Recent work has sought to extract the asymmetry energy at very low density from observables in heavy-ion collisions. The logic employed starts from the assumption that the fragment yields are determined by a minimization of the Helmholtz free energy. As volume is in reality unconstrained, nor can a single freeze-out volume be expected, the physical relevance of the Helmholtz free energy must be questioned. If, for example, the identical logic were used, but the Gibbs free energy was the more relevant quantity to minimize, it would be the asymmetry enthalpy that would be extracted. The purpose of this report is to provide one measure of the difference between the asymmetry energy and enthalpy.

We present the finite amplitude method (FAM), originally proposed in Ref. [17], for superfluid systems. A Hartree-Fock-Bogoliubov code may be transformed into a code of the quasiparticle-random-phase approximation (QRPA) with simple modifications. This technique has advantages over the conventional QRPA calculations, such as coding feasibility and computational cost. We perform the fully self-consistent linear-response calculation for the spherical neutron-rich nucleus ${}^{174}$Sn, modifying the hfbrad code, to demonstrate the accuracy, feasibility, and usefulness of the FAM.

A schematic microscopic method is developed to calculate the $M1$ transition probabilities between the mixed-symmetry and the fully symmetric states in $\gamma$-soft nuclei. The method is based on the random-phase approximation–interacting boson model (RPA-IBM) boson mapping of the most collective isoscalar boson. All other boson modes with higher excitation energies, including the mixed-symmetry boson, are described in the framework of RPA. As an example the $M1$ transition probabilities are calculated for the ${}^{124-134}$Xe isotopes and compared with the experimental data. The results agree well with the data for the ratio $B(M1;1_{ms}^{+}\to 2_2^{+})$/$B(M1;1_{ms}^{+}\to 0_1^{+})$. However, the calculated ratio $B(M1;2_{ms}^{+}\to 2_1^{+})$/$B(M1;1_{ms}^{+}\to 0_1^{+})$ shows a significantly weaker dependence on the mass number than the experimental data.

Based on an isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model, effects of high-density behavior of nuclear symmetry energy in the proton-rich reaction ${}^{22}\mathrm{Si}+{}^{22}\mathrm{Si}$ at a beam energy of 400 MeV/nucleon are studied. It is found that the symmetry energy affects ${\pi }^{+}$ production more than ${\pi }^{-}$. More interestingly, compared to neutron-rich reactions, for ${\pi }^{-}/{\pi }^{+}$ and dense matter’s $N/Z$ ratios, effects of symmetry energy in the proton-rich reaction show contrary behaviors. The practical experiment by using the proton-rich reaction ${}^{22}\mathrm{Si}+{}^{40}\mathrm{Ca}$ to study nuclear symmetry energy is also provided.

The $\alpha +{}^8\text{He}$ low-energy reactions and the exotic structures of ${}^{12}\text{Be}=\alpha +\alpha +4N$ are studied by the application of the generalized two-center cluster model. In the two-neutron transfer reactions, $\alpha +{}^8{\text{He}}_{\text{g.s.}}\to {}^6{\text{He}}_{\text{g.s.}}+{}^6{\text{He}}_{\text{g.s.}}$, resonant structures with a sharp width of $\Gamma <1$ MeV appear in the central collision ($J^{\pi }=0^{+}$). The reaction mechanism is analyzed, and we confirmed that the transfer coupling plays essential roles in the resonance formation with sharp width. Angular distributions for the scattered ${}^6$He are analyzed to extract resonant structures for individual partial waves. We found that, for the low-spin resonances, the angular selection around ${90}^{\circ }$ in the center-of-mass system, which is usually employed in the high-spin resonances of light-ion systems, is not necessarily appropriate to separate the resonance contribution with a definite spin. The validity of the selection angle around 90${}^{\circ }$ is discussed in the higher partial waves.

