In Press

Display Method:         

Activation cross-sections of titanium isotopes at neutron energies of 13.5–14.8 MeV
Fengqun Zhou, Yueli Song, Yong Li, Xiaojun Sun, Shuqing Yuan
Published: , doi: 10.1088/1674-1137/43/9/094001
The cross-sections for 46Ti(n,2n)45Ti, 46Ti(n,p)46m+gSc+47Ti(n,d*)46m+gSc, 46Ti(n,p)46m+gSc, 47Ti(n,p)47Sc+48Ti(n,d*)47Sc, 47Ti(n,p)47Sc, 48Ti(n,p)48Sc+49Ti(n,d*)48Sc,48Ti(n,p)48Sc, and 50Ti(n,α)47Ca reactions were investigated around neutron energies of 13.5–14.8 MeV by means of the activation technique. Fast neutrons were produced by the 3H(d,n)4He reaction. Neutron energies from different directions in the measurements were obtained in advance using the method of cross-section ratios for 90Zr(n,2n)89m+gZr and 93Nb(n,2n)92mNb reactions. The results obtained are analyzed and compared with the experimental data provided by the literature and verified nuclear data in the JEFF-3.3, CENDL-3.1, ENDF/B-VIII.0 libraries, as well as results calculated by Talys-1.9 code.
Novel theoretical constraints for color-octet scalar models
Li Cheng, Otto Eberhardt, Christopher W. Murphy
Published: , doi: 10.1088/1674-1137/43/9/093101
We study the theoretical constraints on a model whose scalar sector contains one color octet and one or two color singlet SU(2)L doublets. To ensure unitarity of the theory, we constrain the parameters of the scalar potential for the first time at the next-to-leading order in perturbation theory. Moreover, we derive new conditions guaranteeing the stability of the potential. We employ the HEPfit package to extract viable parameter regions at the electroweak scale and test the stability of the renormalization group evolution up to the multi-TeV region. Furthermore, we set upper limits on the scalar mass splittings. All results are given for both cases with and without a second scalar color singlet.
Anisotropic evolution of 4-brane in a 6D generalized Randall-Sundrum model
Guang-Zhen Kang, De-Sheng Zhang, Long Du, Jun Xu, Hong-Shi Zong
Published: , doi: 10.1088/1674-1137/43/9/095101
We investigate a 6D generalized Randall-Sundrum brane world scenario with a bulk cosmological constant. Each stress-energy tensor $ T_{ab}^{i} $ on the brane is shown to be similar to a constant vacuum energy. This is consistent with the Randall-Sundrum model, in which each 3-brane Lagrangian yielded a constant vacuum energy. By adopting an anisotropic metric ansatz, we obtain the 5D Friedmann-Robertson-Walker field equations. In a slightly later period, the expansion of the universe is proportional to the square root of time, $ t^{\frac{1}{2}} $, which is similar to the period of the radiation-dominated regime. Moreover, we investigate the case with two $ a(t) $ and two $ b(t) $. In a large range of $ t $, we obtain the 3D effective cosmological constant $ \Lambda_{\rm eff} = -2\Omega/3>0 $, which is independent of the integral constant. Here, the scale factor is an exponential expansion, which is consistent with our present observation of the universe. Our results demonstrate that it is possible to construct a model that solves the dark energy problem, while guaranteeing a positive brane tension.
Tin-accompanied and true ternary fission of 242Pu
M. Zadehrafi, M. R. Pahlavani, M. -R. Ioan
Published: , doi: 10.1088/1674-1137/43/9/094101
True ternary fission and Tin-accompanied ternary fission of 242Pu are studied by using the 'Three Cluster Model'. True ternary fission is considered as a formation of heavy fragments in the region $ 28\leqslant Z_1,Z_2,Z_3\leqslant 38 $ with comparable masses. The possible fission channels are predicted by the potential-energy calculations. Interaction potentials, Q-values and relative yields for all possible fragmentations in equatorial and collinear configurations are calculated and compared. It is found that ternary fission with formation of a double magic nucleus like $ ^{132}{\rm Sn} $ is more probable than the other fragmentations. Also, the kinetic energies of the fragments for the group $ Z_1 = 32 $, $ Z_2 = 32 $ and $ Z_3 = 30 $ are calculated for all combinations in the collinear geometry as a sequential decay.
