The kinetic energy distributions of coincident fission fragments from the thermal-neutron-induced fission of ${}_{}{}^{255}{}_{}{}^{}\mathrm{Fm}$ and ${}_{}{}^{251}{}_{}{}^{}\mathrm{Cf}$ have been measured with phosphorus-diffused silicon detectors. The most probable values for the postneutron total kinetic energy are 192.5±2.9 MeV for ${}_{}{}^{255}{}_{}{}^{}\mathrm{Fm}$ and 182.1±2.7 MeV for ${}_{}{}^{251}{}_{}{}^{}\mathrm{Cf}$. Fragment mass distributions were calculated without applying neutron emission corrections. The resultant mass and kinetic energy distributions for ${}_{}{}^{255}{}_{}{}^{}\mathrm{Fm}$ indicate a predominantly asymmetric mass division combined with appreciable symmetric fission. Fragment pairs near mass symmetry were found to be unusually energetic, which is a characteristic shared with symmetric fission in ${}_{}{}^{257}{}_{}{}^{}\mathrm{Fm}$ and ${}_{}{}^{258}{}_{}{}^{}\mathrm{Fm}$. These results are well described by the two-center model of fission. Thermal-neutron-induced fission cross sections were measured as 3400±170 b for ${}_{}{}^{255}{}_{}{}^{}\mathrm{Fm}$ and 4800 ± 250 b for ${}_{}{}^{251}{}_{}{}^{}\mathrm{Cf}$.

[NUCLEAR REACTIONS, FISSION ${}_{}{}^{255}{}_{}{}^{}\mathrm{Fm}\mathrm{}(n,f)\mathrm{}$, ${}_{}{}^{251}{}_{}{}^{}\mathrm{Cf}\mathrm{}(n,f)\mathrm{}$, $E=0.025\mathrm{}$ eV; measured $\sigma$, fragment $E$; deduced fragment masses.]

A variational scheme of the Schwinger type, used successfully in a previous paper for calculating two-body $t$ matrix elements of all kinds (on shell, half shell, and off shell), is here applied to the three-body collision problem. Numerical results are given for the case of the Amado model of the $N-d$ system. These results show excellent convergence properties, even for the case of fully off-shell amplitudes in the region where the analytic structure is most troublesome. It is shown theoretically that the three-body variational method, if restricted to the case of physical on-shell amplitudes, is formally equivalent to the several variational principles given by Pieper, Schlessinger, and Wright, though the methods may differ considerably in practice. The formal equivalence is used to show that Pieper's recent perturbative calculations of $N-d$ polarization, in which the zero-order problem was approached variationally, have a property not previously noted, namely that even the perturbed solution is fully variational. More generally, a useful degree of cooperation is shown to occur between the present variational method and the perturbation method, making it quite easy to preserve the variational property in a perturbative calculation.

[NUCLEAR REACTIONS ${}_{}{}^2{}_{}{}^{}\mathrm{H}\mathrm{}(n,n)\mathrm{}$, $E=0-40\mathrm{}$ MeV; calculated off-shell amplitudes. Variational method, separable-potential model.]

The presence of the asymmetry seen in the 40.8-keV resonance in the ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}(\gamma ,n_0)$ cross section cannot be explained by either the existence of a second nearby resonance or the ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$ contaminant in the sample.

Differential cross sections and spectroscopic strengths have been measured for the (${}_{}{}^3{}_{}{}^{}\mathrm{He},d$) reaction on targets of ${}_{}{}^{64,66,68,70}{}_{}{}^{}\mathrm{Zn}$ at a ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ energy of 18 MeV. For the three lighter isotopes general agreement is found with the results of the ($d,n$) experiment of Couch et al. Results for the reaction ${}_{}{}^{70}{}_{}{}^{}\mathrm{Zn}({}_{}{}^3{}_{}{}^{}\mathrm{He},d){}_{}{}^{71}{}_{}{}^{}\mathrm{Ga}$ suggest a significant break in the structure of the Ga isotopes at $N=40\mathrm{}$. It is suggested that this may be due to the $n-p$ interaction between nucleons in the same subshell.

