Using the relativistic Vlasov-Uehling-Uhlenbeck (RVUU) equation based on mean fields from the nonlinear relativistic $\text{NL}\rho$ and $\text{NL}\rho \delta$ models, which have same nuclear equation of state and symmetry energy but different symmetry energy slope parameters, we study the effect of medium modification of the pion-production threshold on the total pion yield and the ${\pi }^{-}/{\pi }^{+}$ ratio in Au+Au collisions. We find that the in-medium threshold effect enhances both the total pion yield and the ${\pi }^{-}/{\pi }^{+}$ ratio, compared to those without this effect. Furthermore, including the medium modification of the pion-production threshold leads to a larger ${\pi }^{-}/{\pi }^{+}$ ratio for the $\text{NL}\rho \delta$ model with a larger symmetry energy parameter than the $\text{NL}\rho$ model with a smaller symmetry energy parameter, opposite to that found without the in-medium threshold effect. To reproduce the total pion yield measured by the FOPI Collaboration, we introduce a density-dependent cross section for $\Delta$ baryon production from nucleon-nucleon collisions, which suppresses the total pion yield but hardly changes the ${\pi }^{-}/{\pi }^{+}$ ratio. Because of the small difference in the stiffness of their symmetry energies, the ${\pi }^{-}/{\pi }^{+}$ ratios obtained from both the $\text{NL}\rho$ and $\text{NL}\rho \delta$ models are consistent with the FOPI data within the experimental errors.

We formulate kaon condensation in dense baryonic matter with antikaons fluctuating from the Fermi-liquid fixed point. This entails that in the Wilsonian renormalization group (RG) approach, the decimation is effectuated in the baryonic sector to the Fermi surface while in the meson sector to the origin. In writing the kaon-baryon (KN) coupling, we take a generalized hidden local symmetry Lagrangian for the meson sector endowed with a “mended symmetry” that has the unbroken symmetry limit at high density in which the Goldstone $\pi$, scalar $s$, and vectors $\rho$ (and $\omega )$ and $a_1$ become massless. The vector mesons $\rho$ (and $\omega$) and $a_1$ can be identified as emergent (hidden) local gauge fields and the scalar $s$ as the dilaton field of the spontaneously broken scale invariance at chiral restoration. In matter-free space, when the vector mesons and the scalar meson—whose masses are much greater than that of the pion—are integrated out, then the resulting KN coupling Lagrangian consists of the leading chiral order [$O\left(p^1\right)$] Weinberg-Tomozawa term and the next chiral order [$O\left(p^2\right)$] ${\Sigma }_{\text{KN}}$ term. In addressing kaon condensation in dense nuclear matter in chiral perturbation theory, one makes an expansion in the “small” Fermi momentum $k_F$. We argue that in the Wilsonian RG formalism with the Fermi-liquid fixed point, the expansion is on the contrary in $1/k_F$ with the “large” Fermi momentum $k_F$. The kaon-quasinucleon interaction resulting from integrating out the massive mesons consists of a “relevant” term from the scalar exchange (analog to the ${\Sigma }_{\text{KN}}$ term) and an “irrelevant” term from the vector-meson exchange (analog to the Weinberg-Tomozawa term). It is found that the critical density predicted by the latter approach, controlled by the relevant term with the irrelevant term suppressed, is three times less than that predicted by chiral perturbation theory. This would make kaon condensation take place at a much lower density than previously estimated in chiral perturbation theory.

The possibility of neutron pairing in the ${}^{1}S_0$ channel is studied for dense neutron matter in a vicinity of the ${\pi }^0$ condensation point. The ${}^{1}S_0$ pairing gap $\Delta$ is shown to occur in a model with a pairing force induced by the exchange of a soft neutral pionic mode. The soft pion induced potential $V_{\pi }\left(r\right)$ is characterized by an attenuating oscillatory behavior in coordinate space, while in momentum space all $S$-wave matrix elements $V_{\pi }(p,p^{\prime })$ are positive. The solution of the gap equation reveals strong momentum dependence.

New measurements of reaction cross sections for scattering of ${}^{11}\mathrm{Li}$ from H and C have provided a value for the radius of the neutron density distribution. By using the sensitivity of calculated radii to neutron configuration, I find that the $s^2$ fraction required to reproduce the new radius is $P\left(s^2\right)=0.{33}_{-0.05}^{+0.03}$, in agreement with an earlier estimate of 0.33(6). Calculations of relative cross sections for the reaction ${}^9\mathrm{Li}\left(t,p\right)$ (in reverse kinematics) suggest a method to observe an expected excited $3/2^{-}$ state and to independently determine $P\left(s^2\right)$.

