Core Polarization Research Articles

The Electro-Excitation Form Factors for Low-Lying States of 7Li Nucleus

The transverse electron scattering form factors have been studied for low –lying excited states of 7Li nucleus. These states are specified by J? T= (0.478MeV), (4.63MeV) and (6.68MeV). The transitions to these states are taking place by both isoscalar and isovector components. These form factors have been analyzed in the framework of the multi-nucleon configuration mixing of harmonic oscillator shell model with size parameter brms=1.74fm. The universal two-body of Cohen-Kurath is used to generate the 1p-shell wave functions. The core polarization effects are included in the calculations through effective g-factors and resolved many discrepancies with experiments. A higher configuration effect outside the 1p-shell model space, such as the 2p-shell, enhances the form factors for q-values and reproduces the data. The present results are compared with other theoretical models. PACS: 25.30.Bf Elastic electron scattering - 25.30.Dh Inelastic electron scattering to specific states – 21.60.Cs Shell model – 27.20. +n 5? A ?19

Field intensity dependence of the dissociative multiple ionization of argon dimers in strong femtosecond laser fields

The dissociative ionization of Ar dimers is investigated in femtosecond laser fields with intensities from 260 to 1020 TW/cm2. The three-dimensional momentum and kinetic-energy release of fragmental ions generated from the channels Ar22+→Ar++Ar+, Ar23+→Ar2++Ar+, and Ar24+→Ar2++Ar2+ were measured with a cold-target recoil-ion momentum spectrometer. It is shown that the laser intensity significantly modulates the kinetic energies and angular distributions of fragmental ions from dissociative double ionization. Laser-induced charge-transfer following one-site double ionization contributes relatively more to the dissociative double ionization at lower laser intensity. The calculation results of a one-dimensional model based on the WKB approximation suggest that the charge transfer is suppressed at higher laser intensity due to the core polarization effect. In addition, double, triple, and quadruple dissociative ionizations of Ar dimers are accompanied by frustrated-tunneling ionization that increases with the laser intensity.

Multi-Source Data-Based Investigation of Spatiotemporal Heterogeneity and Driving Mechanisms of Coupling and Coordination in Human Settlements in Urban Agglomeration in the Middle Reaches of the Yangtze River

In the information age, the new wave of the information technology revolution has profoundly changed our mode of production and way of life. Pseudo human settlements (PHS), consisting of digits and information, have become increasingly important in human settlements (HS) systems, and become a strong support for the high-quality development of global HS. Against this background, clarifying the spatiotemporal heterogeneity and driving mechanisms of the coupling and coordination between the PHS and real human settlements (RHS) is of great significance to the high-quality development of HS and providing a reasonable explanation of today’s man–land relationship. Therefore, we developed a theoretical framework system for describing PHS–RHS coupling and coordination based on multi-source data such as internet socialization, public utility, and remote sensing images, etc. Taking the urban agglomeration in the middle reaches of the Yangtze River (UAMRYR), which is the key region consolidating China’s “two horizontal and three vertical” urbanization strategy, as a case study area, we have comprehensively analyzed the spatiotemporal heterogeneity of the coupling and coordination of PHS and RHS and its driving mechanism in UAMRYR during the period of 2011–2021, by comprehensively applying the modified coupling coordination degree (CCD) and other models. The results show are as follows: (1) Temporal process—The CCD exhibited a reverse L-shaped increasing trend. The CCD class varied significantly, with the extremely uncoordinated and severely uncoordinated classes present at the beginning of the study period and disappearing toward the end of the study period, while the well coordinated and highly coordinated classes were absent at the beginning of the study period and appeared toward the end of the study period. (2) Spatial pattern—The CCD exhibited an equilateral triangle-shaped, core–margin spatial pattern and a characteristic of core polarization. Overall, the spatial distribution of the CCD exhibited a characteristic of “high in the central region, low in the eastern and western regions, and balanced in the south–north direction”. (3) Dynamic evolution—The CCD increased more rapidly in the north-eastern direction than in the south-western direction; the CCD exhibited north-eastward migration and dispersion, and the spatial variability decreased. (4) Driving mechanisms—The primary factors affecting the CCD varied significantly over time. The living system was dominant in the PHS, whereas the human system was dominant in the RHS. The PHS had a greater effect than the RHS on the CCD. The study broadens the research scope of human settlements geography, establishes a scientific foundation for advancing urban HS construction in the UAMRYR, and offers theoretical support for the high-quality development of cities in the UAMRYR.

