The $\beta$ decay of ${}^{37}$K is studied in detail. Several new $\beta$ decay branches and $\gamma$-ray transitions are assigned to this nucleus. The $l$-forbidden ${0d}_{3/2}\to {1s}_{1/2}$ Gamow-Teller branch to the first excited state in ${}^{37}$Ar is observed for the first time and its branching ratio measured to be $(42.2\mathrm{}\pm 7.5)\times {10}^{-6}$. Such $l$-forbidden branches are very sensitive to extranucleonic effects such as meson-exchange currents and $\Delta$-isobar excitations. A calculation of these as well as core-polarization and relativistic effects, predict branching ratios of $8\times {10}^{-6}$ with universal $s$-$d$ wave functions and $52\times {10}^{-6}$ with Chung-Wildenthal wave functions.

The high-spin structure of odd-odd ${}^{86}$Nb was studied with the early implementation of GAMMASPHERE using 36 Compton-suppressed Ge detectors and the MICROBALL, a 95-element full-sphere charged-particle detector array. High-spin states were populated using the ${}^{58}$Ni${(}^{32}$S,$3pn)$ reaction at 135 MeV with beams from the 88-Inch Cyclotron at Lawrence Berkeley National Laboratory. A number of bands were observed up to spins as high as ${(31\mathrm{}}^{-})$. The yrast positive-parity band shares many characteristics with the $\pi g_{9/2}\otimes \nu g_{9/2}$ bands in other odd-odd $f$-$p$-$g$ shell nuclei. These similarities include the behavior of the moments of inertia, the magnitude and phase of the signature splitting and its phase reversal near the ${10}^{+}$ state, and the strong alternations in the $B\left(M1\mathrm{}\right)/B\left(E2\mathrm{}\right)\mathrm{}$ strengths. The moments of inertia in the lowest pair of negative-parity bands start out with a sharp upbend and then gradually fall back to the rigid-body value. New positive- and negative-parity bands appear in the quasiparticle alignment region and eventually become yrast. Some additional positive-parity states around spin $17ħ$ are candidates for fully or nearly fully aligned shell-model-like configurations.

We present a calculation of nuclear matter which goes beyond the usual quasiparticle approximation in that it includes part of the off-shell dependence of the self-energy in the self-consistent solution of the single-particle spectrum. The spectral function is separated in contributions for energies above and below the chemical potential. For holes we approximate the spectral function for energies below the chemical potential by a $\delta$ function at the quasiparticle peak and retain the standard form for energies above the chemical potential. For particles a similar procedure is followed. The approximated spectral function is consistently used at all levels of the calculation. Results for a model calculation are presented, the main conclusion is that, although several observables are affected by the inclusion of the continuum contributions, the physical consistency of the model does not improve with the improved self-consistency of the solution method. This is in contrast to expectations based on the crucial role of self-consistency in the proofs of conservation laws.

A parametrization is proposed for hexadecapole tensors, which observes symmetries coming from the $O_h$ group of transformations of the frame of reference defined through the quadrupole deformation and/or the rotation axes. A possible dependence of the hexadecapole deformation parameters on the quadrupole deformation is discussed. The inclusion of octupole deformation is considered.

The axially symmetric rotor plus quasiparticle model for an odd nucleus is generalized to the odd-odd nucleus and special attention is paid to the model basis accounting for γ vibration perturbation around axial symmetry. The method presented in this paper is used for a number of realistic nuclei in the $A=160\mathrm{}$ mass region. Two slightly different calculation schemes are put into practice. The first calculation gives results in qualitative agreement with experiments and the second calculation provides remarkable improvements to the first. A possible explanation of the mechanism for signature inversion of odd-odd nuclei is discussed.

