A phase-space representation of nuclear interactions, which depends on the distance $\vec{r}$ and relative momentum $\vec{p}$ of the nucleons, is presented. A method is developed that permits us to extract the interaction $V(\vec{r},\vec{p})$ from antisymmetrized matrix elements given in a spherical basis with angular momentum quantum numbers, either in momentum- or coordinate-space representation. This representation visualizes in an intuitive way the nonlocal behavior introduced by cutoffs in momentum space or renormalization procedures that are used to adapt the interaction to low-momentum many-body Hilbert spaces, as done in the unitary correlation operator method (UCOM) or with the similarity renormalization group (SRG). It allows us to develop intuition about the various interactions and illustrates how the softened interactions reduce the short-range repulsion in favor of nonlocality or momentum dependence while keeping the scattering phase shifts invariant. It also reveals that these effective interactions can have undesired complicated momentum dependencies at momenta around and above the Fermi momentum. Properties, similarities, and differences of the phase-space representations of the Argonne and the N3LO chiral potential and their UCOM and SRG derivatives are discussed.

We use the model-independent experimental charge density for ${}^{208}\mathrm{Pb}$ to determine a model-independent point-proton density. An improved two-parameter Fermi function representation for the this point-proton density provides input for the analysis of experiments for the neutron density interpreted in terms of neutron skin and halo properties of ${}^{208}\mathrm{Pb}$.

We report a determination of the $n-{}^3\mathrm{He}$ scattering length difference $\Delta b^{\prime }=b_1^{\prime }-b_0^{\prime }=[-5.411\pm 0.031\text{(statistical)}\pm 0.039\text{(systematic)}]$ fm between the triplet and singlet states using a neutron interferometer. This revises our previous result $\Delta b^{\prime }=[-5.610\pm 0.027\text{(statistical)}\pm 0.032\text{(systematic)}]$ fm obtained using the same technique in 2008 [Huber et al., Phys. Rev. Lett. 102, 200401 (2009); Huber et al., Phys. Rev. Lett. 103, 179903(E) (2009)]. This revision is attributable to a reanalysis of the 2008 experiment that now includes a systematic correction caused by magnetic-field gradients near the ${}^3\mathrm{He}$ cell which had been previously underestimated. Furthermore, we more than doubled our original data set from 2008 by acquiring 6 months of additional data in 2013. Both the new data set and a reanalysis of the older data are in good agreement. Scattering lengths of low-$Z$ isotopes are valued for use in few-body nuclear effective field theories, provide important tests of modern nuclear potential models, and, in the case of ${}^3\mathrm{He}$, aid in the interpretation of neutron scattering from quantum liquids. The difference $\Delta b^{\prime }$ was determined by measuring the relative phase shift between two incident neutron polarizations caused by the spin-dependent interaction with a polarized ${}^3\mathrm{He}$ target. The target ${}^3\mathrm{He}$ gas was sealed inside a small, flat-windowed glass cell that was placed in one beam path of the interferometer. The relaxation of ${}^3\mathrm{He}$ polarization was monitored continuously with neutron transmission measurements. The neutron polarization and spin-flipper efficiency were determined separately using ${}^3\mathrm{He}$ analyzers and two different polarimetry analysis methods. A summary of the measured scattering lengths for $n-{}^3\mathrm{He}$ with a comparison to nucleon interaction models is given.

