Radiative pion capture on nucleons is studied in a chiral bag model at pion laboratory momenta in the range $q_L$∼300–500 MeV. We calculate dσ/dΩ and L-R asymmetry. Through detailed balance and time reversal invariance we also calculate dσ/dΩ and P(θ) (nucleon recoil polarization) for pion photoproduction at equivalent photon laboratory momenta. A detailed comparison is made with the data.

The ‘‘optimal’’ approximation in the presence of the realistic nucleon-nucleon forces is tested for the proton-deuteron elastic scattering in the laboratory kinetic energy range between 100 and 450 MeV. The particular emphasis is put on the large scattering angles where the corrections to the pd scattering amplitude are governed by the energy derivative of the off-shell nucleon-nucleon amplitudes. At 180° the second-order relative corrections amount to 10 or 20 % in the energy range up to 320 MeV and are much larger at higher energies, especially at about 400 MeV—the energy corresponding to the zero of the scalar deuteron form factor. In the forward direction the corrections are very small: 1 to 5 %. Their maximum values are found for the proton-bound neutron scattering at the intermediate angles close to 90°.

Using a relativistic nuclear model, we derive the effects of nuclear binding on the parton distribution functions. The probability of finding a parton in a nucleus with fractional $x_A$ momentum is a convolution of the nucleon distribution function in the nucleus with the parton distribution function in the nucleon. Expressions which include nucleon transverse momentum smearing are derived. Figures are presented, and comparisons are made of the parton momentum distributions per nucleon in different nuclei. Finally, we applied the formalism to the production of massive lepton pairs in nuclear collisions (Drell-Yan process).

We have utilized a rapid-transport target system together with a β-ray range telescope to remeasure the half-lives of the N=Z, odd-odd nuclei ${}_{}{}^{66}{}_{}{}^{}\mathrm{As}$ and ${}_{}{}^{70}{}_{}{}^{}\mathrm{Br}$. We find they are 95.77±0.28 ms and 78.54±0.59 ms, respectively. The ${}_{}{}^{66}{}_{}{}^{}\mathrm{As}$ result is in good agreement with the previous study, while the ${}_{}{}^{70}{}_{}{}^{}\mathrm{Br}$ measurement differs somewhat from the previous result.

We have searched for the l-forbidden beta decay of ${}_{}{}^{207}{}_{}{}^{}\mathrm{Tl}$ to the first excited state of ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$ by looking for 570-keV γ rays following the decay of ${}_{}{}^{207}{}_{}{}^{}\mathrm{Tl}$. We find a branching ratio of (2.4±5.6)×${10}^{\mathrm{-}7}$ per ${}_{}{}^{207}{}_{}{}^{}\mathrm{Tl}$ decay. This limit could provide a test for calculations of core polarization, meson exchange, and Δ excitation effects. We also find a branch of (0.54±0.05)% for the l-forbidden M1 transition ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$(898,(3/$2^{\mathrm{-}}$→570,(5/$2^{\mathrm{-}}$) and measure the intensities of γ rays emitted following the decay of ${}_{}{}^{211}{}_{}{}^{}\mathrm{Pb}$.

In exotic decay studies, the branching ratios for spontaneous emissions of fragments heavier than alpha particle have been found to be very sensitive to the shape of the potential barrier. In order to fix the top of barrier correctly, finite range effects are included in our calculations. Experimental Q values for different decay modes are chosen so as to incorporate the shell effects. The shape of the barrier in the overlapping region is approximated by a third-order polynomial suggested by Nix. The cubic barrier is found to be more suitable near the penetrating region. This model is applied to calculate the branching ratios for the spontaneous emission of heavier fragments. The results obtained compare well with those of other theoretical models and experimental values.

Experimental values of magnetic dipole transition strengths between states of sd-shell (A=17–39) nuclei are analyzed with one-body transition densities from complete-space 0$d_{5/2}$-1$s_{1/2}$-0$d_{3/2}$ shell-model wave functions in order to extract empirical values for the higher-order corrections to the model M1 operator. These corrections, or renormalizations, are obtained in terms of the values of the effective single-particle matrix elements which, when combined with the model transition densities, yield a minimum deviation of the model predictions for M1 strengths from a set of selected experimental values. A total of 250 experimental data are investigated. Confirmation that the particular realizations of shell-model wave functions employed in the analysis of the data yield adequate descriptions of the actual nuclear states, and that the set of experimental data provides a thorough and accurate sampling of the relevant phenomena, are prerequisites to obtaining meaningful results from this procedure. These issues are studied with a variety of tests of the internal consistency of the procedures used.

