We give a detailed analysis of the origin of spurious divergences and finite steps that have been recently identified in particle-number-restoration calculations within the nuclear energy density functional framework. We isolate two distinct levels of spurious contributions to the energy. The first one is encoded in the definition of the basic energy density functional itself, whereas the second one relates to the canonical procedure followed to extend the use of the energy density functional to multi-reference calculations. The first level of spuriosity relates to the long-known self-interaction problem and to the newly discussed self-pairing interaction process that might appear when describing paired systems with energy functional methods using auxiliary reference states of Bogoliubov or BCS type. A minimal correction to the second level of spuriosity to the multi-reference nuclear energy density functional proposed in [D. Lacroix, T. Duguet, and M. Bender, Phys. Rev. C 79, 044318 (2009)] is shown to remove completely the anomalies encountered in particle-number-restored calculations. In particular, it restores sum rules over (positive) particle numbers that are to be fulfilled by the particle-number-restored formalism. The correction is found to be on the order of several hundreds of keVs up to about 1 MeV in realistic calculations, which is small compared to the total binding energy but often accounts for a substantial percentage of the energy gain from particle-number restoration and is on the same energy scale as the excitations one addresses with multi-reference energy density functional methods.

We discuss the origin of pathological behaviors that have been recently identified in particle-number-restoration calculations performed within the nuclear energy density functional framework. A regularization method that removes the problematic terms from the multi reference energy density functional and that applies (i) to any symmetry-restoration- and/or generator-coordinate-method-based configuration mixing calculation and (ii) to energy density functionals depending only on integer powers of the density matrices was proposed in [D. Lacroix, T. Duguet, and M. Bender, Phys. Rev. C 79, 044318 (2009)] and implemented for particle-number-restoration calculations in [M. Bender, T. Duguet, and D. Lacroix, Phys. Rev. C 79, 044319 (2009)]. In the present article, we address the viability of noninteger powers of the density matrices in the nuclear energy density functional. Our discussion builds on the analysis already carried out in [J. Dobaczewski et al., Phys. Rev. C 76, 054315 (2007)]. First, we propose to reduce the pathological nature of terms depending on a noninteger power of the density matrices by regularizing the fraction that relates to the integer part of the exponent using the method proposed in [D. Lacroix, T. Duguet, and M. Bender, Phys. Rev. C 79, 044318 (2009)]. Then, we discuss the spurious features brought about by the remaining fractional power. Finally, we conclude that noninteger powers of the density matrices are not viable and should be avoided in the first place when constructing nuclear energy density functionals that are eventually meant to be used in multi reference calculations.

Bottom-up holographic models of QCD, inspired by the anti-de Sitter space/conformal field theory correspondence, have shown a remarkable degree of phenomenological success. However, they rely on a number of bold assumptions. We investigate the reliability of one of the key assumptions, which involves matching the parameters of these models to QCD at high 4D momentum $q^2$ and renormalization scale ${\mu }^2$. We show that this leads to phenomenological and theoretical inconsistencies for scale-dependent quantities such as $\langle \overline{q}q\rangle$.

In the explosive astrophysical environment of a type I x-ray burst, the low $Q$ value of 293(50) keV for proton capture on ${}^{30}\mathrm{S}$ induces a $(p,\gamma )(\gamma ,p)$ equilibrium that may lead to a waiting point in the rapid proton capture ($\mathit{rp}$) process at ${}^{30}\mathrm{S}$. The excitation energies of the first and candidate second $T=3/2$ levels in ${}^{31}\mathrm{S}$ were recently determined to an uncertainty of 2 keV by measuring triton spectra and $t\text{−}p$ angular correlations from the ${}^{31}\mathrm{P}({}^3\mathrm{He},t){}^{31}\mathrm{S}{}^{*}(p){}^{30}\mathrm{P}$ reaction. By using this new information together with existing experimental information on the first $T=3/2$, $A=31$ isobaric multiplet and the isobaric multiplet mass equation, the ${}^{30}\mathrm{S}(p,\gamma ){}^{31}\mathrm{Cl}Q$ value is predicted to be 284(7) keV. Similarly, by using the second $T=3/2$ multiplet, the energy of the dominant resonance in the thermonuclear ${}^{30}\mathrm{S}(p,\gamma ){}^{31}\mathrm{Cl}$ reaction is tentatively predicted to be $E_{\mathrm{c}.\mathrm{m}.}=453(8)$ keV and this supports a ${}^{31}\mathrm{Ar}\hspace{0.5em}{\beta }^{+}$-delayed proton-decay observation of this resonance at $E_{\mathrm{c}.\mathrm{m}.}=461(15)$ keV. These substantial reductions in the uncertainties in the thermonuclear ${}^{30}\mathrm{S}(p,\gamma ){}^{31}\mathrm{Cl}$ reaction rate and $Q$ value constrain the region of temperature-density-composition parameter space where the ${}^{30}\mathrm{S}(p,\gamma )(\gamma ,p)$ equilibrium and the ${}^{30}\mathrm{S}$ waiting point may be active.