Theoretical comparison of transition rate B(E2) and deformation parameter with experimental data for calcium (20Ca) isotopes using shell model theory

A theoretical comparison has been made for some calcium isotopes ([Formula: see text]Ca) which are even–even nuclei and have the atomic mass (Z = 20) with its previous experimental data. Theoretical calculations of some [Formula: see text]Ca isotopes (A = 42, 44, 46, 48, 50, 52) adopted by the shell model theory were performed to calculate the transition rate B(E2), theoretical intrinsic quadruple moments ([Formula: see text] and theoretical deformation parameters ([Formula: see text], [Formula: see text] were calculated by two methods by using different effective interactions for each isotope such as, su3fp, fpbm, fprkb, fpd6, kb3. Through code NuShellX@MSU, the single-body density matrix was calculated. The effects of the core polarization were neglected by adopting various effective charges that were employed, effective charges of conventional (Con-E), effective charges of standard (St-E) and effective charges of Bohr and Mottelson (B-M-E) which were calculated. The theoretical values of the B(E2)Th, the [Formula: see text] and the ([Formula: see text], [Formula: see text] were then compared with the previous experimental data where values of the transition rate B(E2)Th, theoretical intrinsic quadrupole moments [Formula: see text] and theoretical deformation parameter ([Formula: see text], [Formula: see text], using the fpbm, the fpd6 and the kb3 interactions were the best.

Theoretical Modeling of Sr(q+) He (q = 0, 1, 2) van der Waals Systems Including Spin-Orbit Coupling.

Using an ab initio methodology that incorporates pseudopotential technique in conjunction with pair potential approaches, core polarization potentials (CPP), large basis sets of Gaussian type, and full configuration interaction calculations, we investigate interaction of neutral and charged Srq+(q = 0,1,2) with helium atom. In this context, the core-core interaction of Sr2+-He is included using an accurately performed potential for the ground state at CCSD(T) level of calculation. Also, the potential energy curves and permanent and transition dipole moments of the ground state and numerous excited states have been performed respectively for Sr+He and SrHe systems. Subsequently, the spin-orbit effect is considered by utilizing a semiempirical method for states dissociating into Sr+(5p) + He, Sr+(6p) + He, Sr+(4d) + He, Sr+(5d) + He, Sr(5s5p) + He, and Sr(5s4d) + He. The spectroscopic constants of the Srq+(q = 0, 1, 2) He states, with and without spin-orbit interaction, are derived and assessed in comparison to the existing theoretical and experimental studies. Such comparison has revealed good agreement, especially, for the Sr+He ionic system. Additionally, the spin-orbit effect is considered for the X2Σ+ → 22Π1/2,3/2 and X2Σ+ → 32Σ1/2 + transition dipole moments for Sr+He.

UNDULATING POTENTIALS OF RYDBERG Σ+-STATES OF ME-RG MOLECULES: NON-EMPIRICAL TREATMENT OF NA-HE EXCIPLEX

The multi-reference con guration interaction method based on single and double excitations (MR-CISD), l-independent core polarization potential (CPP) and diffuse function-saturated cc-pVQZ and aug-cc-pV5Z basis sets for Na and He atoms, respectively, have been used to perform non-relativistic calculations of potential energy curves and permanent dipole moment functions for the ground and excited electronic states of the exciplex Na-He molecule up to the Na(62S) state. The ab initio results obtained in a wide range of internuclear distances R [1.7, 20.0] (Å) have quantitatively claimed the undulating behavior of interatomic potentials, predicted within the framework of the inelastic scattering theory. It has been established that at large R the interatomic potentials and dipole moments of highly excited (3,6,10)2Σ+ states, converging to Na (n = 4, 5, 62S)+He(22S) atomic limits, are modulated by the nodal structure of the radial Rydberg wave function (n > 3) s-electron of Na atom during its scattering on the remote He atom.

