We use the insight gained from the study of analyticity and unitarity to suggest a new method for the construction of the optical potential for strongly interacting particles. The calculational procedures suggested in this work are such as to associate a distinct physical process with each term in our expansion of the optical potential. By starting with various decompositions of the $A$-body target wave function we can obtain theories of varying complexity. Introducing a decomposition with respect to states of the ($A-1\mathrm{}$)-body system, we obtain a construction of the optical potential based upon the single-scattering approximation. If we introduce a decomposition of the target ground state with respect to states of the ($A-2\mathrm{}$)-body system we obtain a more complex theory. In the extended theory, the first-order optical potential of the simpler model is readily extracted along with a second-order potential that depends on the detailed structure of the two-body density matrix of the target. The role of Pauli and short-range correlations in modifying the calculation of the second-order potential is discussed. The physical picture that emerges from this analysis is different from that obtained from multiple-scattering theory, although the two theories are in general agreement as to the nature of the first-order optical potential. When the fixed-scatterer approximation is used to simplify calculations based upon multiple-scattering theory, the second-order optical potential is found to depend on the two-body correlation function. In contrast, for the theory presented here, we find that the inclusion of Pauli and/or short-range correlations is a relatively minor aspect in the construction of the second-order potential. Indeed, we would obtain a second-order potential for an uncorrelated system.

NUCLEAR REACTIONS Optical potentials, unitarity relations, second-order optical potentials, pion absorption, short-range and Pauli correlations, pseudo optical theorem.

For the fully off-shell extension in the relativistic dynamics, based on a covariant light-front field theory, we define the relative momenta and their proper angular variables such that $-1<{cos\theta }_{\alpha }<1\mathrm{}$. In terms of these variables and the timelike total momenta we write explicitly the Weinberg interaction, corresponding to the exchange of a spinless particle of mass $\mu$. The total momentum dependence and the cluster decomposition property of the Weinberg interaction are presented in detail, together with its energy dependence and other nonlocal features. In the nonrelativistic limit we recover the Yukawa interaction, while for the finite masses the Weinberg interaction is a product of the Yukawa interaction and a form factor. The Weinberg two-body force goes to zero at large energies and is truly nonlocal, in spite of the fact that the underlying field theory has a local Lagrangian.

NUCLEAR REACTIONS Relativistic Yukawa interaction, light-front field theory, cluster decomposition property, and nonlocal features.

Ge(Li) detectors have been used to perform singles, coincidence, and angular correlation measurements on $\gamma$ rays present in the decays of 2.5-h ${}_{}{}^{117}{}_{}{}^{}\mathrm{Cd}_{}^g{}_{}{}^{}\left(\frac{1}{2^{+}}\right)$ and 3.4-h ${}_{}{}^{117}{}_{}{}^{}\mathrm{Cd}_{}^m{}_{}{}^{}\left(\frac{11}{2^{-}}\right)$. A total of 112 of the 114 $\gamma$ rays observed in the decay of ${}_{}{}^{117}{}_{}{}^{}\mathrm{Cd}_{}^g{}_{}{}^{}$ and all 71 of the $\gamma$ rays observed in the decay of ${}_{}{}^{117}{}_{}{}^{}\mathrm{Cd}_{}^m{}_{}{}^{}$ have been placed in a level scheme consisting of 46 excited states. A total of 51 different $\gamma -\gamma$ cascades were measured at 90° and 180°. The $\beta$ branchings from ${}_{}{}^{117}{}_{}{}^{}\mathrm{Cd}_{}^g{}_{}{}^{}$ to ${}_{}{}^{117}{}_{}{}^{}\mathrm{In}_{}^m{}_{}{}^{}$ and ${}_{}{}^{117}{}_{}{}^{}\mathrm{Cd}_{}^m{}_{}{}^{}$ to ${}_{}{}^{117}{}_{}{}^{}\mathrm{In}_{}^g{}_{}{}^{}$ were determined to be 20.4% and < 1%, respectively. The thermal neutron cross sections for the production of ${}_{}{}^{117}{}_{}{}^{}\mathrm{Cd}_{}^g{}_{}{}^{}$ and ${}_{}{}^{117}{}_{}{}^{}\mathrm{Cd}_{}^m{}_{}{}^{}$ were determined to be 43±2 mb and 8±1 mb, respectively. Spin and parity assignments for the levels of ${}_{}{}^{117}{}_{}{}^{}\mathrm{In}$ were made in many instances. The level structure is discussed in relation to the unified model calculation and possible one-proton—two-neutron configurations.

