Using the coalescence model based on nucleons from a blast-wave model with its parameters fitted to the measured proton transverse momentum spectrum and elliptic flow in heavy-ion collisions at the Relativistic Heavy Ion Collider, we study the elliptic flows of light nuclei in these collisions. We find that describing the measured elliptic flows of deuterons (antideuterons) and tritons (helium-3) requires that the emission source for nucleons of high transverse momentum is more elongated along the reaction plane than in the perpendicular direction. Our results thus suggest that the elliptic flows of light nuclei can be used to study the nucleon emission source in relativistic heavy-ion collisions.

We propose a new approach to initialize the hydrodynamic fields, such as energy density distributions and four-flow velocity fields in hydrodynamic modeling of high-energy nuclear collisions at the collider energies. Instead of matching the energy-momentum tensor or putting the initial conditions of quark-gluon fluids at a fixed initial time, we utilize a framework of relativistic hydrodynamic equations with source terms to describe the initial stage. Putting the energy and momentum loss rate of the initial partons into the source terms, we obtain hydrodynamic initial conditions dynamically. The resultant initial profile of the quark-gluon fluid looks highly bumpy as seen in the conventional event-by-event initial conditions. In addition, initial random flow velocity fields also are generated as a consequence of momentum deposition from the initial partons. We regard the partons that survive after the dynamical initialization process as the mini-jets and find sizable effects of both mini-jet propagation in the quark-gluon fluids and initial random transverse flow on the final momentum spectra and anisotropic flow observables. We perform event-by-event (3+1)-dimensional ideal hydrodynamic simulations with this new framework that enables us to describe the hydrodynamic bulk collectivity, parton energy loss, and interplay among them in a unified manner.

The differential cross section for elastic scattering of protons on electrons at rest is calculated, taking into account the QED radiative corrections to the leptonic part of interaction. These model-independent radiative corrections arise due to emission of the virtual and real soft and hard photons as well as to vacuum polarization. We analyze an experimental setup when both the final particles are recorded in coincidence and their energies are determined within some uncertainties. The kinematics, the cross section, and the radiative corrections are calculated and numerical results are presented.

We explore the theoretical observation that within the leading twist approximation, the nuclear effects of shadowing and antishadowing in nonperturbative nuclear parton distribution functions (nPDFs) at the input QCD evolution scale involve diffraction on nucleons of a nuclear target and originate from merging of two parton ladders belonging to two different nucleons, which are close in the rapidity space. It allows us to propose that for a given momentum fraction $x_{IP}$ carried by the diffractive exchange, nuclear shadowing and antishadowing should compensate each other in the momentum sum rule for nPDFs locally on the interval $ln(x/x_{IP})\le 1$. We realize this by constructing an explicit model of nuclear gluon antishadowing, which has a wide support in $x,{10}^{-4}<x<0.2$, peaks at $x=0.05\text{–}0.1$ at the level of $\approx 15\%$ for ${}^{208}\mathrm{Pb}$ at $Q_0^2=4{\mathrm{GeV}}^2$ and rather insignificantly depends on details of the model. We also studied the impact parameter $b$ dependence of antishadowing and found it to be slow.

Theoretical uncertainties in the predictions of inner fission barrier heights in superheavy elements have been investigated in a systematic way for a set of state-of-the-art covariant energy density functionals which represent major classes of the functionals used in covariant density functional theory. They differ in basic model assumptions and fitting protocols. Both systematic and statistical uncertainties have been quantified where the former turn out to be larger. Systematic uncertainties are substantial in superheavy elements and their behavior as a function of proton and neutron numbers contains a large random component. The benchmarking of the functionals to the experimental data on fission barriers in the actinides allows reduction of the systematic theoretical uncertainties for the inner fission barriers of unknown superheavy elements. However, even then, on average they increase on moving away from the region where benchmarking has been performed. In addition, a comparison with the results of nonrelativistic approaches is performed in order to define full systematic theoretical uncertainties over the state-of-the-art models. Even for the models benchmarked in the actinides, the difference in the inner fission barrier height of some superheavy elements reaches $5–6$ MeV. This uncertainty in the fission barrier heights will translate into huge (many tens of the orders of magnitude) uncertainties in the spontaneous fission half-lives.

