Positrons and electrons from the internal pair conversion (IPC) decay of states populated in near-barrier collisions of very heavy ions have been studied using the APEX spectrometer. Using inelastic ${}^{206}\mathrm{Pb}{+}^{206}\mathrm{Pb}$ scattering at 5.90 MeV/nucleon, the gamma and IPC branches of the well-known $E1\mathrm{}$ decay of the first $J^{\pi }{=3\mathrm{}}^{-}$ state were kinematically reconstructed and the IPC-to-gamma branching ratio was determined to be $\beta =(4.0\mathrm{}\pm 0.7)\times {10}^{-4}$. We have also performed experiments with actinide beams or targets; ${}^{238}\mathrm{U}{+}^{181}\mathrm{Ta}$, ${}^{208}\mathrm{Pb}{+}^{238}\mathrm{U}$, ${}^{208}\mathrm{Pb}{+}^{232}\mathrm{Th}$, and ${}^{238}\mathrm{U}{+}^{232}\mathrm{Th}$, which resulted in the observation of new gamma-ray transitions from high-lying states in ${}^{232}\mathrm{Th}$ and ${}^{238}\mathrm{U}$. None of these were populated with sufficient strength such that IPC could produce statistically significantly peaks in positron-electron sum energy spectra.

The strength of electric monopole transitions in the decay out of superdeformed bands is discussed on the basis of the mixing of superdeformed and normal-deformed states. The decay of superdeformed bands in the mass-190 region as well as the decay of the bands in ${}^{133}$Nd and ${}^{135}$Nd is investigated. Even though the values obtained for the electric monopole strength are very large, it is shown that $E$0 transitions cannot play an important role in the decay of superdeformed bands.

Matrix elements of the deuteron axial current are calculated in the covariant spectator scheme of Gross, and compared to a corresponding calculation using light-front dynamics. The results confirm the dominant role in both approaches of the deuteron $D$ state in observable effects beyond the nonrelativistic limit.

By using potentials with a singularity at the origin, the inverse scattering problem at fixed orbital momentum $l$ can be decomposed in two parts. First, the unique singular potential without a bound state corresponding to a given phase shift is constructed; then, bound states may be added without modifying the phase shift. The first step, called the singular inverse problem, is discussed. When the phase shift is smaller at high energies than at zero energy, the obtained effective potential has a repulsive core of the form $\nu (\nu {+1)r}^{-2}$ where $\nu$ is larger than $l$. If the $S$ matrix can be approximated by the product of the $S$ matrix of a reference potential by a rational function of the wave number $k$, the singular potential is a generalized Bargmann potential. It can be constructed with supersymmetric transformations of the reference potential. Each transformation adds a pole to the $S$ matrix. The repulsive core parameter $\nu$ of the final potential is equal to $l$ plus the difference of the number of added poles in the upper and lower half $k$ planes. This generalized Bargmann potential as well as its solutions can be expressed in terms of the reference potential and of Wronskians of its solutions. As an application, we invert the phase shifts of neutron-proton and proton-proton ${}^1{S}_0$ elastic scatterings and obtain in both cases a $\nu =1\mathrm{}$ singular nuclear potential with two wells. In the neutron-proton case, this potential is compared with a regular potential obtained from a Gel’fand-Levitan-Marchenko inversion method.

We examine the role of the ΔΔ intermediate state in $\mathrm{NN}$ scattering in the ${}^1{S}_0$ channel. The computation is performed at lowest order in an effective-field theory involving local four-fermion operators and one-pion exchange using dimensional regularization with minimal subtraction ($\overline{\mathrm{MS}}$). As first discussed by Weinberg, in the theory with only nucleons, the large-scattering length in this channel requires a small scale for the local $N^4$ operators. When Δ's are included (but without pions) a large-scattering length can be obtained from operators with a scale $\sqrt{{2M}_N{(M}_{\Delta }-M_N)},$ but fine-tuning is required. The coefficients of the contact terms involving the Δ fields are not uniquely determined but for reasonable values one finds that, in general, $\mathrm{NN}$ scattering computed in the theory with Δ's looks like that computed in the theory without Δ's. The leading effect of the Δ's is to change the coefficients of the four-nucleon contact terms between the theories with and without Δ's. Further, the decoupling of the Δ's in the limit of large mass and strong coupling is clearly demonstrated. When pions are included, the typical scale for the contact terms is $\sim 100\mathrm{MeV},$ both with and without Δ's and is not set by $\sqrt{{2M}_N{(M}_{\Delta }-M_N)}.$ For reasonable values of contact terms that reproduce the scattering length and effective range (at lowest order) the phase shift is not well reproduced over a larger momentum range as is found in the theory without Δ's at lowest order.

