Nuclear Charge Research Articles

Ionization limits and upper levels in P-XIV and in Cl-XVI

Abstract In this study, the ground state and excited state ionization limits with and without consideration of relativistic effects are computed for a helium-like iso-spectrum level sequence for the following configurations: 1s 2 S 0 1 , 1s3s S 0 1 , 1s3p P 0 o 3 , 1s2p P 1 o 1 , 1s3p P 1 o 1 , 1s4p P 1 o 1 , 1s5p P 1 o 1 , 1s6p P 1 o 1 , 1s3p P 1 o 3 , 1s3s S 1 3 , 1s4s S 1 3 , 1s3d D 2 1 , 1s3d D 2 1 , 1s5d D 2 3 , 1s2d P 2 o 3 , 1s3d D 3 3 , 1s4d D 3 3 , 1s5d D 3 3 for nuclear charge Z . The non-relativistic ionization limits are derived from the weakest bound electron potential model, and relativistic corrections are included by using the Breit-Pauli approximation, which has also been applied to the computed relativistic ionization limits at high-order polynomials in the effective nuclear charge Z ′ . This study suggests two hundred and seventy-two excited states ionization potentials with and without a relativistic effect. Furthermore, it fills the gap of thirty-four excited state ionization potentials and their energies for the following configurations: 1s3s S 0 1 , 1s3p P 0 o 3 , 1s2p P 1 o 1 , 1s3p P 1 o 1 , 1s4p P 1 o 1 , 1s5p P 1 o 1 , 1s6p P 1 o 1 , 1s3p P 1 o 3 , 1s3s S 1 3 , 1s4s S 1 3 , 1s3d D 2 1 , 1s3d D 2 1 , 1s5d D 2 3 , 1s2d P 2 o 3 , 1s3d D 3 3 , 1s4d D 3 3 , 1s5d D 3 3 in P − X I V and, C l − X V I which is very onerous to compute owing to foreign-level configuration mixing causing high perturbation, are currently not listed at NIST. This work shows excellent agreement between the computed values and NIST values. The yield ionization limits I n r and I N , Z ′ departing from NIST ones by not more than 1.0 eV and 0.00001 eV, respectively. Both sets of data reported are precise up to 4 decimal place.

Similarity among quantum-mechanical states: Analysis and applications for central potentials

Abstract The similarity of quantum-mechanical solutions for central potentials is analytically determined and numerically explored for arbitrary dimensionalities. The study here provided focuses on hydrogenic systems and the harmonic oscillator, in respective non-relativistic frameworks. A diversity of analytical expressions for the Quantum Similarity Measure (QSM) and Index (QSI) are provided. Relevant conclusions are derived from the analyses grounded on state quantum numbers, space dimensionality and on the role played by the main characteristic parameters of these systems, namely the nuclear charge in the hydrogenic case, and the angular frequency for the oscillator. For this purpose, a statistical analysis of the QSI values has been performed for a large number both of states and combinations of them in each system. Considering the factorization of QSI into a radial and an angular part, particular attention is paid to the individual contribution of each part in both systems.

Pursuing high-fidelity control of spin qubits in natural Si/SiGe quantum dot

Electron spins in silicon quantum dots are a promising platform for fault-tolerant quantum computing. Low-frequency noise, including nuclear spin fluctuations and charge noise, is a primary factor limiting gate fidelities. Suppressing this noise is crucial for high-fidelity qubit operations. Here, we report on a two-qubit quantum device in natural silicon with universal qubit control, designed to investigate the upper limits of gate fidelities in a non-purified Si/SiGe quantum dot device. By employing advanced device structures, qubit manipulation techniques, and optimization methods, we have achieved single-qubit gate fidelities exceeding 99% and a two-qubit controlled-Z (CZ) gate fidelity of 91%. Decoupled CZ gates are used to prepare Bell states with an average fidelity of 91%, typically exceeding previously reported values in natural silicon devices. These results underscore that even natural silicon has the potential to achieve high-fidelity gate operations, particularly with further optimization methods to suppress low-frequency noise.

