We calculate two-photon exchange amplitudes for the elastic electron-proton scattering, and take into account intermediate hadronic states containing a $\pi N$ system with total angular momentum 1/2 or 3/2, which includes eight different channels. This is the improvement of our previous calculation, where only the $\pi N$ states with quantum numbers of $\mathrm{\Delta }$ resonance were included. The results show good consistency with recent experimental data. At high $Q^2$, newly calculated contributions affect the correction to the measured proton form factor ratio $\mu G_E/G_M$. The total correction becomes somewhat smaller compared to our previous work, but is still significant and grows approximately linearly with $Q^2$. Comparing contributions of different channels, we found that larger contributions come from the channels with quantum numbers of lightest resonances.

The ${}^{86}\mathrm{Se}$ nucleus has been investigated by $\gamma$-ray spectroscopy using an array of Ge detectors placed at the exit of the fission-fragment mass separator Lohengrin of the Institut Laue-Langevin. New transitions have been identified by studying the $\beta$ decay of ${}^{86}\mathrm{As}$. An excitation scheme is proposed and includes a $2_2{}^{+}$ level at 1399 keV and a possible $3^{+}$ level that are well reproduced by shell model calculations with the most recent parametrization. The properties of the excitations indicate a possible onset of $\gamma$ collectivity in ${}^{86}\mathrm{Se}$.

Background: In neutron-rich nuclei around $N=40$ rapid changes in nuclear structure can be observed. While ${}^{68}\mathrm{Ni}$ exhibits signatures of a doubly magic nucleus, experimental data along the isotopic chains in even more exotic Fe and Cr isotopes—such as excitation energies and transition strengths—suggest a sudden rise in collectivity toward $N=40$.

Purpose: Reduced quadrupole transition strengths for low-lying transitions in neutron-rich ${}^{58,60,62}\mathrm{Cr}$ are investigated. This gives quantitative new insights into the evolution of quadrupole collectivity in the neutron-rich region close to $N=40$.

Method: The recoil distance Doppler-shift (RDDS) technique was applied to measure lifetimes of low-lying states in ${}^{58,60,62}\mathrm{Cr}$. The experiment was carried out at the National Superconducting Cyclotron Laboratory (NSCL) with the SeGA array in a plunger configuration coupled to the S800 magnetic spectrograph. The states of interest were populated by means of one-proton knockout reactions.

Results: Data reveal a rapid increase in quadrupole collectivity for ${}^{58,60,62}\mathrm{Cr}$ toward $N=40$ and point to stronger quadrupole deformations compared to neighboring Fe isotopes. The experimental $B(E2$) values are reproduced well with state-of-the-art shell-model calculations using the LNPS effective interaction. A consideration of intrinsic quadrupole moments and ${\mathrm{B}}_{42}$ ratios suggest an evolution toward a rotational nature of the collective structures in ${}^{60,62}\mathrm{Cr}$. Compared to ${}^{58}\mathrm{Cr}$, experimental ${\mathrm{B}}_{42}$ and ${\mathrm{B}}_{62}$ values for ${}^{60}\mathrm{Cr}$ are in better agreement with the $E\left(5\right)$ limit.

Conclusion: Our results indicate that collective excitations in neutron-rich Cr isotopes saturate at $N=38$, which is in agreement with theoretical predictions. More detailed experimental data of excited structures and interband transitions are needed for a comprehensive understanding of quadrupole collectivity close to $N=40$. This calls for additional measurements in neutron-rich Cr and neighboring Ti and Fe nuclei.

