The expressions for the energy-weighted sum rule of the isoscalar and isovector coordinate operators are derived based on the second-order fluctuation of the local densities. Conventional derivation of the Thouless theorem for the energy-weighted sum rule is based on the double commutator of the Hamiltonian, while the present derivation does not assume a Hamiltonian operator and is applicable to nuclear energy density functionals. The expressions include the contribution of the local gauge symmetry breaking of the energy density functional. It is shown that the local gauge invariance of the kinetic and current densities and kinetic pair density is important, while all the other local densities do not contribute to the energy-weighted sum rule of the coordinate operators. The finite-amplitude method calculations are performed and the expressions for the energy-weighted sum rule are numerically examined for the isoscalar and isovector multipole operators up to $L=3$ for selected spherical and axially deformed nuclei.

Particle-decaying states of the light nuclei ${}^{11,12}\mathrm{N}$ and ${}^{12}\mathrm{O}$ were studied using the invariant-mass method. The decay energies and intrinsic widths of a number of states were measured, and the momentum correlations of three-body decaying states were considered. A second $2p$-decaying $2^{+}$ state of ${}^{12}\mathrm{O}$ was observed for the first time, and a higher-energy ${}^{12}\mathrm{O}$ state was observed in the $4p+2\alpha$ decay channel. This $4p+2\alpha$ channel also contains contributions from fissionlike decay paths, including ${}^6\mathrm{Be}_{\mathrm{g}.\mathrm{s}.}+{}^6\mathrm{Be}_{\mathrm{g}.\mathrm{s}.}$. Analogs to these states in ${}^{12}\mathrm{O}$ were found in ${}^{12}\mathrm{N}$ in the $2p+{}^{10}\mathrm{B}$ and $2p+\alpha +{}^6\mathrm{Li}$ channels. The momentum correlations for the prompt $2p$ decay of ${}^{12}\mathrm{O}_{\mathrm{g}.\mathrm{s}.}$ were found to be nearly identical to those of ${}^{16}\mathrm{Ne}_{\mathrm{g}.\mathrm{s}.}$, and the correlations for the new $2^{+}$ state were found to be consistent with sequential decay through excited states in ${}^{11}\mathrm{N}$. The momentum correlations for the $2_1^{+}$ state in ${}^{12}\mathrm{O}$ provide a new value for the ${}^{11}\mathrm{N}$ ground-state energy. The states in ${}^{12}\mathrm{N}/{}^{12}\mathrm{O}$ that belong to the $A=12$ isobaric sextet do not deviate from the quadratic isobaric multiplet mass equation form.

Background: The radiative neutron capture reaction rates of the r-process nucleosynthesis are immensely affected by the microscopic structure of the low-energy spectra of compound nuclei. The relativistic (quasiparticle) time-blocking approximation has successfully provided a good description of the low-energy strength, in particular, the strength associated with pygmy dipole resonance, describing transitions from and to the nuclear ground state. The finite-temperature generalization of this method is designed for thermally excited compound nuclei and has the potential to enrich the fine structure of the dipole strength, especially in the low-energy region.

Purpose: To formulate the thermal extension of RTBA, i.e., finite-temperature relativistic time-blocking approximation (FT-RTBA) for the nuclear response, and to implement it numerically for calculations of the dipole strength in medium-light and medium-heavy nuclei.

Methods: The FT-RTBA equations are derived using the Matsubara Green's function formalism. We show that with the help of a temperature-dependent projection operator on the subspace of the imaginary time it is possible to reduce the Bethe-Salpeter equation for the nuclear response function to a single frequency variable equation also at finite temperatures. The approach is implemented self-consistently in the framework of quantum hadrodynamics and keeps the ability of connecting the high-energy scale of heavy mesons and the low-energy domain of nuclear medium polarization effects in a parameter-free way.

