${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}\mathrm{}(d,p)\mathrm{}{}_{}{}^{89}{}_{}{}^{}\mathrm{Sr}$ excitation curves were measured at 90, 140, 160, and 170° for four states in ${}_{}{}^{89}{}_{}{}^{}\mathrm{Sr}$: the $d_{\frac{5}{2}}$ ground state, 1.03-MeV $s_{\frac{1}{2}}$ state, 2.00-MeV $d$ doublet, and 2.45-MeV $d_{\frac{3}{2}}$ state, at deuteron energies from 5.0 to 10.5 MeV. The excitation curves for ground state and 1.03-MeV $s_{\frac{1}{2}}$ state display cusps at the threshold of the charge-exchange-coupled channel, ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}\mathrm{}(d,n)\mathrm{}{}_{}{}^{89}{}_{}{}^{}\mathrm{Y}_{}^A{}_{}{}^{}$. The data are fit with coupled-channel Born-approximation calculations.

The ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}({}_{}{}^3{}_{}{}^{}\mathrm{He},\alpha ){}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$ reaction was studied by use of the 12-MeV ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ beam of the Argonne EN Tandem Van de Graaff and a broad-range magnetic spectrograph. Energy levels of ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$ up to about 10-MeV excitation were observed, and spectra at 10 angles were taken. Relative spectroscopic factors were extracted with the aid of distorted-wave calculations. The results were compared with previous neutron-pickup reactions on ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$ and with theoretical predictions which were calculated within the framework of the rotational model.

Differential cross sections and polarizations for 39.6-MeV protons elastically scattered from the isotopes ${}_{}{}^{58,60,62,64}{}_{}{}^{}\mathrm{Ni}$ and ${}_{}{}^{64,66,68}{}_{}{}^{}\mathrm{Zn}$ have been measured using the University of Minnesota linear accelerator. An atomic-beam-type polarized source was used for the polarization measurements. The data have been analyzed using both the standard optical model and a recent approach to the optical model developed by Greenlees, Pyle, and Tang, in which the real part of the central potential and the spin-orbit potential are obtained from the two-nucleon potential and the neutron, proton, and matter point-density distributions. Root-mean-square radii of the real central potentials are extracted from the data, but no systematic trend is evident for an isotopic sequence.

Bound states of ${\mathrm{P}}^{33}$ below 4.3-MeV excitation energy have been investigated via the ${\mathrm{P}}^{31}(t,p\gamma ){\mathrm{P}}^{33}$ reaction at triton bombarding energies of 2.45 and 3.10 MeV. Proton and $\gamma$-ray singles measurements, together with $p-\gamma$ coincidence measurements, have determined the principal $\gamma$-ray decay modes for the eight states previously reported below 4.3-MeV excitation energy in ${\mathrm{P}}^{33}$. Evidence is also obtained for the $\gamma$ decay of a previously unreported state at 4.19 MeV. Angular-correlation measurements, in conjunction with lifetime restrictions obtained from Ge(Li) studies of the $\gamma$-ray Doppler shifts, lead to the following determinations of spin parity for these levels [$\mathrm{MeV}\left(J^{\pi }\right)$] in ${\mathrm{P}}^{33}$: 0.0(${\mathrm{½}}^{+}$), $1.43\left({\frac{3}{2}}^{+}\right)$, $1.85\left({\frac{5}{2}}^{+}\right)$, $2.54\left({\frac{3}{2}}^{+}\right)$, $3.28(\frac{3}{2},\frac{5}{2})$, $3.49(\frac{3}{2} or \frac{1}{2})$, $3.63\left({\frac{7}{2}}^{+}\right)$, $4.05(\frac{3}{2},\frac{5}{2})$, $4.19(\frac{5}{2},\frac{7}{2})$, and $4.22\left({\frac{7}{2}}^{-}\right)$. These results serve in part to confirm the previously published assignments for the ground state and first three excited states, and establish new information for the higher-lying states. Restrictions on multipole mixing in the deexcitation transitions are summarized and compared with previous results. Finally, the experimental spectrum of ${\mathrm{P}}^{33}$ levels thus obtained is compared with applicable shell-model calculations for these low-lying levels.

