$\alpha$ decay and spontaneous fission half-lives of 81 superheavy nuclei with $Z=104–112$ and $N=158–166$ have been calculated with simple formulas extracted from the systematics of measured and calculated half-lives. Half-life calculations are performed within the shell model and one-body rate theories for $\alpha$ decay and a dynamical approach for spontaneous fission defined essentially by the shape, the height of fission barrier, the fissility, and the nuclear deformations. We obtained a rather good accordance between calculated and experimental half-lives for 30 nuclei with measured $Q_{\alpha }$ values. We predicted with different fitting formulas the most probable half-lives for 51 nuclides at which there are no experimental data. The rms values for experimental and theoretical half-lives are evaluated and discussed. The comparison of theoretical calculations with experimental data allows us to draw conclusions on the role of the nuclear structure and shell effects in low-energy decay processes.

Delayed emission of protons following $\beta$ decay of neutron deficient nuclei ${}^{26}\mathrm{P}$ and ${}^{27}\mathrm{S}$ was investigated at the ACCULINNA separator in the Flerov Laboratory of Nuclear Reactions at Dubna. Ions of interest, identified in flight, were implanted into the active volume of the gaseous optical time projection chamber, which allowed us to record tracks of charged particles emitted in the decay. Total branching ratios for $\beta$-delayed proton emission and for $\beta$-delayed two-proton emission were determined. In addition, energy spectra for delayed protons below 2 MeV were established. Our findings for ${}^{26}\mathrm{P}$ agree with results of previous experiments. In the case of ${}^{27}\mathrm{S}$, however, the observed probability of delayed proton emission is an order of magnitude larger than reported in literature. Two new strong proton transitions were identified representing decays of the first two excited states of ${}^{27}\mathrm{P}$ to the ground state of ${}^{26}\mathrm{Si}_{}$. The probability ratio of $\gamma$-to-proton emission from these states is discussed.

The transfer reaction ${}^{13}\mathrm{C}({}^{11}\mathrm{B},{}^7\mathrm{Li}){}^{17}\mathrm{O}$ leading to the ground and several excited states of ${}^{17}\mathrm{O}$ was investigated at an incident boron beam energy of 45 MeV. The experimental data were analyzed by means of coupled-channel Born approximation calculations and ${}^{17}\mathrm{O}=\alpha +{}^{13}\mathrm{C}$ spectroscopic factors were extracted from a comparison of the data and the calculations at forward angles. The largest spectroscopic factor obtained was that for the subthreshold 6.356 MeV $1/2^{+}$ state, important for the production of neutrons in the stellar environment, and the squared Coulomb modified asymptotic normalization coefficient, ${\tilde{C}}^2$, is consistent with previous determinations. A significant rise in the experimental data at backward scattering angles suggested the possibility of ${}^{17}\mathrm{O}={}^6\mathrm{Li}+{}^{11}\mathrm{B}$ clustering in some ${}^{17}\mathrm{O}$ states, including the ground state. However, explicit inclusion of ${}^6\mathrm{Li}$ transfer in the calculations could not explain the observed effect. Compound nucleus calculations suggested that while the backward angle rise could be explained by such processes for two of the populated ${}^{17}\mathrm{O}$ states other multistep direct processes must contribute significantly to the other two.

Background: Reactions involving weakly bound nuclei require formalisms able to deal with continuum states. The majority of these formalisms struggle to treat collective excitations of the systems involved. For continuum-discretized coupled channels (CDCC), extensions to include target excitation have been developed but have only been applied to a small number of cases.

Purpose: In this work, we reexamine the extension of the CDCC formalism to include target excitation and apply it to a variety of reactions to study the effect of breakup on inelastic cross sections.

Methods: We use a transformed oscillator basis to discretize the continuum of the projectiles in the different reactions and use the extended CDCC method developed in this work to solve the resulting coupled differential equations. A new code has been developed to perform the calculations.

