The Beliaev-Zelevinsky method, which represents fermion-pair operators by infinite expansions in exact bosons, is applied to the problem of nuclear rotation. In the harmonic order, which is essentially the random-phase approximation (RPA), the rotation, viewed as infinitesimal, is decoupled from the collective vibrations. The higher orders, however, give rise to various band-mixing terms, which may be interpreted as rotation-vibration and higher-order Coriolis interactions, as well as to vibrational anharmonicities and renormalization of the moment of inertia. A systematic approach is given for extracting these higher-order corrections for the idealized case of a two-dimensional system of interacting particles. Both the Hamiltonian and transition operators are treated. The self-consistent-field approximation is then formulated in the boson picture and applied to the cranking model. The advantage of this formulation is that it allows one to establish the correctness of the higher-order cranking model, which is shown to provide the ground-state-band rotational energies with an error of the order of the small boson-expansion parameter (or the square of this parameter, depending on its definition). The usefulness of the cranking model for obtaining the angular momentum dependence of transition operators is also demonstrated. The Appendix illustrates some of the ideas by way of application to a system of particles interacting through a two-dimensional analog of the quadrupole-quadrupole force.

A detailed shell-model calculation is carried out to discuss the properties of the low-lying states of ${\mathrm{Cu}}^{59}$ and ${\mathrm{Ni}}^{59}$ nuclei. An inert ${\mathrm{Ni}}^{56}$ core is assumed and the three extracore particles are considered to occupy the $1p_{\frac{3}{2}}$, $0f_{\frac{5}{2}}$, and $1p_{\frac{1}{2}}$ orbitals. The effect of including the $0g_{\frac{9}{2}}$ orbital is studied. The renormalized reaction matrix elements as derived by Kuo and Brown for this mass region are used. A comparison between the observed and calculated energy levels is made and the wave functions obtained are used to calculate the spectroscopic factors for the ${\mathrm{Ni}}^{58}({\mathrm{He}}^3,d){\mathrm{Cu}}^{59}$ and ${\mathrm{Ni}}^{58}\mathrm{}(d,p)\mathrm{}{\mathrm{Ni}}^{59}$ reactions. The odd-mass Ni isotopes (${\mathrm{Ni}}^{59}$, ${\mathrm{Ni}}^{61}$, ${\mathrm{Ni}}^{63}$, ${\mathrm{Ni}}^{65}$) are then described by the modified Tamm-Dancoff approximation (MTDA) method. The MTDA results for odd Ni isotopes are found to be in quite satisfactory agreement with experiment. These results together with the previous results for even Ni isotopes by Roy, Raj, and Rustgi lead us to believe that the Kuo-Brown matrix elements in conjunction with the MTDA method give a good description of all the Ni isotopes.

The ${\mathrm{Ti}}^{49}(d,{\mathrm{He}}^3){\mathrm{Sc}}^{48}$ reaction was studied at 19.45 and 22.4 MeV, and spectroscopic factors were obtained. There are serious discrepancies between the present result and previous work. The present experiment supports a simple picture of the ${\mathrm{Sc}}^{48}$ nucleus.

${}_{}{}^{20}{}_{}{}^{}\mathrm{O}$ was produced in the reaction ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$(${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$)${}_{}{}^{20}{}_{}{}^{}\mathrm{O}$ and its half-life measured by observing the decay of the 1.06-MeV $\gamma$ transition in ${}_{}{}^{20}{}_{}{}^{}\mathrm{F}$ in a Ge-Li counter. The result is $t_{\frac{1}{2}}=13.57\mathrm{}\pm 0.1$ sec, $logft=3.73\mathrm{}$. Upper limits were obtained for weak $\beta$-decay branches of ${}_{}{}^{20}{}_{}{}^{}\mathrm{O}$ to other states in ${}_{}{}^{20}{}_{}{}^{}\mathrm{F}$ between $E_x=0.984\mathrm{} \mathrm{and} 2.195$ MeV.

The inelastic scattering of deuterons, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, and $\alpha$ particles from ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$, ${}_{}{}^{65}{}_{}{}^{}\mathrm{Cu}$, and ${}_{}{}^{67}{}_{}{}^{}\mathrm{Zn}$ has been investigated to determine whether spin-dependent effects similar to those observed for protons were observable for these projectiles. The inelastic deuteron scattering shows an effect that is similar to, but stronger than, that seen for proton scattering. The angular distributions for ${\mathrm{½}}^{-}$ states are quite different from those for ${\frac{5}{2}}^{-}$ and ${\frac{7}{2}}^{-}$ states in ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$ and ${}_{}{}^{65}{}_{}{}^{}\mathrm{Cu}$. The inelastic ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ scattering exhibits no real structure in its angular distributions for any of the states, so no conclusions may be reached concerning spin-dependent effects for ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ scattering. The inelastic $\alpha$ scattering shows no spin-dependent effect. No definite theoretical explanation for these observations is apparent.

