Inelastic proton scattering from ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ has been measured at beam energies of 24.93, 30.04, 34.78, 34.78, and 39.83 MeV. Angular distributions from 13 to 97° for about 40 inelastic states were obtained. Analyses with both microscopic and macroscopic theories are presented.

Inelastic proton scattering from ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ has been measured at beam energies 25, 30, 35, and 40 MeV. Angular distributions from 13 to 97° for 22 inelastic states were obtained. Analyses with the collective distorted-wave Born approximation are presented. A direct comparison of the excitation of the ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ 3.830-MeV $2^{+}$ and 6.342-MeV $4^{+}$ states is made with the low-lying excited $2^{+}$ and $4^{+}$ states of ${}_{}{}^{50}{}_{}{}^{}\mathrm{Ti}$ and ${}_{}{}^{52}{}_{}{}^{}\mathrm{Co}$.

The nuclear structure of ${}_{}{}^{26}{}_{}{}^{}\mathrm{Al}$ has been studied by means of the ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}({}_{}{}^3{}_{}{}^{}\mathrm{He},p)$ reaction at an incident energy of 18 MeV. 65 levels below 7 MeV in excitation were observed with an energy resolution of 18 keV. Systematics of the angular-distribution shapes allow several assignments of the angular-momentum transfer, resulting in some new spin assignments. Distorted-wave calculations have been performed for those states previously thought to be well described in terms of pure two-particle Nilsson configurations relative to a ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ core.

Potential energy surfaces have been calculated for the mass range $180\le A\le 212$ by using the shell-correction method on the basis of a symmetric two-center shell model. All calculations have been performed both with a constant and with a surface-dependent pairing strength. The results show that the fission barriers calculated with the latter prescription are incompatible with experimental data. The calculations for a constant pairing strength, however, in which the shells at the saddle are calculated on the same basis as those at the ground state, agree reasonably well with experimental data of the Berkeley group. The shell corrections for these nuclei are analyzed separately in detail and are found to exhibit remarkable regular structures which can be explained by an interplay between the shells of the fragments and those of the fissioning nucleus. Finally, the existence of shape-isomeric and the treatment of the zero-point energy in these calculations are discussed.

The existence of different sets of $R$-matrix parameters describing the same cross sections for a given spin-parity state is studied in the context of low-energy neutron reactions in fissile elements. For two fission channels and well-spaced resonances different sets of fission vectors are found describing essentially the same set of cross-section curves.

The ($p,p$) and ($n,p$) quasifree scattering have been studied in the same experiment. The data are compared with single-scattering models and with calculations of the rescattering series up to the third order. Single-scattering calculations give the shape of the spectra, but there is a discrepancy between calculated and experimental absolute values of the cross sections. Calculations of the rescattering effect do not converge below 20 MeV but reproduce both the magnitude and the shape of the quasifree peak above 40 MeV.

We show that the naive solution of the two-hole-line-approximation equations for the many-fermion ground-state energy leads to physically incorrect results. As poles cross the integration contour, residue corrections must be appended to the equations. Unfortunately, the corrected equations do not appear to be solvable for nuclear-type potentials.

The two-particle shell-model spectra of ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{18}{}_{}{}^{}\mathrm{F}$ are studied using effective interactions obtained from phase-shift-equivalent nucleon-nucleon potentials. The spectra depend significantly on the off-shell behavior of the potentials.

We present a generalization of the Hartree-Fock (HF) method incorporating two-body correlations. The correlations are introduced by means of a unitary operator $e^{\mathrm{iF}}$, where $F$ is a Hermitian one- and two-body operator to be determined by the variational principle. Assuming that the matrix elements of $F$ are small so that powers of $F$ higher than the second may be neglected, a set of linear equations determining $F$ is obtained. The relation between our method and methods used to treat singular interactions is discussed. The method is applied to two recently suggested models and is compared with the HF method, second-order perturbation theory, and with the random-phase approximation. It is found that our method yields very good results within the range of validity of our approximations, which seems to call forth applications to more realistic problems. Possible applications to the study of collective phenomena in nuclei are indicated.

