Background: For the study of exotic nuclei it is important to have an optical model potential that is reliable not only for stable nuclei but can also be extrapolated to nuclear systems with exotic numbers of protons and neutrons. An efficient way to obtain such a potential is to develop a microscopic optical potential (MOP) based on a fundamental theory with a minimal number of free parameters, which are adjusted to describe stable nuclei all over the nuclide chart.

Purpose: The choice adopted in the present work is to develop the MOP within a relativistic scheme which provides a natural and consistent relation between the spin-orbit part and the central part of the potential. The Dirac-Brueckner-Hartree-Fock (DBHF) approach provides such a microscopic relativistic scheme, which is based on a realistic nucleon-nucleon interaction and reproduces the saturation properties of symmetric nuclear matter without any adjustable parameter. Its solution using the projection technique within the subtracted $T$-matrix representation provides a reliable extension to asymmetric nuclear matter, which is important to describe the features of isospin asymmetric nuclei. The present work performs a global analysis of the isospin dependent nucleon-nucleus MOP based on the DBHF calculation in symmetric and asymmetric nuclear matter.

Methods: The DBHF approach is used to evaluate the relativistic structure of the nucleon self-energies in nuclear matter at various densities and asymmetries. The Schrödinger equivalent potentials of finite nuclei are derived from these Dirac components by a local density approximation (LDA). The density distributions of finite nuclei are taken from the Hartree-Fock-Bogoliubov approach with Gogny D1S force. An improved LDA approach (ILDA) is employed to get a better prediction of the scattering observables. A ${\chi }^2$ assessment system based on the global simulated annealing algorithm is developed to optimize the very few free components in this study.

Results: The nucleon-nucleus scattering calculations are carried out for a broad spectrum of $n$ and $p$ scattering experiments below 200 MeV with targets ranging from ${}^{12}\mathrm{C}$ to ${}^{208}\mathrm{Pb}$. The scattering observables including the neutron total cross section, proton reaction cross section, elastic scattering angular distribution, analyzing power, and spin rotation are evaluated and compared with the experimental data, as well as with results derived from the widely used phenomenological Koning-Delaroche global potential.

Conclusions: Results with the present relativistic MOP reproduce the $n,p+A$ scattering observables with good accuracy over a broad range of targets and a large region of energies fitting only the free-range factor $t$ in ILDA and minor adjustments of the scalar and vector potentials in the low-density region.

Effects of nuclear mean field and of multiple preequilibrium (PEQ) emission on double differential neutron multiplicity distribution from heavy ion reactions (${}^{12}\mathrm{C}+{}^{165}\mathrm{Ho}$ and ${}^{20}\mathrm{Ne}+{}^{165}\mathrm{Ho}$) at 10–30 MeV/u have been investigated in the framework of the semiclassical formalism for heavy ion reaction (henceforth termed “HION”) developed earlier. HION follows the equilibration of a target+projectile composite system through the kinematics of two-body scattering. In the present work nuclear density distribution in the composite system is estimated in the relativistic mean field (RMF) approach. The nucleon-nucleon collision rates and subsequently the nucleon emission probability are calculated from this density distribution. A second approach based on a semiphenomenological formalism is also used for nuclear density distribution. Energy-angle distribution of neutron multiplicities calculated with this modified HION model coupled with multiple PEQ emission could reproduce the measured data of earlier workers in the projectile energy range of 10–30 MeV/u.

We study the hadronization time of heavy quark in nuclear matter by using the coalescence model and the spatial diffusion constant of a heavy quark from lattice quantum chromodynamic calculations, assuming that the main interaction of a heavy quark at the critical temperature is hadronization. It is found that the hadronization time of a heavy quark is about $3 \mathrm{fm}/c$ for $2\pi T_c{D}_s=6$, if a heavy quark is combined with the nearest light antiquark in coordinate space without any correlation between the momentum of a heavy quark and that of a light antiquark which forms a heavy meson. However, the hadronization time reduces to $0.6–1.2 \mathrm{fm}/c$ for charm and $0.4–0.9 \mathrm{fm}/c$ for bottom, depending on the heavy meson radius, in the presence of momentum correlation. Considering the interspace between quarks and antiquarks at the critical temperature, it seems that the hadronization of a heavy quark does not happen instantaneously but gradually for a considerable time, if started from the thermal distribution of quarks and antiquarks.

