We discuss the dynamics in a finite-density medium including a heavy impurity particle (hadron or quark) with a heavy flavor, charm and bottom, at zero temperature. As a system, we consider a $\overline{D}$ ($B$) meson embedded in nuclear matter as a heavy impurity boson with SU(2) isospin symmetry. As another system, we also consider a charm (bottom) quark embedded in quark matter as a heavy impurity fermion with SU(3) color symmetry. We suppose a vector current interaction with SU($n$) symmetry ($n\ge 2$) for the fermion composing the Fermi surface and the embedded heavy impurity particle, and we calculate the scattering amplitude perturbatively for the small coupling constant up to one-loop level. We obtain that the scattering amplitude has a logarithmic enhancement in the large-mass limit of the heavy impurity particle, and we show that the perturbative calculation breaks down for any small coupling constant in this limit.

We propose a method to compute, for a given potential model, an arbitrary coefficient of the effective-range function expanded as a power series in energy. The method is based on a set of recurrence relations at low energy, that allows a compact and general description to any order in energy for neutral and charged cases. By using the Lagrange mesh technique to compute the $R$ matrix at zero energy, this proposal permits us to compute, with a very good precision, the effective-range parameters. We use a potential model for some nuclear systems to illustrate the effectiveness of this method and to discuss its numerical limitations.

Recently measured fusion cross sections for the neutron-rich system ${}^{20}$O+${}^{12}$C are compared to dynamic, microscopic calculations using time-dependent density functional theory. The calculations are carried out on a three-dimensional lattice and performed both with and without a constraint on the density. The method has no adjustable parameters, and its only input is the Skyrme effective nucleon-nucleon interaction. While the microscopic density constrained time-dependent Hartree-Fock calculations lie closer to the experimental data than standard fusion systematics, they underpredict the experimental data significantly.

A model for computing the probability density of event-by-event participant center-of-mass rapidity $y^{\mathrm{c}.\mathrm{m}.}$ is presented. The evaluations of the $y^{\mathrm{c}.\mathrm{m}.}$ distribution are performed for different collision energies and different centralities. We show that for certain conditions the rapidity distribution is described by a Gaussian with a variance determined mostly by the collision centrality. It is found that the width of the $y^{\mathrm{c}.\mathrm{m}.}$ distribution increases strongly for more peripheral collisions, while it depends weakly on the collision energy. Other theoretical estimates of rapidity distribution are presented and questions of interaction and separation between spectators and participants are discussed.

The half-life of the superallowed Fermi ${\beta }^{+}$ emitter ${}^{14}$O has been determined via simultaneous direct $\beta$ and $\gamma$ counting experiments at TRIUMF's Isotope Separator and Accelerator (ISAC) facility. A $\gamma$-ray counting measurement was performed by detecting the 2312.6-keV $\gamma$ rays emitted from an excited state of the daughter ${}^{14}$N following the implantation of samples at the center of the 8$\pi$ $\gamma$-ray spectrometer, a spherical array of 20 high-purity germanium (HPGe) detectors. A simultaneous $\beta$ counting experiment was performed using a fast plastic scintillator positioned behind the implantation site with a solid angle coverage of $\sim$20$\%$. The results, $T_{1/2}\left(\beta \right)=70.610\pm 0.030\text{s}$ and $T_{1/2}\left(\gamma \right)=70.632\pm 0.094\text{s}$, form a consistent set and, together with eight previous measurements, establish a new average for the ${}^{14}$O half-life of $T_{1/2}=70.619\pm 0.011\text{s}$ with a reduced ${\chi }^2$ of 0.99.

By extending the stochastic mean-field model by including pairing, an approach is proposed for describing the evolution of complex many-body systems in terms of an ensemble of time-dependent Hartree-Fock Bogoliubov trajectories which is determined by incorporating fluctuations in the initial state. The nonlinear evolution of the initial fluctuations provides an approximate description of quantal correlations and fluctuations of collective observables. Since the initial-state fluctuations break particle-number symmetry, the dynamical description in which pairing correlations play a crucial role is greatly improved as compared to the mean-field evolution. The approach is illustrated for a system of particles governed by a pairing Hamiltonian.

