Event-by-event $\gamma$-charge ($\gamma \text{-ch}$) correlation is studied for systems going through QCD chiral phase transition. In this paper, various methods for measuring $\gamma \text{-ch}$ correlation in heavy ion collisions are discussed. Dynamical fluctuation due to the formation of domains of disoriented chiral condensate (DCC) that can affect $\gamma \text{-ch}$ correlation is addressed. We have studied known detector and statistical effects involved in these measurements and suggest suitable robust observables $\Delta {\nu }_{\mathrm{dyn}}$ and $r_{m,1}$ sensitive to small $\gamma \text{-ch}$ correlation signals. These observables are constructed based on moments of multiplicity distributions of photons and charged particles. Estimations of measurable signals from various available models such as an ideal Boltzmann gas of pions, Monte Carlo models based on transport, and minijets are discussed. Collision centrality dependence of the observables is estimated from the central limit theorem and is found to be consistent with the model predictions. Observables are found to be highly sensitive to the fraction of DCC events and to have nonlinear dependence on the fraction of pions carrying DCC signals. The variation of $r_{m,1}$ with order $m$ of its moments is sensitive to the nature and strength of the $\gamma \text{-ch}$ correlation.

Background: Models to calculate small isospin-symmetry-breaking effects in superallowed Fermi decays have been placed under scrutiny in recent years. A stringent test of these models is to measure transitions for which the correction is predicted to be large. The decay of ${}^{32}$Cl decay provides such a test case.

Purpose: The purpose of this paper is to improve the $\gamma$ yields following the $\beta$ decay of ${}^{32}$Cl and to determine the $ft$ values of the the $\beta$ branches, particularly the one to the isobaric-analog state in ${}^{32}$S.

Method: Reaction-produced and recoil-spectrometer-separated ${}^{32}$Cl is collected in a tape and transported to a counting location where $\beta -\gamma$ coincidences are measured with a precisely calibrated high-purity germanium detector.

Results: The precision on the $\gamma$ yields for most of the known $\beta$ branches has been improved by about an order of magnitude, and many new transitions have been observed. We have determined ${}^{32}$Cl-decay transition strengths extending up to $E_x\sim 11$ MeV. The $ft$ value for the decay to the isobaric-analog state in ${}^{32}$S has been measured. A comparison to a shell-model calculation shows good agreement.

Conclusions: We have experimentally determined the isospin-symmetry-breaking correction to the superallowed transition of this decay to be ${({\delta }_C-{\delta }_{\mathrm{NS}})}_{\exp }=5.4\left(9\right)\%$, significantly larger than for any other known superallowed Fermi transition. This correction agrees with a shell-model calculation, which yields ${\delta }_C-{\delta }_{\mathrm{NS}}=4.8\left(5\right)\%$. Our results also provide a way to improve the measured $ft$ values for the $\beta$ decay of ${}^{32}$Ar.

Using a simple model of a neutron star with a perfectly rigid crust constructed with a set of crust and core equations of state that span the range of nuclear experimental uncertainty in the symmetry energy, we calculate the instability window for the onset of the Chandrasekhar-Friedmann-Schutz instability in $r$-mode oscillations for canonical neutron stars ($1.4M_{\odot }$) and massive neutron stars ($2.0M_{\odot }$). In these models the crust-core transition density, and thus crustal thickness, is calculated consistently with the core equation of state (EOS). The EOSs are calculated using a simple model for the energy density of nuclear matter and probe the dependence on the symmetry energy by varying the slope of the symmetry energy at saturation density $L$ from 25 MeV (soft symmetry energy and EOS) to 115 MeV (stiff symmetry energy and EOS) while keeping the EOS of symmetric nuclear matter fixed. For the canonical neutron star, the lower bound of the $r$-mode instability window is reduced in frequency by $\approx 150$ Hz from the softest to the stiffest symmetry energy used, independent of mass and temperature. The instability window also drops by $\approx 100$ Hz, independent of EOS when the mass is raised from $1.4M_{\odot }$ to $2.0M_{\odot }$. Where temperature estimates are available, the observed neutron stars in low-mass x-ray binaries (LMXBs) have frequencies below the instability window for the $1.4M_{\odot }$ models, while some LMXBs fall within the instability window for $2.0M_{\odot }$ stars if the symmetry energy is relatively stiff, indicating that a softer symmetry energy is more consistent with observations within this model. Thus we conclude that smaller values of $L$ help stabilize neutron stars against runaway $r$-mode oscillations. The critical temperature, below which no star can reach the instability window without exceeding its Kepler frequency, varies by nearly an order of magnitude from soft to stiff symmetry energies. When the crust thickness and core EOS are treated consistently, a thicker crust corresponds to a lower critical temperature, the opposite result to previous studies in which the transition density was independent of the core EOS.

