Nuclear Density Functionals Research Articles

η mesons in hot and dense asymmetric nuclear matter

We study the $\eta N$ interactions in the hot and dense isospin asymmetric nuclear matter using two different approaches. In the first approach, the in-medium mass and optical potential of $\eta$-meson have been calculated in the chiral SU(3) model, considering the effect of explicit symmetry breaking term and range terms in the $\eta N$ interaction Lagrangian density. In the second scenario, the conjunction of chiral perturbation theory and chiral SU(3) model is employed. In this case, the next-to-leading order $\eta N$ interactions are evaluated from the chiral perturbation theory (ChPT), and the in-medium contribution of scalar densities are taken as input from chiral SU(3) model. We observe a larger negative mass-shift in the ChPT+chiral model approach compared to the chiral SU(3) model alone as a function of nuclear density. Moreover, the increase in the asymmetry and temperature cause a decrease in the magnitude of mass-shift. We have also studied the impact of $\eta N$ scattering length $a^{\eta N}$ on the $\eta$ meson mass $m^*_\eta$ and observed that the $m^*_\eta$ decrease more for increasing the value of scattering length.

Next-to-leading order QCD predictions for dijet photoproduction in lepton-nucleus scattering at the future EIC and at possible LHeC, HE-LHeC, and FCC facilities

We calculate cross sections for inclusive dijet photoproduction in electron-nucleus scattering in the kinematics of the future EIC and the possible LHeC, HE-LHeC, and the FCC using next-to-leading order (NLO) perturbative QCD and nCTEQ15 and EPPS16 nuclear parton density functions (nPDFs). We make predictions for distributions in the dijet average transverse momentum ${\bar p}_T$, the average rapidity $\bar{\eta}$, the observed nuclear momentum fraction $x_A^{\rm obs}$, and the observed photon momentum fraction $x_{\gamma}^{\rm obs}$. Comparing the kinematic reaches of the four colliders, we find that an increase of the collision energy from the EIC to the LHeC and beyond extends the coverage in all four considered variables. Notably, the LHeC and HE-LHeC will allow one to probe the dijet cross section down to $x_A^{\rm obs} \sim 10^{-4}$ (down to $x_A^{\rm obs} \sim 10^{-5}$ at the FCC). The ratio of the dijet cross sections on a nucleus and the proton, $\sigma_A/(A\sigma_p)$, depends on $x_A^{\rm obs}$ in a similar way as the ratio of gluon densities, $g_A(x_A,\mu^2)/[A g_p(x_A,\mu^2)]$, for which current nPDFs predict a strong suppression due to nuclear shadowing in the region $x_A^{\rm obs} < 0.01$. Dijet photoproduction at future lepton-nucleus colliders can therefore be used to test this prediction and considerably reduce the current uncertainties of nPDFs.

Impact of nuclear density on the mass splitting of the pseudoscalar D meson

We derive the D meson and nucleon interactions from the QCD sum rules. Unifying the chiral SU(3) model, we study the in-medium mass splitting between pseudoscalar D + and D − meson in the hot and dense magnetized nuclear matter. The medium modified quark and gluon condensates are evaluated from the chiral SU(3) model and further plugged into the QCD sum rules to compute the in-medium mass of pseudoscalar D meson. We find that the mass of both and meson increase with the medium density. We calculate the D meson mass in centroid approximation and compared it with the mass of D + and D − meson. By plugging the in-medium mass of D + and D − meson in the mass splitting formula, , we observe non-negligible splitting in the D + and D − mass which increases appreciably as a function of nuclear density. The medium modified mass evaluated in this work can be used as an application to study the decay width of higher charmonia states decaying into D + D − pairs.

Performance Audit of Carbon Emission Intensity in Chinese Inland and Coastal Areas

