Intrinsic fluctuations of the proton saturation momentum generate asymmetric rapidity distributions on an event-by-event basis. We argue that the asymmetric component, $\langle a_1^2\rangle$, of the orthogonal polynomial decomposition of the two-particle rapidity correlation function is a sensitive probe to this distribution of fluctuations. We present a simple model connecting the experimentally measured $\langle a_1^2\rangle$ to the variance, $\sigma$, of the distribution of the logarithm of the proton saturation scale. We find that $\sigma \approx 0.5–1$ describes the asymmetric component of the rapidity correlations recently measured by the ATLAS Collaboration.

Using the Boltzmann transport approach, we study the effect of initial spatial and momentum correlations between a heavy quark pair, such as that produced from a $p+p$ collision, on their collision rate in a partonic medium, which is relevant for their thermalization and the production of quarkonium from regeneration. Characterizing this effect by an effective volume given by the inverse of the ratio of their collision rate to the collision rate of a thermally equilibrated and spatially uniformly distributed heavy quark pair in a unit volume, we find that the effective volume is finite and depends sensitively on the momentum of the heavy quark and the temperature of the medium. Generally, it increases linearly with time $t$ at the very beginning, thus an enhanced collision rate, and the increase then becomes slower due to multiple scattering, and finally it increases as $t^{3/2}$. We further find that the momentum distribution of the colliding heavy quark pair approaches a thermal distribution after about 5 $\mathrm{fm}/c$ with an effective temperature similar to that of the medium even though their transverse momentum spectra initially have a $\delta$-like distribution.

Isovector and isoscalar dipole excitations in ${}^9\mathrm{Be}$ and ${}^{10}\mathrm{Be}$ are investigated in the framework of antisymmetrized molecular dynamics, in which angular-momentum and parity projections are performed. In the present method, 1p-1h excitation modes built on the ground state and a large amplitude $\alpha$-cluster mode are taken into account. The isovector giant dipole resonance (GDR) in $E>20$ MeV shows the two-peak structure, which is understood from the dipole excitation in the $2\alpha$ core part with the prolate deformation. Because of valence neutron modes against the $2\alpha$ core, low-energy $E1$ resonances appear in $E<20$ MeV, exhausting about $20\%$ of the Thomas-Reiche-Kuhn sum rule and $10\%$ of the calculated energy-weighted sum. The dipole resonance at $E\sim 15$ MeV in ${}^{10}\mathrm{Be}$ can be interpreted as the parity partner of the ground state having a ${}^6\mathrm{He}+\alpha$ structure and has remarkable $E1$ strength because of the coherent contribution of two valence neutrons. The isoscalar dipole strength for some low-energy resonances is significantly enhanced by the coupling with the $\alpha$-cluster mode. For the $E1$ strength of ${}^9\mathrm{Be}$, the calculation overestimates the energy-weighted sum (EWS) in the low-energy ($E<20$ MeV) and GDR ($20<E<50$ MeV) regions by a factor of 1.6 and underestimates the width of the GDR, whereas it reasonably describes the GDR energy and also the ratio of the EWS in the low-energy region to that of the GDR region.

Inclusion of time-odd components into the wave function is important for a reliable description of rotational motion by the angular-momentum-projection method; the cranking procedure with infinitesimal rotational frequency is an efficient way to realize it. In the present work we investigate the effect of this infinitesimal cranking for a triaxially deformed nucleus, where there are three independent cranking axes. It is found that the effects of cranking about three axes on the triaxial energy spectrum are quite different and inclusion of all of them considerably modifies the resultant spectrum from the one obtained without cranking. Employing the Gogny D1S force as an effective interaction, we apply the method to the calculation of the multiple $\gamma$ vibrational bands in ${}^{164}\mathrm{Er}$ as a typical example, where the angular-momentum-projected configuration mixing with respect to the triaxial shape degree of freedom is performed. With this method, both the $K=0$ and the $K=4$ two-phonon $\gamma$ vibrational bands are obtained with considerable anharmonicity. Reasonably good agreement, though not perfect, is obtained for both the spectrum and transition probabilities with rather small average triaxial deformation $\gamma \approx 9^{\circ }$ for the ground-state rotational band. The relation to the wobbling motion at high-spin states is also briefly discussed.

