I have analyzed data for inelastic ${\pi }^{+}$ and ${\pi }^{-}$ scatterings to the two lowest $2^{+}$ states of ${}^{14}\mathrm{C}$ to determine proton and neutron matrix elements. In a two-state model, I have then derived one-body transition amplitudes for $p$ shell and ${\left(sd\right)}^2$ transitions. Data are found to be consistent with equal mixing of the $2^{+}$ states but with slightly nonstandard ratios of effective charges. Using effective charges in common usage, mixing is found to be only slightly different from equal—55% of the ${\left(sd\right)}^2$ component in the lower $2^{+}$ state.

This work aims at investigating the projectile binding energy influence on the reaction dynamics, introducing new results and new data analysis methods in order to overcome some typically encountered problems, such as the identification of reaction products differing by few mass units and the discrimination of direct reaction processes. The ${}^{17}\mathrm{O}+{}^{58}\mathrm{Ni}$ collision was studied at five near-barrier energies employing a compact experimental setup consisting of four double-sided silicon strip detectors (DSSSDs). Different reaction processes, namely the elastic and inelastic scattering and the $1n$ stripping, were discriminated by means of a detailed analysis of the experimental energy spectra based on Monte Carlo simulations. The elastic scattering angular distributions were investigated within the framework of the optical model using Woods-Saxon and double-folding potentials. The total reaction cross sections were extracted and the reduced cross sections compared with those obtained for ${}^{17}\mathrm{F}$ ($S_p=0.600$ MeV), the mirror nucleus of ${}^{17}\mathrm{O}$ ($S_n=4.143$ MeV), and for the tightly bound ${}^{16}\mathrm{O}$ projectile. The ${}^{17}\mathrm{O}+{}^{58}\mathrm{Ni}$ total reaction cross sections were larger than those for ${}^{16}\mathrm{O}$ on the same target at the lowest energies studied, becoming identical, within errors, as the incident energy increased above the Coulomb barrier. This behavior was related to a strong contribution from the $1n$-stripping channel at the lowest energies.

Probable projectile-target combinations for the synthesis of the superheavy element ${}^{302}120$ have been studied taking the Coulomb and proximity potential as the interaction barrier. The probabilities of the compound nucleus formation $P_{\mathrm{CN}}$ for the projectile-target combinations found in the cold reaction valley of ${}^{302}120$ are estimated. At energies near and above the Coulomb barrier, we have calculated the capture, fusion, and evaporation residue cross sections for the reactions of all probable projectile-target combinations so as to predict the most promising projectile-target combinations for the synthesis of the superheavy element ${}^{302}120$ in heavy-ion fusion reactions. The calculated fusion and evaporation cross sections for the more asymmetric (“hotter”) projectile-target combination is found to be higher than the less asymmetric (“colder”) combination. It can be seen from the nature of the quasifission barrier height, mass asymmetry, the probability of compound nucleus formation, survival probability, and excitation energy, the systems ${}^{44}\mathrm{Ar}+{}^{258}\mathrm{No}, {}^{46}\mathrm{Ar}+{}^{256}\mathrm{No}, {}^{48}\mathrm{Ca}+{}^{254}\mathrm{Fm}, {}^{50}\mathrm{Ca}+{}^{252}\mathrm{Fm}, {}^{54}\mathrm{Ti}+{}^{248}\mathrm{Cf}$, and ${}^{58}\mathrm{Cr}+{}^{244}\mathrm{Cm}$ in deep region I of the cold reaction valley and the systems ${}^{62}\mathrm{Fe}+{}^{240}\mathrm{Pu}, {}^{64}\mathrm{Fe}+{}^{238}\mathrm{Pu}, {}^{68}\mathrm{Ni}+{}^{234}\mathrm{U}, {}^{70}\mathrm{Ni}+{}^{232}\mathrm{U}, {}^{72}\mathrm{Ni}+{}^{230}\mathrm{U}$, and ${}^{74}\mathrm{Zn}+{}^{228}\mathrm{Th}$ in the other cold valleys are identified as the better projectile-target combinations for the synthesis of ${}^{302}120$. Our predictions on the synthesis of ${}^{302}120$ superheavy nuclei using the combinations ${}^{54}\mathrm{Cr}+{}^{248}\mathrm{Cm}, {}^{58}\mathrm{Fe}+{}^{244}\mathrm{Pu}, {}^{64}\mathrm{Ni}+{}^{238}\mathrm{U}$, and ${}^{50}\mathrm{Ti}+{}^{249}\mathrm{Cf}$ are compared with available experimental data and other theoretical predictions.