Analyzing the Nuclear Structure of 13O-13B and 13N-13C Mirror Nuclei

In the context of the shell model, electromagnetic transitions were used to analyze the nuclear structure of a mirror nucleus with the same mass number, A = 13. The shell model investigation was performed by calculating the root mean square (rms) for the proton, neutron, matter and charge radii, occupancies, the excitation energies, as well as electromagnetic moments, using the elements of a body density matrix of the PSDMOD two-body effective interactions carried out in the psdpn-shell model space. The present results adopted the harmonic oscillator's single particle eigen functions and Hartree-Fock approximation. In addition, the effect of core polarization was added using the effective charge and effective g factors to calculate electromagnetic moments. To acquire a fair analysis of the information, the core polarization has to be present. The outcomes were compared with experimental data

Performance assessment of the effective core potentials under the fermionic neural network: First and second row elements.

The rapid development of deep learning techniques has driven the emergence of a neural network-based variational Monte Carlo (VMC) method (referred to as FermiNet), which has manifested high accuracy and strong predictive power in the electronic structure calculations of atoms, molecules, and some periodic systems. Recently, the implementation of the effective core potential (ECP) scheme has further facilitated more efficient calculations in practice. However, there is still a lack of comprehensive assessments of the ECP's performance under the FermiNet. In this work, we set sail to fill this gap by conducting extensive tests on the first two row elements regarding their atomic, spectral, and molecular properties. Our major finding is that, in general, the qualities of ECPs have been correctly reflected under FermiNet. Two recently built ECP tables, namely, correlation consistent ECP (ccECP) and energy consistent correlated electron pseudopotential (eCEPP), seem to prevail in terms of overall performance. In particular, ccECP performs slightly better on spectral precision and covers more elements, while eCEPP is more systematically built from both shape and energy consistency and better treats the core polarization. On the other hand, the high accuracy of the all-electron calculations is hindered by the absence of relativistic effects as well as the numerical instabilities in some heavier elements. Finally, with further in-depth discussions, we generate possible directions for developing and improving FermiNet in the near future.

Long-Lived Circular Rydberg Qubits of Alkaline-Earth Atoms in Optical Tweezers

Coherence time and gate fidelities in Rydberg atom quantum simulators and computers are fundamentally limited by the Rydberg state lifetime. Circular Rydberg states are highly promising candidates to overcome this limitation by orders of magnitude, as they can be effectively protected from decay due to their maximum angular momentum. We report the first realization of alkaline-earth circular Rydberg atoms trapped in optical tweezers, which provide unique and novel control possibilities due to the optically active ionic core. Specifically, we demonstrate creation of very high-n (n=79) circular states of Sr88. We measure lifetimes as long as 2.55 ms at room temperature, which are achieved via cavity-assisted suppression of black-body radiation. We show coherent control of a microwave qubit encoded in circular states of nearby manifolds, and characterize the qubit coherence time via Ramsey and spin-echo spectroscopy. Finally, circular-state tweezer trapping exploiting the Sr+ core polarizability is quantified via measurements of the trap-induced light shift on the qubit. Our work opens routes for quantum simulations with circular Rydberg states of divalent atoms, exploiting the emergent toolbox associated with the optically active core ion. Published by the American Physical Society 2024

Measurement of infrared magic wavelength for an all-optical trapping of 40Ca+ ion clock

For the first time, we experimentally determine the infrared magic wavelength for the 40Ca+ 4s2S1/2→3d2D5/2 electric quadrupole transition by observation of the light shift canceling in 40Ca+ optical clock. A ‘magic’ magnetic field direction is chosen to make the magic wavelength insensitive to both the linear polarization purity and the polarization direction of the laser. The determined magic wavelength for this transition is 1056.37(9) nm, which is not only in good agreement with theoretical predictions (‘Dirac–Fock plus core polarization’ method) but also more precise by a factor of about 300. Using this measured magic wavelength, we also derive the differential static polarizability to be −44.32(32) a.u., which will be an important input for the evaluation of the blackbody radiation shift at room temperatures. Our work paves a way for all-optical-trapping of 40Ca+ optical clock.

