The distorted-wave matrix element for direct reactions leading to three-body final states is written in terms of convergent integrals. The resulting expression can be evaluated in the Butler approximation, which leads to a diffractive model of the competition of, and interference between, direct breakup and sequential decay reaction mechanisms. Using Amado's methods, I demonstrate the general presence of such interference in processes of interest. Moreover, it should be possible to normalize unstable-state spectroscopic factors by measuring this interference.

Taking into account the mixing of 2p-2h components in the ground state, a method is developed to define the odd-parity excited states of ${\mathrm{O}}^{16}$. Using the effective potential given by Gillet, the excitation energies are given, and the components of the wave functions are put in a form which can be readily used for the computation of electromagnetic transition probabilities. The 3p-3h components in these wave functions are found to be important.

The spins of the ${\mathrm{Mg}}^{24}$ states at 12.74-, 12.85-, and 12.97-MeV excitation, which are populated in the ${\mathrm{Na}}^{23}(p, \alpha \gamma ){\mathrm{Ne}}^{20}$ reaction, have been determined to be $2^{+}$, $2^{-}$, and $2^{-}$, respectively, from $\alpha -\gamma$ correlation measurements. The correlation is measured simply by observing the 1.63-MeV $\gamma$ ray at 0°, and analyzing the $\gamma$-ray line shape in terms of the possible spins of the ${\mathrm{Mg}}^{24}$ states.

A formalism for the analysis of Doppler-broadened $\gamma$-ray line shapes observed in ($a, b\gamma$) reactions, has been developed in order to measure nuclear lifetimes. The technique, which is generally applicable to lifetime determinations in the range 5×${10}^{-15\mathrm{}}$ to ${10}^{-13\mathrm{}}$ sec, has been employed to measure the lifetimes of the levels at 4.43 MeV in ${\mathrm{C}}^{12}$ and 6.92 MeV in ${\mathrm{O}}^{16}$. Results of 65±9 and ${6.4}_{-1.6\mathrm{}}^{+1.9\mathrm{}}$ fsec, respectively, were obtained.

The reactions ${\mathrm{O}}^{18}({\mathrm{He}}^3, p){\mathrm{F}}^{20}$ and ${\mathrm{F}}^{19}(d, p){\mathrm{F}}^{20}$ have been used to study levels in ${\mathrm{F}}^{20}$ up to an excitation energy of 6.043 MeV. The energies of the reaction protons were measured with a broad-range magnetic spectrograph. Excitation energies were obtained for 45 levels in ${\mathrm{F}}^{20}$. The ground-state $Q$ values for the above reactions were also measured and found to be 6.8752±0.0015 MeV for the ${\mathrm{O}}^{18}({\mathrm{He}}^3, p){\mathrm{F}}^{20}$ reaction and 4.3777±0.0009 MeV for the ${\mathrm{F}}^{19}(d, p){\mathrm{F}}^{20}$ reaction.

Two pairs of isobaric analog resonances near 4.1- and 4.9-MeV proton bombarding energy, respectively, have been studied in the ${}_{}{}^{68}{}_{}{}^{}\mathrm{Zn}(p, n){}_{}{}^{68}{}_{}{}^{}\mathrm{Ga}$ reaction. Differential cross sections were measured at 2.5, 30, and 130° for neutrons which leave ${}_{}{}^{68}{}_{}{}^{}\mathrm{Ga}$ in the ground state and 180-keV first excited state in the bombarding energy region from 4.00 to 4.15 MeV. Analog resonances at 4.075 and 4.098 MeV were analyzed according to the Robson theory. Eleven levels in ${}_{}{}^{68}{}_{}{}^{}\mathrm{Ga}$ up to an excitation energy of 1.088 MeV were identified in time-of-flight spectra. Hauser-Feshbach analyses were done on the angular distributions of neutrons leaving ${}_{}{}^{68}{}_{}{}^{}\mathrm{Ga}$ in 4 and 6 residual nucleus states at 4.400 and 4.512 MeV, respectively, an energy region where no analog resonances appear. Excitation functions for seven neutron groups were measured at 100° in the bombarding energy region 4.7 to 5.0 MeV, where two analog resonances, at 4.87 and 4.92 MeV, were seen. An analysis according to the theory of Robson was performed on these resonances in order to obtain spins, parities, and resonance parameters.