The "governor model" of Trainor and the author, based on the assumptions of a rotational flow motion and the existence of a rotationally invariant core in nuclei, is completely reformulated in terms of the better-known deformation parameter ${\beta }_0$. It is shown that this model results in an expression for the ground-state moment of inertia which, in agreement with the empirical study of Mariscotti et al. (the variable-moment-of-inertia model), gives a linear dependence on the deformation parameter (${\mathcal{I}}^{\mathrm{}\left(0\right)\mathrm{}}\propto {\beta }_0$). The hydrodynamical model, based on the irrotational flow motion and using the condition ${\mathcal{I}}^{\mathrm{}\left(0\right)\mathrm{}}\propto \beta _0^{}{}_{}{}^2$, is also reformulated to include all the higher-order corrections to the $J(J+1\mathrm{})\mathrm{}$ law. Both the models are then applied to all the even-even nuclei in the mass regions $152\le A\le 188$ and $A\ge 224$, and the results are compared with experiment. The discussion is restricted to the ground-state rotational bands only. In addition to the rotational-state energies and the ground-state moment of inertia, other nuclear properties, such as the variation of the moment of inertia and the quadrupole moment with the angular momentum, are also investigated.

When neutron reduced widths, ${\Gamma }_n^0$, are evaluated for $N$ adjacent "single-population" resonances for an isotope, it is customary to express the fractional uncertainty in the $s$ strength function, $S_0$, as $\pm {\left(\frac{2.27}{N}\right)}^{\frac{1}{2}}$ or $\pm {\left(\frac{2}{N}\right)}^{\frac{1}{2}}$. It is assumed that the ${\Gamma }_n^0$ follow a Porter-Thomas (P.T.) single-channel distribution with a common $〈{\Gamma }_n^0〉$ for the interval, with no correlation between the different ${\Gamma }_n^0$. If the spacing distribution follows the Wigner formula for nearest neighbor spacings, but with no correlations, the ${\left(\frac{2.27}{N}\right)}^{\frac{1}{2}}$ fractional uncertainty applies for large $N$. For spacings following a statistical "orthogonal ensemble" (O.E.) behavior, the fractional uncertainty in $〈D〉$ is $\approx N^{-1\mathrm{}}$, so the fractional uncertainty in $S_0$ is $\approx {\left(\frac{2}{N}\right)}^{\frac{1}{2}}$ for large $N$. Experimentalists need easy to use rules for smaller $N$. We have used Monte Carlo methods with a P.T. form for ${\Gamma }_n^0$, and O.E. for spacings to establish the upper- and lower-bound values for $S_0$, divided by ${\overline{S}}_0\equiv \frac{{\overline{\Gamma }}_n^0}{\overline{D}}$ (the ratio of the measured averages of ${\Gamma }_n^0$ and $D$). The method of confidence intervals was used. We also suggest a "best choice" ratio for true $S_0$ to measured ${\overline{S}}_0$, all for a range of small $N$. The results should also apply for "single populations" of $p$ levels. The behaviors for ${\Gamma }_n^0$ and $D$ were also studied separately.

We report extensive new data on the isospin-forbidden reaction ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(d,{\alpha }_2){}_{}{}^{10}{}_{}{}^{}\mathrm{B}\mathrm{}\left(1.74\right)\mathrm{}$ for $7.19 \mathrm{MeV}\le E_d\le 13.99 \mathrm{MeV}$. We also report extensive data for the isospin-allowed reactions ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(d,{\alpha }_{0,1,3}){}_{}{}^{10}{}_{}{}^{}\mathrm{B}$. All channels exhibit resonant behavior indicative of compound-nucleus formation. We find no evidence for appreciable direct or semidirect contribution to the ${\alpha }_2$ cross sections. A partial-wave expansion of the ${\alpha }_2$ data fixes $J^{\pi }$ for a number of (isospin-mixed) ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ compound-nuclear levels. Our data do not support either Noble's proposed ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ mechanism or Weller's modification to Noble's proposal.

