A total absorption spectrometer, dedicated to the study of very short-lived atomic species, has been built and installed at the CERN∕ISOLDE mass separator. The $\beta$ decay of the neutron-deficient ${}^{74}\mathrm{Kr}$ nucleus has been studied using this new device. The Gamow-Teller strength distribution has been observed over most of the $Q_{EC}$ window, and a total strength of $0.69\left(3\right)$ $g_A^2∕4\pi$ has been measured for states with excitation energy below $3\text{MeV}$. Shape mixing in the ${}^{74}\mathrm{Kr}$ ground state is inferred from a comparison of the experimental strength distribution with self-consistent, deformed, quasiparticle-random-phase-approximation calculations.

We investigate $fp$ shell $\left({}^{44-58}\mathrm{Fe}\right)$ nuclei in highly excited states. Effects of the thermal and rotational excitations on the separation energy are studied and it is found that these excitations affect the particle stability and alter the boundary of the proton drip line. The shell effects near the proton drip line are seen through the level density parameter $a_e$. Changes in the occupation probability as a function of temperature and spin are studied.

We examine whether or not the surface tension acts to increase the nucleon density in the nuclear interior within a compressible liquid-drop model. We find that it depends on the density dependence of the surface tension, which may in turn be deduced from the neutron skin thickness of stable nuclei.

Pseudospin symmetry is a relativistic symmetry of the Dirac Hamiltonian with scalar and vector mean fields equal and opposite in sign. This symmetry imposes constraints on the Dirac eigenfunctions. We examine extensively the Dirac eigenfunctions of realistic relativistic mean field calculations of deformed nuclei to determine if these eigenfunctions satisfy these pseudospin symmetry constraints.

We use a solvable model to examine double-$\beta$ decay, focusing on the neutrinoless mode. After examining the ways in which the neutrino propagator affects the corresponding matrix element, we address the problem of finite model-space size in shell-model calculations by projecting our exact wave functions onto a smaller subspace. We then test both traditional and more recent prescriptions for constructing effective operators in small model spaces, concluding that the usual treatment of double-$\beta$-decay operators in realistic calculations is unable to fully account for the neglected parts of the model space. We also test the quality of the quasiparticle random phase approximation and examine a recent proposal within that framework to use two-neutrino decay to fix parameters in the Hamiltonian. The procedure eliminates the dependence of neutrinoless decay on some unfixed parameters and reduces the dependence on model-space size, though it does not eliminate the latter completely.

The behavior of the transverse momentum fluctuations with the centrality of the collision shown by the Relativistic Heavy Ion Collider data is naturally explained by the clustering of color sources. In this framework, elementary color sources—strings—overlap forming clusters, so the number of effective sources is modified. These clusters decay into particles with mean transverse momentum that depends on the number of elementary sources that conform each cluster, and the area occupied by the cluster. The transverse momentum fluctuations in this approach correspond to the fluctuations of the transverse momentum of the particles produced by the different clusters, and they behave essentially as the number of effective sources.

We calculate the cross section for the dissociation of $J∕\psi$ by kaons within the framework of a meson-exchange model including anomalous parity interactions. Off-shell effects at the vertices were handled with QCD sum rule estimates for the running coupling constants. The total $J∕\psi$-kaon cross section was found to be $1.0–1.6\text{mb}$ for $4.1⩽\sqrt{s}⩽5\text{GeV}$.

The generalized Goldberger-Treiman relation is combined with the Dashen-Weinstein sum rule to provide a constraint equation between the $g_{K\Sigma N}$ and $g_{K\Lambda N}$ coupling constants. A comprehensive examination of the published phenomenological and theoretical hyperon couplings has yielded a much smaller set of values, spanning the intervals $0.80⩽g_{K\Sigma N}∕\sqrt{4\pi }⩽2.72$ and $-3.90⩽g_{K\Lambda N}∕\sqrt{4\pi }⩽-1.84$, consistent with this criterion. The broken ${\text{SU}}_F\left(3\right)$ and Goldberger-Treiman hyperon couplings satisfy the constraint along with predictions from a Taylor series extrapolation using the same momentum variation as exhibited by $g_{\pi NN}$.

A simple model is proposed to examine the isotopic yields of the fragments from binary fission. For a given charge partition the peaks and widths in the isotope distributions are studied both with the liquid-drop model and with shell modifications. The basis for isoscaling is also explored. The symmetry energy plays a dominant role in both the distributions and the isoscaling behavior. A systematic increase in the isoscaling parameter $\alpha$ with the proton number of the fragment element is predicted in the context of the liquid-drop model. Deviations arising from shell corrections are explored.