[NUCLEAR REACTIONS ${}_{}{}^{64,66,68,70}{}_{}{}^{}\mathrm{Zn}({}_{}{}^3{}_{}{}^{}\mathrm{He},d)$, $E=18\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$, $\theta =15-{80}^{\circ }$. Levels ${}_{}{}^{65-71}{}_{}{}^{}\mathrm{Ga}$, DWBA analysis, deduced $l$ values, $S$.]

A new approach to finite-range distorted-wave Born-approximation calculations was given in a previous paper. This approach utilized plane-wave expansions of the distorted waves and required a testing procedure. A different method for testing these expansions is needed when large heavy ions are considered. This method is presented here.

In the schematic model of a deformed nucleus in which all nucleons are confined to a single $j$ shell (of large degeneracy), the intrinsic state generating the ground-state rotational band is defined by the aligned coupling scheme. A semiclassical evaluation valid for this scheme shows under what conditions the quadrupole deformation dominates over deformations of higher order.

A microscopic isospin interpretation of the ($p,n$) reaction is used to determine the ratio of the rms radii of the neutron and proton distributions in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ from ($p,n$) scattering data at 25.8 MeV. The result for the ratio is $\frac{{〈{r_n}^2〉}^{\frac{1}{2}}}{{〈{r_p}^2〉}^{\frac{1}{2}}}=1.07\mathrm{}\pm 0.03$.

Evidence for a level at 16.43 MeV in ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$ is found in excitation functions measured for outgoing proton channels from the reaction ${}_{}{}^9{}_{}{}^{}\mathrm{Be}+d$. Supporting evidence for this levels is found in earlier works.

We have investigated the states in ${}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}$ at 5.69 and 5.78 MeV through the ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}\mathrm{}(d,p)\mathrm{}$ reaction at 3.6 MeV. Distorted-wave Born-approximation (DWBA) fits have been performed for the angular distributions of these states; they indicate $l=1\mathrm{} \mathrm{and} 0$ for the 5.69- and 5.78-MeV levels, respectively. Spectroscopic factors have been extracted. The correspondence between the states and their analog states in ${}_{}{}^{21}{}_{}{}^{}\mathrm{Na}$ is discussed.

[NUCLEAR REACTIONS ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}\mathrm{}(d,p)\mathrm{}$, $E=3.6\mathrm{}$ MeV measured $\sigma \left(\theta \right)$; ${}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}$ levels deduced $l$, $J$, $\pi$, $S$.]

We have observed 12 $\gamma$ rays in ${}_{}{}^{123}{}_{}{}^{}\mathrm{Sb}$ from the decays of 129-day ${}_{}{}^{123}{}_{}{}^{}\mathrm{Sn}_{}^g{}_{}{}^{}$ and 40-min ${}_{}{}^{123}{}_{}{}^{}\mathrm{Sn}_{}^m{}_{}{}^{}$. These $\gamma$ rays have been incorporated into a level scheme of ${}_{}{}^{123}{}_{}{}^{}\mathrm{Sb}$ with eight excited states. Discrepancies between a previous decay scheme and $\mathrm{Sb}(n,n^{\prime }\gamma )$ studies have been resolved.

[RADIOACTIVITY ${}_{}{}^{123}{}_{}{}^{}\mathrm{Sn}_{}^g{}_{}{}^{}$, ${}_{}{}^{123}{}_{}{}^{}\mathrm{Sn}_{}^m{}_{}{}^{}$ [from ${}_{}{}^{122}{}_{}{}^{}\mathrm{Sn}(n,\gamma )$]; measured $E_{\gamma }$, $I_{\gamma }$. ${}_{}{}^{123}{}_{}{}^{}\mathrm{Sb}$ deduced levels, $\gamma$ branching, $log\mathrm{ft}$, $J^{\pi }$. Enriched targets, Ge(Li) detector.]

The separation method of Moszkowski and Scott has recently been used to generate an effective interaction for inelastic scattering. We investigate this approximation for the two-nucleon ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ state in a realistic model. We find that the method only yields reliable off-shell matrix elements for low energies and momenta near the on-shell point.

We consider the problem of three spinless particles interacting by means of a central potential. The initial state is a free particle labeled number 1 incident on a bound state of particles 2 and 3 and with enough energy to create a three-free-particle final state. We calculate the $S$-wave elastic scattering amplitude both above and below the inelastic threshold using an extension of the Kohn variational principle suggested by Nuttall. For the asymptotic form, we use the simplest function available. The form used has been shown to be incorrect in certain regions of coordinate space. The trial function we use has up to 32 linear parameters and a range of values for a nonlinear parameter. Below breakup convergence is observed towards a unitary result, but in the inelastic region little evidence of convergence is present.