The isoscaling of heavy projectile residues from peripheral heavy-ion reactions at 15–25 MeV/nucleon is employed to obtain information on the process of $N/Z$ equilibration. Recent mass spectrometric data of projectile residues from the reactions of ${}^{86}\mathrm{Kr}$ (15 MeV/nucleon) with ${}^{64,58}\mathrm{Ni}$ and ${}^{124,112}\mathrm{Sn}$ were first analyzed. The isotopically resolved yield distributions of the fragments in the range $Z=26–39$ were employed for the isoscaling analysis. The yield ratios $R_{21}(N,Z)$ of the fragments from each pair of systems exhibit isoscaling (i.e., an exponential dependence on the fragment neutron number $N$ for each atomic number $Z$) with the isoscaling parameter $\alpha$ increasing with decreasing (or increasing) $Z$ away from the projectile. This variation is related to the evolution toward $N/Z$ equilibration with increasing energy dissipation estimated from the residue velocities. In parallel to the new heavy-residue isoscaling data of ${}^{86}\mathrm{Kr}$ at 15 MeV/nucleon, our previous data at 25 MeV/nucleon for the reactions ${}^{86}\mathrm{Kr}+{}^{124,112}\mathrm{Sn}$ and ${}^{64}\mathrm{Ni}+{}^{64,58}\mathrm{Ni}$, ${}^{64}\mathrm{Ni}+{}^{124,112}\mathrm{Sn}$, as well as our data at 15 MeV/nucleon of the lighter system ${}^{40}\mathrm{Ar}+{}^{64,58}\mathrm{Ni}$, were analyzed in a similar way. Calculations with the stochastic nucleon-exchange model DIT (deep inelastic transfer) and the microscopic many-body model CoMD (constrained molecular dynamics) provided an overall fair description of data and valuable guidance for their interpretation. Interestingly, the data of the ${}^{86}\mathrm{Kr}+\mathrm{Ni},\mathrm{Sn}$ reactions at 15 MeV/nucleon show a retardation of the process of $N/Z$ equilibration which, as suggested by the CoMD calculations, is indicative of the collective character of the process. This retardation is not present in the investigated systems at 25 MeV/nucleon (and the light ${}^{40}\mathrm{Ar}+\mathrm{Ni}$ systems at 15 MeV/nucleon), whose behavior is found to be consistent with stochastic nucleon exchange.

Detailed calculations of the yields of projectilelike fragments (with focus on the neutron-rich isotopes) are presented for the interaction of ${}^{86}\mathrm{Kr}$ (15 MeV/nucleon) with ${}^{64}\mathrm{Ni}$, ${}^{58}\mathrm{Ni}$, and ${}^{124}\mathrm{Sn}$, ${}^{112}\mathrm{Sn}$, as well as ${}^{86}\mathrm{Kr}$ (25 MeV/nucleon) with ${}^{124}\mathrm{Sn}$ and compared with our recently published experimental data for these reactions. The calculations are based on a two-step approach: the dynamical stage of the collision was described with the microscopic constrained molecular dynamics (CoMD) model, as well as the phenomenological deep-inelastic transfer (DIT) model and its modified (DITm) version. The deexcitation of the hot projectile fragments was performed with the statistical multifragmentation model (SMM) and the binary-decay model gemini, which provided nearly similar results for the neutron-rich products from the reactions studied. An overall good agreement of the calculations with the experimental results, especially for near-projectile isotopes was observed using both the CoMD model and the DITm model for the dynamical stage. The successful description of the production of neutron-rich isotopes with the CoMD model is of particular importance, due to the predictive power of the microscopic approach that essentially does not depend on the reaction dynamics. Our studies to date suggest that peripheral heavy-ion collisions at this energy range (i.e., well above the Coulomb barrier, but below the Fermi energy), if induced by neutron-rich rare-isotope beams of adequate intensity may offer a unique route to access extremely neutron-rich rare isotopes toward the astrophysical $r$-process path and the presently uncharted neutron drip line.

Background: The time-dependent Hartree-Fock (TDHF) theory has been successful in describing low-energy heavy ion collisions. Recently, we have shown that multinucleon transfer processes can be reasonably described in the TDHF theory combined with the particle-number projection technique.

Purpose: In this work, we propose a theoretical framework to analyze properties of reaction products in TDHF calculations.

Methods: We employ the TDHF theory in three-dimensional Cartesian grid representation combined with particle-number projection method. We develop a theoretical framework to calculate expectation values of operators in the TDHF wave function after collision with the particle-number projection. To show how our method works in practice, the method is applied to ${}^{24}\mathrm{O}+{}^{16}\mathrm{O}$ collisions for two quantities, angular momentum and excitation energy.

Results: The analyses revealed following features of the reaction: The nucleon removal proceeds gently, leaving small values of angular momentum and excitation energy in nucleon removed nuclei. Contrarily, nuclei receiving nucleons show expectation values of angular momentum and excitation energy which increase as the incident energy increases.

Conclusions: The method will be useful for microscopic investigations of reaction mechanisms in low-energy heavy ion collisions as well as for evaluating effects of particle evaporation on multinucleon transfer cross sections.