The phenomenon of band termination of the nuclear collective rotation has been originally discussed by Bohr and Mottelson. The scenario is the following: In the high-spin rotational nucleus, the effect of the Coriolis term produces a tendency to align the angular momenta of individual single particles in a deformed rotating mean field in the direction of the rotation axis. This rotational alignment of the orbits of individual particles tends to create a density distribution symmetric about the rotation axis. The band termination of collective rotation is thus expected, when the density distribution about the rotation axis becomes symmetric, with the total angular momentum being the sum of the contributions of aligned individual particles. The main purpose of this paper is to formulate this scenario of the band termination from the standpoint of nuclear many-body problems and disclose the dynamical mechanism of occurrence of the band termination. It is clarified that the band termination occurs when the intrinsic state in the rotating frame cannot be stable against a variation toward an increase of the collective angular momentum. It is also shown that the value of the collective angular momentum at the band termination is simply an inflection point of the collective rotational energy. The behavior of the single-particle orbitals in the rotating frame is justified and visualized to be in accordance with the scenario of Bohr and Mottelson.

The investigation deals with the relationship between different root-mean-square (rms) radii of light atomic nuclei. The formalism developed operates with translationally invariant operators and intrinsic (antisymmetric in respect to all nucleons and translationally invariant) wave functions. It is shown that at the given matter (pointlike nucleon) rms radius $R_m$ there exist well-defined model-independent lower and upper bounds for pointlike neutron ${(R}_n)$ and point-like proton ${(R}_p)$ rms radii. The neutron skin, defined as the difference of the maximal value of $R_n$ and the minimal value of $R_p$ for many light nuclei with neutron excess, is close to the corresponding model-dependent value, derived analyzing experiments with high-energy radioactive nuclear beams [I. Tanihata, T. Kobayashi, O. Yamakava, S. Shimoura, K. Ekuni, K. Sugimoto, N. Takahashi, T. Shimoda, and H. Sato, Phys. Lett. B 206, 592 (1988)]. It is shown, that in some cases ${(}^{14}$Be, ${}^{14}$B, ${}^{15}$B) it can be larger than those predicted in the work mentioned above.

An exactly solvable model suitable for the description of single- and double-beta decay processes of the Fermi type is introduced. The model is equivalent to the exact shell-model treatment of protons and neutrons in a single-$j$ shell. Exact eigenvalues and eigenvectors are compared to those corresponding to the Hamiltonian in the quasiparticle basis (qp) and with the results of both the standard quasiparticle random phase approximation (QRPA) and the renormalized one (RQRPA). The role of the scattering term of the quasiparticle Hamiltonian is analyzed. The presence of an exact eigenstate with zero energy is shown to be related to the collapse of the QRPA. The RQRPA and the qp solutions do not include this zero-energy eigenvalue in their spectra, probably due to spurious correlations. The meaning of this result in terms of symmetries is presented.

Cross sections for $\mathrm{pp}\to \mathrm{pn}{\pi }^{+}$ have been measured at incident proton energies of 294.3, 299.3, 306.3, 314.1, and 319.2 MeV $(0.11<\eta <0.42)$ to investigate hadronic ${\pi }^{+}$ production near threshold. Pion angular distributions are presented for 294.3, 299.3, and 319.2 MeV. At 294.3 and 299.3 MeV they are consistent with isotropy, indicating $s$-wave dominance for the angular momentum of the ${\pi }^{+}\mathrm{pn}$ system. The shapes of the $\mathrm{pn}$, $n{\pi }^{+}$, and $p{\pi }^{+}$ invariant mass distributions provide further evidence for dominance of $s$-wave mechanisms close to threshold. At 319.2 MeV significant anisotropy indicates contributions from higher partial waves. The total cross sections show an energy dependence consistent with an early partial conservation of axial current based calculation and with a recent calculation that considers only $s$-wave contributions. Tentative values for the strongest contributing partial wave amplitudes are presented.

The low-lying excitation spectra of ${}^{11}$Be and ${}^{19}$O have been calculated on the basis of particle-vibration coupling model. Experimentally observed parity inversion of the ground state and first excited state of ${}^{11}$Be has been reproduced. A fairly good agreement with experiment is obtained regarding excitation energies and spectroscopic factors for both nuclei. Calculated neutron rms radii confirm the observed neutron halo for these nuclei.

