Background: The newly developed self-consistent Gorkov-Green's function approach represents a promising path to the ab initio description of mid-mass open-shell nuclei. The formalism based on a two-nucleon interaction and the second-order truncation of Gorkov's self-energy has been described in detail in Ref. [Somà, Duguet, and Barbieri, Phys. Rev. C 84, 064317 (2011)].

Purpose: The objective is to discuss the methodology used to solve Gorkov's equation numerically and to gauge its performance in view of carrying out systematic calculations of medium-mass nuclei in the future. In doing so, different sources of theoretical error and degrees of self-consistency are investigated.

Methods: We employ Krylov projection techniques with a multi-pivot Lanczos algorithm to efficiently handle the growth of poles in the one-body Green's function that arises as a result of solving Gorkov's equation self-consistently. We first characterize the numerical scaling of Gorkov's calculations based on full self-consistency and on a partially self-consistent scheme coined as “sc0”. Using small model spaces, the Krylov projection technique is then benchmarked against exact diagonalization of the original Gorkov matrix. Next, the convergence of the results as a function of the number $N_{\ell }$ of Lanczos iterations per pivot is investigated in large model spaces. Eventually, the convergence of the calculations with the size of the harmonic oscillator model space is examined.

Results: Gorkov self-consistent Green's function (SCGF) calculations performed on the basis of Krylov projection techniques display a favorable numerical scaling that authorizes systematic calculations of mid-mass nuclei. The Krylov projection selects efficiently the appropriate degrees of freedom while spanning a very small fraction of the original space. For typical large-scale calculations of mid-mass nuclei, a Krylov projection making use of $N_{\ell }\approx 50$ yields a sufficient degree of accuracy on the observables of interest. The partially self-consistent sc0 scheme is shown to reproduce fully self-consistent solutions in small model spaces at the 1$\%$ level. Eventually, Gorkov-Green's function calculations performed on the basis of SRG-evolved interactions show a fast convergence as a function of the model-space size.

Conclusions: The end result is a tractable, accurate and gently scaling ab initio scheme applicable to complete isotopic and isotonic chains in the medium-mass region. The partially self-consistent sc0 scheme provides an excellent compromise between accuracy and computational feasibility and will be the workhorse of systematic Gorkov-Green's function calculations in the future. The numerical scaling and performances of the algorithm employed offers the possibility (i) to apply the method to even heavier systems than those (e.g., ${}^{74}$Ni) already studied so far and (ii) to perform converged Gorkov SCGF calculations based on harder, e.g. original chiral interactions.

Nuclear structure of the ${}^{26}\mathrm{Mg}$ nucleus has been probed, for the first time, using heavy-ion-induced fusion-evaporation reaction and a large array of high-resolution $\gamma$-ray detectors (Clovers). The level structure of the nucleus reported in the earlier studies, using light-ion reactions, has been re-examined and new transitions have been identified. Existing spin-parity assignments have been confirmed and new assignments have been made from anisotropy and polarization measurements. Large basis shell-model calculations, involving cross-shell excitation- have been carried out, for the first time, in ${}^{26}\mathrm{Mg}$ as well as in the neighboring isotopes and the agreement with the experimental level energies is rather remarkable.

The phenomenon of shape coexistence and rapid shape phase transitions expected in deformed odd-$Z$ proton emitters from $Z=51$ to 75 are investigated using the triaxially deformed Nilsson potential and Strutinsky's prescription for the evaluation of shell correction. Calculations suggest prolate and triaxial shapes with large deformations except for a few oblate deformations, along with the occurrence of some coexisting configurations with different intrinsic shapes. Shape coexistence is observed in ${}^{113}$Cs with two energy minima for different shapes at similar energies. Location of the first proton unbound nuclei for odd-$Z$ rare-earth region is predicted and compared with the available experimental data.