The low-lying states of the ${}^9$Li nucleus are investigated with a unified framework of microscopic structure and reaction models. In the structure model, the wave function is fully antisymmetrized and the ${}^9$Li nucleus is described as an $\alpha$+$t$+$n$+$n$ four-body system, and low-lying 1/2${}^{-}$, 3/2${}^{-}$, 5/2${}^{-}$, and 7/2${}^{-}$ states are obtained by the stochastic multiconfiguration mixing method. Using these wave functions, the quasielastic cross section at $E/A$ = 60 MeV and the elastic and inelastic cross sections at $E/A$ = 50 MeV on the ${}^{12}$C target are calculated in the framework of the microscopic coupled channel (MCC) method. The characteristic inelastic angular distribution is seen in the 3/2${}_2^{-}$ state, whose $\alpha$+$t$ cluster structure and valence neutron configurations are discussed in detail. We find the possibility of triaxial deformation and mixing of dineutron components in the ${}^9$Li nucleus.

We used the high-resolution Q3D magnetic spectrograph at the Maier-Leibnitz Laboratory (MLL) Tandem accelerator in Munich to study ${}^{200}$Hg and ${}^{202}$Hg after two-neutron transfer. The results confirm the sharp drop in the number of low-lying $0^{+}$ states towards the ${}^{208}$Pb shell closure. In total, we assigned six $0^{+}$ states in ${}^{200}$Hg and four $0^{+}$ states in ${}^{202}$Hg. The $0^{+}$ excitation energies and the measured $(p,t)$ transfer cross sections indicate a structural change throughout the Hg isotopes, with the most notable result being the peaking in the cross section of the $0_2^{+}$ state in ${}^{200}$Hg.

To investigate the influence of nuclear finite-size effects on the fragmentation in heavy-ion collisions, the fragment charge distributions of ${}^{40}$Ca+${}^{40}$Ca, ${}^{197}$Au+${}^{197}$Au, ${}^{120}$Xe+${}^{129}$Sn, and ${}^{58}$Ni+${}^{48}$Ca at intermediate incident energies are studied by using the improved quantum molecular dynamics model. Both the width of the wave packet at the coordinate space and the surface energy term strongly affect the formation and stability of fragments at intermediate-low energies. The wave-packet width influences the stability and the central densities of the initial nuclei. With increase of incident energies, the influence of the detail in description of individual nucleons and of their interaction via mean field on the fragment distributions weakens gradually.

We assess the ability of future neutron $\beta$ decay measurements of up to $\mathcal{O}\left({10}^{-4}\right)$ precision to falsify the standard model, particularly the $V-A$ law, and to identify the dynamics beyond it. To do this, we employ a maximum likelihood statistical framework which incorporates both experimental and theoretical uncertainties. Using illustrative combined global fits to Monte Carlo pseudodata, we also quantify the importance of experimental measurements of the energy dependence of the angular correlation coefficients as input to such efforts, and we determine the precision to which ill known “second-class” hadronic matrix elements must be determined in order to exact such tests.

Background: The ${}^3$He${(\alpha ,\gamma )}^7$Be reaction is important for the neutrino production in the sun's core and the production of ${}^7$Li during big bang nucleosynthesis. The reaction mechanism is characterized by a strong direct capture component and nearby broad unbound resonance levels.

Purpose: Recent experiments have opened up a new energy window into the reaction mechanism and it becomes more and more evident that, in order to understand the shape of the $S$ factor, theoretical calculations need to take into account possible resonance contributions from higher energies as well.

Method: In the present work, a relatively wide energy window was investigated, $E_{c.m.}=300$–1460 keV, by detecting the prompt $\gamma$ rays from the reaction. An extensive $R$-matrix analysis was performed, utilizing all modern literature capture data, as well as elastic scattering data, which are important in constraining some $R$-matrix parameters.

Results: The new experimental data agree very well with the modern literature data. The final result from the $R$-matrix fit gives a zero-energy $S$ factor of $S\left(0\right)=0.554\left(20\right)$ keV b. A table with the newly calculated reaction rate is given.

Conclusions: The simultaneous $R$-matrix analysis of the ${}^3$He${(\alpha ,\gamma )}^7$Be and ${}^3$He${(\alpha ,\alpha )}^3$He channels yielded a reliable fit, consistent with all the included experimental data sets. In order to further constrain the reaction rate within the $R$-matrix framework, additional high-energy capture data, $\gamma$-ray angular distributions, and the inclusion of other relevant reaction channels are necessary.