Background: Theoretical estimates of the cross sections for the neutrino-nucleus scattering off relevant nuclei for supernova neutrinos are essential for many applications in neutrino physics and astrophysics. The double-$\beta$-decaying nucleus ${}^{136}\mathrm{Xe}$ nucleus is used by the EXO Collaboration in the search for neutrinoless double-$\beta$ decay. A ton-scale experiment based on ${}^{136}\mathrm{Xe}$ could also be used for studies of supernova neutrinos and/or solar neutrinos.

Purpose: The purpose of the present work is, thus, to perform a study of the charged-current and neutral-current nuclear responses to supernova neutrinos for ${}^{136}\mathrm{Xe}$.

Method: The cross sections are computed by using the well-established framework for studies of semileptonic processes in nuclei introduced by O'Connell, Donnelly, and Walecka [Phys. Rev. C 6, 719 (1972)]. The nuclear wave functions of the initial and the final nuclear states for the neutral-current neutrino-nucleus scattering in ${}^{136}\mathrm{Xe}$ are computed by using the quasiparticle random-phase approximation (QRPA). Similarly, the pnQRPA is adopted to construct the initial and final nuclear states which are relevant for the charged-current reactions. The nuclear responses to supernova neutrinos are subsequently computed by folding the cross sections with appropriate energy spectra for the incoming neutrinos.

Results: We present results for the cross sections of the charged-current and neutral-current neutrino and antineutrino scatterings off ${}^{136}\mathrm{Xe}$. Nuclear responses to supernova neutrinos are also given. For the considered scenario for the neutrino mixing we have found that neutrino interactions with matter and so-called collective neutrino oscillations enhance significantly the neutrino and antineutrino flux-averaged cross sections.

Conclusions: We have found that for the charged-current and neutral-current neutrino scatterings off ${}^{136}\mathrm{Xe}$ transitions mediated by the $1^{+}$ multipole are the most important ones. However, for the charged-current antineutrino channel $0^{+}$ and $1^{+}$ transitions are largely suppressed due to the large neutron excess. Transitions to $1^{-}$ and $2^{-}$ final nuclear states are thus relatively more important for the charged-current antineutrino scattering.

A simple model for open quantum systems is analyzed with random matrix theory. The system is coupled to the continuum in a minimal way. In this paper the effect on the level statistics of opening the system is seen. In particular the ${\Delta }_3\left(L\right)$ statistic, the width distribution and the level spacing are examined as a function of the strength of this coupling. The emergence of a super-radiant transition is observed. The level spacing and ${\Delta }_3\left(L\right)$ statistics exhibit the signatures of missed levels or intruder levels as the super-radiant state is formed.

An analytical solution for the Davydov-Chaban Hamiltonian with a sextic oscillator potential for the variable $\beta$ and $\gamma$ fixed to ${30}^{\circ }$ is proposed. The model is conventionally called Z(4)-sextic. For the potential shapes considered, the solution is exact for the ground and $\beta$ bands, while for the $\gamma$ band an approximation is adopted. Due to the scaling property of the problem, the energy and $B\left(E2\right)$ transition ratios depend on a single parameter apart from an integer number which limits the number of allowed states. For certain constraints imposed on the free parameter, which lead to simpler special potentials, the energy and $B\left(E2\right)$ transition ratios are parameter independent. The energy spectra of the ground and first $\beta$ and $\gamma$ bands as well as the corresponding $B\left(E2\right)$ transitions, determined with Z(4)-sextic, are studied as function of the free parameter and presented in detail for the special cases. Numerical applications are done for the ${}^{128,130,132}\mathrm{Xe}$ and ${}^{192,194,196}\mathrm{Pt}$ isotopes, revealing a qualitative agreement with experiment and a phase transition in Xe isotopes.

The ground state of ${}^{16}\mathrm{O}$ is calculated by using a time-dependent density-matrix approach derived from a new truncation scheme of the Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy for reduced density matrices, where a three-body density matrix is approximated by an antisymmetrized product of two-body density matrices. The new scheme is compared with a simpler truncation scheme previously used for the calculation of the ground state of ${}^{16}\mathrm{O}$ where the three-body density matrix is neglected and only two-particle–two-hole elements of the two-body density matrix are considered. It is shown that the results obtained from the two truncation schemes agree well with the exact solution.

