Evidence has been found for a broad unbound state near 1 MeV excitation in ${}^9$B that is a candidate for the long-disputed ${\frac{1}{2}}^{+}$ mirror of the unbound 1.68 MeV state in ${}^9$Be. Reactions of ${}^6$Li${+}^6$Li were studied with a 60 MeV beam incident on a 240 $\mu$g/cm${}^2$ ${}^6$LiF target. The breakup fragments from the decay of the reaction products were detected in five Si-Si-CsI telescope detectors and the breakup particles were reconstructed using the technique of resonant particle spectroscopy. It is shown that contrary to a previous study, the ${\frac{1}{2}}^{+}$ is not populated in the reaction ${}^6$Li(${}^6$Li,$t$)${}^9$B, but that it is populated via the ${}^6$Li(${}^6$Li,$d$)${}^{10}$B reaction. The sequential decays of ${}^{10}$B populated the channels ${}^6$Li(g.s.)$+\alpha$, ${}^6$Li(2.186 MeV)$+\alpha$, ${}^8$Be$+d$, and $pn\alpha \alpha$, with the latter including (${}^9$B$+n$ or ${}^9$Be$+p$) decay from ${}^{10}$B. Decays through ${}^9$B are identified and show the presence of the ${\frac{1}{2}}^{+}$ state as a broad asymmetric peak around 0.8–1.0 MeV with $\Gamma \approx 1.5$ MeV.

An unusually large value of the ${}^{22}$C matter radius has recently been extracted from measured reaction cross sections. The giant size can be explained by a very loose binding that is, however, not known experimentally yet. Within the three-body cluster model we have explored the sensitivity of the $s$-motion-dominated ${}^{22}$C geometry to the two-neutron separation energy. A low energy of a few tens of keV is required to reach the alleged experimental lower value of the matter radius, while the experimental mean radius requires an extremely tiny binding. The dependence of the ${}^{22}$C charge radius on the two-neutron separation energy is also presented. The soft dipole mode in ${}^{22}$C is shown to be strongly affected by the loose binding and should be studied in the process of Coulomb fragmentation.

Within the particle-number conserving highly truncated diagonalization approach (amounting to a severely truncated shell model built on self-consistent mean-field single-particle states), we investigate the isospin mixing in the ground state of axially deformed even-even $N=Z$ nuclei with $A<80$. The Skyrme interaction in its SIII parametrization is used to generate the self-consistent mean-field solution, whereas the effective residual interaction is approximated by density-independent $\delta$ interactions in the $T=0$ and $T=1$ isospin channels. In the correlated ground state of the considered nuclei, the obtained values of the isospin-mixing parameter range from a few tens of a percent to a couple of percents. The pairing correlations in both isospin channels are found to increase a little the isospin-mixing parameter with respect to the Hartree-Fock value by two competing mechanisms. In the $T=0$ channel, isospin mixing is brought mostly by neutron-proton one-pair excitations, whereas in the $T=1$ channel it is essentially generated by the difference between neutron-neutron and proton-proton one-pair excitations.

We optimize the density dependence of a local energy density functional for pairing correlations (pair-DF), taking into account both the isoscalar and the isovector densities. All the experimental pairing gaps in even-even nuclei with $N,Z>8$ are analyzed by performing the Hartree-Fock-Bogoliubov calculation. The new pairing energy density functionals give the best fit for all the pairing gaps with the rms deviation of ${\sigma }_{\text{tot}}=(260$–360) keV, depending on adopted Skyrme interactions in the particle-hole channel. It is shown that the isoscalar-density dependence in the pair-DF can be determined almost uniquely for the several Skyrme forces by adjusting the neutron and proton pairing gaps. An empirical relation among the parameters in the isoscalar part of pair-DF is extracted. The uncertainty of the isovector part is also examined by calculating the pairing gaps of neutron-rich and proton-rich nuclei in a wider region of the nuclear chart. We point out also that the linear isovector-density dependence in the pair-DF can mimic well the Coulomb effect for pairing correlations in neutron-rich nuclei. We discuss finally the predictive power of the pair-DF for pairing properties around drip-line regions.