Strongly magnetized symmetric nuclear matter is investigated within the context of effective baryon-meson exchange models. The magnetic field is coupled to the charge as well as the dipole moment of the baryons by including the appropriate terms in the Lagrangian density. The saturation density of magnetized, symmetric nuclear matter ${\rho }_0\left(B\right)$ was calculated for magnetic fields of the order of ${10}^{17}$ gauss. For the calculated range of ${\rho }_0\left(B\right)$ the binding energy, symmetry energy coefficient $a_4$, and compressibility $K$ of nuclear matter were also calculated. It is found that with an increasing magnetic field ${\rho }_0\left(B\right)$ increases, while the system becomes less bound. Furthermore, the depopulation of proton Landau levels leaves a distinct fluctuating imprint on $K$ and $a_4$. The calculations were also performed for increased values of the baryon magnetic dipole moment. By increasing the dipole moment strength ${\rho }_0\left(B\right)$ is found to decrease, but the system becomes more tightly bound while the fluctuations in $K$ and $a_4$ persist.

Excitation functions for the production of heavy residues have been measured for the collisions ${}^{6,7}\mathrm{Li}+{}^{64}\mathrm{Zn}$ at energies around and below the Coulomb barrier. The cross sections for heavy residue production have been measured using an activation technique, detecting off-line the characteristic atomic x-rays emitted in the electron capture decay of the reaction products. The experimental relative yields of the residues have been compared with statistical model calculations performed by using the code cascade. Such a comparison suggests that heavy residue production is dominated by complete fusion at above-barrier energies, whereas different processes like incomplete fusion and/or transfer become dominant in the sub-barrier energy region. The heavy residue excitation function ratio between the ${}^6$Li- and ${}^7$Li-induced collisions shows an increasing trend as the energy decreases below the barrier.

We study the dilepton production in heavy-ion collisions at energies of 1–2 GeV/nucleon as well as in proton-induced $pp$, $pn$, $pd$, and $p+A$ reactions from 1 up to 3.5 GeV where data have been taken by the HADES Collaboration. For the analysis we employ three different transport models: the microscopic off-shell Hadron-String-Dynamics (HSD) transport approach, the Isospin Quantum Molecular Dynamics (IQMD) approach, as well as the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) approach. We find that the HSD and IQMD models describe very reasonably the elementary $pp$, $pn$, and $\pi N$ reactions despite different assumptions on quantities like the excitation function of the $\Delta$ multiplicity, where solid experimental constraints are not available. Taking these data on elementary collisions as input, the three models provide a good description of the presently available heavy-ion data. In particular, we confirm the experimentally observed enhancement of the dilepton yield (normalized to the multiplicity of neutral pions $N_{{\pi }^0}$) in heavy-ion collisions with respect to that measured in $NN=(pp+pn)/2$ collisions. We identify two contributions to this enhancement: (a) the $pN$ bremsstrahlung which scales with the number of collisions and not with the number of participants, i.e., pions; (b) the dilepton emission from intermediate $\Delta$'s which are part of the reaction cycles $\Delta \to \pi N;\pi N\to \Delta$ and $NN\to N\Delta ;N\Delta \to NN$. With increasing system size more generations of intermediate $\Delta$'s are created. If such $\Delta$ decays into a pion, the pion can be reabsorbed; however, if it decays into a dilepton, the dilepton escapes from the system. Thus, experimentally one observes only one pion (from the last produced $\Delta$), whereas the dilepton yield accumulates the contributions from all $\Delta$'s of the cycle. We show as well that the Fermi motion enhances the production of pions and dileptons in the same way. Furthermore, employing the off-shell HSD approach, we explore the influence of in-medium effects like the modification of self-energies and spectral functions of the vector mesons owing to their interactions with the hadronic environment. We find only a modest influence of the in-medium effects on the dilepton spectra in the invariant mass range where data with small error bars exist.

Quarkonium at temperatures above deconfinement is an open quantum system, whose dynamics is determined not just by a potential energy and mass, but also by a drag coefficient which characterizes its interaction with the medium. We develop a path-integral Monte Carlo method for examining quarkonium at finite-temperature; first, the path-integral approach for open quantum systems is developed analytically for imaginary time, and then the imaginary-time Green function is calculated with a realistic potential, mass, and drag term for quarkonium near deconfinement. We demonstrate that dissipation could affect the Euclidean heavy-heavy correlation functions calculated in lattice simulations at temperatures just above deconfinement.