Gamow-Teller strength distributions and $\beta$-decay half-lives in neutron-deficient Kr and Sr isotopes are investigated within a deformed quasiparticle random phase approximation. The approach is based on a self-consistent Skyrme Hartree-Fock mean field with pairing correlations and residual separable particle-hole and particle-particle forces. A simple two-level model is used to mix the nuclear shapes into the physical ground state. Good agreement with experiment is found with shape mixing coefficients which are consistent with those obtained phenomenologically from mixing of rotational bands.

High-spin level structures of ${}^{94,95}\mathrm{Mo}$ have been reinvestigated via the ${}^{16}\mathrm{O}({}^{82}\mathrm{Se},\mathit{xn}\gamma ){}^{94,95}\mathrm{Mo}(x=4,3)$ reactions at $E({}^{82}\mathrm{Se})=460$ MeV. The previously reported level schemes of these two nuclei have been largely modified up to ∼11 MeV in excitation energy due to identifications of some important linking transitions. Shell-model calculations have been made in the model space of $\pi (p_{1/2},g_{9/2},d_{5/2}){}^4$ and $\nu (d_{5/2},s_{1/2},d_{3/2},g_{7/2},h_{11/2}){}^{2(3)}$ and compared with the modified level schemes. The structures of the newly assigned high-spin states in ${}^{94,95}\mathrm{Mo}$ have been discussed.

Liquid xenon is an important detection medium in direct dark matter experiments, which search for low-energy nuclear recoils produced by the elastic scattering of WIMPs with quarks. The two existing measurements of the relative scintillation efficiency of nuclear recoils below 20 keV lead to inconsistent extrapolations at lower energies. This results in a different energy scale and thus sensitivity reach of liquid xenon dark matter detectors. We report a new measurement of the relative scintillation efficiency below 10 keV performed with a liquid xenon scintillation detector, optimized for maximum light collection. Greater than 95% of the interior surface of this detector was instrumented with photomultiplier tubes, giving a scintillation yield of 19.6 photoelectrons/keV electron equivalent for 122-keV $\gamma$ rays. We find that the relative scintillation efficiency for nuclear recoils of 5 keV is 0.14, staying constant around this value up to 10 keV. For higher energy recoils we measure a value of 0.21, consistent with previously reported data. In light of this new measurement, the XENON10 experiment's upper limits on spin-independent WIMP-nucleon cross section, which were calculated assuming a constant 0.19 relative scintillation efficiency, change from $8.8\times {10}^{-44}\hspace{0.5em}{\mathrm{cm}}^2$ to $9.9\times {10}^{-44}\hspace{0.5em}{\mathrm{cm}}^2$ for WIMPs of mass 100 GeV/$c^2$, and from $4.5\times {10}^{-44}\hspace{0.5em}{\mathrm{cm}}^2$ to $5.6\times {10}^{-44}\hspace{0.5em}{\mathrm{cm}}^2$ for WIMPs of mass 30 GeV/$c^2$.

We have studied the low-lying magnetic spectra of ${}^{12}\mathrm{C}$, ${}^{16}\mathrm{O}$, ${}^{40}\mathrm{Ca}$, ${}^{48}\mathrm{Ca}$, and ${}^{208}\mathrm{Pb}$ nuclei within the random phase approximation (RPA) theory, finding that the description of low-lying magnetic states of doubly-closed-shell nuclei imposes severe constraints on the spin and tensor terms of the nucleon-nucleon effective interaction. We first used four phenomenological effective interactions, and we obtained good agreement with the experimental magnetic spectra and, to a lesser extent, with the electron scattering responses. Then we made self-consistent RPA calculations to test the validity of the finite-range Gogny D1 interaction. For all the nuclei under study, we found that this interaction inverts the energies of all the magnetic states forming isospin doublets.

Based on a relativistic mean-field theory with an effective point coupling between the nucleons, three-dimensional angular momentum projection is implemented for the first time to project out states with designed angular momentum from deformed intrinsic states generated by triaxial quadrupole constraints. The same effective parameter set PC-F1 of the effective interaction is used for deriving the mean field and the collective Hamiltonian. Pairing correlations are taken into account by the BCS method using both monopole forces and zero-range δ forces with strength parameters adjusted to experimental even-odd mass differences. The method is applied successfully to the isotopes ${}^{24}\mathrm{Mg}$, ${}^{30}\mathrm{Mg}$, and ${}^{32}\mathrm{Mg}$.