We show that measurements of the rapidity dependence of transverse momentum correlations can be used to determine the characteristic time ${\tau }_{\pi }$ that dictates the rate of isotropization of the stress energy tensor, as well as the shear viscosity $\nu =\eta /sT$. We formulate methods for computing these correlations using second-order dissipative hydrodynamics with noise. Current data are consistent with ${\tau }_{\pi }/\nu \sim 10$, but targeted measurements can improve this precision.

The excitation function and momentum distribution of ${\eta }^{\prime }$ mesons have been measured in photoproduction off ${}^{93}\mathrm{Nb}$ in the energy range of 1.2–2.9 GeV. The experiment has been performed with the combined Crystal Barrel and MiniTAPS detector system, using tagged photon beams from the ELSA electron accelerator. Information on the sign and magnitude of the real part of the ${\eta }^{\prime }$-Nb potential has been extracted from a comparison of the data with model calculations. An attractive potential of $-(41\pm 10(\mathrm{stat})\pm 15(\mathrm{syst}\left)\right)$ MeV depth at normal nuclear matter density is deduced within model uncertainties. This value is consistent with the potential depth of $-(37\pm 10(\mathrm{stat})\pm 10(\mathrm{syst}\left)\right)$ MeV obtained in an earlier measurement for a light nucleus (carbon). This relatively shallow ${\eta }^{\prime }$-nucleus potential will make the search for ${\eta }^{\prime }$-nucleus bound states more difficult.

We formulate the next-to-leading-order nuclear effective field theory without pions in the two-nucleon sector on a spatial lattice and investigate nonperturbative renormalization group flows in the strong-coupling region by diagonalizing the Hamiltonian numerically. The cutoff (proportional to the inverse of the lattice constant) dependence of the coupling constants is obtained by changing the lattice constant with the binding energy and the asymptotic normalization constant for the ground state being fixed. We argue that the critical line can be obtained by looking at the finite-size dependence of the ground-state energy. We determine the relevant operator and locate the nontrivial fixed point, as well as the physical flow line corresponding to the deuteron in the two-dimensional plane of dimensionless coupling constants. It turns out that the location of the nontrivial fixed point is very close to the one obtained by the corresponding analytic calculation, but the relevant operator is quite different.

The blocking effect caused by the odd particle on the pairing properties of systems with an odd number of fermions at finite temperature interacting via the monopole pairing force is studied within several approximations. The results are compared with the predictions obtained by using the exact solutions of the pairing Hamiltonian. The comparison favors the approximation with the odd particle occupying the top level, which is the closest to the Fermi surface and whose occupation number decreases with increasing temperature.

A fully antisymmetrized random phase approximation calculation employing the continued fraction technique is performed to study nuclear matter response functions with the finite-range Gogny force. The most commonly used parameter sets of this force, as well as some recent generalizations that include the tensor terms, are considered and the corresponding response functions are shown. The calculations are performed at first and second order in the continued fraction expansion and the explicit expressions for the second-order tensor contributions are given. Comparisons between first- and second-order continued fraction expansion results are provided. The differences between the responses obtained at the two orders turn out to be more pronounced for the forces including tensor terms than for the standard Gogny ones. In the vector channels the responses calculated with Gogny forces including tensor terms are characterized by a large heterogeneity, reflecting the different choices for the tensor part of the interaction. For the sake of comparison the response functions obtained considering a $G$-matrix-based nuclear interaction are also shown. As a first application of the present calculation, the possible existence of spurious finite-size instabilities of the Gogny forces with or without tensor terms has been investigated. The positive conclusion is that all the Gogny forces but the GT2 one are free of spurious finite-size instabilities. In perspective, the tool developed in the present paper can be inserted in the fitting procedure to construct new Gogny-type forces.

