Regge poles describing shape resonances ("quasimolecular states") are found to play a prominent role in many optical-model scattering amplitudes and appear to be directly related to the Gruhn-Wall "dip" often observed in the reflection coefficient $\eta \mathrm{}\left(l\right)\mathrm{}$. The Blair smooth-cutoff model is generalized to include such a Regge pole and used to fit angular distributions for elastic ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$+ ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and $\alpha +{}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ scattering, in the 20-30-MeV (c.m.) energy range. It also appears that the smooth-cutoff (strong-absorption) model itself can be interpreted as the result of many overlapping inelastic Regge resonances.

The boundary-condition model of the two-nucleon interaction due to Feshbach and Lomon is used without an external potential tail to determine the ground-state properties of the three-nucleon system for the purpose of studying the off-energy-shell properties of the two-body $T$ matrix. Calculations are performed using an average singlet-triplet $s$-wave interaction giving a completely symmetric triton wave function. The $T$ matrix is separable and depends on three energy-independent parameters — the boundary radius $r_0$ and the boundary condition $f$ at $r_0+\epsilon$ which are determined from the two-nucleon phase shifts, and the boundary condition $b$ at $r_0-\epsilon$ which is specifically an off-shell parameter that does not appear in the on-shell $T$ matrix. With $f=0.11\mathrm{}$ and $r_0=0.95\mathrm{}$ F, the Faddeev equations are solved for the triton energy eigenvalues and spectator functions for several values of $b$. It is found that the binding energy varies from 3.9 to 19.4 MeV for $b$ between 0.5 and 0.6, with a value of 8.5 MeV at $r=0.537\mathrm{}$. The average kinetic energy and charge form factor are determined as a function of $b$, and qualitative agreement of the charge radius with experiment is obtained for $b=0.5-0.6\mathrm{}$. The charge form factor, compared with experiment, does not drop off rapidly enough with $q^2$, indicating the presence of relatively too much large $q$ component in the spectator functions. The changes to be expected from the inclusion of tensor coupling in the boundary parameters are discussed.

The general theory of multiple scattering of pions from nuclei is expressed in a way which does not require the use of a series expansion. In an on-shell approximation this theory may be reduced to the solution of a set of $A$ coupled integral equations. As a demonstration of the method the equations are specialized to the case of the deuteron and solved to give comparison with the experimental data. The deuteron tensor $T_{20}$ is shown to be sensitive to the percentage of $D$ state for deuterons scattered at 0°.

A new, simple, and exact method is given for calculating the reaction matrix $G$ in a two-particle harmonic-oscillator basis. The method makes use of an expansion of the Bethe-Goldstone wave function in terms of solutions of the Schrödinger equation for two interacting particles in a harmonic-oscillator well. Since a two-particle basis is used, the Pauli operator $Q$ is diagonal and can be treated exactly. Reaction matrix elements based on the Hamada-Johnston potential are used in a shell-model calculation of $A=18\mathrm{}$ nuclei. The results are compared with those of earlier calculations using approximate Pauli operators. The dependence of the reaction matrix on the starting energy is studied, and the relationship of this energy to the intermediate-state spectrum and to the Pauli operator $Q$ is discussed. In this same context the difference between using a Brueckner $Q$ and a shell-model $Q$ is also discussed.

The general framework of a recent proposal for constructing classes of two-particle off-shell transition matrices consistent with given bound-state binding energies and a given set of phase shifts for all energies is presented. This establishes certain properties of the underlying potential which previously needed to be assumed. The large arbitrariness in the choice of bound-state wave functions and the lack of correlation, in general, between the choice of bound-state wave functions and the values of the binding energies are demonstrated. A specific method for actually executing the construction program is proposed which should be useful when there exists reason to prefer a particular bound-state wave function.