A study is made of β vibrations in the O(6) limit of the proton-neutron interacting boson model. Using the procedure of Hatch and Levit, the β dependence of the classical limit of an O(6) proton-neutron interacting boson model Hamiltonian is deduced, and the associated eigenvalues are found. The states corresponding to single β-vibration quanta are pure in the O(6) classification, belonging to the second representations from both the [N,0] and [N-1,1] symmetries. This is in contrast to the U(5) limit, where the antisymmetric β vibration corresponds to the lowest mixed-symmetry level.

The relationship between the apparently successful result for the triton binding energy obtained from the static Bonn potentials and the underlying meson theory is investigated. The triton binding is shown to be strongly dependent upon mesic retardation and associated explicit energy dependences in the meson theory of the nucleon-nucleon interaction. Because it is a much closer representation of the full interaction than are its energy-independent counterparts, the energy-dependent one-boson-exchange potential representation of the Bonn interaction is used to gauge the implications of the full interaction. This one-boson-exchange potential, with or without corrections to adapt it for use in conjunction with nonrelativistic (Schrödinger) three-body equations, predicts a triton binding of only ∼6.7 MeV, as compared to a result of about 8.4 MeV obtained with the energy-independent potentials. This difference is traced to the combination of the explicit energy-dependence and the implicit energy dependence introduced through the tensor force, especially in the ${}_{}{}^3{}_{}{}^{}\mathrm{S}_1^{}{}_{}{}^{}$ partial wave. This provides a new perspective on the success of the static Bonn potentials relative to other realistic potentials and relative to the meson-theoretic framework. Implications, especially with regard to the need for investigations of consistent three-body forces, are discussed.

Simple phenomenological two-state coexistence models have previously been developed to describe the ground state and some low-lying $0^{+\mathcal{’}}$ excited state in isotopic chains of even-even medium-mass nuclei. Specifically, these models allow for mixing between a basis ground state and a basis $0^{+}$ intruder state to form the wave functions for the physical ground state and $0^{+\mathcal{’}}$ excited state. The amount of data accounted for by these models is amazing, considering their simplicity. However, these two-state phenomenological models contain inconsistencies that have previously been overlooked. We point out some of these inconsistencies and emphasize that they can be removed by a slight generalization of the two-state coexistence model, without destroying agreement between data and model predictions.

The Virginia NN potential, which is based on an effective quark interchange mechanism at medium and long distances and is supplemented by a six-quark core potential with a P-matrix type parametrization, is used for calculating the triton binding energy. We find that (i) the triton binding energy is sensitive to the six-quark core radius b, (ii) the 34-channel triton calculation yields 8.04 MeV, which is 0.4–0.5 MeV larger than the realistic potential model results.

Overhauser’s suggestion that plane-wave orbitals, which yield a homogeneous-density fluid phase, may not correspond to the ground state of nuclear matter is investigated by an approximate analytic method. Wave functions constructed from so-called Overhauser orbitals, which lead to an oscillating-density crystalline solid phase, are shown to yield an energy gain over the plane wave orbitals only at densities well below the saturation density ${\rho }_0$∼0.17 ${\mathrm{fm}}^{\mathrm{-}3}$. This is in good agreement with previous numerical results. The analytic solution is then generalized to finite temperatures and it is found that the solid phase can survive up to temperatures of approximately 1.1 MeV only. Nuclear matter in the solid phase is similar to an intrinsic semiconductor with an energy gap occurring at the Fermi energy. The gap decreases with the rise in temperature until the melting point is reached where it discontinuously jumps to zero indicating that the transition is of first order.

