Differential scattering cross sections for the elastic and first excited state inelastic scattering of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ from ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ have been measured at ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ laboratory bombarding energy of 33, 36, and 38 MeV and at an ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ bombarding energy of 36 MeV. The experimental results have been analyzed in terms of coupled channels on the basis of a rotational model. For ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ projectiles the deformation of ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ was found by this technique to be ${\beta }_2=-0.30\mathrm{}\pm 0.08$ and ${\beta }_4\ge +0.1\mathrm{}$. The cross sections for the scattering of ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ by ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ could not be described with the deformation parameters obtained from the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ + ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ scattering data. The present results are compared with recent experiments using different projectiles and with the results of recent theoretical calculations.

The attenuated-Doppler-shift method was used to measure the mean lives of low-lying states in ${}_{}{}^{38}{}_{}{}^{}\mathrm{Cl}$ and ${}_{}{}^{40}{}_{}{}^{}\mathrm{K}$. States were populated by the ($d, p$) reaction and the recoil direction was defined by coincidence with the outgoing proton. While the positions of the levels in these two nuclei give encouragement to the belief that many of the states are well described as members of simple particle-hole or particle-particle multiplets, it is immediately apparent that the magnetic dipole transition rates do not fit the simple picture even if effective moments are used. A recent theoretical study has shown that some admixtures that can be expected will significantly alter the $M1\mathrm{}$ rates, but the present results are not in good agreement with the theoretical predictions. Other available lifetime data on these nuclei support the present contention that there are severe discrepancies between the observed rates and those predicted by the best available shell-model calculations.

Collective excitations of ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ were investigated by inelastic proton scattering at 54 MeV. The spectra covered the entire bound-state region for scattering angles between 11 and 58°, and scattered particles were detected in a broad-range spectrograph with energy resolution ≈ 35-40 keV full width at half maximum. The experimental angular distributions were compared to those predicted by distorted-wave Born-approximation calculations, utilizing a collective-model form factor. The location of the low-spin members of a sequence ($2^{+}$-$8^{+}$) of positive-parity states was confirmed. Likely candidates for $J>\mathrm{}8\mathrm{}$ states were found, as well as several collective fragments of $3^{-}$ and $4^{+}$ strengths. No appreciable fragmentation of the $2^{+}$ strength was found. Energy-weighted sum-rule strengths were estimated for all multipoles studied and were compared with the measured values.

NUCLEAR REACTIONS ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}(p, p^{\prime })$, $E=54\mathrm{}$ MeV; measured absolute $\sigma (E, \theta )$. ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ levels, deduced $L$, ${{\beta }_L}^2$. Spectrograph.

Measured excitation functions are compared to detailed evaporation calculations for the reactions ${}_{}{}^{140}{}_{}{}^{}\mathrm{Ce}({}_{}{}^{16}{}_{}{}^{}\mathrm{O}, xn){}_{}{}^{156-x}{}_{}{}^{}\mathrm{Dy}$, ${}_{}{}^{144}{}_{}{}^{}\mathrm{Nd}({}_{}{}^{12}{}_{}{}^{}\mathrm{C}, xn){}_{}{}^{156-x}{}_{}{}^{}\mathrm{Dy}$, ${}_{}{}^{136}{}_{}{}^{}\mathrm{Ba}({}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}, xn){}_{}{}^{156-x}{}_{}{}^{}\mathrm{Dy}$ ($x=5, 6, 7$), ${}_{}{}^{154}{}_{}{}^{}\mathrm{Gd}({}_{}{}^4{}_{}{}^{}\mathrm{He}, xn){}_{}{}^{158-x}{}_{}{}^{}\mathrm{Dy}$ ($x=7, 8, 9$), and ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}({}_{}{}^4{}_{}{}^{}\mathrm{He}, xn){}_{}{}^{185-x}{}_{}{}^{}\mathrm{Re}(x=2, 3, 4)$. The agreement between theory and experiment is found to depend critically on the rate of photon emission within about 10 MeV of the yrast levels. For the first four systems above, good fits are obtained only when the $\gamma$-emission rate is strongly enhanced with respect to the rate indicated by the $\gamma$ width of neutron resonances. $\gamma$ enhancement by the following two methods leads to quite good fits to experiment: (1) a constant (independent of $J$) enhancement of a factor of 100 and (2) enhancement proportional to ($2J+1$). For the system ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}$ + ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ such pronounced enhancement does not seem to be required. These results are interpreted in terms of the structure of the $\gamma$-cascade band. At sufficiently high angular momenta, the $\gamma$-cascade band is predicted to give way to an $\alpha$ band. Possibilities are discussed for experimental verification of some of the theoretical predictions.