The formalism of the relativistic (or Dirac-) Brueckner approach in infinite nuclear matter is described. For the nucleon-nucleon interaction the one-boson exchange potentials Bonn $A,B,C$ and for comparison the Walecka model, are used. The $T$ matrix is determined from the Thompson equation and is projected onto five covariant amplitudes. By the restriction to positive energy states an ambiguity arises in the relativistic Brueckner approach which is discussed here in terms of the pseudoscalar and the pseudovector projection. The influence of the coupling of the nucleon via the $T$ matrix as an effective two-nucleon interaction to the nuclear medium is expressed by the self-energy. In particular we investigate the scalar and vector components of the self-energy for the different one-boson exchange potentials and discuss their density and momentum dependence. We estimate the uncertainty of the self-energy due to the pseudoscalar and the pseudovector choice. Usually the momentum dependence of the self-energy is thought to be weak, however, we find that this depends on the one-boson exchange potentials. For the Bonn potentials, in contrast to the $\sigma \omega$ potential, the momentum dependence is strikingly strong above as well as below the Fermi surface. We compare with the results of other groups and study the effects on the equation of state and the nucleon optical potential.

Pairing correlations in symmetric nuclear matter are studied within a relativistic mean-field approximation based on a field theory of nucleons coupled to neutral $(\sigma$ and $\omega )$ and to charged $\left(\varrho \right)$ mesons. The Hartree-Fock and the pairing fields are calculated in a self-consistent way. The energy gap is the result of a strong cancellation between the scalar and vector components of the pairing field. We find that the pair amplitude vanishes beyond a certain value of momentum of the paired nucleons. This fact determines an effective cutoff in the gap equation. The value of this cutoff gives an energy gap in agreement with the estimates of nonrelativistic calculations.

The shell structure of superheavy nuclei is investigated within various parametrizations of relativistic and nonrelativistic nuclear mean-field models. The heaviest known even-even nucleus ${}_{156}^{264}{\mathrm{Hs}}_{108}$ is used as a benchmark to estimate the predictive value of the models. From that starting point, doubly magic spherical nuclei are searched in the region $Z=110\mathrm{}-140$ and $N=134\mathrm{}$–$298$. They are found at $(Z=114\mathrm{},N=184)$, $(Z=120\mathrm{},N=172)$, or at $(Z=126\mathrm{},N=184)$, depending on the parametrization.

Small-angle $p$-$p$, $p$-$d$, $d$-$\alpha$, and $\alpha$-$\alpha$ correlation functions were measured following the reaction ${}^{16}$O+${}^{27}$Al at 40 MeV/nucleon ${}^{16}$O. These light charged particles (LCP’s) were measured with a closely packed hexagonal array of CsI detectors, located at $35°$, with a center to center opening angle of 2.35$°$ for adjacent detectors. Coincident particles were simultaneously detected in the NSCL $4\pi$ detector. This measurement was intended to be a complement to earlier results from the same system. Based on studies of this system at lower energies and other published correlation measurements, it was expected that at 40 MeV/nucleon there would be significant positive correlations from the nuclear force and deep anticorrelations from Coulomb repulsion. However, correlation functions from this higher energy are remarkably similar to those previously measured at $\approx$15 MeV/nucleon. Correlation functions formed from events with a high multiplicity or high total detected energy (central collisions) are not significantly different from the inclusive measurements. As a possible explanation we suggest that significant correlations are most readily seen in experiments sensitive to LCP’s from fast preequilibrium processes and that measurements at more backward angles are primarily sensitive to LCP’s from a longer-lived source formed after preequilibrium processes are done. This idea is supported by trends of $p$-$p$ correlation functions from a wide range of systems. A schematic calculation based on a Boltzmann-Ueling-Uhlenbeck (BUU) model and statistical emission qualitatively reproduces the results from this work.

Reaction cross sections have been measured at energies ranging from 50 to 70 MeV/nucleon for a variety of exotic neutron rich isotopes of Ar, K, Ca, and Sc. A method where Si detectors are used also as targets has been utilized for the measurements. The strong absorption radii $r_0^2$ have been determined and compared to the results of Glauber-type calculations which used density distributions extracted from the relativistic mean field theory. The isospin dependence of the radii was investigated and a trend similar to the one for lighter nuclei has been observed. The possible existence of halo or skin nuclei has also been addressed.

