The (${}_{}{}^3{}_{}{}^{}\mathrm{He},n$) reaction has been studied on targets of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, and ${}_{}{}^{58,60,62}{}_{}{}^{}\mathrm{Ni}$ at an incident energy of 25 MeV. The observed resolution of the neutron time-of-flight spectrometer used in this work was about 1%. Differential cross sections were obtained for the resolvable final states over the angular range of 0-40° (L). The angular distributions were compared with the predictions of a simple, one-step, two-nucleon-transfer model. In this formalism the diproton stripped from ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is transferred to the target retaining its ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ relative motion. The shapes of the angular distributions were unique for a given $l$ transfer and were, in most cases, generally reproduced by the calculations. For $0^{+}$ targets the $J^{\pi }$ of many final states could be assigned. Comparison of experimental with theoretical relative magnitudes permitted assignment of dominant shell-model configurations. To first approximation the relative transition strengths to final states in ${}_{}{}^{14}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{30}{}_{}{}^{}\mathrm{S}$, and ${}_{}{}^{60}{}_{}{}^{}\mathrm{Zn}$ were consistent with the assumption of two particles coupled to an effectively "closed core."

The variable-moment-of-inertia model for the ground-state rotational bands in even-even nuclei has been extended by adding an anharmonic term to the potential energy. A detailed application of this model, called VMI23, has been made to the ground-state bands of 122 even-even nuclei. It is shown that the inclusion of the anharmonic term improves agreement with the experimental data in many cases, and provides a sensitive means of probing the potential energy surfaces of nuclei.

Dolginov's theory of directional correlations between x rays and $\gamma$ rays emitted after nuclear electron capture is reviewed, simplified in the light of recent advances, and extended to second-forbidden nonunique transitions. Specific predictions are derived for directional correlations between $\mathrm{Pb} L$ x rays and $\gamma$ rays emitted following second-forbidden electron capture and $M4\mathrm{}$ $\gamma$-ray internal conversion in ${}_{}{}^{207}{}_{}{}^{}\mathrm{Bi}$ decay. No average anisotropy was found in a measurement of the directional correlation between $Ll+L\alpha +L\beta$ x rays and 570-keV $\gamma$ rays from ${}_{}{}^{207}{}_{}{}^{}\mathrm{Bi}$; the results is $A=(2\mathrm{}\pm 2)\times {10}^{-3\mathrm{}}$. Suggestions for further work are offered.

A $\gamma -\gamma -\gamma$ angular-correlation method is suggested for the case where all the three $\gamma$ rays are of the same energies. This method was employed for the study of the 308 → 296 → 316-keV cascade in ${\mathrm{Pt}}^{192}$ from the decay of ${\mathrm{Ir}}^{192}$. The $\frac{E_2}{M_1}$ mixing ratio of the 308-keV $\gamma$ rays thus obtained was (-)${4.4}_{-0.7\mathrm{}}^{+1.3\mathrm{}}$.

Differential cross sections for the elastic scattering and inelastic scattering to the low-lying states in ${}_{}{}^{138}{}_{}{}^{}\mathrm{Ba}$ have been measured using 50-MeV $\alpha$ particles. The angular distributions are analyzed in the distorted-wave Born approximation, employing collective-model form factors. Spin and parity assignments of $2^{+}$, $4^{+}$, and $3^{-}$ are verified for states at 1.436, 1.898, and 2.880 MeV. Assignments of $2^{+}$ and $4^{+}$ are made for states at 2.19 and 2.27 MeV. Tentative assignments of $2^{+}$ and $4^{+}$ are made for members of unresolved multiplets at 3.34 and 3.50 MeV. Values of ${\beta }_l{R}^{\prime }$ are obtained for all observed levels. Reasonable agreement for excitation energies and $J^{\pi }$ assignments has been obtained between the present results and previous experimental measurements and with recent theoretical calculations. A comparison of available isoscalar and electromagnetic transition rates in the mass region $115<A<\mathrm{}150\mathrm{}$ indicates that, for the lowest $2^{+}$ states, the ratio of the neutron-to-proton contributions to the isoscalar matrix elements is in the ratio $\frac{N}{Z}$ as predicted by the collective vibrational model, except for the $N=82\mathrm{}$ region. A similar result has previously been observed at the $N=28\mathrm{}$ shell closure.

