Nuclear Charge Density Research Articles

Uncertainty quantification for μ → e conversion in nuclei: charge distributions

Predicting the rate for μ → e conversion in nuclei for a given set of effective operators mediating the violation of lepton flavor symmetry crucially depends on hadronic and nuclear matrix elements. In particular, the uncertainties inherent in this non-perturbative input limit the discriminating power that can be achieved among operators by studying different target isotopes. In order to quantify the associated uncertainties, as a first step, we go back to nuclear charge densities and propagate the uncertainties from electron scattering data for a range of isotopes relevant for μ → e conversion in nuclei, including 40,48Ca, 48,50Ti, and 27Al. We provide as central results Fourier-Bessel expansions of the corresponding charge distributions with complete covariance matrices, accounting for Coulomb-distortion effects in a self-consistent manner throughout the calculation. As an application, we evaluate the overlap integrals for μ → e conversion mediated by dipole operators. In combination with modern ab-initio methods, our results will allow for the evaluation of general μ → e conversion rates with quantified uncertainties.

Study of the Nuclear Structure Properties in Strontium (90,92,94Sr) Isotopes Using Nuclear Shell-model Calculations

In the current research, various nuclear properties energy spectrum, reduced electromagnetic transition probabilities, nuclear moments, and the distributions of both the nuclear charge and mass density as a function of radial distance from the nucleus center (r) were computed for90,92,94Sr isotopes' using the NuShellX@MSU code. The Skyrme (SLy4) potential was utilized to compute the zirconium isotopes' wave functions with mass numbers 90, 92, and 94. By employing the Gloeckner interaction and bare G-matrix, the computed results showed good agreement with the available experimental information on the aforementioned nuclear features of all the above isotopes. Additionally, the spins and parities of energy levels were confirmed and determined in accordance with certain empirical values. Furthermore an acceptable agreement for transition strengthsB(E2;2_1^+→0_1^+ ) for 90,92,94Sr , and the dipole magnetic moment of the ground state in the90Sr isotope, was observed with the available experimental values. In these calculations, new values were predicted for the above nuclear properties, which had not been previously determined experimentally. KEYWORDS: energy spectra; gloeckner interaction; model space; nuShellX code; skyrme potential; transition strengths

Global prediction of nuclear charge density distributions using a deep neural network

Global prediction of nuclear charge density distributions using a deep neural network

Extraction of higher-order radial moments of nuclear charge density from muonic atom spectroscopy

Extraction of higher-order radial moments of nuclear charge density from muonic atom spectroscopy

Theoretical modeling of the above-barrier fusion process for nuclei with [formula omitted] based on the experimental nuclear charge densities

Most of theoretical models of nucleus-nucleus collision are based on the nucleus-nucleus potential. Semi-microscopical double-folding model with the M3Y-Paris NN-forces represents one of the advanced methods for evaluating this potential. Nucleon densities (NDs), being crucial ingredient of this model, must reproduce the experimental nuclear charge densities (NCDs). In theoretical approaches for modeling the fusion process, it is not always so. In the present work, we aim to reach satisfactory description of both the charge nucleon density and the above-barrier fusion cross sections of even-even nuclei with Z=N. We construct an approximation for the ND which is abbreviated as FEV-density (Fermi + Exponential tail with Variable diffuseness). The proton and neutron densities are considered to be identical and having a coordinate-dependent diffuseness. Parameters of the nucleon density are varied to obtain the best fit of the experimental NCD. Then the resulting FEV nucleon densities are used to calculate the nucleus-nucleus potential applying the double-folding model with the density-dependent M3Y-Paris NN-forces. This potential is employed for evaluating the above-barrier fusion cross sections for ten reactions: 32S+12C, 24Mg, 40Ca; 28Si+12C, 16O, 24Mg, 28Si; and 24Mg+12C, 16O, 24Mg where the experimental data are available. The cross sections are calculated using either the barrier penetration model or the trajectory model with surface friction. To find the transmission coefficients for the trajectory model, the Langevin-type equations are solved numerically. For all considered reactions, our trajectory model typically reproduces the above-barrier experimental cross sections within 10–15 % with typical χ2<2. The adjustable parameter of the model, the optimal friction strength KRm, was found to be between 20 and 40 zs·GeV−1 which is in reasonable agreement with two systematics found earlier. We also make predictions for the fusion excitation functions for reactions 32S+16O, 32S+28Si, 24Si+40Ca where we did not manage finding experimental data.