Su, H.W., 2020. Performance audit of carbon emission intensity in Chinese inland and coastal areas. In: Bai, X. and Zhou, H. (eds.), Advances in Water Resources, Environmental Protection, and Sustainable Development. Journal of Coastal Research, Special Issue No. 115, pp. 451-455. Coconut Creek (Florida), ISSN 0749-0208.Energy conservation and emission reduction have gradually changed from a secondary contradiction in the process of China's economic growth to a major contradiction. This study measures the carbon emission intensity of China's provinces over the period of 2005 to 2017. This paper uses the global Moran index, local Moran index, local LISA index and nuclear density function model to analyze the spatial correlation and coordination index of carbon emission intensity in various regions of China. The results finds that: (1) Chinese carbon emission intensity continued to decline, and the intensity of carbon emission of each economic zone is in descending order of southwest, eastern coast, northern coast, middle Yangtze River, southern coast, middle Yellow River, Northeast Comprehensive, Northwest. (2) The regional gap in China's carbon emissions intensity has gradually narrowed. The regional gap contribution has continued to increase during the observation period, and the intra-region gap contribution has continued to decline. There is a phenomenon of “convergence or club convergence” within the regional gap. (3) Chinese carbon emission intensity has a strong spatial autocorrelation among different regions. The carbon emission intensity of the regionally underdeveloped regions has a positive spatial correlation. The carbon emission intensity of the developed regions has a negative spatial correlation, but the spatial effect intensity. Both are weak. (4) The carbon emission intensity of the high-value area and the median area increased first and then decreased, and the gap between regions first narrowed and then expanded.

Properties of spherical and deformed nuclei using regularized pseudopotentials in nuclear DFT

We developed new parameterizations of local regularized finite-range pseudopotentials up to next-to-next-to-next-to-leading order (N3LO), used as generators of nuclear density functionals. When supplemented with zero-range spin–orbit and density-dependent terms, they provide a correct single-reference description of binding energies and radii of spherical and deformed nuclei. We compared the obtained results to experimental data and discussed benchmarks against the standard well-established Gogny D1S functional.

Abnormal odd-even staggering behavior around 132Sn studied by density functional theory * * Supported by National Natural Science Foundation of China (U1732138, 11505056, 11605054, 11975209, 11790325, 11947410, 11847315) and the Outstanding Young Talent Research Fund of Zhengzhou University (152137002)

In this work, we have performed Skyrme density functional theory (DFT) calculations of nuclei around 132Sn to study whether the abnormal odd-even staggering (OES) behavior of binding energies around N = 82 can be reproduced. With the Skyrme forces SLy4 and SkM*, we tested the volume- and surface-type pairing forces and also the intermediate between these two pairing forces, in the Hartree-Fock-Bogoliubov (HFB) approximation with or without the Lipkin-Nogami (LN) approximation or particle number projection after the convergence of HFBLN (PLN). The Universal Nuclear Energy Density Function (UNEDF) parameter sets are also used. The trend of the neutron OES against the neutron number or proton number does not change significantly by tuning the density dependence of the pairing force. Moreover, for the pairing force that is favored more at the nuclear surface, a larger mass OES is obtained, and vice versa. It appears that the combination of volume and surface pairing can give better agreement with the data. In the studies of the OES, a larger ratio of surface to volume pairing might be favored. Additionally, in most cases, the OES given by the HFBLN approximation agrees more closely with the experimental data. We found that both the Skyrme and pairing forces can influence the OES behavior. The mass OES calculated by the UNEDF DFT is explicitly smaller than the experimental one. The UNEDF1 and UNEDF2 forces can reproduce the experimental trend of the abnormal OES around 132Sn. The neutron OES of the tin isotopes given by the SkM* force agrees more closely with the experimental one than that given by the SLy4 force in most cases. Both SLy4 and SkM* DFT have difficulties in reproducing the abnormal OES around 132Sn. Using the PLN method, the systematics of OES are improved for several combinations of Skyrme and pairing forces.

Nuclear shadowing in DIS at electron-ion colliders

We present a revision of predictions for nuclear shadowing in deep-inelastic scattering at small Bjorken $x_{Bj}$ corresponding to kinematic regions accessible by the future experiments at electron-ion colliders. The nuclear shadowing is treated within the color dipole formalism based on the rigorous Green function technique. This allows incorporating naturally color transparency and coherence length effects, which are not consistently and properly included in present calculations. For the lowest $|q\bar q\rangle$ Fock component of the photon, our calculations are based on an exact numerical solution of the evolution equation for the Green function. Here the magnitude of shadowing is tested using a realistic form for the nuclear density function, as well as various phenomenological models for the dipole cross section. The corresponding variation of the transverse size of the $q\bar q$ photon fluctuations is important for $x_{Bj}\gtrsim 10^{-4}$, on the contrary with the most of other models, which use frequently only the eikonal approximation with the "frozen" transverse size. At $x_{Bj}\lesssim 0.01$ we calculate within the same formalism also a shadowing correction for the higher Fock component of the photon containing gluons. The corresponding magnitudes of gluon shadowing correction are compared adopting different phenomenological dipole models. Our results are tested by available data from the E665 and NMC collaborations. Finally, the magnitude of nuclear shadowing is predicted for various kinematic regions that should be scanned by the future experiments at electron-ion colliders.

