17\mathrm{}$ MeV, measured $\sigma (E_t, \theta )$. ${}_{}{}^{70}{}_{}{}^{}\mathrm{Ge}(d, \alpha )$, $E_d=14.5\mathrm{}$ MeV, measured $\sigma \left(E_{\alpha }\right)$. Resolution 7-10 keV. DWBA analysis, deduced $l$, $\pi$, $J$, spectroscopic factors.

Partial cross sections for radiative capture of 24.3 keV neutrons leading to low-lying states of the residual nuclides have been measured for even-$A$ molybdenum targets: ${}_{}{}^{92}{}_{}{}^{}\mathrm{Mo}$, ${}_{}{}^{94}{}_{}{}^{}\mathrm{Mo}$, ${}_{}{}^{96}{}_{}{}^{}\mathrm{Mo}$, and ${}_{}{}^{98}{}_{}{}^{}\mathrm{Mo}$. Absolute values of these cross sections were obtained by use of the ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}(n, \alpha )$ reaction as a reference. These cross sections show correlations to the ($d, p$) spectroscopic factors for the final states. The expected cross sections are calculated using various models. The single-particle estimates and giant dipole resonance extrapolations are shown to be inadequate. Although a valence neutron transition model can account for the observed correlations, it is inadequate to account for the observed strength. The evidence favors a significant contribution from three quasiparticle components in the capturing states.

NUCLEAR REACTIONS Neutron capture $\gamma$ rays, averaged resonance capture 24.3 keV, iron-aluminum beam filter, partial radiative cross sections, correlations between ($n, \gamma$) and ($d, p$), valence transitions, angular correlations, deduced level spins.

The $Q$ values of the (${}_{}{}^3{}_{}{}^{}\mathrm{He}$,${}_{}{}^6{}_{}{}^{}\mathrm{He}$) reaction on ${}_{}{}^{46}{}_{}{}^{}\mathrm{Ti}$, ${}_{}{}^{50}{}_{}{}^{}\mathrm{Cr}$, ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$, and ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$ have been measured, and the excitation energy of levels up to 7 MeV has been determined. Angular distributions from the more strongly populated states have been taken from 4.5 to 27.0° in the laboratory. These angular distributions together with comparison to their $T_z=+\frac{1}{2}$ mirrors have been used as empirical guides to determine the spin and parity of several of the states. The Coulomb displacement energies of particle-hole states in the $T=\frac{1}{2}$ mirrors have been compared to a simple model.

NUCLEAR REACTIONS ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{46}{}_{}{}^{}\mathrm{Ti}$, ${}_{}{}^{50}{}_{}{}^{}\mathrm{Cr}$, ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$(${}_{}{}^3{}_{}{}^{}\mathrm{He}$,${}_{}{}^6{}_{}{}^{}\mathrm{He}$), $E_{{}_{}{}^3{}_{}{}^{}\mathrm{He}}=70\mathrm{}$ MeV, measured $Q$, $\sigma \left(\theta \right)$, excitation energies, obtained mass excess of ${}_{}{}^{43}{}_{}{}^{}\mathrm{Ti}$, ${}_{}{}^{47}{}_{}{}^{}\mathrm{Cr}$, ${}_{}{}^{51}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{55}{}_{}{}^{}\mathrm{Ni}$, deduced Coulomb displacement energies.

The ${}_{}{}^{108,106}{}_{}{}^{}\mathrm{Pd}(p, t){}_{}{}^{106,104}{}_{}{}^{}\mathrm{Pd}$ reactions were studied at 30 MeV proton energies using a quadrupole-dipole-dipole-dipole spectrograph together with a 60 cm wire proportional counter backed by a plastic scintillator. Closely spaced multiplets of states in ${}_{}{}^{104}{}_{}{}^{}\mathrm{Pd}$ of special interest were investigated at 5 keV energy resolution with a 5 cm solid state position sensitive detector. The ($p, t$) strength for population of levels in the even Pd isotopes is found to be close to the corresponding summed strength previously found for population of the core-coupled multiplets in the silver isotopes, a result in accord with a prediction of the weak coupling model.

NUCLEAR REACTIONS ${}_{}{}^{106,108}{}_{}{}^{}\mathrm{Pd}(p, t)$, $E_p=30\mathrm{}$ MeV, measured $\sigma \left(\theta \right)$ and level energies, DWBA analysis, deduced $L$,$J^{\pi }$. Enriched targets, 13 keV resolution, 5 keV for some multiplets.