We investigate the inelastic coupling interaction by studying its effect on the elastic scattering potential, as determined by inverting the elastic scattering S matrix. We first address the effect upon the real and imaginary elastic potentials of including excited states of the target nucleus. We then investigate the effect of a recently introduced coupling potential that has been remarkably successful in reproducing the experimental data for the ${}^{12}\mathrm{C}{+}^{12}\mathrm{C},$ ${}^{12}\mathrm{C}{+}^{24}\mathrm{Mg},$ and ${}^{16}\mathrm{O}{+}^{28}\mathrm{Si}$ reactions over a wide range of energies. This coupling potential has the effect of deepening the real elastic potential in the surface region, thereby explaining a common feature of many phenomenological potentials. It is suggested that one can relate this deepening to the superdeformed state of the compound nucleus ${}^{24}\mathrm{Mg}.$

We evaluate the two-pion decay of the Roper resonance in a model where explicit rescattering of the two final pions is accounted for by the use of unitarized chiral perturbation theory. Our model does not include an explicit ε or σ scalar-isoscalar meson decay mode; instead it generates it dynamically by means of the pion rescattering. The two ways, explicit or dynamically generated, of introducing this decay channel have very different amplitudes. Nevertheless, through interference with the other terms of the model, we are able to reproduce the same phenomenology as models with explicit consideration of the ε meson.

We use three-point proper vertices, as determined by current algebra alone, to calculate the vector minus axial-vector spectral density difference from the imaginary parts of the spin-1 vector and axial-vector current-current correlation functions. These correlators have been constructed using the vector dominance assumption for the currents, in conjunction with the appropriate proper vertices that determine the distribution in strength of their imaginary parts. Setting the single parameter δ=-1/2 that is not determined by current algebra, one obtains excellent fits to the recent experimental data from the ALEPH Collaboration in the vicinity of the lowest $\rho$ resonance, as well as for the timelike electromagnetic form factor of the pion. The axial spectral strength that is concentrated around the $a_1$ axial-vector meson mass is, however, underestimated due to the approximate nature of the calculations in this region. The integrated values of the weighted spectral density difference satisfy the corresponding sum rules with good accuracy.

Relativistic prescriptions relating Sachs form factors to nucleon charge and magnetization densities are used to fit recent data for both the proton and the neutron. The analysis uses expansions in complete radial bases to minimize model dependence and to estimate the uncertainties in radial densities due to limitation of the range of momentum transfer. We find that the proton charge distribution, fitted to recent recoil-polarization data displaying an almost linear decrease in $G_{\mathrm{Ep}}{/G}_{\mathrm{Mp}}$ for $Q^2\gtrsim 1(\mathrm{GeV}{/c)}^2,$ is significantly broader than its magnetization density. We also find that the magnetization density is broader for the neutron than the proton. The neutron charge form factor is consistent with the Galster parametrization over the available range of $Q^2,$ but the relativistic inversion produces a softer radial density. Discrete ambiguities in the inversion method are analyzed in detail. The method of Mitra and Kumari ensures compatibility with pQCD at large $Q^2$ and is most useful for extrapolating form factors. Although a recent observation that ${\mathrm{QF}}_{2p}{/F}_{1p}$ is approximately constant for $2<\mathrm{}{Q}^2<6\mathrm{}(\mathrm{GeV}{/c)}^2$ appears to be inconsistent with the $Q^{-2}$ scaling expected from quark helicity conservation, our analysis fits these data while remaining consistent with pQCD for large $Q^2.$

We investigate $K^{-}$ and $K^0$ condensation in β-equilibrated hyperonic matter within a density dependent hadron field theoretical model. In this model, baryon-baryon and (anti)kaon-baryon interactions are mediated by the exchange of mesons. Density dependent meson-baryon coupling constants are obtained from microscopic Dirac-Brueckner calculations using Groningen and Bonn A nucleon-nucleon potentials. It is found that the threshold of antikaon condensation is not only sensitive to the equation of state but also to antikaon optical potential depth. Only for large values of antikaon optical potential depth does $K^{-}$ condensation set in even in the presence of negatively charged hyperons. The threshold of $K^0$ condensation is always reached after $K^{-}$ condensation. Antikaon condensation makes the equation of state softer thus resulting in smaller maximum mass stars compared with the case without any condensate.