Results: Reactions ${}^{58}\mathrm{Ni}(d,d){}^{58}\mathrm{Ni}^{*}, {}^{24}\mathrm{Mg}(d,d){}^{24}\mathrm{Mg}^{*}, {}^{144}\mathrm{Sm}({}^6\mathrm{Li},{}^6\mathrm{Li}){}^{144}\mathrm{Sm}^{*}$, and ${}^9\mathrm{Be}({}^6\mathrm{Li},{}^6\mathrm{Li}){}^9\mathrm{Be}^{*}$ are studied. Satisfactory agreement is found between experimental data and extended CDCC calculations.

Conclusions: The studied CDCC method has proven to be an accurate tool to describe target excitation in reactions with weakly bound nuclei. Moderate effects of breakup on inelastic observables are found for the reactions studied. Cross-section magnitudes are not modified much, but angular distributions present smoothing when opposed to calculations without breakup.

We present here a comprehensive analysis to understand the optimal atomic conditions for the first experimental observation of nuclear excitation by electron capture (NEEC) for the 6.85 h ${}^{93m}\mathrm{Mo}$ isomer with spin parity $21/2^{+}$. The NEEC process would provide an excitation from the long-lived isomer to a depletion level with spin parity $17/2^{+}$, which lies only 4.85 keV higher in energy, and is itself a shorter-lived isomer that subsequently decays, releasing a substantial amount of stored energy (2429.8 keV). The depletion level decays to a $13/2^{+}$ state through a 267.9-keV transition that offers the opportunity for identification of NEEC because it does not occur in the natural decay of the long-lived isomer. It has been shown that, for the proposed approach, high-precision atomic predictions are essential to understanding the proper physical conditions under which the experimental observation of the NEEC process will be possible using a beam-based scenario.

Very neutron-rich $Z\sim 60$ isotopes produced by in-flight fission of a 345 MeV/nucleon ${}^{238}\mathrm{U}$ beam at the RI Beam Factory, RIKEN Nishina Center, have been studied by delayed $\gamma$-ray spectroscopy. New isomers were discovered in the neutron-rich $N=100$ isotones ${}^{162}\mathrm{Sm}, {}^{163}\mathrm{Eu}$, and ${}^{164}\mathrm{Gd}$. Half-lives, $\gamma$-ray energies, and relative intensities of these isomers were obtained. Level schemes were proposed for these nuclei and the first $2^{+}$ and $4^{+}$ states were assigned for the even-even nuclei. The first $2^{+}$ and $4^{+}$ state energies decrease as the proton numbers get smaller. The energies and the half-lives of the new isomers are very similar to those of $4^{-}$ isomers known in less neutron-rich $N=100$ isotones ${}^{168}\mathrm{Er}$ and ${}^{170}\mathrm{Yb}$. A deformed Hartree-Fock with angular momentum projection model suggests $K^{\pi }=4^{-}$ two-quasiparticle states with $\nu 7/2\left[633\right]\otimes \nu 1/2\left[521\right]$ configurations with similar excitation energy. The results suggest that neutron-rich $N=100$ nuclei are well deformed and the deformation gets larger as $Z$ decreases to 62. The onset of $K$ isomers with the same configuration at almost the same energy in $N=100$ isotones indicates that the neutron single-particle structures of neutron-rich isotones down to $Z=62$ do not change significantly from those of the $Z=70$ stable nuclei. Systematics of the excitation energies of new isomers can be explained without the predicted $N=100$ shell gap.

An influence of the phonon-phonon coupling (PPC) on the $\beta$-decay half-lives and multi-neutron emission probabilities is analyzed within the microscopic model based on the Skyrme interaction with tensor components included. The finite-rank separable approximation is used in order to handle large two-quasiparticle spaces. The even-even nuclei near the $r$-process paths at $N=82$ are studied. The characteristics of ground states, $2^{+}$ excitations, and $\beta$-decay strength of the neutron-rich Cd isotopes are treated in detail. It is shown that a strong redistribution of the Gamow-Teller strength due to the PPC is mostly sensitive to the multi-neutron emission probability of the Cd isotopes.