Results: The method was applied to the medium-light ${}^{48}\mathrm{Ca}, {}^{68}\mathrm{Ni}$, and to the medium-heavy ${}^{100,120,132}\mathrm{Sn}$ nuclei. The excitation energies $E^{*}$ of the considered compound nuclei were calculated and found to increase quickly starting from temperatures $0.5\le T\le 1.0$ MeV. The nucleonic single-particle energies and occupancies change accordingly because of the increasing diffuseness of the Fermi-Dirac distribution with the temperature increase. The dipole response of these nuclei was computed in the FT-RTBA and compared to the finite-temperature relativistic random-phase approximation (RPA). It was found that the giant dipole resonance (GDR) undergoes additional fragmentation (i) due to the thermal unblocking of the transitions between single-particle states located on the same side of the Fermi surface and (ii) because of the general reinforcement of the particle-vibration coupling with the temperature growth. The low-energy part of the dipole strength distribution is moderately enhanced at temperatures $T\le 4.0$ MeV and increases dramatically above this temperature range. The width of the strength distribution grows rapidly with temperature at $T\ge 1.0$ MeV. The energy-weighted sum rule in a wide finite-energy interval remains nearly flat as the temperature increases. The traditional view of the pygmy dipole resonance (PDR) as an oscillation of the weakly bound neutron excess against the isospin-saturated core is nearly maintained up to the temperature $T=5.0$ MeV and changes to the GDR-like pattern above this temperature. The collective behavior of the PDR disappears in the range of temperatures $1.0\le T\le 5.0$ MeV and restores beyond this range which might be, however, already beyond the limit of existence of the nuclei.

Conclusions: We present a consistent microscopic theory and a numerically stable and executable calculation scheme for computing the nuclear response at finite temperature taking into account the PVC spreading mechanism, in addition to the Landau damping. The presented calculations of the dipole response within a self-consistent relativistic framework reveal that, although the Landau damping plays the leading role in the temperature evolution of the strength distribution, (i) at moderate temperatures the PVC effects remain almost as strong as at $T=0$ and (ii) at high temperatures they are tremendously reinforced because of the formation of the new collective low-energy modes. In the dipole channel, the latter effect is responsible for the “disappearance” of the high-frequency GDR or, in other words, brings the GDR to the low-energy domain.

Background: The low-lying electric dipole strength provides insights into the parameters of the nuclear equation of state via its connection with the pygmy dipole resonance and nuclear neutron skin thickness.

Purpose: The aim was to complement the systematic of the pygmy dipole resonance and first study its behavior across the $N=28$ neutron shell closure.

Methods: Photon-scattering cross sections of states of ${}^{50,54}\mathrm{Cr}$ were measured up to an excitation energy of 9.7 MeV via the nuclear resonance fluorescence method using $\gamma$-ray beams from bremsstrahlung and Compton backscattering.

Results: Transitions strengths, spin and parity quantum number, and average branching ratios for 55 excited states, 44 of which were observed for the first time, were determined. The comparison between the total observed strengths of the isotopes ${}^{50,52,54}\mathrm{Cr}$ shows a significant increase above the shell closure.

Conclusions: The evolution of the pygmy dipole resonance is heavily influenced by the shell structure.

A systematic study was performed of microsecond $\gamma$-decaying isomers around ${}^{100}\mathrm{Sn}$ produced in a fragmentation reaction of a ${}^{124}\mathrm{Xe}$ beam at 345 MeV/u at the Radioactive Ion Beam Factory of the RIKEN Nishina Center in Saitama, Japan. Half-lives of isomeric states in that region were remeasured allowing us to improve the currently available experimental information. Reduced transition probabilities were deduced and compared to shell-model calculations in various model spaces. The recently reported low-energy transitions in ${}^{92}\mathrm{Rh}$ and ${}^{96}\mathrm{Ag}$ were remeasured with improved precision. Additionally, experimental information on isomeric ratios, including five new ones, were extracted and compared to a previous experimental study and the sharp cutoff model of fragmentation reaction.