The experimentally observed obvious nonadditivity in the nuclear moment of inertia and angular momentum alignment of multiquasiparticle rotational bands, both in normally deformed and superdeformed nuclei, presents a serious challenge to the traditional BCS treatment for nuclear pairing. It is shown that the systematically observed nonadditivity mainly comes from the destructive interference between blocking effects, and can be satisfactorily accounted for by the particle-number conserving method, in which the blocking effects are treated consistently and exactly.

Under the single-particle potential model, the root-mean-square radii for a number of single-particle states have been calculated by numerically solving the Schrödinger equations, with the binding energies and configurations determined experimentally. By studying the relations between the radii and the separation energies, the scaling laws of valence nucleon distributions for these single-particle states are obtained. In the light of these scaling laws, the necessary conditions for neutron halos and proton halos are, respectively, deduced. The existence region of proton halos is pointed out. It is found that the behavior of valence nucleons around the radii of interaction potentials could not be disregarded.

Self-consistent calculations for excited nuclei are performed in the framework of the relativistic mean-field theory at temperatures between 0 and 4 MeV for 193 spherical even-even nuclei. The temperature dependent macroscopic part of the thermal energy was approximated by a liquid-drop type formula. The average dependence of the single particle level-density parameter a on mass and isospin of the nucleus is established.

The renormalized quasiparticle-RPA is reformulated for even-even nuclei using restrictions imposed by the commutativity of the phonon creation operator with the total particle number operator. This new version, fully-renormalized QRPA (FR-QRPA), is free from the spurious low-energy solutions. Analytical proof is given that the Ikeda sum rule is fulfilled within the FR-QRPA.

A gross estimate of the neutron skin $\left[0.80\right(5\left)\right(N-Z)/A\mathrm{fm}]$ is extracted from experimental proton radii, represented by a four parameter fit, and observed mirror displacement energies (CDE). The calculation of the latter relies on an accurately derived Coulomb energy and smooth averages of the charge symmetry breaking potentials constrained to state of the art values. The only free parameter is the neutron skin itself. The Nolen Schiffer anomaly is reduced to small deviations $(\mathrm{rms}=127\mathrm{}\mathrm{keV})$ that exhibit a secular trend. It is argued that with state of the art shell model calculations the anomaly should disappear. Highly accurate fits to proton radii emerge as a fringe benefit.

A new high-precision $\mathrm{}(p,t)\mathrm{}$ study of the ${}^{158}\mathrm{Gd}$ nucleus was carried out with the Q3D spectrometer at the University of Munich. The result is the observation for the first time of a deformed nucleus with 13 excited $0^{+}$ states below an excitation energy of approximately 3.1 MeV. Seven of these $0^{+}$ states are observed for the first time and an additional three are new confirmations of previous tentative assignments. This abundance of $0^{+}$ states provides significant new information on these poorly understood excitations. ${}^{158}\mathrm{Gd}$ can now be viewed as a unique laboratory for further investigations on the nature of $0^{+}$ excitations in nuclei.

Quadrupole and octupole softness in the even-even $N=Z$ nucleus ${}^{64}\mathrm{Ge}$ is studied on the spherical shell model basis. We carry out the shell model calculation using the pairing plus quadrupole $\mathrm{}\left(\mathrm{QQ}\right)\mathrm{}$ plus octupole $\mathrm{}\left(\mathrm{OO}\right)\mathrm{}$ interaction with monopole corrections. It is shown that ${}^{64}\mathrm{Ge}$ is an unstable nucleus with respect to both the quadrupole and octupole deformations, which is consistent with the previous discussions predicting the $\gamma$ softness and octupole instability. It is demonstrated that the proton-neutron part $Q_p{Q}_n$ of the $\mathrm{QQ}$ interaction is important for the $\gamma$ softness or triaxiality.