Differential cross sections for the excitation of the $0^{+}$ (1.75-MeV), $2^{+}$ (2.18-MeV), $5^{-}$ (2.32-MeV), $4^{+}$ (3.08-MeV), $6^{+}$ (3.45-MeV), $8^{+}$ (3.60-MeV), and the $2^{+}$ (3.31-MeV) levels in ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$ by 40-MeV protons have been measured between 15° and 115°. The data are compared with the results of distorted-wave (DWA) collective-model calculations and DWA microscopic-model calculations. Both macroscopic and microscopic treatments of core polarization are considered. Effects from noncentral components in the projectile-target interaction have been investigated and an imaginary central component has been included in this interaction in the cases where a completely microscopic model is used for the target nucleus. A coupled-channels calculation has been performed in order to investigate multiple excitation contributions to the cross section for the $0^{+}$ (1.75-Mev) state.

A survey was made of $log\mathrm{ft}$ values for forbidden $\beta$ transitions. Three cases, ${}_{}{}^{90m}{}_{}{}^{}\mathrm{Y}$, ${}_{}{}^{65}{}_{}{}^{}\mathrm{Ni}$, and ${}_{}{}^{144}{}_{}{}^{}\mathrm{Pm}$ decays, were examined experimentally. A number of low $log\mathrm{ft}$ values reported in the literature are superseded by more recent larger values. Empirical rules for making spin and parity assignments from $log\mathrm{ft}$ values are proposed.

With the use of $\alpha$ spectroscopy and the helium gas-jet technique the $\alpha$ decay of the previously unknown isotopes, ${}_{}{}^{159}{}_{}{}^{}\mathrm{Hf}$, ${}_{}{}^{160}{}_{}{}^{}\mathrm{Hf}$, and ${}_{}{}^{161}{}_{}{}^{}\mathrm{Hf}$, was observed. These hafnium nuclides were produced by bombarding targets of ${}_{}{}^{144}{}_{}{}^{}\mathrm{Sm}$ and ${}_{}{}^{147}{}_{}{}^{}\mathrm{Sm}$ with ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ ions accelerated in the Oak Ridge isochronous cyclotron. The decay characteristics and mass assignments (made on the basis of yield curve measurements, cross bombardments, and parent-daughter relationships) of the three new $\alpha$ emitters are as follows: (1) ${}_{}{}^{159}{}_{}{}^{}\mathrm{Hf}$, $E_{\alpha }=5.09\mathrm{}\pm 0.01$ MeV, $T_{\frac{1}{2}}=5.6\mathrm{}\pm 0.5$ sec; (2) ${}_{}{}^{160}{}_{}{}^{}\mathrm{Hf}$, $E_{\alpha }=4.77\mathrm{}\pm 0.02$ MeV, $T_{\frac{1}{2}}\sim 12$ sec; and (3) ${}_{}{}^{161}{}_{}{}^{}\mathrm{Hf}$, $E_{\alpha }=4.60\mathrm{}\pm 0.01$ MeV, $T_{\frac{1}{2}}=17\mathrm{}\pm 2$ sec. The latter two isotopes with neutron numbers of 88 and 89 are of some interest with respect to $\alpha$-decay systematics in the 82-neutron region. The only 88-neutron $\alpha$ emitters known up to now are naturally occurring ${}_{}{}^{152}{}_{}{}^{}\mathrm{Gd}$ and long-lived ${}_{}{}^{154}{}_{}{}^{}\mathrm{Dy}$, while ${}_{}{}^{161}{}_{}{}^{}\mathrm{Hf}$ is the first 89-neutron nuclide to exhibit $\alpha$ decay.