The properties of ${}^{12}\mathrm{C},{}^{16}\mathrm{O}$, and ${}^{20}\mathrm{Ne}$ nuclei in strong magnetic fields $B\simeq {10}^{17}$ G are studied in the context of strongly magnetized neutron stars and white dwarfs. The sky3d code is extended to incorporate the interaction of nucleons with the magnetic field and is utilized to solve the time-independent Hartree-Fock equations with a Skyrme interaction on a Cartesian three-dimensional grid. The numerical solutions demonstrate a number of phenomena, which include a splitting of the energy levels of spin-up and -down nucleons, spontaneous rearrangement of energy levels in ${}^{16}\mathrm{O}$ at a critical field, which leads to jump-like increases of magnetization and proton current in this nucleus, and evolution of the intrinsically deformed ${}^{20}\mathrm{Ne}$ nucleus toward a more spherical shape under increasing field strength. Many of the numerical features can be understood within a simple analytical model based on the occupation by the nucleons of the lowest states of the harmonic oscillator in a magnetic field.

High-spin states in ${}^{124}\mathrm{Xe}$ have been populated using the ${}^{80}\mathrm{Se}({}^{48}\mathrm{Ca},4n)$ reaction at a beam energy of 207 MeV and high-multiplicity, $\gamma$-ray coincidence events were measured using the Gammasphere spectrometer. Six high-spin bands with large moments of inertia, similar to those observed in neighboring nuclei, have been observed. The experimental results are compared with calculations within the framework of the cranked Nilsson-Strutinsky model. It is suggested that the configurations of the bands involve excitations of protons across the $Z=50$ shell gap coupled to neutrons within the $N=50–82$ shell or excited across the $N=82$ shell closure.

What effect do particle-emitting resonances have on the scattering cross section? What physical considerations are necessary when modeling these resonances? These questions are important when theoretically describing scattering experiments with radioactive ion beams which investigate the frontiers of the table of nuclides, far from stability. Herein, a novel method is developed that describes resonant nuclear scattering from which centroids and widths in the compound nucleus are obtained when one of the interacting bodies has particle unstable resonances. The method gives cross sections without unphysical behavior that is found if simple Lorentzian forms are used to describe resonant target states. The resultant cross sections differ significantly from those obtained when the states in the coupled channel calculations are taken to have zero width, and compound-system resonances are better matched to observed values.

In a recent publication we have argued that using two very successful $n\text{−}{}^9\mathrm{Be}$ optical potentials [A. Bonaccorso and R. J. Charity, Phys. Rev. C 89, 024619 (2014)] and microscopic projectile densities, it is possible to build a single-folded (light-) nucleus-${}^9\mathrm{Be}$ imaginary optical potential which is more accurate than a double-folded optical potential. By comparing to experimental reaction cross sections, we showed for ${}^8\mathrm{B},{}^8\mathrm{Li}$, and ${}^8\mathrm{C}$ projectiles, that a very good agreement between theory and data could be obtained with such a “bare” potential, at all but the lowest energies where a small semimicroscopic surface term was added to the single-folded potential to take into account projectile breakup. In this paper we extend this study to the case of ${}^9\mathrm{C}$ projectiles and assess the sensitivity to the projectile density used. We then obtained the modulus of the nucleus-nucleus $S$ matrix and parametrize it in terms of a strong-absorption radius $R_s$ and finally extracted the phenomenological energy dependence of this radius. This approach could be the basis for a systematic study of optical potentials for light exotic nuclei scattering on light targets and/or parametrizations of the $S$ matrix. Furthermore our study will serve to make a quantitative assessment of the description of the core-target part of knockout reactions, in particular their localization in terms of impact parameters.

Background: The astrophysical $r$-process occurs in an explosive astrophysical event under extremely neutron-rich conditions, leading to $\left(n,\gamma \right)-\left(\gamma ,n\right)$ equilibrium along isotopic chains which peaks around neutron separation energies of a few MeV. Nuclei with larger $Z$ are usually produced by ${\beta }^{-}$ decay, but under certain conditions also $\alpha$-induced reactions may become relevant for the production of nuclei with $Z+2$.