Phenomenological effective interactions like Skyrme forces are currently used in mean-field calculations in nuclear physics. Mean-field models have strong analogies with the first order of the perturbative many-body problem and the currently used effective interactions are adjusted at the mean-field level. In this work, we analyze the renormalizability of the nuclear many-body problem in the case where the effective Skyrme interaction is employed in its standard form and the perturbative problem is solved up to second order. We focus on symmetric nuclear matter and its equation of state, which can be calculated analytically at this order. It is shown that only by applying specific density dependence and constraints to the interaction parameters can renormalizability be guaranteed in principle. This indicates that the standard Skyrme interaction does not in general lead to a renormalizable theory. To achieve renormalizability, other terms should be added to the interaction and employed perturbatively only at first order.

The half-life of the neutron-rich nuclide ${}^{60}\mathrm{Fe}$ has been in dispute in recent years. A measurement in 2009 published a value of $(2.62\pm 0.04)\times {10}^6$ years, almost twice that of the previously accepted value from 1984 of $(1.49\pm 0.27)\times {10}^6$ yr. This longer half-life was confirmed in 2015 by a second measurement, resulting in a value of $(2.50\pm 0.12)\times {10}^6$ yr. All three half-life measurements used the grow-in of the $\gamma$-ray lines in ${}^{60}\mathrm{Ni}$ from the decay of the ground state of ${}^{60}\mathrm{Co}$ ($t_{1/2}=5.27$ yr) to determine the activity of a sample with a known number of ${}^{60}\mathrm{Fe}$ atoms. In contrast, the work presented here measured the ${}^{60}\mathrm{Fe}$ activity directly via the 58.6 keV $\gamma$-ray line from the short-lived isomeric state of ${}^{60}\mathrm{Co}$ ($t_{1/2}=10.5$ min), thus being independent of any possible contamination from long-lived ${}^{60\mathrm{g}}\mathrm{Co}$. A fraction of the material from the 2015 experiment with a known number of ${}^{60}\mathrm{Fe}$ atoms was used for the activity measurement, resulting in a half-life value of $(2.72\pm 0.16)\times {10}^6$ yr, confirming again the longer half-life. In addition, ${}^{60}\mathrm{Fe}/{}^{56}\mathrm{Fe}$ isotopic ratios of samples with two different dilutions of this material were measured with accelerator mass spectrometry to determine the number of ${}^{60}\mathrm{Fe}$ atoms. Combining this with our activity measurement resulted in a half-life value of $(2.69\pm 0.28)\times {10}^6$ yr, again agreeing with the longer half-life.

We study the role of triaxial deformation in the proton-emitting nucleus ${}^{109}\mathrm{I}$. We analyze the rotational spectrum as well as the decay width within the nonadiabatic quasiparticle approach. The parent nuclear wave functions are calculated using a modified rotation-particle coupling where the matrix elements of the Hamiltonian representing the rotational states of the parent nucleus are written in terms of the rotational energies of the daughter nucleus. The measured spectrum of the daughter nucleus ${}^{108}\mathrm{Te}$ suggests a strong role of either triaxial or vibrational degrees of freedom which is applicable for ${}^{109}\mathrm{I}$ also. With these results we successfully explain the spectra of the parent and daughter and also the decay width in a unified way which enables us to establish the configuration of the rotational bands and the decaying state.