The calculated cross sections for elastic Coulomb electron scattering from the phase-shift analysis method and the eikonal approximation are compared. It is shown that the phase-shift analysis method can reproduce the experimental data very well for both light and heavy nuclei. Then the phase-shift analysis is used to investigate elastic electron scattering along the O and S isotopic chains, where the charge densities are obtained from relativistic mean-field theory. Results show that the minima of the differential cross section shift inward and upward with the increase of the neutron number.

The electric quadrupole interaction of ${}^{209}\mathrm{Po}$ high spin isomers in a Bi single crystal has been investigated by the time-differential perturbed angular distribution (TDPAD) technique. A two-level analysis procedure for the $17/2^{-}$and $13/2^{-}$ subsequent isomers was employed. The spectroscopic electric quadrupole moments were measured as $|Q(17/2^{-})|=65.9(7)e\hspace{0.5em}{\mathrm{fm}}^2$ and $|Q(13/2^{-})|=12.6(5)e\hspace{0.5em}{\mathrm{fm}}^2$. The experimental values of equilibrium deformations were extracted.

The abundances of antiprotons and protons are considered within momentum-integrated Boltzmann equations describing Little Bangs, i.e., fireballs created in relativistic heavy-ion collisions. Despite a large antiproton annihilation cross section we find a small drop of the ratio of antiprotons to protons from 170 MeV (chemical freeze-out temperature) to 100 MeV (kinetic freeze-out temperature) for CERN-SPS and BNL-RHIC energies thus corroborating the solution of the previously exposed “antiproton puzzle”. In contrast, the Big Bang evolves so slowly that the antibaryons are kept for a long time in equilibrium resulting in an exceedingly small fraction. The adiabatic path of cosmic matter in the phase diagram of strongly interacting matter is mapped out.

Relations are derived in the framework of the Bohr Hamiltonian that express the matrix elements of the deformation-dependent components of the mass tensor through the experimental data on the energies and the $E2$ transitions relating the low-lying collective states. These relations extend the previously obtained results for the intrinsic mass coefficients of the well-deformed axially symmetric nuclei on nuclei of arbitrary shape. The expression for the mass tensor is suggested, which is sufficient to satisfy the existing experimental data on the energy weighted sum rules for the $E2$ transitions for the low-lying collective quadrupole excitations. The mass tensor is determined for ${}^{106,108}\mathrm{Pd}$, ${}^{108\text{−}112}\mathrm{Cd}$, ${}^{134}\mathrm{Ba}$, ${}^{150}\mathrm{Nd}$, ${}^{150-154}\mathrm{Sm}$, ${}^{154-160}\mathrm{Gd}$, ${}^{164}\mathrm{Dy}$, ${}^{172}\mathrm{Yb}$, ${}^{178}\mathrm{Hf}$, ${}^{188\text{−}192}\mathrm{Os}$, and ${}^{194\text{−}196}\mathrm{Pt}$.

The correlation between the trigger and associated particles in jets produced on near and away sides of high-$p_T$ triggers in heavy-ion collisions is studied. Hadronization of jets on both sides is treated by thermal-shower and shower-shower recombinations. The energy loss of semihard and hard partons traversing the nuclear medium is parametrized in a way that renders a good fit of the single-particle inclusive distributions at all centralities. The associated hadron distribution in the near-side jet can be determined showing weak dependence on system size because of trigger bias. The inverse slope increases with trigger momentum in agreement with data. The distribution of associated particles in the away-side jet is also studied with careful attention given to antitrigger bias that is due to the longer path length that the away-side jet recoiling against the trigger jet must propagate in the medium to reach the opposite side. Centrality dependence is taken into account after determining a realistic probability distribution of the dynamical path length of the parton trajectory within each class of centrality. For symmetric dijets with $p_T^{\mathrm{trig}}=p_T^{\mathrm{assoc}}(\mathrm{away})$, it is shown that the per-trigger yield is dominated by tangential jets. For unequal $p_T^{\mathrm{trig}}$, $p_T^{\mathrm{assoc}}(\mathrm{near})$ and $p_T^{\mathrm{assoc}}(\mathrm{away})$, the yields are calculated for various centralities, showing an intricate relationship among them. The near-side yield agrees with data both in centrality dependence and in $p_T^{\mathrm{assoc}}(\mathrm{near})$ distribution. The average parton momentum for the recoil jet is shown to be always larger than that of the trigger jet for fixed $p_T^{\mathrm{trig}}$ and centrality and for any measurable $p_T^{\mathrm{assoc}}(\mathrm{away})$. With the comprehensive treatment of dijet production described here, it is possible to answer many questions regarding the behavior of partons in the medium under conditions that can be specified on measurable hadron momenta.