The ($t,p$) reaction on ${}_{}{}^{138,140}{}_{}{}^{}\mathrm{Ce}$ at 15-MeV incident energy and the ($p,t$) process on ${}_{}{}^{142}{}_{}{}^{}\mathrm{Ce}$ at 21.5 MeV have been studied. Differential cross sections were measured between 12 and 66° in 6° intervals and $L=0\mathrm{} \mathrm{and} 2$ assignments made. Less extensive data on ${}_{}{}^{136, 142}{}_{}{}^{}\mathrm{Ce}\mathrm{}(t,p)\mathrm{}$ and ${}_{}{}^{140}{}_{}{}^{}\mathrm{Ce}\mathrm{}(p,t)\mathrm{}$ were also acquired and a ${}_{}{}^{140}{}_{}{}^{}\mathrm{Ce}\mathrm{}(t,t)\mathrm{}$ angular distribution was obtained at 15 MeV. The strongest $L=0\mathrm{}$ and $L=2\mathrm{}$ transitions are discussed in relation to the pairing-vibrational model; in particular the 3226-keV state in ${}_{}{}^{140}{}_{}{}^{}\mathrm{Ce}$ was found to contain about 70% of the (1, 1) two-phonon strength and several candidates for pairing-quandrupole-vibrational states are noted. Anharmonic effects on the energies of pairing-phonon states are considered and a discussion of the observed $3^{-}$ strengths is included.

The elastic scattering of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ by ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{70}{}_{}{}^{}\mathrm{Ge}$, and ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$ has been studied in the vicinity of the Coulomb barrier for the purpose of extracting optical-model parameters and barrier heights. Angular distributions were measured from 30° to 170° in the lab in 10° steps and in the bombarding energy range from 30 to 60 MeV in 2-MeV steps. No discrete ambiguities in the real potentials were found, probably due to the large imaginary potentials. Barrier heights determined with the optical-model parameters were found to be consistent with Greiner's calculated barrier heights and 10-20% lower than the ordinary Coulomb barrier $\frac{Z_1{Z}_2{e}^2}{1.35(A_1^{\frac{1}{3}}+A_2^{\frac{1}{3}})}$.

We determined mass-yield distributions from fission of ${}_{}{}^{234}{}_{}{}^{}\mathrm{U}$ and ${}_{}{}^{236}{}_{}{}^{}\mathrm{U}$ with 14.8-MeV neutrons. We measured the yields of 24 products covering the mass range 66-161 for ${}_{}{}^{234}{}_{}{}^{}\mathrm{U}$ and for 30 products covering the mass range 66-172 for ${}_{}{}^{236}{}_{}{}^{}\mathrm{U}$. We estimated total chain yields by correcting for the effects of nuclear-charge dispersion in fission. The mass-yield curves are similar to those for fission of ${}_{}{}^{233}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$, and ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ with 14.8-MeV neutrons. We measured the independent fractional chain yields of the following nuclides: for ${}_{}{}^{234}{}_{}{}^{}\mathrm{U}$: ${}_{}{}^{96}{}_{}{}^{}\mathrm{Nb}$, (1.54 ± 0.10) × ${10}^{-3\mathrm{}}$; ${}_{}{}^{136}{}_{}{}^{}\mathrm{Cs}$, 0.095 ± 0.006; for ${}_{}{}^{236}{}_{}{}^{}\mathrm{U}$: ${}_{}{}^{96}{}_{}{}^{}\mathrm{Nb}$, (2.7 ± 0.3) × ${10}^{-4\mathrm{}}$; ${}_{}{}^{126}{}_{}{}^{}\mathrm{Sb}$, 0.096 ± 0.010; ${}_{}{}^{136}{}_{}{}^{}\mathrm{Cs}$, 0.022 ± 0.002.