The reduced transition probability $B\left(E2\right)\uparrow$ of the first excited $2^{+}$ state in the nucleus ${}^{104}\mathrm{Sn}$ was measured via Coulomb excitation in inverse kinematics at intermediate energies. A value of 0.173(28) $e^2\mathrm{b}{}^2$ was extracted from the absolute cross section on a Pb target. Feeding contributions in ${}^{104}\mathrm{Sn}$ from higher lying states were estimated by a reference measurement of the stable ${}^{112}\mathrm{Sn}$. Corresponding only to a moderate decrease of excitation strength relative to the almost constant values observed in the proton-rich, even-$A {}^{106-114}\mathrm{Sn}$ isotopes, present state-of-the-art shell-model predictions, which include proton and neutron excitations across the $N=Z=50$ shell closures as well as standard polarization charges, underestimate the experimental findings.

Borromean nuclear cluster structures are expected at the corresponding drip lines. We locate the regions in the nuclear chart with the most promising constituents, it being protons and $\alpha$ particles and investigate in details the properties of the possible Borromean two-$\alpha$ systems in medium-heavy nuclei. We find in all cases that the $\alpha$ particles are located at the surface of the core nucleus as dictated by Coulomb and centrifugal barriers. The two lowest three-body bound states resemble a slightly contracted ${}^8\text{Be}$ nucleus outside the core. The next two excited states have more complex structures but with strong components of linear configurations with the core in the middle. $\alpha$-removal cross sections would be enhanced with specific signatures for these two different types of structures. The even-even Borromean two-$\alpha$ nucleus, ${}^{142}\mathrm{Ba}$, is specifically investigated and predicted to have ${}^{134}\text{Te}\text{−}\alpha \text{−}\alpha$ structure in its ground state and low-lying spectrum.

The spontaneous fission of ${}^{252}\mathrm{Cf}$ serves as an excellent benchmark of prompt emission in fission since experimental data can be obtained without the need of an incident beam. With the purpose of providing experimental data on the prompt fission neutron properties in correlation with fission-fragment characteristics, an experiment on ${}^{252}\mathrm{Cf}$(SF) has been performed. In addition, the experiment serves as a benchmark of setup and analysis procedures for measurements of fluctuations in the prompt-neutron properties as a function of incident neutron energy in fission of the major actinides ${}^{235}\mathrm{U}$ and ${}^{239}\mathrm{Pu}$. The experiment employs a twin Frisch grid ionization chamber as fission-fragment detector while neutrons were counted by using a liquid scintillator placed along the symmetry axis of the ionization chamber. Average neutron multiplicity has been obtained as a function of fission-fragment mass and total kinetic energy (TKE). The average multiplicity as a function of mass agrees well with available data in the literature in the mass range from 80 to 170 u. The existence of additional sawtooth structures in the far asymmetric mass region could not be confirmed, although the statistical accuracy of the present experiment is as good as the previous study where such structures have been reported [Nucl. Phys. A 490, 307 (1988).]. The available data in the literature on the TKE dependence of the multiplicity show strong deviations. Therefore, effort was focused on investigating experimental factors in low-efficiency neutron-counting experiments that may lead to faulty determination of this dependence. Taking these factors into account, a result that agrees well with data from high-efficiency neutron-counting experiments is obtained. The experimental arrangement allows determination of the angle between the detected neutron and the fission axis, which permits the neutron properties to be transformed into the fission-fragment rest frame. Fission neutron emission spectra in the fragment center-of-mass frame have thereby been obtained as a function of the fission-fragment mass and TKE.

In this study we evaluate the dynamical collisional energy loss of heavy quarks, their interaction rate, as well as the different transport coefficients (drag and diffusion coefficients, $\widehat{q}$, etc). We calculate these different quantities for (i) perturbative partons (on-shell particles in the vacuum with fixed and running coupling) and (ii) for dynamical quasi-particles (off-shell particles in the QGP medium at finite temperature $T$ with a running coupling in temperature as described by the dynamical quasiparticles model). We use the perturbative elastic $\left[q\right(g)Q\to q(g\left)Q\right]$ cross section for the first case and the infrared enhanced hard thermal loop cross sections for the second. The results obtained in this work demonstrate the effects of a finite parton mass and width on the heavy-quark transport properties and provide the basic ingredients for an explicit study of the microscopic dynamics of heavy flavors in the QGP–as formed in relativistic heavy-ion collisions–within transport approaches developed previously by the authors.