Fission fragments from neutron-induced fission of ${}^{235}$U produced at the high-flux reactor of the Institut Laue-Langevin, Grenoble, were separated with the Lohengrin separator to provide a beam of neutron-rich ${}^{85}$As nuclei. The ${\beta }^{-}$ decay of ${}^{85}$As to ${}^{85}$Se was studied using $\gamma$-$\gamma$ and $\beta$-$\gamma$ coincidence techniques. ${}^{85}$Se was also studied using the prompt-$\gamma$ coincidence data from spontaneous fission of ${}^{248}$Cm and ${}^{252}$Cf measured with the Eurogam2 and Gammasphere Ge arrays, respectively. The combination of $\beta$ decay and prompt-$\gamma$ data enabled the determination of spins and parities of low-energy excited states in ${}^{85}$Se. There are new arguments supporting the $5/2^{-}$ assignment for the ground state of ${}^{85}$As.

The sensitivity of the calculated matter radius to the binding energy is exploited to estimate the $2n$ binding energy of ${}^{22}$C, using a recent experimental value of $R_m=5.4\left(9\right)\mathrm{fm}$. The result is $B_{2n}<220\mathrm{keV}$, significantly smaller than another recent estimate.

Within the nonlinear relativistic mean field model, we derive the analytical expression of the nuclear matter fourth-order symmetry energy $E_{\mathrm{sym},4}\left(\rho \right)$. Based on two accurately calibrated interactions FSUGold and IU-FSU, our results show that the value of $E_{\mathrm{sym},4}\left(\rho \right)$ at normal nuclear matter density ${\rho }_0$ is generally less than 1 MeV, confirming the empirical parabolic approximation to the equation of state for asymmetric nuclear matter at ${\rho }_0$. However, we find that the $E_{\mathrm{sym},4}\left(\rho \right)$ may become non-negligible at high densities. Furthermore, the analytical form of the $E_{\mathrm{sym},4}\left(\rho \right)$ provides the possibility to study the higher-order effects on the isobaric incompressibility of asymmetric nuclear matter, that is, $K_{\mathrm{sat}}\left(\delta \right)=K_0+K_{\mathrm{sat},2}{\delta }^2+K_{\mathrm{sat},4}{\delta }^4+\mathcal{O}\left({\delta }^6\right)$, where $\delta =({\rho }_n-{\rho }_p)/\rho$ is the isospin asymmetry, and we find that the value of $K_{\mathrm{sat},4}$ is generally small compared with that of the $K_{\mathrm{sat},2}$. In addition, we study the effects of the $E_{\mathrm{sym},4}\left(\rho \right)$ on the proton fraction $x_p$ and the core-crust transition density ${\rho }_t$ and pressure $P_t$ in neutron stars. Interestingly, we find that, compared with the results from the empirical parabolic approximation, including the $E_{\mathrm{sym},4}\left(\rho \right)$ contribution can significantly enhance the $x_p$ at high densities and strongly reduce the ${\rho }_t$ and $P_t$ in neutron stars, demonstrating that the widely used empirical parabolic approximation may cause large errors in determining the $x_p$ at high densities as well as the ${\rho }_t$ and $P_t$ in neutron stars within the nonlinear relativistic mean field model, consistent with previous nonrelativistic calculations.

Cluster states in ${}^9$Li are investigated with calculations of a ${}^6$He-$t$ cluster model. Results suggest ${}^6$He-$t$ cluster states near the ${}^6$He-$t$ threshold energy. These states construct a $K^{\pi }=1/2^{-}$ band and their neutron configuration is similar to that of the $K^{\pi }=0_2^{+}$ band in ${}^{10}$Be.

A new Skyrme-like energy density suitable for studies of strongly elongated nuclei was determined in the framework of the Hartree-Fock-Bogoliubov theory using the recently developed model-based, derivative-free optimization algorithm pounders. A sensitivity analysis at the optimal solution has revealed the importance of states at large deformations in driving the parameterization of the functional. The good agreement with experimental data on masses and separation energies, achieved with the previous parameterization unedf0, is largely preserved. In addition, the new energy density unedf1 gives a much improved description of the fission barriers in ${}^{240}$Pu and neighboring nuclei.