A microscopic cluster model of the nucleus-nucleus bremsstrahlung based on an extension of the Siegert theorem, i.e., based on the charge density rather than on the current, allows including implicitly a part of the effects of meson-exchange currents. This approach was developed in a previous paper for zero-spin nuclei and applied to the $\alpha +\alpha$ bremsstrahlung. This model is extended to colliding nuclei with nonzero spins and applied to the $\alpha +p$ and $\alpha +n$ bremsstrahlungs. A comparison between the bremsstrahlung cross sections for these mirror systems is made. The importance of the meson-exchange currents on the $\alpha +N$ bremsstrahlungs is discussed by comparing the $E1$ and $E2$ components of the bremsstrahlung cross sections obtained in the Siegert approach where these currents are partly included and in the non-Siegert approach where they are fully neglected.

The nuclide ${}^{262}\mathrm{Db}$ was produced in the ${}^{248}\mathrm{Cm}$(${}^{19}\mathrm{F}$,5$n$)${}^{262}\mathrm{Db}$ reaction at beam energies of 103.1 and 97.4 MeV. Decay properties of ${}^{262}\mathrm{Db}$ were investigated with a rotating wheel apparatus for α and spontaneous fission (SF) spectrometry under low background conditions attained by a gas-jet transport system coupled to the RIKEN gas-filled recoil ion separator. Based on genetically correlated α-α and α-SF decay chains, a total of 76 chains were assigned to ${}^{262}\mathrm{Db}$ and its α-decay daughter nuclide ${}^{258}\mathrm{Lr}$. No correlated decay chain was observed for Db produced in the ${}^{248}\mathrm{Cm}$(${}^{19}\mathrm{F}$,4$n$)Db reaction and its daughter Lr. The half-lives of ${}^{262}\mathrm{Db}$ and ${}^{258}\mathrm{Lr}$ were measured to be $T_{1/2}=33.8_{-3.5}^{+4.4}$ and $3.{54}_{-0.36}^{+0.46}\mathrm{s}$, respectively, and they confirmed the literature data. The α-particle energy $\left(E_{\alpha }\right)$ and intensity ($I_{\alpha }$) of ${}^{262}\mathrm{Db}$ were revised to $E_{\alpha }$ = 8.46 ± 0.04 MeV ($I_{\alpha }$ = 70 ± 5%) and $E_{\alpha }$ = 8.68 ± 0.03 MeV ($I_{\alpha }$ = 30 ± 5%). The SF activity with $T_{1/2}$ = 30.2 ± 6.1 s was assigned to ${}^{262}\mathrm{Db}$, and the SF branch of ${}^{262}\mathrm{Db}$ was determined to be $b_{\mathrm{SF}}$ = 52 ± 4%. From an observation of two SF decays which correlated to the α decay of ${}^{262}\mathrm{Db}$, an electron capture (EC) decay with $b_{\mathrm{EC}}$ = 2.6 ± 1.8% was suggested in ${}^{258}\mathrm{Lr}$. The production cross sections for the ${}^{248}\mathrm{Cm}$(${}^{19}\mathrm{F}$,5$n$)${}^{262}\mathrm{Db}$ reaction were determined to be 2.1 ± 0.7 nb at 103.1 MeV and $0.{23}_{-0.11}^{+0.18}\mathrm{nb}$ at 97.4 MeV, whereas, those for the ${}^{248}\mathrm{Cm}$(${}^{19}\mathrm{F}$,4$n$)Db reaction were the upper limits of ≤0.064 nb at 103.1 MeV and ≤0.13 nb at 97.4 MeV. These cross sections are discussed by comparing with the literature data as well as the theoretical prediction.

The optical-model potential for the n + ${}^9$Be reaction is obtained by two methods. The first method is from a modification and generalization of previous work [Bonaccorso and Bertsch, Phys. Rev. C 63, 044604 (2001)] and the second is from a dispersive-optical-model fit. The two potentials and also quantities derived from the $S$ matrices used to calculate neutron knockout cross sections are compared.