The isotopes ${\mathrm{K}}^{47}$, ${\mathrm{Ca}}^{50}$, and ${\mathrm{Sc}}^{50}$ were formed by the bombardment of ${\mathrm{Ca}}^{48}$ with 3.3-MeV tritons. Half-lives of 18.1 ± 1.0, 13.9 ± 0.6, and 102.5 ± 0.5 sec, respectively, were measured by following the decay of the $\gamma$ rays emitted by these nuclides. The $\gamma$ rays were observed with a Ge(Li) detector, and $\gamma$-ray energies and relative intensities were obtained. ${\mathrm{K}}^{47}$ decays to the second and third excited states of ${\mathrm{Ca}}^{47}$; ${\mathrm{Ca}}^{50}$ to the fourth excited state of ${\mathrm{Sc}}^{50}$; and ${\mathrm{Sc}}^{50}$ to the second and third excited states of ${\mathrm{Ti}}^{50}$. The results for ${\mathrm{K}}^{47}$, together with previous results, establish the spin-parity of the 2578- and 2599-keV levels of ${\mathrm{Ca}}^{47}$ as ${\frac{3}{2}}^{+}$ and ${\mathrm{½}}^{+}$, respectively. The results for ${\mathrm{Sc}}^{50}$ and ${\mathrm{Ca}}^{50}$ are consistent with previous work, but are more accurate.

The ${\mathrm{Zn}}^{64}$ compound nucleus was formed at an excitation energy of 33.3 MeV using tow different target-projectile systems: 26.0-MeV protons on ${\mathrm{Cu}}^{63}$ and 31.3-MeV $\alpha$ particles on ${\mathrm{Ni}}^{60}$. Neutrons were detected with nuclear emulsions using the internal-radiator method. Exposures were made simultaneously at the following angles: 18, 33, 90, 147, and 162°. The c.m. energy spectra (2-15 MeV) of the two systems are very nearly the same. For both systems symmetry about 90° in the c.m. angular distributions is seen up to about 6 MeV followed by a forward peaking at higher energies. The symmetric (compound-nuclear) parts of the angular distributions differ significantly in anisotropy. For the $p+{\mathrm{Cu}}^{63}$ system the distribution is essentially isotropic while for the $\alpha +{\mathrm{Ni}}^{60}$ system we have an average anisotropy of about 1.4. We also observe for the $\alpha +{\mathrm{Ni}}^{60}$ system a slight but significant increase in anisotropy with energy of the emitted neutron (1.290 ± 0.047 at 2 MeV to 1.649 ± 0.119 at 6 MeV). The changes in average anisotropy, as we change target-projectile systems, are basically consistent with multiple-emission calculations using a rigid-sphere moment of inertia ($r_0=1.22\mathrm{}$ F). The change in anisotropy with emission energy is not seen in the calculations. It is estimated that, for the $p+{\mathrm{Cu}}^{63}$ and $\alpha +{\mathrm{Ni}}^{60}$ systems, direct-reaction neutrons constitute 5 and 3% of the total observed neutron spectra.

The neutron pick-up reactions ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}\mathrm{}(p,d)\mathrm{}{}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ and ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}\mathrm{}(p,d)\mathrm{}{}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$ have been studied at a bombarding proton energy of 27.3 MeV. Several angular distributions were analyzed with the distortedwave Born approximation and the resulting spectroscopic factors and sum rule are given. The results indicate that the neutron configuration of the silicon isotopes contains $1d_{\frac{5}{2}}$, $2s_{\frac{1}{2}}$, and $1d_{\frac{3}{2}}$ components. A small $f$-wave neutron component has been found in ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$. Strong $d_{\frac{5}{2}}$ transitions have been observed to the unresolved doublet ($J^{\pi }=3^{+},2^{+}$; $T=1\mathrm{}$) at 9.32 MeV in ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ and to the ($J^{\pi }={\frac{5}{2}}^{+}$; $T=\frac{3}{2}$) level at 8.32 MeV in ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$. These states are the isobaric analogs to the states of ${}_{}{}^{28}{}_{}{}^{}\mathrm{Al}$ (0 and 0.031 MeV) and to the ground state of ${}_{}{}^{29}{}_{}{}^{}\mathrm{Al}$, respectively. The $J^{\pi }=4^{+}$ state at 4.61 MeV in ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ was excited in the ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}\mathrm{}(p,d)\mathrm{}{}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ reaction, indicating target excitation effects in single-nucleon-transfer reactions.