Within the dinuclear system model the charge, mass, and isotopic distributions of the products in the reactions ${}^{78}\mathrm{Kr}+{}^{40}\mathrm{Ca}$ and ${}^{86}\mathrm{Kr}+{}^{48}\mathrm{Ca}$ are predicted at bombarding energy 10 MeV/nucleon. The heavy-ion phase-space exploration code is applied to take into consideration the pre-equilibrium emission of light particles. The competition is treated between complete fusion followed by the decay of compound nucleus and quasifission channels. The possible explanation of the odd-even staggering in the yield of the final reaction products at high excitation energies is discussed.

The production of (anti-)deuteron and (anti-)${}^3\text{He}$ nuclei in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV has been studied using the ALICE detector at the LHC. The spectra exhibit a significant hardening with increasing centrality. Combined blast-wave fits of several particles support the interpretation that this behavior is caused by an increase of radial flow. The integrated particle yields are discussed in the context of coalescence and thermal-statistical model expectations. The particle ratios, ${}^3\text{He}/d$ and ${}^3\text{He}/p$, in Pb-Pb collisions are found to be in agreement with a common chemical freeze-out temperature of $T_{\mathrm{chem}}\approx 156$ MeV. These ratios do not vary with centrality which is in agreement with the thermal-statistical model. In a coalescence approach, it excludes models in which nucleus production is proportional to the particle multiplicity and favors those in which it is proportional to the particle density instead. In addition, the observation of 31 anti-tritons in Pb-Pb collisions is reported. For comparison, the deuteron spectrum in $pp$ collisions at $\sqrt{s}=7$ TeV is also presented. While the $p/\pi$ ratio is similar in $pp$ and Pb-Pb collisions, the $d/p$ ratio in $pp$ collisions is found to be lower by a factor of 2.2 than in Pb-Pb collisions.

We study the effects of correlations on cumulants and their ratios of net-proton multiplicity distributions which have been measured for central (0%–5%) $\text{Au}+\text{Au}$ collisions at the Relativistic Heavy Ion Collider (RHIC). This effect has been studied by assuming individual proton and antiproton distributions as a Poisson or negative binomial distribution (NBD). In spite of significantly correlated production due to baryon number, electric charge conservation, and kinematical correlations of protons and antiprotons, the measured cumulants of the net-proton distribution follow the independent-production model. In the present work we demonstrate how the introduction of the correlations will affect the cumulants and their ratios for the difference distributions. We have also demonstrated this study using the proton and antiproton distributions obtained from the hijing event generator.

The world experimental data on cross section and kinematic distribution in $p+p$ and $p+A$ collisions at $\sqrt{s}=6.8–7000$ GeV are systematically examined. The $\sqrt{s}$ dependence of the inclusive cross section, rapidity, and transverse momentum distributions are studied phenomenologically. We explore empirical formulas to obtain the total cross section, rapidity, and transverse momentum $\left(p_T\right)$ distribution. This is crucial for the interpretation of $A+A J/\psi$ results at the BNL Relativistic Heavy Ion Collider when the $p+p$ reference data are not available. In addition, the cross section at midrapidity and transverse momentum distributions in $p+p$ collisions at $\sqrt{s}=39$ and 62.4 GeV are evaluated.

The $\mathrm{\Lambda }\left(1405\right)$ resonance production reaction is investigated within the framework of the coupled-channels Alt-Grassberger-Sandhas (AGS) equations. We perform full three-body calculations for the $\overline{K}NN\text{−}\pi YN$ amplitudes on the physical real energy axis and investigate how the signature of the $\mathrm{\Lambda }\left(1405\right)$ appears in the cross sections of the $K^{-}d\to \pi \mathrm{\Sigma }n$ reactions, also in view of the planned E31 experiment at J-PARC. Two types of meson-baryon interaction models are considered: an energy-dependent interaction based on chiral $SU\left(3\right)$ effective field theory, and an energy-independent version that has been used repeatedly in phenomenological approaches. These two models have different off-shell properties that imply correspondingly different behavior in the three-body system. We investigate how these features show up in differential cross sections of $K^{-}d\to \pi \mathrm{\Sigma }n$ reactions. Characteristic patterns distinguishing between the two models are found in the invariant mass spectrum of the final $\pi \mathrm{\Sigma }$ state. The $K^{-}d\to \pi \mathrm{\Sigma }n$ reaction, with different (${\pi }^{\pm }{\mathrm{\Sigma }}^{\mp }$ and ${\pi }^0{\mathrm{\Sigma }}^0$) charge combinations in the final state, is thus demonstrated to be a useful tool for investigating the subthreshold behavior of the $\overline{K}N$ interaction.