We use multiple scattering and energy conservation arguments to describe ${dn/d\eta |}_{N_A{N}_A}$ as a function of ${dn/d\eta |}_{pp}$ in the framework of string percolation. We discuss the pseudorapidity $\eta$ and beam rapidity $Y$ dependence of particle densities. We present our results for $\mathit{pp}$, Au-Au, and Pb-Pb collisions at RHIC and LHC.

Additional information is reported on single-neutron states above the doubly closed-shell nucleus ${}^{132}$Sn. A radioactive ion beam of ${}^{134}$Te($N=82$) at 565 MeV and a stable ion beam of ${}^{136}$Xe($N=82$) at 560 MeV were used to study single-neutron states in the $N=83$ nuclei ${}^{135}$Te and ${}^{137}$Xe, respectively, by (${}^{13}$C, ${}^{12}$C$\gamma$) and (${}^9$Be, ${}^8$Be$\gamma$) direct reactions in inverse kinematics. Particle-$\gamma$ and particle-$\gamma$-$\gamma$ coincidence measurements using CsI and HPGe arrays allowed determination of decay paths, high-precision level energies, multipolarities of transitions, and relative cross sections. One-neutron transfer with heavy ions is employed to gain selectivity to both low- and high-spin single-neutron states above the $N=82$ shell closure. Results are presented for the $13/2_1^{+}$ states in the $N=83$ nuclei ${}^{135}$Te and ${}^{137}$Xe at 2108.8(9) keV and 1752.6(3) keV, respectively, and for the $3_1^{-}$ collective octupole state observed at 3749(5) keV in ${}^{134}$Te($N=82$) inelastic scattering, all previously unknown. While the $13/2_1^{+}$ state (or $\nu 1i_{13/2}$ centroid) in ${}^{133}$Sn($Z=50$, $N=83$) remains unknown, the present results provide the best empirical prediction of its energy available to date.

Proton-nucleus scattering provides a useful tool to determine either the parameters entering in the assumed shape of the neutron distribution or to test the reliability of the theoretically calculated neutron distributions in the target nuclei. We have used the Bethe-Brueckner-Hartree-Fock approach to calculate the optical potential for analyzing the experimental observables (e.g., differential cross section and polarization) for $p$-${}^{4,6,8}$He and $p$-${}^{6,7,9,11}$Li scattering. The calculation requires mainly two inputs: (1) the nucleon-nucleon (NN) interaction and (2) the nucleon distributions in target nuclei. Various local realistic internucleon (NN) potentials such as Reid93, Urbana v-14, and Argonne v-18 along with several model nucleon density distributions are employed in generating the nucleon-nucleus optical potential. We study the sensitivity of the calculated physical observables on the NN interaction and the density distributions used. It is observed that all the NN interactions and also the different density distributions reproduce rather well the experimental differential cross sections while the calculated polarization is more sensitive to the NN interaction and also to the density distribution used. Thus the polarization data can be used as an additional constraint on the determination of nucleon (especially neutron) density distributions in nuclei. Some results of the representative cases highlighting these features are presented and discussed in detail for illustration.

The event-by-event multiplicity distribution, the energy densities and energy density weighted eccentricity moments ${\epsilon }_n$ (up to $n=6$) at early times in heavy-ion collisions at both the BNL Relativistic Heavy Ion Collider (RHIC) ($\sqrt{s}=200\mathrm{GeV}$) and the CERN Large Hardron Collider (LHC) ($\sqrt{s}=2.76\mathrm{TeV}$) are computed in the IP-Glasma model. This framework combines the impact parameter dependent saturation model (IP-Sat) for nucleon parton distributions (constrained by HERA deeply inelastic scattering data) with an event-by-event classical Yang-Mills description of early-time gluon fields in heavy-ion collisions. The model produces multiplicity distributions that are convolutions of negative binomial distributions without further assumptions or parameters. In the limit of large dense systems, the $n$-particle gluon distribution predicted by the Glasma-flux tube model is demonstrated to be nonperturbatively robust. In the general case, the effect of additional geometrical fluctuations is quantified. The eccentricity moments are compared to the MC-KLN model; a noteworthy feature is that fluctuation dominated odd moments are consistently larger than in the MC-KLN model.

