We have studied the $\beta$ decay of the $T_z=-1,f_{7/2}$ shell nuclei ${}^{54}\mathrm{Ni},{}^{50}\mathrm{Fe},{}^{46}\mathrm{Cr}$, and ${}^{42}\mathrm{Ti}$ produced in fragmentation reactions. The proton separation energies in the daughter $T_z=0$ nuclei are relatively large $(\approx 4$–5 MeV) so studies of the $\gamma$ rays are essential. The experiments were performed at GSI as part of the Stopped-beam campaign with the RISING setup consisting of 15 Euroball Cluster Ge detectors. From the newly obtained high precision $\beta$-decay half-lives, excitation energies, and $\beta$ branching ratios, we were able to extract Fermi and Gamow-Teller transition strengths in these $\beta$ decays. With these improved results it was possible to compare in detail the Gamow-Teller (GT) transition strengths observed in beta decay including a sensitivity limit with the strengths of the $T_z=+1$ to $T_z=0$ transitions derived from high resolution $\left({}^3\mathrm{He},t\right)$ reactions on the mirror target nuclei at RCNP, Osaka. The accumulated $B$(GT) strength obtained from both experiments looks very similar although the charge exchange reaction provides information on a broader energy range. Using the “merged analysis” one can obtain a full picture of the $B$(GT) over the full $Q_{\beta }$ range. Looking at the individual transitions some differences are observed, especially for the weak transitions. Their possible origins are discussed.

The interplay between isospin-symmetry-breaking and shape-coexistence effects in $A\approx 70$ analogs is self-consistently treated within the beyond-mean-field complex excited VAMPIR variational model with symmetry projection before variation using an effective interaction obtained from a $G$ matrix based on the charge-dependent Bonn CD potential. Results are presented on Coulomb energy differences, mirror energy differences, triplet energy differences, and triplet displacement energy in the $A=70$ and $A=74$ isovector triplets.

Background: In this new era of radioactive beam facilities, the discovery of novel modes of excitation in nuclei far away from stability represents an area of intense research activity. In addition, some of these modes of excitation, particularly the isoscalar monopole and isovector dipole resonances, appear to be sensitive to the uncertain density dependence of the symmetry energy.

Purpose: It is the main goal of this paper to examine the emergence, evolution, and nature of both the soft and giant isoscalar monopole modes as a function of neutron excess in three unstable nickel isotopes: ${}^{56}\mathrm{Ni},{}^{68}\mathrm{Ni}$, and ${}^{78}\mathrm{Ni}$.

Methods: The distribution of isoscalar monopole strength is computed in a relativistic random-phase approximation by using several accurately calibrated effective interactions. In particular, a nonspectral Green's function approach is adopted that allows for an exact treatment of the continuum without any reliance on discretization. The discretization of the continuum is neither required nor admitted.

Results: In the case of ${}^{56}\mathrm{Ni}$, the lack of low-energy strength results in a direct correlation between the centroid energy of the giant monopole resonance and the incompressibility coefficient of symmetric nuclear matter. In contrast, the large neutron excess in both ${}^{68}\mathrm{Ni}$ and ${}^{78}\mathrm{Ni}$ generates a significant, yet relatively featureless, amount of low-energy strength that is driven by transitions into the continuum. Moreover, the evolution of monopole strength with neutron excess displays sensitivity to the density dependence of the symmetry energy.

Conclusions: It is suggested that future measurements of the distribution of isoscalar monopole strength at radioactive beam facilities using a very long chain of both stable and unstable isotopes could place important constraints on the equation of state of neutron-rich matter and ultimately on the properties of neutron stars. However, given the nature of the low-energy monopole excitations, a proper treatment of the continuum is absolutely essential.

Background: Information about the ${}^6\mathrm{Li}(d,\alpha ){}^4\mathrm{He}$ reaction rates of astrophysical interest can be obtained by extrapolating direct data to lower energies, or by indirect methods. The indirect Trojan horse method, as well as various $R$-matrix and polynomial fits to direct data, estimate electron screening energies much larger than the adiabatic limit. Calculations that include the subthreshold resonance estimate smaller screening energies.

Purpose: Obtain the ${}^6\mathrm{Li}{(d,\alpha )}^4\mathrm{He}$ reaction $R$-matrix parameters and the bare astrophysical $S$ factor for energies relevant to the stellar plasmas by fitting $R$-matrix formulas for the subthreshold resonances to the $S$-factor data above 60 keV.