The mean lifetimes of the levels of ${}_{}{}^{37}{}_{}{}^{}\mathrm{Ar}$ below 3.0-MeV excitation energy have been measured by applying the Doppler-shift-attenuation method to the ${}_{}{}^{34}{}_{}{}^{}\mathrm{S}(\alpha ,n){}_{}{}^{37}{}_{}{}^{}\mathrm{Ar}$ reaction ($Q_0=-4.629\mathrm{}$ MeV). A 450-μg/c${\mathrm{m}}^2$ CdS target (enriched to 85.61% in ${}_{}{}^{34}{}_{}{}^{}\mathrm{S}$) evaporated onto a 1-μ Ni foil was bombarded with $\alpha$ particles ranging in energy from 7.6 to 8.8 MeV. $\gamma$ rays were detected at 0, 37, 45, 55, 90, and 143° to the beam axis with a 30-cc Ge(Li) detector. The following mean lifetimes were found: $\tau (1.41\mathrm{}-\mathrm{M}\mathrm{e}\mathrm{V}\mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l})={1.08}_{-0.13\mathrm{}}^{+0.17\mathrm{}}$ psec, $\tau \mathrm{}\left(2.22\right)=380\mathrm{}\pm 50$ fsec, $\tau \mathrm{}\left(2.49\right)={775}_{-89\mathrm{}}^{+105\mathrm{}}$ fsec, and $\tau \mathrm{}\left(2.80\right)=14\mathrm{}\pm 11$ fsec. Excitation energies for the first five excited states were determined from the ground-state transitions. All five levels were found to undergo $\gamma$ decay 100% to the ground state; upper limits were set on other possible transitions. Analysis of the $\gamma$-ray angular distributions for the levels at 1.61 and 2.49 MeV gave spins in agreement with previous assignments. The angular-distribution and lifetime measurements yield a most probable spin-parity assignment of (${\frac{7}{2}}^{+}$) for the 2.22-MeV level. The experimental transition strengths for the positive-parity states are in good agreement with predictions of many-particle shell-model calculations.

The ${}_{}{}^{86}{}_{}{}^{}\mathrm{Sr}({}_{}{}^3{}_{}{}^{}\mathrm{He},d){}_{}{}^{87}{}_{}{}^{}\mathrm{Y}$ reaction was studied at a laboratory beam energy of 20 MeV to test the possible closed-subshell behavior of the 38-proton configuration. The ground-state $Q$ value is found to be 0.346 ± 0.015 MeV. Several new states were identified below an excitation energy of 3.45 MeV. A distorted-wave analysis was used to assign $l$ values for the stripping transitions. Spectroscopic strengths agree well with sum-rule expectations for the $2p$, $1f$, and $1g_{\frac{7}{2}}$ configurations. Comparison with the results of Picard and Bassani for the ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}({}_{}{}^3{}_{}{}^{}\mathrm{He},d){}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$ reaction indicates qualitative agreement with shell-model expectations for $2p$ and $1g$ strengths but significant deviations for $1f$ strength and for low-lying $2d$ strength.

The energy-dependent $\beta -\gamma$ circular polarization was measured in order to set better limits on the matrix-element ratio $\Lambda =\int \frac{\overrightarrow{\alpha }}{\left(\int \frac{i\overrightarrow{\mathrm{r}}}{\rho }\right)}$ for the 696-keV first-forbidden $\beta$ transition of ${\mathrm{Rb}}^{86}$. The results show that $\Lambda$ is consistent with the Fujita-Eichler relation, so the contributions of the off-diagonal matrix elements of the Coulomb Hamiltonian to $\Lambda$ are small for this transition. The nuclear matrix elements are in agreement with previous results, but the limits of error have been reduced.

Employing ${\mathrm{Ni}}^{56}$ as core, and Kuo and Brown renormalized matrix elements for the Hamada-Johnston nucleon-nucleon potential as the residual interaction, the level structure of both ${\mathrm{Cu}}^{60}$ and ${\mathrm{Zn}}^{60}$ is studied within the framework of the shell model. The four active nucleons are allowed to populate the $1p_{\frac{3}{2}}$, $0f_{\frac{5}{2}}$, and $1p_{\frac{1}{2}}$ single-particle orbitals. A comparison with the observed level spectra is made, and good agreement with those levels whose spins and parity are definitely known is found. Other levels whose spins and parity assignments are not definite have corresponding theoretical levels which should help in determining their spins in the future measurements.