The neutron capture and fission cross sections of ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$ were analyzed up to 60 eV with the multilevel formalism of Reich and Moore. The statistical distribution of the $R$-matrix parameters obtained in this analysis has been investigated in detail. After corrections for the "missed levels," the observed statistical distributions of the parameters and level spacings agree well with the expected Porter-Thomas distributions and Wigner law, respectively. The average values of the resonance parameters do not agree for the same cross sections with the values obtained by other authors on the basis of the single-level formalism. The $R$-matrix parameters obtained in this analysis have been transformed into equivalent Kapur-Peierls parameters and compared with a set of Kapur-Peierls parameters obtained directly, from the same data, in a previous analysis. The comparison of the two sets of Kapur-Peierls parameters illustrates the nonuniqueness of the least-squares fit analysis of the same data with the Kapur-Peierls formalism. The set of resonance parameters obtained in this work has also been used to compute the fission cross section at liquid nitrogen temperature, for comparison with existing measurements, and to "mock up" the cross sections in the unresolved resonance region near 1 keV, where $S$-wave processes still dominate.

A preliminary report on the discovery of isomeric states in ${}_{}{}^{250}{}_{}{}^{}\mathrm{Fm}$ and ${}_{}{}^{254}{}_{}{}^{}\mathrm{No}$ was included in a recent article on $\alpha$-emitting isotopes of element 104. The existence and assignments of the 1.8 ± 0.1-sec isomer to ${}_{}{}^{250}{}_{}{}^{}\mathrm{Fm}$ and the 0.28 ± 0.04-sec isomer to ${}_{}{}^{254}{}_{}{}^{}\mathrm{No}$ have now been confirmed by cross-bombardment techniques. Isomeric ratios based on measurements of collection efficiency of recoil atoms from the decay of isomeric states are given. An interpretation of the even-even isomers as high-spin two-quasiparticle states is discussed.

Three methods for the normalization of shell-model nuclei to liquid-drop-model nuclei are described and evaluated. The first, the familiar Strutinsky method, is sensitive to the number of levels above the Fermi level used and is not readily applicable to a single-particle model using a finite potential well. The second method involves the smoothing of the single-particle energies by means of an arbitrary function fitted in the least-squares sense. The third method involves the assumption that the need for the normalization lies in the inadequacy of the volume-correction term used in the calculation of the single-particle energies. Using an arbitrary function fitted by least squares, the best volume-correction function is found that causes the shell-model ground-state energies to be normalized to the liquid-drop-model energies. This method involves only the levels up to the Fermi level and consequently is readily applicable to a finite potential well.

An analysis of earlier reported cross-section data from ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}(\alpha , {\alpha }^{\prime })$, (${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$'), and ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$(${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$') reactions at $E_{\alpha }=90\mathrm{}$ MeV and $E_{{}_{}{}^3{}_{}{}^{}\mathrm{He}}=75\mathrm{}$ MeV confirms the discovery of a new giant resonance at $E^{*}\approx 11$ MeV in heavy nuclei. From the magnitude of the cross sections and theoretical sum-rule prescriptions, it is found that the resonance may be interpreted as a giant-quadrupole state but not, as recently suggested, a giant-monopole state.

We investigate the problem of relativistic corrections to the Hamiltonian of two nucleons interacting with each other and with an external electromagnetic field. We find, in addition to well-known corrections to the kinetic energy and to the Foldy-Wouthuysen reduction, a correction to the potential energy. This effect depends on the way in which the nonrelativistic limit of the dynamical variables is taken. The correction vanishes in the c.m. system, but leads to a nonzero correction to the electromagnetic Hamiltonian. We define the current and charge densities, verify the conservation of current, and verify the low-energy theorem for bremsstrahlung.

The Mössbauer effect following Coulomb excitation of the 43.8-keV state of ${}_{}{}^{161}{}_{}{}^{}\mathrm{Dy}$ was studied for several Dy compounds and Dy metal. At 85°K, using 3.3-MeV $\alpha$ particles, effects as large as 3.5% were observed; a scintillation counter gave typical counting rates of 2000 counts/sec; 43.8-keV $\gamma$ rays made up about one third of the total count rate. The half-life of this state predicts $2{\Gamma }_0=8\mathrm{}$ mm/sec; the narrowest single line observed was 16 mm/sec. Dy-metal spectra taken at various temperatures were interpreted assuming a normal hyperfine interaction plus a central peak due to relaxation effects. The extracted value of the nuclear magnetic-dipole moment for this level of $(-0.134\mathrm{}\pm 0.005){\mu }_N$ agrees with the value calculated using the Nilsson model. The extracted value of the ratio of the intrinsic quadrupole moments of the ground and excited states of 1.12 ± 0.27 agrees with the value of 1.0 predicted by the Nilsson model. The extracted difference in the nuclear radius for the ground and excited states is $\frac{\delta R}{R}=(-1.2\mathrm{}\pm 0.6)\times {10}^{-5\mathrm{}}$. A radiation-damage induced isomer shift corresponding to ${\mathrm{Dy}}^{4+}$ was observed in the Dy${\mathrm{F}}_3$ target at liquid-nitrogen temperature.