The proton density distribution of ${}^{206}\mathrm{Hg}$ is calculated in the framework of the Skyrme-Hartree-Fock approach with the SLy5, SLy5 + T, and SLy5 + ${\mathrm{T}}_w$ interactions. It is shown that the central density drops strongly with the SLy5 and SLy5 + T interactions due to the vacancy of the $3s_{1/2}$ orbital. This means that the density depression in the interior of the nucleus is not so much influenced by the tensor force of the SLy5 + T interaction. However, with the SLy5 + ${\mathrm{T}}_w$ interaction the bubble structure does not exist because the tensor force effect of this interaction leads to the inversion between the single-proton states $3s_{1/2}$ and $1h_{11/2}$ $(3s_{1/2}-1h_{11/2}$ inversion) so that the $3s_{1/2}$ state is fully occupied by protons. In addition, a detailed discussion on the antibubble effect from the pairing interaction is performed by using the Skyrme-Hartree-Fock-Bogoliubov approach. It is found that a proton bubble structure in ${}^{206}\mathrm{Hg}$ is unlikely to appear because of the paring correlation.

The proton-nucleus interaction at the 1–3 GeV energy range is studied by means of the newly developed Spallation Model with Cascade++ (SMC++). A mechanism consisting in Dynamic Clustering in a Nuclear Medium (DCNM) is suggested. This mechanism allows for high energy transfer to the target nucleus, fast energy dissipation, and formation of light charged particles (LCPs). Results of model simulation are compared to the broad set of experimental data. Significant improvement for p, d, t, and ${}^3\mathrm{He}$ double-differential cross section calculations is achieved when compared to traditional spallation models utilizing only binary collision and surface coalescence for LCP creation.

Background: Measurements of forward exclusive meson production at different squared four-momenta of the exchanged virtual photon, $Q^2$, and at different four-momentum transfer, $t$, can be used to probe QCD's transition from meson-nucleon degrees of freedom at long distances to quark-gluon degrees of freedom at short scales. Ratios of separated response functions in ${\pi }^{-}$ and ${\pi }^{+}$ electroproduction are particularly informative. The ratio for transverse photons may allow this transition to be more easily observed, while the ratio for longitudinal photons provides a crucial verification of the assumed pole dominance, needed for reliable extraction of the pion form factor from electroproduction data.

Purpose: We perform the first complete separation of the four unpolarized electromagnetic structure functions $L/T/LT/TT$ in forward, exclusive ${\pi }^{\pm }$ electroproduction on deuterium above the dominant resonances.

Method: Data were acquired with 2.6–5.2-GeV electron beams and the $\mathrm{HMS}+\mathrm{SOS}$ spectrometers in Jefferson Lab Hall C at central $Q^2$ values of 0.6, 1.0, and 1.6 ${\text{GeV}}^2$ at $W=1.95$ GeV, and $Q^2=2.45$ ${\text{GeV}}^2$ at $W=2.22$ GeV. There was significant coverage in $\varphi$ and $\epsilon$, which allowed separation of ${\sigma }_{L,T,LT,TT}$.

Results: ${\sigma }_L$ shows a clear signature of the pion pole, with a sharp rise at small $-t$. In contrast, ${\sigma }_T$ is much flatter versus $t$. The longitudinal/transverse ratios evolve with $Q^2$ and $t$ and at the highest $Q^2=2.45$ ${\text{GeV}}^2$ show a slight enhancement for ${\pi }^{-}$ production compared to ${\pi }^{+}$. The ${\pi }^{-}/{\pi }^{+}$ ratio for transverse photons exhibits only a small $Q^2$ dependence, following a nearly universal curve with $t$, with a steep transition to a value of about 0.25, consistent with $s$-channel quark knockout. The ${\sigma }_{TT}/{\sigma }_T$ ratio also drops rapidly with $Q^2$, qualitatively consistent with $s$-channel helicity conservation. The ${\pi }^{-}/{\pi }^{+}$ ratio for longitudinal photons indicates a small isoscalar contamination at $W=1.95$ GeV, consistent with what was observed in our earlier determination of the pion form factor at these kinematics.

Conclusions: The separated cross sections are compared to a variety of theoretical models, which generally describe ${\sigma }_L$ but have varying success with ${\sigma }_T$. Further theoretical input is required to provide a more profound insight into the relevant reaction mechanisms for longitudinal and transverse photons, such as whether the observed transverse ratio is indeed attributable to a transition from pion to quark knockout mechanisms and provide useful information regarding the twist-3 transversity generalized parton distribution, $H_T$.

Wave functions arising from a pairing Hamiltonian $E\left(0\right),$ i.e., one in which the interaction is only between $J=0^{+},T=1$ pairs, lead to magnetic dipole and Gamow-Teller (GT) transition rates that are much larger than those from an interaction $E\left(J_{\text{max}}\right)$ in which a proton and a neutron couple to $J=2j$. With realistic interactions the results are between the two extremes. In the course of this study we found that certain $M1$ and GT matrix elements vanish with $E\left(0\right)$. These are connected to seniority and reduced isospin selection rules. We also relate our results to the single $j$ scissors mode.