We analyze dilepton emission from hot and dense matter using a hybrid approach based on the ultrarelativistic quantum molecular dynamics (UrQMD) transport model with an intermediate hydrodynamic stage for the description of heavy-ion collisions at relativistic energies. During the hydrodynamic stage, the production of lepton pairs is described by radiation rates for a strongly interacting medium in thermal equilibrium. In the low-mass region, hadronic thermal emission is evaluated by assuming vector meson dominance including in-medium modifications of the $\rho$ meson spectral function through scattering from nucleons and pions in the heat bath. In the intermediate-mass region, the hadronic rate is essentially determined by multipion annihilation processes. Emission from quark-antiquark annihilation in the quark gluon plasma (QGP) is taken into account as well. When the system is sufficiently dilute, the hydrodynamic description breaks down and a transition to a final cascade stage is performed. In this stage dimuon emission is evaluated as commonly done in transport models. By focusing on the enhancement with respect to the contribution from long-lived hadron decays after freezeout observed at the SPS in the low-mass region of the dilepton spectra, the relative importance of the different thermal contributions and of the two dynamical stages is investigated. We find that three separated regions can be identified in the invariant mass spectra. Whereas the very low and the intermediate-mass regions mostly receive contribution from the thermal dilepton emission, the region around the vector meson peak is dominated by the cascade emission. Above the $\rho$-peak region the spectrum is driven by QGP radiation. Analysis of the dimuon transverse mass spectra reveals that the thermal hadronic emission shows an evident mass ordering not present in the emission from the QGP. A comparison of our calculation to recent acceptance-corrected NA60 data on invariant as well as transverse mass spectra is performed.

A central issue in hadron spectroscopy is to deduce—and interpret—resonance parameters, namely, pole positions and residues, from experimental data, for those are the quantities to be compared to lattice QCD or model calculations. However, not every structure in the observables derives from a resonance pole: the origin might as well be branch points, either located on the real axis (when a new channel composed of stable particles opens) or in the complex plane (when at least one of the intermediate particles is unstable). In this paper we demonstrate first the existence of such branch points in the complex plane and then show on the example of the $\pi N$ $P_{11}$ partial wave that it is not possible to distinguish the structures induced by the latter from a true pole signal based on elastic data alone.

Compound states manifest themselves as bound states, resonances, or primitives, and their character is determined by their interaction with the continuum. If the interaction experiences a perturbation, a compound state can change its manifestation. Phase analysis of nucleon-nucleon scattering indicates the existence of primitives in the ${}^3{S}_1$, ${}^1{S}_0$, and ${}^3{P}_0$ channels. Electromagnetic interaction can shift primitives from the unitary cut, turning them into narrow resonances. We evaluate this effect on the ${}^1{S}_0$ proton-proton scattering channel in the framework of the Simonov-Dyson model. We show that electromagnetic interaction turns a primitve with a mass of $2000$ MeV into a dibaryon resonance of approximately the same mass and a width of 260 keV. Narrow resonances of a similar nature may occur in other nucleon-nucleon channels. Experimental confirmation of the existence of narrow resonances would have important implications for the theory of nucleon-nucleon interaction.

We have formulated and calculated the differential cross section for the formation of the simplest double-$\overline{K}$ nuclear cluster system, $K^{-}{K}^{-}pp$, in the reaction process $p+p\to K^{+}+K^{+}+{\Lambda }^{*}+{\Lambda }^{*}\to K^{+}+K^{+}+K^{-}{K}^{-}pp$, where ${\Lambda }^{*}$ is a quasibound $K^{-}p$ state corresponding to the $\Lambda \left(1405\right)$ resonance. From a comprehensive study of the calculated effects of the binding and density of $K^{-}{K}^{-}pp$ on the cross section, we find that the bound-state peak of $K^{-}{K}^{-}pp$ dominates over the spectrum when and only when the system is dense. This is understood as meaning that the two ${\Lambda }^{*}$ doorway particles interact immediately within a short distance, assisted by a large momentum transfer ($\sim 1.8$ GeV/$c$) and a short collision length ($\sim 0.3$ fm), which helps to enlarge the ${\Lambda }^{*}-{\Lambda }^{*}$ sticking into a dense $K^{-}{K}^{-}pp$ system. This mechanism is similar to that for a single $\overline{K}$ cluster ($K^{-}pp$) formation, which has just been proven by a DISTO experiment. The $K^{-}{K}^{-}$ repulsion causes an energy shift to somewhat lower binding and a reduction in the peak cross section, but does not change the basic character of this reaction.

