The effective interaction with hard-core potentials is studied when both a correlated and an uncorrelated basis is used. While the use of a correlated basis leads to a series expansion which is uniquely defined to any order, the use of an uncorrelated basis leads to a series expansion which is not uniquely defined to any order, although the series can converge to a unique result. A method is given for evaluating this series perturbatively, which is numerically simple and improves the accuracy of calculation of matrix elements of operators sensitive to the core region. It does not require the rearrangement of the graphs in ladder-type terms; the rearrangement can be done whenever it is convenient. The separation method and the reference-spectrum method are discussed in the light of the present method.

The distorted-wave impulse approximation for inelastic scattering of protons from nuclei has been modified to include double-scattering contributions. The correction was cast in terms of directly measurable or phenomonological quantities to obviate the effects of specific nuclear models. Although the "exact" form of the correction is a complicated nonlocal operator in the space of the scattering proton, a simplified version of the correction was found which, along with a finite-range corrections, gave a remarkably good account of the strength of cross sections for inelastic scattering off ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ at 45 and 100 MeV.

A large number of nuclear levels in the light nuclei ${\mathrm{O}}^{16}$, ${\mathrm{Ne}}^{20}$, ${\mathrm{O}}^{17}$, ${\mathrm{F}}^{17}$, ${\mathrm{C}}^{13}$, and ${\mathrm{N}}^{13}$ are classified in terms of the Regge trajectories in the channels (${\mathrm{C}}^{12},\alpha$), (${\mathrm{O}}^{16},\alpha$), (${\mathrm{O}}^{16},n$), (${\mathrm{O}}^{16},p$), (${\mathrm{C}}^{12},n$), and (${\mathrm{C}}^{12},p$), respectively. The mirror nuclei (${\mathrm{O}}^{17}$, ${\mathrm{F}}^{17}$) and (${\mathrm{C}}^{13}$, ${\mathrm{N}}^{13}$) have isobaric analog trajectories. The Regge trajectories obtained by coupling a nucleon with the first excited state of an ${\mathrm{O}}^{16}$ or ${\mathrm{C}}^{12}$ nucleus are also constructed from the levels of ${\mathrm{O}}^{17}$ (or ${\mathrm{F}}^{17}$) and ${\mathrm{C}}^{13}$ (or ${\mathrm{N}}^{13}$), respectively. (${\mathrm{O}}^{16}$, nucleon) and (${\mathrm{C}}^{12}$, nucleon) are spin-zero-spin-½ systems and contain trajectories corresponding to both $J=l-\frac{1}{2}$ and $J=l+\frac{1}{2}$ couplings.

The charge form factor of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ is calculated using the nonlocal nucleon-nucleon interaction constructed by Kahana, Lee, and Scott. In the framework of perturbation theory one-particle-one-hole (1p-1h) and two-particle-two-hole (2p-2h) excitations are taken into account, and the defect wave function is obtained. The calculation is in qualitative agreement with the experimentally determined form factor in that the distinctive diffraction minimum is predicted, but beyond momentum transfer of 3 ${\mathrm{fm}}^{-1\mathrm{}}$ the calculated form factor is too small. The agreement is improved if the 1p-1h terms are omitted.

The $R$-matrix theory of nuclear scattering is used to consider the meaning of spectroscopic factors for unbound states. Potential scattering is explicitly calculated by constructing an $R$ function which is equivalent to the potential. The compound effects are then parametrized in the usual $R$-matrix fashion with the spectroscopic factors being explicitly included as parameters. The spectroscopic factors are found by fitting data. The spectroscopic factors are very sensitive to the choice of the various resonance parameters, and the validity of spectroscopic factors as a meaningful quantity for unbound states is discussed in the light of several calculations. Several types of resonances found in the reactions ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}\mathrm{}(n,n)\mathrm{}{}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}\mathrm{}(n,n)\mathrm{}{}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ are considered. These include the cases of very narrow and very broad resonances and a double-resonance situation.