The ridge structure at $\Delta E_{\gamma }=\pm$30 keV, observed previously in the reaction 187 MeV ${}^{37}\mathrm{Cl}{+}^{120}$Sn and attributed to an hyperdeformed nuclear shape, has been studied in a high statistics proton-$\gamma$ coincidence experiment. The presence of the ridge is confirmed but it is correlated to a set of $\gamma$-ray energies different from those proposed in earlier works. Some discrete transitions associated with this structure, which accounts for only $\sim 3\times {10}^{-5}$ of the fusion evaporation cross section, are proposed.

We measured the spin observables $A_y,$ $P$, and $S_{{\mathrm{NN}}^{\prime }}$ for the ${}^{208}$Pb${\mathrm{}(p,n)\mathrm{}}^{208}$Bi reaction at 135 MeV at laboratory angles of 0$°$, 3$°$, 6$°$, and 9$°$. The overall energy resolution was about 1 MeV. Data for $S_{{\mathrm{NN}}^{\prime }}$ are compared with distorted-wave impulse-approximation calculations that use random-phase approximation wave functions. Comparisons are also made for the ${}^{48}$Ca${\mathrm{}(p,n)\mathrm{}}^{48}$Sc reaction. The agreement between these calculations and the data is generally good, after adjustment of the nucleon-nucleon interaction in the random-phase approximation calculations to place the 0${}^{+}$ isobaric-analog states at the correct excitation energies. A single adjustment of the nucleon-nucleon force works for both target nuclei.

Measurements of the differential cross section and the analyzing powers ${\mathrm{iT}}_{11},$ $T_{20},$ $T_{21},$ and $T_{22}$ for ${}^6$Li-${}^4$He elastic scattering have been made at incident ${}^6$Li energies of 5.5 and 19.6 MeV. The measurements cover an angular range of ${\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}=18.8\mathrm{}°$–$165°$ at 19.6 MeV, and ${\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}=37.8\mathrm{}°$–$160°$ at 5.5 MeV. The data are compared to several different optical model calculations. Also, the calibration of a ${}^6\overrightarrow{\mathrm{Li}}$ polarimeter, which employs ${}^6\overrightarrow{\mathrm{Li}}$-${}^4$He elastic scattering, is described.

Connections between exclusive and inclusive electron scattering are explored within the framework of the relativistic plane-wave impulse approximation, beginning with an analysis of the model-independent kinematical constraints to be found in the missing-energy–missing-momentum plane. From the interplay between these constraints and the spectral function basic features of the exclusive and inclusive nuclear responses are seen to arise. In particular, the responses of the relativistic Fermi gas and of a specific hybrid model with bound nucleons in the initial state are compared. The latter facilitates extrapolations from light nuclei to very heavy ones where the former model has some validity. As expected, the exclusive responses are significantly different in the two models, whereas the inclusive ones are rather similar. By extending previous work on the relativistic Fermi gas, a reduced response is introduced for the hybrid model such that it fulfills the Coulomb and the higher-power energy-weighted sum rules. Although incorporating specific classes of off-shellness for the struck nucleons, it is found that the reducing factor required is largely model independent and, as such, yields a reduced response that is useful for studies of scaling and of the Coulomb sum rule. In particular, guided by the difference between the energy-weighted sum rules of the two models a new scaling variable appropriate for heavy nuclei is devised. Finally, a version of the relativistic Fermi gas which has zeroth, first, and second energy-weighted moments of the longitudinal response that agree rather well with those of the hybrid model is constructed: this version thus incorporates a priori the binding effects of the struck nucleons while retaining the simplicity of the original Fermi gas and provides the basis for future extensions of the model.

We calculate the final spin polarization and rotation vectors for epithermal neutrons scattered from ${}^{232}\mathrm{Th}$ within the optical model and assess the influence of the parity-violating interactions. The role of local doorways considered responsible for the sign correlation is assessed and its effect on the spin observables is considered.