Charge radii of 11−16C, 13−17N and 15−18O determined from their charge-changing cross-sections and the mirror-difference charge radii

Charge-changing cross-sections (CCCSs) of 11−16C, 13−17N and 15−18O on a carbon target have been determined at energies around 300 MeV/nucleon. A nucleon separation energy-dependent correction factor has been introduced to the Glauber model calculation for extracting the nuclear charge radii from the experimental CCCSs. The charge radii of 11C, 13,16N and 15O thus were determined for the first time. With the new radii, we studied the experimental mirror-difference charge radii (ΔRchmirror) of 11B-11C, 13C-13N, 15N-15O, 17N-17Ne pairs for the first time. We find that the ΔRchmirror values of 13C-13N and 15N-15O pairs follow well the empirical relation to the isospin asymmetry predicted by the abinitio calculations, while ΔRchmirror of 11B-11C and 17N-17Ne pairs deviate from such relation by more than two standard deviations.

Smooth trends in fermium charge radii and the impact of shell effects

The quantum-mechanical nuclear-shell structure determines the stability and limits of the existence of the heaviest nuclides with large proton numbers Z ≳ 100 (refs. 1–3). Shell effects also affect the sizes and shapes of atomic nuclei, as shown by laser spectroscopy studies in lighter nuclides4. However, experimental information on the charge radii and the nuclear moments of the heavy actinide elements, which link the heaviest naturally abundant nuclides with artificially produced superheavy elements, is sparse5. Here we present laser spectroscopy measurements along the fermium (Z = 100) isotopic chain and an extension of data in the nobelium isotopic chain (Z = 102) across a key region. Multiple production schemes and different advanced techniques were applied to determine the isotope shifts in atomic transitions, from which changes in the nuclear mean-square charge radii were extracted. A range of nuclear models based on energy density functionals reproduce well the observed smooth evolution of the nuclear size. Both the remarkable consistency of model prediction and the similarity of predictions for different isotopes suggest a transition to a regime in which shell effects have a diminished effect on the size compared with lighter nuclei.

Alchemical insights into approximately quadratic energies of iso-electronic atoms.

Accurate quantum mechanics based predictions of property trends are so important for material design and discovery that even inexpensive approximate methods are valuable. We use the alchemical integral transform to study multi-electron atoms and to gain a better understanding of the approximately quadratic behavior of energy differences between iso-electronic atoms in their nuclear charges. Based on this, we arrive at the following simple analytical estimate of energy differences between any two iso-electronic atoms, ΔE≈-(1+2γNe-1)ΔZZ̄. Here, γ ≈ 0.3766 ± 0.0020 Ha corresponds to an empirical constant, and Ne, ΔZ, and Z̄, respectively, to electron number, nuclear charge difference, and average. We compare the formula's predictive accuracy using experimental numbers and non-relativistic, numerical results obtained via density functional theory (pbe0) for the entire periodic table up to Radon. A detailed discussion of the atomic helium-series is included.

Why are information-theoretic descriptors powerful predictors of atomic and molecular polarizabilities.

We rationalize the excellent performance of information-theoretic descriptors for predicting atomic and molecular polarizabilities. It seems that descriptors which capture information about the change in valence-shell structure, especially the relative Fisher information measures, are particularly useful. Using this, we can rationalize why the G3 form of the relative Fisher information, which measures the deviation of effective nuclear charge between an atom-in-a-molecule and the reference pro-atom, is especially effective as a predictor of molecular polarizability. There are no methods used in this paper, which relies on mathematical derivation and analysis.

Quantifying mass-dependent isotope fractionation and nuclear field shift effects for the light rare Earth elements in hydrous systems