A chiral quark-model approach is adopted to study the $\gamma p\to {\pi }^{0}p$ and $\gamma n\to {\pi }^{0}n$ reactions. Good descriptions of the total and differential cross sections and single-polarization observables are obtained from the pion production threshold up to the second resonance region. It is found that (i) the $n=0$ shell resonance $\mathrm{\Delta }\left(1232\right)P_{33}$, the $n=1$ shell resonances $N\left(1535\right)S_{11}$ and $N\left(1520\right)D_{13}$, and the $n=2$ shell resonance $N\left(1720\right)P_{13}$ play crucial roles in these two processes. They are responsible for the first, second, and third bump structures in the cross sections, respectively. (ii) Furthermore, obvious evidence of $N\left(1650\right)S_{11}$ and $\mathrm{\Delta }\left(1620\right)S_{31}$ is also found in the reactions. They notably affect the cross sections and the polarization observables from the second resonance region to the third resonance region. (iii) The $u$-channel background plays a crucial role in the reactions. It has strong interferences with the $s$-channel resonances. (iv) The $t$-channel background seems to be needed in the reactions. Including the $t$-channel vector-meson exchange contribution, the descriptions in the energy region $E_{\gamma }=600–900$ MeV are improved significantly. The helicity amplitudes of the main resonances, $\mathrm{\Delta }\left(1232\right)P_{33}, N\left(1535\right)S_{11}, N\left(1520\right)D_{13}, N\left(1720\right)P_{13}, N\left(1650\right)S_{11}$, and $\mathrm{\Delta }\left(1620\right)S_{31}$, are extracted and compared with the results from other groups.

We estimate dissipative properties, viz., shear and bulk viscosities of hadronic matter using relativistic Boltzmann equation in relaxation time approximation within the framework of excluded-volume hadron resonance gas (EHRG) model. We find that at zero baryon chemical potential the shear viscosity to entropy ratio ($\eta /s$) decreases with temperature while at finite baryon chemical potential this ratio shows the same behavior as a function of temperature but reaches close to the Kovtun-Son-Starinets (KSS) bound. Further along the chemical freezeout curve, ratio $\eta /s$ is almost constant apart from small initial monotonic rise. This observation may have some relevance to the experimental finding that the differential elliptic flow of charged hadrons does not change considerably at lower center-of-mass energy. We further find that bulk viscosity to entropy density ($\zeta /s$) decreases with temperature while this ratio has higher value at finite baryon chemical potential at higher temperature. Along the freezeout curve $\zeta /s$ decreases monotonically at lower center-of-mass energy and then saturates.

The nucleon mean-field potential has been thoroughly investigated in an extended Hartree-Fock (HF) calculation of nuclear matter (NM) using the CDM3Y3 and CDM3Y6 density dependent versions of the M3Y interaction. The single-particle (SP) energies of nucleons in NM are determined according to the Hugenholtz–Van Hove theorem, which gives rise naturally to a rearrangement term (RT) of the SP potential at the Fermi momentum. Using the RT obtained exactly at the different NM densities and neutron-proton asymmetries, a consistent method is suggested to take into account effectively the momentum dependence of the RT of the SP potential within the standard HF scheme. To obtain a realistic momentum dependence of the nucleon optical potential (OP), the high-momentum part of the SP potential was accurately readjusted to reproduce the observed energy dependence of the nucleon OP over a wide range of energies. The impact of the RT and momentum dependence of the SP potential on the density dependence of the nuclear symmetry energy and nucleon effective mass has been studied in detail. The high-momentum tail of the SP potential was found to have a sizable effect on the slope of the symmetry energy and the neutron-proton effective mass splitting at supranuclear densities of the NM. Based on a local density approximation, the folding model of the nucleon OP of finite nuclei has been extended to take into account consistently the RT and momentum dependence of the nucleon OP in the same mean-field manner, and successfully applied to study the elastic neutron scattering on the lead target at the energies around the Fermi energy.

Decay of ${}^{210}\mathrm{Po}$ compound nucleus formed in light- and heavy-ion induced fusion reactions has been analyzed simultaneously using a consistent prescription for fission barrier and nuclear level density incorporating shell correction and its damping with excitation energy. Good descriptions of all the excitation functions have been achieved with a fission barrier of $21.9\pm 0.2$ MeV, indicating no significant shell correction at the saddle point. For this barrier height, the predicted statistical prefission neutrons in heavy-ion fusion-fission are much smaller than the experimental values, implying the presence of dynamical neutrons due to dissipation even at these low excitation energies $\left(\sim 50\mathrm{MeV}\right)$ in the mass region $A\sim 200$. When only heavy-ion induced fission excitation functions and the prefission neutron multiplicities are included in the fits, the deduced best-fit fission barrier depends on the assumed fission delay time, during which dynamical neutrons can be emitted. A fission delay of $(0.8\pm 0.1)\times {10}^{-19}$ s has been estimated corresponding to the above fission barrier height, assuming that the entire excess neutrons over and above the statistical model predictions are due to the dynamics. The present observation has implication on the study of fission time scale and nuclear viscosity using neutron emission as a probe.