Properties of the relativistic nucleon self-energy decomposition of the symmetry energy as well as the equation of state (EOS) of pure neutron matter (PNM) are explored systematically within the QCD sum rules (QCDSR). Our main conclusions are as follows: (1) The five self-energy decomposition terms of the symmetry energy according to the nucleon Lorentz structure are carefully studied, leading to the conclusion that the symmetry energy increases as the nucleon sigma term ${\sigma }_{\mathrm{N}}$ increases and the contributions to the symmetry energy due to the momentum dependence of the self-energies in symmetric nuclear matter (SNM) are very small compared with those from other decomposition terms. (2) A smaller strange quark mass is found to generate a larger symmetry energy, and this correlation is useful for understanding the origins of the uncertainties on the (nucleonic matter) symmetry energy from quark level. (3) The EOS of PNM at low densities can be effectively approximated by $E_{\mathrm{n}}\left(\rho \right)\approx E_{\mathrm{n}}^{\mathrm{FFG}}\left(\rho \right)+(M\rho /2{\langle \overline{q}q\rangle }_{\mathrm{vac}})[(1-\xi )({\sigma }_{\mathrm{N}}/2m_{\mathrm{q}})-5]$ which depends only on several physical quantities such as $m_{\mathrm{q}},{\sigma }_{\mathrm{N}}$ and ${\langle \overline{q}q\rangle }_{\mathrm{vac}}$, and this formula already has predictive power and the results are found to be consistent with those from other celebrated microscopic many-body theories at low densities. (4) The higher order density terms in quark condensates are shown to be important to describe the empirical EOS of PNM in the density region around and above nuclear saturation density, and these higher order density terms are also found to hinder the appearance of chiral symmetry restoration in PNM at high densities. (5) The symmetry energy is shown to depend strongly on the five-dimensional condensate ${\langle g_{\mathrm{s}}{q}^{†}\sigma \mathcal{G}q\rangle }_{\rho ,\delta }$, providing a useful approach to explore the symmetry energy through knowledge on the condensates which can be extracted from hadronic physics. (6) The twist-4 four-quark condensates are shown to have significant effects on the EOS of both SNM and PNM but have minor effects on the symmetry energy, and combined with the analyses on the effects of the higher order density terms in the chiral condensates, three parameter sets of QCDSR are constructed and they are shown to be able to describe the EOS of PNM and the symmetry energy within a wide range of densities. Our results in the present work demonstrate that the QCDSR approach can provide a useful way to understand the properties of dense nucleonic matter from nonperturbative QCD vacuum.

Background: The production of ${}^7\mathrm{Be}$ and ${}^7\mathrm{Li}$ nuclei plays an important role in primordial nucleosynthesis, nuclear astrophysics, and fusion energy generation. The ${}^3\mathrm{He}(\alpha ,\gamma ){}^7\mathrm{Be}$ and ${}^3\mathrm{H}(\alpha ,\gamma ){}^7\mathrm{Li}$ radiative-capture processes are important to determine the ${}^7\mathrm{Li}$ abundance in the early universe and to predict the correct fraction of $pp$-chain branches resulting in ${}^7\mathrm{Be}$ versus ${}^8\mathrm{B}$ neutrinos. The ${}^6\mathrm{Li}(p,\gamma ){}^7\mathrm{Be}$ has been investigated recently hinting at a possible cross section enhacement near the thershold. The ${}^6\mathrm{Li}(n,{}^3\mathrm{H}){}^4\mathrm{He}$ process can be utilized for tritium breeding in machines dedicated to fusion energy generation through the deuteron-tritium reaction, and is a neutron cross section standard used in the measurement and evaluation of fission cross sections.

Purpose: In this work we study the properties of ${}^7\mathrm{Be}$ and ${}^7\mathrm{Li}$ within the no-core shell model with continuum (NCSMC) method, using chiral nucleon-nucleon interactions as the only input, and analyze all the binary mass partitions involved in the formation of these systems.

Methods: The NCSMC is an ab initio method applicable to light nuclei that provides a unified description of bound and scattering states and thus is well suited to investigate systems with many resonances and pronounced clustering like ${}^7\mathrm{Be}$ and ${}^7\mathrm{Li}$.

Results: Our calculations reproduce all the experimentally known states of the two systems and provide predictions for several new resonances of both parities. Some of these new possible resonances are built on the ground states of ${}^6\mathrm{Li}$ and ${}^6\mathrm{He}$, and thus represent a robust prediction. We do not find any resonance in the $p+{}^6\mathrm{Li}$ mass partition near the threshold. On the other hand, in the $p+{}^6\mathrm{He}$ mass partition of ${}^7\mathrm{Li}$ we observe an $S$-wave resonance near the threshold producing a very pronounced peak in the calculated $S$ factor of the ${}^6\mathrm{He}(p,\gamma ){}^7\mathrm{Li}$ radiative-capture reaction.