A procedure is given for defining explicitly the noncollective states of the degenerate schematic model for nuclear particle-hole configurations. The method is based on the view that the degenerate model is an approximation to the nondegenerate particle-hole model. In the collective-noncollective basis with a single force type, the separable particle-hole Tamm-Dancoff Hamiltonian matrix is transformed into one which is diagonal except for the row and column of the one collective state. The multipole strength of any noncollective state of the nondegenerate problem is given in perturbation theory in terms of the collective-noncollective matrix elements, which are expressed in terms of the parameters of the assumed separable multipole interaction. Application of the sharing formulas is made to Landau damping of the collective state due to mixing with the noncollective states. The relative contribution to the width due to the nondegeneracy and the nonseparable nature of the interaction are examined. Another application examines the random-phase-approximation energy distribution of isospin shared by the isoscalar and isovector collective states with the noncollective states over the giant quadrupole resonance region in ${}_{}{}^{118}{}_{}{}^{}\mathrm{Sn}$.

Coefficients of fractional parentage (CFP’s) in an L-S (or J-T) coupling scheme have recently been computed by using a new algorithm extending two procedures introduced many years ago: a factorization procedure introduced by Jahn and a combination of numerical and analytic methods introduced by Bayman and Lande. As a consequence of the factorization, coefficients of fractional parentage between states of arbitrary permutational symmetry must be computed within each angular momentum subspace separately. The new algorithm is extended here to calculate Hamiltonian matrix elements in the second quantized formalism. The matrix elements of the creation and annihilation operators, within each individual subspace, between states of arbitrary symmetry, are defined to be proportional to the corresponding coefficients of fractional parentage. The matrix elements for the one- and two-body operators in the Hamiltonian are constructed by combining the matrix elements in the individual subspaces using a new sum-over-path-overlaps technique. This procedure is extremely efficient for quark shell model calculations, where the quarks carry multiple quantum numbers of angular momentum, or more general, type (L, S, color, and flavor).

The matrix elements of the pair field between orbitals of a deformed rotating potential as a function of the rotational frequency are studied within a semiclassical model. The oscillations, which were previously found by solving the motion of nucleons in an $i_{13/2}$ orbital, arise from the interference between the single-particle motion at the crossing points of an orbit with the time reversed of its partner.

A microscopic method for analyzing the properties of even-even nuclei in terms of many interacting bosons is proposed. An exact boson image of the underlying shell-model Hamiltonian is derived and the dynamical behavior of the original fermion system is studied directly in the boson picture using the mean-field approximation. The resulting ideal boson states are shown to be free from the admixtures of spurious components, so that the cumbersome procedure of constructing the physical boson states can be avoided. The method is applied to calculating the energy spectra as well as the electron scattering form factors for the $0^{+}$→$0^{+}$ and $0^{+}$→$2^{+}$ transitions in ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$. In all the cases under consideration, the agreement with experimental data is very good. The effect of the space truncation on the results is investigated as well.

A description of the intrinsic (geometrical) structure of the Sp(6) fermion dynamical symmetry model is presented using the coherent state method. A detailed analytical study of the critical behavior of this model is given for the intrinsic ground state as a function of the fundamental control parameter: the valence particle number. The results show that the effect of the Pauli principle is to ‘‘limit’’ the deformation and to cause a transition from axial to triaxial symmetry.

It is found that exact and perturbative treatments of the imaginary potential at sub-Coulomb energies in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$${+}^{12}$C provide close agreement in calculations of both the real and imaginary phase shifts at energies away from resonance.

We have measured cross sections and analyzing powers for ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$(p,p’) at $E_p$=135 MeV, observing the ${(3/2\mathrm{}}^{\mathrm{-}}$ and ${(5/2\mathrm{}}^{\mathrm{-}}$ members of the ground-state rotational band. Folding model calculations were performed using a density-dependent effective interaction in the local density approximation. The quadrupole contribution to elastic scattering was evaluated in distorted wave approximation. We find the elastic quadrupole contribution to be important for q>1.5 ${\mathrm{fm}}^{\mathrm{-}1}$, in good agreement with data. The effect on the elastic analyzing power data is quite large.

We propose a new method to calculate the particle-hole Green’s function for an infinite system of fermions in the long-wavelength limit of the random-phase approximation. Contrary to the standard approach the present method does not require approximating the residual particle-hole interaction by a sum of separable terms. The method can also be applied to the Landau theory of Fermi liquids. We illustrate the method by evaluating the response function of nuclear matter in the long-wavelength limit for two different isospin channels.