We estimate differential rapidity cross sections for $J/\Psi$ and ${\rm Y}\left(1S\right)$ production via Cu-Cu and Au-Au collisions at the BNL Relativistic Heavy Ion Collider (RHIC), and the relative probabilities of ${\Psi }^{\prime }\left(2S\right)$ to $J/\Psi$ production via $p$-$p$ collisions using our recent theory of mixed heavy-quark hybrids, in which the ${\Psi }^{\prime }\left(2S\right)$ mesons have approximately equal normal $q\overline{q}$ and hybrid $q\overline{q}g$ components. We also estimate the relative probabilities of ${\Psi }^{\prime }\left(2S\right)$ to $J/\Psi$ production via Cu-Cu and Au-Au collisions, which will be measured in future RHIC experiments. We also review production ratios of ${\rm Y}\left(2S\right)$ and ${\rm Y}\left(3S\right)$ to ${\rm Y}\left(1S\right)$ in comparison to recent experimental results.This is an extension of our recent work on $p$-$p$ collisions for possible tests of the production of quark-gluon plasma via $A$-$A$ collisions at RHIC.

Spectra of $K_S^0$ mesons and $\Lambda$ hyperons were measured in p + C interactions at 31 GeV/$c$ with the large acceptance NA61/SHINE spectrometer at the CERN SPS. The data were collected with an isotropic graphite target with a thickness of 4% of a nuclear interaction length. Interaction cross sections, charged pion spectra, and charged kaon spectra were previously measured using the same data set. Results on $K_S^0$ and $\Lambda$ production in p + C interactions serve as a reference for the understanding of the enhancement of strangeness production in nucleus-nucleus collisions. Moreover, they provide important input for the improvement of neutrino flux predictions for the T2K long baseline neutrino oscillation experiment in Japan. Inclusive production cross sections for $K_S^0$ and $\Lambda$ are presented as a function of laboratory momentum in intervals of the laboratory polar angle covering the range from 0 up to 240 mrad. The results are compared with predictions of several hadron production models. The $K_S^0$ mean multiplicity in production processes $\langle n_{K_S^0}\rangle$ and the inclusive cross section for $K_S^0$ production ${\sigma }_{K_S^0}$ were measured and amount to 0.127 $\pm$ 0.005 (stat) $\pm$ 0.022 (sys) and 29.0 $\pm$ 1.6 (stat) $\pm$ 5.0 (sys) mb, respectively.

Various model-independent aspects of the $\overline{K}N\to K\Xi$ reaction are investigated, starting from the determination of the most general structure of the reaction amplitude for $\Xi$ baryons with $J^P={\frac{1}{2}}^{\pm }$ and ${\frac{3}{2}}^{\pm }$ and the observables that allow a complete determination of these amplitudes. Polarization observables are constructed in terms of spin-density matrix elements. Reflection symmetry about the reaction plane is exploited, in particular, to determine the parity of the produced $\Xi$ in a model-independent way. In addition, extending the work of Biagi et al. [Z. Phys. C 34, 175 (1987)], a way of determining simultaneously the spin and parity of the ground state of $\Xi$ baryons as well as those of the excited $\Xi$ states is presented.

The limits on time-reversal invariant tensor-type weak currents from nuclear and neutron $\beta$ decays are evaluated including most recent experimental data. We find that $-0.14\times {10}^{-2}<(C_T+C_T^{\prime })/C_A<1.4\times {10}^{-2}$ and $-0.16<(C_T-C_T^{\prime })/C_A<0.16$ (90% C.L.), while for the case $C_T=C_T^{\prime }$ the limits are $0.0\times {10}^{-2}<C_T/C_A<0.4\times {10}^{-2}$. These limits are shown to be more stringent than those from recent measurements of the radiative pion decay. In addition, the sensitivity of future ${10}^{-3}$-level correlation measurements is investigated.

The cross section of the ${}^{62}\mathrm{Ni}$($n,\gamma$) reaction was measured with the time-of-flight technique at the neutron time-of-flight facility n_TOF at CERN. Capture kernels of 42 resonances were analyzed up to 200 keV neutron energy and Maxwellian averaged cross sections (MACS) from $kT=$ 5–100 keV were calculated. With a total uncertainty of $4.5$%, the stellar cross section is in excellent agreement with the the KADoNiS compilation at $kT=30$ keV, while being systematically lower up to a factor of 1.6 at higher stellar temperatures. The cross section of the ${}^{63}\mathrm{Ni}$($n,\gamma$) reaction was measured for the first time at n_TOF. We determined unresolved cross sections from 10 to 270 keV with a systematic uncertainty of 17%. These results provide fundamental constraints on $s$-process production of heavier species, especially the production of Cu in massive stars, which serve as the dominant source of Cu in the solar system.