RADIOACTIVITY ${}_{}{}^{117}{}_{}{}^{}\mathrm{Cd}_{}^g{}_{}{}^{}$ and ${}_{}{}^{117}{}_{}{}^{}\mathrm{Cd}_{}^m{}_{}{}^{}$ [from ${}_{}{}^{116}{}_{}{}^{}\mathrm{Cd}$($n$,$\gamma$)]; measured $E_{\gamma }$, $I_{\gamma }$, $\gamma -\gamma$ coin, $\gamma -\gamma \left(\theta \right)$; deduced $\beta$ branch, $log\mathrm{ft}$, $\sigma (n,\gamma )$, $A_{22}$, $\delta$. ${}_{}{}^{117}{}_{}{}^{}\mathrm{In}$ deduced levels, $J$, $\pi$. Enriched target, Ge(Li) detectors, Compton suppression.

Starting from the $\mathrm{ds}$-shell interaction of Kuo, orthogonal polynomial and Brillouin-Wigner expansions for effective interactions in the dominant configuration space for low-lying states of ${}_{}{}^{22}{}_{}{}^{}\mathrm{Na}$ ($J=2\mathrm{}$, $T=0\mathrm{}$) have been calculated. Although the states represented have no more than 27% of their strength in the model space, the orthogonal polynomial series converges in low order and good predictions can be obtained with only a third order theory, especially if self consistency is required. For the Brillouin-Wigner expansion, however, we find that higher-order approximations (∼7th order) are required to achieve reasonable accuracy for states lying below the lowest eigenvalue of the interaction in the excluded space. For higherlying states the Brillouin-Wigner self-consistent results diverge.

NUCLEAR STRUCTURE Effective interaction; statistical spectroscopy; orthogonal polynomial expansion; Brillouin-Wigner expansion; renormalization; selfconsistency: ${}_{}{}^{22}{}_{}{}^{}\mathrm{Na}$.

We treat the three-particle problem in nuclear matter for the special class of two-body potentials for which the two-body interaction energy vanishes. We compare the results obtained using the variational method, the Bethe-Faddeev method, and a slightly modified version of the latter in which certain fourth-order diagrams, which can lead to divergences, are eliminated.

NUCLEAR STRUCTURE Bethe-Faddeev, three-body problem in nuclear matter, variational method.

A shell-model calculation of high-spin phenomena in the highly neutron deficient Ba-Ce-Nd region is reported. An inert spherically symmetric $Z=50=N$ core is assumed with extracore nucleons distributed among the $g_{\frac{7}{2}}$, $d_{\frac{5}{2}}$, $d_{\frac{3}{2}}$, $s_{\frac{1}{2}}$ normal-parity orbitals and the unique parity $h_{\frac{11}{2}}$ orbital with the number of particles within each set fixed. The normal-parity subspace is further truncated to a single irreducible representation of pseudo SU(3) made effective through the mapping $\left(g_{\frac{7}{2}}{d}_{\frac{5}{2}}{d}_{\frac{3}{2}}{s}_{\frac{1}{2}}\right)\to \left({\tilde{f}}_{\frac{7}{2}}{\tilde{f}}_{\frac{5}{2}}{\tilde{p}}_{\frac{3}{2}}{\tilde{p}}_{\frac{1}{2}}\right)$. A five-dimensional quasispin classification is used for the unique-parity $h_{\frac{11}{2}}$ space which is restricted to states with seniority zero and two. Using a surface delta interaction we are able to reproduce the observed backbending in ${}_{56}{}^{126}{}_{}{}^{}\mathrm{Ba}_{70}^{}{}_{}{}^{}$. The model affords a microscopic look at Coriolis antipairing and pair realignment phenomena.