Purpose: The uncertainties of the reaction rates of these $\alpha$-induced reactions are discussed within the statistical model. As an example, $\alpha$-induced $\left(\alpha ,n\right)$ and $(\alpha ,xn)$ reaction cross sections for the neutron-rich ${}^{86}\mathrm{Se}$ nucleus are studied in detail.

Method: In a first step, the relevance of $\left(\alpha ,n\right)$ and $(\alpha ,xn)$ reactions is analyzed. Next the uncertainties are determined from a variation of the $\alpha$-nucleus potential which is the all-dominant parameter for the astrophysical $Z\to Z+2$ reaction rate.

Results: It is found that the $r$-process flow towards nuclei with larger $Z$ is essentially influenced only by the $\alpha$-nucleus potential whereas the other ingredients of the statistical model play a very minor role. This finding is based on the fact that the flow towards larger $Z$ depends on the sum over all $\left(\alpha ,xn\right)$ cross sections, which is practically identical to the total $\alpha$-induced reaction cross section.

Conclusions: $\alpha$-nucleus potentials play an important role under certain $r$-process conditions because the flow towards larger $Z$ depends sensitively on the total $\alpha$-induced reaction cross section. The uncertainty of the reaction rate is about a factor of two to three at higher temperatures and exceeds one order of magnitude at very low temperatures.

Background: The Cd isotopes are well studied, but experimental data for the rare isotopes are sparse. At energies above the Coulomb barrier, higher states become accessible.

Purpose: Remeasure and supplement existing lifetimes and magnetic moments of low-lying states in ${}^{106}\mathrm{Cd}$.

Methods: In an inverse kinematics reaction, a ${}^{106}\mathrm{Cd}$ beam impinging on a ${}^{12}\mathrm{C}$ target was used to Coulomb excite the projectiles. The high recoil velocities provide a unique opportunity to measure $g$ factors with the transient-field technique and to determine lifetimes from lineshapes by using the Doppler-shift-attenuation method. Large-scale shell-model calculations were carried out for ${}^{106}\mathrm{Cd}$.

Results: The $g$ factors of the $2_1^{+}$ and $4_1^{+}$ states in ${}^{106}\mathrm{Cd}$ were measured to be $g\left(2_1^{+}\right)=+0.398\left(22\right)$ and $g\left(4_1^{+}\right)=+0.23\left(5\right)$. A lineshape analysis yielded lifetimes in disagreement with published values. The new results are $\tau ({}^{106}\mathrm{Cd};2_1^{+})=7.0\left(3\right)\mathrm{ps}$ and $\tau ({}^{106}\mathrm{Cd};4_1^{+})=2.5\left(2\right)\mathrm{ps}$. The mean life $\tau ({}^{106}\mathrm{Cd};2_2^{+})=0.28\left(2\right)\mathrm{ps}$ was determined from the fully-Doppler-shifted $\gamma$ line. Mean lives of $\tau ({}^{106}\mathrm{Cd};4_3^{+})=1.1\left(1\right)\mathrm{ps}$ and $\tau ({}^{106}\mathrm{Cd};3_1^{-})=0.16\left(1\right)\mathrm{ps}$ were determined for the first time.

Conclusions: The newly measured $g\left(4_1^{+}\right)$ of ${}^{106}\mathrm{Cd}$ is found to be only 59% of the $g\left(2_1^{+}\right)$. This difference cannot be explained by either shell-model or collective-model calculations.