The M3Y-type semirealistic interaction is applied to deformed nuclei for the first time. Constrained Hartree-Fock calculations assuming axial symmetry are implemented for the $N=20$ isotones ${}^{30}\mathrm{Ne}$, ${}^{32}\mathrm{Mg}$, ${}^{34}\mathrm{Si}$ and the $N=28$ isotones ${}^{40}\mathrm{Mg}$, ${}^{42}\mathrm{Si}$, ${}^{44}\mathrm{S}$ with the M3Y-P6 interaction. The results match the experimental data well. Effects of the realistic tensor force on the nuclear quadrupole deformation are investigated in relation to the loss of the $N=20$ and 28 magic numbers. The tensor force is confirmed to favor the deformation for the $N=28$ nuclei owing to the closure of the $jj$ shell (i.e., $n0f_{7/2}$), while favoring the sphericity for the $N=20$ nuclei owing to the $\ell s$ closure of $N=20$.

Background: Two new $J^{\pi }=0^{+}$ states are recently observed a few MeV above the Hoyle state (the second $0^{+}$ state in ${}^{12}\mathrm{C}$). Their characteristics are only briefly discussed in theory and are still mysterious.

Purpose: I give for the first time a comprehensive understanding of the structures of the $0^{+}$ states by analyzing their wave functions and discuss relationship with the Hoyle state, similarities, and differences between the states.

Method: I extend a microscopic $\alpha$-cluster model called the Tohsaki-Horiuchi-Schuck-Röpke (THSR) wave function so as to incorporate the $2\alpha +\alpha$ asymmetric configuration explicitly. The so-called $r^2$-constraint method to effectively eliminate spurious continuum components is also used.

Results: The $0_3{}^{+}$ state is shown to have a very large squared overlap with a single configuration of the extended THSR wave function in an orthogonal space to the Hoyle state as well as to the ground state. The $0_4{}^{+}$ state has a maximal squared overlap with a single extended THSR wave function with an extremely prolately deformed shape.

Conclusions: The $0_3{}^{+}$ state appears as a family of the Hoyle state to have a higher nodal structure in the internal motions of the $3\alpha$ clusters, due to the orthogonalization to the Hoyle state. The $0_4{}^{+}$ state dominantly has a linear-chain structure, where the $3\alpha$ clusters move freely in a nonlocalized way, like a one-dimensional gas of the $3\alpha$ clusters.

Breakup cross sections are determined for the Borromean nucleus ${}^{22}\mathrm{C}$ by using a four-body eikonal model, including Coulomb corrections. Bound and continuum states are constructed within a ${}^{20}\mathrm{C}+n+n$ three-body model in hyperspherical coordinates. We compute continuum states with the correct asymptotic behavior through the $R$-matrix method. For the $n+n$ potential, we use the Minnesota interaction. As there is no precise experimental information on ${}^{21}\mathrm{C}$, we define different parameter sets for the ${}^{20}\mathrm{C}+n$ potentials. These parameter sets provide different scattering lengths, and resonance energies of an expected $3/2^{+}$ excited state. Then we analyze the ${}^{22}\mathrm{C}$ ground-state energy and rms radius, as well as $E1$ strength distributions and breakup cross sections. The $E1$ strength distribution presents an enhancement at low energies. Its amplitude is associated with the low binding energy, rather than with a three-body resonance. We show that the shape of the cross section at low energies is sensitive to the ground-state properties. In addition, we suggest the existence of a low-energy $2^{+}$ resonance, which should be observable in breakup experiments.

Background: Recent high-precision measurements of $\alpha$-induced reaction data below the Coulomb barrier have pointed out questions about the $\alpha$-particle optical-model potential (OMP) which are still unanswered within various mass ranges.

Purpose: The applicability of previous optical potential and eventual uncertainties and/or systematic errors of the OMP assessment at low energies can be further considered on this basis.