The contributions of helicity-flip matrix elements to the deuteron form factors are discussed in the light-cone frame. Normalized ${A(Q}^2)$, ${B(Q}^2)$, $G_Q{(Q}^2)$, and $T_{20}$ are obtained in a simple QCD-inspired model. As a result of the kinematical enhancement, the helicity-flip matrix elements contribute significantly to $G_M$ and $G_Q$ while $\eta$ is small. Our numerical results are consistent with data in the intermediate energy region.

The nonmesonic decay of the hypertriton is calculated based on a hypertriton wave function and $3N$ scattering states, which are rigorous solutions of three-body Faddeev equations using realistic $\mathrm{NN}$ and hyperon-nucleon interactions. The pion exchange together with heavier meson exchanges for the $\Lambda N\to \mathrm{NN}$ transition is considered. The total nonmesonic decay rate is found to be 0.5% of the free $\Lambda$ decay rate. Integrated as well as differential decay rates are given. The $p$- and $n$-induced decays are discussed thoroughly and it is shown that the corresponding total rates cannot be measured individually.

The influence of relativistic contributions to deuteron electrodisintegration is systematically studied in various kinematic regions of energy and momentum transfer. As theoretical framework the equation-of-motion and the unitarily equivalent $S$-matrix approaches are used. In a $\mathrm{}(p/M)\mathrm{}$ expansion, all leading order relativistic $\pi$-exchange contributions consistent with the Bonn one-boson-exchange potential model (OBEPQ) are included. In addition, static heavy-meson-exchange currents including boost terms, $\gamma \pi \rho /\omega$ currents, and $\Delta$-isobar contributions are considered. Sizable effects from the various relativistic two-body contributions, mainly from $\pi$ exchange, have been found in inclusive form factors and exclusive structure functions for a variety of kinematic regions.

High spin states in the doubly odd ${}^{122}\mathrm{I}$ nucleus have been investigated through γ-γ and charged particle-γ coincidence measurements following the ${}^{116}{\mathrm{C}\mathrm{d}+}^{11}\mathrm{B}$ and ${}^{110}{\mathrm{P}\mathrm{d}+}^{16}\mathrm{O}$ fusion-evaporation reactions, respectively. The level scheme has been established up to ${\mathrm{I}}^{\pi }{=(26\mathrm{}}^{-}).\mathrm{}$ Two collective $\Delta I=1\mathrm{}$ coupled bands have been observed and are assigned the $\pi {(g}_{7/2}{/d}_{5/2})\otimes \nu h_{11/2}$ and $\pi g_{9/2}^{-1}\otimes \nu h_{11/2}$ configurations. Of these, the $\pi {(g}_{7/2}{/d}_{5/2})\otimes \nu h_{11/2}$ band was known earlier but had been assigned the $\pi g_{9/2}^{-1}\otimes \nu h_{11/2}$ configuration. A low lying ${21}^{-}$ state feeds this band and is interpreted as a noncollective oblate $\pi [g_{7/2}{(d}_{5/2}{)}^2{]}_{15/2+}\otimes \nu [{(h}_{11/2}{)}^3{]}_{27/2-}$ configuration. In addition, a $\Delta I=2\mathrm{}$ sequence has been identified and is proposed to be based on the $\pi h_{11/2}\otimes \nu h_{11/2}$ configuration. The theoretical interpretations for the assigned configurations are discussed in the framework of total Routhian surface calculations, which also predict several noncollective oblate states in the spin range $21<~I<~33.$

Excited states of ${}^{112}$Sb were investigated through the ${}^{112}$Sn$(p,n\gamma )$${}^{112}$Sb reaction. $\gamma$-ray, $\gamma \gamma$-coincidence, and internal conversion electron spectra were measured with Ge(HP) $\gamma$ and superconducting magnetic lens plus Si(Li) electron spectrometers at 8.5, 8.9, 9.1, and 9.3 MeV bombarding proton energies. A significantly extended level scheme was constructed. Spins and parities have been assigned to the levels from Hauser-Feshbach analysis of reaction cross sections, internal conversion coefficients, angular distribution of the $\gamma$ rays, and decay properties of the states. The low lying states were assigned to proton-neutron multiplets on the basis of their decay properties. The energy splitting of these multiplets have been calculated using the parabolic rule.