We calculated the phase shifts of the coupled ${}^3{D}_3\text{−}{}^3{G}_3$ partial waves of nucleon-nucleon scattering taking into account the ${}^7{S}_3$ $\Delta \text{−}\Delta$ channel coupling in the framework of two constituent quark models: the quark delocalization color screening model and the chiral quark model. Our results show that there is a resonance from ${}^7{S}_3^{\Delta \Delta }$ coupling to the ${}^3{D}_3^{NN}$ and ${}^3{G}_3^{NN}$ partial waves in both of these two models, which is consistent with the $d$* resonance observed by WASA-at-COSY collaboration. The resonance structure in the ${}^3{D}_3^{NN}$ partial wave is remarkable, whereas in the ${}^3{G}_3^{NN}$ phase shifts there is only a small bump around the resonance energy. This result is in agreement with the recent experimental results of WASA-at-COSY Collaboration.

An analysis of the differential cross sections of the ${}^{12}\mathrm{C}(d,p){}^{13}\mathrm{C}$ (ground state, or g.s., $1/2_1^{+}$) and ${}^{10}\mathrm{Be}(d,p){}^{11}\mathrm{Be}$ (g.s., $1/2_1^{-}$) reactions at the incident deuteron energies of 11.8, 25.9, and 30 MeV for the first system, and 12.0 and 25.0 MeV for the second system has been performed by applying the coupled-reaction-channels method. The spectroscopic factors $S_{\text{expt}}$, asymptotic normalization coefficients (ANCs), and rms radii of the last neutron in the ground states and the first excited states of the stable ${}^{13}\mathrm{C}$ and the radioactive ${}^{11}\mathrm{Be}$ nuclei were extracted. The existence of neutron halos in the first excited state of ${}^{13}\mathrm{C}$ and the ground state of ${}^{11}\mathrm{Be}$ is confirmed. The rms radii of halos in these states were found to be $5.72\pm 0.16$ and $8.0\pm 0.2$ fm, respectively, in agreement with experimental results. We showed that a halo is also formed in the 0.32 MeV $1/2_1^{-}$ excited state of ${}^{11}\mathrm{Be}$. The halo radius in this state was determined for the first time and was found to be $R_h=4.65\pm 0.20$ fm.

The cross sections of ${}^{78}\mathrm{Se}(n,p){}^{78}\mathrm{As}$ and ${}^{80}\mathrm{Se}(n,p){}^{80}\mathrm{As}$ reactions were measured at five neutron energies over the range 13.73 MeV to 14.77 MeV using ${}^{56}\mathrm{Fe}$ and ${}^{19}\mathrm{F}$ as monitor elements, respectively. The cross sections were also theoretically estimated using EMPIRE-II and TALYS codes over 10 MeV to 20 MeV neutrons and matched with the experimental cross sections by making proper choice of the model parameters. The theoretical and experimental cross sections of ${}^{80}\mathrm{Se}(n,p){}^{80}\mathrm{As}$ reaction are smaller as compared to the ${}^{78}\mathrm{Se}(n,p){}^{78}\mathrm{As}$ reaction at each neutron energy. This difference is attributed to the competing ${}^{80}\mathrm{Se}\left(n,2n\right){}^{79}\mathrm{Se}$ and ${}^{80}\mathrm{Se}(n,\alpha ){}^{77}\mathrm{Ge}^{\mathrm{m}}$ reactions, which effectively decrease the cross sections of ${}^{80}\mathrm{Se}(n,p){}^{80}\mathrm{As}$ reaction as compared to that of the ${}^{78}\mathrm{Se}(n,p){}^{78}\mathrm{As}$ reaction over the neutron energy range used in the present work. The cross sections of ${}^{78}\mathrm{Se}(n,p){}^{78}\mathrm{As}$ and ${}^{80}\mathrm{Se}(n,p){}^{80}\mathrm{As}$ reactions estimated by the EMPIRE-II code initially increase but later on decrease with neutron energy, respectively, above 16 MeV and 19 MeV, whereas those estimated by the TALYS code continuously increase with neutron energy. The present results indicate that the trends in the variation of cross section with neutron energy depend on the model used in the calculations. The cross sections of the ${}^{80}\mathrm{Se}(n,p){}^{80}\mathrm{As}$ reaction at different neutron energies reported in the present work can be added as a new data in the nuclear data library.

Recently, a new approach for solving the three-body problem for (d,p) reactions in the Coulomb-distorted basis in momentum space was proposed. Important input quantities for such calculations are the scattering matrix elements for proton- (neutron-) nucleus scattering. We present a generalization of the the Ernst-Shakin-Thaler scheme in which a momentum space separable representation of proton-nucleus scattering matrix elements in the Coulomb basis can be calculated. The success of this method is demonstrated by comparing $S$-matrix elements and cross sections for proton scattering from ${}^{12}\mathrm{C},{}^{48}\mathrm{Ca}$, and ${}^{208}\mathrm{Pb}$ with the corresponding coordinate space calculations.

