A general formalism for the scattering of heavy ions, which is especially convenient to study the antisymmetrization effects, is developed. Antisymmetrization effects are investigated by expanding the completely antisymmetrized wave function according to the number of exchanged nucleons. The particle-core model for the scattering of nuclei with loosely bound nucleons is presented. A formula for the additional contribution to the effective potential due to antisymmetrization effects is obtained by calculating the expectation value of the Hamiltonian with intrinsic wave functions. Application of the formalism is illustrated for the ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ + ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ scattering problem and its usefulness is demonstrated.

The $\mathrm{T}\mathrm{}(p,n)\mathrm{}{}_{}{}^3{}_{}{}^{}\mathrm{He}$ neutron source reaction has been reinvestigated utilizing the time-of-flight technique. This study was motivated by the lack of cross-section data above 13 MeV, by large uncertainties in the zero-degree absolute cross sections, and by the need to improve the accuracy of both the absolute and relative cross-section data. Angular distributions were measured from 0°-140° at proton energies of 6, 7, 10, 11, 12, 13, 14, 15, and 16 MeV with a neutron detector whose relative efficiency was established to ± 1.5%. Absolute cross sections at zero degrees were obtained by normalization of the zero-degree yields measured with the neutron detector to precise charged-particle cross sections obtained for the reaction $\mathrm{T}(p,{}_{}{}^3{}_{}{}^{}\mathrm{He})n$. These results were compared to data obtained with a proton-recoil counter telescope.

We use the Faddeev formalism to investigate the variation of the trinucleon binding energy and electromagnetic form factors with phase-equivalent transformations of the Reid softcore potential. The transformed nucleon-nucleon interactions used in our calculations are the same as, or slight variations of, those considered by Haftel and Tabakin in studies of nuclear matter. The corresponding transformed two-nucleon wave functions are essentially unchanged for nucleon separations greater than 1 fm. The variation of the trinucleon binding energy follows the same trend as (but is generally much smaller than) the corresponding variation of $\frac{E_B}{A}$ for nuclear matter. The largest increase in $E_B$ (trinucleon) is 0.19 MeV, which gives $E_B\left(\mathrm{total}\right)\approx 6.9$ MeV. The position of the minimum of the calculated $\left|F_{\mathrm{ch}}^{{}_{}{}^3{}_{}{}^{}\mathrm{He}}\right(Q^2\left)\right|$ (experimental value: $Q^2\approx {11.8}^{-2\mathrm{}}$) varies between $Q^2=14.4\mathrm{} \mathrm{and} 18$ ${\mathrm{fm}}^{-2\mathrm{}}$.

The Glauber theory of multiple scattering is extended so as to include the contributions of $N^{*}$ production and is applied to the elastic scattering of a nucleon from various nuclei for incident momenta in the range from 1.7 to 30 GeV/c. The momentum dependence of the nucleon-nucleus total cross sections is discussed. The influences of the inclusion of $N^{*}$ effects on the structure of the second maximum in the differential cross section is also investigated.

An optical potential for elastic scattering of mesons on a nucleus is developed theoretically which is self-consistent at all distances from the center of the nucleus. Application is made to the case of scattering of pions on ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ in the (3-3)-resonance energy region for the Fermigas model and the shell model of the nucleus. Pair correlations are included. Energy-dependent empirically fitted parameters are used as inputs for the pion-nucleon interaction. For the shell model a downward energy shift of 30-45 MeV, as well as considerable broadening, is predicted for the (3-3) pion-nucleus resonance. Graphs of the differential cross-section for various energies are included, with discussion of some significant features. Effects of inclusion and exclusion of the self-consistency requirement are considered.

Shell-model calculations have been performed for the nuclei ${}_{}{}^{22}{}_{}{}^{}\mathrm{Na}$ and ${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}$. The model space is made up of all Pauli-allowed combinations of six particles in the orbits $0d_{\frac{5}{2}}$, $1s_{\frac{1}{2}}$, and $0d_{\frac{3}{2}}$. An inert ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ core is assumed. The two-body interaction which is employed has been obtained by empirically modifying some of the matrix elements of Kuo's interaction in order to achieve an rms best fit between the observed energies of 72 levels in the $A=18\mathrm{}-22$ region and the corresponding shell-model eigenvalues. Single-particle energies are taken from the ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ spectrum. Calculated results for excitation energies, electromagnetic transition strengths, and spectroscopic factors for single-nucleon transfer are presented and compared with existing data.