The mean lifetime of the 1.472-MeV level ($J^{\pi }={\frac{1}{2}}^{+}$) in ${\mathrm{O}}^{19}$ has been measured using the Doppler-shift attenuation method and found to be ${\tau }_m=1.22\mathrm{}\pm 0.36$ psec. The level decays (1.4 ± 0.2)% to the ground state ($J^{\pi }={\frac{5}{2}}^{+}$) and (98.6 ± 0.2)% to the state at 96 keV ($J^{\pi }={\frac{3}{2}}^{+}$). Energies of the first and second excited states of ${\mathrm{O}}^{19}$ were measured as 96.0 ± 0.5 and 1472 ± 1 keV, respectively. The experimental results are compared with a theoretical calculation.

The polarization and the differential scattering cross section for neutrons scattered from ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$ have been measured for $0.075\le E_n\le 2.2$ MeV. These results, together with those from the ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}(n,{\alpha }_0){}_{}{}^7{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}(n,{\alpha }_1){}_{}{}^7{}_{}{}^{}\mathrm{Li}_{}^{*}{}_{}{}^{}$ (0.48 MeV), ${}_{}{}^7{}_{}{}^{}\mathrm{Li}(\alpha ,\alpha ){}_{}{}^7{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^7{}_{}{}^{}\mathrm{Li}(\alpha ,{\alpha }^{\prime }){}_{}{}^7{}_{}{}^{}\mathrm{Li}_{}^{*}{}_{}{}^{}$ (0.48 MeV), and other reactions leading to states in ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$, have been simultaneously interpreted in one consistent $R$-matrix calculation. The calculated results are in good agreement with most of the data and give new information about states in ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$. The level parameters obtained for these states and the calculated reaction cross sections are consistent with the corresponding quantities in the mirror nucleus ${}_{}{}^{11}{}_{}{}^{}\mathrm{C}$. Quantitative explanations are given both for the well-known $\frac{1}{v}$ behavior of the cross section for the ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}(n,\alpha ){}_{}{}^7{}_{}{}^{}\mathrm{Li}$ reaction and for the $\frac{{\alpha }_0}{{\alpha }_1}$ branching ratio.

Expressions for the ratio of $\mathrm{ft}$ values for mirror $\beta$ decays are given in the treatment of nuclei as elementary particles with emphasis on the effects of second-class currents. The results are compared with the corresponding ones in the usual impulse-approximation treatment with off-mass-shell and meson-exchange corrections. Theoretical implications of the data of Wilkinson and Alburger are examined.

The excitation energies and $\gamma$-ray decay modes of the low-lying states of ${\mathrm{Cl}}^{34}$ have been studied using the ${\mathrm{S}}^{32}({\mathrm{He}}^3,p\gamma ){\mathrm{Cl}}^{34}$ reaction. Some lifetime limits were obtained by the Dopplershift-attenuation method. The lifetimes of the $(J^{\pi },T)=(1^{+},0)$ levels at 461 and 666 keV, and the ($2^{+}$, 0) level at 1230 keV were measured to be 7.1 ± 0.7, 12.8 ± 1.0, and 19.4 ± 1.4 psec, respectively, using the recoil-distance (plunger) technique with the ${\mathrm{P}}^{31}(\alpha ,n\gamma ){\mathrm{Cl}}^{34}$ reaction. The transition strengths from these three levels are discussed qualitatively in terms of calculations involving simple configurations, and are compared with recent detailed shell-model calculations.

Employing Hartree-Fock (HF), spherical BCS, and Hartree-Fock-Bogoliubov approximations and using central Yukawa (CY) and Kuo-Brown renormalized matrix elements for the Hamada-Johnston (HJ) interaction, a study of the behavior of nuclear shapes for the even Ni isotopes is carried out. Nuclear properties such as binding energy with respect to the ${\mathrm{Ca}}^{40}$ core, intrinsic quadrupole and hexadecapole moments, spectroscopic pickup strengths with special emphasis on the pickup strength for the $j=\frac{7}{2}$ state are calculated for different shapes and compared. It is found that the theoretical values of binding energy corresponding to shapes with minimum energy compare well with the experimental values. Addition of more neutrons to ${\mathrm{Ni}}^{56}$ decreases considerably the occupation probability for the protons in the $j=\frac{7}{2}$ state for all the shapes and approximations for the HJ interaction. With the CY interaction, the pickup strength in the $j=\frac{7}{2}$ state is not much affected for the BCS solution but it decreases in other approximations. It is found that the self-consistent solution for ${\mathrm{Ni}}^{56}$ corresponding to the HJ interaction does not converge to a spherical shape; instead it gives an oblate HF solution.