We develop a scheme to take into account the effects of short-range nucleon-nucleon correlations in the nucleon-pair wave function by solving the Bethe-Goldstone equation for a coarse-grained delta shell potential in $S$-wave configuration. The $S$-wave delta shell potential has been adjusted to reproduce the ${}^1{S}_0$ phase shifts of the AV18 potential for this partial wave up to 2 GeV in the laboratory kinetic energy. We show that a coarse-grained potential can describe the high momentum tail of the back-to-back correlated pairs and the $G$ matrix in momentum space. We discuss the easiness and robustness of the calculation in coordinate space and the future improvements and utilities of this model. This work suggests the possibility of using perturbation theory for describing the short-range correlations and, related to this, to substitute the $G$ matrix by an appropriate coarse-grained potential.

Background: The coexistence of different geometric shapes at low energies presents a universal structure phenomenon that occurs over the entire chart of nuclides. Studies of the shape coexistence are important for understanding the microscopic origin of collectivity and modifications of shell structure in exotic nuclei far from stability.

Purpose: The aim of this work is to provide a systematic analysis of characteristic signatures of coexisting nuclear shapes in different mass regions, using a global self-consistent theoretical method based on universal energy density functionals and the quadrupole collective model.

Method: The low-energy excitation spectrum and quadrupole shape invariants of the two lowest $0^{+}$ states of even-even nuclei are obtained as solutions of a five-dimensional collective Hamiltonian (5DCH) model, with parameters determined by constrained self-consistent mean-field calculations based on the relativistic energy density functional PC-PK1, and a finite-range pairing interaction.

Results: The theoretical excitation energies of the states, $2_1^{+},4_1^{+},0_2^{+},2_2^{+},2_3^{+}$, as well as the $B(E2;0_1^{+}\to 2_1^{+})$ values, are in very good agreement with the corresponding experimental values for 621 even-even nuclei. Quadrupole shape invariants have been implemented to investigate shape coexistence, and the distribution of possible shape-coexisting nuclei is consistent with results obtained in recent theoretical studies and available data.

Conclusions: The present analysis has shown that, when based on a universal and consistent microscopic framework of nuclear density functionals, shape invariants provide distinct indicators and reliable predictions for the occurrence of low-energy coexisting shapes. This method is particularly useful for studies of shape coexistence in regions far from stability where few data are available.

We present a study of nuclear shape coexistence in the region of neutron-deficient lead isotopes. The midshell gold isotopes ${}^{180,185,188,190}\mathrm{Au}$ $\left(Z=79\right)$, the two long-lived nuclear states in ${}^{197}\mathrm{At}$ $\left(Z=85\right)$, and the neutron-rich nuclide ${}^{219}\mathrm{At}$ were produced by the ISOLDE facility at CERN and their masses were determined with the high-precision Penning-trap mass spectrometer ISOLTRAP. The studied gold isotopes address the trend of binding energies in a region of the nuclear chart where the nuclear charge radii show pronounced discontinuities. Significant deviations from the atomic-mass evaluation were found for ${}^{188,190}\mathrm{Au}$. The new trend of two-neutron separation energies is smoother, although it does reveal the onset of deformation. The origin of this effect is interpreted in connection to the odd-even staggering of binding energies, as well as theoretically by Hartree-Fock-Bogoliubov calculations including quasiparticle blocking. The role of blocking for reproducing the large odd-even staggering of charge radii in the mercury isotopic chain is illustrated.

Lifetimes of low-lying yrast states in neutron-rich ${}^{94,96,98}\mathrm{Sr}$ have been measured by Germanium-gated $\gamma -\gamma$ fast timing with $\mathrm{LaBr}3\left(\mathrm{Ce}\right)$ detectors using the EXILL&FATIMA spectrometer at the Institut Laue-Langevin. Sr fission products were generated using cold-neutron-induced fission of ${}^{235}\mathrm{U}$ and stopped almost instantaneously within the thick target. The experimental $B\left(E2\right)$ values are compared with results of Monte Carlo shell-model calculations made without truncation on the occupation numbers of the orbits spanned by eight proton and eight neutron orbits and show good agreement. Similarly to the Zr isotopes, the abrupt shape transition in the Sr isotopes near neutron number $N=60$ is identified as being caused by many-proton excitations to its $g_{9/2}$ orbit.