Excitation energies of 57 states in ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ from 5.4 to 8.4 MeV were measured with accuracy of ±2 to ±3 KeV. Energies of particles from the ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}(p,p^{\prime }){}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ and ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}(d,\alpha ){}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ reactions were measured with the Notre Dame 50-cm broad-range spectrograph. In the range 5.4 to 7.0 MeV values agree within 5.5 keV with other recent ($p,p^{\prime }$) work and within 4.6 keV with recent $\gamma$-ray work. Systematic discrepancies in the ($p,p^{\prime }$) values increasing to 20 keV at 8.3 MeV are found. Resolution was sufficient to measure excitation energies separated by 5 keV. The existence of two pairs of closely spaced levels in the region of the first $T=\frac{3}{2}$ state was confirmed. The first and second $T=\frac{3}{2}$ levels were identified by the low cross section of the ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}(d,\alpha ){}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ reaction. The value of this accurately measured proton spectrum for calibration purposes is discussed.

The $\gamma$ radiation emitted following thermal-neutron capture in ${\mathrm{Ni}}^{64}$ has been studied in singles and coincidence with 15-, 30-, and 40-${\mathrm{cm}}^3$ Ge(Li) detectors. $\gamma$ rays of the following energies (in keV) and relative intensities (in parentheses) were assigned to ${\mathrm{Ni}}^{65}$: 63.6 (13), 247.1 (0.5), 310.5 (23.0), 382.0 (0.7), 628.8 (7.3), 692.2 (1.5), [726 (0.2)], 1107.4 (3.8), [1418 (0.2)], 2083.8 (0.6), 2147.2 (0.3), 3950.2 (1.1), 4679.5 (3.8), 5405.2 (9.2), 5787.1 (18), 6034.0 (70). All these transitions were incorporated in a level scheme for the ${\mathrm{Ni}}^{65}$ nucleus with levels at the following energies: 63.6 ± 0.3, 310.5 ± 0.2, 692.3 ± 0.3, 1417.9 ± 0.4, and 2147.2 ± 0.5 keV. A lower lifetime limit of $\tau >3\mathrm{}$ μsec was measured and a conversion coefficient $\alpha \sim 5$ deduced for the 63.5-keV state. These are consistent with the ${\frac{1}{2}}^{-}$ assignment made in a study of the ${\mathrm{Ni}}^{64}\mathrm{}(d,p)\mathrm{}{\mathrm{Ni}}^{65}$ reaction. A ${\frac{3}{2}}^{-}$ assignment is suggested for the 310.5-keV state by the branching ratio to the 63.6-keV level and the ground state. The neutron separation energy is 6097.6 ± 0.6 keV for ${\mathrm{Ni}}^{65}$ and 6837.6 ± 1.0 keV for ${\mathrm{Ni}}^{63}$. The strengths of the five observed primary transitions and corresponding proton groups in the ($d,p$) reaction have been compared and a correlation co-efficient of 0.8 obtained. The $\gamma$ decay of the ${\mathrm{Ni}}^{65}$ ground state was also investigated.

Elastic cross sections for electron scattering from ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}$ and ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ are given for the momentum-transfer range from 0.7 to 2.9 ${\mathrm{fm}}^{-1\mathrm{}}$. The data were analyzed by means of a phase-shift code using phenomenological Fermi charge distributions modified with small undulations. The difference of the ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}$ and ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ charge distributions has been compared with a $2s_{\frac{1}{2}}$ proton distribution and with other nuclear models.