Method: Nuclear model parameters based on the analysis of recent independent data, particularly $\gamma$-ray strength functions, have been involved within statistical model calculation of the $(\alpha ,x)$ reaction cross sections.

Results: The above-mentioned potential provides a consistent description of the recent $\alpha$-induced reaction data with no empirical rescaling factors of the $\gamma$ and/or nucleon widths.

Conclusions: A suitable assessment of $\alpha$-particle optical potential below the Coulomb barrier should involve the statistical-model parameters beyond this potential on the basis of a former analysis of independent data.

The electromagnetic (EM) field pattern created by spectators in relativistic heavy-ion collisions plants a seed of positive (negative) magnetic helicity in the hemisphere above (below) the reaction plane. Owing to the chiral anomaly, the magnetic helicity interacts with the fermionic helicity of the collision system and causes photons emitted in upper and lower hemispheres to have different preferences in the circular polarization. Similar helicity separation for massive particles, owing to the global vorticity, is also possible. In this paper, we lay out a procedure to measure the variation of the circular polarization with respect to the reaction plane in relativistic heavy-ion collisions for massless photons, as well as similar polarization patterns for vector mesons decaying into two daughters. We propose to study the yield differentially and compare the yield between upper and lower hemispheres to identify and quantify such effects.

The quadrupole transition rate for the $4_1^{+}\to 2_1^{+}$ transition of ${}^{58}\mathrm{Ni}$ was determined from an application of the recoil distance method with the Gamma-Ray Energy Tracking In-beam Nuclear Array (GRETINA). The present result of the $B(E2;4_1^{+}\to 2_1^{+})$ was found to be ${50}_{-6}^{+11}{e}^2{\mathrm{fm}}^4$, which is about three times smaller than the literature value, indicating substantially less collectivity than previously believed. Shell model calculations performed with the GXPF1A effective interaction agree with the present data and the validity of the standard effective charges in understanding collectivity in the nickel isotopes is discussed.

The unbound nucleus ${}^7\mathrm{He}$ has been investigated via the reaction of a 16.8 MeV ${}^6\mathrm{He}$ radioactive ion beam on a ${}^9\mathrm{Be}$ target. The measurement of the outgoing ${}^8\mathrm{Be}$ through its well characterized two-$\alpha$ decay permitted the energy of the ${}^6\mathrm{He}+n$ system to be reconstructed. Through comparison with a complete Monte Carlo simulation incorporating $R$-matrix lineshapes, the ${}^7\mathrm{He}$ ground state was determined to lie 0.380(28) MeV above the neutron decay with a width of $\mathrm{\Gamma }=0.179\left(21\right)$ MeV. A neutron spectroscopic factor $\text{SF}=0.608\left(18\right)$ was extracted in agreement with the most recent calculations. Significant evidence was found for a broad resonance lying at 2.6(2) MeV above threshold with a ${\mathrm{\Gamma }}_{\text{FWHM}}=2.3\left(3\right)$ MeV. These parameters are fully consistent with the properties of $1/2^{-}$ state reported by Wuosmaa et al. [Phys. Rev. C 72, 061301(R) (2005)]. Limits were also put on the presence of narrow resonances seen in earlier experiments.

In this article, we introduce a freeze-out scheme for the dynamical models near the QCD critical point through coupling the decoupled classical particles with the order parameter field. With a modified distribution function that satisfies specific static fluctuations, we calculate the correlated fluctuations of net protons on the hydrodynamic freeze-out surface. A comparison with recent STAR data shows that our model calculations could roughly reproduce energy-dependent cumulant $C_4$ and $\kappa {\sigma }^2$ of net protons through tuning the related parameters. However, the calculated $C_2$ and $C_3$ with both Poisson and binomial baselines are always above the experimental data due to the positive contributions from the static critical fluctuations. To qualitatively and quantitatively describe all the related experimental data, the dynamical critical fluctuations and more realistic noncritical fluctuation baselines should be investigated in the near future.