The neutral-current elastic scattering of neutrinos on carbon and ${\mathit{CH}}_2$ targets is computed using the relativistic distorted-wave impulse approximation with a relativistic optical potential. Results for exclusive and inclusive neutrino reactions on a ${}^{12}$C target are presented. We show that the nuclear effects on the shape of the four-momentum transferred squared distribution $d\sigma /d{Q}_{QE}^2$ in neutrino neutral-current and charged-current quasielastic scattering are similar. We also calculate the flux-averaged neutral-current elastic differential cross section $d\sigma /d{Q}_{QE}^2$ for neutrino scattering from ${\mathit{CH}}_2$, as well as the neutral-current to charged-current cross section ratio as functions of $Q_{QE}^2$. The axial mass $M_A$ is extracted from a fit of the $d\sigma /d{Q}_{QE}^2$ cross section measured in the MiniBooNE experiment. The extracted value of $M_A=1.28\pm 0.05$ GeV is consistent within errors with the MiniBooNE result. Additionally, for proton kinetic energies above the Cherenkov threshold, the strange-quark contribution to the neutral-current axial vector form factor at $Q_{QE}^2=0$, $\Delta s$, was extracted from a fit to MiniBooNE data for the $\nu p\to \nu p$ to $\nu N\to \nu N$ cross section ratio. This value is found to be $\Delta s=-0.11\pm 0.36$

The neutron capture cross sections of the Zr isotopes play an important role in nucleosynthesis studies. The $s$-process reaction flow between the Fe seed and the heavier isotopes passes through the neutron magic nucleus ${}^{90}\mathrm{Zr}$ and through ${}^{91,92,93,94}\mathrm{Zr}$, but only part of the flow extends to ${}^{96}\mathrm{Zr}$ because of the branching point at ${}^{95}\mathrm{Zr}$. Apart from their effect on the $s$-process flow, the comparably small isotopic ($n,\gamma$) cross sections make Zr also an interesting structural material for nuclear reactors. The ${}^{94}\mathrm{Zr}$ ($n,\gamma$) cross section has been measured with high resolution at the spallation neutron source n_TOF at CERN and resonance parameters are reported up to 60 keV neutron energy.

Formulas for the most positive and most negative values of the expectation of the spin operator are given and compared with single-particle values. The Nilsson model is used to evaluate these expectations and a scenario is discussed where the value is greater than one.

Pentagon and triangle shapes in ${}^{28}\mathrm{Si}$ and ${}^{12}\mathrm{C}$ are discussed in relation to nuclear density waves. In the antisymmetrized molecular dynamics calculations, the $K^{\pi }=5^{-}$ band in ${}^{28}\mathrm{Si}$ and the $K^{\pi }=3^{-}$ band in ${}^{12}\mathrm{C}$ are described by the pentagon and triangle shapes, respectively. These negative-parity bands can be interpreted as the parity partners of the $K^{\pi }=0^{+}$ ground bands and they are constructed from the parity-asymmetric-intrinsic states. The pentagon and the triangle shapes originate in $7\alpha$- and $3\alpha$-cluster structures, respectively. In a mean-field picture, they are described also by the static one-dimensional density waves at the edge of the oblate states. In analyses with ideal $\alpha$-cluster models using Brink-Bloch cluster wave functions and that with a simplified model, we show that the static edge density waves for the pentagon and triangle shapes can be understood by spontaneous breaking of axial symmetry, i.e., the instability of the oblate states with respect to the edge density waves. The density wave is enhanced in the $Z=N$ nuclei due to the proton-neutron coherent density waves, while it is suppressed in $Z\ne N$ nuclei.