${}_{}{}^{28}{}_{}{}^{}\mathrm{P}$ has been formed in the ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}\mathrm{}(p,n)\mathrm{}{}_{}{}^{28}{}_{}{}^{}\mathrm{P}$ reaction at $E_p=16.5\mathrm{} \mathrm{and} 20$ MeV and its $\gamma$-ray spectrum was measured by means of two different target-transfer and Ge(Li) detector systems. $\gamma$-efficiency calibrations of the detectors were carried out with several radioactivity and neutron-capture $\gamma$-ray sources. Nine excited states of ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ up to 9382 keV are found to be populated in ${}_{}{}^{28}{}_{}{}^{}\mathrm{P}$ decay and the various positron and $\gamma$-ray branching ratios have been derived. The ${}_{}{}^{28}{}_{}{}^{}\mathrm{P}$ positron branch to the 1779-keV first excited state of ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ is ${68.4}_{-2.8\mathrm{}}^{+2.0\mathrm{}}$%. Comparison of this with the corresponding mirror ${\beta }^{-}$ decay of ${}_{}{}^{28}{}_{}{}^{}\mathrm{Al}$ gives $\frac{{\mathrm{}\left(\mathrm{ft}\right)\mathrm{}}^{+}}{{\mathrm{}\left(\mathrm{ft}\right)\mathrm{}}^{-}}={0.96}_{-0.03\mathrm{}}^{+0.04\mathrm{}}$ in striking disagreement with the results derived from earlier experimental data. The $\mathrm{ft}$ of (2.95 ± 0.23)× ${10}^3$ sec for ${}_{}{}^{28}{}_{}{}^{}\mathrm{P}$ ${\beta }^{+}$ decay to the ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ $T=1\mathrm{}$ analog state at 9316 keV agrees with that expected for a pure vector transition. A review is presented of mirror symmetry in even-$A$ systems with the conclusion that they do not reveal significant evidence for second class currents.

Differential ($p,2p$) cross sections to various final states have been measured for eight different nuclei in the Ni region at an incident energy of 17 MeV, for the case of protons emerging at an angle of ±90°. The coincident proton energy spectrum shows that the ($p,2p$) reaction consists of a ($p,p^{\prime }$) reaction followed by the boiloff of a proton. An attempt has been made to explain the observed cross sections by assuming that the ($p,p^{\prime }$) reaction is a compound process and that the subsequent proton boiloff is given by statistical theory. In this model, the relative probability for populating various final states depends on the spin cutoff parameter of the decaying compound nucleus, as well as the total radiation width. It is found that it is also necessary to take into account that the proton widths obey a Porter-Thomas distribution in order to reproduce the observed proton-$\gamma$ competition near threshold. The measured total radiation width, using typical values of the spin cutoff parameter, is approximately a factor of 5 below the average values obtained from neutron-capture work and a factor of 2 below the value obtained from an extrapolation of the giant dipole resonance. A direct study of the spin cutoff parameter was possible only for ${\mathrm{Fe}}^{54}$. For the other even-even nuclei, the excited states are weak or obscured by contaminants, while for the odd-even targets, the ($p,p^{\prime }$) spectrum indicates that a significant portion of the ($p,p^{\prime }$) reaction is due to a direct process. The ${\mathrm{Fe}}^{54}$ cross sections are best fit by increasing the value of the spin cutoff parameter to a value above that obtained by assuming a rigid-body value for the moment of inertia.

High-resolution measurements of the $\gamma$ rays following neutron inelastic scattering in ${}_{}{}^{85}{}_{}{}^{}\mathrm{Rb}$ and ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$ have been made for neutron energies between 0.3 and 2.2 MeV. An enriched ${}_{}{}^{85}{}_{}{}^{}\mathrm{Rb}$ scatterer was used for isotopic identification. Eight new levels were assigned in ${}_{}{}^{85}{}_{}{}^{}\mathrm{Rb}$ below 1445 keV excitation and two new levels below 1739 keV were observed in ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$. Branching ratios and differential $\gamma$-ray production cross sections at 95° were also determined.

$\frac{E2\mathrm{}}{M1\mathrm{}}$ mixing ratios of the decays of the 1.62-, 1.37-, and 0.03-MeV states in ${}_{}{}^{28}{}_{}{}^{}\mathrm{Al}$ are obtained from correlation measurements using a ${}_{}{}^{28}{}_{}{}^{}\mathrm{Mg}$ source. The smallness of the measured $E2\mathrm{}$ component in the 1.37 → 0.03-MeV transition disagrees with recent shell-model calculations, but supports a rotational-model interpretation of some low-lying states.