On the possibility to determine neutrino mass hierarchy via supernova neutrinos with short-time characteristics
Junji Jia, Yaoguang Wang, Shun Zhou
Published: , doi: 10.1088/1674-1137/43/9/095102
In this paper, we investigate whether it is possible to determine the neutrino mass hierarchy via a high-statistics and real-time observation of supernova neutrinos with short-time characteristics. The essential idea is to utilize distinct times-of-flight for different neutrino mass eigenstates from a core-collapse supernova to the Earth, which may significantly change the time distribution of neutrino events in the future huge water-Cherenkov and liquid-scintillator detectors. For illustration, we consider two different scenarios. The first case is the neutronization burst of $ \nu^{}_e$ emitted in the first tens of milliseconds of a core-collapse supernova, while the second case is the black hole formation during the accretion phase for which neutrino signals are expected to be abruptly terminated. In the latter scenario, it turns out only when the supernova is at a distance of a few Mpc and the fiducial mass of the detector is at the level of gigaton, might we be able to discriminate between normal and inverted neutrino mass hierarchies. In the former scenario, the probability for such a discrimination is even less due to a poor statistics.
Applicability of 9Be global optical potential to reactions of 7,10,11,12Be
Yong-Li Xu, Yin-Lu Han, Hai-Ying Liang, Zhen-Dong Wu, Hai-Rui Guo, Chong-Hai Cai
Published: , doi: 10.1088/1674-1137/43/9/094102
Elastic scattering angular distributions and total reaction cross-sections of 7,10,11,12Be projectiles are predicted by the systematic 9Be global phenomenological optical model potential for target mass numbers ranging from 24 to 209. These predictions provide a detailed analysis by their comparison with the available experimental data. Furthermore, these elastic scattering observables are also predicted for some targets out of the mass number range. The results are in reasonable agreement with the existing experimental data, and they are presented in this study.
Nearby dark matter subhalo that accounts for the DAMPE excess
Yi Zhao, Xiao-Jun Bi, Su-Jie Lin, Peng-Fei Yin
Published: , doi: 10.1088/1674-1137/43/8/085101
The precise spectrum of electrons and positrons at high energies plays an important role in understanding their origin. DArk Matter Particle Explorer has reported their first measurement of the $e^+e^- $ spectrum from 25 GeV to 4.6 TeV. This spectrum reveals a tentative peak at ~1.4 TeV, which requires a nearby source of $e^+e^- $. In this work, we study the properties of a large nearby dark matter subhalo that accouns for this spectral peak, such as its mass and distance from Earth, for different concentration models. We compare spectra of the sources in 3FGL with that from DM annihilation in the subhalo, and find ten candidates that have comparable gamma-ray spectra. However, according to the N-body simulation, the probability that such a large subhalo is close enough to Earth is less than 0.1%.
The Buchdahl stability bound in Eddington-inspired Born-Infeld gravity
Wei-Xiang Feng, Chao-Qiang Geng, Ling-Wei Luo
Published: , doi: 10.1088/1674-1137/43/8/083107
We give the Buchdahl stability bound in Eddington-inspired Born-Infeld (EiBI) gravity. We show that this bound depends on an energy condition controlled by the model parameter $\kappa$. From this bound, we can constrain $\kappa\lesssim 10^{8}\;{\rm{m}}^2$ if a neutron star with a mass around $3M_{\odot}$ is observed in the future. In addition, to avoid the potential pathologies in EiBI, a Hagedorn-like equation of state associated with $\kappa$ at the center of a compact star is inevitable, which is similar to the Hagedorn temperature in string theory.