The 29-day isomer ${}_{}{}^{179m_2}{}_{}{}^{}\mathrm{Hf}$ has been found to decay via 21.03- and 257.32-keV transitions to the ${\frac{21}{2}}^{+}$ and ${\frac{19}{2}}^{+}$ members of the ground-state rotational band of ${}_{}{}^{179}{}_{}{}^{}\mathrm{Hf}$. From conversion-electron studies, $M2\mathrm{}$ and $E3\mathrm{}$ multipolarities were deduced, respectively, for the 21.03- and 257.32-keV isomeric transitions. The spin and parity ${\frac{25}{2}}^{-}$ is assigned to the isomeric state.

The $\gamma$ rays emitted from 3 to 2000 nsec after spontaneous fission of ${}_{}{}^{252}{}_{}{}^{}\mathrm{Cf}$ have been studied in detail. Both fission fragments were stopped on Si detectors; a Ge detector was used to detect $\gamma$ rays from the fragments on one Si detector. A time-to-amplitude converter was started on the fission-fragment signal and stopped on the $\gamma$-ray signal. For each event the two fission-fragment kinetic energies, the $\gamma$-ray energy, and the time delay were recorded. The data were then analyzed to obtain the energy, half-life, and intensity of each $\gamma$ ray as well as the mass of the emitting fission fragment. Some 144 $\gamma$ rays were so analyzed, corresponding to more than 80 isomeric states.

$\gamma$ rays were observed from practically all masses. However, the intensity was concentrated in the mass regions near 96, 108, 134, and 146. The energy spectrum consisted of a group of $\gamma$ rays below 500 keV and a group near 1300 keV. The high-energy group associated with masses 134 and 136 dominates the energy intensity after 50 nsec. A strong cascade from a 162-nsec isomeric state is assigned to ${}_{ 52}{}^{134}{}_{}{}^{}\mathrm{Te}_{82}^{}{}_{}{}^{}$, and a 3000-nsec isomeric state to ${}_{ 54}{}^{136}{}_{}{}^{}\mathrm{Xe}_{82}^{}{}_{}{}^{}$. Rotational cascades were not observed, in contradiction with earlier low-resolution work. The observed energies and half-lives can be accounted for by $E1\mathrm{}$, $M1\mathrm{}$, or $E2\mathrm{}$ transitions, either allowed or $K$ forbidden by a few units. The interpretation of these results is that the initially high spins of the fragments have less effect on the delayed $\gamma$ rays than was previously thought.

Fragment kinetic energy distributions were obtained for fissions leading to the emission of a particular $\gamma$ ray. The $\gamma$ ray serves to restrict the events to those having a definite final isotope for one fragment. The average kinetic energy of such events is found to be slightly greater than the average for all fissions yielding the same mass.

The static quadrupole moments of the 511.7-keV $2^{+}$ state in ${\mathrm{Pd}}^{106}$ and the 373.8-keV $2^{+}$ state in ${\mathrm{Pd}}^{110}$ have been determined by employing Coulomb-excitation techniques. Foils (∼175 μg/${\mathrm{cm}}^2$) of separated Pd isotopes were bombarded with 25- and 30-MeV ${\mathrm{O}}^{16}$ ions and 55- and 56-MeV ${\mathrm{S}}^{32}$ ions from the Purdue University and Argonne National Laboratory tandem accelerators. The angular distributions of the inelastically scattered ions were measured in coincidence with the deexcitation $\gamma$ rays to determine the relative excitation probabilities. The experimental data were fitted using the Winther-de Boer multiple-Coulomb-excitation program so that the sign and magnitude of the static quadrupole moment could be extracted. The effect of higher excited states on the excitation probability of the $2^{+}$ state has been calculated using the matrix elements determined by Robinson et al. and the Winther-de Boer program. Self-consistency of the oxygen and sulfur data suggests that the excitation via the second $2^{+}$ state interferes constructively so as to increase the excitation probability. With this choice for the interference via the second $2^{+}$ state, the values of the static quadrupole moments are $Q_{22}=-0.458\mathrm{}\pm 0.059$ b for ${\mathrm{Pd}}^{106}$ and $Q_{22}=-0.483\mathrm{}\pm 0.049$ b for ${\mathrm{Pd}}^{110}$. If the excitation via the second $2^{+}$ state interferes destructively, the values of the static quadrupole moments are $Q_{22}=-0.282\mathrm{}\pm 0.059$ b for ${\mathrm{Pd}}^{106}$ and $Q_{22}=-0.266\mathrm{}\pm 0.049$ b for ${\mathrm{Pd}}^{110}$.