We analyzed mass-yield distributions from fission of ${}_{}{}^{233}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{234}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{236}{}_{}{}^{}\mathrm{U}$, and ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ with 14.8-MeV neutrons to study the details of the fission distribution as a function of target mass number at a fairly low excitation energy. The fission yields of individual products, both cumulative and independent, vary smoothly and as expected with uranium target mass number. The over-all distribution of yields becomes significantly narrower as the uranium mass number is increased. The average neutron emission associated with the very-low-yield products is about 3.5, significantly less than the value of about 4.5 for the fission fragments as a whole. This difference may be due to an increase in energy required for reactions leading to the low-yield products. The peak/valley ratio increases by a factor of more than 2 as the mass number is increased from 233 to 238, and decreases linearly with increasing excitation energy, with the even-mass and odd-mass uranium isotopes defining lines that are approximately parallel and separated by 1.4 MeV. This difference can be explained either by an odd-even effect in the neutron-evaporation/fission competition as a function of target mass number, or by an odd-even effect in the ratio of symmetric to asymmetric fission as a function of mass number. One consequence of the rapid change in peak/valley ratio with mass number is that fission of ${}_{}{}^{232}{}_{}{}^{}\mathrm{U}$ with 14.8-MeV neutrons would be expected to produce a flat-topped mass-yield distribution, with a peak/valley ratio of about unity, while fission of lower-mass uranium isotopes would be expected to be predominantly symmetric. The average value of $\frac{\Delta Z_p}{\Delta A}$ was found to be -0.16 ± 0.02 for the shielded product ${}_{}{}^{96}{}_{}{}^{}\mathrm{Nb}$ and -0.20 ± 0.01 for ${}_{}{}^{136}{}_{}{}^{}\mathrm{Cs}$. This difference may be due to the change in prefission neutron emission with uranium mass number. All of the available data on fractional chain yields for fission of ${}_{}{}^{236}{}_{}{}^{}\mathrm{U}_{}^{*}{}_{}{}^{}$ at $E^{*}=6.4\mathrm{} \mathrm{and} 21.3$ MeV were used to estimate $\Delta Z_p\mathrm{}\left(A\right)\mathrm{}$ for $\Delta E^{*}=15\mathrm{}$ MeV. The scatter in the $\Delta Z_p$ values is too large to allow a smooth curve to be drawn relating $\Delta Z_p$ as a function of mass number. It was found, however, that $\Delta Z_p$ values are larger on the average for heavy-fragment products ($\Delta Z_p=0.49\mathrm{}\pm 0.05$) than for light-fragment products ($\Delta Z_p=0.26\mathrm{}\pm 0.03$) over this range of excitation energy. The well-known $Z_p\mathrm{}\left(A\right)\mathrm{}$ function for thermal-neutron fission of ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$, together with the $\frac{\Delta Z_p}{\Delta A}$ and $\frac{\Delta Z_p}{\Delta E^{*}}$ relationships reported here, can be used to estimate $Z_p$ values and fractional chain yields for fission of the various uranium isotopes with 14.8-MeV neutrons.

The level structures of ${}_{}{}^{108}{}_{}{}^{}\mathrm{Ag}$ and ${}_{}{}^{110}{}_{}{}^{}\mathrm{Ag}$ have been investigated via the ($d,p$) stripping reaction on isotopically enriched targets of ${}_{}{}^{107}{}_{}{}^{}\mathrm{Ag}$ and ${}_{}{}^{109}{}_{}{}^{}\mathrm{Ag}$ at an incident deuteron energy of 10.0 MeV. The over-all experimental resolution was approximately 20 keV. Proton groups leading to 57 states in ${}_{}{}^{108}{}_{}{}^{}\mathrm{Ag}$ with excitation energies up to 2.78 MeV and 37 states in ${}_{}{}^{110}{}_{}{}^{}\mathrm{Ag}$ with excitation energies up to 1.66 MeV have been identified. Orbital angular momentum transfer values and spectroscopic factors have been extracted for 19 states in ${}_{}{}^{108}{}_{}{}^{}\mathrm{Ag}$ and for 23 states in ${}_{}{}^{110}{}_{}{}^{}\mathrm{Ag}$ using the zero-range distorted-wave Born approximation including an approximation for the nonlocality of the optical potential and a finite-range correction. In ${}_{}{}^{108}{}_{}{}^{}\mathrm{Ag}$, six $l=0\mathrm{}$, nine $l=2\mathrm{}$, one $l=4\mathrm{}$, one admixture of $l=0\mathrm{}$ and $l=2\mathrm{}$, and two admixtures of $l=2\mathrm{}$ and $l=4\mathrm{}$ are assigned. In ${}_{}{}^{110}{}_{}{}^{}\mathrm{Ag}$, six $l=0\mathrm{}$, $l=2\mathrm{}$, and one admixture of $l=2\mathrm{}$ and $l=0\mathrm{}$ are assigned. It is possible that a small fraction of $l=2\mathrm{}$ transitions in ${}_{}{}^{110}{}_{}{}^{}\mathrm{Ag}$ are masked with $l=4\mathrm{}$ transitions. On this assumption, the effective numbers of neutrons outside the closed $g_{\frac{9}{2}}$ orbital in ${}_{}{}^{108}{}_{}{}^{}\mathrm{Ag}$ and ${}_{}{}^{110}{}_{}{}^{}\mathrm{Ag}$ are consistent with the expected values. The summed strengths of the single-particle orbitals are consistent with those of neighboring isotones.