Methods: The bare $S$ factor is calculated using the single- and the two-level $R$-matrix formulas for the closest to the threshold $0^{+}$ and $2^{+}$ subthreshold states at $22.2,20.2$, and $20.1$ MeV. The electron screening potential $U{}_{\mathrm{e}}$ is then obtained by fitting it as a single parameter to the low-energy data. The calculations are also done by fitting $U{}_{\mathrm{e}}$ simultaneously with other parameters.

Results: The low-energy $S$ factor is dominated by the $2^{+}$ subthreshold resonance at $22.2$ MeV. The influence of the other two subthreshold states is small. The resultant electron screening is smaller than the adiabatic value. The fits that neglect the electron screening above 60 keV produce a significantly smaller electron screening potential. The calculations show a large ambiguity associated with a choice of the initial channel radius.

Conclusions: The $R$-matrix fits do not show a significantly larger $U_e$ than predicted by the atomic physics models. The $R$-matrix best fit provides $U{}_{\mathrm{e}}=149.5$ eV and $S_b\left(0\right)=21.7$ MeV b.

The earlier study of excitation functions of ${}^{105}\mathrm{Ag}^{*}$, formed in the ${}^{12}\mathrm{C}+{}^{93}\mathrm{Nb}$ reaction, based on the dynamical cluster-decay model (DCM), using the pocket formula for nuclear proximity potential is extended to the use of other nuclear interaction potentials derived from the Skyrme energy density functional (SEDF) based on the semiclassical extended Thomas Fermi (ETF) approach and to the use of the extended-Wong model of Gupta and collaborators. The Skyrme forces used are the old SIII and SIV and the new SSk, GSkI, and KDE0(v1) given for both normal and isospin-rich nuclei, with densities added in the frozen-density approximation. Taking advantage of the fact that different Skyrme forces provide different barrier characteristics, we look for the “barrier modification” effects in terms of choosing an appropriate force and hence for the existence or nonexistence of noncompound nucleus (nCN) effects in this reaction. Interestingly, independent of the choice of Skyrme or proximity force, the extended-Wong model fits the experimental data nicely, without any barrier modification and hence no nCN component in the measured fusion cross section, which consists of light-particle evaporation residue (ER) and intermediate-mass fragments (IMFs) up to mass 13, i.e., ${\sigma }_{\mathrm{fusion}}^{\mathrm{Expt}.}={\sigma }_{\mathrm{ER}}+{\sigma }_{\mathrm{IMFs}}$. However, the predicted fusion cross section due to the extended-Wong model is much larger, possibly because of the so-far missing fusion-fission (ff) component in the data. On the other hand, in agreement with the earlier work using the pocket proximity potential, the DCM fits only some data (mainly IMFs) for only some Skyrme forces, and hence it presents the chosen reaction as a case of a large nCN component, whose empirically estimated content is fitted for use of the DCM with a fragment preformation factor taken equal to one, i.e., using $\mathrm{DCM}\left(P_0=1\right)$, by introducing “barrier modification” through changing the neck-length parameter $\Delta R$ for a best fit to the empirical nCN data in each (ER and IMF) decay channel. Also, the ff component of the DCM is predicted to lie around the symmetric mass $A/2\pm 16$. All calculations are made for deformed and oriented coplanar nuclei.

The excited states of the odd-$Z$ proton rich nuclei ${}^{131-136}\mathrm{Eu}$ are explored theoretically to look for the appearance of shape phase transitions and the phenomena of shape coexistence as a function of temperature and angular momentum. These nuclei remain well deformed with $\beta$ $\approx$ $0.15-0.2$ at the temperatures of the order of $1.5-2.0$ MeV and hence the potential candidates for the experimental probes of nuclear shapes. The phenomenon of shape coexistence is observed with coexisting oblate noncollective and rarely seen prolate noncollective shapes at low temperatures where the effects of rotation are predominant.

The preformation probability of an $\alpha$ cluster inside radioactive parent nuclei is investigated. The calculations are employed in the framework of the density-dependent cluster model for both even-even and odd-$A$ isotopes with $74\le Z\le 83$. A realistic density-dependent nucleon-nucleon ($NN$) interaction with a finite-range exchange part is used to calculate the microscopic $\alpha$-nucleus potential in the well-established double-folding model. The main effect of antisymmetrization under exchange of nucleons between the $\alpha$ and daughter nuclei has been included in the folding model through the finite-range exchange part of the $NN$ interaction. The calculated potential is then implemented to find both the assault frequency and the penetration probability of the $\alpha$ particle by means of the Wentzel-Kramers-Brillouin approximation in combination with the Bohr-Sommerfeld quantization condition. We investigated the correlation between the $\alpha$-particle preformation probability, $S_{\alpha }$, and the energy levels of the parent nucleus for $\alpha$ emitters with atomic number $74\le Z\le 83$. Based on the similarity in the behavior of $S_{\alpha }$ with the neutron number for two nuclei, we try to predict or confirm the unknown or doubted nuclear spins and parities in this mass region.