Isobaric analog resonances in proton scattering experiments are analyzed using a set of coupled optical equations which include both elastic and inelastic channels as well as other channels which can couple to these via the charge-exchange operator ($\overrightarrow{\tau }·\overrightarrow{\mathrm{T}}$). The method has been applied to the particular case of ${\mathrm{Sr}}^{88}+p$, in which only the $p_0\left(0_1^{+}\right)$ and $p_1\left(2_1^{+}\right)$ proton channels are dominant and mixing of the ($j\times 0_1^{+}$) and ($j^{\prime }\times 2_1^{+}$) configurations describes the primary fragmentation of the $2d_{\frac{5}{2}}$, $3s_{\frac{1}{2}}$, $2d_{\frac{3}{2}}$, and $j^{\prime }\times 2_1^{+}$ neutron states in the parent nucleus ${\mathrm{Sr}}^{89}$. Our purpose in this investigation was to see whether or not one could obtain a consistent match to both the level structure of the bound parent analog system and the analog resonance data in the various open channels with a general expression for the effective nucleon-nucleus interaction. Restricting as many parameters and potential terms as possible using independent sources of data, we obtained a detailed fit to the level structure of ${\mathrm{Sr}}^{89}$ and the resonant ${\mathrm{Sr}}^{88}(p,p_0)$ and ($p,p_1^{\prime }$) excitation functions, the resonant ${\mathrm{Sr}}^{88}\mathrm{}(p,n)\mathrm{}$ total cross-section data, and the elastic polarization functions for an incident proton energy from $E_p=4.8\mathrm{} \mathrm{to} 8.2$ MeV. The predicted on-resonance $p^{\prime }\left(2_1^{+}\right)$ angular distributions follow the main features of the data but not the finer details. It was found that the interference between the resonance and the direct inelastic background depends mostly on the nuclear rather than the Coulomb core excitation, and that direct inelastic charge-exchange does not affect the results. Our ability to fit all of the data in a consistent manner is interpreted as a confirmation of the main features of the generalized potential model assumed.

The ($d,{\mathrm{He}}^3$) reaction on ${\mathrm{Ti}}^{46}$ and ${\mathrm{Ti}}^{48}$ was studied at 19.5 MeV using a magnetic spectrometer. Results were analyzed in terms of distorted-wave Born-approximation theory from which transferred $l$ values and spectroscopic factors were obtained. Transitions with $l=1\mathrm{}$ to the 0.808-MeV state in ${\mathrm{Sc}}^{47}$ and to three states in ${\mathrm{Sc}}^{45}$ were observed, indicating the presence of $2p$ protons in the ground state of Ti. The single-particle strength appears concentrated in one level in ${\mathrm{Sc}}^{47}$, but considerable fragmentation of the strength is seen in ${\mathrm{Sc}}^{45}$. It was found that most of the $d_{\frac{3}{2}}$ strength is carried by the 0.763-MeV state of ${\mathrm{Sc}}^{47}$, and that the spectroscopic factor for the first ${\frac{3}{2}}^{+}$ level in ${\mathrm{Sc}}^{45}$, at 12 keV, is 2.8, or 70% of the sum-rule limit. Three more states with $l=2\mathrm{}$ were found in ${\mathrm{Sc}}^{45}$, one of them known to have $J^{\pi }={\frac{5}{2}}^{+}$. Assuming that the other two (1.304 and 1.799 MeV) levels have $J^{\pi }={\frac{3}{2}}^{+}$, the sum of the spectroscopic factors for them is 1.07, or about 25% of the sum-rule limit.