Calibration of nuclear charge density distribution by back-propagation neural networks

Calibration of nuclear charge density distribution by back-propagation neural networks

Erratum: Nuclear charge densities in spherical and deformed nuclei: Toward precise calculations of charge radii [Phys. Rev. C 103 , 054310 (2021)

Received 14 April 2023DOI:https://doi.org/10.1103/PhysRevC.107.069901©2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasLepton induced nuclear reactionsNuclear charge distributionNuclear structure & decaysNucleon distributionNuclear Physics

Experimental nuclear charge density and theoretical description of the above-barrier light heavy-ion fusion process* *Supported by the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS.”

Theoretical modeling of nucleus-nucleus collisions is often based on the nucleus-nucleus potential. One of the advanced methods for constructing this potential is the semi-microscopical double-folding model with M3Y-Paris NN-forces. Proton and neutron densities are significant components of this model. The correct nucleon density (ND) must reproduce the experimental nuclear charge density (NCD). However, those who deal with modeling the fusion process typically disregard this circumstance. We aim to achieve a good description of both the nuclear charge density and above-barrier fusion cross sections of even-even light nuclei with . We consider several versions of NDs available in literature and construct our own approximation for the ND of the even-even spherical nuclei 12C, 16O, and 40Ca, abbreviated as FE-density (Fermi+exponential). We carefully compare the NCDs resulting from different versions of NDs with the experimental NCDs. After finding the nucleus-nucleus potential using the double-folding model with the density dependent M3Y-Paris NN-forces and FE densities, we evaluate the above-barrier fusion cross sections for five reactions, 12C+12C, 12C+16O, 16O+16O, 16O+40Ca, and 40Ca+40Ca, for which experimental data are available. The cross sections are calculated using two approaches: a) the barrier penetration model and b) the trajectory model with surface friction (TM). To find the transmission coefficients for the TM, the Langevin equations are employed. For all considered reactions, our TM typically reproduces the above-barrier experimental cross sections within 10−15%. The only adjustable parameter of the model, the optimal friction strength , is found to be approximately 90 for the light reactions 12C+12C, 12C+16O, and 16O+16O and approximately 15 for the heavy reactions 16O+40Ca and 40Ca+40Ca. The latter findings are in reasonable agreement with the systematics found previously. Thus, the FE-recipe allows highly accurate and simultaneous reproduction of both the nuclear charge density and above-barrier fusion cross sections of five reactions involving 12C, 16O, and 40Ca nuclei.

Revisited relativistic Dirac-Hartree-Fock X-ray scattering factors. II. Chemically relevant cations and selected monovalent anions for atoms with Z = 3-112.

The previously described approach for determination of the relativistic atomic X-ray scattering factors (XRSFs) at the Dirac-Hartree-Fock level [Olukayode et al. (2023). Acta Cryst. A79, 59-79] has been used to evaluate the XRSFs for a total of 318 species including all chemically relevant cations [Greenwood & Earnshaw (1997). Chemistry of the Elements], six monovalent anions (O-, F-, Cl-, Br-, I-, At-), the ns1np3 excited (valence) states of carbon and silicon, and several exotic cations (Db5+, Sg6+, Bh7+, Hs8+ and Cn2+) for which the chemical compounds have been recently identified, thus significantly extending the coverage relative to all the earlier studies. Unlike the data currently recommended by the International Union of Crystallography (IUCr) [Maslen et al. (2006). International Tables for Crystallography, Vol. C, Section 6.1.1, pp. 554-589], which originate from different levels of theory including the non-relativistic Hartree-Fock and correlated methods, as well as the relativistic Dirac-Slater calculations, the re-determined XRSFs come from a uniform treatment of all species within the same relativistic B-spline Dirac-Hartree-Fock approach [Zatsarinny & Froese Fischer (2016). Comput. Phys. Comm. 202, 287-303] that includes the Breit interaction correction and the Fermi nuclear charge density model. While it was not possible to compare the quality of the generated wavefunctions with that from the previous studies due to a lack (to the best of our knowledge) of such data in the literature, a careful comparison of the total electronic energies and the estimated atomic ionization energies with experimental and theoretical values from other studies instils confidence in the quality of the calculations. A combination of the B-spline approach and a fine radial grid allowed for a precise determination of the XRSFs for each species in the entire 0 ≤ sin θ/λ ≤ 6 Å-1 range, thus avoiding the necessity for extrapolation in the 2 ≤ sin θ/λ ≤ 6 Å-1 interval which, as was shown in the first study, may lead to inconsistencies. In contrast to the Rez et al. work [Acta Cryst. (1994), A50, 481-497], no additional approximations were introduced when calculating wavefunctions for the anions. The conventional and extended expansions were employed to produce interpolating functions for each species in both the 0 ≤ sin θ/λ ≤ 2 Å-1 and 2 ≤ sin θ/λ ≤ 6 Å-1 intervals, with the extended expansions offering a significantly better accuracy at a minimal computational overhead. The combined results of this and the previous study may be used to update the XRSFs for neutral atoms and ions listed in Vol. C of the 2006 edition of International Tables for Crystallography.