Role of the Center of Mass Correction in Magnetic Form Factors for 19O and 21Na Exotic Nuclei with Different Interactions

The transverse magnetic electron scattering form factors of 19O and 21Na exotic nuclei were studied in the plane wave Born approximation (PWBA). The shell model calculations with three sd-shell interactions, USDA, USDB, and Wildenthal, were carried out for the ground and low-lying excited states. The exact center of mass correction in the Born approximation picture through the translation-invariant shell model (TISM) was included to modify the transverse form factors. The measured magnetic dipole moments were well reproduced with the core polarization (CP) effect introduced through the effective g-factors. The occupancies percentage with respect to the valence nucleons was also calculated.

Indications for the Substantial Predominance of Short-Range Effects on Inelastic Coulomb Form Factors for Various States in the 26Mg Nucleus

Short-range effects on C2, C3, as well as C4 form factors in the 26Mg nucleus, were examined. The charge density distribution in this nucleus was also tested by means of one and two body fragments of cluster enlargement in cooperation with single-particle wave functions of harmonic potential. The correlation of Jastrow form was employed to inset the influence of short-range into the two body fragment of cluster enlargement. The nucleus of 26Mg was assumed to own a 16O-core with (A-16) nucleons dispersed over the sd-model space. The form factors in 26Mg nucleus ascend from the core-polarization and model space involvements. The form of Tassie model, subject to the charge density, was used to determine the transition density of core polarization. The one body density matrix elements required for determining the transition density of model space for various transitions in 26Mg were found via carrying out shell model computations using the OXBASH program with the universal-sd interaction of Wildenthal. The present calculations were subjected to the oscillator and correlation parameters symbolized by and respectively. These parameters are self-sufficiently generated for every specific nucleus by fitting between the calculated and observed elastic form factors. For determining the charge density, elastic form factors and inelastic Coulomb form factors for dissimilar excited states in 26Mg, one value is needed for and This study shows indications for the substantial predominance of short-range influences on current computations, where considering these influences look to be requisite for carrying out a distinguished adjustment in calculated results which ultimately leads to a remarkable explication of the data throughout all the considered momentum transfers.

STUDYING INELASTIC TRANSVERSE ELECTRON SCATTERING FORM FACTORS OF THE ISOSCALAR TRANSITIONS IN 10B NUCLEUS

The inelastic transverse electron scattering form factors are studied for the fourisoscalar transitions for the states of 10B nucleus. These states are specifiedby J T  =1+0 (0.718 MeV), 1 0 2 (2.154 MeV), 2+0 (3.587 MeV) and 3 0 2 (4.774MeV). These form factors are analyzed in the framework of the harmonic oscillatorshell model.The transverse form factors have been calculated in the framework of the multinucleonconfiguration mixing shell model using the two-body interaction of Cohenand Kurath (C-K) to generate the 1p-shell wave function. The core polarization (CP)effects are included in the calculations through effective g-factors. A higherconfiguration effect outside the 1p-shell model space enhances the form factors forq-values and reasonably reproduces the data. The value of the size parameter (b) ischosen to reproduce the root mean square charge radius. The present results arecompared with available experimental data and with that of other models.PACS:21.60-n,21.60 Cs, 25.30Dh,27.20 th

INELASTIC LONGITUDINAL C6 ELECTRON SCATTERING FORM FACTORS IN Ti-50, (RESIDUAL INTERACTION CONSIDERATION)

The single orbit 1f7/2 has been adopted as a model space. The use of modern realistic M3Y effective nucleon- nucleon interaction with two sets of fitting parameters (Ried fitting (M3Y-P1), and Paris fitting (M3Y-P0)) beside the use of MSDI has been done as a residual interactions within the calculation of core polarization effects in Inelastic longitudinal electron scattering C6 form factor in Ti-50 within the framework of first order perturbation theory (microscopic theory) with 2ћω excitation energy coupling the core orbits to the higher configurations one across the model space at normal transition. Harmonic oscillator wave functions (H.O) has been adopted as a single particle wave functions in 1f7/2 and with the aid of F7MBZ model space 1f7/2 effective interaction to generate the model space wave functions. The present results have been compared with