The improving sensitivity of mass-spectrometers has opened the potential of using stable isotope signatures of the rare Earth elements (REE) as geochemical tracers. However, thus far only limited studies have utilised REE stable isotopes, despite resolvable variations having been observed in a range of systems. An interesting but poorly explored area remains variations in aqueous environments across a range of temperatures including seawater, marine sediments, ion adsorption deposits or hydrothermal systems. Furthermore, the magnitudes and competing effects of mass-dependent isotope fractionation and mass-independent nuclear field shift effects, which can be significant factor for heavy elements especially at high temperatures, remain poorly understood.To contribute to a holistic understanding of REE isotope signatures, we calculated reduced partition function ratios (as 103lnβ) for mass-dependent and nuclear field shift effects for aqueous La, Ce, and Nd complexes from first principles. Theoretical calculations were compared with experimental data, and this demonstrates that calculations involving a combination of two explicit hydration shells and additional implicit solvation effects are required to accurately describe the coordination and molecular vibrations of aqueous complexes. This data was then combined with speciation modelling of seawater and hydrothermal fluids to assess isotope fractionation in hydrous systems. The predicted magnitude of isotope fractionation is significant in low (T = 25 °C) temperature systems (Δ139/138LaMax-Min = 0.20 ‰, Δ142/140CeMax-Min = 0.33 ‰, Δ146/144NdMax-Min = 0.34 ‰) and remains above currently achievable analytical uncertainties even at high (T = 500 °C) temperatures (±0.015 ‰ for δ146/144Nd; ±0.040 ‰ for δ142/140Ce). Unless oxidation occurs, which is only relevant for Ce in terrestrial environments, nuclear field shift effects are negligible even at temperatures up to 500 °C. The large difference in nuclear charge radius between 140Ce and 142Ce strongly enriches the lighter Ce isotope in the higher oxidation state (103lnβCe(IV)-Ce(III) = −0.45 at 25 °C) which almost completely cancels out the opposing mass-dependent effect (103lnβCe(IV)-Ce(III) = +0.46 at 25 °C). This means that variations in δ142/140Ce isotope signatures cannot easily be related to oxidation in ancient or recent environments.

Breit interaction in dielectronic recombination of hydrogenlike xenon ions: storage-ring experiment and theory

Abstract Electron-ion collision spectroscopy of the KLL dielectronic recombination (DR) resonances of hydrogenlike xenon ions was performed at a heavy-ion storage ring with a resolving power that is competitive with x-ray spectroscopy of inner-shell transitions in highly charged ions. The $$KL_{1/2}L_{1/2}$$ K L 1 / 2 L 1 / 2 , $$KL_{1/2}L_{3/2}$$ K L 1 / 2 L 3 / 2 , and $$KL_{3/2}L_{3/2}$$ K L 3 / 2 L 3 / 2 resonance groups and even parts of their fine structure are individually resolved. The resonance strengths were measured on an absolute scale and compared with results from multi-configuration Dirac–Fock (MCDF) calculations. These are in excellent agreement with the experimental findings when QED effects on the resonance energies and the Breit interaction are considered. As already found for DR of hydrogenlike uranium (Bernhardt et al. in Phys Rev A 83:020701(R), 2011), this interaction is particularly strong for the $$KL_{1/2}L_{1/2}$$ K L 1 / 2 L 1 / 2 resonance group. For U$$^{91+}$$ 91 + , it increases the $$KL_{1/2}L_{1/2}$$ K L 1 / 2 L 1 / 2 DR resonance strength by 40%. For Xe$$^{53+}$$ 53 + , the increase is found to amount to 25%, confirming the prediction that the influence of the Breit interaction grows with increasing nuclear charge. A comprehensive appendix treats the derivation of experimental and theoretical merged-beams recombination rate coefficients for interacting beams of relativistic electrons and ions. Graphical abstract

Prediction of ground state charge radius using support vector regression

Abstract We systematically investigate the prediction of nuclear charge radii using a support vector regression (SVR) model in machine learning(ML), specifically employing a radial basis function (RBF) kernel. Our model is designed to capture the global structure of the radius surface through the utilization of feature spaces encompassing both (N, Z) and (N, Z, A). We achieved a root mean square deviation of 0.019 fm with respect to 885 measured charge radii (Z ⩾ 8). By incorporating the atomic mass number as an additional feature, the model successfully reproduces the charge radii of ( 40 − 50 Ca), ( 74 − 96 Kr), ( 120 − 148 Ba), and ( 183 − 199 Au) isotopes. Furthermore, our ML method demonstrated an extrapolation capability with a deviation of 0.016 fm relative to 10 022 calculated charge radii based on the Weizsacker–Skyrme model. The SVR model’s performance is further tested across different regions of the charge radii table, demonstrating significant agreement with experimental data and underscoring the efficacy of the RBF kernel in nuclear charge radii prediction.