Measurements of the angular distributions of the (${}_{}{}^3{}_{}{}^{}\mathrm{He},d$) and ($d,{}_{}{}^3{}_{}{}^{}\mathrm{He}$) reactions on the stable, even-mass $N=82\mathrm{}$ isotones are presented and discussed. In each of the residual nuclei formed in these reactions, ${}_{}{}^{135}{}_{}{}^{}\mathrm{I}$, ${}_{}{}^{137}{}_{}{}^{}\mathrm{Cs}$, ${}_{}{}^{139}{}_{}{}^{}\mathrm{La}$, ${}_{}{}^{141}{}_{}{}^{}\mathrm{Pr}$, ${}_{}{}^{143}{}_{}{}^{}\mathrm{Pm}$, and ${}_{}{}^{145}{}_{}{}^{}\mathrm{Eu}$, the lowest two levels are populated with significant strength, one by $l_p=4\mathrm{}$ transfer and one by $l_p=2\mathrm{}$ transfer. Analysis indicates that these states result from coupling a $1g_{\frac{7}{2}}$ or $2d_{\frac{5}{2}}$ proton (or proton hole) to the respective $J^{\pi }=0^{+}$ target ground states. The relative energies of these states change as a function of mass, the ${\frac{5}{2}}^{+}$ state lying 590 keV above the ${\frac{7}{2}}^{+}$ state in ${}_{}{}^{135}{}_{}{}^{}\mathrm{I}$, and 330 keV below the ${\frac{7}{2}}^{+}$ state in ${}_{}{}^{145}{}_{}{}^{}\mathrm{Eu}$. Spectroscopic factors extracted from the data with distorted-wave Born-approximation analysis indicate that the active particles in the target ground states predominantly occupy the $1g_{\frac{7}{2}}$ and $2d_{\frac{5}{2}}$ orbits, with the ratio of $1g_{\frac{7}{2}}$ protons to $2d_{\frac{5}{2}}$ protons varying from 3.5/0.5 for ${}_{}{}^{136}{}_{}{}^{}\mathrm{Xe}$ to 6.3/3.6 for ${}_{}{}^{144}{}_{}{}^{}\mathrm{Sm}$. The pickup reactions reveal small admixtures of $1h_{\frac{11}{2}}$, $3s_{\frac{1}{2}}$, and $2d_{\frac{3}{2}}$ protons into the heavier target ground states. These orbits, together with the $1g_{\frac{7}{2}}$ and $2d_{\frac{5}{2}}$, constitute the major shell which fills between $Z=50\mathrm{}$ and 82. The stripping experiments locate the centroid energies of these higher three orbits relative to the ${\frac{5}{2}}^{+}$ and ${\frac{7}{2}}^{+}$ states. It is found that the centroids of the $1h_{\frac{11}{2}}$, $3s_{\frac{1}{2}}$, and $2d_{\frac{3}{2}}$ single-particle states relative to the ground states decrease monotonically from excitations of 1.9, 2.1, and 2.1 MeV, respectively, in ${}_{}{}^{137}{}_{}{}^{}\mathrm{Cs}$ to excitations of 0.72, 0.81, and 1.1 MeV in ${}_{}{}^{145}{}_{}{}^{}\mathrm{Eu}$.

The magnetic dipole moments of $p_{\frac{1}{2}}$-shell nuclei are calculated by the first-order perturbation theory. It is shown that the tensor force which causes the configuration mixing is important to explain observed data of these moments.

Lifetime and branching-ratio studies have been made in ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ utilizing the ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}(p,\gamma ){}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ reaction. Emphasis was given to measurements on levels at 7380, 7416, 7935, 8328, and 9163 keV as possible candidates for the $2^{+}$ state of an excited prolate rotational band. Combining these lifetime and branching-ratio results to obtain $E2\mathrm{}$ transition strengths for inter- and intraband transitions leads to the conclusion that an excited prolate rotational band is an unlikely possibility. Lifetimes of the 8328- and the 9415-keV states have been measured as ${150}_{- 50}^{+120\mathrm{}}$ fsec and ${130}_{-50\mathrm{}}^{+75\mathrm{}}$ fsec, respectively. A remeasurement of the lifetime of the $0^{+}$ level at 4975 keV is in substantial agreement with other recent measurements.