Conclusions: While we do not find a resonance near the thershold in the $p+{}^6\mathrm{Li}$ channel, in the case of ${}^6\mathrm{He}+p$ reaction a resonant $S$-wave state is predicted at a very low energy above the reaction threshold, which could be relevant for astrophysics and its implications should be investigated. We note though that this state lies above the three-body breakup threshold not included in our method and may be influenced by three-body continuum correlations.

The Oslo method has been applied to particle-$\gamma$ coincidences following the ${}^{239}\mathrm{Pu}(d,p)$ reaction to obtain the nuclear level density (NLD) and $\gamma$-ray strength function ($\gamma \mathrm{SF}$) of ${}^{240}\mathrm{Pu}$. The experiment was conducted with a 12 MeV deuteron beam at the Oslo Cyclotron Laboratory. The low spin transfer of this reaction leads to a spin-parity mismatch between populated and intrinsic levels. This is a challenge for the Oslo method as it can have a significant impact on the extracted NLD and $\gamma \mathrm{SF}$. We have developed an iterative approach to ensure consistent results even for cases with a large spin-parity mismatch, in which we couple Green's function transfer calculations of the spin-parity dependent population cross section to the nuclear decay code rainier. The resulting $\gamma \mathrm{SF}$ shows a pronounced enhancement between 2–4 MeV that is consistent with the location of the low-energy orbital $M1$ scissors mode.

The possibility of application of the dinuclear system model to the simultaneous description of $\alpha$ decay, cluster radioactivity, and spontaneous fission is discussed. The half-lives of cluster decay and spontaneous fission for the nuclei ${}^{232,234,236}\mathrm{U}, {}^{236,238}\mathrm{Pu}, {}^{242}\mathrm{Cm}$, and ${}^{248}\mathrm{Cf}$ are calculated within the same approach and compared with existing experimental data. The cluster radioactivity in the ${}^{248}\mathrm{Cf}$ nucleus is predicted.

A dynamical calculation of pentaquark systems with quark contents $uudd\overline{s}$ is performed in the framework of a quark delocalization color screening model with the help of the resonating group method. The effective potentials between baryon and meson clusters are given, and the possible bound states or resonances are investigated. The single calculations show that the $N{K}^{*}$ with $I=0,J^P={\frac{1}{2}}^{-},\mathrm{\Delta }{K}^{*}$ with $I=1,J^P={\frac{1}{2}}^{-}$, and $\mathrm{\Delta }{K}^{*}$ with $I=2,J^P={\frac{3}{2}}^{-}$ are all bound, but they all turn into scattering states by coupling with the corresponding open channels. A possible resonance state $\mathrm{\Delta }{K}^{*}$ with $I=1,J^P={\frac{5}{2}}^{-}$ is proposed. The mass is around 2110.5 MeV, and the decay modes are $NK$ in $D$ wave and $NK\pi \pi$ in $P$ waves.

The Ginzburg-Landau (GL) effective theory is a useful tool to study a superconductivity or superfluidity near the critical temperature, and usually the expansion up to the fourth-order in terms of order parameters is sufficient for the description of the second-order phase transition. In this paper, we discuss the GL equation for the neutron ${}^{3}P_2$ superfluidity relevant for interior of neutron stars. We derive the GL expansion up to the eighth order in the condensates and find that this order is necessary for the system to have the unique ground state, unlike the ordinary cases. Starting from the $LS$ potential, which provides the dominant attraction between two neutrons at the high density, we derive the GL equation in the path-integral formalism, where the auxiliary field method and the Nambu-Gor'kov representation are used. We present the detailed description for the trace calculation necessary in the derivation of the GL equation. As numerical results, we show the phase diagram of the neutron ${}^{3}P_2$ superfluidity on the plane spanned by the temperature and magnetic field, and we find that the eighth-order terms lead to a first-order phase transition, whose existence was predicted in the Bogoliubov-de Gennes equation but has not been found thus far within the framework of the GL expansion up to the sixth order. The first-order phase transition will affect the interior structures inside the neutron stars.