Background: Unbound single-particle states become important in determining the properties of a hot nucleus as its temperature increases. We present relativistic mean field (RMF) for hot nuclei considering not only the self-consistent temperature and density dependence of the self-consistent relativistic mean fields but also the vapor phase that takes into account the unbound nucleon states.

Purpose: The temperature dependence of the pairing gaps, nuclear deformation, radii, binding energies, entropy, and caloric curves of spherical and deformed nuclei are obtained in self-consistent RMF calculations up to the limit of existence of the nucleus.

Method: We perform Dirac-Hartree-Bogoliubov (DHB) calculations for hot nuclei using a zero-range approximation to the relativistic pairing interaction to calculate proton-proton and neutron-neutron pairing energies and gaps. A vapor subtraction procedure is used to account for unbound states and to remove long range Coulomb repulsion between the hot nucleus and the gas as well as the contribution of the external nucleon gas.

Results: We show that $p-p$ and $n-n$ pairing gaps in the ${}^1\mathrm{S}_0$ channel vanish for low critical temperatures in the range $T_{c^p}\approx 0.6–1.1\mathrm{MeV}$ for spherical nuclei such as ${}^{90}\mathrm{Zr}$, ${}^{124}\mathrm{Sn}$, and ${}^{140}\mathrm{Ce}$ and for both deformed nuclei ${}^{150}\mathrm{Sm}$ and ${}^{168}\mathrm{Er}$. We found that superconducting phase transition occurs at $T_{c^p}=1.03{\mathrm{\Delta }}_{pp}\left(0\right)$ for ${}^{90}\mathrm{Zr}$, $T_{c^p}=1.16{\mathrm{\Delta }}_{pp}\left(0\right)$ for ${}^{140}\mathrm{Ce}$, $T_{c^p}=0.92{\mathrm{\Delta }}_{pp}\left(0\right)$ for ${}^{150}\mathrm{Sm}$, and $T_{c^p}=0.97{\mathrm{\Delta }}_{pp}\left(0\right)$ for ${}^{168}\mathrm{Er}$. The superfluidity phase transition occurs at $T_{c^p}=0.72{\mathrm{\Delta }}_{nn}\left(0\right)$ for ${}^{124}\mathrm{Sn}$, $T_{c^p}=1.22{\mathrm{\Delta }}_{nn}\left(0\right)$ for ${}^{150}\mathrm{Sm}$, and $T_{c^p}=1.13{\mathrm{\Delta }}_{nn}\left(0\right)$ for ${}^{168}\mathrm{Er}$. Thus, the nuclear superfluidity phase—at least for this channel—can only survive at very low nuclear temperatures and this phase transition (when the neutron gap vanishes) always occurs before the superconducting one, where the proton gap is zero. For deformed nuclei the nuclear deformation disappear at temperatures of about $T_{c^s}=2.0–4.0\mathrm{MeV}$, well above the critical temperatures for pairing, $T_{c^p}$. If we associate the melting of hot nuclei into the surrounding vapor with the liquid-gas phase transition our results indicate that it occurs at temperatures around $T=8.0–10.0\mathrm{MeV}$, somewhat higher than observed in many experimental results.

Conclusions: The change of the pairing fields with the temperature is important and must be taken into account in order to define the superfluidity and superconducting phase transitions. We obtain a Hamiltonian form of the pairing field calibrated by an overall constant $c_{\mathrm{pair}}$ to compensate for deficiencies of the interaction parameters and of the numerical calculation. When the pairing is not zero, the states close to the Fermi energy make the principal contribution to the anomalous density that appears in the pairing field. By including temperature through the use of the Matsubara formalism, the normal and anomalous densities are multiplied by a Fermi occupation factor. This leads to a reduction in the anomalous density and in the pairing as the temperature increases. When the temperature increases $\left(T\ge 4\mathrm{MeV}\right)$, the effects of the vapor phase that take into account the unbound nucleon states become important, allowing the study of nuclear properties of finite nuclei from zero to high temperatures.