An individual particle-track counting technique, employing electron-microscope image plates, has been used to obtain accurate electron intensities with a high-resolution permanent-magnet spectrograph. The $L$-subshell ratios of the 99-keV transition in ${}_{}{}^{195}{}_{}{}^{}\mathrm{Pt}$, have been remeasured as $\frac{L_{\mathrm{I}}}{L_{\mathrm{II}}}=7.68\mathrm{}\pm 0.30$, $\frac{L_{\mathrm{II}}}{L_{\mathrm{III}}}=3.67\mathrm{}\pm 0.20$, and $\frac{L_{\mathrm{I}}}{L_{\mathrm{III}}}=28.3\mathrm{}\pm 1.4$. These ratios are consistent with an $\frac{E2\mathrm{}}{M1\mathrm{}}$ multipole mixing ratio of $0.114\le \left|\delta \right|\le 0.133$ and a penetration parameter of $-2\mathrm{}\le \lambda \le 2.5$. Earlier double-focusing spectrometer results have been analyzed on the $\left|\delta \right|$ vs $\lambda$ plane and were found to be consistent with $\left|\delta \right|=0.160\mathrm{}\pm 0.003$ and $\lambda =-16.5\mathrm{}\pm 1.8$, which are in disagreement with both the present data and with more recent double-focusing spectrometer data.

New estimates for the height of the fission barriers imply new values for the pairing gap at the deformation corresponding to the second saddle points. Current barriers imply $2{\Delta }_s=1.7\mathrm{}\pm 0.3$ MeV and 1.6±0.3 MeV for ${}_{}{}^{236}{}_{}{}^{}\mathrm{U}$ and ${}_{}{}^{240}{}_{}{}^{}\mathrm{Pu}$, respectively. Uncertainties in the reported values of $2{\Delta }_s$ for ${}_{}{}^{210}{}_{}{}^{}\mathrm{Po}$ and ${}_{}{}^{227}{}_{}{}^{}\mathrm{Ra}$ are also discussed.

[NUCLEAR STRUCTURE ${}_{}{}^{236}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{240}{}_{}{}^{}\mathrm{Pu}$; reevaluate pairing gap at fission saddle point.]

The spinner technique was used for a search for superheavy elements in chemical compounds, minerals, and in targets which were irradiated with 24-GeV protons. For minerals and chemical compounds upper limits for the concentration of eka-elements of ${10}^{-13\mathrm{}}$-${10}^{-14\mathrm{}}$ g per gram of the homolog element were obtained, assuming a half-life for spontaneous fission of ${10}^9$ yr. Production cross sections of the order of ${10}^{-39\mathrm{}}$ ${\mathrm{cm}}^2$ were established as upper limits for the formation of eka-elements and actinides in tungsten targets irradiated by high-energy protons, if half-lives of one year are assumed.

[RADIOACTIVITY Fission of superheavy elements ($Z=110-115\mathrm{}$) from natural samples, limits for $T_{\frac{1}{2}}$, measured with the spinner technique.

NUCLEAR REACTIONS $W$ ($p$, recoil) actinides, eka-elements ($Z=110-115\mathrm{}$), $E_p=24\mathrm{}$ GeV, measurement of spontaneous fission with spinner technique.]

A coupled-channel study of the five-nucleon system is performed with the resonating-group method. The channels which are explicitly considered are the $d+{}_{}{}^3{}_{}{}^{}\mathrm{He}$ (or $d+{}_{}{}^3{}_{}{}^{}\mathrm{H}$) and the $p+\alpha$ (or ($n+\alpha$) channels. Three- and more-body breakup channels are not included in the calculation, but their effects are crudely taken into account by the introduction of phenomenological imaginary potentials into the formulation. The nucleon-nucleon potential used is purely central, but does yield correct values for the two-nucleon effective-range parameters. Differential scattering and reaction cross sections are calculated at various energies. The result shows that for the $d+{}_{}{}^3{}_{}{}^{}\mathrm{He}$ and $p+\alpha$ differential scattering cross sections, the calculated values in general agree quite well with the experimental data. For the $d+{}_{}{}^3{}_{}{}^{}\mathrm{He}\rightleftarrows p+\alpha$ differential reaction cross sections, the comparison between theory and experiment is somewhat less satisfactory. Although the general features of the experimental angular distributions are well reproduced, the magnitude of the calculated cross section is somewhat too low.