The electron-capture branch decay of the 7.23-min ${\frac{7}{2}}^{+}$ isomer at 25.5 keV in ${}_{}{}^{105}{}_{}{}^{}\mathrm{Ag}$ has been investigated by means of Ge(Li) and NaI(T1) spectroscopy, using sources which were both chemically and isotopically processed. We find that (0.34±0.07)% of the isomeric states decay by the electron-capture process to at least nine levels in ${}_{}{}^{105}{}_{}{}^{}\mathrm{Pd}$. The strongest transitions are to levels at 0 keV [(27 ± 16)%, $logft=6.1\mathrm{}$, 306.25 KeV [(10 ± 1.5)%, 6.3], 319.18 keV [(48 ± 10)%, 5.6], 929.41 keV [(5.3 ± 3.0)%, 5.7], and 1098.39 keV [(2.0 ± 0.8)%, 5.6]. An interpretation of the properties states in ${}_{}{}^{105}{}_{}{}^{}\mathrm{Pd}$ in terms of the Nilsson model including Coriolis interactions is attempted.

Neutron time-of-flight spectroscopy measurements were made for a range of sample thicknesses of ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$ and ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ using the Nevis synchrocyclotron. These included transmission measurements using 200- and 40-m paths, self-indication measurements at 40 m, and Moxon-Rae capture measurements at 33 m. Resonance energies and ${\Gamma }_n$ values were obtained for $n=302\mathrm{}$ levels in ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$ to 4.0 keV and 269 levels in ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ to 4.6 keV, with essentially no missed $s$ levels and inclusion of a significant number of $p$ levels. ${\Gamma }_{\gamma }$ values were obtained for 84 levels in ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$ and 71 in ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ to 2400 eV, with $〈{\Gamma }_{\gamma }〉=[21.2\mathrm{}\pm 0.3 (\mathrm{stat}.\mathrm{})\pm 0.9 (\mathrm{syst}.\mathrm{}\left)\right] \mathrm{meV} \left({}_{}{}^{232}{}_{}{}^{}\mathrm{Th}\right) \mathrm{and} [22.9\mathrm{}\pm 0.5 (\mathrm{stat}.\mathrm{})\pm 0.9 (\mathrm{syst}.\mathrm{}\left)\right] \mathrm{meV} \left({}_{}{}^{238}{}_{}{}^{}\mathrm{U}\right)$. In both cases a ${\chi }^2$ analysis gives ∼100 degrees of freedom including the effects of measurement errors. The values for the resonance energies were obtained from the data before the analysis was completed for ${\Gamma }_n$ and ${\Gamma }_{\gamma }$ values. The division of the levels into $s$ and $p$ populations, described in detail elsewhere, was made to achieve a "best" fit to many statistical tests relating to the orthogonal-ensemble theory for single level populations, with a resulting good fit to numerous tests. For the chosen $s$ level population, ${10}^4 S_0=(0.84\mathrm{}\pm 0.08) \mathrm{for} {}_{}{}^{232}{}_{}{}^{}\mathrm{Th} \mathrm{and} (1.08\mathrm{}\pm 0.10) \mathrm{for} {}_{}{}^{238}{}_{}{}^{}\mathrm{U}$. The $s$ population $〈D〉=16.7\mathrm{} \mathrm{eV} \left({}_{}{}^{232}{}_{}{}^{}\mathrm{Th}\right) \mathrm{and} 20.8 \mathrm{eV} \left({}_{}{}^{238}{}_{}{}^{}\mathrm{U}\right)$. The fits to the Porter-Thomas theory for ${\Gamma }_n^0$ distributions were generally good for the full 3-keV regions, with a small anomaly for the behavior of ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$ to 500 eV which has been reported by others. The remaining $p$ levels have ${\Gamma }_n$ values which are consistent with $p$ strength function ${10}^4 S_1\sim 0.9 \mathrm{for} {}_{}{}^{232}{}_{}{}^{}\mathrm{Th} \mathrm{to} 400$ eV and ${10}^4 S_1\sim 1.4 \mathrm{for} {}_{}{}^{238}{}_{}{}^{}\mathrm{U} \mathrm{to} 1200$ eV. Larger $S_1$ values by other groups are due to their inclusion as stronger $p$ levels, ones which we call $s$ levels. Effective potential scattering radii were found to be (9.1 ± 0.3) fm for ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$ and (9.6 ± 0.3) fm for ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$.