Utilizing a recently found class of exact, analytic rotating solutions of nonrelativistic fireball hydrodynamics, we calculate analytically the single-particle spectra, the elliptic flows, and two-particle Bose-Einstein correlation functions for rotating and expanding fireballs with spheroidal symmetry. We demonstrate that rotation generates final state momentum anisotropies even for a spatially symmetric, spherical initial geometry of the fireball. The mass dependence of the effective temperatures as well as the Hanbury Brown–Twiss (HBT) radius parameters and the elliptic flow are shown to be sensitive not only to radial flow effects but also to the magnitude of the initial angular momentum.

The transition helicity amplitudes from the proton ground state to the $N\left(1440\right)1/2^{+}, N\left(1520\right)3/2^{-}$, and $\mathrm{\Delta }\left(1620\right)1/2^{-}$ resonances (${\gamma }_{v}p{N}^{*}$ electrocouplings) were determined from the analysis of nine independent onefold differential ${\pi }^{+}{\pi }^{-}p$ electroproduction cross sections off a proton target, taken with CLAS at photon virtualities $0.5{\text{GeV}}^2<Q^2<1.5$ ${\mathrm{GeV}}^2$. The phenomenological reaction model employed for separation of the resonant and nonresonant contributions to this exclusive channel was further developed. The $N\left(1440\right)1/2^{+}, N\left(1520\right)3/2^{-}$, and $\mathrm{\Delta }\left(1620\right)1/2^{-}$ electrocouplings were obtained from the resonant amplitudes of charged double-pion electroproduction off the proton in the aforementioned area of photon virtualities for the first time. Consistent results on ${\gamma }_{v}p{N}^{*}$ electrocouplings available from independent analyses of several $W$ intervals with different nonresonant contributions offer clear evidence for the reliable extraction of these fundamental quantities. These studies also improved the knowledge on hadronic branching ratios for the $N\left(1440\right)1/2^{+}, N\left(1520\right)3/2^{-}$, and $\mathrm{\Delta }\left(1620\right)1/2^{-}$ decays to the $\pi \mathrm{\Delta }$ and $\rho N$ final states. These new results provide a substantial impact on the QCD-based approaches that describe the $N^{*}$ structure and demonstrate the capability to explore fundamental ingredients of the nonperturbative strong interaction that are behind the excited nucleon state formation.

We present measurements of $\mathrm{\Omega }$ and $\varphi$ production at midrapidity from Au+Au collisions at nucleon-nucleon center-of-mass energies $\sqrt{s_{NN}}=7.7, 11.5, 19.6$, 27, and 39 GeV by the STAR experiment at the BNL Relativistic Heavy Ion Collider (RHIC). Motivated by the coalescence formation mechanism for these strange hadrons, we study the ratios of $N({\mathrm{\Omega }}^{-}+{\overline{\mathrm{\Omega }}}^{+})/\left[2N\left(\varphi \right)\right]$. These ratios as a function of transverse momentum $p_T$ fall on a consistent trend at high collision energies, but start to show deviations in peripheral collisions at $\sqrt{s_{NN}}=19.6$, 27, and 39 GeV, and in central collisions at 11.5 GeV in the intermediate $p_T$ region of $2.4-3.6$ GeV/$c$. We further evaluate empirically the strange quark $p_T$ distributions at hadronization by studying the $\mathrm{\Omega }/\varphi$ ratios scaled by the number of constituent quarks (NCQ). The NCQ-scaled $\mathrm{\Omega }/\varphi$ ratios show a suppression of strange quark production in central collisions at 11.5 GeV compared to $\sqrt{s_{NN}}\ge 19.6$ GeV. The shapes of the presumably thermal strange quark distributions in 0–60% most central collisions at 7.7 GeV show significant deviations from those in 0–10% most central collisions at higher energies. These features suggest that there is likely a change of the underlying strange quark dynamics in the transition from quark matter to hadronic matter at collision energies below 19.6 GeV.