Energy levels in ${}_{}{}^{49}{}_{}{}^{}\mathrm{Cr}$ have been studied using the ${}_{}{}^{50}{}_{}{}^{}\mathrm{Cr}({}_{}{}^3{}_{}{}^{}\mathrm{He},\alpha ){}_{}{}^{49}{}_{}{}^{}\mathrm{Cr}$ reaction. Angular distributions of $\alpha$ particles were measured and compared with distorted-wave Born-approximation calculations to determine $l$ values. $\alpha -\gamma$ angular correlations were also measured. The following spin-parity assignments are consistent with our results for the levels indicated: 0.27 MeV ${\frac{7}{2}}^{-}$, 1.07 MeV (${\frac{5}{2}}^{-},{\frac{9}{2}}^{-}$), 1.57 MeV (${\frac{5}{2}}^{-},{\frac{7}{2}}^{-},{\frac{11}{2}}^{-}$), 1.71 MeV (${\frac{1}{2}}^{-},{\frac{3}{2}}^{-}$), 1.74 MeV ${\frac{3}{2}}^{-}$, 1.98 MeV ${\frac{3}{2}}^{-}$, 2.43 MeV ${\frac{5}{2}}^{-}$, 2.58 MeV ${\frac{1}{2}}^{+}$, 2.61 MeV ${\frac{3}{2}}^{-}$, 3.24 MeV ${\frac{5}{2}}^{-}$, 3.51 MeV (${\frac{5}{2}}^{-},{\frac{7}{2}}^{-}$), 3.93 MeV ${\frac{1}{2}}^{-}$, 4.76 MeV ${\frac{7}{2}}^{-}$, 5.57 MeV ${\frac{3}{2}}^{+}$, 6.43 MeV ${\frac{1}{2}}^{+}$, 6.47 MeV ${\frac{1}{2}}^{+}$, 6.76 MeV ${\frac{1}{2}}^{+}$. Branching ratios for the decays of these levels were measured. Multipole mixing ratios were extracted from the correlation data.

Energy-averaged angular distributions have been measured at 16.8 MeV for scattering to the ground state and first two excited states at ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$. Direct and compound-nuclear contributions have been estimated. Optical-model fits to the elastic scattering data with three discrete real potentials ($V=34, 57, \mathrm{and} 83$ MeV) were greatly improved by an $l$-dependent absorption. Only two well depths (50 and 80 MeV) gave reasonable $0^{+}$-$2^{+}$ coupled-equation fits. Slightly better results for $0^{+}$-$2^{+}$-$4^{+}$ coupling were obtained by including a $j$-dependent absorption with $V=50\mathrm{}$ MeV, $W=4.0\mathrm{}$ MeV, $R=4.94\mathrm{}$ F, ${\beta }_2=0.40\mathrm{}$, and ${\beta }_4=0.0\mathrm{}$.

The ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}(\alpha ,\gamma ){}_{}{}^{44}{}_{}{}^{}\mathrm{Ti}$ reaction has been used to study the nucleus ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ti}$. The mass excess of ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ti}$ has been determined to be -37 541 ± 10 keV. Radiative yields and angular distributions of deexcitation $\gamma$ rays from resonances at 4.22-, 4.26-, and 4.52-MeV $\alpha$ energy, and angular distributions of $\gamma$ rays between bound levels have been measured using Ge(Li) detectors. Bound states have been found at 1083 ($2^{+}$), 1905 ($0^{+}$), 2454 ($4^{+}$), 2531 ($2^{+}$), 2886 ($2^{+}$), 3175, 3415 (2, 3), 3645 and 3942 keV, and mixing ratios and branching ratios for the decays of some of these levels are reported. The ground state and first excited $2^{+}$ and $4^{+}$ states can be explained in terms of ${\mathrm{}\left(\mathrm{fp}\right)\mathrm{}}^4$ configurations. Some of the other low-energy states probably require interpretation in terms of particle-hole configurations. Relative reduced $E2\mathrm{}$ transition strengths from the 2531-keV ($2^{+}$) state are determined and suggest that the 1905- and 2531-keV states may be the beginning of a rotational band.