An X‐Ray Absorption Spectroscopy Investigation into the Fundamental Structure of Liquid Metal Alloys

Gallium and gallium alloys have gained significant interest due to gallium's low melting point. This property allows for gallium‐based catalysts to take advantage of the unique reaction environments only available in the liquid state. While understanding of the catalytic properties of liquid metals is emerging, a comprehensive investigation into the fundamental structures of these materials has yet to be undertaken. Herein, the structure of liquid gallium, along with related liquid alloys EGaIn, EGaSn, and Galinstan are explored using X‐ray absorption spectroscopy (XAS). In contrast to some other studies that show dimers, analysis of the XAS data both in X‐ray absorption near edge structure and extended X‐ray absorption fine structure shows that when fully dissolved the materials are largely homogenous with no obvious signs of local structures. Ga shows a bond contraction when melted which is consistent with its increase in density; however, an expansion in bond length is observed when alloyed with In and Sn. XAS data indicate that the effective nuclear charge (Zeff) of In and Sn follows the trend expected based on electronegativity. Molecular dynamic (MD) simulations are performed to simulate the structure and trends between MD and XAS; the trends agree well but MD overestimates bond lengths.

Controlling Ultrafast Magnetization Dynamics via Coherent Phonon Excitation in a Ferromagnet Monolayer.

Exploring ultrafast magnetization control in 2D magnets via laser pulses is established, yet the interplay between spin dynamics and the lattice remains underexplored. Utilizing real-time time-dependent density functional theory (rt-TDDFT) coupled with Ehrenfest dynamics and nonadiabatic molecular dynamics (NAMD) simulations, we systematically investigate the laser-induced spin-nuclei dynamics with pre-excited A1g and E2g coherent phonons in the 2D ferromagnet Fe3GeTe2 (FGT) monolayer. Selective pre-excitation of coherent phonons under ultrafast laser irradiation significantly alters the local spin moment of FGT, consequently inducing additional spin loss attributed to the nuclear motion-induced asymmetric interatomic charge transfer. Excited spin-resolved charge undergoes a bidirectional spin-flip between spin-down and spin-up states, characterized by a subtle change in the spin moment within approximately 100 fs, followed by unidirectional spin-flip, which will further contribute to the spin moment loss of FGT within tens of picoseconds. Our results shed light on the coupling of coherent phonons with magnetization dynamics in 2D limit.

New definitions of the effective nuclear charge and its application to estimate the matrix element [formula omitted]

New definitions of the effective nuclear charge are proposed to evaluate the orbital wave function and the dipole matrix element ⟨n,l|r|n′,l′⟩ for the non-hydrogenic atoms or ions. It is found that the commonly used effective nuclear charge defined by the orbital energy is insufficiently precise to estimate the orbital wave functions and matrix elements ⟨n,l|r|n′,l′⟩. Instead, the effective nuclear charge defined by ⟨r⟩ or ⟨r2⟩ are more advantageous. It is shown that the effective nuclear charge method becomes increasingly precise to predict wave functions and matrix elements as the orbital angular momentum, the principle quantum number and the degree of ionization increase. Good accuracy is achieved when principal quantum numbers are identical n=n′ or when both orbital quantum numbers l and l′ are non-zero. When s-orbitals are involved (l or l′ equal to zero) the precision is decreasing.

Electron Screening in Laboratory Nuclear Reactions

A thorough understanding of nuclear reaction rates at low energies is essential for improving our understanding of energy generation in stars and primordial and stellar nucleosynthesis. At low energies, fusion reactions between charged particles are strongly suppressed by the presence of the Coulomb barrier, which classically inhibits the penetration of one nucleus into another. The barrier penetration causes the cross section to have a steep energy dependence at low energies, making cross section measurements very challenging. Furthermore, little is known about the impact of surrounding electrons in stellar plasmas that are currently beyond the reach of experiments. As a result, measuring the bare cross sections as accurately as possible is essential. Reaction rate measurements at very low energies have been made possible in recent years by the development of high-current low-energy accelerators as well as enhanced target and detection methods. Nevertheless, the presence of atomic electrons, which alter the Coulomb barrier by screening the nuclear charge and increase the cross section at low energies compared to the case of bare nuclei, complicates these observations. A review of the experimental and corresponding theoretical work on laboratory electron screening performed so far will be presented.

