It is shown that starting with a correlated wave function for nuclear matter of a general form one may make direct correspondence to the conventional diagrammatic theory of Brueckner, Bethe, and Goldstone. In particular, in this work we show that the expression for the three-body-cluster energy is the same as that obtained by Bethe. Also, it is shown that the current approximation which neglects the potential for particle states in the diagrammatic approach corresponds to a neglect of a coupling between the two-body (Bethe-Goldstone) equation and the equation for the three-body-cluster wave function (Bethe-Faddeev). The theory presented here provides a clarification of the relation of the $n$-body-cluster wave functions and the structure of the wave function of the entire system.

Two classes of two-body Hamiltonians are constructed such that the energy eigenfunctions of the members of each class are identical below some cutoff energy $E_c$. In one class the phase shifts for energies greater than $E_c$ remain fixed for all Hamiltonians in the class, although the corresponding eigenfunctions are different for small distances of separation. In the other class the phase shifts for the various members of the class also differ for energies greater than $E_c$.

The energies of the lowest five $T=1\mathrm{}$ states in ${\mathrm{F}}^{18}$ and ${\mathrm{Ne}}^{18}$ are predicted on the basis of a calculation (a) using a realistic force tuned to fit the ${\mathrm{O}}^{18}$ members of the same multiplets and (b) including the known Coulomb interactions between protons. The nucleons are permitted to be in the $1d_{\frac{5}{2}}$ and $1s_{\frac{1}{2}}$ levels, the latter being described by Woods-Saxon wave functions. Particle-particle, hole-particle, and hole-hole corrections are included. Reasonable agreement with experiment is obtained for all but the excited $0^{+}$ multiplet. It is necessary to introduce a small (short ranges and attractive) charge-dependent force to explain the ${\mathrm{F}}^{18}$ data.

Following Brandow's suggestion of setting $QUQ=0\mathrm{}$, where $U$ is the single-particle potential, the Bethe-Goldstone equation becomes $\Psi =\Phi -\left[\frac{Q}{(QTQ-\omega }\right]v\Psi$. This equation has been approximated by replacing $Q$ with the Eden-Emery Pauli operator and by neglecting $\hat{T}\chi$, where $\hat{T}$ is the off-diagonal part of the c.m. kinetic energy operator in the oscillator representation. Care has been taken to retain $\hat{T}\Phi$, which is a large term. The approximate equation has been solved iteratively. It yields defect functions with the bulk of the effect of $Q$ built in. Correction terms to our approximate results have been estimated. A very satisfactory feature of the present approach is that there is considerable cancellation between the so-called spectral and Pauli correction terms. The biggest correction term is $〈\chi \left|\hat{T}\right|\chi 〉$, which can be as large as 0.5 MeV in the triplet even case.

The Hauser-Feshbach formalism is generalized to include isospin. Examination of the consequences of this extension for typical nuclei indicates that significant enhancement in the cross section for emission of protons in proton-induced reactions is predicted. Level widths and densities deduced from fluctuation measurements are also affected. The results of some proton-induced reactions are interpreted in terms of isospin effects; new experiments are proposed which should yield information on isospin mixing and on level widths for states with differing isospin.

A new mode of positron annihilation has been investigated experimentally. In this annihilation process without emission of radiation, the excess energy liberated is given to the nucleus involved. The experimental evidence for this process was established by observing the conversion electrons from ${}_{}{}^{115m}{}_{}{}^{}\mathrm{In}$, first excited level (335 keV, ${\frac{1}{2}}^{-}$), after irradiation of natural indium foils by positrons from the ${\beta }^{+}$ decay of ${}_{}{}^{22}{}_{}{}^{}\mathrm{Na}$. Using the experimental data obtained, we have attempted to evaluate the cross section for positrons having just the energy corresponding to that necessary to excite ${}_{}{}^{115}{}_{}{}^{}\mathrm{In}$ from the ground state to an excited level which may decay to the isomeric level concerned. The experimental value of the cross section is found to be ∼${10}^{-24\mathrm{}}$ ${\mathrm{cm}}^2$, while the theoretical value estimated by Present and Chen is ∼${10}^{-26\mathrm{}}$ ${\mathrm{cm}}^2$. Possible reasons for this difference are discussed.