The presence of scaling variables in experimental observables provides very valuable indications of the dynamics underlying a given physical process. In the last years, the search for geometric scaling, that is the presence of a scaling variable which encodes all geometrical information of the collision as well as other external quantities as the total energy, has been very active. This is motivated, in part, for being one of the genuine predictions of the color glass condensate formalism for saturation of partonic densities. Here we extend these previous findings to the case of experimental data on elliptic flow. We find an excellent scaling for all centralities and energies, from the BNL Relativistic Heavy Ion Collider to the CERN Large Hadron Collider, with a simple generalization of the scaling previously found for other observables and systems. Interestingly the case of the photons, difficult to reconcile in most formalisms, nicely fits the scaling curve. We discuss the possible interpretations of this finding in terms of initial or final state effects.

The $E_r^{\mathrm{c.m.}}=458$ keV resonance in ${}^{22}\mathrm{Ne}\left(p,\gamma \right){}^{23}\mathrm{Na}$ is an ideal reference resonance for measurements of cross sections and resonance strengths in noble gas targets. We report on a new measurement of the strength of this resonance. Data analysis employed the TFractionFitter class of root combined with geant simulations of potential decay cascades from this resonance. This approach allowed us to extract precise primary branching ratios for decays from the resonant state, including a new primary branch to the 7082-keV state in ${}^{23}\mathrm{Na}$. Our new resonance strength of $\omega \gamma$(458 keV) = 0.583(43) eV is more than $1\sigma$ higher than a recent high-precision result that relied on literature branching ratios.

Excited states were investigated in ${}^{21}\mathrm{F}$ and ${}^{25}\mathrm{Na}$ using the ${}^9\mathrm{Be}\left({}^{14}\mathrm{C},pn\gamma \right)$ reaction at 30, 35, and 45 MeV and the ${}^9\mathrm{Be}\left({}^{18}\mathrm{O},pn\gamma \right)$ reaction at 35 MeV. Protons were detected and identified in an $E-\mathrm{\Delta }E$ telescope at $0^{\circ }$ in coincidence with one or more $\gamma$ radiations in the FSU Compton-suppressed Ge detector array. Many new levels and electromagnetic decays were observed, especially among the higher spin states. Angular distributions and mean lifetimes were measured wherever possible in both nuclei. The energy levels of the positive-parity states in the two nuclei agree rather well with shell model calculations using both the USDA and WBP interactions up to the highest spins observed of $13/2\hslash$. Both a weak coupling approximation and shell model calculations using the WBP interaction generally reproduce the negative-parity states in ${}^{21}\mathrm{F}$. The shell model calculations reproduce relatively well the measured $M1$ and $E2$ transitions in both nuclei, but overpredict the parity-changing $E1$ transitions in ${}^{21}\mathrm{F}$, the only nucleus in which negative-parity states were observed in the present experiment.

The cluster approach, which allows us to take into account both shape deformation parameters and cluster degrees of freedom, is developed to describe alternating-parity rotational bands. The important ingredient of the model is the dinuclear system concept in which the wave function of the nucleus is treated as a superposition of a mononucleus and two-cluster configurations. The model is applied to describe the multiple positive and negative parity rotational bands in ${}^{240}\mathrm{Pu}$. The observed excitation spectrum and the angular momentum dependences of the parity splitting and of the electric $E1$ and $E2$ transition moments are explained. Special emphasis is made on the investigation of the recently measured positive parity $0_2^{+}$ rotational band of reflection-asymmetric nature. The results suggest that this band might be understood as being built on the lowest excited state in the mass asymmetry degree of freedom. The $B\left(E1\right)/B\left(E2\right)$ branching ratios between the reduced transition probabilities of decay from the states of the $0_2^{+}$ band to the first negative parity band and to the groundstate band, respectively, are calculated and compared with experimental data.