Single- and two-nucleon antikaon absorption in nuclear matter with chiral meson-baryon interactions

We developed a microscopic model for antikaon absorption on two nucleons in nuclear matter. The absorption is described within a meson-exchange picture and the primary $K^-N$ interaction strength is derived from state-of-the-art chiral coupled channel meson-baryon interaction models. We took into account the medium modification of the $K^-N$ scattering amplitudes due to the Pauli correlations. We derived the $K^-NN$ as well as $K^-N$ optical potentials as functions of nuclear matter density including the real part of the $K^-NN$ potential. We calculated the $K^-$ single- and two-nucleon absorption fractions and branching ratios for various mesonic and non-mesonic channels. We confirmed the crucial role of in-medium effects in our calculations. Our results are in very good agreement with available experimental data from old bubble chamber experiments as well as with the latest results from the AMADEUS collaboration.

Examination of photon strength functions and nuclear level density in Pt196 from the γ -ray spectra measured at the DANCE facility

Background: The nuclear level density (NLD) and photon strength functions (PSFs) are necessary quantities for calculating the interaction of photons with nuclei, in particular the reaction cross sections. As such, they are important especially in nuclear astrophysics and in the development of advanced nuclear technologies.Purpose: The presence of a resonancelike structure in the $E1$ PSF at $\ensuremath{\gamma}$-ray energy of about 5.5 MeV was reported in $\ensuremath{\gamma}$-soft $A\ensuremath{\approx}200$ nuclei from several experimental techniques. However, as data from different experiments are not fully consistent, additional information on PSFs in this region is of great interest. In addition, present PSF models have difficulties to describe resonancelike structures for energies below the neutron separation energy ${S}_{n}$. There are also open questions about the energy and parity dependence of the NLD.Methods: The $\ensuremath{\gamma}$ rays following the radiative neutron capture on $^{195}\mathrm{Pt}\phantom{\rule{4pt}{0ex}}s$-wave resonances were measured with the highly segmented $\ensuremath{\gamma}$-ray calorimeter Detector for Advanced Neutron Capture Experiments at the Los Alamos Neutron Science Center. The $\ensuremath{\gamma}$-ray energy spectra for different multiplicities were gathered for several resonances of both possible spins.Results: The $\ensuremath{\gamma}$-ray energy spectra were analyzed within the statistical model and allowed us to get information about the NLD and PSFs in $^{196}\mathrm{Pt}$. Neither the PSFs from any previous experiment nor any available PSFs models are able to describe our spectra. We were able to find PSFs and NLD that reasonably describe experimental spectra and impose various restrictions on these quantities.Conclusions: The presence of a resonancelike structure in the $E1$ PSF at a $\ensuremath{\gamma}$-ray energy of about 5.6 MeV is confirmed. The constant temperature energy dependence is favored for a NLD with a significant parity dependence up to an excitation energy of at least 4 MeV. The preferred $M1$ PSF shape is close to a Lorentzian tail of the spin-flip resonance.

The Saturation properties of Nuclear Matter Using Different Three-Body Force at zero and finite temperature

We have used the three-body force (3BF) to modify the two body forces to achieve the empirical saturation points as well as study the ground state properties for symmetric nuclear matter using the Brueckner-Hartree-Fock approximation (BHF) with the Argonne AV18 potential at zero and finite temperature. Besides the energy per nucleon (E/A) as a function of nuclear density ρ is calculated. Further, the correction of the two-body dependent potential (correction 1) is added to shift and improve the saturation properties of the nuclear matter from ρ_o=0.265 〖fm〗^(-3) to ρ_o=0.149 〖fm〗^(-3) at E/A = -16.142 MeV towards to the empirical saturation point ρ_o=0.16 〖fm〗^(-3). In addition, the pressure p for symmetric nuclear matter for zero-temperature T=0 as a function of density ρ/ρ_o using the Argonne AV18 potential is calculated revealing good agreement between our calculations and the experimental data. On other hand, more calculations for the pressure are added at different energies T= 4, 8, 12, 18 and 20 MeV. Also, the level-density parameter as a function of density ρ is calculated for the BHF approach. Moreover, the internal energy F for the symmetric nuclear matter as a function of density ρ using the Argonne AV18 potential for continuous choice at T= 4, 8, 12, 18 and 20 MeV for the BHF with and without 3BF is calculated.

Energy-weighted sum rule for nuclear density functional theory

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.