Lifetimes of $2_1^{+}$ and $4_1^{+}$ states as well as some negative-parity and nonyrast states in ${}^{188–200}\mathrm{Hg}$ were measured using $\gamma -\gamma$ electronic fast timing techniques with the ${\mathrm{LaBr}}_3\left(\mathrm{Ce}\right)$ detector array of the GRIFFIN spectrometer. The excited states were populated in the $\epsilon /{\beta }^{+}$ decay of $J^{\pi }=7^{+}/2^{-}{}^{188–200}\mathrm{Tl}$ produced at the TRIUMF-ISAC facility. The deduced $B\left(E2\right)$ values are compared to different interacting boson model predictions. The precision achieved in this paper over previous ones allows for a meaningful comparison with the different theoretical models of these transitional Hg isotopes, which confirms the onset of state mixing in ${}^{190}\mathrm{Hg}$.

A systematic study of the thermal-photon thermometer is presented for heavy-ion collisions at intermediate energies via the isospin-dependent quantum molecular dynamics model. We find that the duration of the thermal hard photons production is more than $500\mathrm{fm}/c$. The divergence between the initial temperature and the final measurement temperature is about 5%. The isospin dependence of the nuclear temperature is consistent between the initial temperature and the final measurement temperature. As a comparison, the slope and double-isotope ratio thermometers are also discussed.

The analyzing powers ${}^{T}T_{10},{}^{T}T_{20}$, and ${}^{T}T_{30}$ for the ${}^{12}\mathrm{C}({}^7\mathrm{Li},t$) reaction were measured and combined with new and previously determined angular distributions to probe the role of multistep processes through coupled channel Born approximation (CCBA) calculations employing new $\alpha$-particle spectroscopic amplitudes calculated with the phenomenological shell model in the unrestricted $psd$ space. Good descriptions of the cross-section angular distributions could be obtained except for the larger angles for the 6.05 MeV $0^{+}$ and 6.13 MeV $3^{-}$ states, while the analyzing powers were not generally described. The calculations presented demonstrate the sensitivity of the angular distributions of both the differential cross sections and the analyzing powers to various multistep routes. While the measured analyzing power ${}^{T}T_{30}$ is roughly zero for all states, the various CCBA calculations produced large and highly oscillatory values for this observable, showing that other multistep processes must be present beyond those taken into account in this work. Standard distorted wave Born approximation (DWBA) calculations were also carried out and these show considerable differences from the CCBA results but the description of the analyzing powers, while slightly improved, is still poor.

We investigate theoretically production cross sections of the $J^{\pi }=0^{+}$ ground state of a ${}_{\mathrm{\Lambda }}{}^4\mathrm{He}$ hypernucleus in the ${}^4\mathrm{He}(\pi , K$) reaction with a distorted-wave impulse approximation using the optimal Fermi-averaged $\pi N\to K\mathrm{\Lambda }t$ matrix. We demonstrate the sensitivity of the production cross sections to the $\mathrm{\Lambda }$ wave functions obtained from $3N-\mathrm{\Lambda }$ potentials and to meson distorted waves in eikonal distortions. It is shown that the calculated laboratory cross sections of the $0^{+}$ ground state in ${}_{\mathrm{\Lambda }}{}^4\mathrm{He}$ amount to ${(d\sigma /d\mathrm{\Omega })}_{\mathrm{lab}}\simeq 11\mu \mathrm{b}/\mathrm{sr}$ at $p_{\pi }=1.05\mathrm{GeV}/c$ in the $K$ forward direction because of an advantage of the use of an $s$-shell target nucleus such as ${}^4\mathrm{He}$. The importance of the recoil effects and the energy dependence of the $\pi N\to K\mathrm{\Lambda }$ cross sections is also discussed.

In recent years the understanding of the limits of the smallest possible droplet of the quark gluon plasma has been called into question. Experimental results from both the Large Hadron Collider and the Relativistic Heavy Ion Collider have provided hints that the quark gluon plasma may be produced in systems as small as that formed in $p\mathrm{Pb}$ or $d\mathrm{Au}$ collisions. Yet alternative explanations still exist from correlations arising from quarks and gluons in a color glass condensate picture. In order to resolve these two scenarios, a system-size scan has been proposed at the Large Hadron Collider for collisions of ArAr and OO. Here we make predictions for a possible future run of ArAr and OO collisions at the Large Hadron Collider and study the system-size dependence of a variety of flow observables. We find that linear response (from the initial conditions to the final flow harmonics) becomes more dominant in smaller systems, whereas the $\text{linear}+\text{cubic}$ response can accurately predict multiparticle cumulants for a wide range of centralities in large systems.

