The Woods-Saxon (WS) basis is suggested to replace the widely used harmonic oscillator basis for solving the relativistic mean-field theory in order to generalize it to study exotic nuclei. As an example, the relativistic Hartree theory is solved for spherical nuclei in a Woods-Saxon basis obtained by solving either the Schrödinger equation or the Dirac equation (labeled as SRHSWS and SRHDWS, respectively, and SRHWS for both). In SRHDWS, the negative energy states in the Dirac sea must be properly included. The WS basis in SRHDWS could be smaller than that in SRHSWS, which will simplify the deformed problem. The results from SRHWS are compared in detail with those from solving the spherical relativistic Hartree theory in the harmonic oscillator basis (SRHHO) and those in the coordinate space (SRHR). All of these approaches give identical nuclear properties such as total binding energies and root mean square radii for stable nuclei. For exotic nuclei, e.g., ${}^{72}\mathrm{Ca},$ SRHWS satisfactorily reproduces the neutron density distribution from SRHR, while SRHHO fails. It is shown that the Woods-Saxon basis can be extended to more complicated situations for exotic nuclei where both deformation and pairing have to be taken into account.

The effective Skyrme interaction has been used extensively in mean-field models for several decades and many different parametrizations of the interaction have been proposed. All of these give similar agreement with the experimental observables of nuclear ground states as well as with the properties of infinite symmetric nuclear matter at the saturation density $n_0.$ However, when applied over a wider range of densities (up to $\sim {3n}_0)$ they predict widely varying behavior for the observables of both symmetric and asymmetric nuclear matter. A particularly relevant example of naturally occurring asymmetric nuclear matter is the material of which neutron stars are composed. At around nuclear matter density, this can be well represented as a mixture of neutrons, protons, electrons, and muons $(n+p+e+\mu$ matter) in $\beta$-equilibrium, and these densities turn out to be the key ones for determining the properties of neutron-star models with masses near to the widely used “canonical” value of ${1.4M}_{\odot }.$ By constructing equations of state for neutron-star matter using the different Skyrme parametrizations, calculating corresponding neutron-star models and then comparing these with observational data, an additional constraint can be obtained for the values of the Skyrme parameters. Such a constraint is particularly relevant because the parametrizations are initially determined by fitting to the properties of doubly closed-shell nuclei and it is an open question how suitable they then are for nuclei with high values of isospin, such as those at the neutron drip-line and beyond. The neutron-star environment provides an invaluable testing ground for this. We have carried out an investigation of 87 different Skyrme parametrizations in order to examine how successful they are in predicting the expected properties of infinite nuclear matter and generating plausible neutron-star models. This is the first systematic study of the predictions of the various Skyrme parametrizations for the density dependence of the characteristic observables of nuclear matter; the density dependence of the symmetry energy for $\beta$-equilibrium matter turns out to be a crucial property for indicating which Skyrme parameter sets will apply equally well for finite nuclei and for neutron-star matter. Only 27 of the 87 parametrizations investigated pass the test of giving satisfactory neutron-star models and we present a list of these.

Several experiments have extracted proton electromagnetic form factors from elastic cross section measurements using the Rosenbluth technique. Global analyses of these measurements indicate approximate scaling of the electric and magnetic form factors $\left({\mu }_p{G}_{E_p}{/G}_{M_p}\approx 1\right),$ in contrast to recent polarization transfer measurements from Jefferson Lab. We present here a global reanalysis of the cross section data aimed at understanding the disagreement between the Rosenbluth extraction and the polarization transfer data. We find that the individual cross section measurements are self-consistent, and that the new global analysis yields results that are still inconsistent with polarization measurements. This discrepancy indicates a fundamental problem in one of the two techniques, or a significant error in polarization transfer or cross section measurements. An error in the polarization data would imply a large error in the extracted electric form factor, while an error in the cross sections implies an uncertainty in the extracted form factors, even if the form factor ratio is measured exactly.

We study quantum phase transitions between spherical, prolate, and oblate nuclear ground-state shapes using the interacting $\mathrm{sd}$-boson model $(sd$-IBM) and demonstrate the analogy between the IBM results (also results of any axially symmetric quadrupole collective model) and predictions of the Landau theory of phase transitions in classical thermodynamics. A detailed comparison of the two frameworks is performed exploiting the concept of “specific heat,” introduced in four alternative ways in the quantum case. All these definitions (two of them based on spectroscopic features of the ground state, the others on a randomized version of the model) lead to similar peaked forms of the “specific heat” at the point of the quantum phase transition. We analyze the effect of an increasing boson number on these curves and observe convergence to the singular phase-transitional behavior in the classical limit. Other observable signatures of the IBM structural phase transitions are also discussed with the aim to facilitate the location of a particular nucleus in the parameter space (extended Casten triangle) near the transitions.