The parabolic approximation to the equation of state of the isospin asymmetric nuclear matter (ANM) is widely used in the literature to make predictions for the nuclear structure and the neutron star properties. Based on the realistic M3Y-Paris and M3Y-Reid nucleon-nucleon interactions, we investigate the effects of the higher-order symmetry energy on the proton fraction in neutron stars and the location of the inner edge of their crusts and their core-crust transition density and pressure, thermodynamically. Analytical expressions for different-order symmetry energy coefficients of ANM are derived using the realistic interactions mentioned above. It is found that the higher-order terms of the symmetry-energy coefficients up to its eighth order $\left(E_{\mathrm{sym}8}\right)$ contributes substantially to the proton fraction in β-stable neutron star matter at different nuclear matter densities, the core-crust transition density and pressure. Even by considering the symmetry-energy coefficients up to $E_{\mathrm{sym}8},$ we obtain a significant change of about 40% in the transition pressure value from the one based on the exact equation of state. The slope parameters of the symmetry energies for the M3Y-Paris (Reid) interaction, at the saturation density, are $L=47.51(50.98),$ $L_4=-0.47(-1.43),$ $L_6=0.58(0.67)$, and $L_8=0.126(0.133)$ MeV. Using equations of state based on both Paris and Reid effective interactions which provide saturation incompressibility of symmetric nuclear matter in the range of $220\le K_0\le 270$ MeV, we estimate the ranges $0.090\le {\rho }_t\le 0.095{\mathrm{fm}}^{-3}$ and $0.49\le P_t\le 0.59\mathrm{MeV}{\mathrm{fm}}^{-3}$ for the liquid–core-solid-crust transition density and pressure, respectively. The corresponding range of the proton fraction obtained at this ${\rho }_t$ range is $0.029\le x_{p\left(t\right)}\le 0.032.$

For thefirst time primary hot isotope distributions are experimentally reconstructed in intermediate heavy-ion collisions and used with antisymmetrized molecular dynamics (AMD) calculations to determine density, temperature, and symmetry energy coefficient in a self-consistent manner. A kinematical focusing method is employed to reconstruct the primary hot fragment-yield distributions for multifragmentation events observed in the reaction system ${}^{64}\mathrm{Zn}+{}^{112}\mathrm{Sn}$ at 40 MeV/nucleon. The reconstructed yield distributions are in good agreement with the primary isotope distributions of AMD simulations. The experimentally extracted values of the symmetry energy coefficient relative to the temperature, $a_{\text{sym}}/T$, are compared with those of the AMD simulations with different density dependence of the symmetry energy term. The calculated $a_{\text{sym}}/T$ values change according to the different interactions. By comparison of the experimental values of $a_{\text{sym}}/T$ with those of calculations, the density of the source at fragment formation was determined to be $\rho /{\rho }_0=(0.63\pm 0.03)$. Using this density, the symmetry energy coefficient and the temperature are determined in a self-consistent manner as $a_{\text{sym}}=(24.7\pm 1.9)\text{MeV}$ and $T=(4.9\pm 0.2)$ MeV.

Two basic concepts of nuclear vorticity, hydrodynamical (HD) and Rawenthall-Wambach (RW), are critically inspected. As a test case, we consider the interplay of irrotational and vortical motion in isoscalar electric dipole $E1(T=0)$ modes in ${}^{208}\mathrm{Pb}$, namely the toroidal and compression modes. The modes are described in a self-consistent random-phase approximation (RPA) with the Skyrme force SLy6. They are examined in terms of strength functions, transition densities, current fields, and form factors. It is shown that the RW conception (suggesting the upper component of the nuclear current as the vorticity indicator) is not robust. The HD vorticity is not easily applicable either because the definition of a velocity field is too involved in nuclear systems. Instead, the vorticity is better characterized by the toroidal strength which closely corresponds to HD treatment and is approximately decoupled from the continuity equation.