$\alpha$-active isotopes in the rare-earth region were investigated by bombarding ${}_{}{}^{156}{}_{}{}^{}\mathrm{Dy}$ and ${}_{}{}^{162}{}_{}{}^{}\mathrm{Er}$ targets with ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ ions accelerated in the Oak Ridge isochronous cyclotron. In the experiments recoil nuclei ejected from the thin targets were stopped in helium gas, swept through an orifice, and deposited on catcher foils. After each bombardment the activity collected on the catchers was assayed with an $\alpha$-particle Si(Au) spectrometer. In the case of the ${}_{}{}^{156}{}_{}{}^{}\mathrm{Dy}$ target relative yields were obtained as a function of bombarding energy for known erbium, holmium, and dysprosium nuclides. Excitation functions determined from statistical-model calculations were found to be in reasonable agreement with the shapes of the experimental (${}_{}{}^3{}_{}{}^{}\mathrm{He},xn$) and (${}_{}{}^3{}_{}{}^{}\mathrm{He},pxn$) curves but not with those of the (${}_{}{}^3{}_{}{}^{}\mathrm{He},\alpha \mathrm{xn}$) curves. Experimentally, the yields for (${}_{}{}^3{}_{}{}^{}\mathrm{He},pxn$) and (${}_{}{}^3{}_{}{}^{}\mathrm{He},\alpha \mathrm{xn}$) products were found to be ∼3 to 5 times greater than those for (${}_{}{}^3{}_{}{}^{}\mathrm{He},xn$) products. The statistical-model calculations, contrastingly, indicated the (${}_{}{}^3{}_{}{}^{}\mathrm{He},xn$) and (${}_{}{}^3{}_{}{}^{}\mathrm{He},pxn$) cross sections to be comparable and ∼5 times greater than those for (${}_{}{}^3{}_{}{}^{}\mathrm{He},\alpha \mathrm{xn}$) products. Similar yields were measured for nuclides observed in bombardments of the ${}_{}{}^{162}{}_{}{}^{}\mathrm{Er}$ target and were used in the assignment of two new $\alpha$-emitting isotopes to ${}_{}{}^{156}{}_{}{}^{}\mathrm{Yb}$ and ${}_{}{}^{157}{}_{}{}^{}\mathrm{Yb}$. Their half-lives and $\alpha$-decay energies were measured to be: (1) ${}_{}{}^{156}{}_{}{}^{}\mathrm{Yb}$, 24 ± 1 sec, 4.80 ± 0.01 MeV, and (2) ${}_{}{}^{157}{}_{}{}^{}\mathrm{Yb}$, 34 ± 3 sec, 4.50 ± 0.01 MeV. The assignment of the 4.80-MeV $\alpha$ group to ${}_{}{}^{156}{}_{}{}^{}\mathrm{Yb}$ was clearly established by noting a generic relationship between it and its known $\alpha$-decay daughter, ${}_{}{}^{152}{}_{}{}^{}\mathrm{Er}$. A similar clear-cut confirmation, based on a generic relationship, was not possible for ${}_{}{}^{157}{}_{}{}^{}\mathrm{Yb}$. The previously unknown nuclide, ${}_{}{}^{151}{}_{}{}^{}\mathrm{Er}$, was found in the ${}_{}{}^{156}{}_{}{}^{}\mathrm{Dy}$ bombardments by noting an initial growth period in the 4.60-MeV $\alpha$-particle group known to follow the decay of its daughter, ${}_{}{}^{151m}{}_{}{}^{}\mathrm{Ho}$. From this growth the half-life of ${}_{}{}^{151}{}_{}{}^{}\mathrm{Er}$ was found to be 23 ± 2 sec. The existence of 5.3-min ${}_{}{}^{155}{}_{}{}^{}\mathrm{Er}$, previously observed by us in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ bombardments of ${}_{}{}^{156}{}_{}{}^{}\mathrm{Dy}$, was confirmed. Its $\alpha$-decay energy was measured to be 4.01 ± 0.01 MeV, in agreement with the value reported earlier.

