A study of the $4\alpha$ linear-chain structure in high-lying collective excitation states of ${}^{16}\mathrm{O}$ with covariant density functional theory is presented. The low-spin states are obtained by configuration mixing of particle-number and angular-momentum projected quadrupole deformed mean-field states with the generator coordinate method. The high-spin states are determined by cranking calculations. These two calculations are based on the same energy density functional PC-PK1. We have found a rotational band at low spin with the dominant intrinsic configuration considered to be the one whereby $4\alpha$ clusters stay along a common axis. The strongly deformed rod shape also appears in the high-spin region with the angular momentum $13\hslash \text{to}18\hslash$; however, whether the state is a pure $4\alpha$ linear chain is less obvious than for the low-spin states.

The structures of excited states in ${}^{34}\mathrm{S}$ are investigated using the antisymmetrized molecular dynamics and generator coordinate method (GCM). The GCM basis wave functions are calculated via energy variation with a constraint on the quadrupole deformation parameter $\beta$. By applying the GCM after parity and angular momentum projections, the coexistence of two positive- and one negative-parity superdeformed (SD) bands are predicted, and low-lying states and other deformed bands are obtained. The SD bands have structures of ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ + two valence neutrons in molecular orbitals around the two ${}^{16}\mathrm{O}$ cores in a cluster picture. The configurations of the two valence neutrons are ${\delta }^2$ and ${\pi }^2$ for the positive-parity SD bands and ${\pi }^1{\delta }^1$ for the negative-parity SD band. The structural changes of the yrast states are also discussed.

The magnetic dipole strength in the energy region of the spin-flip resonance is investigated in ${}^{128}\mathrm{Xe}$ and ${}^{134}\mathrm{Xe}$ using quasimonoenergetic and linearly polarized $\gamma$-ray beams at the High-Intensity $\gamma$-Ray Source facility in Durham, North Carolina, USA. Absorption cross sections were deduced for the magnetic and electric and dipole strength distributions separately for various intervals of excitation energy, including the strength of states in the unresolved quasicontinuum. The magnetic dipole strength distributions show structures resembling a resonance in the spin-flip region around an excitation energy of 8 MeV. The electric dipole strength distributions obtained from the present experiments are in agreement with the ones deduced from an earlier experiment using broad-band bremsstrahlung instead of a quasimonoenergetic beam. The experimental magnetic and electric dipole strength distributions are compared with phenomenological approximations and with predictions of a quasiparticle random phase approximation in a deformed basis.

The properties of dynamic (least action) fission paths are analyzed and compared to the ones of the more traditional static (least energy) paths. Both the Barcelona-Catania-Paris-Madrid and Gogny D1M energy density functionals are used in the calculation of the Hartree-Fock-Bogoliubov (HFB) constrained configurations providing the potential energy and collective inertias. The action is computed as in the Wentzel-Kramers-Brillouin method. A full variational search of the least-action path over the complete variational space of HFB wave functions is cumbersome and probably unnecessary if the relevant degrees of freedom are identified. In this paper, we consider the particle number fluctuation degree of freedom that explores the amount of pairing correlations in the wave function. For a given shape, the minimum action can be up to a factor of 3 smaller than the action computed for the minimum energy state with the same shape. The impact of this reduction on the lifetimes is enormous and dramatically improves the agreement with experimental data in the few examples considered.

States in ${}^{112}\mathrm{Cd}$ have been studied with the ${}^{111}\mathrm{Cd}(\vec{d},p){}^{12}\mathrm{Cd}$ reaction using 22 MeV polarized deuterons. The protons from the reaction were momentum analyzed with a Q3D magnetic spectrograph, and spectra have been recorded with a position-sensitive detector located on the focal plane. Angular distributions of cross sections and analyzing powers have been constructed for the low-lying negative-parity states observed, including the $3^{-},4^{-}$, and $5^{-}$ members of the previously assigned quadrupole-octupole quintuplet. The $5^{-}$ member at 2373-keV possess the second largest spectroscopic strength observed, and is reassigned as having the $s_{\frac{1}{2}}\otimes h_{\frac{11}{2}}$ two-quasineutron configuration as the dominate component of its wave function.