Differential-cross-section and polarization measurements are presented for the elastic scattering of 9.8-MeV protons by ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}$, ${}_{}{}^{64}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{68}{}_{}{}^{}\mathrm{Zn}$, ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$, ${}_{}{}^{120}{}_{}{}^{}\mathrm{Sn}$, and ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}$. In general, the angular range 17-160° was covered with an accuracy of ±2% for the cross section and ±0.02 for the polarization measurements. The data are analyzed using an optical model in three ways: (1) using individual data sets for each element and either a seven- or a nineparameter model; (2) using all the data simultaneously and a "global" search routine; (3) using individual data sets and the folding version of G. W. Greenlees, G. J. Pyle, and Y. C. Tang. The analysis using procedure (1) suggests the model is overparameterized at 9.8 MeV. These difficulties are overcome to some extent using procedures (2) and (3).

The most surprising result of the analysis is the insensitivity of the fitting to the choice of spin-orbit parameters at this energy even though relatively accurate and extensive polarization data are available. Thus, in the global analysis, spin-orbit radius parameters anywhere in the range 0.7 to 1.2 F give ${\chi }^2$ values within 5% of the optimum. The analysis using the folding version of the model indicates that additional effects are present in the interaction which are not included in the description.

The intrinsic structure of ${\mathrm{Re}}^{183}$, ${\mathrm{Re}}^{185}$, and ${\mathrm{Re}}^{187}$ has been studied using the (${\mathrm{He}}^3,d$) and ($\alpha ,t$) reactions on targets of ${\mathrm{W}}^{182}$, ${\mathrm{W}}^{184}$, and ${\mathrm{W}}^{186}$. Transfer $l$ values have been determined from angular distributions in the (${\mathrm{He}}^3,d$) reaction, and from cross-section ratios in the two different proton stripping reactions. Spectroscopic factors have been obtained by comparison with distorted-wave Born-approximation calculations. The low-lying states are found to be well described by the Nilsson model, except that the ${\frac{1}{2}}^{+}\mathrm{}\left[400\right]\mathrm{}$ and ${\frac{11}{2}}^{-}\mathrm{}\left[505\right]\mathrm{}$ intrinsic states show mixing with vibrational states. The results also indicate strong mixing of the ${\frac{1}{2}}^{+}\mathrm{}\left[400\right]\mathrm{}$ and ${\frac{3}{2}}^{+}\mathrm{}\left[402\right]\mathrm{}$ states with ${\frac{1}{2}}^{+}\mathrm{}\left[660\right]\mathrm{}$ and ${\frac{3}{2}}^{+}\mathrm{}\left[651\right]\mathrm{}$ states arising from the $N=6\mathrm{}{i}_{\frac{13}{2}}$ spherical state.

Coulomb-excitation experiments have been performed to measure transition probabilities of collective quadrupole states in ${}_{}{}^{178}{}_{}{}^{}\mathrm{Hf}$. A search for $\beta$-vibrational levels yielded negative results. Upper limits are placed on the excitation of the known $2^{+}$ levels at 1276 and 1496 keV. The $B{\mathrm{}\left(E2\mathrm{}\right)\mathrm{}}_{\mathrm{exc}}$ values are $<~2\times {10}^{-51\mathrm{}}{e}^2$ ${\mathrm{cm}}^4$ and $<~{10}^{-50\mathrm{}}{e}^2$ ${\mathrm{cm}}^4$ for the 1276- and 1496-keV levels, respectively. Neither of these levels has sufficient excitation strength to be designated as the $2^{+}$ level of the collective $\beta$ band. The $J=2\mathrm{}$ level of the $K^{\pi }=2^{+}$ collective $\gamma$ band is established at 1175 keV, with $B{\mathrm{}\left(E2\mathrm{}\right)\mathrm{}}_{\mathrm{exc}}=(10.0\mathrm{}\pm 0.8)\times {10}^{-50\mathrm{}}{e}^2$ ${\mathrm{cm}}^4$. The angular distribution of the deexcitation $\gamma$ rays from this level yields $\delta =-32\mathrm{}$ with limits $\delta >32\mathrm{} or <-11\mathrm{}$, and $>99\% E2\mathrm{}$ multipolarity for the 1081.5-keV $2_{\gamma }^{+}\to 2_g^{{}^{+}}$ transition. The reduced $\gamma$-ray branching ratio of the ($2_{\gamma }\to 2_g$)-to-($2_{\gamma }\to 0_g$) transition yields a band-mixing parameter $z_2=(23\mathrm{}\pm 10)\times {10}^{-3\mathrm{}}$.