Evidence for the decays of ${{\Lambda^+_{c}\to\Sigma^+\eta}}$ and $ {{\Sigma^+\eta^\prime}}$
M. Ablikim, M. N. Achasov, S. Ahmed, M. Albrecht, M. Alekseev, A. Amoroso, F. F. An, Q. An, Y. Bai, O. Bakina, R. Baldini Ferroli, Y. Ban, K. Begzsuren, D. W. Bennett, J. V. Bennett, N. Berger, M. Bertani, D. Bettoni, F. Bianchi, I. Boyko, R. A. Briere, H. Cai, X. Cai, O. Cakir, A. Calcaterra, G. F. Cao, S. A. Cetin, J. Chai, J. F. Chang, W. L. Chang, G. Chelkov, G. Chen, H. S. Chen, J. C. Chen, M. L. Chen, P. L. Chen, S. J. Chen, Y. B. Chen, W. Cheng, G. Cibinetto, F. Cossio, H. L. Dai, J. P. Dai, A. Dbeyssi, D. Dedovich, Z. Y. Deng, A. Denig, I. Denysenko, M. Destefanis, F. De Mori, Y. Ding, C. Dong, J. Dong, L. Y. Dong, M. Y. Dong, Z. L. Dou, S. X. Du, P. F. Duan, J. Z. Fan, J. Fang, S. S. Fang, Y. Fang, R. Farinelli, L. Fava, S. Fegan, F. Feldbauer, G. Felici, C. Q. Feng, M. Fritsch, C. D. Fu, Y. Fu, Q. Gao, X. L. Gao, Y. Gao, Y. G. Gao, Z. Gao, B. Garillon, I. Garzia, A. Gilman, K. Goetzen, L. Gong, W. X. Gong, W. Gradl, M. Greco, L. M. Gu, M. H. Gu, Y. T. Gu, A. Q. Guo, L. B. Guo, R. P. Guo, Y. P. Guo,
Published: , doi: 10.1088/1674-1137/43/8/083002
We study the hadronic decays of $ \Lambda_{c}^{+} $ to the final states $ \Sigma^{+}\eta $ and $ \Sigma^+\eta^\prime $, using an $ e^+e^- $ annihilation data sample of 567 pb-1 taken at a center-of-mass energy of 4.6 GeV with the BESIII detector at the BEPCII collider. We find evidence for the decays $ \Lambda_{c}^{+}\rightarrow\Sigma^{+}\eta $ and $ \Sigma^+\eta^\prime $ with statistical significance of $ 2.5\sigma $ and $ 3.2\sigma $, respectively. Normalizing to the reference decays $ \Lambda_c^+\to\Sigma^+\pi^0 $ and $ \Sigma^+\omega $, we obtain the ratios of the branching fractions $ \displaystyle\frac{{\mathcal B}(\Lambda_c^+\to\Sigma^+\eta)}{{\mathcal B}(\Lambda_c^+\to\Sigma^+\pi^0)} $ and $ \displaystyle\frac{{\mathcal B}(\Lambda_c^+\to\Sigma^+\eta^\prime)}{{\mathcal B}(\Lambda_c^+\to\Sigma^+\omega)} $ to be $ 0.35 \pm 0.16 \pm 0.02 $ and $ 0.86 \pm 0.34 \pm 0.04 $, respectively. The upper limits at the 90% confidence level are set to be $ \displaystyle\frac{{\mathcal B}(\Lambda_c^+\to\Sigma^+\eta)}{{\mathcal B}(\Lambda_c^+\to\Sigma^+\pi^0)}<0.58 $ and $ \displaystyle\frac{{\mathcal B}(\Lambda_c^+\to\Sigma^+\eta^\prime)}{{\mathcal B}(\Lambda_c^+\to\Sigma^+\omega)}<1.2 $. Using BESIII measurements of the branching fractions of the reference decays, we determine $ \mathcal{B}({\Lambda_{c}^{+}\rightarrow\Sigma^{+}\eta}) = (0.41\pm0.19\pm0.05) $% (<0.68%) and $ \mathcal{B}({\Lambda_{c}^{+}\rightarrow\Sigma^{+}\eta'}) = (1.34\pm0.53\pm0.19) $% (<1.9%). Here, the first uncertainties are statistical and the second systematic. The obtained branching fraction of $ \Lambda_c^+\to\Sigma^+\eta $ is consistent with the previous measurement, and the branching fraction of $ \Lambda_{c}^{+}\rightarrow\Sigma^{+}\eta^{\prime} $ is measured for the first time.