We report on the $\beta$-delayed neutron emission probability ($P_{1n}$) measurements of the ${}^{82,83,84}\mathrm{Ga}$ ($N=51,52,53$) precursors performed in one single experiment using the ${}^3\mathrm{He}$ neutron-counter TETRA at the ALTO facility in Orsay. Altogether our results for the three $A=82,83$, and 84 Ga precursors point towards a sizable $P_{1n}$ staggering in the $N=50$ region, similar to the one already observed just after the $N=28$ shell closure in the K isotopes chain, hinting at a similar mechanism. We will discuss the possible microscopic origin of this behavior, i.e., the existence in the light $N=51$ isotones of low-lying components of the so called pygmy Gamow-Teller resonance, already well established at $Z=36$, and persisting toward ${}^{79}\mathrm{Ni}$.

The spinodal instabilities in hot asymmetric nuclear matter and some important critical parameters derived thereof are studied by using six different families of relativistic mean-field models. The slopes of the symmetry energy coefficient vary over a wide range within each family. The critical densities and proton fractions are more sensitive to the symmetry energy slope parameter at temperatures much below its critical value ($T_c\sim 14-16\mathrm{MeV}$). The spread in the critical proton fraction at a given symmetry energy slope parameter is noticeably larger near $T_c$, indicating that the equation of state of warm asymmetric nuclear matter at subsaturation densities is not sufficiently constrained. The distillation effects are sensitive to the density dependence of the symmetry energy at low temperatures which tend to wash out with increasing temperature.

It is seen by a coupled-channel $NN$ scattering calculation that in the intermediate two-baryon $N\mathrm{\Delta }$ or $\mathrm{\Delta }\mathrm{\Delta }$ system the width of the state is greatly diminished due to the relative kinetic energy of the two baryons, since the internal energy of the particles, available for pionic decay, is smaller. Specifically, a state-dependent effect arises from the centrifugal barrier in $L\ne 0 N\mathrm{\Delta }$ or $\mathrm{\Delta }\mathrm{\Delta }$ systems. The double $\mathrm{\Delta }$ width can become even smaller than the free width of a single $\mathrm{\Delta }$. This has some bearing to the interpretation of the $d^{\prime }\left(2380\right)$ resonance recently discovered at COSY.

We apply the density matrix expansion (DME) at Hartree-Fock level with long-range chiral effective field theory interactions defined in coordinate space up to next-to-next-to-leading order. We consider chiral potentials both with and without explicit $\mathrm{\Delta }$ isobars. The challenging algebra associated with applying the DME to three-nucleon forces is tamed using a new organization scheme, which will also facilitate generalizations. We include local regulators on the interactions to mitigate the effects of singular potentials on the DME couplings and simplify the optimization of generalized Skyrme-like functionals.

Background: Strongly deformed oblate superheavy nuclei form an intriguing region where the toroidal nuclear structures may bifurcate from the oblate spheroidal shape. The bifurcation may be facilitated when the nucleus is endowed with a large angular moment about the symmetry axis with $I=I_z$. The toroidal high-$K$ isomeric states at their local energy minima can be theoretically predicted using the cranked self-consistent Skyrme-Hartree-Fock method.

Purpose: We use the cranked Skyrme-Hartree-Fock method to predict the properties of the toroidal high-spin isomers in the superheavy nucleus ${}^{304}120_{184}$.

Method: Our method consists of three steps: First, we use the deformation-constrained Skyrme-Hartree-Fock-Bogoliubov approach to search for the nuclear density distributions with toroidal shapes. Next, using these toroidal distributions as starting configurations, we apply an additional cranking constraint of a large angular momentum $I=I_z$ about the symmetry $z$ axis and search for the energy minima of the system as a function of the deformation. In the last step, if a local energy minimum with $I=I_z$ is found, we perform at this point the cranked symmetry- and deformation-unconstrained Skyrme-Hartree-Fock calculations to locate a stable toroidal high-spin isomeric state in free convergence.