We compute electron-capture rates for ${}^{54,56}$Fe and Ge isotopes using a self-consistent microscopic approach. The single-nucleon basis and the occupation factors in the target nucleus are calculated in the finite-temperature Skyrme Hartree-Fock model, and the $J^{\pi }=0^{\pm }$, $1^{\pm }$, $2^{\pm }$ charge-exchange transitions are determined in the finite-temperature random-phase approximation (RPA). The scheme is self-consistent; i.e., both the Hartree-Fock and the RPA equations are based on the same Skyrme functional. Several interactions are used in order to provide a theoretical uncertainty on the electron-capture rates for different astrophysical conditions. Comparing electron-capture rates obtained either with different Skyrme sets or with different available models indicates that differences up to one to two orders of magnitude can arise.

A correct determination of the spin-isospin properties of the nuclear effective interaction should lead to, among other improvements, an accurate description of the Gamow-Teller resonance (GTR). These nuclear excitations impact on a variety of physical processes: from the response in charge-exchange reactions of nuclei naturally present in the Earth, to the description of the stellar nucleosynthesis and of the pre-supernova explosion core-collapse evolution of massive stars in the Universe. A reliable description of the GTR provides also stringent tests for neutrinoless double-$\beta$ decay calculations. We present a new Skyrme interaction as accurate as previous forces in the description of finite nuclei and of uniform matter properties around saturation density, and that accounts well for the GTR in ${}^{48}$Ca, ${}^{90}$Zr, and ${}^{208}$Pb, and the isobaric analog resonance and spin dipole resonance in ${}^{90}$Zr and ${}^{208}$Pb.

A novel approach is developed to find the three-body breakup amplitudes and cross sections within the modified Faddeev equation framework. The method is based on the latticelike discretization of the three-body continuum with a three-body stationary wave-packet basis in momentum space. The approach makes it possible to simplify drastically all the three- and few-body breakup calculations due to discrete representation for the few-body continuum and lattice representation for all the scattering operators entering the integral equation kernels. As a result, the few-body breakup can be treated as a particular case of multichannel scattering in which part of the channels represents the true few-body continuum states. As an illustration for the novel approach, an accurate calculations for the three-body breakup process $n+d\to n+n+p$ with nonlocal and local $NN$ interactions are calculated. The results obtained reproduce nicely the benchmark calculation results using the traditional Faddeev scheme which requires much more tedious and time-consuming calculations.

Background: The $\beta$ decays of ${}^3$H and ${}^6$He can play an important role in testing nuclear wave-function calculations and fixing low-energy constants in effective-field theory approaches. However, there exists a large discrepancy between previous measurements of the ${}^6$He half-life.

Purpose: Our measurement aims at resolving this long-standing discrepancy in the ${}^6$He half-life and providing a reliable $ft$ value and Gamow-Teller matrix element for comparison with theoretical ab initio calculations.

Method: We measured the ${}^6$He half-life by counting the $\beta$-decay electrons with two scintillator detectors operating in coincidence.

Results: The measured ${}^6$He half-life is $806.89\pm 0.{11}_{\mathrm{stat}}{}_{-0.19}^{+0.23}{}_{\mathrm{syst}}$ ms corresponding to a relative precision of $3\times {10}^{-4}$. Calculating the statistical rate function we determined the $ft$ value to be $803.{04}_{-0.23}^{+0.26}$ s.