Excitation functions are reported for the reactions of ${}_{}{}^{164}{}_{}{}^{}\mathrm{Dy}$ with ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$ to produce ${}_{}{}^{200}{}_{}{}^{}\mathrm{Po}$ and ${}_{}{}^{199}{}_{}{}^{}\mathrm{Po}$. The cross sections are much smaller than the calculated values and it is concluded that this is due to an angular momentum cutoff and to a large fission width. The reaction threshold at a laboratory energy of 4.2 MeV per nucleon indicates a low Coulomb barrier ($r_0=1.45\mathrm{}$ fm).

The ($d,p$) and ($d,t$) reactions into the five odd tungsten isotopes from ${}_{}{}^{179}{}_{}{}^{}\mathrm{W}$ to ${}_{}{}^{187}{}_{}{}^{}\mathrm{W}$ were studied with 12-MeV incident deuterons. It was found that many gross discrepancies between the experimental cross sections and those calculated using the Nilsson model and the distorted-wave Born approximation could be eliminated or reduced by inclusion in the cross-section calculations of the Coriolis interaction with reduced coupling matrix elements. In particular, the highly distinctive systematics of the cross sections in different isotopes could be reproduced. An energy-dependent systematic reduction of the matrix elements which satisfactorily accounts for the experimental observations is suggested.

In the decay of the 4.2-min isomeric state in ${}_{}{}^{152}{}_{}{}^{}\mathrm{Tb}$, $8\gamma$ rays are found to be associated with the deexcitation of levels in ${}_{}{}^{152}{}_{}{}^{}\mathrm{Tb}$ and $25\gamma$ rays with that in ${}_{}{}^{152}{}_{}{}^{}\mathrm{Gd}$. Experimental studies were made chiefly with Ge(Li)$\gamma$-ray detectors in singles and coincidence modes. Conversion-electron spectra were obtained with a Si(Li) spectrometer. The isomeric state, believed to be an $8^{+}$ state, is at 501.8 keV, and the isomeric transition is a 159.59-keV $E3\mathrm{}$ transition to a level at 342.2 keV. Other levels in ${}_{}{}^{152}{}_{}{}^{}\mathrm{Tb}$ are proposed at 58.9, 65.1, and 106.7 keV. An alternative but less likely level scheme is also possible. The ground state ($2^{-}$) and levels at 58.9, 342.2, and 501.8 keV appear to be best described in terms of Nilsson states. The electron-capture decay of the 501.8-keV isomeric state is by an allowed unhindered transition ($log\mathrm{ft} 4.7$) which leads almost entirely to a level at 2394.5 keV in ${}_{}{}^{152}{}_{}{}^{}\mathrm{Gd}$. The deexcitation of the latter level populates $6^{+}$ and $8^{+}$ members of the quasiground-state and quasi-$\beta$-vibrational bands. The quasirotational character of levels in ${}_{}{}^{152}{}_{}{}^{}\mathrm{Gd}$ which has been proposed by Sakai and coworkers appears to be amply confirmed. A previously unreported level in ${}_{}{}^{152}{}_{}{}^{}\mathrm{Gd}$ at 1861.7 keV ($5^{+}$) is proposed. In contrast to previous work, no $\alpha$-decay branch was observed.