In this paper, we implement the use of a $\pi N\mathrm{\Delta }$(1232) vertex interaction containing both first- and second-order derivative terms, as required by renormalization and power-counting considerations. As was previously shown, both interactions present quantization shortcomings but can be used in a pertubative calculation. Our results indicate that the usual $\pi$ derivative plus the spin-3/2 gauge invariant (derivative also in the $\mathrm{\Delta }$ field) should be included in amplitude calculations, as also all higher derivative interactions respecting chiral invariance. We show that both interactions make essentially the same resonant contribution to the elastic ${\pi }^{+}p$ cross section, so changing the ratio between both coupling constants amounts to a correction of the background. The elastic ${\pi }^{+}p$ cross section up to 300 MeV changes only mildly when that ratio is changed, but the total ${\pi }^{-}p$ scattering, which has poor fit within both interactions separately, can be much improved in the same energy range by tuning the ratio between both coupling constants.

An investigation of the calculated $\alpha$-decay half-lives of super heavy nuclei (SHN) reveals that the diffuseness parameter is a great bottleneck for achieving accurate results and predictions. In particular, when universal proximity function is adopted for nuclear potential, half-life is found to vary significantly and nonlinearly as a function of diffuseness parameter. To overcome this limiting hurdle, a new semiempirical formula for diffuseness that is dependent on charge and neutron numbers is proposed in this work. With the model at hand, half-lives of 218 SHN are computed, for 68 of which there exists available experimental data and 150 of which are predicted. The calculations of half-lives for 68 SHN are compared against experimental data and the calculated data obtained by using deformed Woods-Saxon, deformed Coulomb potentials model, and six semiempirical formulas. The predictions of 150 SHN are compared against the predictions of seven of the current best semiempirical formulas. Calculations of the present study are in good agreement with the experimental half-lives outperforming all but ImSahu semiempirical formula. Moreover, the predictions of our model are consistent with predictions of the semiempirical formulas. We strongly conclude that more attention should be directed toward obtaining accurate diffuseness parameter values for using it in nuclear calculations.

The elastic scattering of the weakly bound radioactive nuclei ${}^8\mathrm{B}$ and ${}^7\mathrm{Be}$ from a ${}^{208}\mathrm{Pb}$ target was measured for the first time in the energy range around the Coulomb barrier. The data were analyzed using the optical model and the continuum discretized coupled channels (CDCC) formalisms. The reaction cross sections extracted from the optical model fits clearly indicate a remarkably enhanced reaction probability for the very weakly bound ${}^8\mathrm{B}$ ($S_p=137.5\mathrm{keV}$) compared to similar mass nuclei interacting with the same target nucleus. CDCC calculations assuming a ${}^3\mathrm{He}+{}^4\mathrm{He}$ cluster model well described the ${}^7\mathrm{Be}$ experimental elastic scattering angular distributions, whereas the use of a ${}^7\mathrm{Be}+p$ cluster model of ${}^8\mathrm{B}$ with an inert ${}^7\mathrm{Be}$ core gave a relatively poor description of the corresponding experimental data, suggesting that this model may be too simplistic and the possibility of core excitation should not be ignored.

With the imminent construction of an electron-ion collider in the USA, both saturation physics and nuclear shadowing physics will be important for the same processes for the first time, particularly for the exclusive production of vector mesons, such as the $J/\mathrm{\Psi }$. In this paper we investigate the underlying assumptions commonly made when phenomenologically investigating this process from a shadowing and saturation perspective. We use the bSat model which is commonly used to describe saturation physics, and a calculation by Ryskin which is commonly used when describing nuclear shadowing at leading twist. It is expected that the bSat model is equivalent to Ryskin's result in the hard-scattering and nonrelativistic limits. By explicitly taking these limits we show that the bSat model does indeed become equivalent to Ryskin's result. However, two more approximations are needed for this result. First, the factorization and renormalization scales in the bSat model have to be independent of the dipole radius, and second, we need to omit a term in the overlap between the vector meson and virtual photon wave functions. We show that for the typical dipole radius of the $J/\mathrm{\Psi }$, the different approximations offset each other and the bSat model agrees very well with Ryskin's calculation in hard-scattering and nonrelativistic limits.