The behavior of several nuclear properties with temperature is analyzed within the framework of the finite temperature Hartree-Fock-Bogoliubov (FTHFB) theory with the Gogny force and large configuration spaces. Thermal shape fluctuations in the quadrupole degree of freedom, around the mean field solution, are taken into account with the Landau prescription. As representative examples the nuclei ${}^{164}\mathrm{Er},$ ${}^{152}\mathrm{Dy},$ and ${}^{192}\mathrm{Hg}$ are studied. Numerical results for the superfluid to normal and deformed to spherical shape transitions are presented. We found a substantial effect of the fluctuations on the average value of several observables. In particular, we get a decrease in the critical temperature $T_c$ for the shape transition as compared with the plain FTHFB prediction as well as a washing out of the shape transition signatures. The new values of $T_c$ are closer to those found in Strutinsky calculations and with the pairing plus quadrupole model Hamiltonian.

We study to what extent a measurement of the $m_{\perp }$ spectra for hadrons and their resonances can resolve ambiguities in the statistical model description of particle production. We describe in a quantitative analysis how physical assumptions about the freeze-out geometry and dynamics influence the particle spectra. Considering ratios of $m_{\perp }$ distribution of resonance-particle ratios (such as $K^{*}/K,$ ${\Sigma }^{*}/\Lambda ,{\eta }^{\prime }/\eta )$ we observe significant sensitivity to fireball freeze-out geometry and flow dynamics.

Effects of neutrino trapping on K and $\overline{K}$ production and $\overline{K}$ condensation in supernova matter are studied in the density-dependent relativistic hadron field theory and in the nonlinear $\sigma -\omega$ model with the parameter set Tm1. Our results show that critical densities for $\overline{K}$ condensation with neutrino trapping are shifted to higher densities compared with those of neutrino free. Threshold energies for K and $\overline{K}$ production are not sensitive to the effects induced by neutrino trapping. Meanwhile, it is shown that the effects of neutrino trapping decrease the maximum masses of protoneutron stars.

The ${}^{51}\mathrm{V}{(d,}^2\mathrm{He}{)}^{51}\mathrm{Ti}$ charge-exchange reaction has been investigated at an incident energy of 171 MeV and scattering angles near $0°.$ The two protons in the ${}^1{S}_0\mathrm{}\left(\mathrm{pp}\right)\mathrm{}$ state (denoted as ${}^2\mathrm{He})$ were both momentum analyzed and detected by the same spectrometer and detector. Spectra with a resolution of about 125 keV (full width at half maximum) have been obtained allowing identification of many levels in ${}^{51}\mathrm{Ti}$ with high precision. The ${\mathrm{GT}}^{+}$ strength distribution for transitions to levels up to about 6 MeV of excitation energy has been extracted. The results are compared with a large-scale shell-model calculation in the full $\mathrm{pf}$ shell.

Modern effective-theory techniques are applied to the nuclear many-body problem. A novel approach is proposed for the renormalization of operators in a manner consistent with the construction of the effective potential. To test this approach, a one-dimensional, yet realistic, nucleon-nucleon potential is introduced. An effective potential is then constructed by tuning its parameters to reproduce the exact effective-range expansion and a variety of bare operators are renormalized in a fashion compatible with this construction. Predictions for the expectation values of these effective operators in the ground state reproduce the results of the exact theory with remarkable accuracy (at the 0.5% level). This represents a marked improvement over a widely practiced approach that uses effective interactions but retains bare operators. Further, it is shown that this improvement is more impressive as the operator becomes more sensitive to the short-range structure of the potential. We illustrate the main ideas of this work using the elastic form factor of the deuteron as an example.

Ground-state properties of ${}^{16}\mathrm{O}$ and ${}^{40}\mathrm{Ca}$ are calculated with a low-momentum nucleon-nucleon potential $V_{\mathrm{low}-\mathrm{k}},$ derived from the chiral next-to-next-to-next-to-leading-order interaction recently constructed by Entem and Machleidt. The smooth $V_{\mathrm{low}-\mathrm{k}}$ is used directly in a Hartree-Fock approach, avoiding the difficulties of the Brueckner-Hartree-Fock procedure. Corrections up to third order in the Goldstone expansion are evaluated, leading to results that are in very good agreement with experiment. Convergence properties of the expansion are examined.