We provide an equation of state for hot nuclear matter in $\beta$ equilibrium by applying a momentum-dependent effective interaction. We focus on the study of the equation of state of high-density and high-temperature nuclear matter, containing leptons (electrons and muons) under the chemical equilibrium condition in which neutrinos have left the system. The conditions of charge neutrality and equilibrium under the $\beta$-decay process lead first to the evaluation of proton and lepton fractions and then to the evaluation of internal energy, free energy, and pressure, and in total to the equation of state of hot nuclear matter. Thermal effects on the properties and equation of state of nuclear matter are assessed and analyzed in the framework of the proposed effective interaction model. Special attention is given to the study of the contribution of the components of $\beta$-stable nuclear matter to the entropy per particle, a quantity of great interest in the study of structure and collapse of supernova.

We discuss the sensitivity of the three-particle azimuthal cumulant method for a search and study of conical emission in central relativistic $A+A$ collisions. Our study is based on a multicomponent Monte Carlo model that includes flow background, Gaussian monojets, jet flow, and Gaussian conical signals. We find the observation of conical emission is hindered by the presence of flow harmonics of fourth order ($v_4$) but remains feasible even in the presence of a substantial background. We consider the use of probability cumulants for the suppression of second-order flow harmonics. We find that although probability cumulant significantly reduce $v_2^2$ contributions, they also complicate the cumulant of jets and conical emission. The use of probability cumulants is therefore not particularly advantageous in searches for conical emission. We find the sensitivity of the (density) cumulant method depends inextricably on strengths of $v_2$, $v_4$, background, and non-Poisson character of particle production. It thus cannot be expressed in a simple form and without specific assumptions about the values of these parameters.

The neutron-rich isotopes ${}^{65,67}\mathrm{Fe}$ and ${}^{65}\mathrm{Co}$ have been produced at the LISOL facility, Louvain-La-Neuve, in the proton-induced fission of ${}^{238}\mathrm{U}$. Beams of these isotopes have been extracted with high selectivity by means of resonant laser ionization combined with mass separation. Yrast and near-yrast levels of ${}^{65}\mathrm{Co}$ have also been populated in the ${}^{64}\mathrm{Ni}+{}^{238}\mathrm{U}$ reaction at Argonne National Laboratory. The level structure of ${}^{65}\mathrm{Co}$ could be investigated by combining all the information from both the ${}^{65}\mathrm{Fe}$ and ${}^{65}\mathrm{Co}\beta$ decay and the deep-inelastic reaction. The ${}^{65}\mathrm{Fe}$, ${}^{65}\mathrm{Co}$, and ${}^{67}\mathrm{Fe}$ decay schemes and the ${}^{65}\mathrm{Co}$ yrast structure are fully established. The ${}^{65,67}\mathrm{Co}$ level structures can be interpreted as resulting from the coexistence of core-coupled states with levels based on a low-energy proton-intruder configuration.

We develop a new ab initio many-body approach capable of describing simultaneously both bound and scattering states in light nuclei, by combining the resonating-group method with the use of realistic interactions, and a microscopic and consistent description of the nucleon clusters. This approach preserves translational symmetry and the Pauli principle. We outline technical details and present phase-shift results for neutron scattering on ${}^3\mathrm{H}$, ${}^4\mathrm{He}$, and ${}^{10}\mathrm{Be}$ and proton scattering on ${}^{3,4}\mathrm{He}$, using realistic nucleon-nucleon ($\mathit{NN}$) potentials. Our $A=4$ scattering results are compared to earlier ab initio calculations. We find that the CD-Bonn $\mathit{NN}$ potential in particular provides an excellent description of nucleon-${}^4\mathrm{He}S$-wave phase shifts. In contrast, the experimental nucleon-${}^4\mathrm{He}P$-wave phase shifts are not well reproduced by any $\mathit{NN}$ potential we use. We demonstrate that a proper treatment of the coupling to the $n\text{−}{}^{10}\mathrm{Be}$ continuum is successful in explaining the parity-inverted ground state in ${}^{11}\mathrm{Be}$.

Results are presented on event-by-event fluctuations of transverse momenta $p_T$ in central $\mathrm{Pb}+\mathrm{Pb}$ interactions at $20A$, $30A$, $40A$, $80A$, and $158A$ GeV. The analysis was performed for charged particles at forward center-of-mass rapidity ($1.1<y_{\pi }^{*}<2.6$). Three fluctuation measures were studied: the distribution of average transverse momentum $M(p_T)$ in the event, the ${\Phi }_{p_T}$ fluctuation measure, and two-particle transverse momentum correlations. Fluctuations of $p_T$ are small and show no significant energy dependence in the energy range of the CERN Super Proton Synchrotron. Results are compared with QCD-inspired predictions for the critical point, and with the UrQMD model. Transverse momentum fluctuations, similar to multiplicity fluctuations, do not show the increase expected for freeze-out near the critical point of QCD.