Quasifission is the primary reaction mechanism that prevents the formation of superheavy elements in heavy-ion fusion experiments. Employing the time-dependent density functional theory approach, we study quasifission in the systems ${}^{40,48}\mathrm{Ca}+{}^{238}\mathrm{U}$. Results show that for ${}^{48}\mathrm{Ca}$ projectiles the quasifission is substantially reduced in comparison to the ${}^{40}\mathrm{Ca}$ case. This partly explains the success of superheavy element formation with ${}^{48}\mathrm{Ca}$ beams. For the first time, we also calculate the repartition of excitation energies of the two fragments in a dynamic microscopic theory. The differences between both systems are interpreted in terms of initial neutron to proton asymmetry of the colliding partners.

Background: The microscopic composition and properties of infinite hadronic matter at a wide range of densities and temperatures have been subjects of intense investigation for decades. The equation of state (EoS) relating pressure, energy density, and temperature at a given particle number density is essential for modeling compact astrophysical objects such as neutron stars, core-collapse supernovae, and related phenomena, including the creation of chemical elements in the universe. The EoS depends not only on the particles present in the matter, but, more importantly, also on the forces acting among them. Because a realistic and quantitative description of infinite hadronic matter and nuclei from first principles in not available at present, a large variety of phenomenological models has been developed in the past several decades, but the scarcity of experimental and observational data does not allow a unique determination of the adjustable parameters.

Purpose: It is essential for further development of the field to determine the most realistic parameter sets and to use them consistently. Recently, a set of constraints on properties of nuclear matter was formed and the performance of 240 nonrelativistic Skyrme parametrizations was assessed [M. Dutra et al., Phys. Rev. C 85, 035201 (2012)] in describing nuclear matter up to about three times nuclear saturation density. In the present work we examine 263 relativistic-mean-field (RMF) models in a comparable approach. These models have been widely used because of several important aspects not always present in nonrelativistic models, such as intrinsic Lorentz covariance, automatic inclusion of spin, appropriate saturation mechanism for nuclear matter, causality, and, therefore, no problems related to superluminal speed of sound in medium.

Method: Three different sets of constraints related to symmetric nuclear matter, pure neutron matter, symmetry energy, and its derivatives were used. The first set (SET1) was the same as used in assessing the Skyrme parametrizations. The second and third sets (SET2a and SET2b) were more suitable for analysis of RMF and included, up-to-date theoretical, experimental and empirical information.

Results: The sets of updated constraints (SET2a and SET2b) differed somewhat in the level of restriction but still yielded only 4 and 3 approved RMF models, respectively. A similarly small number of approved Skyrme parametrizations were found in the previous study with Skyrme models. An interesting feature of our analysis has been that the results change dramatically if the constraint on the volume part of the isospin incompressibility $\left(K_{\tau ,\mathrm{v}}\right)$ is eliminated. In this case, we have 35 approved models in SET2a and 30 in SET2b.

Conclusions: Our work provides a new insight into application of RMF models to properties of nuclear matter and brings into focus their problematic proliferation. The assessment performed in this work should be used in future applications of RMF models. Moreover, the most extensive set of refined constraints (including nuclear matter and finite-nuclei-related properties) should be used in future determinations of new parameter sets to provide models that can be used with more confidence in a wide range of applications. Pointing to reasons for the many failures, even of the frequently used models, should lead to their improvement and to the identification of possible missing physics not included in present energy density functionals.

Based on the density-dependent relativistic mean field theory, the properties for nuclear matter and neutron stars with the effective interaction $\mathrm{DD}\text{−}\mathrm{ME}\delta$ including the isovector scalar channel which disentangle the effects of isovector scalar and isovector vector channels by fitting microscopic calculations. The influences of the isovector scalar $\delta$ meson on properties of asymmetric nuclear matter at high densities are discussed in detail. The results support that the isovector scalar channel can soften the equation of state through the effects on the nucleon effective mass and the scalar $\sigma$ field and impact the behavior of the nuclear matter symmetry energy. Because of the influence on the symmetry energy by the $\delta$ meson, a larger proton fraction in neutron stars is predicted by the $\mathrm{DD}\text{−}\mathrm{ME}\delta$ calculation, which strongly affects the cooling process of the star. The maximum masses of neutron stars given by the $\mathrm{DD}\text{−}\mathrm{ME}\delta$ calculation is $1.97M_{⨀}$ which is in reasonable agreement with PSR J1614 − 2230 ($1.97 \pm 0.04 M_{⨀}$) and PSR J0348 + 0432 $(2.01 \pm 0.04 M_{⨀})$. Among all the selected interactions, $\mathrm{DD}\text{−}\mathrm{ME}\delta$ gives the smallest radius range. The radius for the 1.4 solar mass neutron star calculated by $\mathrm{DD}\text{−}\mathrm{ME}\delta$ is in good agreement with the prediction [Astrophys. J. Lett. 765, L5 (2013)] according to the resent observations.