The comparison of positron-proton and electron-proton elastic scattering cross sections is a sensitive test for the presence of two-photon exchange contributions. Thirty years ago, positron data were considered adequate to set tight limits on the size of two-photon corrections. More recently, these radiative corrections have again become a matter of great interest as a possible explanation for the discrepancy between Rosenbluth and polarization transfer measurements of the proton electromagnetic form factors. We have reexamined the electron and positron scattering data to see if they can accommodate two-photon effects of the size necessary to account for the Rosenbluth-polarization transfer discrepancy. The data are consistent with simple estimates of the two-photon contributions necessary to explain the discrepancy. In fact, they strongly favor a large $\epsilon$-dependent correction to the positron to electron ratio, providing the first direct experimental evidence for a two-photon contribution to unpolarized lepton-proton scattering.

The first $2^{+}$ states in $N=20$ isotones including neutron-rich nuclei ${}^{32}\mathrm{Mg}$ and ${}^{30}\mathrm{Ne}$ are studied by the Hartree-Fock-Bogoliubov plus quasiparticle random phase approximation method based on the Green’s function approach. The residual interaction between the quasiparticles is consistently derived from the Hamiltonian density of Skyrme interactions with explicit velocity dependence. The $B(E2,0_1^{+}\to 2_1^{+})$ transition probabilities and the excitation energies of the first $2^{+}$ states are well described within a single framework. We conclude that pairing effects account largely for the anomalously large $B\left(E2\right)$ value and the very low excitation energy in ${}^{32}\mathrm{Mg}$.

Nuclear many-body calculations are computationally demanding. An estimate of their accuracy is often hampered by the limited amount of computational resources even on present-day supercomputers. We provide an extrapolation method based on perturbation theory, so that the binding energy of a large basis-space calculation can be estimated without diagonalizing the Hamiltonian in this space. The extrapolation method is tested for ${}^3\mathrm{H}$ and ${}^6\mathrm{Li}$ nuclei. It will extend our computational abilities significantly and allow for reliable error estimates.

Using phase-equivalent supersymmetric partner potentials, a general result from the inverse problem in quantum scattering theory is illustrated, i.e., bound-state properties cannot be extracted from the phase shifts of a single partial wave, as a matter of principle. In particular, recent $R$-matrix analyses of the ${}^{12}\mathrm{C}+\alpha$ system, extracting the asymptotic normalization constant of the $2^{+}$ subthreshold state $C_{12}$, from the $\ell =2$ elastic-scattering phase shifts and bound-state energy, are shown to be unreliable. In contrast, this important constant in nuclear astrophysics can be deduced from the simultaneous analysis of the $\ell =0,2,4,6$ partial waves in a simplified potential model. A new supersymmetric inversion potential and existing models give $C_{12}=144.5\pm 8.5\times {10}^3{\text{fm}}^{-1∕2}$.

Collective anisotropic particle flow, a general phenomenon present in relativistic heavy-ion collisions, can be separated from direct particle-particle correlations of different physics origin by virtue of its specific azimuthal pattern. We provide expressions for flow-induced two-particle azimuthal correlations, if one of the particles is detected under fixed directions with respect to the reaction plane. We consider an ideal case when the reaction plane angle is exactly known, as well as present the general expressions in case of finite event-plane resolution. We foresee applications for the study of generic two-particle correlations at large transverse momentum originating from jet fragmentation.

The lowest-lying states of the Borromean nucleus ${}^{17}\mathrm{Ne}\left({}^{15}\mathrm{O}+p+p\right)$ and its mirror nucleus ${}^{17}\mathrm{N}\left({}^{15}\mathrm{N}+n+n\right)$ are compared by using the hyperspheric adiabatic expansion. Three-body resonances are computed by use of the complex scaling method. The measured size of ${}^{15}\mathrm{O}$ and the low-lying resonances of ${}^{16}\mathrm{F}\left({}^{15}\mathrm{O}+p\right)$ are first used as constraints to determine both central and spin-dependent two-body interactions. The interaction obtained reproduces relatively accurately both experimental three-body spectra. The Thomas-Ehrman shifts, involving excitation energy differences, are computed and found to be less than $3\%$ of the total Coulomb energy shift for all states.

Low-lying shell-model states may be approximated accurately by a sum over products of proton and neutron states. The optimal factors are determined by a variational principle and result from the solution of rather low-dimensional eigenvalue problems. Application of this method to $sd$-shell nuclei, $pf$-shell nuclei, and to no-core shell-model problems shows that very accurate approximations to the exact solutions may be obtained. Their energies, quantum numbers, and overlaps with exact eigenstates converge exponentially fast as the number of retained factors is increased.