Optical pumping with the 2537 Å intercombination line of mercury has been used to orient four nuclear spin $I=\frac{13}{2}$ isomers of mercury and two $I=\frac{1}{2}$ radiosiotopes as well as stable $I=\frac{1}{2}$ ${}_{}{}^{199}{}_{}{}^{}\mathrm{Hg}$ and $I=\frac{3}{2}$ ${}_{}{}^{201}{}_{}{}^{}\mathrm{Hg}$. Measurements of ratios of the nuclear-magnetic-resonance frequencies of these isotopes to that of ${}_{}{}^{199}{}_{}{}^{}\mathrm{Hg}$ contained in the same sample cell have been made. The results are:

Independent measurements also give $\frac{{\nu }_{195m}}{{\nu }_{195}}=0.148\mathrm{}4051\left(3\right)\mathrm{}$ and $\frac{{\nu }_{197m}}{{\nu }_{197}}=0.149\mathrm{}8984\left(3\right)\mathrm{}$. Values of $A\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$ are combined with the above ratios to give differential hyperfine-structure anomalies. Magnetic moments and hyperfine-structure anomalies are calculated by means of a nuclear configuration-mixing model and compared with the experimental results.

A Ge(Li)-Ge(Li) directional-correlation system has been utilized to obtain directional-correlation functions for the 1-3 sequence, $I_i(L_1, L_1^{\prime })2(E0, M1, E2)2(L_3, L_3^{\prime })L_f$, in ${}_{}{}^{160}{}_{}{}^{}\mathrm{Dy}$, ${}_{}{}^{134}{}_{}{}^{}\mathrm{Ba}$, ${}_{}{}^{110}{}_{}{}^{}\mathrm{Cd}$, and ${}_{}{}^{82}{}_{}{}^{}\mathrm{kr}$. The following $E0\mathrm{}$ admixtures were determined: $\frac{T\left(E0\mathrm{}\right)\mathrm{}}{T\left(E{2}_{\gamma }\right)}\le 0.010$ (${}_{}{}^{160}{}_{}{}^{}\mathrm{Dy}$, 879 keV), $\frac{T\left(E0\mathrm{}\right)\mathrm{}}{T\left(E{2}_{\gamma }\right)}<0.045\mathrm{}$ (${}_{}{}^{134}{}_{}{}^{}\mathrm{Ba}$, 563 keV), $\frac{T\left(E0\mathrm{}\right)\mathrm{}}{T\left(E{2}_{\gamma }\right)}={0.097}_{-0.097\mathrm{}}^{+0.139\mathrm{}}$ (${}_{}{}^{110}{}_{}{}^{}\mathrm{Cd}$, 818 keV), and $\frac{T\left(E0\mathrm{}\right)\mathrm{}}{T\left(E{2}_{\gamma }\right)}={0.009}_{-0.009\mathrm{}}^{+0.073\mathrm{}}$ (${}_{}{}^{82}{}_{}{}^{}\mathrm{Kr}$, 563 keV). In addition, combinations of NaI(Tl) and Ge(Li) detectors have been utilized to obtain mixing ratios for other transitions in the above nuclei.

The neutron total cross section of ${}_{}{}^{242}{}_{}{}^{}\mathrm{Pu}$ has been measured from 600 eV to 81 keV using the new Lawrence Livermore Laboratory Linac. Parameters were obtained for those resonances below 4 keV with significant fission strengths. These parameters were used to study the fission widths of the intermediate structure in ${}_{}{}^{242}{}_{}{}^{}\mathrm{Pu}$+$n$ and the coupling matrix elements between the levels in the primary and intermediate wells in the double-humped fission potential barrier. The results show that the couplings in ${}_{}{}^{242}{}_{}{}^{}\mathrm{Pu}$+$n$ is very weak; the magnitude of the average coupling matrix element is less than 0.5 the level spacing in the primary well. The distribution of the fission widths of the levels in the primary well about their expected values is found to be consistent with a Porter-Thomas distribution. However, the distribution of the square of the coupling matrix element appears to require more than one degree of freedom, apparently implying two independent and equally accessible routes across the inner barrier to the deformed configuration. The Wigner distribution is shown to adequately describe the spacings between levels in the intermediate well. These measurements, taken together with Lynn's theory, suggest that fission from the 2741-eV resonance is primarily through the isomeric state. If verified experimentally, this would mean about a ${10}^4$ increase in probability for isomeric fission compared to that induced by other reactions. Our results indicate comparable inner and outer barrier heights for the double-humped fission barrier in the compound system ${}_{}{}^{245}{}_{}{}^{}\mathrm{Pu}$.