Nuclear matter under astrophysical conditions is explored with time-dependent and static Hartree-Fock calculations. The focus is in a regime of densities where matter segregates into liquid and gaseous phases unfolding a rich scenario of geometries, often called nuclear pasta shapes (e.g., spaghetti, lasagna). Particularly the appearance of the different phases depending on the proton fraction and the transition to uniform matter are investigated. In this context the neutron background density is of special interest, because it plays a crucial role in the type of pasta shape that is built. The study is performed in two dynamical ranges, once for hot matter and once at temperature zero, to investigate the effect of cooling.

Background: We consider the muon capture reaction ${\mu }^{-}+{}^2\mathrm{H}\to {\nu }_{\mu }+n+n$, which presents a “clean” two-neutron $\left(nn\right)$ system in the final state. We study here its capture rate in the doublet hyperfine initial state $\left({\Gamma }^D\right)$. The total capture rate for the muon capture ${\mu }^{-}+{}^3\mathrm{He}\to {\nu }_{\mu }+{}^3\mathrm{H}$ $\left({\Gamma }_0\right)$ is also analyzed, although, in this case, the $nn$ system is not so clean anymore.

Purpose: We investigate whether ${\Gamma }^D$ (and ${\Gamma }_0)$ could be sensitive to the $nn$ $S$-wave scattering length $\left(a_{nn}\right)$, and we check on the possibility to extract $a_{nn}$ from an accurate measurement of ${\Gamma }^D$.

Method: The muon capture reactions are studied with nuclear potentials and charge-changing weak currents, derived within chiral effective field theory. The next-to-next-to-next-to-leading-order chiral potential with cutoff parameter $\Lambda =500$ MeV is used, but the low-energy constant (LEC) determining $a_{nn}$ is varied so as to obtain $a_{nn}=-18.95,-16.0,-22.0$, and $+18.22$ fm. The first value is the present empirical one, while the last one is chosen such as to lead to a di-neutron bound system with a binding energy of 139 keV. The LEC's $c_D$ and $c_E$, present in the three-nucleon potential and axial-vector current $\left(c_D\right)$, are constrained to reproduce the $A=3$ binding energies and the triton Gamow-Teller matrix element.

Results: The capture rate ${\Gamma }^D$ is found to be $399\left(3\right){\mathrm{s}}^{-1}$ for $a_{nn}=-18.95$ and $-16.0$ fm; and $400\left(3\right){\mathrm{s}}^{-1}$ for $a_{nn}=-22.0$ fm. However, in the case of $a_{nn}=+18.22$ fm, the result of $275\left(3\right){\mathrm{s}}^{-1}$ $\mathrm{[}135\left(3\right){\mathrm{s}}^{-1}]$ is obtained, when the di-neutron system in the final state is unbound (bound). The total capture rate ${\Gamma }_0$ for muon capture on ${}^3\mathrm{He}$ is found to be 1494(15), 1491(16), 1488(18), and 1475(16) ${\mathrm{s}}^{-1}$ for $a_{nn}=-18.95,-16.0,-22.0$, and $+18.22$ fm, respectively. All the theoretical uncertainties are due to the fitting procedure and radiative corrections.

Conclusions: Our results seem to exclude the possibility of constraining a negative $a_{nn}$ with an uncertainty of less than $\sim \pm 3$ fm through an accurate determination of the muon capture rates, but the uncertainty on the present empirical value will not complicate the interpretation of the (forthcoming) experimental results for ${\Gamma }^D$. Finally, a comparison with the already available experimental data discourages the possibility of a bound di-neutron state (positive $a_{nn})$.