The elastic scattering of ${\mathrm{He}}^3$ by ${\mathrm{He}}^4$ at 44.5 MeV (c.m.) is considered within the resonating-group formalism. The existence of open reaction channels is taken into account approximately by the introduction of a phenomenological local imaginary potential into the usual resonating-group formulation of the scattering problem. By choosing the shape and strength of this potential in a reasonable manner, it is found that a fairly good fit to the experimental differential cross section can be obtained in both the forward and the backward directions. From this study it is also found that the contribution to the differential cross section at backward angles comes mainly from exchange processes which are contained in the resonating-group formalism through the use of a totally antisymmetrized wave function. The real part of the phase shift is found to have a distinct odd-even feature, and from this it is shown that if one wishes to describe the experimental scattering data by using a complex local potential, then the real part of this potential must have a significant amount of Majorana space-exchange component.

A simple model of an $S$-state separable $n-p$ and $n-n$ interaction, with a hard-shell repulsion in the singlet state, is applied to study the effect of the charge dependence of nuclear forces on the ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ ground-state energy $E_T$, and on the $n-d$-doublet scattering length ${}_{}{}^2{}_{}{}^{}a$. Several values of the $n-n$-singlet scattering parameters - all within the range of recent experimental estimates - have been used in fixing the parameters of the $n-n$ interaction. All the resulting values of $E_T$ and ${}_{}{}^2{}_{}{}^{}a$ stay close to the Phillips line. This indicates that the charge dependence is not the factor which could help us in accounting for the new experimental values of ${}_{}{}^2{}_{}{}^{}a$ and $E_T$.

The reaction ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}({}_{}{}^{14}{}_{}{}^{}\mathrm{N},\alpha ){}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ has been studied at bombarding energies of 20.2 and 28.0 MeV. Differential cross sections at forward angles were only 0.01 to 0.02 mb/sr for the strongest transitions. It was impossible to identify transitions to the high-spin states that were observed to be selectively populated in recent ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}({}_{}{}^{12}{}_{}{}^{}\mathrm{C},\alpha ){}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^{16}{}_{}{}^{}\mathrm{O},\alpha ){}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ studies.

Using the non-central particle-hole interaction determined from a fit of the energy spectra of the non-normal-parity states in ${}_{}{}^{15}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, and ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$, we have reproduced the energy spectrum of the non-normal-parity states in ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ satisfactorily via a shell-model calculation. The important contribution from $T=1\mathrm{}$ states of ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ coupled to a $1p_{\frac{1}{2}}$ hole in the ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ wave functions is pointed out.

Distorted-wave calculations have been performed for the reaction ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}\mathrm{}(d,p)\mathrm{}{}_{}{}^{19}{}_{}{}^{}\mathrm{O}$ to the ${\frac{5}{2}}^{+}$ ground state and the ${\mathrm{½}}^{+}$ state at 1.467 MeV in ${}_{}{}^{19}{}_{}{}^{}\mathrm{O}$, as well as for the reaction ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}({}_{}{}^3{}_{}{}^{}\mathrm{He},d){}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ leading to the analogs of these states — the (bound) ${\frac{5}{2}}^{+}$ state at 7.540 MeV and the (unbound) ${\mathrm{½}}^{+}$ state at 8.795 MeV in ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$. The resulting spectroscopic factors are in good agreement with each other, although previous work had suggested a discrepancy. However, the spectroscopic factors are only about half as large as the shell-model predictions.

Normal-parity states of the $A=6, 7, 8, \mathrm{and} 9$ systems are calculated within the framework of the ${\mathrm{}\left(0p\right)\mathrm{}}^{A-4\mathrm{}}$ shell-model basis. The two-nucleon interaction matrix elements deduced by the Sussex group are used to compute the interactions between $0p$-shell particles as well as the interactions of individual $0p$-shell particles with the ${\mathrm{}\left(0s\right)\mathrm{}}^4$ core. The only adjustable parameter in the calculation is the oscillator length associated with the shell-model basis, although the range of acceptable values for this parameter is limited by the experimental rms radius for the nucleus under consideration. The agreement between calculated and experimental energy levels is poor. However, a strengthening of the ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ interaction greatly improves the results.

The radiative-pion-capture rate from a number of low-lying Bohr orbits in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ is calculated. It is shown that the peak in the $\gamma$ spectrum is caused by transitions to broad $2^{-}$ and $1^{-}$ resonances in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. The angular correlation of the low-energy neutrons with the direction of the $\gamma$ ray is shown to be strongly dependent on the orbital-angular-momentum value of the Bohr orbit from which capture occurs, thus affording an independent check of atomic deexcitation studies in pionic atoms.