Excited states of the stable nucleus ${}^{195}$Pt have been studied using an in-beam $\gamma$-ray spectroscopic technique following the incomplete fusion of ${}^7$Li on an ${}^{192}$Os target at 44 MeV. A level scheme built on the $I^{\pi }=13/2^{+}$ isomer has been established up to $I^{\pi }=33/2^{-}$ at an excitation energy of about 2.6 MeV. Spin and parity values of these states have been assigned from an analysis of anisotropy ratios of $\gamma$ rays and by analogy with the neighboring nuclei. A comparison of the observed structures with the yrast states in the neighboring even-even ${}^{196}$Pt core indicates that the identified levels may be regarded as arising from the weak coupling of a $\nu \mathrm{i}$${}_{13/2}$ neutron hole to the core states.

A computer code is presented for solving the equations of the Hartree-Fock-Bogoliubov (HFB) theory by the gradient method, motivated by the need for efficient and robust codes to calculate the configurations required by extensions of the HFB theory, such as the generator coordinate method. The code is organized with a separation between the parts that are specific to the details of the Hamiltonian and the parts that are generic to the gradient method. This permits total flexibility in choosing the symmetries to be imposed on the HFB solutions. The code solves for both even and odd particle-number ground states, with the choice determined by the input data stream. Application is made to the nuclei in the $\mathit{sd}$ shell using the universal $\mathit{sd}$-shell interaction B (USDB) shell-model Hamiltonian.

A high-energy-resolution ${}^9\mathrm{Be}$(${}^3\mathrm{He}$,$t$)${}^9\mathrm{B}$ charge-exchange reaction was performed around a scattering angle of $0^{°}$ and at an intermediate incident energy of 140 MeV/nucleon for the study of precise Gamow-Teller (GT) transition strengths. The energy resolution of 30 keV allowed a precise deconvolution of the spectrum and the determination of angular distributions of cross sections, excitation energies, and decay widths. The GT strength of 10 states has been determined for the first time using the GT strength of the analogous $\beta$ decays of ${}^9\mathrm{Li}$ and ${}^9\mathrm{C}$ as standards. The large difference between the GT strengths going to the low-lying $T=1/2$ and the highly excited $T=3/2$ states is interpreted as a result of their different spatial structures. The obtained GT strength distribution is compared to the results of a ($p$,$n$) experiment with lower resolution performed in the 1980s. In particular, the width of the 16.8 MeV, $J^{\pi }=(5/2^{+}$) state has been determined for the first time.

The restoration of particle number within energy density functional theory is analyzed. It is shown that the standard method based on configuration mixing leads to a functional of both the projected and nonprojected densities. As an alternative that might be advantageous for mass models, nuclear dynamics, and thermodynamics, we propose to formulate the functional in terms directly of the one-body and two-body density matrices of the state with good particle number. Our approach does not contain the pathologies recently observed when restoring the particle number in an energy density functional framework based on transition density matrices and can eventually be applied with functionals having arbitrary density dependencies.

An exact treatment of the Coulomb interaction is performed within the Skyrme-Hartree-Fock/Bardeen-Cooper-Schrieffer approach for even-even nuclei ranging from light to superheavy nuclei. A test of the usual Slater approximation for the exchange part is carried out. The error made on the exchange term of the Coulomb interaction when using this approximation follows two schematic patterns. Beyond a decreasing behavior when increasing the mass number $A$, a more important structural effect has been found. The relative error ranges roughly from 0 to 8% being maximal for light closed proton (sub-)shell nuclei and minimal for open proton (sub-)shell nuclei.