We explore, within the framework of an algebraic $\text{sp}\left(4\right)$ shell model, discrete approximations to various derivatives of the energies of the lowest isovector-paired $0^{+}$ states of atomic nuclei in the $40⩽A⩽100$ mass range. The results show that the symplectic model can be used to successfully interpret fine structure effects driven by the proton-neutron ($pn$) and like-particle isovector pairing interactions as well as interactions with higher $J$ multipolarity. A finite energy difference technique is used to investigate two-proton and two-neutron separation energies, observed irregularities found around the $N=Z$ region, and the like-particle and $pn$ isovector pairing gaps. A prominent staggering behavior is observed between groups of even-even and odd-odd nuclides. An oscillation, in addition to that associated with changes in isospin values, that tracks with alternating seniority quantum numbers related to the isovector pairing interaction is also found.

The contribution of thermal fluctuations to the widths of isoscalar giant multipole resonances (GMR) in heated nuclei is studied. Starting from the collisional kinetic equation, it is shown that an additional contribution to the nuclear friction and the corresponding GMR widths arises due to the nonlinear dissipativity effect. It is also shown that the magnitude of the contributions of the thermal fluctuations to the nuclear friction coefficient and the GMR widths do not exceed $\sim 20\%$.

Level schemes of ${}^{111}\mathrm{Rh}$ and ${}^{113}\mathrm{Rh}$ are proposed from the analysis of $\gamma \text{−}\gamma \text{−}\gamma$ coincidence data from a ${}^{252}\mathrm{Cf}$ spontaneous fission source with Gammasphere. These schemes have the highest excitation energies and spins yet established in these nuclei, as well as weakly populated bands not reported in earlier fission-$\gamma$ work. From these data, information on shapes is inferred. By analogy with lighter $Z=45$ odd-even isotopes, tentative spins and parities are assigned to members of several rotational bands. In this region triaxial nuclear shapes are known to occur, and we carried out calculations for ${}^{111}\mathrm{Rh}$ and ${}^{113}\mathrm{Rh}$ with the triaxial-rotor-plus-particle model. The $7∕2^{+}\pi g_{9∕2}$ bands of both nuclei, as well as lighter isotopes studied by others, show similar signature splitting. Our model calculations give a reasonable fit to the signature splitting, collective sidebands, and transition probabilities at near-maximum triaxiality with $\gamma \approx 28°$. For the $K=1∕2^{+}\left[431\right]$ band, experiment and model calculations do not fit well, which is accounted for by greater prolate deformation of the $K=1∕2^{+}$ band, a case of shape coexistence. Our data on ${}^{110,112}\mathrm{Rh}$ show no backbending and thus support the idea of the band crossing in the ground band of the odd-A neighbors being due to alignment of an $h_{11∕2}$ neutron pair. In ${}^{111,113}\mathrm{Rh}$ above the band crossing (spins $\approx 21∕2\hslash$) the ground band appears to split, with two similar branches. We consider the possibility that chiral doubling may be involved, but there are not enough levels to determine that.

A multinucleon transfer reaction between a thin self-supporting ${}_{\mathrm{\hspace{0.5em}78}}{}^{198}\mathrm{Pt}$ target and an $850\text{MeV}$ ${}_{\mathrm{\hspace{0.5em}54}}{}^{136}\mathrm{Xe}$ beam has been used to populate and study the structure of the $N=80$ isotone ${}_{\mathrm{\hspace{0.5em}56}}{}^{136}\mathrm{Ba}$. Making use of time-correlated $\gamma$-ray spectroscopy, evidence for an $I^{\pi }=\left({10}^{+}\right)$ isomeric state has been found with a measured half-life of $91\pm 2\text{ns}$. Prompt-delayed correlations have also enabled the tentative measurement of the near-yrast states which lie above the isomer. Shell-model calculations suggest that the isomer has a structure which can be assigned predominantly as ${\left(\nu h_{11∕2}\right)}_{{10}^{+}}^{-2}$. The results are discussed in terms of standard and pair-truncated shell-model calculations, and compared to the even-$Z$ $N=80$ isotones ranging from ${}_{\mathrm{\hspace{0.5em}50}}{}^{130}\mathrm{Sn}$ to ${}_{\mathrm{\hspace{0.5em}68}}{}^{148}\mathrm{Er}$. A qualitative explanation of the observed dramatic decrease in the $B(E2:{10}^{+}\to 8^{+})$ value for the $N=80$ isotones at ${}^{136}\mathrm{Ba}$ is given in terms of the increasing single-hole energy of the $h_{11∕2}$ neutron configuration as the proton subshell is filled. The angular momentum transfer to the binary fragments in the reaction has also been investigated in terms of the average total $\gamma$-ray fold versus the scattering angle of the recoils.