The new proton radioactivities ${}^{165,166,167}\mathrm{Ir}$ and ${}^{171}\mathrm{Au}$ have been observed. The Ir isotopes were produced via the ${}^{92}\mathrm{Mo}{(}^{78}\mathrm{Kr}{,pxn)}^{165,166,167}\mathrm{Ir}$ reactions at 357 and 384 MeV. ${}^{171}\mathrm{Au}$ was produced via the ${}^{96}\mathrm{Ru}{(}^{78}\mathrm{Kr}{,p2n)}^{171}\mathrm{Au}$ reaction at 389 MeV. The proton emitters were each identified by position, time, and energy correlations between the implantation of a residual nucleus into a double-sided silicon strip detector, the observation of a decay proton, and the subsequent observation of a decay alpha particle from the daughter nucleus (${}^{164,165,166}$Os and ${}^{170}\mathrm{Pt},$ respectively). Both ${}^{166}\mathrm{Ir}$ and ${}^{167}\mathrm{Ir}$ have proton-emitting ground and isomeric states, which also decay by alpha emission. The proton-decay rates have been reproduced by calculations using the WKB barrier penetration approximation and a low-seniority shell-model calculation of the spectroscopic factors. The alpha decays of the four nuclei are followed by chains of alpha decays, allowing the determination of single-particle orbital orderings. Mass information has also been obtained from the alpha-decay chains because a connection to a known mass can be obtained for one of the nuclei. Ground-state mass excesses are reported for ${}^{151}\mathrm{Tm},$ ${}^{154}\mathrm{Yb},$ ${}^{155}\mathrm{Lu},$ ${}^{158}\mathrm{Hf},$ ${}^{159}\mathrm{Ta},$ ${}^{162}\mathrm{W},$ ${}^{163}\mathrm{Re},$ ${}^{166}\mathrm{Os},$ ${}^{167}\mathrm{Ir},$ and ${}^{170}\mathrm{Pt}.$ The mass excess for ${}^{171m}\mathrm{Au}$ is also given. Proton separation energies are also deduced for the odd-$Z$ alpha daughter nuclei of the Ir proton emitters.

The level structure of ${}^{227}\mathrm{Th}$ has been studied using the α decay of ${}^{231}\mathrm{U}.$ The use of mass-separated ${}^{231}\mathrm{U}$ sources and high-resolution α-particle and γ-ray spectroscopy enabled the identification of 16 excited levels of ${}^{227}\mathrm{Th}.$ The angular distribution of α particles in the decay of low-temperature oriented ${}^{227}\mathrm{Th}$ is consistent with a ${}^{227}\mathrm{Th}$ ground-state spin of 1/2. The low-lying levels of ${}^{227}\mathrm{Th}$ can be interpreted in terms of a ${K=1/2\mathrm{}}^{\pm }$ parity doublet and a ${K=3/2\mathrm{}}^{+}$ band coupled with the ${1/2}^{+}$ member of the parity doublet by the Coriolis interaction.

The low-spin levels of the odd-odd nucleus ${}^{168}\mathrm{Lu}$ from ${}^{168}\mathrm{Hf}$ ${(T}_{1/2}=25.95\mathrm{}\min )$ electron-capture decay were investigated by direct γ and γ-γ coincidence measurements. The sources of ${}^{168}\mathrm{Hf}$ were produced with the ${}^{156}\mathrm{Gd}{(}^{16}\mathrm{O},4n)$ reaction and radiochemically separated using chromatographic methods. A level scheme of 39 new levels in the ${}^{168}\mathrm{Lu}$ nucleus was proposed, accounting for 107 of 119 observed γ transitions assigned to ${}^{168}\mathrm{Hf}$ electron-capture decay. Transition multipolarities, level-spins, and parities were deduced or proposed. A tentative decay scheme was proposed. Level structure was discussed in the framework of the particle-rotor and Nilsson models.