Synthesis and Characterization of N,N,O-Tridentate Aminophenolate Zinc Complexes and Their Catalysis in the Ring-Opening Polymerization of Lactides.

A series of aminophenolate ligands with various pendant groups and associated ethyl Zn complexes were synthesized and studied as catalysts for the ring-opening polymerization (ROP) of lactides (LAs). The thiophenylmethyl group (L4ZnEt) increased the catalytic activity more than the benzyl group (L1ZnEt) did, and 2-fluorobenzyl (L3ZnEt) and 2-methoxybenzyl (L2ZnEt) groups had the opposite effect. In addition, the LA polymerization mechanism proved by Nuclear Magnetic Resonance and Density Function Theory was that LA was attracted by H···O bond of an α-hydrogen of the LA molecule and the phenoxyl oxygen of the catalyst. After the dissociation of amino group from the Zn atom, the benzyl alcohol initiated LA without replacing the ethyl group of Zn complex. It is the first case where the ethyl group is regarded as a ligand and cannot be replaced by benzyl alcohol, and this information is very important for the mechanism study of ROP.

A study of shell structure in normal to exotic nuclides within relativistic Hartree–Bogoliubov approximation

The purpose of this work is to study theoretically the shell structure of even–even isotopes in Si, S, Ar and Ca and isotones at neutron number N = 0, 28, 50 and 82. We employed Covariant Relativistic self-consistent mean field models analogous to Kohn–Sham density functional theory to construct the Nuclear Density Functionals from Lagrangian densities based on meson exchange and point coupling models. The pairing correlations of nucleons are considered by the relativistic Hartree–Bogoliubov functional based on quasi-particle operators of Bogoliubov transformations. The theoretical calculations of shell closure parameter [Formula: see text](N) and the differential variation of the two-neutron separation energy [Formula: see text](Z, N) provide recognizable signature of shell closure at N = 14 and 20 in case of Si, N = 14, 20 and 28 in S, Ar and Ca isotopes and are consistent with recent experimental investigations of new sub-shell gaps.

Nuclear parton density functions from dijet photoproduction at the EIC

We study the potential of dijet photoproduction measurements at a future electron-ion collider (EIC) to better constrain our present knowledge of the nuclear parton distribution functions. Based on theoretical calculations at next-to-leading order and approximate next-to-next-to-leading order of perturbative QCD, we establish the kinematic reaches for three different EIC designs, the size of the parton density function modifications for four different light and heavy nuclei from He-4 over C-12 and Fe-56 to Pb-208 with respect to the free proton, and the improvement of EIC measurements with respect to current determinations from deep-inelastic scattering and Drell-Yan data alone and when also considering data from existing hadron colliders.

Role of exact pairing in the description of nuclear level density and radiative strength function

An approach utilizing the microscopic pairing Hamiltonian is proposed to simultaneously describe the nuclear level density and radiative strength function, taking into account the thermal effects of the exact pairing as well as the giant resonances within the phonon-damping model. The good agreement between the results of calculations and experimental data extracted by the Oslo group for 170,171,172Yb isotopes demonstrates the importance of exact thermal pairing in the description of nuclear level densities at low and intermediate excitation energies and invalidates the assumption based on the Brink-Axel hypothesis in the description of the radiative strength functions.

Capture and photonuclear reaction rates involving charged-particles: Impacts of nuclear ingredients and future measurement on ELI-NP

The astrophysical p-process is an important way of nucleosynthesis to produce the stable and proton-rich nuclei beyond Fe which can not be reached by the s- and r-processes. In the present study, the impact of nuclear ingredients, especially the nuclear potential, level density and strength function, to the astrophysical re-action rates of (p,γ), (α,γ), (γ,p), and (γ,α) reactions are systematically studied. The calculations are performed basad on the modern reaction code TALYS for about 3000 stable and proton-rich nuclei with 12≤Z≤110. In particular, both of the Wood-Saxon potential and the microscopic folding potential are taken into account. It is found that both the capture and photonuclear reaction rates are very sensitive to the nuclear potential, thus the better determination of nuclear potential would be important to reduce the uncertainties of reaction rates. Meanwhile, the Extreme Light Infrastructure-Nuclear Physics (ELI-NP) facility is being developed, which will provide the great opportunity to experimentally study the photonuclear reactions in p-process. Simulations of the experimental setup for the measurements of the photonuclear reactions 96Ru(γ,p) and 96Ru(γ,α) are performed. It is shown that the experiments of photonuclear reactions in p-process based on ELI-NP are quite promising.