The quasielastic scattering of 50-MeV $\alpha$ particles has been used as a tool to study the cluster configurations of the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ nucleus by means of the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}(\alpha ,\alpha x)Y$ reaction. Data have been obtained in kinematically complete experiments and at exact quasielastic angles for those cases corresponding to $x=p, d, t$, He, and $\alpha$. Analysis has been carried out in the framework of the plane-wave impulse approximation. Quasielastic cross sections have been measured and experimental momentum distributions extracted. Theoretical fits to these distributions using simple Gaussian and exponential functions have been calculated and used to determine both absolute and relative clustering probabilities with fair success. The more reliable relative probabilities indicate strong $p, d$, and $\alpha$ clustering in ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ and rather weak $t$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ clustering.

The damping of single-particle wave functions, using nonlocal potentials derived in the Hartree-Fock (HF), and no-polarization approximations with respect to wave functions obtained from "equivalent" local potentials is investigated for low-energy $n-{}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ scattering. It is found that strong damping due to the HF exchange term occurs only if the basic nucleon-nucleon interaction is nonlocal; when local interactions are used, a small amount of anti-damping occurs. A study is made of the effect of adding two-body correlations to the ground-state target wave function, where it is found that strong damping effects occur for local nucleon-nucleon interactions.

Using the ${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}({}_{}{}^3{}_{}{}^{}\mathrm{He},d){}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$ reaction at a bombarding energy of 15 MeV, excitation energies and angular distributions have been obtained for 96 levels below $E_x=10.2\mathrm{}$ MeV in ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$. Data were recorded in 3.75° steps in a multiangle spectrograph. Angular distributions were compared with distorted-wave Born-approximation predictions; values of transferred angular momentum and spectroscopic strength were extracted for 42 levels, including the three lowest $T=\frac{3}{2}$ states. An empirical forward-angle $J$ dependence has been used to distinguish between $J_f^{\pi }={\frac{3}{2}}^{+}$ and ${\frac{5}{2}}^{+}$ for $l_P=2\mathrm{}$ transfers. The summed $l_P=0\mathrm{}$ and $l_P=2\mathrm{}$ spectroscopic strengths agree with theoretical expectations. The results of the present investigation are combined with previous information and discussed in terms of the rotational model. The low-lying negative-parity states are examined in terms of their particle or hole character. The results for both positive- and negative-parity states suggest significant deviations from the predictions of a simple rotational model, even with band mixing.

22 levels of ${\mathrm{Cl}}^{34}$ below $E_x=4.7\mathrm{}$ MeV are populated by the $\gamma$-ray decay of the three resonances at $E_p=1058, 1098, \mathrm{and} 1121$ keV in the reaction ${\mathrm{S}}^{33}(p,\gamma ){\mathrm{Cl}}^{34}$. These resonances, selected for study because of their dominant modes of $\gamma$ decay to levels above 2.7 MeV for which limited prior data exist, were investigated with an 80-${\mathrm{cm}}^3$ Ge(Li) detector, and with Ge(Li)-NaI coincidence and angular-correlation techniques. The results obtained for levels below 2.3 MeV are in general agreement with other recent work. A new result is a probable $J=3\mathrm{}$ assignment for the 2.180-MeV level. For higher-lying levels, $\gamma$-ray decay schemes and excitation energies with errors in the range from ±0.3 to ±2.3 keV were determined for 14 bound states in the range $2.3<\mathrm{}{E}_x<4.7\mathrm{}$ MeV and the three resonance levels. The reaction $Q$ value was determined with the result $Q=5139.9\mathrm{}\pm 0.9$ keV. The following $J^{\pi }$ assignments (energies in MeV) result from the combination of the present work with a recent ${\mathrm{S}}^{33}({\mathrm{He}}^3,d){\mathrm{Cl}}^{34}$ study: 2.72, $2^{-}$; 3.55, $3^{-}$; 3.60, $4^{\mathrm{}(-)\mathrm{}}$; 3.63, $5^{-}$; 3.77, $1^{-}$; 3.98, $3^{-}$; 4.08, $4^{-}$; 4.14, 2; 4.35, probably $1^{-}$; 4.42, 1, 2, or 3; 4.51, probably $2^{-}$; and 4.64, 2, 1, or 3. The resonance level assignments are $J^{\pi }\mathrm{}\left(1058\right)=3^{\mathrm{}(-)\mathrm{}}$, $J^{\pi }\mathrm{}\left(1098\right)=4^{\mathrm{}(-)\mathrm{}}$, and $J^{\pi }\mathrm{}\left(1121\right)=1^{-}$. It is shown that the three resonances are probably each odd-parity $T=1\mathrm{}$ levels. The probable shell-model configurations of some of the odd-parity levels are discussed.