Shape polarization in the tin isotopes near N = 60 from precision g-factor measurements on short-lived 11/2− isomers

The g factors of 11/2− isomers in semimagic 109Sn and 111Sn (isomeric lifetimes τ=2.9(3) ns and τ=14.4(7) ns, respectively) were measured by an extension of the Time Differential Perturbed Angular Distribution technique, which uses LaBr3 detectors and the hyperfine fields of a gadolinium host to achieve precise measurements in a new regime of short-lived isomers. The results, g(11/2−;109Sn)=−0.186(8) and g(11/2−;111Sn)=−0.214(4), are significantly lower in magnitude than those of the 11/2− isomers in the heavier isotopes and depart from the value expected for a near pure neutron h11/2 configuration. Broken-symmetry density functional theory calculations applied to the sequence of 11/2− states reproduce the magnitude and location of this deviation. The g(11/2−) values are affected by shape core polarization; the odd 0h11/2 neutron couples to Jπ=2+,4+,6+... configurations in the weakly-deformed effective core, causing a decrease in the g-factor magnitudes.

Polarization factors and their effects on the rotational gyromagnetic ratio

The effect of the polarizations on the collective gyromagnetic ratio (g R ) has been investigated in detail using the Rotational Invariant Quasiparticle Phonon Nuclear Model (RI-QPNM). The model includes an axially symmetric mean-field potential, monopole pairing, spin-dependent residual interactions, and the restoration forces determined according to Pyatov’s prescription for rotational invariance. The restoration of the rotational symmetry gives a solution at the zero energy associated with the rotational branch of nucleonic motion, allowing us to obtain the g R -factors of the core. The remaining solutions lead to the appearance of configuration mixing in the excitation spectrum of the odd-mass deformed nucleus. The configuration mixing quenches both spin and angular momentum matrix elements and affects the contribution of the odd particle to the g R . It has been demonstrated that the polarization factors associated with the ΔK = 1 matrix elements are essential to achieve quantitative agreement with the experimental data. It has also been shown that the general assumption for core polarization, i.e., is insufficient to explain the experimental data.

Density-dependent relativistic mean field approach and its application to single-Λ hypernuclei in oxygen hyperisotopes* *Supported by the Fundamental Research Funds for the Central Universities, Lanzhou University (lzujbky-2022-sp02, lzujbky-2023-stlt01), the National Natural Science Foundation of China (11875152, 12275111), and the Strategic Priority Research Program of Chinese Academy of Sciences (XDB34000000)

The in-medium feature of nuclear force, which includes both nucleon-nucleon () and hyperon-nucleon () interactions, impacts the description of single-Λ hypernuclei. With the alternated mass number or isospin of hypernuclei, such effects may be unveiled by analyzing the systematic evolution of the bulk and single-particle properties. From a density-dependent meson-nucleon/hyperon coupling perspective, a new effective interaction in the covariant density functional (CDF) theory, namely, DD-LZ1-, is obtained by fitting the experimental data of Λ separation energies for several single-Λ hypernuclei. It is then used to study the structure and transition properties of single-Λ hypernuclei in oxygen hyperisotopes, in comparison with those determined using several selected CDF Lagrangians. A discrepancy is explicitly observed in the isospin evolution of spin-orbit splitting with various effective interactions, which is attributed to the divergence of the meson-hyperon coupling strengths with increasing density. In particular, the density-dependent CDFs introduce an extra contribution to reduce the value but enhance the isospin dependence of the splitting, which originates from the rearrangement terms of Λ self-energies. In addition, the characteristics of hypernuclear radii are studied along the isotopic chain. Owing to the impurity effect of the Λ hyperon, a size shrinkage is observed in the matter radii of hypernuclei compared with the cores of normal nuclei, and its magnitude is further elucidated to correlate with the incompressibility of nuclear matter. Moreover, there is a sizable model-dependent trend in which the Λ hyperon radii evolve with neutron number, which is decided partly by the in-medium interactions and core polarization effects.