The absolute cross sections for the production of ${\mathrm{Sc}}^{44m}$ and ${\mathrm{Sc}}^{44g}$ by the ${\mathrm{Sc}}^{45}({\mathrm{He}}^3, \alpha )$ reaction have been determined at 1-MeV intervals from 6-19 MeV. The experimentally determined isomer-ratio function has only a limited variance over the energy range studied. Calculations of the Huizenga-Vandenbosch type were performed. Spin cutoff parameters of 2 and 4 gave poor fits of the isomer data. Recoil ranges for ${\mathrm{Sc}}^{44m}$ and ${\mathrm{Sc}}^{44g}$ in ${\mathrm{Sc}}^{45}$ were determined. Recoil energies for ${\mathrm{Sc}}^{44}$ were calculated assuming (1) a compound-nucleus mechanism and (2) a pickup-type mechanism. Recoil ranges for ${\mathrm{Sc}}^{44}$ in ${\mathrm{Sc}}^{45}$ were then calculated using the formulation of Lindhard, Scharff, and Schiott. Comparison of the experimental recoil ranges with the calculated values resulted in poor agreement with both calculations. The inability to fit the isomer-ratio data with a spin cutoff parameter of 2, and the poor agreement of the experimental recoil ranges with the compound-nucleus-mechanism calculation, are interpreted as evidence for the occurrence of non-compound-nucleus-type processes.

Energy spectra of internal-conversion electrons following ($p, 2n$) reactions leading to even-even final nuclei in the $Z\simeq 82$ region were measured. $E0\mathrm{}$ transitions leading from the $0^{+}$ member of the two-phonon triplet to the $0^{+}$ ground state were found, and the systematics of their transition rates was studied. They compete poorly with $E2\mathrm{}$ transitions to the first excited ($2^{+}$) state, and the $E0\mathrm{}$ transition rapidly becomes relatively less probable with decreasing $A$ in this region.

Shell-model calculations are performed for bound $0^{+}$ states of ${\mathrm{Ca}}^{42}$ and ${\mathrm{Ni}}^{58}$. The neutron configurations $1f_{\frac{7}{2}}$, $2p_{\frac{3}{2}}$, $2p_{\frac{1}{2}}$, $1f_{\frac{5}{2}}$, and $1g_{\frac{9}{2}}$ are included, as well as states in which one of the neutrons is in the shell-model continuum. These continuum contributions have little effect on energy eigenvalues, but modify the wave functions in the vicinity of the nuclear surface. The calculated wave functions yield one-particle-transfer form factors whose logarithmic derivatives at large radius are consistent with the neutron separation energies. Comparison is made with other procedures for calculating form factors within the framework of the ordinary shell model. It is found that the conventional well-depth procedure underestimates the ($p, d$) cross sections for populating highly excited states, relative to low-lying states, by about 50%. Two-neutron-transfer cross sections are also calculated and are found to be in agreement with those yielded by the well-depth procedure. However, some of our form factors exhibit an extra node at 8 F, showing that they do not decay like a Hankel function.

The quasiparticle Tamm-Dancoff and random-phase approximations have been applied to ${\mathrm{Sn}}^{116}$ and ${\mathrm{Sn}}^{120}$ using realistic shell-model interactions derived from the Tabakin and Yale-Shakin potentials. It is found that the two approximations are very similar for both spectra and nuclear states.

The $\beta -\gamma$ circular polarization $P_{\gamma }$ has been measured as a function of the $\beta$-particle energy for ${\mathrm{La}}^{140}$ and for ${\mathrm{Co}}^{60}$. The ${\mathrm{Co}}^{60}$ results confirm that $P_{\gamma }$ is proportional to $\frac{v}{c}$. The results for the 2.2-MeV transition of ${\mathrm{La}}^{140}$ show that the original prediction for the vector-matrix-element ratio is not correct for this transition. However, the results are consistent with predictions based on the conserved-vector-current (CVC) theory if the approach suggested by Damgaard and Winther is followed. This interpretation yields information on third-forbidden matrix elements.

Experimental data are used to determine the first-forbidden matrix elements for the 2.2-MeV $\beta$ transition of ${\mathrm{La}}^{140}$. The results show that the matrix-element ratio ($\frac{\int \overrightarrow{\alpha }}{\int i\overrightarrow{\mathrm{r}}}$) does not agree with the usual theoretical prediction which assumes the Ahrens-Feenberg approximation. The size of the experimental vector-matrix-element ratio can be understood on the basis of significant off-diagonal contributions in the Coulomb Hamiltonian. The theory of conserved vector current is used to investigate impurities in the isobaric analog to the ground state of ${\mathrm{La}}^{140}$. In addition, the contribution of third-forbidden matrix elements to the transition is investigated.

The failure to observe fission tracks in old Pb-rich and Au-rich minerals restricts the spontaneous fission rates of Au and Pb to ≲1×${10}^{-25\mathrm{}}$ per year per Au atom and <3×${10}^{-24\mathrm{}}$ per year per Pb atom (at 95% confidence level). No fission-track evidence for superheavy elements in these or other minerals rich in heavy elements has been found. These negative results are not compatible with recent proportional-counter data and track data of Flerov and co-workers.