Global analysis of quadrupole shape invariants based on covariant energy density functionals

Coexistence of different geometric shapes at low energies presents a universal structure phenomenon that occurs over the entire chart of nuclides. Studies of the shape coexistence are important for understanding the microscopic origin of collectivity and modifications of shell structure in exotic nuclei far from stability. The aim of this work is to provide a systematic analysis of characteristic signatures of coexisting nuclear shapes in different mass regions, using a global self-consistent theoretical method based on universal energy density functionals and the quadrupole collective model. The low-energy excitation spectrum and quadrupole shape invariants of the two lowest $0^{+}$ states of even-even nuclei are obtained as solutions of a five-dimensional collective Hamiltonian (5DCH) model, with parameters determined by constrained self-consistent mean-field calculations based on the relativistic energy density functional PC-PK1, and a finite-range pairing interaction. The theoretical excitation energies of the states: $2^+_1$, $4^+_1$, $0^+_2$, $2^+_2$, $2^+_3$, as well as the $B(E2; 0^+_1\to 2^+_1)$ values, are in very good agreement with the corresponding experimental values for 621 even-even nuclei. Quadrupole shape invariants have been implemented to investigate shape coexistence, and the distribution of possible shape-coexisting nuclei is consistent with results obtained in recent theoretical studies and available data. The present analysis has shown that, when based on a universal and consistent microscopic framework of nuclear density functionals, shape invariants provide distinct indicators and reliable predictions for the occurrence of low-energy coexisting shapes. This method is particularly useful for studies of shape coexistence in regions far from stability where few data are available.

Nuclear parton density functions from jet production in DIS at an EIC

We investigate the potential of inclusive-jet production in deep-inelastic scattering (DIS) at a future Electron-Ion Collider (EIC) to improve our current knowledge of nuclear parton density functions (PDFs). We demonstrate that the kinematic reach is extended similarly to inclusive DIS, but that the uncertainty of the nuclear PDFs, in particular of the gluon density at low Bjorken-x, is considerably reduced, by up to an order of magnitude compared to the present situation. Using an approximate next-to-next-to-leading order (aNNLO) calculation implemented in the program JetViP, we also make predictions for three different EIC designs and for four different light and heavy nuclei.

From bare interactions, low-energy constants, and unitary gas to nuclear density functionals without free parameters: Application to neutron matter

We further progress along the line of Ref. [Phys. Rev. {\bf A 94}, 043614 (2016)] where a functional for Fermi systems with anomalously large $s$-wave scattering length $a_s$ was proposed that has no free parameters. The functional is designed to correctly reproduce the unitary limit in Fermi gases together with the leading-order contributions in the s- and p-wave channels at low density. The functional is shown to be predictive up to densities $\sim0.01$ fm$^{-3}$ that is much higher densities compared to the Lee-Yang functional, valid for $\rho < 10^{-6}$ fm$^{-3}$. The form of the functional retained in this work is further motivated. It is shown that the new functional corresponds to an expansion of the energy in $(a_s k_F)$ and $(r_e k_F)$ to all orders, where $r_e$ is the effective range and $k_F$ is the Fermi momentum. One conclusion from the present work is that, except in the extremely low--density regime, nuclear systems can be treated perturbatively in $-(a_s k_F)^{-1}$ with respect to the unitary limit. Starting from the functional, we introduce density--dependent scales and show that scales associated to the bare interaction are strongly renormalized by medium effects. As a consequence, some of the scales at play around saturation are dominated by the unitary gas properties and not directly to low-energy constants. For instance, we show that the scale in the s-wave channel around saturation is proportional to the so-called Bertsch parameter $\xi_0$ and becomes independent of $a_s$. We also point out that these scales are of the same order of magnitude than those empirically obtained in the Skyrme energy density functional. We finally propose a slight modification of the functional such that it becomes accurate up to the saturation density $\rho\simeq 0.16$ fm$^{-3}$.

Simultaneous Microscopic Description of Nuclear Level Density and Radiative Strength Function.

The nuclear level density (NLD) and radiative strength function (RSF) are simultaneously described within a microscopic approach, which takes into account the thermal effects of the exact pairing as well as the giant resonances within the phonon-damping model. The good agreement between the results of calculations and experimental data extracted by the Oslo group for ^{170,171,172}Yb isotopes shows the importance of exact thermal pairing in the description of NLD at low and intermediate excitation energies. It also invalidates the assumption based on the Brink-Axel hypothesis in the description of the RSF.