Novel Ultrafast Molecular Imaging Based on the Combination of X-ray and Electron Diffraction

Recent development of X-ray free-electron lasers and megaelectronvolt radio-frequency electron guns have made ultrafast X-ray and electron diffraction measurements possible, thereby capturing chemical dynamics with atomic-spatial and femtosecond-temporal resolutions. We present a unified formulation of standard homodyne-detected and heterodyne-detected signals for both techniques. Noting that X-rays scatter from molecular electrons while electrons scatter from both molecular electrons and nuclei, we show how the two diffraction signals can be combined to reveal novel chemical information that is unavailable by solely using each technique alone. By subtracting the homodyne-detected X-ray and electron diffraction signals, a mixed electronic-nuclear interference in electron diffraction can be identified with a self-heterodyne nature for the direct imaging of attosecond electron dynamics where the scattering off molecular nuclei serves as a local oscillator for the scattering off molecular electrons. By subtracting heterodyne-detected X-ray and electron diffraction, the purely nuclear charge density can be singled out.

Revisited relativistic Dirac-Hartree-Fock X-ray scattering factors. I. Neutral atoms with Z = 2-118.

In this first of a series of publications, the X-ray scattering factors for neutral atoms are revisited. Using the recently developed DBSR_HF program [Zatsarinny & Froese Fischer (2016). Comput. Phys. Comm. 202, 287-303] the fully relativistic Dirac-Hartree-Fock ground-state wavefunctions for all atoms with Z = 2-118 (He-Og) have been calculated using the extended average level scheme and including both the Breit interaction correction to the electronic motion due to magnetic and retardation effects, and the Fermi distribution function for the description of the nuclear charge density. The comparison of our wavefunctions with those obtained in several previous studies in terms of the total and orbital (spinor) electronic energies, and a number of local and integrated total and orbital properties, confirmed the quality of the generated wavefunctions. The employed dense radial grid combined with the DBSR_HF's B-spline representation of the relativistic one-electron orbitals allowed for a precise integration of the X-ray scattering factors using a newly developed Fortran program SF. Following the established procedure [Maslen et al. (2006). International Tables for Crystallography, Vol. C, Section 6.1.1, pp. 554-589], the resulting X-ray scattering factors have been interpolated in the 0 ≤ sin θ/λ ≤ 2 Å-1 and 2 ≤ sin θ/λ ≤ 6 Å-1 ranges using the recommended analytical functions with both the four- (which is a current convention) and five-term expansions. An exhaustive comparison of the newly generated X-ray scattering factors with the International Union of Crystallography recommended values and those from a number of previous studies showed an overall good agreement and allowed identification of a number of typos and inconsistencies in the recommended quantities. A detailed analysis of the results suggests that the newly derived values may represent an excellent compromise among all the previous studies. The determined conventional interpolating functions for the two sin θ/λ intervals show, on average, the same accuracy as the recommended parametrizations. However, an extension of each expansion by only a single term provides a significant improvement in the accuracy of the interpolated values for an overwhelming majority of the atoms. As such, an updated set of the fully relativistic X-ray scattering factors and the interpolating functions for neutral atoms with Z = 2-118 can be easily incorporated into the existing X-ray diffraction software with only minor modifications. The outcomes of the undertaken research should be of interest to members of the crystallographic community who push the boundaries of the accuracy and precision of X-ray diffraction studies.