Results: We have theoretically located two toroidal high-spin isomeric states of ${}^{304}120_{184}$ with an angular momentum $I=I_z=81\hslash$ (proton 2p-2h, neutron 4p-4h excitation) and $I=I_z=208\hslash$ (proton 5p-5h, neutron 8p-8h) at the quadrupole moment deformations $Q_{20}=-297.7$ b and $Q_{20}=-300.8$ b with energies 79.2 and 101.6 MeV above the spherical ground state, respectively. The nuclear density distributions of the toroidal high-spin isomers ${}^{304}120_{184}(I_z=81\hslash$ and $208\hslash )$ have the maximum density close to the nuclear matter density, 0.$16{\mathrm{fm}}^{-3}$, and a torus major to minor radius aspect ratio $R/d=3.25$.

Conclusions: We demonstrate that aligned angular momenta of $I_z=81\hslash$ and $208\hslash$ arising from multiparticle-multihole excitations in the toroidal system of ${}^{304}120_{184}$ can lead to high-spin isomeric states, even though the toroidal shape of ${}^{304}120_{184}$ without spin is unstable. Toroidal energy minima without spin may be possible for superheavy nuclei with higher atomic numbers, $Z\gtrsim 122$, as reported previously [A. Staszczak and C. Y. Wong, Acta Phys. Pol. B 40, 753 (2008)].

Background: The quenching of spin-isospin modes in nuclei is an important field of research in nuclear structure. It has an impact on astrophysical reaction rates and on fundamental processes like neutrinoless double-$\beta$ decay. Gamow–Teller (GT) and spin-flip $M1$ strengths are quenched. Concerning the latter, the $J^{\pi }=1^{+}$ resonance in the doubly magic nucleus ${}^{48}\mathrm{Ca}$, dominated by a single transition, serves as a reference case.

Purpose: The aim of the present work is to search for weak $M1$ transitions in ${}^{48}\mathrm{Ca}$ with a high-resolution $(p,p^{\prime })$ experiment at 295 MeV and forward angles including $0^{\circ }$ and a comparison with results from a similar study using backward-angle electron scattering at low momentum transfers in order to estimate their contribution to the total $B\left(M1\right)$ strength in ${}^{48}\mathrm{Ca}$.

Methods: The spin-$M1$ cross sections of individual peaks in the spectra are deduced with a multipole decomposition analysis (MDA) and converted to reduced spin-$M1$ transition strengths by using the unit cross-section method. For a comparison with electron-scattering results, corresponding reduced $B\left(M1\right)$ transition strengths are extracted following the approach outlined in Birkhan et al. [Phys. Rev. C 93, 041302(R) (2016)].

Results: In total, 30 peaks containing a $M1$ contribution are found in the excitation energy region 7–13 MeV. The resulting $B\left(M1\right)$ strength distribution compares well to the electron-scattering results considering different factors limiting the sensitivity in both experiments and the enhanced importance of mechanisms breaking the proportionality of nuclear cross sections and electromagnetic matrix elements for weak transitions as studied here. The total strength of 1.14(7) ${\mu }_{\mathrm{N}}^2$ deduced assuming a nonquenched isoscalar part of the $(p,p^{\prime })$ cross sections agrees with the $(e,e^{\prime })$ result of 1.21(13) ${\mu }_{\mathrm{N}}^2$. A bin-wise analysis above 10 MeV provides an upper limit of 1.51(17) ${\mu }_{\mathrm{N}}^2$.

Conclusions: The present results confirm the previous electron-scattering work that weak transitions contribute about 25% to the total $B\left(M1\right)$ strength in ${}^{48}\mathrm{Ca}$ and the quenching factors of GT and spin-$M1$ strength are then comparable in $fp$-shell nuclei. Thus, the role of meson-exchange currents seems to be negligible in ${}^{48}\mathrm{Ca}$, in contrast to $sd$-shell nuclei.