$\beta$-delayed two- and three-neutron emission is modeled with the effective density model and sequential neutron emission model based on the statistical level density of daughter nuclides. The results show a significant reduction in the delayed two- and three-neutron emission probability compared to other available calculations. Predictions for some selected isotopes, which may soon be available for experimental spectroscopic measurements, are presented.

The PHENIX experiment at the Relativistic Heavy Ion Collider has performed a systematic study of $K_S^0$ and $K^{*0}$ meson production at midrapidity in $p+p,d+\mathrm{Au}$, and $\mathrm{Cu}+\mathrm{Cu}$ collisions at $\sqrt{s_{{}_{\mathit{NN}}}}=200$ GeV. The $K_S^0$ and $K^{*0}$ mesons are reconstructed via their $K_S^0\to {\pi }^0(\to \gamma \gamma ){\pi }^0(\to \gamma \gamma )$ and $K^{*0}\to K^{\pm }{\pi }^{\mp }$ decay modes, respectively. The measured transverse-momentum spectra are used to determine the nuclear modification factor of $K_S^0$ and $K^{*0}$ mesons in $d+\text{Au}$ and $\mathrm{Cu}+\mathrm{Cu}$ collisions at different centralities. In the $d+\mathrm{Au}$ collisions, the nuclear modification factor of $K_S^0$ and $K^{*0}$ mesons is almost constant as a function of transverse momentum and is consistent with unity, showing that cold-nuclear-matter effects do not play a significant role in the measured kinematic range. In $\mathrm{Cu}+\mathrm{Cu}$ collisions, within the uncertainties no nuclear modification is registered in peripheral collisions. In central collisions, both mesons show suppression relative to the expectations from the $p+p$ yield scaled by the number of binary nucleon-nucleon collisions in the $\mathrm{Cu}+\mathrm{Cu}$ system. In the $p_T$ range $2–5 \mathrm{GeV}/c$, the strange mesons $(K_S^0,K^{*0})$ similarly to the $\varphi$ meson with hidden strangeness, show an intermediate suppression between the more suppressed light quark mesons $\left({\pi }^0\right)$ and the nonsuppressed baryons $(p,\overline{p})$. At higher transverse momentum, $p_T>5 \mathrm{GeV}/c$, production of all particles is similarly suppressed by a factor of $\approx 2$.

The Ginzburg-Landau theory of phase transitions is modified and used to investigate the heat capacity, energy, entropy, and order parameter of the paired phases of ${}^{208}\mathrm{Pb},{}^{88}\mathrm{Sr},{}^{48}\mathrm{Ca}$, and ${}^{20}\mathrm{Ne}$. We use the Fermi gas model to calculate the thermodynamic properties of the normal phase of the nucleons. Our results show that the total heat capacities of the studied nuclei have an $\mathsf{S}$-shape behavior, which is in accordance with the semi-empirical data, and the order parameter does not approach zero at a specific critical temperature.

Eighty years after its experimental discovery, a description of induced nuclear fission based solely on the interactions between neutrons and protons and quantum many-body methods still poses formidable challenges. The goal of this paper is to contribute to the development of a predictive microscopic framework for the accurate calculation of static properties of fission fragments for hot fission and thermal or slow neutrons. To this end, we focus on the ${}^{239}\mathrm{Pu}\left(n,f\right)$ reaction and employ nuclear density functional theory with Skyrme energy densities. Potential energy surfaces are computed at the Hartree-Fock-Bogoliubov approximation with up to five collective variables. We find that the triaxial degree of freedom plays an important role, both near the fission barrier and at scission. The impact of the parametrization of the Skyrme energy density and the role of pairing correlations on deformation properties from the ground state up to scission are also quantified. We introduce a general template for the quantitative description of fission fragment properties. It is based on the careful analysis of scission configurations, using both advanced topological methods and recently proposed quantum many-body techniques. We conclude that an accurate prediction of fission fragment properties at low incident neutron energies, although technologically demanding, should be within the reach of current nuclear density functional theory.