Lifetimes of several low-lying levels in ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$, and ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ have been measured using the Doppler-shift attenuation method. The levels were populated by the $X(\alpha ,{\alpha }^{\prime })X^{*}$ reaction using 22-MeV $\alpha$ particles from the Indiana University cyclotron. The backscattered $\alpha$ particles were detected in an annular surface-barrier particle detector, and coincident $\gamma$ rays resulting from the decay of the nuclear states were detected by a 16.7-${\mathrm{cm}}^3$ lithium-drifted germanium detector. A new form for the velocity of the recoiling ions as a function of time, which is suitable for heavy target backings and high initial recoil velocities ($\sim 0.03c$), was used. The results for the mean lifetimes, in units of ${10}^{-15\mathrm{}}$ sec, for the excited states in parentheses (MeV) are the following: ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$(4.12) 169±34, (4.23) 185±33, (5.23) 173±46, (6.01) 124±20; ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$(2.94) ${60}_{-20\mathrm{}}^{+12\mathrm{}}$; ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$(4.61) ${83}_{-12\mathrm{}}^{+15\mathrm{}}$. These results are compared with previously reported values, and best averages are suggested.

The decay modes of 10 ${}_{}{}^{49}{}_{}{}^{}\mathrm{Ca}$ states have been investigated utilizing the reaction ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}(d,p\gamma ){}_{}{}^{49}{}_{}{}^{}\mathrm{Ca}_{}^{*}{}_{}{}^{}$. On the basis of the resulting decay scheme and some previously measured $l_n$ values, $J^{\pi }$ assignments of (${\frac{5}{2}}^{-}$), ($\frac{3}{2},\frac{1}{2}$) are made to the 3.586- and 4.272-MeV levels, respectively. A new level at 4.885 MeV is assigned $J=(\frac{9}{2},\frac{7}{2})$. The ${}_{}{}^{49}{}_{}{}^{}\mathrm{Ca}$ level structure is discussed in terms of particle-core coupling models.

Ground-state band levels to $6^{+}$ in ${}_{}{}^{84}{}_{}{}^{}\mathrm{Kr}$, $6^{+}$ in ${}_{}{}^{82}{}_{}{}^{}\mathrm{Kr}$, $8^{+}$ in ${}_{}{}^{80}{}_{}{}^{}\mathrm{Kr}$, and ${10}^{+}$ in ${}_{}{}^{78}{}_{}{}^{}\mathrm{Kr}$ have been identified with 20-65-MeV ($\alpha ,xn\gamma$) reactions on enriched Se targets with $x=2, 3, \mathrm{and} 4$. The data are in-beam and radioactive $\gamma$ spectra, angular distributions, relative and absolute excitation functions and ∼3-nsec time distributions. All transitions in the ground-state bands are ≳95% prompt (≳3 nsec) except for ${}_{}{}^{84}{}_{}{}^{}\mathrm{Kr}$, in which the 6 → 4, 4 → 2, and 2 → 0 transitions have the same intensities of long-lived (≳200-nsec) component in addition to the prompt component. Multipole mixing ratios of three other transitions in ${}_{}{}^{82}{}_{}{}^{}\mathrm{Kr}$ are obtained from the angular distributions. The systematics of level energies in the ground-state bands of various Se, Kr, Mo, and Ru isotopes are analyzed with a phenomenological equation. This reveals three limiting types of nuclei.