In this paper we study the volume and surface symmetry energy coefficients ($c_{\mathrm{sym}}^{\left(V\right)}$ and $c_{\mathrm{sym}}^{\left(S\right)}$) by using the double differences of “experimental” symmetry energies. We assume $a_{\mathrm{sym}}=c_{\mathrm{sym}}^{\left(V\right)}-c_{\mathrm{sym}}^{\left(S\right)}/A^{1/3}$ and obtain $c_{\mathrm{sym}}^{\left(V\right)}=31.26\pm 0.32$ MeV and $c_{\mathrm{sym}}^{\left(S\right)}=52.15\pm 1.12$ MeV, or $c_{\mathrm{sym}}^{\left(V\right)}=32.10\pm 0.31$ MeV and $c_{\mathrm{sym}}^{\left(S\right)}=58.91\pm 1.08$ MeV, depending on the form of the Wigner energy. The uncertainties of these coefficients are smaller than those in the literature. The values of $c_{\mathrm{sym}}^{\left(V\right)}$ and ${\kappa }_{S/V}$ are unstable for different mass regions if one assumes $a_{\mathrm{sym}}=c_{\mathrm{sym}}^{\left(V\right)}/(1+{\kappa }_{S/V}/A^{1/3})$. We notice an odd-even staggering in the double differences of “experimental” symmetry energies under a few situations, and suggest that the pairing interaction might not be properly taken into account in the current mass formulas.

Evaporation residues resulting from fusion of ${}^{20}$O incident ions with ${}^{12}$C target nuclei have been measured for the first time. The cross-section associated with compound nuclei that de-excite via emission of charged particles is extracted. The resulting excitation function is compared with the predictions of a standard fusion model followed by statistical decay code. A significant underprediction of the measured cross-section by the fusion-evaporation model raises the question of whether the fusion cross-section is larger for the neutron-rich projectile or the statistical de-excitation is incorrectly predicted.

We propose a new variational Monte Carlo (VMC) method with an energy variance extrapolation for large-scale shell-model calculations. This variational Monte Carlo is a stochastic optimization method with a projected correlated condensed pair state as a trial wave function, and is formulated with the $M$-scheme representation of projection operators, the Pfaffian and the Markov-chain Monte Carlo. Using this method, we can stochastically calculate approximated yrast energies and electromagnetic transition strengths. Furthermore, by combining this VMC method with energy variance extrapolation, we can estimate exact shell-model energies.

The most intense $\gamma$-ray line observable from novae is likely to be from positron annihilation associated with the decay of ${}^{18}$F. The uncertainty in the destruction rate of this nucleus through the ${}^{18}$F($p$,$\alpha$)${}^{15}$O reaction presents a limit to interpretation of any future observed $\gamma$-ray flux. Direct measurements of the cross section of both this reaction and the ${}^{18}$F($p,p$)${}^{18}$F reaction have been performed between center of mass energies of 0.5 and 1.9 MeV. Simultaneous fits to both data sets with the $R$-matrix formalism reveal several resonances, with the inferred parameters of populated states in ${}^{19}$Ne in general agreement with previous measurements. Of particular interest, extra strength has been observed above $E_{\mathrm{c}.\mathrm{m}.}\sim$1.3 MeV in the ${}^{18}$F($p,p$)${}^{18}$F reaction and between 1.3–1.7 MeV in the ${}^{18}$F($p$,$\alpha$)${}^{15}$O reaction. This is well described by a broad 1/2${}^{+}$ state, consistent with both a recent theoretical prediction and an inelastic scattering measurement. The astrophysical implications of a broad subthreshold partner to this state are discussed.

We explore the influence of the in-medium nucleon-nucleon cross section, symmetry potential, and impact parameter on isospin sensitive observables in intermediate-energy heavy-ion collisions with the ImQMD05 code, a modified version of the quantum molecular dynamics model. At incident velocities above the Fermi velocity, we find that the density dependence of the symmetry potential plays a more important role on the double neutron-to-proton ratio DR$(n/p)$ and the isospin transport ratio $R_i$ than the in-medium nucleon-nucleon cross sections, provided that the latter are constrained to a fixed total $NN$ collision rate. We also explore both DR$(n/p)$ and $R_i$ as a function of the impact parameter. Since the copious production of intermediate mass fragments is a distinguishing feature of intermediate-energy heavy-ion collisions, we examine the isospin transport ratios constructed from different groups of fragments. We find that the values of the isospin transport ratios for projectile rapidity fragments with $Z⩾20$ are greater than those constructed from the entire projectile rapidity source. We believe experimental investigations of this phenomenon can be performed. These may provide significant tests of fragmentation time scales predicted by ImQMD calculations.

The properties of isobaric ratios, between nuclei produced in the same reaction, are investigated using the canonical and grand-canonical statistical ensembles. Although the grand-canonical formulas furnish a means to correlate the ratios with the liquid drop parameters, finite size effects make it difficult to obtain their actual values from fitting nuclear collision data.