We make use of a subtraction procedure, introduced to overcome double-counting problems in beyond-mean-field theories, in the second random-phase-approximation (SRPA) for the first time. This procedure guarantees the stability of the SRPA (so that all excitation energies are real). We show that the method fits perfectly into nuclear density-functional theory. We illustrate applications to the monopole and quadrupole response and to low-lying $0^{+}$ and $2^{+}$ states in the nucleus ${}^{16}\mathrm{O}$. We show that the subtraction procedure leads to (i) results that are weakly cutoff dependent and (ii) a considerable reduction of the SRPA downwards shift with respect to the random-phase approximation (RPA) spectra (systematically found in all previous applications). This implementation of the SRPA model will allow a reliable analysis of the effects of two particle-two hole configurations (2p2h) on the excitation spectra of medium-mass and heavy nuclei.

We study the effect of a hidden charm nuclear excited state $N_{c\overline{c}}^{*}$ in the ${\pi }^{-}p\to D^{-}{\mathrm{\Sigma }}_c^{+}$ reaction near threshold using an effective Lagrangian approach. We calculate the background contribution of the $t$ and $u$ channels by the $D^{*0}$ vector meson exchange and ${\mathrm{\Sigma }}_c^{++}$ intermediate state, respectively. We show that the consideration of a $N_{c\overline{c}}^{*}$ resonance provides an enhancement of the total cross section close to the reaction threshold. We also evaluate the differential cross section for different energies and we study the angle dependence. It is expected that our model calculations will be tested in future experiments.

The outer-crust structure and composition of a cold, non-accreting magnetar are studied. We model the outer crust to be made of fully equilibrated matter where ionized nuclei form a Coulomb crystal embedded in an electron gas. The main effects of the strong magnetic field are those of quantizing the electron motion in Landau levels and of modifying the nuclear single-particle levels producing, on average, an increased binding of nucleons in nuclei present in the Coulomb lattice. The effect of a homogeneous and constant magnetic field on nuclear masses has been predicted by using a covariant density functional in which induced currents and axial deformation due to the presence of a magnetic field that breaks time-reversal symmetry have been included self-consistently in the nucleon and meson equations of motion. Although not yet observed, for $B\gtrsim {10}^{16}$ G both effects contribute to produce different compositions—odd-mass nuclei are frequently predicted—and to increase the neutron-drip pressure as compared to a typical neutron star. Specifically, in such a regime, the magnetic-field effects on nuclei favor the appearance of heavier nuclei at low pressures. As $B$ increases, such heavier nuclei are also preferred up to larger pressures. For the most extreme magnetic field considered, $B={10}^{18}$ G, and for the models studied, almost the whole outer crust is made of ${}_{40}^{92}{\mathrm{Zr}}_{52}$.

It is currently a big challenge to accurately determine the symmetry energy $E_{\mathrm{sym}}\left(\rho \right)$ and the pure neutron matter equation of state $E_{\mathrm{PNM}}\left(\rho \right)$ even their values around saturation density ${\rho }_0$. We find that the electric dipole polarizability ${\alpha }_{\mathrm{D}}$ in ${}^{208}\mathrm{Pb}$ can be determined uniquely by the magnitude of $E_{\mathrm{sym}}\left(\rho \right)$ or almost equivalently $E_{\mathrm{PNM}}\left(\rho \right)$ at subsaturation densities around ${\rho }_0/3$, shedding light upon the genuine correlation between ${\alpha }_{\mathrm{D}}$ and $E_{\mathrm{sym}}\left(\rho \right)$. By analyzing the experimental data of ${\alpha }_{\mathrm{D}}$ in ${}^{208}\mathrm{Pb}$ from the Research Center for Nuclear Physics using a number of nonrelativistic and relativistic mean-field models, we obtain very stringent constraints on $E_{\mathrm{sym}}\left(\rho \right)$ and $E_{\mathrm{PNM}}\left(\rho \right)$ around ${\rho }_0/3$. The obtained constraints are found to be in good agreement with the results extracted in other analyses. In particular, our results provide for the first time the experimental constraints on $E_{\mathrm{PNM}}\left(\rho \right)$ around ${\rho }_0/3$, which are in harmony with the recent determination of $E_{\mathrm{PNM}}\left(\rho \right)$ from microscopic theoretical studies and potentially useful in constraining the largely uncertain many-nucleon interactions in microscopic calculations of neutron matter.