The first direct experimental evidence of a multiparticle-hole ground state configuration of the neutron-rich ${}^{33}\mathrm{Mg}$ isotope has been obtained via intermediate energy (400 A MeV) Coulomb dissociation measurement. The major part $\sim (70\pm 13)\%$ of the cross section is observed to populate the excited states of ${}^{32}\mathrm{Mg}$ after the Coulomb breakup of ${}^{33}\mathrm{Mg}$. The shapes of the differential Coulomb dissociation cross sections in coincidence with different core excited states favor that the valence neutron occupies both the $s_{1/2}$ and $p_{3/2}$ orbitals. These experimental findings suggest a significant reduction and merging of $sd-pf$ shell gaps at $N\sim 20$ and 28. The ground state configuration of ${}^{33}\mathrm{Mg}$ is predominantly a combination of ${}^{32}\mathrm{Mg}(3.0,3.5\mathrm{MeV};2^{-},1^{-})⨂{\nu }_{s_{1/2}}$, ${}^{32}\mathrm{Mg}(2.5\mathrm{MeV};2^{+})⨂{\nu }_{p_{3/2}}$, and ${}^{32}\mathrm{Mg}(0;0^{+})⨂{\nu }_{p_{3/2}}$. The experimentally obtained quantitative spectroscopic information for the valence neutron occupation of the $s$ and $p$ orbitals, coupled with different core states, is in agreement with Monte Carlo shell model (MCSM) calculation using 3 MeV as the shell gap at $N=20$.

The recently observed possible antimagnetic rotation band in ${}^{101}\mathrm{Pd}$ is investigated by the cranked shell model with pairing correlations treated by a particle-number-conserving method, in which the blocking effects are taken into account exactly. The experimental moments of inertia and reduced $B\left(E2\right)$ transition probabilities and their variations with the rotational frequency $\omega$ are well reproduced. By analyzing the $\omega$ dependence of the occupation probability of each cranked Nilsson orbital near the Fermi surface and the contributions of valence orbitals in each major shell to the total angular momentum alignment, the upbending mechanism of $\nu h_{11/2}$ in ${}^{101}\mathrm{Pd}$ is understood clearly. The proton angular momentum alignment and its influence on the two-shears-like mechanism are also discussed.

We present results of the time blocking approximation (TBA) for giant resonances in light-, medium-, and heavy-mass nuclei. The TBA is an extension of the widely used random-phase approximation (RPA) adding complex configurations by coupling to phonon excitations. A new method for handling the single-particle continuum is developed and applied in the present calculations. We investigate in detail the dependence of the numerical results on the size of the single-particle space and the number of phonons as well as on nuclear matter properties. Our approach is self-consistent, based on an energy-density functional of Skyrme type where we used seven different parameter sets. The numerical results are compared with experimental data.

Background: In earlier work, inversion of $S$ matrix for 330 MeV ${}^{16}\mathrm{O}$ on ${}^{12}\mathrm{C}$ resulted in highly undulatory potentials; the $S$ matrix resulted from the inclusion of strong coupling to states of projectile and target nuclei. $L$-independent $S$-matrix equivalent potentials for other explicitly $L$-dependent potentials have been found to be undulatory.

Purpose: To investigate the possible implications of the undulatory dynamic polarization potential for an underlying $L$ dependence of the ${}^{16}\mathrm{O}$ on ${}^{12}\mathrm{C}$ optical potential.

Methods: $S$ matrix to potential, $S_L\to V\left(r\right)$, inversion which yields local potentials that reproduce the elastic channel $S$ matrix of coupled channel (CC) calculations, will be applied to the $S$ matrix for 115.9 MeV ${}^{16}\mathrm{O}$ on ${}^{12}\mathrm{C}$. Further, $S_L$ for explicitly $L$-dependent potentials are inverted and the resulting $L$-independent potentials are characterized and compared with the undulatory potentials found for ${}^{16}\mathrm{O}$ on ${}^{12}\mathrm{C}$.

Results: Some of the undulatory features exhibited by the potentials modified by channel coupling for 115.9 MeV ${}^{16}\mathrm{O}$ on ${}^{12}\mathrm{C}$ can be simulated by simple parameterized $L$-dependent potentials.

Conclusions: The elastic scattering of ${}^{16}\mathrm{O}$ by ${}^{12}\mathrm{C}$ is a particularly favorable case for revealing the effective $L$ dependence of the potential modified by channel coupling. Nevertheless, there is no reason to suppose that undularity is not a generic property leading in many cases to the choice: nucleus-nucleus potentials are (i) smooth and $L$-dependent, (ii) $L$-independent and undulatory, or (iii) both.