Extinction coefficients of surface atmospheric aerosol above LHAASO
Wen-Xuan Pi, Min Huang, Feng-Rong Zhu, Yu He, Ning Xie, Yong Zhang, Qi-Hui Chen, Huan-Yu Jia
Published: , doi: 10.1088/1674-1137/43/8/085001
We investigate the extinction coefficients of the surface atmospheric aerosol over the Large High Air Shower Observatory (LHAASO), located at the Haizi Mountain, Daocheng County, China. To this end, we utilize the Longtin model, Mie scattering theory, and experimental data obtained by the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO). Our theoretical calculations show that the total extinction coefficients of the atmospheric aerosol at the wavelength of 200–500 nm are inversely proportional to the laser wavelength, and influenced by the wind speed. From July 2015 to October 2016, the extinction coefficient of the surface atmospheric aerosols at 532 nm wavelength reached 0.04 km−1 with no wind, while it increased to 0.1 km−1 with gusts. In this period, the extinction coefficients of the surface atmospheric aerosol at 532 nm wavelength, obtained by the CALIPSO, change from 0.01 to 0.07 km−1, which is less than the values obtained the theoretical calculation and larger than the average of Tibetan Plateau in 2006−2016. These calculations and experimental evidence provide important arguments to the model of atmospheric aerosol to be applied in the calibration of LHAASO. Our results suggest that the extinction coefficients over LHAASO require further study, including research on the size distribution, shape, concentration of aerosols particles, wind dependence, relative humidity dependence, etc.
Novel self-consistent mean field approximation and its application in strong interaction phase transitions
Fei Wang, Yakun Cao, Hongshi Zong
Published: , doi: 10.1088/1674-1137/43/8/084102
We propose a novel self-consistent mean field approximation method by means of a Fierz transformation, taking the Nambu-Jona-Lasinio model as an example. This new self-consistent mean field approximation introduces a new free parameter α to be determined experimentally. When α assumes the value of 0.5, the approximation reduces to the mean field calculation commonly used in the past. Subsequently, we study the influence of the undetermined parameter α on the phase diagram of the two-flavor strong interaction matter. The value of α plays a crucial role in the strong interaction phase diagram, as it not only changes the position of the phase transition point of strong interaction matter, but also affects the order of the phase transition. For example, when α is greater than the critical value $ \alpha_c = 0.71$, then the strong interaction matter phase diagram no longer has a critical end point. In addition, in the case of zero temperature and finite density, we found that when α > 1.044, the pseudo-critical chemical potential corresponds to ~4–5 times the saturation density of the nuclear matter, which agrees with the expected results from the picture of the hadrons degree of freedom. The resulting equations of state of strong interaction matter at low temperatures and high densities will have an important impact on studies concerning the mass radius relationship of neutron stars and the merging process of binary neutron stars.
Universal scaling of conserved charge in stochastic diffusion dynamics
Shanjin Wu, Huichao Song
Published: , doi: 10.1088/1674-1137/43/8/084103
We explore the Kibble-Zurek scaling of conserved charge using stochastic diffusion dynamics. The characteristic scales $ \tau_{\rm{KZ}}$ and $ l_{\rm{KZ}}$ are determined and used to properly rescale the traditional correlation function and cumulant. We construct universal functions for the two-point correlation $ C(y_1-y_2;\tau)$ and the second-order cumulant $ K(\Delta y,\tau)$ of the conserved charge in the critical regime, both of which are, near the critical point, insensitive to both the initial temperature and a parameter in the mapping between the 3D Ising model and the hot QCD system.
Three-loop vacuum integral with four-propagators using hypergeometry
Zhi-Hua Gu, Hai-Bin Zhang
Published: , doi: 10.1088/1674-1137/43/8/083102
A hypergeometric function is proposed to calculate the scalar integrals of Feynman diagrams. In this study, we verify the equivalence between the Feynman parametrization and the hypergeometric technique for the scalar integral of the three-loop vacuum diagram with four propagators. The result can be described in terms of generalized hypergeometric functions of triple variables. Based on the triple hypergeometric functions, we establish the systems of homogeneous linear partial differential equations (PDEs) satisfied by the scalar integral of three-loop vacuum diagram with four propagators. The continuation of the scalar integral from its convergent regions to entire kinematic domains can be achieved numerically through homogeneous linear PDEs by applying the element method.