Background: A previous measurement of the $\beta \text{−}\gamma$ directional coefficient in ${}^{22}\mathrm{Na}\beta$ decay was used to extract recoil-order form factors. The data indicate the requirement of a significant induced-tensor matrix element for the decay. This conclusion largely relies on a standard-model-allowed weak magnetism form factor which was determined using an unpublished value of the analog $2_1^{+}\to 3_1^{+}$ $\gamma$ branch in ${}^{22}\mathrm{Na}$, with the further assumption that the transition is dominated by its isovector $M1$ component.

Purpose: Our aim is to determine the $2_1^{+}\to 3_1^{+}$ width in ${}^{22}\mathrm{Na}$ in order to obtain an independent measurement of the weak magnetism form factor for the $\beta$ decay.

Methods: A ${}^{21}\mathrm{Ne}(p,\gamma )$ resonance reaction on an implanted target was used to produce the first $2^{+}$ state in ${}^{22}\mathrm{Na}$ at $E_x=1952$ keV. Deexcitation $\gamma$ rays were registered with two 100% relative efficiency high purity germanium detectors.

Results: We obtain for the first time an unambiguous determination of the $2_1^{+}\to 3_1^{+}$ branch in ${}^{22}\mathrm{Na}$ to be $0.45\left(8\right)\%$.

Conclusions: Using the conserved vector current (CVC) hypothesis, our branch determines the weak magnetism form factor for ${}^{22}\mathrm{Na}\beta$ decay to be $|b/A{c}_1|=8.9\left(1.2\right)$. Together with the $\beta \text{−}\gamma$ angular correlation coefficient, we obtain a large induced-tensor form factor for the decay that continues to disagree with theoretical predictions. Two plausible explanations are suggested.

With a Yang-Mills flux-tube initial state and a high-resolution (3+1)D particle-in-cell relativistic (PICR) hydrodynamics simulation, we calculate the $\mathrm{\Lambda }$ polarization for different energies. The origination of polarization in high energy collisions is discussed, and we find linear impact parameter dependence of the global $\mathrm{\Lambda }$ polarization. Furthermore, the global $\mathrm{\Lambda }$ polarization in our model decreases very quickly in the low energy domain, and the decline curve fits well the recent results of Beam Energy Scan (BES) program launched by the STAR Collaboration at the Relativistic Heavy Ion Collider (RHIC). The time evolution of polarization is also discussed.

Exact solution of the nuclear mean-field plus separable pairing model is reexamined. New auxiliary constraints for solving the Bethe ansatz equations of the model are proposed. By using these auxiliary constraints, the Bethe ansatz form of eigenvectors of the mean-field plus separable pairing Hamiltonian with nondegenerate single-particle energies and nondegenerate separable pairing strengths purposed previously is verified. Since the solutions of the model with one- and two-orbit cases are known, verification of the solutions for these two special cases is made. To demonstrate structure and features of the solution, the model with three orbits in the $ds$ shell is taken as a nontrivial example, of which two-pair results and the ground state of the three-pair case are provided explicitly. Since the number of equations involved increases with the number of orbits and pairs, to solve these equations for a large number of orbits and pairs seems still difficult.

Background: The hyperon impurity effect in nuclei has been extensively studied in different mean-field models. Recently, there is a controversy about whether the $\mathrm{\Lambda }$ hyperon is more tightly bound in the normal deformed (ND) states than that in the superdeformed (SD) states.

Purpose: This article is aimed to provide a beyond-mean-field study of the low-lying states of hypernuclei with shape coexistence and to shed some light on the controversy.

Method: The models of relativistic mean field and beyond based on a relativistic point-coupling energy functional are adopted to study the low-lying states of both ${}_{\mathrm{\Lambda }}{}^{37}\mathrm{Ar}$ and ${}^{36}\mathrm{Ar}$. The wave functions of low-lying states are constructed as a superposition of a set of relativistic mean-field states with different values of quadrupole deformation parameter. The projections onto both particle number and angular momentum are considered.