It is possible to employ virtual decay paths, including two-particle transfer, to calculate the nuclear matrix element of neutrinoless double-$\beta$ decay under the closure approximation, in addition to the true double-$\beta$ path. In the quasiparticle random-phase approximation (QRPA) approach, it is necessary to introduce the product wave functions of the like-particle and proton-neutron QRPA ground states, for achieving consistency between the calculations of the true and virtual paths. Using these different paths, the problem of whether or not these two methods give equivalent nuclear matrix elements (NMEs) is investigated. It is found that the two results are inequivalent, resulting from the different many-body correlations included in the two QRPA methods, i.e., the use of the product wave functions alone is not sufficient. The author proposes introduction of the proton-neutron pairing interaction with an adequate strength in the double-$\beta$-path method, which carries less many-body correlations without this supplemental interaction, for obtaining the NME equivalent to that of the two-particle-transfer-path method. The validity of the proposed modified approach is examined.

Background: The study of excited states in mirror nuclei allows us to extract information on charge-dependent (i.e., isospin-nonconserving) interactions in nuclei.

Purpose: To extend previous studies of mirror nuclei in the $f_{\frac{7}{2}}$ region, investigating charge symmetry breaking of the strong nuclear force.

Methods: $\gamma$-ray spectroscopy has been performed for the mirror $(T_z=\pm \frac{3}{2})$ pair ${}^{53}\text{Ni}$ and ${}^{53}\text{Mn}$, produced via mirrored one-nucleon knockout reactions.

Results: Several new transitions have been identified in ${}^{53}\text{Ni}$ from which a new level scheme has been constructed. Cross sections for knockout have been analyzed and compared with reaction model calculations where evidence is found for knockout from high-spin isomeric states. Mirror energy differences between isobaric analog states have been computed, compared to large scale shell-model calculations, and interpreted in terms of isospin-nonconserving effects. In addition, lifetimes for the long-lived $J^{\pi }={\frac{5}{2}}_1^{-}$ analog states in both ${}^{53}\text{Mn}$ and ${}^{53}\text{Ni}$ have been extracted through lineshape analysis, giving half-lives of $t_{\frac{1}{2}}=120\left(14\right)$ ps and $t_{\frac{1}{2}}=198\left(12\right)$ ps, respectively.

Conclusions: The inclusion of a set of isovector isospin-nonconserving matrix elements to the shell-model calculations gave the best agreement with the experimental data.

In random-interaction ensembles, three proportional correlations between quadrupole moments of the first two $I^{\pi }=2^{+}$ states robustly emerge, including $Q\left(2_1^{+}\right)=\pm Q\left(2_2^{+}\right)$ correlations previously remarked by a realistic nuclear survey, and the $Q\left(2_2^{+}\right)=-\frac{3}{7}Q\left(2_1^{+}\right)$ correlation, which is only observed in the $sd$-boson space. These correlations can be microscopically characterized by the rotational SU(3) symmetry and quadrupole vibrational U(5) limit, respectively, according to the Elliott model and the $sd$-boson mean-field theory. The anharmonic vibration may be another phenomenological interpretation for the $Q\left(2_1^{+}\right)=-Q\left(2_2^{+}\right)$ correlation, whose spectral evidence, however, is insufficient.

The low-lying level structures of nuclei in the vicinity of ${}^{78}\mathrm{Ni}$ were investigated using in-beam $\gamma$-ray spectroscopy to clarify the nature of the nuclear magic numbers $Z=28$ and $N=50$ in systems close to the neutron drip line. Nucleon knockout reactions were employed to populate excited states in ${}^{80}\mathrm{Zn}$ and ${}^{82}\mathrm{Zn}$. A candidate for the $4_1^{+}$ level in ${}^{80}\mathrm{Zn}$ was identified at 1979(30) keV, and the lifetime of this state was estimated to be ${136}_{-67}^{+92}$ ps from a line-shape analysis. Moreover, the energy of the $2_1^{+}$ state in ${}^{82}\mathrm{Zn}$ is reported to lie at 621(11) keV. The large drop in the $2_1^{+}$ energy at ${}^{82}\mathrm{Zn}$ indicates the presence of a significant peak in the $E\left(2_1^{+}\right)$ systematics at $N=50$. Furthermore, the $E\left(4_1^{+}\right)/E\left(2_1^{+}\right)$ and $B(E2;4_1^{+}\to 2_1^{+})/B(E2;2_1^{+}\to 0_{\mathrm{g}.\mathrm{s}.}^{+})$ ratios in ${}^{80}\mathrm{Zn}$ were deduced to be $1.32\left(3\right)$ and $1.{12}_{-60}^{+80}$, respectively. These results imply that ${}^{80}\mathrm{Zn}$ can be described in terms of two-proton configurations with a ${}^{78}\mathrm{Ni}$ core and are consistent with a robust $N=50$ magic number along the Zn isotopic chain. These observations, therefore, indicate a persistent $N=50$ shell closure in nuclei far from the line of $\beta$ stability, which in turn suggests a doubly magic structure for ${}^{78}\mathrm{Ni}$.