The lifetimes of the 1.38-MeV $0^{+}$ state in ${}_{}{}^{92}{}_{}{}^{}\mathrm{Zr}$ and the 1.30-MeV $0^{+}$ state in ${}_{}{}^{94}{}_{}{}^{}\mathrm{Zr}$ were measured by a particle-$\gamma$ delayed coincidence technique. These states were excited with the ($p, p^{\prime }$) reaction at proton analog-resonance energies of 7.90 MeV for ${}_{}{}^{92}{}_{}{}^{}\mathrm{Zr}$ and 8.12 MeV for ${}_{}{}^{94}{}_{}{}^{}\mathrm{Zr}$. The mean lifetimes obtained from the logarithmic slope of the time spectra are $\tau =240\mathrm{}\pm 40$ psec for the 1.380-MeV state in ${}_{}{}^{92}{}_{}{}^{}\mathrm{Zr}$ and $\tau =462\mathrm{}\pm 30$ psec for the 1.30-MeV state in ${}_{}{}^{94}{}_{}{}^{}\mathrm{Zr}$. For both of these measurements the prompt-resolution function was obtained simultanously with the $0^{+}$ decay curve by observing the short-lived time spectrum for the first excited $2^{+}$ state.

New half-life values are given for ${}_{}{}^{145}{}_{}{}^{}\mathrm{Eu}$, ${}_{}{}^{146}{}_{}{}^{}\mathrm{Gd}$, ${}_{}{}^{149}{}_{}{}^{}\mathrm{Eu}$, ${}_{}{}^{151}{}_{}{}^{}\mathrm{Tb}$, ${}_{}{}^{153}{}_{}{}^{}\mathrm{Sm}$, ${}_{}{}^{153}{}_{}{}^{}\mathrm{Tb}$, ${}_{}{}^{153}{}_{}{}^{}\mathrm{Dy}$, ${}_{}{}^{155}{}_{}{}^{}\mathrm{Tb}$, and ${}_{}{}^{155}{}_{}{}^{}\mathrm{Dy}$. Absolute abundances are reported for prominent $\gamma$ rays associated with the decay of ${}_{}{}^{143}{}_{}{}^{}\mathrm{Pm}$, ${}_{}{}^{146}{}_{}{}^{}\mathrm{Gd}$, ${}_{}{}^{149}{}_{}{}^{}\mathrm{Pm}$, ${}_{}{}^{149}{}_{}{}^{}\mathrm{Eu}$, and ${}_{}{}^{153}{}_{}{}^{}\mathrm{Dy}$.

The structure of ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ has been investigated using the ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}(d, {}_{}{}^3{}_{}{}^{}\mathrm{He}){}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ reaction at 50 MeV. Angular distributions have been measured from 10-50° lab for 15 levels in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. These states in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ are considered to be populated through their [$1h_{\frac{9}{2}}$, ${\mathrm{}\left(\mathrm{nlj}\right)\mathrm{}}^{-1\mathrm{}}$] proton particle-hole components. Spectroscopic factors have been extracted for each state and compared with those predicted by a recent random-phase-approximation calculation of Kuo and Brown. Generally good agreement between theory and experiment results.

The excited levels of ${\mathrm{In}}^{109}$ have been investigated from the decay of ${\mathrm{Sn}}^{109}$ with high-resolution Ge(Li) and Si(Li) detectors and with standard scintillation counters. ${\mathrm{Sn}}^{109}$ was produced by the ($\alpha , n$) reaction on enriched ${\mathrm{Cd}}^{106}$. $\gamma$ rays of the following energies (in keV) and intensities have been assigned to the decay of ${\mathrm{Sn}}^{109}$: 119(<1), 223(∼2), 330.5(17.1), 335(4.5), 345(3), 390(6.4), 437(4.6), 442(5), 526(5.5), 609(2), 649.5(68), 725(1.5), 790(∼2), 839(0.7), 843(0.6), 872(∼1), 950(<1), 1028(17.8), 1037(12.7), 1098(100), 1120(9.1), 1221(0.7), 1321 (37.4), 1443(1.8), 1465(33.8), 1488(17.8), 1497(∼1), 1574(18.8), 1618 and 1622(2.5), 1688(2.0), 1712(1.9), 1729(2.6), 1741(1), 1762(3.5), 1823(1.5), 1841(<1), 1912(15.5), 1930(1.4), 1935(0.3), 1944(3.1), 1952(0.3), 1963(0.1), 1976(0.2), 2053(5.8), 2126(3.6), 2160(2.3), 2193(3.7), 2275 and 2278(1.6), 2349(<1), 2541(7.9), 2595(1.5), 2786(3.9), 2811(0.8), 2860(2.3), 2939(0.27), 3010(0.37), 3033(0.37), 3050(0.97), 3062(0.23), 3074(0.08), 3314(0.22), 3360(0.07), and 3393 (0.35). The use of two Ge(Li) detectors in coincidence studies has revealed the presence of several previously unreported transitions. Based on $\gamma -\gamma$ and $\beta -\gamma$ coincidence results, a consistent level scheme of ${\mathrm{In}}^{109}$ is given. The spin and parity assignments of some of the low excited levels of ${\mathrm{In}}^{109}$ are discussed.