Femtoscopy is providing information on system size and its dynamics in heavy-ion collisions. At ultrarelativistic energies, such as those obtained at the Large Hadron Collider (LHC), significant production of pions, kaons, and protons enables femtoscopic measurements for these particles. In particular, the dependence of system size on pair momentum and particle type is interpreted as evidence for strong collective flow. Such phenomena are naturally modeled by hydrodynamics. We present calculations within the (3+1)D hydrodynamic model coupled to statistical hadronization code therminator 2, corresponding to Pb-Pb collisions at $\sqrt{s_{\mathit{NN}}}=2.76$ TeV. We obtain femtoscopic radii for pions, kaons, and protons, as a function of pair transverse momentum and collision centrality. We find that an approximate universal scaling of radii with pair transverse mass and final-state event multiplicity is observed and discuss the consequences for the interpretation of experimental measurements.

The femtoscopy correlation radii for $d\text{−}\mathrm{Au}$ collisions at 200 GeV are calculated in the hydrodynamic model and compared to data of the PHENIX Collaboration. For asymmetric systems, such as $d\text{−}\mathrm{Au}$ or $p$-Pb collisions, the correlation radius $R_{\mathrm{out}-\mathrm{long}}$ is estimated and predicted to be nonzero. It appears due to different lifetimes of the parts of the fireball at positive and negative rapidities. Azimuthally sensitive Hanbury Brown-Twiss analysis with respect to the second-order event plane shows a significant angular dependence of the radii. It reflects the strong azimuthal asymmetry of the $d\text{−}\mathrm{Au}$ source geometry and flow for central interactions.

Precise reaction cross sections (${\sigma }_R$) for ${}^{24-38}\mathrm{Mg}$ on C targets at energies around 240 MeV/nucleon have been measured at the Radioactive Isotope Beam Factory at RIKEN. The ${\sigma }_R$ for ${}^{36-38}\mathrm{Mg}$ have been measured for the first time. An enhancement of ${\sigma }_R$ compared to the systematics for spherical stable nuclei has been observed, especially in the neutron-rich region, which reflects the deformation of those isotopes. In the vicinity of the drip line the ${\sigma }_R$ for ${}^{37}\mathrm{Mg}$ is especially large. It is shown by analysis using a recently developed theoretical method that this prominent enhancement of ${\sigma }_R$ for ${}^{37}\mathrm{Mg}$ should come from the $p$-orbital halo formation breaking the $N=28$ shell gap.

We present microscopic calculations of light and medium mass nuclei and the equation of state of symmetric and asymmetric nuclear matter using different nucleon-nucleon interactions, including a new Argonne version that has the same spin-isospin structure as local chiral forces at next-to-next-to-leading order. The calculations are performed using auxiliary field diffusion Monte Carlo (AFDMC) combined with an improved variational wave function and sampling technique. The AFDMC method can now be used to successfully calculate the energies of very light to medium mass nuclei as well as the energy of isospin-asymmetric nuclear matter, demonstrating microscopically the quadratic dependence of the energy on the symmetry energy.

Isospin transport occurring within dinuclear projectile-like fragments (PLFs) produced in heavy-ion collisions is explored as a probe of the nuclear symmetry energy. Within the framework of the constrained molecular dynamics (CoMD) model, the existence of the long-lived dinuclear PLFs, for up to $800 \mathrm{fm}/c$, is observed. It is demonstrated that changes in the $\langle N/Z\rangle$ of the two fragments resulting from the breakup of the dinuclear PLF is due to isospin transport. The rate of the transport between the two fragments is shown to be dependent on the slope of the symmetry energy at saturation density. Comparison of the CoMD calculations with experimental data establishes that the evolution of $\langle N/Z\rangle$ could be used to constrain the density dependence of the symmetry energy.

Background: A primary goal of deuteron electrodisintegration is the possibility of extracting the deuteron momentum distribution. This extraction is inherently fraught with difficulty, as the momentum distribution is not an observable and the extraction relies on theoretical models dependent on other models as input.

Purpose: We present a new method for extracting the momentum distribution which takes into account a wide variety of model inputs thus providing a theoretical uncertainty due to the various model constituents. To test the extraction, pseudodata were generated, and the extracted “experimental” distribution, which has theoretical uncertainty accounted by this extraction method, can be compared to the theoretical distribution. This procedure can provide an upper bound on the deuteron momentum distribution.

Method: The calculations presented here are using a Bethe-Salpeter-like formalism with a wide variety of bound state wave functions, form factors, and final state interactions.