Prediction of nuclear charge density distribution with feedback neural network

Prediction of nuclear charge density distribution with feedback neural network

Nuclear charge radii of Cr46–62 isotopes and reaction cross sections for p−Cr

The nuclear charge radii and density distributions for $^{46--62}\mathrm{Cr}$ have been calculated in the frameworks of both relativistic and nonrelativistic self-consistent mean-field models. The relativistic Hartree-Bogoliubov model with density-dependent meson-exchange functional DD-ME2 and the nonrelativistic Hartree-Fock-Bogoliubov model with the Gogny D1S interaction, hereafter referred to as DIRHB and HFB, respectively, are used to compute ground-state properties of even $^{46--62}\mathrm{Cr}$ isotopes. Both calculations for the root-mean-squared charge radii reveal the characteristic kink at the $N$ = 28 shell closure in accordance with the corresponding experimental radii. The point proton and neutron density distributions calculated from both DIRHB and HFB are used to obtain the optical potentials for $p$-Cr at an incident proton energy of 65 MeV. The elastic scattering differential and total reaction cross sections, computed from the semimicroscopic proton optical potentials, have been derived by folding each of the target matter densities with the Jeukenne-Lejeune-Mahaux-Bruye\ifmmode \acute{r}\else \'{r}\fi{}es (JLMB) energy- and density-dependent internucleon interaction. The calculated elastic scattering differential cross sections for stable even isotopes, $^{50,52,54}\mathrm{Cr}$, using the respective DIRHB and HFB densities in the folding model reproduce the corresponding cross-section data well. The correlation between root-mean-squared charge radii and nuclear reaction observables obtained from the DIRHB and HFB calculations have been used in the folding model approach to predict the reaction cross sections for $p\text{\ensuremath{-}}^{46--62}\mathrm{Cr}$ at an incident proton energy of 65 MeV.

Effect of Incompressibility and Symmetry Energy Density on Charge Distribution and Radii of Closed-Shell Nuclei

In this work, the effect of incompressibility modulus KNM and symmetry energy density J on charge distribution and root-mean-square radii of neutron Rn and proton Rp has been investigated for light, medium and heavy closed-shell nuclei 40, 48Ca, 90Zr, 116Sn, 144Sm and 208Pb within the framework of self-consistent Hartree-Fock (HF) with 20 types of Skyrme interactions having wide range of nuclear properties such as incompressibility modulus KNM and symmetry energy density J. The nuclear charge densities have been obtained and compared with the experiment data to give us a picture about the internal structure of the investigated nuclei. Also, the sensitivity of proton and neutron root-mean-square radii to nuclear matter properties has been examined by determining and discussion the statistical Pearson linear correlation coefficient.

Imaging Purely Nuclear Quantum Dynamics in Molecules by Combined X-ray and Electron Diffraction.

Monitoring the motions of atoms and molecules in the course of chemical processes is a central goal of femtochemistry. Optical spectroscopic signals are usually sensitive to electronic properties such as dipoles, polarizabilities, and electronic charge densities rather than to nuclear motions. In this theoretical study, we propose a novel measurement that solely and directly monitors the evolving nuclear wave packet and can thereby unambiguously image photochemical events in real time. We demonstrate how nuclear charge densities can be singled out by subtracting the ultrafast gas-phase X-ray and electron diffraction signals in the photodissociation of thiophenol as it passes through two conical intersections. This signal can reveal the shape and trajectory of the nuclear wave packets as well as the electronic coherences in the vicinity of conical intersections.

Extraction of the second and fourth radial moments of nuclear charge density from the elastic electron-nucleus scattering

The expression for the radial moments of the nuclear charge density has been discussed under the plane wave Born approximation method recently, which is significant to investigate the nuclear surface thickness and neutron distribution radius. In this paper, we extend the studies of extracting second-order moment and fourth-order moment from the Coulomb form factors |F C(q)|2 by the distorted wave Born approximation (DWBA) at the small momentum transfer q region. Based on the relativistic mean-field calculations, the DWBA form factors are expanded into q 4, where the corresponding charge distributions are corrected by the contributions of neutron and spin–orbit densities. In the small q region, it is found that the experimental |F C(q)|2 can be well reproduced by considering the contributions of the at the small q region. Through further analyzing the second-order and fourth-order expansion coefficients of the , the relationship between the expansion coefficients and proton number Z is obtained. By the relationship, we extract the and from the limited experimental data of form factors at the small q region. Within the permissible range of error, the extracted are consistent with the experimental data in this paper.

Propagatory dynamics of nucleus-acoustic waves excited in gyrogravitating degenerate quantum plasmas electrostatically confined in curved geometry

A theoretic model to investigate the dynamics of the longitudinal nucleus-acoustic waves (NAWs) in gyrogravitating electrostatically confined degenerate quantum plasma (DQP) system in spherically symmetric geometry is constructed. The model setup consists of non-degenerate heavy nuclear species (HNS), lighter nuclear species (LNS), and quantum degenerate electronic species (DES). It specifically considers the influences of the Bohm potential, Coriolis rotation, viscoelasticity, and electrostatic confinement pressure (ECP, scaling quadratically in density). A standard normal spherical mode analysis gives a generalized dispersion relation (septic). It highlights the dependency of various atypical instability response on the equilibrium plasma parameters. A numerical illustrative platform portrays that the relative nuclear charge-to-mass coupling parameter (beta) acts as a destabilizing agency and the heavy-to-light nuclear charge density ratio (mu) acts as a stabilizing agency in both the non-relativistic (NR) and ultra-relativistic (UR) limits. Another interesting conjuncture is that the Coriolis rotation introduces a destabilizing influence on the system in both the limits. The progressive analysis presented herein has correlations and consistencies in the dynamic growth backdrop of various compact astro objects and their circumvent atmospheres, such as white dwarfs, neutron stars, etc.