Differential cross sections for the inelastic scattering of 166-MeV $\alpha$ particles from the $3^{-}$ levels of ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ are presented. A distorted-wave Born-approximation microscopic analysis is made utilizing an effective $\alpha$-nucleon interaction previously determined from a study of elastic scattering. In considering the results obtained, various aspects of nuclear structure implicit in the calculations of microscopic wave functions are implicated: the effective nucleon-nucleon interaction, the importance of nucleon correlations, and the extent of the configuration space. Electromagnetic transition probabilities and inelastic electron scattering form factors calculated with the microscopic wave functions used in the $\alpha$-particle analysis are compared with experimental results. No effective charge is required to obtain agreement.

The 110-min ${\beta }^{-}$ decay of the ${\frac{7}{2}}^{-}$ ground state of ${}_{}{}^{41}{}_{}{}^{}\mathrm{Ar}$ to excited states of ${}_{}{}^{41}{}_{}{}^{}\mathrm{K}$ was investigated by observation of the deexcitation ${}_{}{}^{41}{}_{}{}^{}\mathrm{K}$ $\gamma$ rays with a Ge(Li) detector. In addition, both ($p^{\prime },\gamma$) coincidence measurements and a magnetic spectrometer study were made of the reaction ${}_{}{}^{41}{}_{}{}^{}\mathrm{K}(p,p^{\prime }){}_{}{}^{41}{}_{}{}^{}\mathrm{K}$ at proton energies between 5.3 and 5.8 MeV. The ($p^{\prime },\gamma$) work gave $\gamma$-ray decay-mode information used in the analysis of the ${\beta }^{-}$-decay studies. The magnetic spectrometer studies confirmed a new level of ${}_{}{}^{41}{}_{}{}^{}\mathrm{K}$ at 1594 ± 3 keV observed in the ($p^{\prime },\gamma$) work. The ${\beta }^{-}$ decay to the ${}_{}{}^{41}{}_{}{}^{}\mathrm{K}$ sixth excited state ($E_x=1677.0\mathrm{}\pm 0.3$ keV) observed previously by Pratt was confirmed. The branch was found to be (5.2 ± 0.5) × ${10}^{-2\mathrm{}}$%, corresponding to an allowed $log{f}_{0}t$ value of 7.68 ± 0.04. Rather severe upper limits were placed on any other branches to excited states except the major one to the ${\frac{7}{2}}^{-}$ state at 1294 keV.

Fractional cumulative yields of ${}_{}{}^{132}{}_{}{}^{}\mathrm{Te}$ and ${}_{}{}^{134}{}_{}{}^{}\mathrm{Te}$ have been measured from thermal-neutron-induced fission of ${}_{}{}^{245}{}_{}{}^{}\mathrm{Cm}$ and ${}_{}{}^{249}{}_{}{}^{}\mathrm{Cf}$. The yields, expressed as ratios of atoms of tellurium to atoms of tellurium plus iodine, are 0.94 ± 0.01 and 0.59 ± 0.07 for ${}_{}{}^{245}{}_{}{}^{}\mathrm{Cm}$ fission, and 0.76 ± 0.02 and 0.36 ± 0.05 for ${}_{}{}^{249}{}_{}{}^{}\mathrm{Cf}$ fission. Fractional yields based on estimated total chain yields are the same as above for ${}_{}{}^{132}{}_{}{}^{}\mathrm{Te}$ but decrease to 0.56 ± 0.08 and 0.29 ± 0.06 for ${}_{}{}^{134}{}_{}{}^{}\mathrm{Te}$. The yielas are not consistent with similar yields from ${}_{}{}^{233}{}_{}{}^{}\mathrm{U}$ and ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$ fission.

The $\gamma$-ray decay of fission product ${}_{}{}^{140}{}_{}{}^{}\mathrm{Xe}$ has been studied using TRISTAN, the Ames Laboratory on-line isotope separator. Extensive coincidence data have been obtained using two Ge-(Li) detectors and a buffer tape system. 120 of the approximately 140 $\gamma$ rays observed have been placed in a level scheme for ${}_{}{}^{140}{}_{}{}^{}\mathrm{Cs}$ with 27 excited levels. The level density at low energy is quite high, with six excited levels occurring in the first 120 keV. Tentative spin-parity assignments and possible shell-model interpretations are discussed.