A new high-spin isomer ${}_{}{}^{179m_2}{}_{}{}^{}\mathrm{Hf}$ has been produced by irradiation of isotopically enriched ${}_{}{}^{176}{}_{}{}^{}\mathrm{Yb}$ with $\alpha$ particles. To investigate its decay, Ge(Li) $\gamma$-ray spectra, Si(Li) conversion-electron spectra, and NaI(Tl)-Ge(Li) and Ge(Li)-Ge(Li) $\gamma -\gamma$ coincidence spectra have been recorded. $\gamma$ rays with energies 122.7, 146.2, 169.8, 192.8, 217.0, 236.6, 257.5, 268.9, 316.0, 362.6, 409.8, and 453.7 keV have been attributed to the decay of the isomer. These decay with a half-life of (29±1) day. The coincidence measurements establish that the quanta with energies 122.7 through 236.6 keV are in cascade, while the $\gamma$ rays with energies 268.9 through 453.7 keV represent crossover transitions within a rotational band with levels up to $I=\frac{21}{2}$ built on the ${}_{}{}^{179}{}_{}{}^{}\mathrm{Hf}$ ground state. The rotational-model quantity $\frac{{(g_K-g_R)}^2}{{Q_0}^2}$ has been derived from $\gamma$ intensity measurements of the cascade and crossover transitions. It is constant within the experimental error for all members of the band. The values for the gyromagnetic ratios $g_K=-0.202\mathrm{}\pm 0.027$ and $g_R=0.160\mathrm{}\pm 0.014$ have been deduced.

Neutron transmission measurements have been carried out for ${\mathrm{Dy}}^{161}$, ${\mathrm{Dy}}^{162}$, ${\mathrm{Dy}}^{163}$, and ${\mathrm{Dy}}^{164}$, employing the fast-chopper facility of the Brookhaven Graphite Research Reactor. The $s$-wave neutron strength functions ($S^0$), resonance parameters, average level spacings, and potential-scattering radii have been determined. The values of the neutron strength functions of ${\mathrm{Dy}}^{161}$, ${\mathrm{Dy}}^{162}$, ${\mathrm{Dy}}^{163}$, and ${\mathrm{Dy}}^{164}$ are 1.85 ± 0.15, 2.3 ± 0.5, 1.7 ± 0.2, and 1.2 ± 0.5, all in units of ${10}^{-4\mathrm{}}$. The corresponding average total radiation widths of Dy isotopes are found to be 114 ± 10, 155 ± 15, 109 ± 8, and 55 ± 3 meV. A correlation between total radiation width and $S^0$ seems to be evident. Furthermore, examination of the present and previous results for the rare-earth isotopes indicates that there is a systematic trend of decrease of $S^0$ with increasing mass number for the even-even target nuclei. Absorption-resonance integrals and thermal cross sections are computed from the resonance parameters and are compared with direct measurements of other experiments.

Levels in ${}_{}{}^{110}{}_{}{}^{}\mathrm{Cd}$ have been studied through the decay of ${}_{}{}^{110g}{}_{}{}^{}\mathrm{Ag}\left(1^{+}\right)$ using NaI(Tl) and Ge(Li) detectors. The following $\gamma$-ray energies (intensities in parentheses) were observed: 657.8 ± 0.2(100), 815.6 ± 0.3(0.98), 1125.9 ± 0.3(0.36), 1186.4 ± 0.7(0.056), 1421.8 ± 1.3(0.044), 1475.8 ± 1.3(0.11), 1630.0 ± 1.2(0.048), 1674.2 ± 0.9(0.15), and 1783.3 ± 1.3(0.17) keV. Coincidence measurements performed with a NaI(Tl)-Ge(Li) system showed peaks at 816 and 1126 keV in coincidence with the 657.8-keV line. The 815.6-keV peak in the singles spectrum is a doublet composed of the 818.00-keV component depopulating the $2^{+}$ state at 1475 ± 0.05 keV and a 815.5-keV $\gamma$ ray. It is proposed that the low-energy component depopulates the twophonon, $0^{+}$ level at 1473.2 ± 0.3 keV. A level at 1783.6 ± 0.3 keV is also assigned and estimates of $log\mathrm{ft}$ values to all levels are given. Using a multichannel analyzer in the multiscalar mode, the half-life of ${}_{}{}^{110g}{}_{}{}^{}\mathrm{Ag}$ was measured as 24.7 ± 0.7 sec.