Forty-six-point angular distributions for the elastic scattering of $\alpha$ particles by ${}_{}{}^{36}{}_{}{}^{}\mathrm{Ar}$ have been measured with a gas target from 12.83 to 17.83 MeV in 20-keV intervals throughout the angular range from 29.0 to 167.8° (c.m.). Optical-model fits to the data smoothed in energy with a Lorentzian weighting function have been obtained. The computed cross sections were obtained from an incoherent sum of a direct contribution calculated from the optical model and a compound-elastic term based on Hauser-Feshbach theory. Parameters found for the compound-elastic-scattering term are consistent with the systematics for such parameters determined from fluctuation theory. The importance of compound-nuclear processes in the inelastic scattering is confirmed by a coupled-channel calculation. Although there is some indication of discrete ambiguous potentials in the analysis, no set exists for which the fits are comparably good. Fits to the data were not improved by the inclusion of $l$-dependence in the imaginary potential. Parameter values determined by the analysis were $U=182.2\mathrm{}$ MeV and $W_S=36.4\mathrm{}$ MeV (surface imaginary), with a fixed real well-radius value of 4.9 F chosen to be consistent with previous analyses of electron scattering data.

Thirty-four levels in ${\mathrm{Tb}}^{158}$ have been observed up to an excitation energy of 1166 keV utilizing 12-MeV deuterons and the reaction ${\mathrm{Tb}}^{159}\mathrm{}(d,t)\mathrm{}{\mathrm{Tb}}^{158}$. The ground-state $Q$ value was determined to be -1870 ± 15 keV. The spectrum has been interpreted in terms of the coupling of the [$411\uparrow$] Nilsson proton orbital with the neutron orbitals prominent in the ($d,t$) spectrum of ${\mathrm{Gd}}^{157}$. This interpretation has resulted in the determination of relative energies due to the residual neutron-proton interaction for eight different configurations. The observed singlet-triplet splitting energies for the [$521\uparrow$], [$402\downarrow$], and [$400\uparrow$] neutron orbitals coupled to the [$411\uparrow$] proton orbital were measured to be +132, -111, and +136 keV, respectively. Theoretical calculations of these energies made for a zero-range spin-dependent central potential gave values of +174, -186, and +136 keV, respectively.

Fission-fragment angular correlations and fission probabilities have been measured for a series of odd-$A$ uranium and plutonium isotopes excited by ($d,p$), ($t,d$), and ($t,p$) reactions. The following fissioning nuclei have been studied: (1) ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$ from ($d,pf$), ($t,pf$); (2) ${}_{}{}^{237}{}_{}{}^{}\mathrm{U}$ from ($d,pf$), ($t,df$), ($t,pf$); (3) ${}_{}{}^{239}{}_{}{}^{}\mathrm{U}$ from ($d,pf$); (4) ${}_{}{}^{241}{}_{}{}^{}\mathrm{Pu}$ from ($d,pf$), ($t,df$), ($t,pf$); and (5) ${}_{}{}^{243}{}_{}{}^{}\mathrm{Pu}$ from ($d,pf$), ($t,df$). Fission probabilities and angular-correlation coefficients for each case are compared with previously reported ($n,f$) results. The direct-reaction experiments show fission thresholds at excitation energies equal to or less than threshold energies observed in ($n,f$) experiments. Some qualitative characteristics of the transition-state spectrum for the nuclei studied are determined from comparisons of the direct-reaction and ($n,f$) results.

A study is made of the characteristics of magic nuclei displayed in a Hartree-Fock calculation. It is seen that the known doubly-closed-shell nuclei are clearly distinguished by the behavior of the energy as a function of neutron and proton number. The existence of these characteristics for the superheavy nucleus with $Z=120\mathrm{}$ and $N=178\mathrm{}$ indicates that this may also be a magic nucleus. Single-particle-model calculations have indicated $Z=114\mathrm{}$ as the magic nucleus. Possible reasons for this difference are discussed.