Given a set of collective variables, a method is proposed to obtain the associated conjugated collective momenta and masses starting from a microscopic time-dependent mean-field theory. The construction of pairs of conjugated variables is the first step to bridge microscopic and macroscopic approaches. The method is versatile and can be applied to study a large class of nuclear processes. An illustration is given here with the fission of ${}^{258}\mathrm{Fm}$. Using the quadrupole moment and eventually higher-order multipole moments, the associated collective masses are estimated along the microscopic mean-field evolution. When more than one collective variable is considered, it is shown that the off-diagonal matrix elements of the inertia play a crucial role. Using the information on the quadrupole moment and associated momentum, the collective evolution is studied. It is shown that dynamical effects beyond the adiabatic limit are important. Nuclei formed after fission tend to stick together for a longer time leading to a dynamical scission point at a larger distance between nuclei compared to the one anticipated from the adiabatic energy landscape. The effective nucleus-nucleus potential felt by the emitted nuclei is finally extracted.

Background: The ${}^{14}\mathrm{O}(\alpha ,p){}^{17}\mathrm{F}$ reaction plays an important role as the trigger reaction for the x-ray burst.

Purpose: The direct measurement of ${}^{14}\mathrm{O}(\alpha ,p){}^{17}\mathrm{F}$ was made for studying the resonant states in ${}^{18}\mathrm{Ne}$ and determining the reaction rate of ${}^{14}\mathrm{O}(\alpha ,p){}^{17}\mathrm{F}$ at astrophysical temperatures.

Methods: The differential cross section of the ${}^{14}\mathrm{O}(\alpha ,p){}^{17}\mathrm{F}$ reaction was measured using a 2.5-MeV/u ${}^{14}\mathrm{O}$ radioactive beam and the thick target method in inverse kinematics. Three sets of $\mathrm{\Delta }E-E$ Si telescopes were installed and coincidence measurements were performed. We analyzed single-proton decay events using the time-of-flight (TOF) information of the recoiling protons.

Results: The excitation function of ${}^{14}\mathrm{O}(\alpha ,p){}^{17}\mathrm{F}$ was acquired for excitation energies between 7.2 and 10.4 MeV in ${}^{18}\mathrm{Ne}$ by considering the two channels which decay to the ground state and first excited state of ${}^{17}\mathrm{F}$. Several new, as well as previously known, states in ${}^{18}\mathrm{Ne}$ were observed and their resonance parameters were extracted from $R$-matrix analysis. The contributions of four resonances over the excitation energy range, $7<E_x<8.2\mathrm{MeV}$, to the ${}^{14}\mathrm{O}(\alpha ,p){}^{17}\mathrm{F}$ reaction rate were calculated.

Conclusions: We observed very strong single-proton decay events, but did not observe strong double-proton decay events as in a previous study by Fu et al. The reaction rates contributed by the 7.35-, 7.58-, and 7.72-MeV states were estimated to be dominant at temperatures $T_9>2$. Among these three states, the 7.35-MeV state was found to enhance the reaction rate by a factor of 10 greater than the other two resonance states.

The possibility of an $nn\mathrm{\Lambda }$ bound state is investigated in the framework of pionless effective field theory at leading order. A system of coupled integral equations are constructed in the spin-isospin basis, of which numerical solutions are investigated. In particular, we make use of the limit cycle behavior, i.e., cyclic singularities of coupled integral equations of the system, which would be associated with the formation of a three-body bound state, the so-called Efimov state, in the unitary limit. Furthermore, we find that, when the sharp momentum cutoff introduced in the integral equations is taken to be significantly larger than the hard scale of the effective theory, the coupling of a three-body contact interaction becomes cyclically singular indicating the onset of an Efimov-like bound state formation. However, the paucity of empirical information to determine the parameters of the theory precludes a definitive conclusion on the existence of such a bound state. As a simple test of the feasibility of the $nn\mathrm{\Lambda }$ bound system in nature, we explore the cutoff dependence of the theory, and uncertainties of the present study are discussed as well.