Mixing of the low-lying three- and five-quark $\Omega$ states with spin-parity quantum numbers ${\frac{1}{2}}^{-}$ and ${\frac{3}{2}}^{-}$ is investigated, employing an instanton-induced quark-antiquark pair creation model, which precludes transitions between $s^3$ and $s^4\overline{s}$ configurations. Models with hyperfine interactions between quarks are of three different kinds, namely, one-gluon-exchange (OGE), Goldstone-boson-exchange (GBE), and an instanton-induced interaction (INS). Numerical results show that the instanton-induced pair creation causes strong mixing between the three- and five-quark configurations with spin $3/2$, and that this mixing decreases the energy of the lowest spin $3/2$ states in all three different hyperfine interaction models to $\sim 1750\pm 50$ MeV. On the other hand, transition couplings between $s^3$ and $s^{3}q\overline{q}$ states with spin $1/2$ caused by instanton-induced $q\overline{q}$ creation is very small and the resulting mixing of three- and five-quark configurations in the OGE and INS models is negligible, while the mixing of the spin $1/2$ states in GBE model is not; but effects of this mixing on energies of mixed states are also very small. Accordingly, the lowest $\Omega$ states with negative parity in all three hyperfine interactions models have spin $3/2$.

A delayed, 76.5-keV transition has been observed in coincidence with ${}^{97}$Rb at the Lohengrin mass spectrometer via $\gamma$-ray and conversion-electron spectroscopy. The multipolarity of the delayed transition was determined to be $E1$ and its measured half-life is 5.1(4) $\mu$s. Comparisons with the results of Hartree-Fock-Bogoliubov and quasiparticle-rotor model calculations allow a spin and parity of ${(1/2,3/2)}^{-}$ to be assigned to this state. The isomer is likely to be one of the low-lying prolate-deformed $3/2^{-}\left[312\right]$, or oblate-deformed $1/2^{-}\left[321\right]$, $3/2^{-}\left[321\right]$ quasiparticle excitations. A new decay branch of the ($9/2^{+}$), 830.8-keV isomer of ${}^{97}$Sr has also been observed in the same experiment, allowing a spin of ${(5/2)}^{+}$ to be assigned to the 522.5-keV state. This level is likely to have a high-seniority spherical configuration.

Background: The shape-phase transition at $N$ $=$ 88–90, and the role of $Z$ $=$ 64 subshell effect therein has been a subject of study on empirical basis and in the context of the $N_p$N${}_n$ scheme, but a microscopic view of the same has been lacking.

Purpose: A microscopic view of the $N$ $=$ 88–90 shape-phase transition is developed. The $Z$ $=$ 64 subshell effect is viewed in terms of the Nilsson single-particle orbitals in this region.

Method: The dynamic pairing plus quadrupole model is employed to predict the occupation probabilities of the neutron and proton deformed, single-particle orbitals. The nuclear structure of Ba–Dy ($N$ > 82) nuclei is studied and the shape equilibrium parameters derived.

Results: The filling of neutron orbitals at $N$ $=$ 86, 88, and 90 plays an important role in the shape-phase transition. The filling of the proton Nilsson orbitals of varying slopes leads to the variation of nuclear structure with varying $Z$, which leads to the $Z$ $=$ 64 subshell effect, which disappears at $N=90$.

Conclusions: The effect of the $n$-$p$ interaction of the π$h_{11/2}$ and ν$h_{9/2}$ orbitals, along with the contribution of the ν$i_{13/2}$ orbital leads to the shape-phase transition at $N=88-90$. The slopes of proton Nilsson orbitals explain the $Z$ $=$ 64 subshell effect.

High-spin states of ${}^{99}$Rh were studied through in-beam $\gamma$-ray spectroscopy by using the reaction ${}^{68}$Zn(${}^{37}$Cl, $\alpha$2$n$). The upper part of the band based on the $g_{9/2}$ proton orbital was rearranged in four parallel cascades. Negative parity was tentatively assigned for the side-band that previously had no parity assignment. This negative-parity band was interpreted as having the configuration of $\pi (g_{9/2}{)}^5\nu \left[\right(d_{5/2}{g}_{7/2}{)}^3\left(h_{11/2}\right)]$ and extended up to ${\frac{51}{2}}^{(-)}$, which is possibly a terminating state. The band based on the $p_{1/2}$ proton orbital was observed up to ${\frac{29}{2}}^{-}$ and its property was compared with those of neighboring odd-$Z$ nuclei from the two different viewpoints, one of which is a weakly deformed soft rotor with spin alignments and the other is vibrational to rotational evolution along the band.