Background: Deformation energy surfaces map how the total binding energy of a nuclear system depends on the geometrical properties of intrinsic configurations, thereby providing a powerful tool to interpret nuclear spectroscopy and large-amplitude collective-motion phenomena such as fission. The global behavior of the deformation energy is known to be directly connected to the surface properties of the effective interaction used for its calculation.

Purpose: The precise control of surface properties during the parameter adjustment of an effective interaction is key to obtain a reliable and predictive description of nuclear properties. The most relevant indicator is the surface-energy coefficient $a_{\mathrm{surf}}$. There are several possibilities for its definition and estimation, which are not fully equivalent and require a computational effort that can differ by orders of magnitude. The purpose of this study is threefold: first, to identify a scheme for the determination of $a_{\mathrm{surf}}$ that offers the best compromise between robustness, precision, and numerical efficiency; second, to analyze the correlation between values for $a_{\mathrm{surf}}$ and the characteristic energies of the fission barrier of ${}^{240}\text{Pu}$; and third, to lay out an efficient and robust procedure for how the deformation properties of the Skyrme energy density functional (EDF) can be constrained during the parameter fit.

Methods: There are several frequently used possibilities to define and calculate the surface energy coefficient $a_{\mathrm{surf}}$ of effective interactions built for the purpose of self-consistent mean-field calculations. The most direct access is provided by the model system of semi-infinite nuclear matter, but $a_{\mathrm{surf}}$ can also be extracted from the systematics of binding energies of finite nuclei. Calculations can be carried out either self-consistently [Hartree-Fock (HF)], which incorporates quantal shell effects, or in one of the semiclassical extended Thomas-Fermi (ETF) or modified Thomas-Fermi (MTF) approximations. The latter is of particular interest because it provides $a_{\mathrm{surf}}$ as a numerical integral without the need to solve self-consistent equations. Results for semi-infinite nuclear matter obtained with the HF, ETF, and MTF methods will be compared with one another and with $a_{\mathrm{surf}}$, as deduced from ETF calculations of very heavy fictitious nuclei.

Results: The surface energy coefficient of 76 parametrizations of the Skyrme EDF have been calculated. Values obtained with the HF, ETF, and MTF methods are not identical, but differ by fairly constant systematic offsets. By contrast, extracting $a_{\mathrm{surf}}$ from the binding energy of semi-infinite matter or of very large nuclei within the same method gives the same result within the numerical uncertainties.

Conclusions: Despite having some drawbacks compared to the other methods studied here, the MTF approach provides sufficiently precise values for $a_{\mathrm{surf}}$ such that it can be used as a very robust constraint on surface properties during a parameter fit at negligible additional cost. While the excitation energy of superdeformed states and the height of fission barriers is obviously strongly correlated to $a_{\mathrm{surf}}$, the presence of shell effects prevents a one-to-one correspondence between them. As in addition the value of $a_{\mathrm{surf}}$ providing realistic fission barriers depends on the choices made for corrections for spurious motion, its “best value” (within a given scheme to calculate it) depends on the fit protocol. Through the construction of a series of eight parametrizations SLy5s1–SLy5s8 of the standard Skyrme EDF with systematically varied $a_{\mathrm{surf}}$ value, it is shown how to arrive at a fit with realistic deformation properties.

In this paper we study the nucleon-pair approximation for $T=0$ states of ${}^{96}\mathrm{Cd}$ in the $1p_{1/2}1p_{3/2}0f_{5/2}0g_{9/2}$ shell with the JUN45 interaction. The lowest seniority scheme and the isoscalar spin-one pair approximation are not enough to describe the states. The isoscalar spin-aligned pair approximation is reasonably good for the yrast $2^{+}, 4^{+}, 6^{+}, {12}^{+}, {14}^{+}$, and ${16}^{+}$ states as pointed out previously. Not only the yrast positive-parity states but also nonyrast states and negative-parity states are well described by both the isovector pair approximation and the isoscalar pair approximation. We calculate overlaps between nucleon-pair basis states and shell-model wave functions. The largest overlaps and the corresponding nucleon-pair basis states are presented. We find that isovector spin-zero pairs, isovector spin-two pairs, and isoscalar spin-aligned pairs are the dominant building blocks in these states.