At moderate excitation energies fragment angular distributions are determined by an effective moment of inertia characteristic of the saddle-point deformation. We have performed a microscopic calculation which shows that at low excitation energy the experimentally deduced effective moment of inertia corresponds to the outer barrier. This is consistent with recent theoretical calculations showing that the inner barrier is unstable with respect to distortions destroying axial symmetry of the nuclear shape. At higher excitation energies the effective moment of inertia becomes characteristic of the liquid-drop-model saddle deformation. The transition is expected to occur at a fairly high excitation energy and may provide an explanation for the observation that the effective moment of inertia continues to increase at excitation energies well above that where pairing effects have disappeared.

A revised and extended level scheme for ${}_{}{}^{94}{}_{}{}^{}\mathrm{Tc}$ results from the combined study of neutron and $\gamma$-ray spectra emitted at proton energies near isobaric analog resonances. The cross sections for the ${}_{}{}^{94}{}_{}{}^{}\mathrm{Mo}(p, n){}_{}{}^{94}{}_{}{}^{}\mathrm{Tc}$ reactions and relative yields of $\gamma$ rays from the decay of the states of ${}_{}{}^{94}{}_{}{}^{}\mathrm{Tc}$ have been measured on the energy interval between 5.35 to 6.1 MeV in the vicinity of three analog resonances. The energies of neutrons emitted were measured by the time-of-flight technique. Excitation energies of levels in ${}_{}{}^{94}{}_{}{}^{}\mathrm{Tc}$ were determined from the neutron spectra and the energies of the $\gamma$ rays observed. The enhancement of the neutron and $\gamma$ ray yields with measurements of neutron angular distributions has been compared with statistical model calculations. The results provide spin-parity assignments to two levels and suggest others. Of particular interest is the location of the $2^{-}$ and $3^{-}$ states separated by an energy of 142 keV. The results illustrate the use of the statistical analysis at isobaric analog resonances according to the method of Robson for the extraction of spectroscopic information about nuclei. Comparison with shell-model calculations is given.

The $\beta$ decay of ${}_{}{}^{168}{}_{}{}^{}\mathrm{Ho}$ to levels in the strongly deformed ${}_{}{}^{168}{}_{}{}^{}\mathrm{Er}$ nucleus has been studied using Ge(Li) spectroscopy. Over 150 $\gamma$ rays were observed, about half of which could be assigned to ${}_{}{}^{168}{}_{}{}^{}\mathrm{Ho}$ decay. Among the rotational bands that have been identified in ${}_{}{}^{168}{}_{}{}^{}\mathrm{Er}$ are the ground state, the $\gamma$ band at 821.109 keV, and $K^{\pi }=4^{-} \mathrm{and} 3^{-}$ bands at 1093.898 and 1541.33 keV, respectively. At higher energies, evidence was obtained for bands having energies ($I^{\pi }K$) of 1848.20 ($2^{+}$2), 1930.23 ($2^{+}$2), 2192.97 ($2^{-}$2), and 2424.87 ($2^{+}$2) keV. $\beta$-decay $log\mathrm{ft}$ values to levels of ${}_{}{}^{168}{}_{}{}^{}\mathrm{Er}$ support a $3^{+}$3 assignment for the ${}_{}{}^{168}{}_{}{}^{}\mathrm{Ho}$ ground state.

Astrophysical superheavy-element synthesis by rapid neutron capture is studied by utilizing nuclear masses from energy-density functional calculations and a new $\beta$-decay formula in a modified r-process code. We find reduced abundances for elements with large atomic numbers relative to those predicted by conventional mass formulas. Calculations have been performed with fission barriers corresponding to both large and small values of the surface-symmetry contribution to the deformation energy. Our results, based on a different mass-formula parametrization, show that it is possible to synthesize superheavy elements in the r process even for very large surface-symmetry contributions if certain mass-formula terms are modified. Also, a more realistic formula for $\beta$-decay rates yields r-process fission-cycle times which are about 1 order of magnitude shorter than previous values.