${}^{10}\mathrm{Be}$ and ${}^{16}\mathrm{C}$ spectroscopy has been investigated by analyzing their breakup events on ${\mathrm{CH}}_2$ and ${\mathrm{CD}}_2$ targets. Breakup fragments have been detected by means of the CHIMERA detector. In particular, we investigated cluster decays of ${}^{10}\mathrm{Be}$ in ${}^4\mathrm{He}+{}^6\mathrm{He}$ and of ${}^{16}\mathrm{C}$ in ${}^6\mathrm{He}+{}^{10}\mathrm{Be}$ and ${}^4\mathrm{He}+{}^6\mathrm{He}+{}^6\mathrm{He}$. From the relative energy analysis of breakup fragments, we investigate the spectroscopy of excited states of projectile nuclei. In the ${}^{10}\mathrm{Be}$ case we observe known states at 9.51, 10.16, 10.6, and 11.8 MeV. Further, we suggest the existence of a new state at 13.5 MeV, possibly $6^{+}$ as indicated from angular correlation analysis. The relative energy $(E_{\mathrm{rel}}+E_{\mathrm{th}})$ spectrum of ${}^{16}\mathrm{C}$, reconstructed starting from ${}^6\mathrm{He}+{}^{10}\mathrm{Be}$ correlations, shows a peak at about 20.6 MeV, probably related to the existence of an high-lying excited state. Non-vanishing yields are also seen in the triple coincidences ${}^4\mathrm{He}+{}^6\mathrm{He}+{}^6\mathrm{He}$.

Finding the best model to describe the α-decay process is an old and ongoing challenge in nuclear physics. The present paper systematically studied α-decay half-lives for the favored ground-state-to-ground-state transitions of 344 isotopes of nuclei with 52 $\le Z \le$ 107 using 28 versions of the proximity potential model in the framework of the Wentzel-Kramers-Brillouin approximation. The present paper introduces the best proximity versions with the fewest deviations with respect to experimental values. The models for Proximity 1977 (Prox. 77)-set 4, Prox. 77-set 5, and Dutt 2011 with the root-mean-square deviations (RMSDs) of <1 were found to predict α-decay half-lives better than the other models. Comparison with fusion studies shows that Dutt 2011 is an appropriate model both for α-decay studies and for the prediction of the barrier characteristic in heavy-ion fusion reactions. The calculation of α-decay half-lives was repeated for even-even, even-odd, odd-even, and odd-odd nuclei. This detailed comparative study reveals that for these versions the half-lives of the even-even nuclei with RMSDs of <0.6 show less deviation than the even-odd, odd-even, and odd-odd nuclei.

There are indications of formation of a thermalized medium in high multiplicity $pp$ collisions at energies available at the CERN Large Hadron Collider. It is possible that such a medium may reach high enough energy density and temperature that a transient stage of quark-gluon plasma, where chiral symmetry is restored, may be achieved. Due to rapid three-dimensional expansion, the system will quickly cool, undergoing a spontaneous chiral symmetry breaking transition. We study the dynamics of the chiral field, after the symmetry breaking transition, for such an event using a reaction-diffusion equation approach which we have recently applied for studying QCD transitions in relativistic heavy-ion collisions. We show that the interior of such a rapidly expanding system is likely to lead to the formation of a single large domain of disoriented chiral condensate (DCC), which has been a subject of intensive search in earlier experiments. We argue that large multiplicity $pp$ collisions naturally give rise to required boundary conditions for the existence of slowly propagating front solutions of the reaction-diffusion equation with resulting dynamics of the chiral field leading to the formation of a large DCC domain.