A weak ${}^{107}\mathrm{Te}$ $\alpha$-decay branch to an excited state in ${}^{103}\mathrm{Sn}$ was observed. This is the first observation of $\alpha$ decay fine structure in the island of $\alpha$ emitters above the $Z=50\mathrm{}$ shell gap. The energy difference between $\alpha$ particles feeding the ground state and the excited state is 162(4) keV. This implies an excitation energy of 168(4) keV for the excited state in ${}^{103}\mathrm{Sn}.$ In addition, three $\alpha$ particles feeding the excited state were detected in coincidence with 168-keV $\gamma$ rays, firmly establishing their assignment. The energy of the excited state coincides with the energy of the first excited state in ${}^{103}\mathrm{Sn}$ proposed from in-beam $\gamma$-ray studies by Fahlander et al. [1]. The branching ratio of 0.47(9)% deduced for the decay to the excited state is about a factor of 6 lower than the value calculated using the WKB approximation. Other possible cases of the $\alpha$-decay fine structure in the region are also discussed.

The fragment production in multifragmentation of finite nuclei is affected by the critical temperature of nuclear matter. We show that this temperature can be determined on the basis of the statistical multifragmentation model (SMM) by analyzing the evolution of fragment distributions with the excitation energy. This method can reveal a decrease of the critical temperature that, e.g., is expected for neutron-rich matter. The influence of isospin on fragment distributions is also discussed.

The ${}^3\mathrm{He}({\mu }^{-},{\nu }_{\mu }{)}^3\mathrm{H}$ weak capture is studied using correlated-hyperspherical-harmonics wave functions, obtained from realistic Hamiltonians consisting of the Argonne $v_{14}$ or Argonne $v_{18}$ two-nucleon, and Tucson-Melbourne or Urbana-IX three-nucleon interactions. The nuclear weak charge and current operators have vector and axial-vector components with one- and two-body contributions. The axial-vector current includes the nucleon and $\Delta$ induced pseudoscalar terms, with coupling constants $g_{\mathrm{PS}}$ and $g_{\mathrm{PS}}^{*}$ derived from pion-pole dominance and partially conserved-axial-current hypothesis. The strength of the leading two-body operator is adjusted to reproduce the Gamow-Teller matrix element in tritium $\beta$ decay. The calculated total capture rate is within $\sim 0.5\%$ of the most recent measurement, $1496\pm 4{\sec }^{-1}.$ The predictions for the capture rate and angular correlation parameters $A_v,$ $A_t,$ and $A_{\Delta }$ are found to be only very weakly dependent on the model input Hamiltonian. The variation of the observables with $g_{\mathrm{PS}}$ and $g_{\mathrm{PS}}^{*}$ and the theoretical uncertainties deriving from the model-dependent procedure used to constrain the axial current are investigated.

Electrodisintegration of the three-nucleon bound state with two-body final states is described. The description uses nucleon degrees of freedom extended to include the excitation of a single nucleon to a $\Delta$ isobar. The baryonic interaction and the electromagnetic current couple nucleonic states and states with a $\Delta$ isobar. Exact solutions of three-particle scattering equations are employed for the initial and final states of the reactions; due to the excitation of the $\Delta$ isobar an effective three-nucleon force is included. The current has one-baryon and two-baryon contributions. Theoretical predictions for the reactions with selected kinematic specifications are given. The role of the $\Delta$ isobar in the description of the considered processes is discussed and its effect on observables is quantitatively isolated.