High-spin states in the nucleus ${}^{116}$Te have been studied with the reaction ${}^{64}$Ni${(}^{56}$Fe,$2p2n)$ at 236 MeV using an early implementation of the Gammasphere array. Three rotational bands extending to spins $I\sim \left(25\mathrm{}-42\right)ħ$ and excitation energies $E_{\mathrm{ex}}\sim \left(11\mathrm{}-24\right)$ MeV have been identified and connected to known low-lying states. In the most extended band, a gradual decrease in the dynamic moment of inertia ${\mathcal{J}}^{\mathrm{}\left(2\right)\mathrm{}}$ with increasing rotational frequency has been observed and interpreted as evidence for smooth band termination. Several energetically favored states based on aligned single-particle configurations also have been found to coexist with weakly deformed collective structures at low spins.

The transitional nuclei ${}_{\hspace{0.5em}42}^{100}\mathrm{Mo}$, ${}_{\hspace{0.5em}44}^{104}\mathrm{Ru}$, and ${}_{\hspace{0.5em}46}^{108}\mathrm{Pd}$ have been studied as products of binary reactions formed by a ${}_{36}^{86}$Kr beam impinging on a ${}_{\hspace{0.5em}46}^{110}\mathrm{Pd}$ target. The yrast states are observed above the region of the first backbend. In each case this backbend is associated with the breaking of the first neutron ${(h}_{11/2}{)}^2$ pair. The results are consistent with the predictions of cranked shell model calculations and the systematics of neighboring nuclei.

The renormalized proton-neutron quasiparticle random-phase approximation model (RQRPA) has been used to calculate double-β-decay matrix elements and associated transition half-lives for two-neutrino double β decay of parent nuclei ${}^{76}\mathrm{Ge},$ ${}^{78}\mathrm{Kr},$ ${}^{82}\mathrm{Se},$ ${}^{96}\mathrm{Zr},$ ${}^{106}\mathrm{Cd},$ and ${}^{130}\mathrm{Te}$ to the ground state and excited one- and two-phonon states of their daughter nuclei. The results are compared to ordinary proton-neutron QRPA and experiments. In addition, the violation of the Ikeda sum rule in the RQRPA is examined and discussed.

42 superdeformed (SD) bands, which have a pronounced increase in the dynamic moment of inertia ${\mathcal{J}}^{\mathrm{}\left(2\right)\mathrm{}}$ with rotational frequency $ħ\omega$ in the $A\sim$190 region, are studied using the exponential model with pairing attenuation. The level spins are suggested and the parameters ${\mathcal{J}}_0$ and ${\Delta }_0$ are determined for these bands. The excellent agreement between the calculated $E_{\gamma }$ and the observed $E_{\gamma }$ gives good support to the model. The parameters ${\mathcal{J}}_0$, ${\Delta }_0$ and the band head moment of inertia ${\mathcal{J}}_{\mathrm{b}.\mathrm{h}.\mathrm{}}$ show evident odd-even effects which may indicate different intrinsic structure in the studied SD nuclei.

Skyrme-like hyperon-nucleon potentials are derived from $G$-matrix calculations and shown to reproduce well the $\Lambda$ single-particle spectra of hypernuclei measured at BNL and KEK. Previously known potentials are reexamined systematically. The fit of the spectra can restrict the radii of $\Lambda$ orbits in hypernuclear ground states, $\Lambda$ well depth and effective mass in nuclear matter, and polarization of nuclear cores caused by hyperon rather tightly. The implications of the $\Lambda N$ spin-orbit force to the spectra are considered. Hartree-Fock calculations of binding energies of ${}_{\Lambda \Lambda }^{13}$B with density-dependent $G$-matrix $\Lambda \Lambda$ potentials are presented, taking note of the core-rearrangement effects induced by $\Lambda N$ interactions.

The so-called self-consistent quasiparticle random phase approximation, accounting for a better treatment of ground-state correlations, is applied to a schematic Hamiltonian, describing the Fermi beta decay process. The self-consistent procedure coupling the BCS minimum with the quantum fluctuations yields an exact fulfillment of the Ikeda sum rule. The role of the ground-state correlations is analyzed in the case of the double beta decay process.