Conclusions: Our result resolves the previous discrepancy by providing a higher-precision result with careful analysis of potential systematic uncertainties. The result provides a reliable basis for future precision comparisons with ab initio calculations.

The ${}^1{S}_0$ pairing gap in isospin-symmetric nuclear matter and finite nuclei is investigated using the chiral nucleon-nucleon potential at the next-to-next-to-next-to-leading order (N${}^3$LO) order in the two-body sector and the next-to-next-to-leading order (N${}^2$LO) order in the three-body sector. To include realistic nuclear forces in the relativistic Hartree-Bogoliubov (RHB) framework, we employ a separable form of the pairing interaction that is adjusted to the nuclear matter pairing gap computed with a bare nuclear force. The separable pairing force is applied to the analysis of pairing properties for several isotopic and isotonic chains of spherical nuclei.

Large-scale calculations of the $E1$ strength are performed within the random phase approximation (RPA) based on the relativistic point-coupling mean field approach in order to derive the radiative neutron capture cross sections for all nuclei of astrophysical interest. While the coupling to the single-particle continuum is taken into account in an explicit and self-consistent way, additional corrections like the coupling to complex configurations and the temperature and deformation effects are included in a phenomenological way to account for a complete description of the nuclear dynamical problem. It is shown that the resulting $E1$-strength function based on the PCF1 force is in close agreement with photoabsorption data as well as the available experimental $E1$ strength data at low energies. For neutron-rich nuclei, as well as light neutron-deficient nuclei, a low-lying so-called pygmy resonance is found systematically in the 5–10 MeV region. The corresponding strength can reach 10% of the giant dipole strength in the neutron-rich region and about 5% in the neutron-deficient region, and is found to be reduced in the vicinity of the shell closures. Finally, the neutron capture reaction rates of neutron-rich nuclei is found to be about 2–5 times larger than those predicted on the basis of the nonrelativistic RPA calculation and about a factor 50 larger than obtained with traditional Lorentzian-type approaches.

Collinear laser spectroscopy was performed on the ${}^{63,64,66,68-82}$Ga isotopes with neutron numbers from $N=32$ to $N=51$. These measurements were carried out at the ISOLDE radioactive ion beam facility at CERN. Here we present the nuclear mean-square charge radii extracted from the isotope shifts and, for the lighter isotopes, new spin and moment values. New ground-state nuclear spin and moments were extracted from the hyperfine spectra of ${}^{63,70}$Ga, measured on an atomic transition in the neutral atom. The ground-state spin of ${}^{63}$Ga is determined to be $I=3/2$. Analysis of the trend in the change in mean-square charge radii of the gallium isotopes demonstrates that there is no evidence of anomalous charge radii behavior in gallium in the region of $N=32$.

High-spin states of ${}^{101}$Pd were studied through in-beam $\gamma$-ray spectroscopy by using the reaction ${}^{68}$Zn(${}^{37}$Cl, $1p3n$). The band based on the $h_{11/2}$ neutron orbital was extended up to (${\frac{51}{2}}^{-}$), and the band based on the $d_{5/2}$ neutron orbital was revised. Various transitions decaying to these bands were observed, and consequently several side bands were established. Electric dipole transitions from the $\nu h_{11/2}$ band to the $\nu d_{5/2}$ band were also observed. The structure of the $\nu h_{11/2}$ band is discussed from the viewpoint of antimagnetic rotation based on a semiclassical particle-rotor model by taking neutron alignments into account. The possible existence of octupole correlations is also discussed on the basis of $B\left(E1\right)/B\left(E2\right)$ ratios for the decays of the $\nu h_{11/2}$ band.

We study the transverse flow for the systems having various isospin ratios. We find that the transverse flow is sensitive toward the neutron content and, in fact, increases with the neutron content of a reaction. We also study the sensitivity of the transverse flow toward the density dependence of the symmetry energy and find that the flow increases with the stiffness of the symmetry energy. The relative contribution of the symmetry energy and isospin dependence of the nucleon-nucleon cross section is also investigated.