Regulator functions applied to two- and three-nucleon forces are a necessary ingredient in many-body calculations based on chiral effective field theory interactions. These interactions have been developed recently with a variety of different cutoff forms, including regulating both the momentum transfer (local) and the relative momentum (nonlocal). While in principle any regulator that suppresses high-momentum modes can be employed, in practice artifacts are inevitable in current power counting schemes. Artifacts from particular regulators may cause significant distortions of the physics or may affect many-body convergence rates, so understanding their nature is important. Here we characterize the differences between cutoff effects using uniform matter at Hartree–Fock and second order in the interaction as a test-bed. This provides a clean laboratory to isolate phase-space effects of various regulators on both two- and three-nucleon interactions. We test the normal-ordering approximation for three-nucleon forces in nuclear matter and find that the relative size of the residual $3N$ contributions is sensitive to the employed regularization scheme.

A combined analysis of the reactions ${\pi }^{-}p\to K^0\mathrm{\Lambda }$ and $\eta n$ is carried out with a chiral quark model. The data in the center-of-mass (c.m.) energy range from threshold up to $W\simeq 1.8$ GeV are reasonably described. For ${\pi }^{-}p\to K^0\mathrm{\Lambda }$, it is found that $N\left(1535\right)S_{11}$ and $N\left(1650\right)S_{11}$ play crucial roles near threshold. The $N\left(1650\right)S_{11}$ resonance contributes to the reaction through configuration mixing with $N\left(1535\right)S_{11}$. The constructive interference between $N\left(1535\right)S_{11}$ and $N\left(1650\right)S_{11}$ is responsible for the peak structure around threshold in the total cross section. The $n$-pole, $u$-, and $t$-channel backgrounds provide significant contributions to the reaction as well. For the ${\pi }^{-}p\to \eta n$ process, the “first peak” in the total cross section is dominated by $N\left(1535\right)S_{11}$, which has a sizeable destructive interference with $N\left(1650\right)S_{11}$. Around $P_{\pi }\simeq 1.0\text{GeV}/c$ ($W\simeq 1.7$ GeV), there seems to be a small bump structure in the total cross section, which might be explained by the interference between the $u$ channel and $N\left(1650\right)S_{11}$. The $N\left(1520\right)D_{13}$ resonance affects the angle distributions of the cross sections notably, although no obvious effects are seen in the total cross section. The role of $P$-wave state $N\left(1720\right)P_{13}$ should be further confirmed by future experiments. If $N\left(1720\right)P_{13}$ has a narrow width of $\mathrm{\Gamma }\simeq 120$ MeV as found in our previous work by a study of the ${\pi }^0$ photoproduction processes, obvious evidence should be seen in the ${\pi }^{-}p\to K^0\mathrm{\Lambda }$ and $\eta n$ processes as well. Finally, we give our predictions of the $s$-channel isospin-$\frac{1}{2}$ resonance contributions to the $\pi N\to \pi N$ reactions.

Background: Level sequences of rotational character have been observed in several nuclei in the $A=60$ mass region. The importance of the deformation-driving $\pi f_{7/2}$ and $\nu g_{9/2}$ orbitals on the onset of nuclear deformation is stressed.

Purpose: A measurement was performed in order to identify collective rotational structures in the relatively neutron-rich ${}^{62}\mathrm{Ni}$ isotope.

Method: The ${}^{26}\mathrm{Mg}\left({}^{48}\mathrm{Ca},2\alpha 4n\gamma \right){}^{62}\mathrm{Ni}$ complex reaction at beam energies between 275 and 320 MeV was utilized. Reaction products were identified in mass $\left(A\right)$ and charge $\left(Z\right)$ with the fragment mass analyzer (FMA) and $\gamma$ rays were detected with the Gammasphere array.

Results: Two collective bands, built upon states of single-particle character, were identified and sizable deformation was assigned to both sequences based on the measured transitional quadrupole moments, herewith quantifying the deformation at high spin.

Conclusions: Based on cranked Nilsson-Strutinsky calculations and comparisons with deformed bands in the $A=60$ mass region, the two rotational bands are understood as being associated with configurations involving multiple $f_{7/2}$ protons and $g_{9/2}$ neutrons, driving the nucleus to sizable prolate deformation.