Study of Monte Carlo event generators for proton-proton collisions at LHC energies in the forward region
Alexandru Cătălin ENE, Alexandru JIPA, Lavinia-Elena GIUBEGA
Published: , doi: 10.1088/1674-1137/43/8/083001
In this paper we present a comparative study between PYTHIA, EPOS, QGSJET, and SIBYLL generators. The global event observables considered are the charged energy flow, charged particle distributions, charged hadron production ratios and V0 ratios. The study is performed in the LHCb and TOTEM fiducial phase spaces on minimum bias simulated data samples for pp collisions at $\sqrt{s}$ = 7 TeV , using the reference measurements from these experiments. In the majority of cases, the measurements are within a band defined by the most extreme predictions. The observed differences between the predictions and the measurements seem to be, in most part, caused by extrapolation from the central pseudorapidity region (|η|$\leqslant$ 2.5), in which the generators were mainly tuned.
Phenomenology of $\,{{b\to c\tau\bar\nu }}\,$ decays in a scalar leptoquark model
Han Yan, Ya-Dong Yang, Xing-Bo Yuan
Published: , doi: 10.1088/1674-1137/43/8/083105
During the past few years, signs of lepton flavor universality (LFU) violation have been observed in $ b \to c \tau \bar\nu $ and $ b \to s \ell^+ \ell^- $ transitions. Recently, the $ D^* $ and $ \tau $ polarization fractions $ P_L^{D^*} $ and $ P_L^\tau $ in $ B \to D^* \tau \bar\nu $ decay were likewise measured by the Belle collaboration. Motivated by these intriguing results, we revisit the $ R_{D^{(*)}} $ and $ R_{K^{(*)}} $ anomalies in a scalar leptoquark (LQ) model, where two scalar LQs, one of which is a $ SU(2)_L $ singlet and the other a $ SU(2)_L $ triplet, are introduced simultaneously. We consider five $ b \to c \tau \bar\nu $ mediated decays, $ B \to D^{(*)}\tau \bar\nu $, $ B_c \to \eta_c \tau \bar\nu $, $ B_c \to J/\psi \tau \bar\nu $, and $ \Lambda_b \to \Lambda_c \tau \bar\nu $, and focus on the LQ effects on the $ q^2 $ distributions of the branching fractions, LFU ratios, and various angular observables in these decays. Under the combined constraints of the available data on $ R_{D^{(*)}} $, $ R_{J/\psi} $, $ P_L^\tau(D^*) $, and $ P_L^{D^*} $, we perform scans for the LQ couplings and make predictions for a number of observables. Numerically it is found that both the differential branching fractions and LFU ratios are largely enhanced by the LQ effects, with the latter expected to provide testable signatures at the SuperKEKB and High-Luminosity LHC experiments.
Spin determination by in-plane angular correlation analysis in various coordinate systems
Biao Yang, Yan-Lin Ye, Jian-Ling Lou, Xiao-Fei Yang, Jing-Jing Li, Yang Liu, Wei Liu, Han-Zhou Yu
Published: , doi: 10.1088/1674-1137/43/8/084001
In the excitation of the resonant state followed by the sequential cluster-decay, the in-plane angular correlation method is usually employed to determine the spin of the mother nucleus. However, the correlation pattern exhibited in a two-dimensional angular-correlation spectrum depends on the selected coordinate system. In particular, the parity-symmetric and axial-symmetric processes should be presented in a way to enhance the correlation pattern, whereas the non-symmetric process should be plotted separately to reduce the background. In this study, three coordinate systems previously adopted for correlation patterns in the literature are described and compared to each other. The consistency among these systems is evaluated based on the experimental data analysis for the 10.29-MeV state in 18O. A spin-parity of 4+ is obtained for all three coordinate systems.