Angular distributions and differential range spectra at angles of 15, 60, 90, 120, and 165° to the beam direction have been measured for ${\mathrm{Tb}}^{149}$ recoiling from thin gold targets irradiated with 2.2-GeV protons. The observed mean velocities decrease monotonically from a value of 0.264 ${\mathrm{}(\mathrm{M}\mathrm{e}\mathrm{V}/\mathrm{a}\mathrm{m}\mathrm{u})\mathrm{}}^{1/2}$ at 15° to 0.149 ${\mathrm{}(\mathrm{M}\mathrm{e}\mathrm{V}/\mathrm{a}\mathrm{m}\mathrm{u})\mathrm{}}^{1/2}$ at 165°. The ratio of integrated intensity in the forward hemisphere to that backward is 3.10. The experimental results are consistent with the symmetry requirements of a two-step model for the reaction, provided that there is a positive correlation between $v_{\parallel }$, the forward component of velocity due to the first step, and $V$, the velocity due to the second step. However, there are substantial quantitative discrepancies between the experimental results and calculations based on the cascade-evaporation model which is commonly used to describe the two steps of a high-energy nuclear reaction. The calculations predict a value of $〈v_{\parallel }〉$ twice as large as that observed and a much weaker correlation between $V$ and $v_{\parallel }$. These effects are discussed in terms of possible contributions from heavy-fragment emission in both steps of the reaction. Systematics of the average energies of various recoil products suggest an empirical correlation that may be useful in distinguishing fission from "deep spallation."

The $\gamma$-ray spectra following slow-neutron capture in a target of ${\mathrm{Rh}}^{103}$ have been measured with the fast-chopper time-of-flight facility at the high flux beam reactor at Brookhaven National Laboratory. A total of 145 radiative intensities, involving transitions from seven resonances and 16 unresolved resonances, to levels in ${\mathrm{Rh}}^{104}$ have been recorded. A neutron binding energy of 6999.3±1.5 keV is obtained. From these high-energy $\gamma$-ray data, several spin assignments for levels in ${\mathrm{Rh}}^{104}$ are made. The distribution of transition probabilities in rhodium is not consistent with the Porter-Thomas distribution; values of $\nu ={2.70}_{-0.40\mathrm{}}^{+0.53\mathrm{}}$ and $\nu ={2.45}_{-0.40\mathrm{}}^{+0.38\mathrm{}}$ are obtained as best fits to the class of ${\chi }^2$ distribution functions to spin-0 and spin-1 resonances, respectively. The gross shape of the $\gamma$-ray spectrum shows an enhancement of strength to states near 1 MeV in excitation energy, both for thermal and resonance capture. It is shown that this enhancement is not due to a direct-reaction process, and it is suggested that the presence of doorway states may be responsible for this enhancement.

The threshold photodisintegration of ${\mathrm{Pb}}^{208}$ and the thermal-neutron capture by ${\mathrm{Pb}}^{207}$ is considered. It is shown that the magnitude of the thermal capture cross section and the asymmetry of the resonance observed in the ($\gamma ,n$) reaction at 41 ke V above threshold may be explained by extrapolating the giant resonance amplitude and the amplitude of a subthreshold resonance into the appropriate energy domains. It is found that the direct (optical) processes are small compared with the effects of the "resonance tails."

The predictions of asymmetric collective models with pure quadrupole, pure octupole, and mixed quadrupole-plus-octupole shapes are developed for negative-parity states in deformed even nuclei in an effort to determine the usefulness of the asymmetric model as a tool to distinguish surface shapes. The models are applied to the data for ${}_{}{}^{228}{}_{}{}^{}\mathrm{Th}$, ${}_{}{}^{232}{}_{}{}^{}\mathrm{U}$, and ${}_{}{}^{234}{}_{}{}^{}\mathrm{U}$, and the comparison indicates that the energy and electric quadrupole branching-ratio predictions are independent of surface-shape multipolarity.

Differential cross sections for elastic and inelastic proton scattering on ${}_{}{}^{94}{}_{}{}^{}\mathrm{Zr}$ were measured between 6.0- and 8.5-MeV bombarding energy. The decay of analogs of states in ${}_{}{}^{95}{}_{}{}^{}\mathrm{Zr}$ to the ground state and the 0.92 MeV ($2^{+}$), 1.30 MeV ($0^{+}$), 1.66 MeV ($2^{+}$), and 2.06 MeV ($3^{-}$) states in ${}_{}{}^{94}{}_{}{}^{}\mathrm{Zr}$ was investigated. In the analysis of the inelastic proton groups, the enhancement of the Hauser-Feshbach background, as well as the interference of the resonance amplitude with direct nuclear excitation were taken into account. Spins, spectroscopic factors, and possible weak-coupling configurations in the parent system are derived and compared with results previously obtained for ${}_{}{}^{91}{}_{}{}^{}\mathrm{Zr}$ and ${}_{}{}^{93}{}_{}{}^{}\mathrm{Zr}$.