NUCLEAR STRUCTURE ${}_{56}{}^{126}{}_{}{}^{}\mathrm{Ba}$; Shell-model interpretation of backbending, pair realignment, and Coriolis antipairing; $h_{\frac{11}{2}}$; $g_{\frac{7}{2}}{d}_{\frac{5}{2}}{d}_{\frac{3}{2}}{s}_{\frac{1}{2}}$ configurations with pseudo-S${\mathrm{U}}_3$ truncation.

Previously developed techniques which sum the squares of proton single particle wave functions to obtain nuclear charge densities are applied to the study of neutron distribution in ${}_{}{}^{40,48}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{58,64}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{116,124}{}_{}{}^{}\mathrm{Sn}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ by comparing to those neutron densities deduced from 800 MeV proton elastic scattering data. The proton and neutron single particle wave functions are derived from a one-body, nonlocal Woods-Saxon binding potential whose parameters are adjusted to give the experimental single particle energies. Empirical spectroscopic factors determine the appropriate occupation probabilities for the single particle levels near the Fermi surface. Proper attention is given to nonorthogonality problems and to the removal of the spurious center-of-mass motion. These semiphenomenological neutron densities are compared to the predictions of the density matrix expansion variant of Hartree-Fock theory and to densities which are empirically deduced from recent 800 MeV polarized proton elastic scattering data. These "experimental" neutron distributions are obtained from approximate second order Kerman, McManus, and Thaler optical potential analyses using essentially "model independent" neutron densities. Qualitatively good agreement is obtained between the semiphenomenological neutron densities computed here, the density matrix expansion predictions, and the empirical results.

NUCLEAR STRUCTURE Sums of squares of single particle wave functions; nonlocal potentials; nonorthogonality effects; computed proton and neutron one-body densities for ${}_{}{}^{40,48}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{58,64}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{116,124}{}_{}{}^{}\mathrm{Sn}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$.

The possibility of taking plane-wave orbitals of a Hartree-Fock determinant to fill $k$ space differently from the "normal" Fermi sphere is investigated for several two-body potentials including the "homework" $v_0$, $v_1$, and $v_2$—taken from the Reid nucleon-nucleon force—as well as a sum-of-Gaussians potential chosen to fit the deuteron binding and size. A random-search and random-walk numerical algorithm shows that, provided the potential strengths are made large enough, a single-shell "abnormal" occupation is always found to be lower in energy than the normal one if sufficient attraction is present in the two-body interaction. No abnormal occupation is possible for, among other pair interactions, the electron or charged-boson fluid, the repulsive square barrier, and a common form of the He-He interaction.

NUCLEAR STRUCTURE plane-wave Hartree-Fock; nuclear matter.

The validity of the results of finite basis, constrained variational calculations with unbounded operators has remained unquestioned despite the mathematical difficulties in an infinite basis pointed out by Fonte and Schiffrer. It will be shown here that the difficulties associated with unbounded operators are not restricted to infinite bases and that, in fact, the consequences are equally severe in finite bases. The demonstration will be made both for a one dimensional, one body model and in a full three dimensional, many body calculation typical of those currently being employed in nuclear physics. The correct procedure for imposing such constraints, e.g. the quadrupole constraint, and the validity of previous calculations remain open questions.

NUCLEAR STRUCTURE Nonconvergence of variational calculations studied in finite bases.

We reply to the criticism of our method for the analysis of doorway fine structure.

NUCLEAR REACTIONS Analysis of doorway fine structure.

A search for $2\hslash \omega$ $M1$ excitations in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ has been made under conditions of maximum sensitivity by means of 180° scattering of 60 MeV electrons. The results do not show the strength predicted by Speth et al.