The stability and/or instability of ${}_{60}^{133-137}\mathrm{Nd},$ ${}_{64}^{144-158}\mathrm{Gd},$ ${}_{80}^{176-194}\mathrm{Hg},$ and ${}_{82}^{192-198}\mathrm{Pb}$ parents are studied with respect to the $\alpha$ and heavy-cluster decays. The $\alpha$-decay studies also include the heavier ${}^{199-210}\mathrm{Pb}$ nuclei, for reasons of spherical magic shells at $Z=82\mathrm{}$ and $N=126.\mathrm{}$ The calculations are made by using the preformed cluster-decay model, and the obtained $\alpha$-decay half-lives are compared with the available experimental data. Having met with a very good success for the comparisons of $\alpha$-decay half-lives and in giving the associated known magic or submagic closed-shell structures of both the parent nuclei and daughter products, the interplay of closed-shell effects in the cluster-decay calculations is investigated. The cluster-decay calculations also give the closed shell effects of known spherical magicities, both for the parent and daughter nuclei, and further predict new (deformed) closed-shells at $Z=72\mathrm{}–74$ and $N=96\mathrm{}–104$ due to both the stability and instability of Hg and Pb parents against cluster decays. Specifically, a new deformed daughter radioactivity is predicted for various cluster decays of ${}^{186-190}\mathrm{Hg}$ and ${}^{194,195}\mathrm{Pb}$ parents with the best possible measurable cases identified as the ${}^8\mathrm{Be}$ and ${}^{12}\mathrm{C}$ decays of ${}^{176,177}\mathrm{Hg}$ and/or ${}^{192}\mathrm{Pb}$ parents. The predicted decay half-lives are within the measurable limits of the present experimental methods. The interesting point to note is that the parents with measurable cluster-decay rates are normal deformed nuclei at the transition between normal and superdeformation.

The configuration mixing between the first two $0^{+}$ states in ${}^{98}\mathrm{Sr},$ which have very different deformation, has been reanalyzed by introducing the term involving the intrinsic $E2\mathrm{}$ matrix element between them in a two-state-mixing model calculation. A mixing strength of $\approx 2.6\%$ was determined using the known $E0\mathrm{}$ strength and the intrinsic $E2\mathrm{}$ matrix elements for those two $0^{+}$ states. This mixing strength is nearly a factor of 4 weaker than that of the early analysis. Comparison is made to a similar case of configuration mixing in ${}^{100}\mathrm{Zr}.$

A study of the effects of meson-exchange currents and isobar configurations in $A\left(\overrightarrow{e}{,e}^{\prime }\overrightarrow{p}\right)B$ reactions is presented. We use a distorted wave impulse approximation model where final-state interactions are treated through a phenomenological optical potential. The model includes relativistic corrections in the kinematics and in the electromagnetic one- and two-body currents. The full set of polarized response functions is analyzed, as well as the transferred polarization asymmetry. Results are presented for proton knockout from closed-shell nuclei for moderate to high momentum transfer.

We investigate the structure of ${}^{22}\mathrm{Mg}$ just above the proton threshold using shell-model and Coulomb-energy calculations. Our results disagree with some earlier work in identifying which levels are most important for the ${}^{21}\mathrm{Na}(p,\gamma )$ reaction.

We propose a new method of analytic continuation in the coupling constant combined with the complex scaling method (ACCC+CSM). In ACCC+CSM, the analytic continuation is carried out by using a resonant solution, which is obtained by using CSM. By using this method, for the first time, we obtain a resonant solution $(E=3.0\mathrm{}-i15.6\mathrm{}\mathrm{MeV}),$ which corresponds to the soft dipole resonance in ${}^6\mathrm{He}.$

Electromagnetic transition probabilities were measured using the recoil distance Doppler-shift technique and the ${}^{40}\mathrm{Ca}{(}^{152}\mathrm{Sm}{,4n)}^{188}\mathrm{Pb}$ reaction at a beam energy of 805 MeV to investigate shape coexistence in ${}^{188}\mathrm{Pb}.$ For the first time, a plunger was combined with Gammasphere and the Argonne Fragment Mass Analyzer. It was possible to measure the lifetimes of two states in the prolate band of ${}^{188}\mathrm{Pb}$ and, thus, provide for the first time evidence for the collectivity of this band. A three-level mixing calculation revealed that the first $2^{+}$ state is predominantly of prolate character.