Background: Lifetimes of nuclear excited states in fission fragments have been studied in the past following isotope separation, thus giving access mainly to the fragments' daughters and only to long-lived isomeric states in the primary fragments. For the first time now, short-lived excited states in the primary fragments, produced in neutron-induced prompt fission of ${}^{235}\mathrm{U}$ and ${}^{241}\mathrm{Pu}$, were studied within the EXILL&FATIMA campaign at the intense neutron-beam facility of the Institute Laue-Langevin in Grenoble.

Purpose: We aim to investigate the quadrupole collective properties of neutron-rich even-even ${}^{138,140,142}\mathrm{Xe}$ isotopes lying between the double shell closure $N=82$ and $Z=50$ and a deformed region with octupole collectivity.

Method: The $\gamma$ rays emitted from the excited fragments were detected with a mixed array consisting of 8 HPGe EXOGAM Clover detectors (EXILL) and 16 ${\mathrm{LaBr}}_3$(Ce) fast scintillators (FATIMA). The detector system has the unique ability to select the interesting fragment making use of the high resolution of the HPGe detectors and determine subnanosecond lifetimes using the fast scintillators. For the analysis the generalized centroid difference method was used.

Results: We show that quadrupole collectivity increases smoothly with increasing neutron number above the closed $N=82$ neutron shell. Our measurements are complemented by state-of-the-art theory calculations based on shell-model descriptions.

Conclusions: The observed smooth increase in quadrupole collectivity is similar to the evolution seen in the measured masses of the xenon isotopic chain and is well reproduced by theory. This behavior is in contrast to higher $Z$ even-even nuclei where abrupt change in deformation occurs around $N=90$.

We present for the first time evidence for the existence of a dynamically refracted primary bow for ${}^9\mathrm{Be}+{}^{16}\mathrm{O}$ scattering. This is demonstrated through the use of coupled channel calculations with an extended double folding potential derived from the density-dependent effective two-body force and precise microscopic cluster wave functions for ${}^9\mathrm{Be}$. The calculations reproduce the experimental Airy structure in ${}^9\mathrm{Be}+{}^{16}\mathrm{O}$ scattering well. It is found that coupling of a weakly bound ${}^9\mathrm{Be}$ nucleus to excited states plays the role of a booster lens, dynamically enhancing the refraction over the static refraction due to the Luneburg lens mean field potential between the ground states of ${}^9\mathrm{Be}$ and ${}^{16}\mathrm{O}$.

The separate quark flavor contributions to the pion and kaon valence quark distribution functions are studied, along with the corresponding electromagnetic form factors in the space-like region. The calculations are made using the solution of the Bethe-Salpeter equation for the model of Nambu and Jona-Lasinio with proper-time regularization. Both the pion and kaon form factors and the valence quark distribution functions reproduce many features of the available empirical data. The larger mass of the strange quark naturally explains the empirical fact that the ratio $u_{K^{+}}\left(x\right)/u_{{\pi }^{+}}\left(x\right)$ drops below unity at large $x$, with a value of approximately $M_u^2/M_s^2$ as $x\to 1$. With regard to the elastic form factors we report a large flavor dependence, with the $u$-quark contribution to the kaon form factor being an order of magnitude smaller than that of the $s$-quark at large $Q^2$, which may be a sensitive measure of confinement effects in QCD. Surprisingly though, the total $K^{+}$ and ${\pi }^{+}$ form factors differ by only 10%. In general we find that flavor breaking effects are typically around 20%.

Hagedorn states are the key to understanding how all hadrons observed in high-energy heavy-ion collisions seem to reach thermal equilibrium so quickly. An assembly of Hagedorn states is formed in elementary hadronic or heavy-ion collisions at hadronization. Microscopic simulations within the transport model UrQMD allow us to study the time evolution of such a pure nonequilibrated Hagedorn state gas to a thermally equilibrated hadron resonance gas by using dynamics, which unlike strings fully respect detailed balance. Propagation, repopulation, rescatterings, and decays of Hagedorn states provide the yields of all hadrons up to a mass of $m=2.5\mathrm{GeV}$. Ratios of feed-down-corrected hadron multiplicities are compared to corresponding experimental data from the ALICE Collaboration at LHC. The quick thermalization within $t=1–2\mathrm{fm}/c$ of the emerging hadron resonance gas exposes Hagedorn states as a tool to understand hadronization.