Four $\alpha$-decay chains initiated by ${}_{}{}^{225}{}_{}{}^{}\mathrm{Pa}$, ${}_{}{}^{224}{}_{}{}^{}\mathrm{Pa}$, ${}_{}{}^{223}{}_{}{}^{}\mathrm{Pa}$, and ${}_{}{}^{222}{}_{}{}^{}\mathrm{Pa}$ were produced by the bombardment of thallium, lead, and bismuth targets with beams of ${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}$, ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$, ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$, ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$, and ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ at the Berkeley heavy-ion linear accelerator. The reaction products were transported from the reaction cell by the helium-jet technique and their decay was measured with a semiconductor detector. Energy values, excitation functions, half-lives, and genetic relationships of individual peaks were determined. Two new techniques based on the use of a time-to-amplitude converter were developed for the measurement of μsec half-lives of daughter products, and five half-lives in the μsec range were measured.

These new $\alpha$ data help to determine the trends in $\alpha$-decay energies for isotopes of odd-$Z$ elements, particularly in the poorly defined region just above the 126-neutron shell. This allows more accurate predictions of $\alpha$-decay properties of many unknown nuclei. Some anomalous behavior of the apparent $\alpha$-decay energies for nuclei with 133 and 135 neutrons is pointed out.

The difference in the total neutron cross section due to nuclear orientation, $\Delta {\sigma }_{\mathrm{def}}$, has been measured for ${}_{}{}^{165}{}_{}{}^{}\mathrm{Ho}$ over the energy range of 2 to 135 MeV. The results show that $\Delta {\sigma }_{\mathrm{def}}$ oscillates as well as changing sign, contrary to our classical concept of the interaction. The data, both ${\sigma }_{\mathrm{t}}$ and $\Delta {\sigma }_{\mathrm{def}}$, are successfully fitted by adiabatic coupled-channel calculations using the optical model. The parameters for the optical model were determined by fitting ${\sigma }_{\mathrm{t}}$ and ${\sigma }_{\mathrm{R}}$ data (over approximately the same energy range as in the present work) for the two spherical nuclei Cd and Pb. The only additional quantity introduced was the quadrupole deformation parameter for ${}_{}{}^{165}{}_{}{}^{}\mathrm{Ho}$ which is known to be 0.33. The data for $\Delta {\sigma }_{\mathrm{def}}$ can also be explained quite well by a simple semiempirical model which makes use of the black-nucleus model, the nuclear Ramsauer effect, and the experimental ${\sigma }_{\mathrm{t}}$ data. The temperature dependence of $\Delta {\sigma }_{\mathrm{def}}$ agrees very well with our calculated values for the degree of nuclear orientation, which is consistent with ${}_{}{}^{165}{}_{}{}^{}\mathrm{Ho}$ being almost a pure quadrupole-shaped nucleus.

A 10-cc coaxial Ge(Li) detector and a 2-in.×2-in. NaI(Tl) detector were used in conjunction with a multichannel coincidence configuration to investigate the following $\gamma -\gamma$ directional correlations in the decay of 11.1-day ${\mathrm{Nd}}^{147}$: 319-91, 398-91, 440-91, 121-319, and 276-319 keV. Using the well-established values of $\frac{7}{2}$ and $\frac{5}{2}$ for the ground and 91-keV levels, respectively, and an admixture of $(1.6\mathrm{}\pm 0.4)\% E2\mathrm{}$ for the 91-keV transition, this experiment favored the following spin assignments to the various levels: 410 ($\frac{3}{2}$), 489 ($\frac{5}{2}$), 531 ($\frac{5}{2}$), and 686 keV ($\frac{5}{2}$). The $M1+E2\mathrm{}$ multipolarity mixtures obtained, which are in agreement with nuclear-orientation and internal-conversion measurements reported by previous investigators, for each of the respective $\gamma$ transitions are: $121 (1.5\mathrm{}\pm 0.5)\% E2\mathrm{}$, $276 \left(\sim 1\right)\% E2\mathrm{}$, $319 (11\mathrm{}\pm 2)\% E2\mathrm{}$, $398 (3\mathrm{}\pm 2)\% E2\mathrm{}$, and 440 keV $(27\mathrm{}\pm 7)\% E2\mathrm{}$. A 310-keV $\gamma$ ray proposed by several investigators was directly observed in the Ge(Li) spectrum; measurements indicate that this peak decays with the half-life of ${\mathrm{Nd}}^{147}$.