Fission cross sections and fission fragment mass distributions were measured in the reactions of ${}^{40}$Ca+${}^{238}$U and ${}^{48}$Ca+${}^{238}$U at energies around the Coulomb barrier. Fusion probabilities were calculated based on the fluctuation dissipation model. The measured mass distributions for both reactions showed an asymmetric shape at low incident energies, whereas the distribution changed to a flat shape at higher energies. The variation of the mass distribution is explained by a change of the ratio between fusion and quasifission with nuclear orientation. The calculation reproduced the mass distributions and their energy dependence. The trajectories for fusion-fission were used to determine the fusion probability. Fusion probabilities for both reactions are identical as function of the center-of-mass energy ($E_{\mathrm{c}.\mathrm{m}.}$), but they differ when plotted as function of the excitation energy ($E^{*}$). Evaporation residue cross sections were calculated for the reaction ${}^{48}$Ca+${}^{238}$U using a statistical model and the obtained fusion cross sections as input values. The results are compared to experimental data.

Background: Neutron activation cross sections for energies around 14 MeV are required for various applications. Because cross-section data for the rare-earth elements are too scarce, there is a need for their accurate measurement and refinement. The accuracy of the evaluation and cross-section trend studies can be improved with reliable experimental data too.

Purpose: The purpose of the paper is to provide measurements of new cross-section data and earlier published cross-section data with much better accuracy for lanthanide elements—Dy, Er, and Yb—and the re-evaluation of available systematics for (n,x) reactions.

Methods: The cross sections for (n,x) reactions were measured at (d-t) neutron energies with the activation technique. Theoretical calculations of cross-section values have been performed with the talys-1.2 code.

Results: The sets of cross sections for (n,p), (n,2n), and (n,α) reactions were analyzed and the systematics were tested over the 156 ≤ $A$ ≤ 176 mass region. The ${}^{156}$Dy(n,p)${}^{156}$Tb and ${}^{162}$Er(n,p)${}^{162}$Ho${}^{(m+g)}$ cross-section values at 14.7 MeV neutron energy are reported for the first time. The ${}^{176}$Yb(n,d+pn)${}^{175}$Tm, ${}^{176}$Yb(n,n’α)${}^{172}$Er, ${}^{162,163}$Dy(n,x)${}^{162}$Tb, and ${}^{163,164}$Dy(n,x)${}^{163}$Tb cross sections are obtained with much better accuracy. The reevaluation of systematics for (n,p) cross sections and the reexamination of a presence of isotopic effect in the target nuclei mass range was performed. It was done based on original and earlier available data.

Conclusions: Obtained experimental results can be used for nuclear reaction model testing and could be considered as supplementary ones for nuclear data evaluation. The straight-line systematic dependence for (n,α) cross section was confirmed. For Er isotopes, a clear isotopic effect was observed in case of ($n$,$p$) reactions and pointed out the necessity of reconsidering the systematics.

Collective excitations and trajectory deflection are investigated to lower the applicable energy range of the intranuclear cascade model to around 50 MeV. First, inclusive $(p,p^{\prime }x)$ reaction processes that lead to noncollective and collective excitations are formulated under the Born approximation. Then, collective excitations and trajectory deflection are introduced into the framework of the intranuclear cascade model. As collective excitations, low-energy vibrational excitations and giant resonances are considered. The trajectory deflection is assumed to be given by the experimental angular distribution of proton-nucleus elastic scattering. Finally, numerical calculations are conducted for $(p,p^{\prime }x)$ reactions on ${}^{56}$Fe at 29.9 and 61.5 MeV. The predictive capability of the proposed model is validated through comparison with experimental observations. The proposed model gives reasonably good predictions of $(p,p^{\prime }x)$ reactions and proton elastic scatterings.