[NUCLEAR REACTIONS ${}_{}{}^3{}_{}{}^{}\mathrm{He}\mathrm{}(d,d)\mathrm{}$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}\mathrm{}(d,p)\mathrm{}$, ${}_{}{}^4{}_{}{}^{}\mathrm{He}\mathrm{}(p,d)\mathrm{}$, ${}_{}{}^4{}_{}{}^{}\mathrm{He}\mathrm{}(p,p)\mathrm{}$, $E=0-50\mathrm{}$ MeV; calculated $\sigma \left(\theta \right)$. Resonating-group method; coupled-channel calculation.]

A measurement has been made of the branching ratio, $\frac{{\Gamma }_{\mathrm{rad}}}{\Gamma }$, for electromagnetic transitions from the 7.65-MeV state of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. This ratio is of particular interest in that the rate of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ synthesis in stellar helium burning is proportional to ${\Gamma }_{\mathrm{rad}}$. The 7.65-MeV state was excited by inelastic scattering of 24-MeV $\alpha$ particles on ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, and electromagnetic transitions were identified by detecting coincidences between the inelastic $\alpha$ particles and the associated ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ ions remaining after $\gamma$-ray or electron-pair emission. It was found that $\frac{{\Gamma }_{\mathrm{rad}}}{\Gamma }=(4.2\mathrm{}\pm 0.2)\times {10}^{-4\mathrm{}}$, which may be compared to the previous best value of (2.9±0.3)×${10}^{-4\mathrm{}}$. The new result, combined with available information on the width and branching ratio for electron-pair emission, leads to a radiative width ${\Gamma }_{\mathrm{rad}}={\Gamma }_{\gamma }+{\Gamma }_{e^{\pm }}=(3.9\mathrm{}\pm 1.2)$ meV.

[NUCLEAR STRUCTURE ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, 7.65-MeV state; measured $\frac{{\Gamma }_{\mathrm{rad}}}{\Gamma }$. Helium burning.]

A comprehensive study has been completed on the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ radiative-capture reactions ${}_{}{}^9{}_{}{}^{}\mathrm{Be}-({}_{}{}^3{}_{}{}^{}\mathrm{He},\gamma ){}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, leading to the first four states of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, and ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}({}_{}{}^3{}_{}{}^{}\mathrm{He},\gamma ){}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, leading to the first five states in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$. Excitation functions have been extended to excitations of 45 and 35 MeV, respectively, by bombarding natural ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ and isotopically enriched ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ targets with ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ from the Wright Nuclear Structure Laboratory MP tandem accelerator. Angular distributions have been taken at many key energies. These experiments utilized a large NaI(Tl) $\gamma$-radiation detector and plastic-scintillator cosmic-ray anticoincidence shield built as part of this program, and the IBM 360/44 on-line data acquisition system. Several resonances have been found. The experiment appears to confirm the role of 3p-3h configurations immediately above the giant resonances of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$. Microscopic $R$-matrix calculations based on the Wang and Shakin 1p-1h and 3p-3h ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ wave functions have been conducted. Detailed comparison of these calculations with our data and ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}(p,{\gamma }_0){}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ data suggests that the source of much of the intermediate structure seen in the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ giant resonance may stem from the mixing of 1p-1h doorway configurations with 3p-3h configurations.

[NUCLEAR REACTIONS ${}_{}{}^6{}_{}{}^{}\mathrm{Be}({}_{}{}^3{}_{}{}^{}\mathrm{He},\gamma )$, $E=3-26\mathrm{}$ MeV; ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}({}_{}{}^3{}_{}{}^{}\mathrm{He},\gamma )$, $E=3-16\mathrm{}$ MeV; measured $\sigma (E;E_{\gamma },\theta )$. ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ deduced levels $J$, $\pi$, resonance parameters. Natural ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ target. Enriched ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ target.]