Results: The $\mathrm{\Lambda }$ binding energies in both ND and SD states of ${}_{\mathrm{\Lambda }}{}^{37}\mathrm{Ar}$ are studied in the case of the $\mathrm{\Lambda }$ hyperon occupying the $s,p$, or $d$ state in the spherical limit, respectively. For comparison, four sets of nucleon-hyperon point-coupling interactions are used, respectively. Moreover, the spectra of low-lying states in ${}^{36}\mathrm{Ar}$ and ${}_{{\mathrm{\Lambda }}_s}{}^{37}\mathrm{Ar}$ are calculated based on the same nuclear energy density functional. The results indicate that the SD states exist in ${}_{\mathrm{\Lambda }}{}^{37}\mathrm{Ar}$ for all four effective interactions. Furthermore, the ${\mathrm{\Lambda }}_s$ reduces the quadrupole collectivity of ND states to a greater extent than that of SD states. For ${}_{\mathrm{\Lambda }}{}^{37}\mathrm{Ar}$, the beyond-mean field decreases the ${\mathrm{\Lambda }}_s$ binding energy of the SD state by 0.17 MeV, but it almost has no effect on that of the ND state.

Conclusions: In ${}_{{\mathrm{\Lambda }}_s}{}^{37}\mathrm{Ar}$, the ${\mathrm{\Lambda }}_p$ and ${\mathrm{\Lambda }}_d$ binding energies of the SD states are always larger than those of the ND states. For ${\mathrm{\Lambda }}_s$, the conclusion depends on the effective nucleon-hyperon interaction. Moreover, the beyond-mean-field model calculation indicates that the ${\mathrm{\Lambda }}_s$ hyperon is less bound in the SD state than that in the ND state.

Two-photon optical pumping of the 7.6-eV nuclear isomer in the singly ionized atoms of ${}^{229}\mathrm{Th}$ is considered. Differences between two mechanisms of the pumping, nuclear excitation in the electronic transition (NEET) and bound internal conversion (BIC), are derived and analyzed numerically. The BIC mechanism turns out to be more effective, by orders of magnitude, in accordance with previous calculations. Moreover, a numerical smallness in the NEET scheme is explicitly pointed out concerning singly and doubly charged ions. That is related to the smallness of the final vertex, responsible for conservation of energy. In the case of BIC, the calculated pumping rate of the isomer for the most effective scheme may be as high as 0.$03{\mathrm{s}}^{-1}$.

The nuclear $\alpha$ decay of heavy nuclei is investigated based on the nuclear energy density functional, which leads to the $\alpha$ potential inside the parent nucleus in terms of the proton and neutron density profiles of the daughter nucleus. We use the Skyrme force model, Gogny force model, and relativistic mean-field model to get the nucleon density profiles inside heavy nuclei. Once the nucleon density profiles are determined, the parameters of the nuclear $\alpha$ potential are fitted to the observed $\alpha$ decay half-lives of heavy nuclei. This approach is then applied to predict unknown $\alpha$ decay half-lives of heavy nuclei. To estimate the $Q$ values of unobserved $\alpha$ decays, we make use of the liquid droplet model.

Photon-nuclear reaction in a transport model frame, namely an extended quantum molecular dynamics model, has been realized at the photon energy of 70–140 MeV in the quasi-deuteron regime. For an important application, we pay a special focus on photonuclear reactions of ${}^{12}\mathrm{C}(\gamma ,np){}^{10}\mathrm{B}$ where ${}^{12}\mathrm{C}$ is considered as different configurations including $\alpha$ clustering. Obvious differences for some observables have been observed among different configurations, which can be attributed to spatial-momentum correlation of a neutron-proton pair inside nucleus, and therefore it gives us a sensitive probe to distinguish the different configurations including $\alpha$ clustering with the help of the photonuclear reaction mechanism.

We present measurements of elliptic flow ($v_2$) of electrons from the decays of heavy-flavor hadrons ($e_{\mathrm{HF}}$) by the STAR experiment. For Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV we report $v_2$, for transverse momentum ($p_T$) between 0.2 and 7 $\mathrm{GeV}/c$, using three methods: the event plane method ($v_2\left\{\mathrm{EP}\right\}$), two-particle correlations ($v_2\left\{2\right\}$), and four-particle correlations ($v_2\left\{4\right\}$). For Au+Au collisions at $\sqrt{s_{NN}}=62.4$ and 39 GeV we report $v_2\left\{2\right\}$ for $p_T<2\mathrm{GeV}/c$. $v_2\left\{2\right\}$ and $v_2\left\{4\right\}$ are nonzero at low and intermediate $p_T$ at 200 GeV, and $v_2\left\{2\right\}$ is consistent with zero at low $p_T$ at other energies. The $v_2\left\{2\right\}$ at the two lower beam energies is systematically lower than at $\sqrt{s_{NN}}=200$ GeV for $p_T<1\mathrm{GeV}/c$. This difference may suggest that charm quarks interact less strongly with the surrounding nuclear matter at those two lower energies compared to $\sqrt{s_{NN}}=200$ GeV.