The fractional branch for $\alpha$-particle decay of the 12.15-MeV $6^{+}$ state in ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ to the 6.13-MeV $3^{-}$ state in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ has been measured by coincident detection of 6.13-MeV $\gamma$ rays and $\alpha$ particles from the reaction ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^{12}{}_{}{}^{}\mathrm{C},\alpha ){}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$. The measured width ratio, $\frac{{\Gamma }_{{\alpha }^{\prime }}}{\Gamma }=(6.0\mathrm{}\pm 1.5)\%$, together with the previously known quantity $\frac{{\Gamma }_{{\alpha }^{\prime }}{\Gamma }_{\alpha }}{\Gamma }=7.7\mathrm{}\pm 3.8$ eV, implies a ground-state width of ${\Gamma }_{\alpha }=128\mathrm{}\pm 72$ eV. The corresponding reduced width is about ${10}^{-3\mathrm{}}$ of a single-particle unit: This value is consistent with the known small $\alpha$-particle reduced widths for the $0^{+}$, $2^{+}$, and $4^{+}$ states which have been suggested to be members of a rotational band built on an 8p-4h intrinsic state.

The differential analyzing power, $A\left(\theta \right)$, was measured in the quasielastic ($p,n$) reaction on ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$, ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{116}{}_{}{}^{}\mathrm{Sn}$, and ${}_{}{}^{120}{}_{}{}^{}\mathrm{Sn}$. The energy of the incident polarized proton beam was 24.5 MeV except in the case of ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ where it was 20.3 MeV. The $A\left(\theta \right)\text{'}\mathrm{s}$ were oscillatory with a large forward-angle maximum of ± (0.25 to 0.35). Distorted-wave Born-approximation calculations using a macroscopic model give reasonable agreement with the data for ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ and ${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}$. ${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}$. For the Sn isotopes, good agreement is found when an isospin-dependent spin-orbit term is added to the form factor. The sign of this term agrees with that given by a simple model, but its magnitude is poorly determined due to optical-model ambiguities.

60-point angular distributions for the scattering of $\alpha$ particles to the first four states in ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ ($0^{+}$, $2^{+}$, $4^{+}$, $0^{+}$) were measured from 21 to 28 MeV in 125-keV steps. Fluctuations with full width at half maximum of less than 300 keV were observed in all four channels. Compound-nuclear contributions to energy-averaged data have been estimated (20% to the $2^{+}$ state, 30% to the $4^{+}$ and $0_{4.97}^{+}$ states) at 25.2, 26.2, and 27.2 MeV. Optical-model fits to the elastic scattering and coupled-channel fits to the $0^{+}$, $2^{+}$, $4^{+}$ states give slightly better agreement with an angular-momentum-dependent absorption. The coupled-channel calculations give an over-all poor reproduction of the and it is not possible to extract a hexadecapole deformation for ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$. The extracted value of the quadrupole deformation parameter is ${\beta }_2=-0.26\mathrm{}\pm 0.08$ while an upper limit can be placed on the hexadecapole deformation parameter $\left|{\beta }_4\right|\le 0.1$.

The continuous spectrum of photons accompanying the allowed electron-capture transition from ${}_{}{}^{54}{}_{}{}^{}\mathrm{Mn}$ to the first excited state in ${}_{}{}^{54}{}_{}{}^{}\mathrm{Cr}$, as well as that from ${}_{}{}^{51}{}_{}{}^{}\mathrm{Cr}$ to the first excited state in ${}_{}{}^{51}{}_{}{}^{}\mathrm{V}$ have been measured in coincidence with the nuclear $\gamma$ rays from the deexcitation of these states. The end-point energy of the spectrum from ${}_{}{}^{54}{}_{}{}^{}\mathrm{Mn}$ was determined to be 518 ± 8 keV, which is somewhat at variance with the value 537 ± 4 keV calculated from accepted mass differences. The probability of radiative capture relative to ordinary nonradiative capture was determined to be (15.4 ± 0.8) × ${10}^{-5\mathrm{}}$ for ${}_{}{}^{54}{}_{}{}^{}\mathrm{Mn}$ in the energy range 82-515 keV. This is considerably larger than the value 10.9 × ${10}^{-5\mathrm{}}$ predicted by the relativistic theory of Martin and Glauber. The shape of the photon spectrum is nevertheless in excellent agreement with the theoretical prediction. For ${}_{}{}^{51}{}_{}{}^{}\mathrm{Cr}$ the end point was determined to be 424 ± 16 keV in excellent agreement with accepted mass differences. The relative rate of radiative capture with a photon energy greater than 130 keV was determined to be (7.2 ± 0.4) × ${10}^{-5\mathrm{}}$, in disagreement with the theoretical value of 5.5 × ${10}^{-5\mathrm{}}$, while the spectrum shape agrees excellently with the theory. A survey of the experimental verification of the Martin and Glauber theory is presented.