Results: In the examples we compared, the original distribution was typically within the error band of the extracted distribution. The input wave functions do contain some outliers which are discussed in the text. Due to the reliance on the theoretical calculation to obtain this quantity, any extraction method should account for the theoretical error inherent in these calculations due to model inputs.

Conclusions: The extraction method works well and provides a systematic way to investigate the deuteron momentum distribution, while accounting for theoretical uncertainty and providing a theoretical error band.

The use of finite harmonic oscillator spaces in many-body calculations introduces both infrared (IR) and ultraviolet (UV) errors. The IR effects are well approximated by imposing a hard-wall boundary condition at a properly identified radius $L_{\mathrm{eff}}$. We show that duality of the oscillator implies that the UV effects are equally well described by imposing a sharp momentum cutoff at a momentum ${\Lambda }_{\mathrm{eff}}$ complementary to $L_{\mathrm{eff}}$. By considering two-body systems with separable potentials, we show that the UV energy corrections depend on details of the potential, in contrast to the IR energy corrections, which depend only on the $S$-matrix. An adaptation of the separable treatment to more general interactions is developed and applied to model potentials as well as to the deuteron with realistic potentials. The previous success with a simple phenomenological form for the UV error is also explained. Possibilities for controlled extrapolations for $A>2$ based on scaling arguments are discussed.

The $\alpha$-cluster states of ${}^{16}\mathrm{C}$ are investigated by using antisymmetrized molecular dynamics. It is shown that two different types of $\alpha$-cluster states exist: triangular and linear-chain states. The former has an approximate isosceles triangular configuration of $\alpha$ particles surrounded by four valence neutrons occupying the $sd$ shell, while the latter has the linearly aligned $\alpha$ particles with ${\left(sd\right)}^2{\left(pf\right)}^2$ neutrons. It is found that the structure of the linear-chain state is qualitatively understood in terms of the $3/2_{\pi }^{-}$ and $1/2_{\sigma }^{-}$ molecular orbits as predicted by molecular-orbital model, but there exists a non-negligible ${}^{10}\mathrm{Be}+\alpha +2n$ correlation. The bandhead energies of the triangular and linear-chain rotational bands are 8.0 and 15.5 MeV, and the latter is close to the ${}^4\mathrm{He}+{}^{12}\mathrm{Be}$ and ${}^6\mathrm{He}+{}^{10}\mathrm{Be}$ threshold energies. It is also shown that the linear-chain state becomes the yrast state at $J^{\pi }={10}^{+}$ with $E_x=27.8$ MeV owing to its very large moment of inertia comparable with hyperdeformation.

In this paper we study low-lying states under random interactions in the framework of the fermion dynamical symmetry model (FDSM), regardless of the ground state spin. Very strong correlations are found for $R_6$ versus $R_4$ (where $R_I\equiv E_{I_1^{+}}/E_{2_1^{+}})$ for the entire ensemble. We present arguments on the origin of these regular patterns in terms of the dynamical symmetries of the FDSM. The regular patterns of $B(E2;4_1^{+}\to 2_1^{+})$ versus $B(E2;2_1^{+}\to 0_1^{+})$ are found.

Electric quadrupole strength functions have been deduced from averages of a large number of $E2$ transition strengths calculated within the shell model for the nuclides ${}^{94}\mathrm{Mo}$ and ${}^{95}\mathrm{Mo}$. These strength functions are at variance with phenomenological approximations as provided by the Reference Input Parameter Library RIPL-3 for calculations of reaction rates on the basis of the statistical model.

Existing data on near-barrier fusion excitation functions of medium and heavy nucleus-nucleus systems have been analyzed by using a simple diffused-barrier formula derived assuming the Gaussian shape of the barrier-height distributions. The fusion cross section is obtained by folding the Gaussian barrier distribution with the classical expression for the fusion cross section for a fixed barrier. The energy dependence of the fusion cross section, thus obtained, provides good description to the existing data on near-barrier fusion and capture excitation functions for medium and heavy nucleus-nucleus systems. The theoretical values for the parameters of the barrier distribution are estimated which can be used for fusion or capture cross-section predictions that are especially important for planning experiments for synthesizing new superheavy elements.

In nuclear collisions at highest accessible Large Hadron Collider (LHC) energies, often more than one dijet pairs deposit momentum into the deconfined expanding medium. With the help of 3+1 dimensional relativistic hydrodynamic simulation we show that this leads to measurable contribution to the anisotropy of collective transverse expansion. Hard partons generate streams in plasma which merge if they come close to each other. This mechanism correlates the resulting contribution to flow anisotropy with the fireball geometry and causes an increase of the elliptic flow in noncentral collisions.