Background: The role of pre-equilibrium emission within the heavy-ion fusion process has not been fully characterized. An accurate description of this process is important for understanding the formation of the compound nucleus in fusion reactions.

Purpose: We develop a systematic description, based on experimental measurements, of the strength of the pre-equilibrium process in heavy-ion fusion reactions.

Method: With a view to study pre-equilibrium emission process, the excitation functions for some neutron emission channels occurring in the fusion of ${}^{12}\mathrm{C}$ with ${}^{128}\mathrm{Te}$ and ${}^{169}\mathrm{Tm}$, and of ${}^{16}\mathrm{O}$ with ${}^{159}\mathrm{Tb},{}^{169}\mathrm{Tm}$, and ${}^{181}\mathrm{Ta}$, respectively, have been measured at incident energies from near the Coulomb barrier to $\approx 7$ MeV/nucleon. The off-line $\gamma$-ray spectrometry–based activation technique has been used for the measurements of excitation functions. The measured excitation functions have been compared with theoretical predictions based on pure statistical model code pace4 and Geometry Dependent Hybrid (GDH)-based code alice-91. The strength of pre-equilibrium emission has also determined from comparison of the experimental excitation functions and the pace4 calculations.

Results: The measured excitation functions are satisfactorily reproduced by the pace4 calculations in the energy region up to the peak position. However, at relatively higher energies, the enhancement of experimental cross sections in the tail portion of excitation functions as compared to the theoretical predictions of code pace4 has been observed. The observed deviation may be attributed to the pre-equilibrium emission of particles during the thermalization of the compound nucleus. Further, alice-91 calculations which include PE emission satisfactorily reproduce the experimental data even at higher energies, indicating the significant contribution of pre-equilibrium emissions.

Conclusions: Analysis of data clearly indicates that pre-equilibrium emission is an important reaction mechanism even at low projectile energies where the compound nucleus reaction mechanism dominates, and pre-equilibrium fraction ‘$P_{FR}$ strongly depends on excitation energy available for surface nucleons in composite systems above the Coulomb barrier and the mass of the composite system.

The astrophysical factor of ${}^8\mathrm{B}{(p,\gamma )}^9\mathrm{C}$ at zero energy, $S_{18}\left(0\right)$, is determined by a three-body coupled-channels analysis of the transfer reaction ${}^8\mathrm{B}{(d,n)}^9\mathrm{C}$ at 14.4 MeV/nucleon. Effects of the breakup channels of $d$ and ${}^9\mathrm{C}$ are investigated with the continuum-discretized coupled-channels method. It is found that, in the initial and final channels, respectively, the transfer process through the breakup states of $d$ and ${}^9\mathrm{C}$, its interference with that through their ground states in particular, gives a large increase in the transfer cross section. The finite-range effects with respect to the proton-neutron relative coordinate are found to be about 20%. As a result of the present analysis, $S_{18}\left(0\right)=22\pm 6\mathrm{eV}\mathrm{b}$ is obtained, which is smaller than the result of the previous distorted-wave Born approximation analysis by about 51%.

Exclusive and kinematically complete measurements of the double pionic fusion to ${}^3\mathrm{He}$ have been performed in the energy region of the so-called ABC effect, which denotes a pronounced low-mass enhancement in the $\pi \pi$-invariant mass spectrum. The experiments were carried out with the WASA detector setup at COSY (the cooler synchrotron at Forschungszentrum Jülich). Similar to the observations in the basic $pn\to d{\pi }^0{\pi }^0$ reaction and in the $dd\to {}^4\mathrm{He}{\pi }^0{\pi }^0$ reaction, the data reveal a correlation between the ABC effect and a resonance-like energy dependence in the total cross section. Differential cross sections are well described by the hypothesis of $d^{*}$ resonance formation during the reaction process in addition to the conventional $t$-channel $\Delta \Delta$ mechanism. The deduced $d^{*}$ resonance width can be understood from collision broadening due to Fermi motion of the nucleons in initial and final nuclei.

Incoherent $\eta$ photoproduction on the deuteron is studied, with the main emphasis on the role of final-state interactions. In addition to the previously studied mechanisms of $NN$ and $\eta N$ rescatterings, the role of an intermediate pion exchange is considered in detail, where first a pion is photoproduced on one nucleon and then rescatters into an $\eta$ meson on the other, the spectator nucleon. It is found that the role of this pion-mediated contribution is comparable in size to that of $\eta N$ rescattering. Results for total and semi-inclusive differential cross sections and associated polarization observables are presented. In particular, polarization observables show significant sensitivity to final-state interactions.