The reaction mechanism of pre-equilibrium proton-induced $\alpha$-particle emission from ${}^{93}\mathrm{Nb}$ at an incident energy of 100 MeV was investigated with polarized projectiles. A formalism based on the statistical multistep direct emission model of Feshbach, Kerman, and Koonin was found to give a reasonably good reproduction of cross section and analyzing power angular distributions at various emission energies. Existing experimental distributions for the same reaction at an incident energy of 65 MeV were also analyzed with the same model. The incident-energy variation from 65 MeV up to 160 MeV was found to be consistent with the predictions of the basic model. However, whereas knockout of an $\alpha$ cluster is the dominant reaction mechanism in the final stage at the lowest and highest incident energies, at 100 MeV a pickup process competes with comparable intensity in yield.

We compare the flowlike correlations in high multiplicity proton-nucleus $\left(p+A\right)$ and nucleus-nucleus $\left(A+A\right)$ collisions. At fixed multiplicity, the correlations in these two colliding systems are strikingly similar, although the system size is smaller in $p+A$. Based on an independent cluster model and a simple conformal scaling argument, where the ratio of the mean free path to the system size stays constant at fixed multiplicity, we argue that flow in $p+A$ emerges as a collective response to the fluctuations in the position of clusters, just like in $A+A$ collisions. With several physically motivated and parameter free rescalings of the recent LHC data, we show that this simple model captures the essential physics of elliptic and triangular flow in $p+A$ collisions. We also explore the implications of the model for jet energy loss in $p+A$, and predict slightly larger transverse momentum broadening in $p+A$ than in $A+A$ at the same multiplicity.

We study the evolution of a gluon system under conditions of density and temperature similar to those explored in the early stage of ultrarelativistic heavy-ion collisions. We first describe the implementation of the relativistic Boltzmann-Nordheim (RBN) transport approach that includes in the collision integral the quantum effects of Bose-Einstein statistics. Then, we describe the evolution of a spatially uniform gluon system in a box under elastic collisions solving the RBN for various initial conditions. We discuss the critical phase-space density that leads to the onset of a Bose-Einstein condensate (BEC) and the time scale for this process to occur. In particular, thanks to the fact that RBN allows one to relax the small angle approximation, we study the effect at both small and large screening mass $m_D$. For small $m_D\ll T$ we see that our solution of RBN is in agreement with the recent extensive studies within a Fokker-Planck scheme in small angle approximation. For the same total cross section but with large $m_D\simeq 2T$ (large angle scatterings), we see a significant time speed-up of the onset of BEC with respect to small $m_D\ll T$. This further strengthens the possibility that at least a transient BEC is formed in the early stage of ultrarelativistic heavy-ion collisions.

We develop a self-consistent description of hot nuclei within the relativistic Thomas-Fermi approximation using the relativistic mean-field model for nuclear interactions. The temperature dependence of the symmetry energy and other physical quantities of a nucleus are calculated by employing the subtraction procedure in order to isolate the nucleus from the surrounding nucleon gas. It is found that the symmetry energy coefficient of finite nuclei is significantly affected by the Coulomb polarization effect. We also examine the dependence of the results on nuclear interactions and make a comparison between the results obtained from relativistic and nonrelativistic Thomas-Fermi calculations.

Background: Extensions of single-reference (SR) energy-density functionals (EDFs) to multireference (MR) applications involve using the generalized Wick theorem (GWT), which leads to singular energy kernels that cannot be properly integrated to restore symmetries, unless the EDFs are generated by true interactions.

Purpose: We propose a new method to regularize the MR EDFs, which is based on using auxiliary quantities obtained by multiplying the kernels with appropriate powers of overlaps.

Methods: Regularized matrix elements of two-body interactions are obtained by integrating the auxiliary quantities and then solving simple linear equations.

Results: We implement the new regularization method within the self-consistent Skyrme-Hartree-Fock approach and we perform a proof-of-principle angular-momentum projection (AMP) of states in odd-odd nucleus ${}^{26}\mathrm{Al}$. We show that for EDFs generated by true interactions, our regularization method gives results identical to those obtained within the standard AMP procedure. We also show that for EDFs that do not correspond to true interactions, it gives stable and converging results that are different from unstable and nonconverging standard AMP values.

Conclusions: The new regularization method proposed in this work may provide us with a relatively inexpensive and efficient tool to generalize SR EDFs to MR applications, thus allowing for symmetry restoration and configuration mixing performed for typical nuclear EDFs, which most often do not correspond to true interactions.