We determine the root-mean-square proton charge radius, $R_p$, from a fit to low-$Q^2$ electron-proton elastic-scattering cross-section data with the higher moments fixed (within uncertainties) to the values predicted by chiral perturbation theory. We obtain $R_p=0.855\left(11\right)$ fm. This number falls between the value obtained from muonic hydrogen analyses and the CODATA value (based upon atomic hydrogen spectroscopy and electron-proton scattering determinations).

Background: Recent years have seen considerable effort in associating the shell evolution (SE) for a chain of isotones or isotopes with the underlying nuclear interactions. In particular, it has been fairly well established that the tensor part of the Skyrme interaction is indispensable for understanding certain SE above $Z,N=50$ shell closures, as a function of nucleon numbers.

Purpose: The purpose of the present work is twofold: (1) to study the effect of deformation due to blocking on the SE above $Z,N=50$ shell closures and (2) to examine the optimal parametrizations in the tensor part which gives a proper description of the SE above $Z,N=50$ shell closures.

Methods: I use the Skyrme-Hartree-Fock-Bogoliubov (SHFB) method to compute the even-even vacua of the $Z=50$ isotopes and $N=50$ isotones. For Sb and odd-$A$ Sn isotopes, I perform calculations with a blocking procedure which accounts for the polarization effects, including deformations.

Results: The blocking SHFB calculations show that the light odd-$A$ Sb isotopes, with only one valence proton occupying down-sloping $\mathrm{\Omega }=11/2^{-}$ and $\mathrm{\Omega }=7/2^{+}$ Nilsson orbits, assume finite oblate deformations. This reduces the energy differences between $11/2^{-}$ and $7/2^{+}$ states by about 500 keV for ${}_{51}{\mathrm{Sb}}_{56-66}$, bringing the energy-difference curve closer to the experimental one. With une2t1 energy density functional (EDF), which differs from unedf2 parametrization by tensor terms, a better description of the slope of $\mathrm{\Delta }e(\pi 1h_{11/2}-\pi 1g_{7/2})$ as a function of neutron number has been obtained. However, the trend of $\mathrm{\Delta }e(\pi 1g_{7/2}-\pi 2d_{5/2})$ curve is worse using une2t1 EDF. $\mathrm{\Delta }e(\nu 3s_{1/2}-\nu 2d_{5/2})$ and $\mathrm{\Delta }e(\nu 1g_{7/2}-\nu 2d_{5/2})$ curve for $N=50$ isotones using une2t1 seems to be consistent with experimental data. The neutron SE of $\mathrm{\Delta }e(\nu 1h_{11/2}-\nu 1g_{7/2})$ and $\mathrm{\Delta }e(\nu 1g_{7/2}-\nu 2d_{5/2})$ for Sn isotopes are shown to be sensive to ${\alpha }_T$ tensor parameter.

Conclusions: Within the Skyrme self-consistent mean-field model, the deformation degree of freedom has to be taken into account for Sb isotopes, $N=51$ isotones, and odd-$A$ Sn isotopes when discussing variation of quantities like shell gap etc. The tensor terms are important for describing the strong variation of $\mathrm{\Delta }E({\mathrm{\Omega }}^{\pi }=11/2^{-}-7/2^{+})$ in Sb isotopes. The SE of $1/2^{+}$ and $7/2^{+}$ states in $N=51$ isotones may show signature for the existence of tensor interaction. The experimental excitation energies of $11/2^{-}$ and $7/2^{+}$ states in odd-$A$ Sn isotopes close to ${}^{132}\mathrm{Sn}$ give prospects for constraining the ${\alpha }_T$ parameter.