Nuclear charge densities in spherical and deformed nuclei: Toward precise calculations of charge radii

Background: Precise measurements of atomic transitions affected by electron-nucleus hyperfine interactions offer sensitivity to explore basic properties of the atomic nucleus and study fundamental symmetries, including the search for new physics beyond the standard model of particle physics. In particular, such measurements, augmented by atomic and nuclear calculations, will enable extraction of the higher-order radial moments of the charge-density distribution in spherical and deformed nuclei. The new data impose higher precision requirements on a theoretical description.Purpose: The nuclear charge density is composed of the proton point distribution folded with the nucleonic charge distributions. The latter induce subtle relativistic corrections due to the coupling of nucleon magnetic moments with the nuclear spin-orbit density. Additional corrections come from the effect of center-of-mass projection. We assess the precision of nuclear charge density calculations by studying the behavior of relativistic and center-of-mass motion corrections to the second and fourth charge radial moments. Special attention has been paid to the magnetic spin-orbit density associated with the local variations of the spin-orbit current.Methods: The calculations for semimagic and open-shell nuclei are performed in the framework of self-consistent mean-field theory using quantified energy density functionals and density-dependent pairing forces. We used the general expression for the spin-orbit form factor that is valid for spherical and deformed nuclei.Results: We studied the impact of various correction terms on the charge radii, fourth radial moments, diffraction radii, and surface thickness of spherical and deformed nuclei. The spin-orbit corrections to charge radial moments and surface thickness show strong shell fluctuations which can make an appreciable effect when aiming at high-precision predictions of isotopic shifts. The inclusion of relativistic and center-of-mass corrections impacts the quality of energy density functionals optimized to charge radii data.Conclusions: To establish reliable constraints on the existence of new forces from isotope shift measurements, precise calculations of nuclear charge densities of deformed nuclei are needed. The proper inclusion of the spin-orbit charge density and other correction terms is essential when aiming at extraction of subtle effects which become particularly visible in isotopic trends. It is also important when developing high-quality nuclear energy density functionals optimized using heterogeneous datasets involving absolute charge radii, differential charge radii, and charge form factor properties deduced from electron-scattering data.

The mean square radius of the neutron distribution and the skin thickness derived from electron scattering

Abstract The second-order moment of the nuclear charge density ($R^2_c$) is dominated by the mean square radius (msr) of the point proton distribution ($R_p^2$), while the fourth-order moment($Q^4_c$) depends on the msr of the point neutron one ($R_n^2$) also. Moreover, $R^2_n$ is strongly correlated to $R^2_c$ in nuclear models. According to these facts, the linear relationship between various moments in the nuclear mean field models are investigated with the use of the least-squares method for $^{40}$Ca, $^{48}$Ca and $^{208}$Pb. From the intersection of the obtained straight line and the line of the experimental value for $R^2_c $ or $Q^4_c$ determined through electron scattering, the values of $R_p$ and $R_n$ are estimated. Since relativistic and non-relativistic models provide different lines, the obtained values of $R_n$ and the skin thickness ($R_n-R_p$) differ from each other in the two frameworks.

Preparation of an amphoteric lignin copolymer and its value in the papermaking industry

Lignin biomass is an important renewable woody material that can be converted into high value-added products through physical and chemical reactions, such as paper strength additives. In this study, a cationic methacryloyloxyethyl trimethylammonium chloride monomer (DMC) and anionic acrylic monomer (AA) were grafted onto softwood kraft lignin through free radical polymerization to prepare an amphoteric lignin copolymer. Fourier transform infrared spectroscopy (FTIR), proton nuclear magnetic resonance spectroscopy (1H NMR), elemental analysis, and charge density analysis methods confirmed that the anionic and cationic monomers were successfully grafted onto the lignin. The grafting ratios of AA and DMC monomer in the lignin-DMC-AA copolymer were 62.4% and 51.3%, respectively. The application of lignin-DMC-AA copolymer as a paper additive for enhancing the physical properties of paper sheets was studied in the papermaking industry. The results indicated that the copolymer had a maximum increase in physical strength at around 2 wt% lignin-DMC-AA. The amount absorbed on the fibers was 18.5 mg/g, and the retention of the lignin-DMC-AA copolymer was over 90%.