Chemically separated and isotopically separated sources of 6.2-day ${}_{}{}^{206}{}_{}{}^{}\mathrm{Bi}$ produced by the ($p,xn$) reactions on lead were used to study the excited states of ${}_{}{}^{206}{}_{}{}^{}\mathrm{Pb}$. $\gamma$-ray data were taken with a Compton-suppression spectrometer and with a Ge(Li)-Ge(Li) two-parameter analyzer system. From these, 66 $\gamma$ rays were identified in the decay of ${}_{}{}^{206}{}_{}{}^{}\mathrm{Bi}$ and 61 of these transitions have been placed from coincidence results, energy sums and differences, and intensity considerations in a decay scheme with 19 excited states. New levels at 2826.4, 2939.6, 3225.5, and 3244.1 keV have been deduced. Spins and parities for all but one excited state were deduced from published internal-conversion electron intensities, relative $\gamma$-ray intensities, $log\mathrm{ft}$ values, and existing angular distribution measurements from particle reactions. The branching ratios, transition multipolarities, and lifetimes for many of the ${}_{}{}^{206}{}_{}{}^{}\mathrm{Pb}$ levels were calculated by using the wave functions that result from shell-model calculations with phenomenological as well as realistic interactions, and calculations using the two-nucleon random phase approximation.

Isobaric analog states have been observed in the neutron spectra of ($p,n$) reactions on targets of ${}_{}{}^{206}{}_{}{}^{}\mathrm{Pb}$, ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$, ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$, and ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$. After removal of instrumental resolution effects, the natural widths are, respectively, 196 ± 26, 203 ± 32, 202 ± 34, and 151 ± 34 keV. Except in the ${}_{}{}^{206}{}_{}{}^{}\mathrm{Pb}$ case, these widths are substantially smaller than those observed in $\overline{p}$ spectra from ($p,n\overline{p}$) experiments on the same target nuclei but are in agreement with ($p,p^{\prime }$) resonance results in the two cases that have been measured.

We propose that in the region of two quasiparticle excitations, there exist $K=0\mathrm{}$ rotational bands such that: (a) $K\pi =0_{+}$, occurs with only odd-$J$ values; and (b) $K\pi =0_{-}$, occurs with only even-$J$ values. Properties of such anomalous bands are investigated.

The analysis of particle-evaporation spectra with the approximate theory which neglects angular momentum leads to ambiguous values of the level-density parameter $a$. This ambiguity can be removed by using the exact theory which explicitly includes angular momentum.

The half-lives of ${}_{}{}^{171}{}_{}{}^{}\mathrm{Ta}$ and ${}_{}{}^{172}{}_{}{}^{}\mathrm{Ta}$ were determined. The nuclides were produced by the spallation reaction ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}\mathrm{}(p,pxn)\mathrm{}$ at a proton bombarding energy of 450 MeV. The half-life of ${}_{}{}^{171}{}_{}{}^{}\mathrm{Ta}$ was found to be 23.3 ± 0.3 min, in good agreement with the literature value. A previously unreported $\gamma$ ray at 1087 keV is probably assignable to ${}_{}{}^{171}{}_{}{}^{}\mathrm{Ta}$ decay. The half-life of ${}_{}{}^{172}{}_{}{}^{}\mathrm{Ta}$ was found to be 36.7 ± 0.4 min.

A recent suggestion that the 4.385-MeV ${\frac{7}{2}}^{+}$ state in ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ is in the ground-state rotational band and that the 5.473-MeV ${\frac{7}{2}}^{+}$ state is in an excited band appears to be contradicted by $\gamma$-decay data and by data from the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ (${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$) ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ reaction - both of which assign the 5.473-MeV state to the ground-state band.

A shell-model study of the $A=4\mathrm{}$ system previously performed with purely central forces was repeated using both the Tabakin and Sussex interactions. Agreement with the experimental spectrum improved. Some shift of the $E1\mathrm{}$ strength to the lower of the 1-, $T=1\mathrm{}$ levels occurred, but the bulk of the strength remained in the state at higher energy. Over-all results achieved with the Sussex interaction were comparable to those obtained using the Tabakin potential.

A new method based on plane-wave representations is developed and applied to the theory of direct reactions. The coefficients of the plane-wave expansions of propagators are determined either by the requirement that they fit the scattering matrix for an auxiliary potential both on and off the momentum shell or by the use of an effective unit operator. Such expansions lead to the reduction of typical direct reaction problems to simple matrix algebra, the basic matrices being either plane-wave matrices or auxiliary potential matrices. Particular attention is given here to finite-range distorted-wave matrix elements and coupled-channels theory, where the possible advantages of the present approach can be understood even at a formal level.