Neutron—neutron-hole configurations of states in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ were studied by proton scattering through the $d_{\frac{5}{2}}$ isobaric analog resonance in ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$. Angular distributions for the scattered protons were taken from 60 to 173° for the states in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ which have excitation energies between 4.69 and 6.30 MeV. The on-resonance—to—off-resonance ratio for these states was at most 15:1. The resolution in all spectra was 18 keV or better. The data were analyzed to obtain total proton inelastic scattering cross sections. With this information and the proton single-particle widths extracted from elastic scattering data, total inelastic proton partial widths were calculated. Final-state spins were specified by fitting the observed angular distributions with an appropriate expression for the differential cross section and by comparing those results to information derived from other experiments.

A search for the parity-nonconserving contribution to the $\gamma$ decay of ${}_{}{}^{159}{}_{}{}^{}\mathrm{Tb}$ has been made. A complete description of the experimental technique is presented. The angular distribution of the 363-keV line of ${}_{}{}^{159}{}_{}{}^{}\mathrm{Tb}$ was measured with a pair of Ge(Li) detectors. The ${}_{}{}^{159}{}_{}{}^{}\mathrm{Gd}$ parent atoms were located in the +453-kG hyperfine field of Gd${\mathrm{Fe}}_2$ held at 28 mK by a ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ dilution refrigerator. The resulting 7% polarization of the ${}_{}{}^{159}{}_{}{}^{}\mathrm{Gd}$ led to a $P_1\left(cos\Theta \right)$ term of +(2.7 ± 1.8) × ${10}^{-4\mathrm{}}$ in the $\gamma$-ray angular distribution, where $\Theta$ is measured with respect to the nuclear polarization. Thus, for full Tb polarization, the asymmetry would be +(4.5 ± 3.0) × ${10}^{-3\mathrm{}}$ $P_1\left(cos\Theta \right)$, peaked in the direction of Tb nuclear spin alignment. This sign of the $P_1\left(cos\Theta \right)$ term is based on an assumed negative moment of the ${}_{}{}^{159}{}_{}{}^{}\mathrm{Gd}$ parent. We measure the magnitude of this moment to be $(0.22\mathrm{}\pm 0.05){\mu }_N$.

The 637- and 723-keV states in ${\mathrm{Xe}}^{131}$ have been investigated by employing the technique of nuclear resonance fluorecence. The angular distribution of the resonantly scattered radiation from the 637-keV level is consistent with the assignment of either spin and parity ${\frac{5}{2}}^{+}$, decaying to the ground state predominantly by an $M1\mathrm{}$ transition, or a spin and parity of ${\frac{7}{2}}^{+}$ with the decay to the ground state being pure $E2\mathrm{}$. Considering the results of other investigators, a ${\frac{7}{2}}^{+}$ assignment appears to be the correct choice. Assuming a spin of $\frac{7}{2}$, the mean life of the 637-keV level is found to be 1.8 ± 0.8 psec. The fact that resonant scattering from the 723-keV level was observed with a source of gaseous ${\mathrm{II}}^{131}$ is attributed to Coulomb fragmentation of the ${\left({\mathrm{IXe}}^{131}\right)}^{+}$ molecular ion formed following the $\beta$ decay of ${\mathrm{I}}^{131}$. The angular distribution of the resonantly scattered 723-keV $\gamma$ rays is consistent with a spin and parity assignment of ${\frac{5}{2}}^{+}$ to this level, and a pure $M1\mathrm{}$ decay to the ground state. Our results indicate that the mean life of the 723-keV level is greater than 1.5 psec.