Excitation functions for ($\alpha ,xn$), ($\alpha ,\alpha n$), and ($\alpha ,2p$) reactions upon niobium targets have been measured for incident $\alpha$-particle energies from 15 to 41 MeV Excited states in ${\mathrm{Mo}}^{95}$ have been studied by observing the decay of the 61-day isotope ${\mathrm{Tc}}^{95m}$, which was produced by the ${\mathrm{Nb}}^{93}(\alpha ,2n)$ reaction. The energies and the intensities of the $\gamma$ rays resulting from this decay have been measured. The angular-correlation coefficients of the two strongest cascades in ${\mathrm{Mo}}^{95}$ have been found to be $A_{22}=-0.292\mathrm{}\pm 0.005$ and $A_{44}=-0.001\mathrm{}\pm 0.006$ for the 582-204-keV cascade, and $A_{22}=-0.196\mathrm{}\pm 0.006$ and $A_{44}=-0.003\mathrm{}\pm 0.008$ for the 835-204-keV cascade. The mean life of the 204-keV state has been measured by the delayed-coincidence technique and found to be 1.09 ± 0.02 nsec. The $g$ factor of the 204-keV state has been measured to be -0.26 ± 0.02. A summary of a number of calculations concerning the nuclear structure of ${\mathrm{Mo}}^{95}$ is given, and some predictions of the Kisslinger-Kumar model of near-spherical nuclei for ${\mathrm{Mo}}^{95}$ are presented. The technique of perturbed angular correlations has been used to measure the hyperfine fields at the molybdenum nucleus in iron and nickel hosts. These fields have been found to be ${\mathrm{B}}_{\mathrm{e}\mathrm{f}\mathrm{f}}\left(\mathrm{Mo}\mathrm{in}\mathrm{Fe}\right)=-236\mathrm{}\pm 19$ kG and ${\mathrm{B}}_{\mathrm{e}\mathrm{f}\mathrm{f}}\left(\mathrm{Mo}\mathrm{in}\mathrm{Ni}\right)=-29.9\mathrm{}\pm 5.1$ kG at 55°C.

States up to 5.6 MeV in excitation energy in ${\mathrm{Pb}}^{207}$ were studied by the ${\mathrm{Pb}}^{208}\mathrm{}(d,t)\mathrm{}$, ${\mathrm{Pb}}^{206}\mathrm{}(d,p)\mathrm{}$, and ${\mathrm{Pb}}^{207}(d,d^{\prime })$ reactions at a deuteron bombarding energy of 17 MeV. Over 100 states were observed and 70 angular distributions were measured and compared with distorted-wave Born approximation calculations for the ($d,p$), and ($d,t$) reactions. Special emphasis was placed on obtaining accurate excitation energies to compare those states excited in more than one reaction. In ${\mathrm{Pb}}^{206}\mathrm{}(d,p)\mathrm{}$, some of the two-hole-one-particle (2h-1p) states are found to be fragmented. The $i_{\frac{11}{2}}$ and $j_{\frac{15}{2}}$ 2h-1p states are tentatively identified. Many of the weaker (less than 5 μb/sr) transitions in ($d,t$) have angular distributions which do not follow DWBA - possibly indicating other than one-step reaction mechanisms. Observation of the 2h-1p states in ($d,t$) indicate that the ${\mathrm{Pb}}^{208}$ closed shell contains about $4.7\% {\left(2\mathrm{}{g}_{\frac{9}{2}}\right)}^2$, $\lesssim 4.7\% {\left(3\mathrm{}{d}_{\frac{5}{2}}\right)}^2$, and $\lesssim 1.2\% {\left(4\mathrm{}{s}_{\frac{1}{2}}\right)}^2$ particle-${\mathrm{Pb}}^{206}$ core admixture.

The cross sections of ($p,2p$), ($p,pn$), and ($p,2n$) reactions at 400 MeV on the separated isotopes of cadmium were determined. The ($p,pn$) cross sections exhibit abrupt variations within a narrow target mass range. The data are examined in terms of the currently accepted mechanisms for high-energy ($p,2\mathrm{}$ nucleon) reactions. An estimate is made of the relative contribution of direct knockout processes versus the two-step inelastic scattering and neutron evaporation mechanism. There does not appear to be any obvious explanation for the abrupt cross-section variations. The cross section of the cadmium ($p,2p$) reactions is inversely proportional to the neutron skin thickness. This is consistent with the conclusion that these reactions take place predominantly by direct knockout processes and in the peripheral region of the nucleus.