Differential cross sections of the ($p,n$) reactions have been measured as a function of angle at several proton energies from 2.6 to 5.9 MeV. Neutron groups corresponding to the ground and 21 excited levels have been observed, and excitation energies fixed to within ±5 keV in these measurements. The good agreement between the measured cross sections and those calculated in the Wolfenstein-Hauser-Feshbach (WHF) formalism for levels of known spin and the agreement between measured and calculated neutron angular distributions permitted tentative assignments to many levels of unknown spin. Angular distributions of the ($p,n\gamma$) transitions were measured at 4.9-MeV proton energy, with transitions from 19 excited levels observed. A decay scheme and excitation energies with ±2-keV uncertainty were obtained from the $\gamma$-ray measurements. Analysis of the angular distributions in the WHF formalism together with the neutron measurements provided the following excitation energies in keV and spin assignments: $2272$, $\frac{5}{2}$, $\frac{7}{2}$; $2405$, $\frac{3}{2}$; $2571$, ($\frac{7}{2}$); $2685$, $\frac{7}{2}$; $2949$, $\frac{9}{2}$; $3004$, ($\frac{3}{2}, \frac{5}{2}$); $3199$, $\frac{5}{2}$, $\frac{7}{2}$, $\frac{9}{2}$; $3248$, ($\frac{9}{2}$). Tentative assignments are in parentheses.

The level and decay schemes are in good agreement with mixed-configuration shell-model calculations for the first levels of a given spin. For higher levels the comparison of calculated and measured schemes suggests an inadequate model space in those calculations which allow only one proton excited out of the $f_{\frac{7}{2}}$ shell.

The mean lifetimes of levels of ${}_{}{}^{52}{}_{}{}^{}\mathrm{Cr}$ to 4.5 MeV in excitation energy have been measured by the Doppler-shift-attenuation method. States in ${}_{}{}^{52}{}_{}{}^{}\mathrm{Cr}$ were populated by the reaction ${}_{}{}^{51}{}_{}{}^{}\mathrm{V}-({}_{}{}^3{}_{}{}^{}\mathrm{He},d){}_{}{}^{52}{}_{}{}^{}\mathrm{Cr}$ at 11.0 MeV using natural vanadium targets. $\gamma$ rays were detected with a 37.5-${\mathrm{cm}}^3$ Ge(Li) detector at 30, 90, and 150° to the beam axis. The following mean lifetimes (in units of ${10}^{-13\mathrm{}}$ sec) were found: $\tau (1434\mathrm{}-\mathrm{k}\mathrm{e}\mathrm{V}\mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l})={9.9}_{-2.5\mathrm{}}^{+4.5\mathrm{}}$, $\tau \mathrm{}\left(2369\right)={15.0}_{-2.5\mathrm{}}^{+5.0\mathrm{}}$, $\tau \mathrm{}\left(2766\right)={20}_{-5\mathrm{}}^{+7\mathrm{}}$, $\tau \mathrm{}\left(2965\right)={6.8}_{-1.9\mathrm{}}^{+3.2\mathrm{}},$ $\tau \mathrm{}\left(3114\right)>29\mathrm{}$, $\tau \mathrm{}\left(3162\right)={1.2}_{-0.4\mathrm{}}^{+0.6\mathrm{}}$, $\tau \mathrm{}\left(3414\right)={3.2}_{-0.7\mathrm{}}^{+1.2\mathrm{}}$, $\tau \mathrm{}\left(3469\right)>50\mathrm{}$, $\tau \mathrm{}\left(3472\right)>27\mathrm{}$, $\tau \mathrm{}\left(3617\right)>11\mathrm{}$, $\tau \mathrm{}\left(3947\right)={1.5}_{-0.4\mathrm{}}^{+0.6\mathrm{}}$, $\tau \mathrm{}\left(4015\right)={8.4}_{-2.5\mathrm{}}^{+4.6\mathrm{}}$, $\tau \mathrm{}\left(4040\right)={7.4}_{-2.0\mathrm{}}^{+3.6\mathrm{}}$, $\tau \mathrm{}\left(4563\right)={3.9}_{-0.9\mathrm{}}^{+1.7\mathrm{}}$. The lifetime results combined with the results of previous particle-$\gamma$ correlation experiments indicate $J^{\pi }=4^{+} \mathrm{and} 5^{+}$ for the 3414- and 4015-keV levels, respectively.

The reaction ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}({}_{}{}^3{}_{}{}^{}\mathrm{He},t){}_{}{}^{89}{}_{}{}^{}\mathrm{Zr}$ to $T_{<}$ states in ${}_{}{}^{89}{}_{}{}^{}\mathrm{Zr}$ shows that the angular distributions have shapes characteristic of nonallowed $L$ transfers and are in disagreement with microscopic predictions. The antianalog states appear not to be unique in possessing this feature.