The aim of this work is to provide a precise and accurate measurement of the ${}^{238}\mathrm{U}$($n,\gamma$) reaction cross section in the energy region from 1 eV to 700 keV. This reaction is of fundamental importance for the design calculations of nuclear reactors, governing the behavior of the reactor core. In particular, fast reactors, which are experiencing a growing interest for their ability to burn radioactive waste, operate in the high energy region of the neutron spectrum. In this energy region most recent evaluations disagree due to inconsistencies in the existing measurements of up to 15%. In addition, the assessment of nuclear data uncertainty performed for innovative reactor systems shows that the uncertainty in the radiative capture cross section of ${}^{238}\mathrm{U}$ should be further reduced to 1–3% in the energy region from 20 eV to 25 keV. To this purpose, addressed by the Nuclear Energy Agency as a priority nuclear data need, complementary experiments, one at the GELINA and two at the n_TOF facility, were proposed and carried out within the 7th Framework Project ANDES of the European Commission. The results of one of these ${}^{238}\mathrm{U}$($n,\gamma$) measurements performed at the n_TOF CERN facility are presented in this work. The $\gamma$-ray cascade following the radiative neutron capture has been detected exploiting a setup of two ${\mathrm{C}}_6{\mathrm{D}}_6$ liquid scintillators. Resonance parameters obtained from this work are on average in excellent agreement with the ones reported in evaluated libraries. In the unresolved resonance region, this work yields a cross section in agreement with evaluated libraries up to 80 keV, while for higher energies our results are significantly higher.

Background: While diproton emission was first theorized in 1960 and first measured in 2002, it was first observed only in 2012. The measurement of ${}^{14}\mathrm{Be}$ in coincidence with two neutrons suggests that ${}^{16}\mathrm{Be}$ does decay through the simultaneous emission of two strongly correlated neutrons.

Purpose: In this work, we construct a full three-body model of ${}^{16}\mathrm{Be}$ (as ${}^{14}\mathrm{Be}+n+n$) in order to investigate its configuration in the continuum and, in particular, the structure of its ground state.

Method: In order to describe the three-body system, effective $n-{}^{14}\mathrm{Be}$ potentials were constructed, constrained by the experimental information on ${}^{15}\mathrm{Be}$. The hyperspherical $R$-matrix method was used to solve the three-body scattering problem, and the resonance energy of ${}^{16}\mathrm{Be}$ was extracted from a phase-shift analysis.

Results: In order to reproduce the experimental resonance energy of ${}^{16}\mathrm{Be}$ within this three-body model, a three-body interaction was needed. For extracting the width of the ground state of ${}^{16}\mathrm{Be}$, we use the full width at half maximum of the derivative of the three-body eigenphase shifts and the width of the three-body elastic scattering cross section.

Conclusions: Our results confirm a dineutron structure for ${}^{16}\mathrm{Be}$, dependent on the internal structure of the subsystem ${}^{15}\mathrm{Be}$.

We use quasiparticle anisotropic hydrodynamics to study an azimuthally symmetric boost-invariant quark-gluon plasma including the effects of both shear and bulk viscosities. In quasiparticle anisotropic hydrodynamics, a single finite-temperature quasiparticle mass is introduced and fit to the lattice data in order to implement a realistic equation of state (EoS). We compare results obtained by using the quasiparticle method with the standard method of imposing the EoS in anisotropic hydrodynamics and viscous hydrodynamics. Using these three methods, we extract the primordial particle spectra, total number of charged particles, and average transverse momentum for various values of the shear viscosity to entropy density ratio $\eta /s$. We find that the three methods agree well for small shear viscosity to entropy density ratio $\eta /s$, but differ at large $\eta /s$, with the standard anisotropic EoS method showing suppressed production at low transverse-momentum compared with the other two methods considered. Finally, we demonstrate explicitly that, when using standard viscous hydrodynamics, the bulk-viscous correction can drive the primordial particle spectra negative at large $p_T$. Such behavior is not seen in either anisotropic hydrodynamics approach, irrespective of the value of $\eta /s$.