Target foil stacks of iron were bombarded with beams of helions at incident energies ≤ 70 MeV. $\gamma$ spectra of individual foils were measured and analyzed to obtain excitation functions for production of ${}_{}{}^{56,57}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{55,56,57,58}{}_{}{}^{}\mathrm{Co}$, ${}_{}{}^{52,54,56}{}_{}{}^{}\mathrm{Mn}$, and ${}_{}{}^{51}{}_{}{}^{}\mathrm{Cr}$; for ${}_{}{}^{53}{}_{}{}^{}\mathrm{Fe}$ and ${}_{}{}^{52}{}_{}{}^{}\mathrm{Mn}$, data were obtained for both ground and isomeric states. The yields of ${}_{}{}^{56}{}_{}{}^{}\mathrm{Co}$ and ${}_{}{}^{57}{}_{}{}^{}\mathrm{Co}$ are much larger than those of the respective Ni isobars. Recoil measurements (to determine momentum transfer to the target nucleus) were made at $E_h=41\mathrm{} \mathrm{and} 51$ MeV. These data show ${}_{}{}^{57}{}_{}{}^{}\mathrm{Co}$ to result principally from direct reactions. There is also evidence of a large contribution by direct reactions to the ${}_{}{}^{56}{}_{}{}^{}\mathrm{Co}$ yield. The excitation-function data are compared with predictions of compound-nucleus evaporation theory; these indicate compound-nucleus reactions to be the dominant contributor to the yields of ${}_{}{}^{51}{}_{}{}^{}\mathrm{Cr}$, ${}_{}{}^{52,54}{}_{}{}^{}\mathrm{Mn}$, ${}_{}{}^{52,53}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{55}{}_{}{}^{}\mathrm{Co}$, and ${}_{}{}^{56,57}{}_{}{}^{}\mathrm{Ni}$.

Relative angular distributions of neutrons from the ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}\mathrm{}(p,n)\mathrm{}{}_{}{}^{48}{}_{}{}^{}\mathrm{Sc}$ reaction to four positiveparity states in ${}_{}{}^{48}{}_{}{}^{}\mathrm{Sc}$ have been measured at 11 proton energies between 1.955 and 1.995 MeV. This energy interval encompasses a number of the components of the ${\frac{3}{2}}^{-}$ isobaric analog of the ${}_{}{}^{49}{}_{}{}^{}\mathrm{Ca}$ ground state in ${}_{}{}^{49}{}_{}{}^{}\mathrm{Sc}$. The neutron decay of ${}_{}{}^{49}{}_{}{}^{}\mathrm{Sc}$ in the region of the two largest components is discussed in terms of a model of the ($p,n$) reaction in which the isospin-violating forces are assumed to manifest themselves through boundary-condition mixing only. The gross features of most of the data throughout this energy interval can be described in terms of two $T<\mathrm{}{\frac{3}{2}}^{-}$ states and a number of ${\frac{3}{2}}^{+}$ and ${\frac{5}{2}}^{+}$ levels. The branching ratio for neutron decay to the various levels in ${}_{}{}^{48}{}_{}{}^{}\mathrm{Sc}$ suggests that the two major ${\frac{3}{2}}^{-}$ components have fairly simple but somewhat different shell-model configurations.

Muon absorption is investigated for nuclei with an excess of neutrons in order to answer the question: Are the studies carried out in previous works on $N=Z$ nuclei valid for a larger class of nuclei with $N>Z$ and possibly heavier? If so, to what extent? The present study indicates that the conventional shell-model techniques yield similar results for a more complex class of nuclei. Several selected nuclei are taken as examples; the ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}$ nucleus is thoroughly studied.