The average-resonance-neutron-capture spectra of ${}_{}{}^{147}{}_{}{}^{}\mathrm{Sm}(n,\gamma ){}_{}{}^{148}{}_{}{}^{}\mathrm{Sm}$ and ${}_{}{}^{149}{}_{}{}^{}\mathrm{Sm}(n,\gamma ){}_{}{}^{150}{}_{}{}^{}\mathrm{Sm}$ obtained with the Argonne in-pile ($n,\gamma$) facility are used to develop and extend the level schemes of ${}_{}{}^{148}{}_{}{}^{}\mathrm{Sm}$ and ${}_{}{}^{150}{}_{}{}^{}\mathrm{Sm}$. In particular, the experiment gives information about the spin and parity assignments of 33 levels with excitation energies from 0 to 2.7 MeV in ${}_{}{}^{148}{}_{}{}^{}\mathrm{Sm}$ and 47 levels from 0 to 2.5 MeV in ${}_{}{}^{150}{}_{}{}^{}\mathrm{Sm}$. Unique spin and parity assignments are given for almost all the states below 2.2 MeV in both isotopes. In many cases in which previous experiments gave conflicting indications, the new data led to definite spin assignments. The neutron binding energies in ${}_{}{}^{148}{}_{}{}^{}\mathrm{Sm}$ and ${}_{}{}^{150}{}_{}{}^{}\mathrm{Sm}$ were found to be 8140.6±1.8 and 7986.4±1.8 keV, respectively, after correction for the energy spectrum of the captured neutrons.

With barium isotopes of mass 130, 132, 134, 136, and 138 as targets, proton elastic scattering excitation functions have been obtained at several angles. In the proton energy range 7.0-12.0 MeV, we observed several resonances which correspond to isobaric analogs of the low-lying states of the target-plus-neutron systems. The resonance data have been analyzed to extract proton elastic widths, total widths, and resonance energies. Spectroscopic factors have been extracted by comparing the measured proton elastic widths with the single-particle widths calculated on the basis of a shell-model description of the analog state. The spectroscopic factors so determined are compared with those from the $\mathrm{Ba}\mathrm{}(d,p)\mathrm{}$ reaction to the parent analog states. The variation of single-particle width with the parameters of the bound-state neutron well has been investigated. From the analog resonance energies and the $Q$ values for the parent states in $\mathrm{Ba}\mathrm{}(d,p)\mathrm{}$ reactions, the Coulomb shifts of the principal resonances have been found.

An experiment has been performed on the thermal-neutron-induced fission of ${\mathrm{U}}^{235}$, in which the energies of complementary fission fragments and the time of flight of one fragment were measured. Fragment masses after neutron emission were obtained directly from this information. Pre-neutron masses and kinetic energies were deduced by means of a reflection method which simulates a double-time-of-flight experiment. Subtraction of post-neutron from primary fragment masses then gave the number of neutrons emitted by single fragments in each event. Among the results presented are the distributions of the numbers of neutrons emitted by single fragments of fixed mass. This information is very difficult to obtain from other types of experiments, and there has been no previous publication of such results for any fissioning nucleus. The results also include the average number of neutrons emitted as a function of mass and total kinetic energy, as well as mass distributions in fixed kinetic energy intervals, and total kinetic energy distributions at fixed fragment masses.

The Doppler-shift attenuation method was used to obtain the mean lives of the first two excited states in ${}_{}{}^{29}{}_{}{}^{}\mathrm{P}$: $\tau \left(1.38\mathrm{} \mathrm{MeV}\right)=(2.1\mathrm{}\pm 0.6)\times {10}^{-13\mathrm{}}$ sec and $\tau \left(1.95\mathrm{} \mathrm{MeV}\right)=\left({3.2}_{-1.1\mathrm{}}^{+1.5\mathrm{}}\right)\times {10}^{-13\mathrm{}}$ sec. The excited states were populated by the reaction ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}\mathrm{}(d,n)\mathrm{}{}_{}{}^{29}{}_{}{}^{}\mathrm{P}$ using deuteron energies ranging from 2.93 to 3.50 MeV. Pulse-shape discrimination was employed for the neutron-$\gamma$-ray coincidence measurements. The results are compared with those in ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$ and with the predictions of the strong-coupling rotational model.

The bootstrap theory is applied to the case of pairing vibrations; an approximation used by Dang and Klein in their treatment of pairing is shown to be consistent with the bootstrap theory. A modified Tamm-Dancoff approximation is described. The numerical results for ${\mathrm{Ni}}^{58,60,62}$ are compared with the exact solutions and with the results of Dang and Klein.

Some recent calculations based on the statistical model have employed the adiabatic assumption inconsistently. In particular, the high central repulsive core in ion-ion collisions is due to a trial density function which leads to unphysically large densities in the close-in region.