Based on a counting scheme that explicitly takes into account the large momentum $\sqrt{{\mathrm{Mm}}_{\pi }}$ characteristic for pion production in nucleon-nucleon collisions we calculate all diagrams for the reaction $N\overrightarrow{N}\mathrm{NN}\pi$ at threshold up to next-to-leading-order. At this order there are no free parameters and the size of the next-to-leading- order contributions is in line with the expectation from power counting. The sum of loop corrections at that order vanishes for the process $p\overrightarrow{p}\mathrm{pp}{\pi }^0$ at threshold. The total contribution at next-to-leading-order from loop diagrams that include the delta degree of freedom vanishes at threshold in both reaction channels $p\overrightarrow{p}\mathrm{pp}{\pi }^0,pn{\pi }^{+}.$

We have measured the ratios of normalized yields for the elastic scattering of charged pions from ${}^3\mathrm{H}$ ${\mathrm{and}}^3\mathrm{He}$ in the backward hemisphere. At $T_{\pi }=180\mathrm{}\mathrm{MeV},$ we have completed the angular distribution measured earlier, adding six new data points in the angular range from $119°$ to $169°$ in the $\pi$-nucleus center of mass. We also measured an excitation function with data points at $T_{\pi }=142,$ 180, 220, and 256 MeV at the largest angle achievable with our detector—between $160°$ and $170°$ in the $\pi$-nucleus center of mass. The data, taken as a whole, show an apparent role reversal of the two charge-symmetric ratios $r_1$ and $r_2$ in the backward hemisphere. For data $>~100°$ we observe a strong dependence of the ratios on $-t,$ independent of $T_{\pi }$ or ${\theta }_{\pi }.$ The superratio R data match very well with calculations based on the forward-hemisphere data that predict the value of the difference between the even-nucleon radii of ${}^3\mathrm{H}$ ${\mathrm{and}}^3\mathrm{He}.$ Comparisons are also made with recent calculations incorporating different wave functions and double-scattering models.

We discuss the experimental and theoretical status of charge-symmetry violation (CSV) in the elastic scattering of ${\pi }^{+}$ and ${\pi }^{-}$ on ${}^3\mathrm{H}$ and ${}^3\mathrm{He}.$ Analysis of the experimental data for the ratios $r_1,$ $r_2,$ and R at $T_{\pi }=142,$ 180, 220, and 256 MeV provides evidence for the presence of CSV. We describe pion scattering from the three-nucleon system in terms of single- and double-scattering amplitudes. External and internal Coulomb interactions as well as the ${\Delta }_{33}$-mass splitting are taken into account as sources of CSV. Reasonable agreement between our theoretical calculations and the experimental data is obtained for $T_{\pi }=180,$ 220, and 256 MeV. For these energies, it is found that the ${\Delta }_{33}$-mass splitting and the internal Coulomb interaction are the most important contributions for CSV in the three-nucleon system. The CSV effects are rather sensitive to the choice of pion-nuclear scattering mechanisms, but at the same time, our theoretical predictions are much less sensitive to the choice of the nuclear wave function. It is found, however, that data for $r_2$ and R at $T_{\pi }=142\mathrm{}\mathrm{MeV}$ do not agree with the predictions of our model, which may indicate that there are additional mechanisms for CSV which are important only at lower energies.

The rotational invariance under the usual physical angular momentum of the ${\mathrm{su}}_q\mathrm{}\left(2\right)\mathrm{}$ Hamiltonian for a description of rotational nuclear spectra is explicitly proved, and a connection of this Hamiltonian to the formalisms of Amal’sky and Harris is provided. In addition, a Hamiltonian for rotational spectra is introduced, based on the construction of irreducible tensor operators (ITO’s) under ${\mathrm{su}}_q\mathrm{}\left(2\right)\mathrm{}$ and the use of q-deformed tensor products and q-deformed Clebsch-Gordan coefficients. The rotational invariance of this ${\mathrm{su}}_q\mathrm{}\left(2\right)\mathrm{}$ ITO Hamiltonian under the usual physical angular momentum is explicitly proved, a simple closed expression for its energy spectrum (the “hyperbolic tangent formula”) is introduced, and its connection to the Harris formalism is established. Numerical tests in a series of Th isotopes are provided.