Measurements have been made of the asymmetric proton yields about the ${}_{}{}^5{}_{}{}^{}\mathrm{Li}$ recoil direction using the sequential reaction ${}_{}{}^6{}_{}{}^{}\mathrm{Li}({}_{}{}^3{}_{}{}^{}\mathrm{He},\alpha p){}_{}{}^4{}_{}{}^{}\mathrm{He}$ for both the ground and first excited states of ${}_{}{}^5{}_{}{}^{}\mathrm{Li}$ at a beam energy of 1.54 MeV. Measurements were made out of the reaction plane, and the results are in qualitative agreement with the predictions of a model proposed by Reimann, Martin, and Vogt. Distorted-wave Born-approximation stripping theory may also be capable of explaining the asymmetric results.

The elastic scattering of 600-MeV protons from light nuclei has been studied at the National Aeronautics Space Administration Space Radiation Effects Laboratory (SREL) synchrocyclotron. Differential cross sections have been obtained for the scattering of protons from hydrogen, deuterium, helium-3, and helium-4. Polarization was measured for deuterium and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ nuclei. The $p-p$ cross-section data are in excellent agreement with the predictions from the Livermore phase shifts. Small-angle $p-D$, $p-{}_{}{}^3{}_{}{}^{}\mathrm{He}$ elastic scattering data are compared with calculations based on the multiple-scattering theories of Watson and Glauber.

Approximate values for the residual neutron-proton interaction in mirror nuclei are derived from binding energy data. The comparison shows no indications for significant symmetry-breaking charge-dependent nuclear effects.

The use of elastic ${\pi }^{\pm }$-nucleus scattering to explore the relative neutron-proton distributions in nuclei is studied theoretically. The large difference between ${\pi }^{+}-N$ and ${\pi }^{-}-N$ interactions in the nuclear surface leads to substantial effects. Neutron-radius determinations to 0.1 F appears feasible.

From phenomenological considerations, a mass formula is derived to calculate the interaction energy among the last two neutrons and last two protons in a nucleus. This interaction energy is the intra-$\alpha$-cluster energy of the last $\alpha$ cluster in the nucleus. Then from a proper analysis of these intra-$\alpha$-cluster energies, a separation of the intra- and inter-$\alpha$-cluster energies out of the total binding energy of the nucleus is made. Clear ideas about the sizes of the $\alpha$ clusters relative to the size of the free $\alpha$ particle and also about the degree of $\alpha$ clustering in each $\alpha$ nucleus are obtained. Positive evidence supporting the additive nature of the $\alpha -\alpha$-cluster interaction is found. Finally, the intra-$\alpha$-cluster interaction energies are compared with the $\mathrm{nn}$-, $\mathrm{pp}$-, and $\mathrm{np}$-interaction energies in the same even-even self-conjugate nuclei in order to explore the similarities between the nature of two-body and four-body interactions.

One- and two-term nonlocal separable potentials are determined to fit all partial $S$-, $P$-, and $D$-wave experimental phase shifts up to the first energy resonance at about $E_{\pi }=180\mathrm{}$ MeV (lab). The theoretical and experimental phase shifts, scattering lengths, and volumes are in good agreement. The practical use of this potential in nuclear physics calculations is simplified by the choice of simple form factors and of identical ranges in all $S$, $P$, and $D$ relative states.

We have measured the yields of specific final states excited in the capture of negative muons by ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ and ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$. The yields are compared with the cross sections for excitation of the analog states by 180° electron scattering and with the relative populations of levels produced by the decay of the giant-dipole-resonance states.

A unique spin assignment of $J=4\mathrm{}$ is obtained for the level at 2068.7 keV in ${}_{}{}^{26}{}_{}{}^{}\mathrm{Al}$ which previously had a spin assignment of $J=3\mathrm{}$. The level was populated with the reaction ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}\mathrm{}(p,n)\mathrm{}{}_{}{}^{26}{}_{}{}^{}\mathrm{Al}$ at a proton energy of 7.4 MeV and the angular distribution of the ground-state $\gamma$ ray determined. The excitation energy and the $E2\mathrm{}$ strengths indicate that this level and the level at 3404 keV with $J=5\mathrm{}$ are members of a $K=3\mathrm{}$ rotational band based on the $3^{+}$ level at 417 keV. This proposed band, based on the parallel coupling configuration of a particle in Nilsson orbit $5 (\Omega =\frac{5}{2})$ with a particle in orbit $9 (\Omega =\frac{1}{2})$, is evidence of further rotational structure in ${}_{}{}^{26}{}_{}{}^{}\mathrm{Al}$.