NUCLEAR REACTIONS ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$($e$,$e^{\prime }$), $E=60\mathrm{}$ MeV, $\theta =180\mathrm{}°$, measured $\sigma (E,180\mathrm{}°)$.

A direct relationship is demonstrated between the interacting boson approximation and the conventional quasiparticle formalism. Numerical calculations are carried out for the Sn isotopes using a Hamiltonian derived from a realistic nucleon-nucleon interaction.

NUCLEAR STRUCTURE quasiparticle formalism, interacting boson approximation.

States in ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$ with spins between $\frac{9}{2}$ and $\frac{27}{2}$ have been observed with the ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$($\alpha$,$2n\gamma$) reaction at 35.9 MeV. The previously reported ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$ decay scheme is corrected.

NUCLEAR REACTIONS ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$($\alpha$,$2n\gamma$)${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$; measured $\gamma -\gamma$ coincidence, $I(E_{\alpha },{\theta }_{\gamma })$, $E_{\gamma }$; deduced $J^{\pi }$. Enriched target, Ge(Li) detectors.

Inclusive ($p$,${\pi }^{+}$) cross sections have been measured for fourteen targets from ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$ to ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ at ≈ 8 MeV and ≈ 16 MeV above threshold by detecting ${\mu }^{+}$ decays. The cross sections are largest near mass 40 and increase rapidly with excitation energy.

NUCLEAR REACTIONS ($p$,${\pi }^{+}$) $A$ dependence, $T_p-T_{\mathrm{threshold}}: 8-16$ MeV, measured inclusive cross sections.

Remarkably similar bell-shaped angular distributions are observed in the ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$($p$,$p^{\prime }$) reaction at 40 MeV to some negative parity states in ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$. Two-step ($p$,$d$,$p^{\prime }$) coupled channel calculations give a good account of these angular distributions.

NUCLEAR REACTIONS ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$($p$,$p^{\prime }$)${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, $E=40\mathrm{}$ MeV; measured $\sigma (E_p;\theta )$, $E_p=8.864, 9.148, \mathrm{and} 11.293$ MeV; CRC ($p$,$d$,$p^{\prime }$) calculations, deduced reaction mechanism.

It is shown that non-plane-wave single-particle Hartree-Fock orbitals giving rise to a "spin-density-wave-like" structure give lower energy than plane waves beyond a certain relatively low density in both nuclear and neutron matter with homework pair potentials $v_1$ and $v_2$.

NUCLEAR STRUCTURE Nuclear matter, Hartree-Fock: nuclear structure.

Angular distributions have been measured for the ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$($p$,$n$)${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$(0.0 and 3.95 MeV) reactions at $E_p=35\mathrm{}$ MeV. The differential cross sections for the two $1^{+}$ states (0.0 and 3.95 MeV) have been compared with antisymmetrized distorted-wave Born-approximation calculations based on phenomenological and realistic effective two-nucleon interactions. In contrast to recent analyses of spin-sensitive measurements, the ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$($p$,$n$)${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$(g.s.) data definitely favor the inclusion of an isovector ténsor interaction.

NUCLEAR REACTIONS ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$($p$,$n$)${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, $E=35\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$. DWBA analysis, deduced tensor force.

The $S$- and $D$-state components of the deuteron-triton overlap integral and of the form factor required for a distorted-wave Born-approximation analysis of ($d$,$t$) reactions have been calculated for a number of variational triton wave functions corresponding to realistic nucleon-nucleon potentials. It is found that the calculated overlap functions decay too rapidly for large $n-d$ separations, and this has important consequences for the corresponding distorted-wave Born-approximation form factors. In particular, the parameter $D_2$, which measures the relative importance of the $D$-state form factor in the low-momentum limit, is found to be more than a factor of 2 smaller than the best experimental value. A more direct calculation of the form factors leads to a much larger value of $D_2$.

NUCLEAR REACTIONS DWBA theory; calculated deuteron-triton overlap and form factors for ($d$,$t$) reactions.