${ {b\rightarrow c\tau\bar{\nu}}}$ decay in supersymmetry with R-parity violation
Dong-Yang Wang, Ya-Dong Yang, Xing-Bo Yuan
Published: , doi: 10.1088/1674-1137/43/8/083103
In past years, several hints of lepton flavor universality (LFU) violation have emerged from the $ b \to c \tau \bar\nu $ and $ b \to s \ell^+ \ell^- $ data. More recently, the Belle Collaboration has reported the first measurement of the $ D^* $ longitudinal polarization fraction in the $ B \to D^* \tau \bar\nu $ decay. Motivated by this intriguing result, along with the recent measurements of $ R_{J/\psi} $ and $ \tau $ polarization, we present the study of $ b \to c \tau \bar\nu $ decays in supersymmetry (SUSY) with $ R $-parity violation (RPV). We consider $ B \to D^{(*)} \tau \bar\nu $, $ B_c \to \eta_c \tau \bar\nu $, $ B_c \to J/\psi \tau \bar\nu $ and $ \Lambda_b \to \Lambda_c \tau \bar\nu $ modes and focus on the branching ratios, LFU ratios, forward-backward asymmetries, polarizations of daughter hadrons, and the $ \tau $ lepton. The RPV SUSY was capable of explaining the $ R_{D^{(*)}} $ anomalies at the $ 2\sigma $ level, after taking into account various flavor constraints. In the allowed parameter space, the differential branching fractions and LFU ratios are largely enhanced by the SUSY effects, especially in the large dilepton invariant mass region. Moreover, a lower bound $ {\mathcal B}(B^+ \to K^+ \nu \bar\nu) > 7.37 \times $ 10−6 is obtained. These observables could provide testable signatures at the high-luminosity LHC and SuperKEKB, and correlate with direct searches for SUSY.
${K^\pi=5^-}$ rotational bands in neutron-rich Mo, Ru, and Pd nuclei
A-Can Dai, Fu-Rong Xu, Wu-Yang Liang
Published: , doi: 10.1088/1674-1137/43/8/084101
The collective rotations of the $ K^\pi = 5^- $ configuration in neutron-rich Mo, Ru and Pd isotopes were systematically investigated by the configuration-constrained cranking shell model based on the Skyrme Hartree-Fock method with pairing treated by shell-model diagonalization. The calculations efficiently reproduce the experimental moments of inertia of both the ground-state and side bands. Rotational bands built on two-particle $ K^\pi = 5^- $ configurations have been the subject of intense study. Possible configurations were assigned to the observed $ 5^- $ bands in 102-106Mo, 108-112Ru and 112-114Pd. We predict the existence of the $ 5^- $ bands in 108,110Mo. These results provide deep insights into the structure of neutron-rich nuclei, and provide useful information for future experiments.
Relativistic corrections of the fragmentation functions for a heavy quark to Bc and ${{B}_{\!\!{c}}^*}~$
Deshan Yang, Wenjie Zhang
Published: , doi: 10.1088/1674-1137/43/8/083101
In this paper, we compute the relativistic corrections of the fragmentation functions (FFs) for a heavy quark to Bc and $ B_c^* $ within the framework of non-relativistic QCD (NRQCD) factorization. The non-singlet and singlet DGLAP evolutions are also presented.
Neutral regular black hole solution in generalized Rastall gravity
Kai Lin, Wei-Liang Qian
Published: , doi: 10.1088/1674-1137/43/8/083106
We investigate the static, spherically symmetric regular black hole solutions in the generalized Rastall gravity. In particular, the prescription of Rastall gravity implies that the present approach does not necessarily involve nonlinear electrodynamics. Subsequently, the resulting regular black hole solutions can be electrically and magnetically neutral. The general properties of the regular black hole solutions are explored. Moreover, specific solutions are derived and discussed, particularly regarding the parameter related to the degree of violation of the energy-momentum conservation in the Rastall theory.
Perturbative QCD for J/ψ inclusive production via initial state radiation in ${{e^+e^-}}$ collisions
Bin Gong, Yu-Dong Wang, Jian-Xiong Wang
Published: , doi: 10.1088/1674-1137/43/8/083104
The process $ e^+e^-\to J/\psi +X $ with the center-of-mass (CM) energy in the range from 3.7 to 10.6 GeV is calculated up to the next-to-leading order (NLO) in quantum chromodynamics (QCD). At 10.6 GeV, the result is consistent with the experimental result from Belle. However, the predictions are much smaller than the background in the measurements at BESIII in the low CM energy range from 3.7 to 4.6 GeV. This indicates that the convergence of the QCD perturbative expansion becomes worse as the CM energy is closer to the inclusive $ J/\psi $ production threshold. For a further study of the QCD mechanism of $ J/\psi $ production in $ e^+e^- $ collisions with different CM energies, the initial state radiation effect of $ e^+e^-\to J/\psi+gg $ and $ e^+e^-\to J/\psi+c \bar{c} $ are calculated in QCD NLO. The results are plotted and the number of events for different CM energy bins are provided for SuperKEKB. This provides a method to precisely test the validity of perturbative predictions for $ J/\psi $ production in future measurements.