Thermal fluctuations affect the dynamics of systems near critical points, the evolution of the early universe, and two-particle correlations in heavy-ion collisions. For the latter, numerical simulations of nearly ideal, relativistic fluids are necessary. The correlation functions of noise in relativistic fluids are calculated, stochastic integration of the noise in $3+1$-dimensional viscous hydrodynamics is implemented, and the effect of noise on observables in heavy-ion collisions is discussed. Thermal fluctuations will cause significant variance in the event-by-event distributions of integrated $v_2$ while changing average values even when using the same initial conditions, suggesting that including thermal noise will lead to refitting of the hydrodynamical parameters with implications for understanding the physics of hot QCD.

We determine the chiral constants of the nucleon-nucleon two-pion exchange potential deduced from chiral perturbation theory. By using a coarse-grained representation of the short-distance interactions with 30 parameters, the partial wave analysis fit gives ${\chi }^2/\nu =1.07$ to a mutually consistent set of 6713 data previously built from all proton-proton and neutron-proton scattering data published from 1950 to 2013 with laboratory energies below 350 MeV. We obtain $(c_1,c_3,c_4)=(-0.41\pm 1.08,-4.66\pm 0.60,4.31\pm 0.17){\mathrm{GeV}}^{-1}$ with an almost $100\%$ anticorrelation between $c_1$ and $c_3$. We also provide the errors in the short-distance parameters and propagate them to the deuteron properties and low partial wave phase shifts.

The charge-exchange $({}^3\mathrm{He},t)$ scattering to the isobaric analog state (IAS) of the target can be considered as “elastic” scattering of ${}^3\mathrm{He}$ by the isovector term of the optical potential (OP) that flips the projectile isospin. Therefore, the accurately measured charge-exchange scattering cross section for the IAS can be a good probe of the isospin dependence of the OP, which is determined exclusively within the folding model by the difference between the neutron and proton densities and isospin dependence of the nucleon-nucleon interaction. Given the neutron skin of the target related directly to the same density difference, it can be well probed in the analysis of the charge-exchange $({}^3\mathrm{He},t)$ reactions at medium energies when the two-step processes can be neglected and the $t$-matrix interaction can be used in the folding calculation. For this purpose, the data of the $({}^3\mathrm{He},t)$ scattering to the IAS of ${}^{90}\mathrm{Zr}$ and ${}^{208}\mathrm{Pb}$ targets at $E_{\mathrm{lab}}=420$ MeV have been analyzed in the distorted wave Born approximation using the double-folded charge-exchange form factor. The neutron skin deduced for these two nuclei turned out to be in a good agreement with the existing database.

The root-mean-square (rms) nuclear charge radii of superheavy odd-$A$ and odd-odd nuclei are tentatively pursued by the deduction of experimental $\alpha$ decay data. The framework of calculating $\alpha$ decay half-lives is constructed via the combination of the improved two-potential approach with the density-dependent cluster model. In this procedure, the charge distribution of daughter nuclei is determined to exactly reproduce the measured $\alpha$ decay half-lives. Next, the rms charge radius of daughter nuclei is obtained by using the corresponding charge distribution. For comparison, the previously proposed formula of our group is employed to estimate the rms charge radii as well. Besides the reasonable agreement between the extracted nuclear charge radii and the available experimental values, the nuclear radii of heaviest odd-$A$ and odd-odd nuclei are extracted from the $\alpha$ decay energies and half-lives. This can be considered as an effective attempt in terms of the nuclear size in the superheavy mass region.

We perform realistic shell-model calculations for nuclei with valence nucleons outside ${}^{48}\mathrm{Ca}$, employing two different model spaces. The matrix elements of the effective two-body interaction and electromagnetic multipole operators have been calculated within the framework of many-body perturbation theory, starting from a low-momentum potential derived from the high-precision CD-Bonn free nucleon-nucleon potential. The role played by the neutron orbital $1d_{5/2}$ has been investigated by comparing experimental data on yrast quadrupole excitations of isotopic chains north-east of ${}^{48}\mathrm{Ca}$ with the results of calculations including or not including this single-particle state in the model space.