The level structure of ${}^{120}\mathrm{Te}$ has been examined utilizing gamma-ray spectroscopy following the $(\alpha ,2n\gamma )$ reaction and ${}^{120}\mathrm{I}$ decay. Excitation functions, $\gamma -\gamma$ coincidences, and angular distributions were measured. Spectroscopic information, e.g., spins, branching ratios, and multipole-mixing ratios, was obtained for many new levels below 4.5 MeV in excitation energy. The level scheme was examined from the viewpoint of an anharmonic vibrator model, the general collective model, the particle-core coupling model, and interacting-boson-model-based intruder models. Particular aspects of the level sequence can be reproduced by each of these models, but the agreement with transition rate data is modest. The $B\left(E2\mathrm{}\right)\mathrm{}$ transition rate ratios are most consistent with the simple U(5) pattern. The higher-spin intruder states are identified in ${}^{120}\mathrm{Te}$ by comparison to the known band structures and decay patterns of the $N=66\mathrm{}$ and $N=68\mathrm{}$ tin and cadmium nuclei. The intruder signature vanishes below spin-8, where there is strong mixing between states.

Low-spin states in the odd-odd $N=Z$ nucleus ${}^{58}\mathrm{Cu}$ were investigated with the ${}^{58}\mathrm{Ni}(p,n\gamma {)}^{58}\mathrm{Cu}$ fusion evaporation reaction at the FN-TANDEM accelerator in Cologne. $\gamma \gamma$-coincidences, $\gamma \gamma$-angular correlations, and signs of $\gamma$-ray polarizations were measured. Seventeen low-spin states below 3.6 MeV and 17 new transitions were observed. Ten multipole mixing ratios and 17 $\gamma$-branching ratios were determined for the first time. New detailed spectroscopic information on the $2_2^{+}$ state, the isobaric analogue state (IAS) of the $2_1^{+},T=1\mathrm{}$ state of ${}^{58}\mathrm{Ni},$ makes ${}^{58}\mathrm{Cu}$ the heaviest odd-odd $N=Z$ nucleus with known ${B(E2;2\mathrm{}}^{+},T=\overrightarrow{1}{0}^{+},T=1)$ value. The $4^{+}$ state at 2.751 MeV, observed here for the first time, is identified as the IAS of the $4_1^{+},T=1\mathrm{}$ state in ${}^{58}\mathrm{Ni}.$ The new data are compared to full $\mathrm{pf}$-shell-model calculations with the GXPF1 residual interaction and to calculations within a ${\mathrm{pf}}_{5/2}$ configurational space with a residual surface $\delta$ interaction. The role of the ${}^{56}\mathrm{Ni}$ core excitations for the low-spin structure in ${}^{58}\mathrm{Cu}$ is discussed.

Using the strong $1^{-}$ state in ${}^{20}\mathrm{Ne}$ as a standard, we have analyzed data for α transfer on ${}^{15}\mathrm{N}$ and have extracted $\alpha$ widths for six states between 5.3 and 6.6 MeV in ${}^{19}\mathrm{F}.$ Additionally, results for the 3.91-MeV state allow an estimate of the $\alpha$ width for the mirror ${}^{19}\mathrm{Ne}\mathrm{}\left(4.03\right).$

Electromagnetic and nuclear inelastic scattering of the halo nucleus ${}^{11}\mathrm{Be}$ have been investigated by a measurement of the one-neutron removal channel, utilizing a secondary ${}^{11}\mathrm{Be}$ beam with an energy of 520 MeV/nucleon impinging on lead and carbon targets. All decay products, i.e., ${}^{10}\mathrm{Be}$ fragments, neutrons, and $\gamma$ rays have been detected in coincidence. Partial cross sections for the population of ground and excited states in ${}^{10}\mathrm{Be}$ were determined for nuclear diffractive breakup as well as for electromagnetically induced breakup. The partial cross sections for ground-state transitions have been differentiated further with respect to excitation energy, and the dipole-strength function associated solely with transitions of the halo ${2s}_{1/2}$ neutron to the continuum has been derived. The extracted dipole strength integrated from the neutron threshold up to 6.1 MeV excitation energy amounts to ${0.90\left(6\right)e}^2{\mathrm{fm}}^2.$ A spectroscopic factor for the $\nu {2s}_{1/2}{\otimes }^{10}\mathrm{Be}{(0\mathrm{}}^{+})$ single-particle configuration of 0.61(5) and a root-mean-square radius of the ${2s}_{1/2}$ neutron wave function of 5.7(4) fm have been deduced.