Absolute nuclear charge radius by Na-like spectral line separation in high-Z elements

Abstract We describe a novel technique to determine absolute nuclear radii of high-Z nuclides. Utilizing accurate theoretical atomic structure calculations together with precise measurements of extreme ultraviolet transitions in highly charged ions this method allows for precise determinations of absolute nuclear charge radii based upon the well-known nuclear radii of their neighboring elements. This method can work for elements without stable isotopes, and its accuracy may be competitive with current methods (electron scattering and muonic x-ray spectroscopy).

A unique approach to address avoided crossings in the charge stabilization curve for LUMO identification.

In quantum chemistry, Lowest Unoccupied Molecular Orbital (LUMO) is important for studying various chemical processes, including photochemical reactions, electron attached states, and electron excites states. Recently, an effective method has been introduced that involves the use of the Parametric Equation of Motion (PEM) in conjunction with the nuclear charge stabilization method for precise identification of true LUMO. However, the inclusion of extra diffuse functions in the basis set, which is necessary for describing electron-attached and electron-excited states, can cause issues due to the presence of the same symmetry states, leading to avoided crossing. Identifying the true LUMO among these avoided crossings is challenging due to the mixing of states and the exchange of their orbital character. This article introduces a modification of the PEM to identify the true LUMO by preventing the stabilization of specific states involved in avoided crossings. The present method is highly effective and requires minimal computational cost.

Simultaneous extraction of the weak radius and the weak mixing angle from parity-violating electron scattering on C12

We study the impact of nuclear structure uncertainties on a measurement of the weak charge of C12 at the future Mainz Energy Recovering Superconducting Accelerator (MESA) facility in Mainz. Information from a large variety of nuclear models, accurately calibrated to the ground-state properties of selected nuclei, suggest that a 0.3% precision measurement of the parity-violating asymmetry at forward angles will not be compromised by nuclear structure effects, thereby allowing a world-leading determination of the weak charge of C12. Furthermore, we show that a combination of measurements of the parity-violating asymmetry at forward and backward angles for the same electron-beam energy can be used to extract information on the nuclear weak charge distribution. We conclude that a 0.34% precision on the weak radius of C12 may be achieved by performing a 3% precision measurement of the parity-violating asymmetry at backward angles. Published by the American Physical Society 2024

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.

Multifunctional surface modification to enhance the electrochemical performance of lithium-rich manganese-based cathode materials

The preparation of high-performance lithium-rich manganese-based cathode materials (LLOs) require attention to the redox of anions and the migration of transition metals (TM) during the cycling process. In this study, Ce ion-doped Li-rich cathode coated with La0.2Ce0.8O2, which has abundant oxygen vacancies on its surface, was prepared. The presence of the oxygen storage material La0.2Ce0.8O2 can effectively absorb the irreversible oxygen generated during cycling, preventing it from reacting with the electrolyte to form thick cathode electrolyte interface (CEI) coatings. These coatings hinder the relative activity of lattice oxygen in the bulk phase, reducing the specific capacity of the material. Additionally, the 5d metal ion Ce carries a large nuclear charge, causing a 'pinning effect' when it integrates into the LLOs structure. This effect reduces thermal oscillation in the lattice, impedes TM migration during battery charging and discharging, and effectively prevents voltage decay. Results indicate that after 100 cycles at 1C and 25 °C, the surface-coated materials maintain a discharge-specific capacity of 194 mAh/g, compared to 158 mAh/g for uncoated material. Voltage decay decreased from 4.4 mV/cycle to 1.8 mV/cycle, with an ICE of 91.5 % versus the original material's 82.8 %. The modified material also exhibits improved rate performance, retaining a specific capacity of 162 mAh/g at 3C, in contrast to the original material's 123 mAh/g.

Geometric properties of the first singlet S-wave excited state of two-electron atoms near the critical nuclear charge

Abstract In this work the geometric structure parameters and radial density distribution of 1s2s 1 S excited state of the two-electron atomic system near the critical nuclear charge Z c were calculated in detail under tripled Hylleraas basis set. Contrary to the localized behavior observed in the ground and the doubly excited 2p 2 3 P e states, for this state our results identify that while the behavior of the inner electron increasingly resembles that of a hydrogen-like atomic system, the outer electron in the excited state exhibits diffused hydrogen-like character and becomes perpendicular to the inner electron as nuclear charge Z approaches Z c. This study provides insights into the electronic structure and stability of the two-electron system in the vicinity of the critical nuclear charge.