The neutron-evaporation residue cross sections ${\sigma }_{2n}$, ${\sigma }_{3n}$, and ${\sigma }_{4n}$ in the hot fusion reaction ${}^{48}\mathrm{Ca}{+}^{249}\mathrm{Bk}{\to }^{297}{117}^{*}$ are calculated at the compound-nucleus (CN) excitation energies $E_{\text{CN}}^{*}=35.3$ and 39.3 MeV, by taking the superheavy-region proton magic $Z=126$ and neutron magic $N=184$, within the dynamical cluster-decay model. However, the above-stated production cross sections could not be fitted if the incoming nuclei and/or decay fragments were considered to be spherical. On the other hand, with inclusion of deformation effects up to quadrupole deformations ${\beta }_{2i}$ and with the “optimum” orientations ${\theta }_i^{\text{opt}}$, the ${\sigma }_{2n}$ and ${\sigma }_{3n}$ cross sections were fitted nicely, but ${\sigma }_{4n}$ were still underestimated by about 25$\%$, indicating the possibility of some other competing evaporation residue, like ${}^4$He decay, contributing to 4$n$-decay cross sections. Also, a possible contribution of a fusion-fission component is predicted which, together with ${}^4$He decay, needs experimental verification. Other important results are that (i) the angular momentum does not show any significant influence on the fragmentation path of the $Z=117$ nucleus formed in this reaction, and (ii) the barrier modification is found to be more important for the lower-angular-momentum states, and for the lightest neutron cluster, independent of the CN excitation energy.

Excited states in ${}^{195}$Au have been studied experimentally via the ${}^{192}$Os(${}^7$Li, 4$n$) reaction at a beam energy of 44 MeV. Based on the $\gamma$-$\gamma$-$t$ coincidence measurement, a level scheme consisting of 15 new transitions and 10 new levels is established for ${}^{195}$Au. The triaxial shape-polarizing effect of the high-$j$ $h_{11/2}$ proton hole was studied by total Routhian surface calculations. By comparing with the level structures in the odd-$A$ Au isotopes and the even-even core Hg nuclei, configurations are proposed to the rotational bands and three-quasiparticle states observed in ${}^{195}$Au.

The isospin character, the collective or single-particle nature, and the sensitivity to the slope of the nuclear symmetry energy of the low-energy isovector dipole response (known as pygmy dipole resonance) are nowadays under debate. In the present work we study, within the fully self-consistent nonrelativistic mean field (MF) approach based on Skyrme Hartree-Fock plus random phase approximation (RPA), the measured even-even nuclei ${}^{68}$Ni, ${}^{132}$Sn, and ${}^{208}$Pb. To analyze the model dependence in the predictions of the pygmy dipole strength, we employ three different Skyrme parameter sets. We find that both the isoscalar and the isovector dipole responses of all three nuclei show a low-energy peak that increases in magnitude, and is shifted to larger excitation energies, with increasing values of the slope of the symmetry energy at saturation. We highlight the fact that the collectivity associated with the RPA state(s) contributing to this peak is different in the isoscalar and isovector case, or in other words it depends on the external probe. While the response of these RPA states to an isovector operator does not show a clear collective nature, the response to an isoscalar operator is recognizably collective, for all analyzed nuclei and all studied interactions.

The statistical Hauser-Feshbach (HF) model performs poorly in calculating the ($\gamma$, $\alpha$) rates that are critical to the $p$ process. Experimental work on elastic scattering of the tellurium isotopic chain [A. Palumbo et al. (unpublished)] provided a new parametrization of the $\alpha$-optical potential and consequently new HF calculations of the ($\alpha$,$x$) cross sections on ${}^{120-130}$Te. However, reliable experimental cross sections of these isotopes have not been measured at energies relevant to the $p$ process. To test the reliability of the HF calculations, we measured the ($\alpha$,$n$) cross sections on ${}^{120}$Te, one of the $p$ nuclei, using the activation technique. The results are compared with the HF model calculations.

Within the framework of nuclear field theory (NFT), the spectrum of atomic nuclei is described in terms of collective and quasiparticle degrees of freedom, that is, of elementary modes of excitation that are directly related to experiment and of their coupling, whose strength and form factors are the basic ingredients entering in the calculations of absolute cross sections of inelastic and of one- and two-particle transfer reactions. We present a detailed discussion of the solution of the Dyson equation, also known as the Nambu-Gor'kov equations in the case of a superfluid system, which propagates medium polarization processes calculated making use of NFT to all orders of perturbation, resulting in the dressing of quasiparticles and in the induced pairing interaction. The formalism is applied to the superfluid nucleus ${}^{120}$Sn. Results concerning the low-energy spectrum, that is, the quasiparticle strength distribution of the neighboring odd-A nuclei ${}^{119}$Sn and ${}^{121}$Sn, are presented and compared with the experimental findings.