Particle-Particle Collective Excitations of Sn isotopes

In this paper, energy-level schemes and reduced electric transition strengths of neutron-rich Tin isotopes 102, 110, 116, 120, 122Sn (Z=50) are studied using collective models, that is, particle-particle Tamm-Dancoff Approximation and particle-particle Random Phase Approximation. According to these models, the excited states of closed-core A+2 systems with multipolarity J and isospin T can be described as a linear combination of particle-particle pairs. In our investigation, the low-lying states of the investigated isotopes 102, 110, 116, 120, 122Sn are described by acting two-particle operators on a correlated core 100Sn, 108Sn, 114Sn, 118Sn, and 120Sn, respectively. The Hamiltonian is diagonalized within the model space include {1g7/2, 2d5/2, 2d3/2, 3s1/2 and 1h11/2} orbits, using the matrix elements of neutron-neutron interaction and modified surface delta interaction. The calculated values are checked by using the resultant eigenvalues and eigenvectors to calculate the excitation energies and reduced electric transition strengths. Our calculated results are compared to the available experimental data, and these comparisons led to reasonable agreements. Effective charges are also used to account for the core polarization effect.

Critically Evaluated Atomic Data for the Au iv Spectrum

A spectral investigation of triply ionized gold (Au iv) has been carried out in the wavelength region of 500–2106 Å. The gold spectra were photographed at the National Institute of Standards and Technology, USA, on a 10.7 m normal incidence vacuum spectrograph (NIVS) using a sliding spark source as well as on a 3 m NIVS at the Antigonish laboratory in Canada with a triggered spark source. Our analysis is theoretically supported by the pseudorelativistic Hartree–Fock (HFR) formalism with a superposition of configuration interactions implemented in Cowan's suite of codes. Radiative transition parameters are also calculated using the HFR+CPOL (core polarization effects) model and the multiconfiguration Dirac–Hartree–Fock approach, and their comparisons are used to evaluate the transition rate data. All the previously reported levels of the 5d 8, 5d 76s, and 5d 76p configurations are confirmed, except one, and three are newly established. The missing 1 S 0 level of 5d 8 is now established at 55,277.8 cm−1. A total of 981 observed lines (E1 type), classified to 1031 transitions, including 133 newly identified, enabled us to optimize 139 energy levels. Several astrophysically important transitions, forbidden (M1- and E2-type) lines of 5d 8 and 5d 76s, are provided with their Ritz wavelengths and radiative parameters. A critically evaluated set of energy levels, observed and Ritz wavelengths along with their uncertainties, transition rates, and uniformly scaled intensities of Au iv lines have been presented. Also, large-scale atomic data to compute the opacity of Au iv in the kilonova ejecta have been supplemented in this work.

Spectroscopic Properties of the Alkali-Krypton Diatomic M-Kr (M = Rb, Cs, and Fr) van der Waals Systems Including the Spin-Orbit Coupling.

Using an ab initio approach based on pseudopotential technique, pair potential approach, core polarization potentials, and large Gaussian basis sets, we investigate interaction of heavy alkali-krypton diatomic M-Kr (M = Rb, Cs, and Fr) van der Waals dimers. In this context, the core-core interactions for M+-Kr (M = Rb, Cs, and Fr) are calculated at coupled-cluster single and double excitation (CCSD) level and included in the total potential energy. Therefore, the potential energy curves are performed for 14 electronic states: eight of 2Σ+ symmetry, four of 2Π symmetry, and two of 2Δ symmetry. Furthermore, for each M-Kr dimer, the spin-orbit coupling has been considered for the B2Σ+, A2Π, 32Σ+, 22Π, 52Σ+, 32Π, and 12Δ states. In addition, the transition dipole moment has been determined, including the spin-orbit effect using the rotational matrix issued from the spin-orbit potential energy calculations.