We systematically investigate the competition between $\alpha$ decay and spontaneous fission in the region of superheavy odd-$Z$ nuclei up to $Z=121$. The heavier cluster emissions are somewhat of interest for these superheavy nuclei (SHN) as well. In detail, on the basis of the density-dependent cluster model, the deformed $\alpha$-core potential is obtained from the double-folding integral. The $\alpha$-decay half-lives of involved nuclei are then achieved within the improved two-potential approach. On the other hand, the spontaneous fission half-lives are given by the employed formula related to the fissility parameter and the fission barrier height. It is interesting that the decay characteristic of studied nuclei is discussed with varying of the $Z$ and $N$ numbers to some extent, including the tentative detection on the “island of stability.” The present results can be expected to be useful in the future experiment particularly for the unknown elements 119 and 121, namely the identification of synthesized SHN.

Total-Routhian-surface calculations have been performed to investigate the shape evolutions of $A\sim 80$ nuclei: ${}^{80-84}\mathrm{Zr},{}^{76-80}\mathrm{Sr}$, and ${}^{84,86}\mathrm{Mo}$. Shape coexistences of spherical, prolate, and oblate deformations have been found in these nuclei. Particularly for the nuclei ${}^{80}\mathrm{Sr}$ and ${}^{82}\mathrm{Zr}$, the energy differences between two shape-coexisting states are less than 220 keV. At high spins, the $g_{9/2}$ shell plays an important role in shape evolutions. It has been found that the alignment of the $g_{9/2}$ quasiparticles drives nuclei to be triaxial.

Exotic cluster radioactivity is proposed to constrain neutron skin thickness of ${}^{208}\mathrm{Pb}$ and the density slope of symmetry energy $L\left({\rho }_0\right)$. Based on the density-dependent cluster model (DDCM) with the M3Y effective nucleon-nucleon interaction, the neutron skin thickness of ${}^{208}\mathrm{Pb}$ is closely related to the density slope $L\left({\rho }_0\right)$ where the cluster radioactivity serves as a link between them. The single-nucleon potential constructed from the M3Y nucleon-nucleon interaction, especially its isovector part, is found to be particularly important in determining the neutron skin in a finite nucleus and the density slope parameter $L\left({\rho }_0\right)$ in nuclear matter. The correlation between the neutron skin thickness of ${}^{208}\mathrm{Pb}$ and the density slope parameter is obtained from cluster radioactivity where the standard Fermi-form density parameterizations and the standard M3Y effective interactions are assumed in DDCM.

We report on the first measurement of the azimuthal anisotropy $\left(v_2\right)$ of dielectrons $(e^{+}{e}^{-}$ pairs) at mid-rapidity from $\sqrt{s_{NN}}=200$ GeV Au + Au collisions with the STAR detector at the Relativistic Heavy Ion Collider (RHIC), presented as a function of transverse momentum $\left(p_T\right)$ for different invariant-mass regions. In the mass region $M_{ee}<1.1$ $\mathrm{GeV}/c^2$ the dielectron $v_2$ measurements are found to be consistent with expectations from ${\pi }^0,\eta ,\omega$, and $\varphi$ decay contributions. In the mass region $1.1<M_{ee}<2.9\mathrm{GeV}/c^2$, the measured dielectron $v_2$ is consistent, within experimental uncertainties, with that from the $c\overline{c}$ contributions.

The eikonal, partial wave (PW) Lippmann-Schwinger, and three-dimensional Lippmann-Schwinger (LS3D) methods are compared for nuclear reactions that are relevant for space radiation applications. Numerical convergence of the eikonal method is readily achieved when exact formulas of the optical potential are used for light nuclei $\left(A\le 16\right)$, and the momentum-space representation of the optical potential is used for heavier nuclei. The PW solution method is known to be numerically unstable for systems that require a large number of partial waves, and, as a result, the LS3D method is employed. The effect of relativistic kinematics is studied with the PW and LS3D methods and is compared to eikonal results. It is recommended that the LS3D method be used for high-energy nucleon-nucleus reactions and nucleus-nucleus reactions at all energies because of its rapid numerical convergence and stability.