Respective Ground States Research Articles

Dissociative recombination of rotationally cold ArH+

We have experimentally studied dissociative recombination (DR) of electronically and vibrationally relaxed ArH+ in its lowest rotational levels, using an electron-ion merged-beams setup at the Cryogenic Storage Ring. We report measurements for the merged-beams rate coefficient of ArH+ and compare it to published experimental and theoretical results. In addition, by measuring the kinetic energy released to the DR fragments, we have determined the internal state of the DR products after dissociation. At low collision energies, we find that the atomic products are in their respective ground states, which are only accessible via nonadiabatic couplings to neutral Rydberg states. Published theoretical results for ArH+ have not included this DR pathway. From our measurements, we have also derived a kinetic temperature rate coefficient for use in astrochemical models. Published by the American Physical Society 2024

2,2]Paracyclophane Bridged, Thiophene Based Macrocycles: Synthesis and Electronic Properties in Different Redox States.

The study of through-space electronic coupling in π-conjugated systems remains an underexplored area. In this work, we present the facile synthesis of two isomeric macrocycles (1 and 2) bridged by [2,2]paracyclophane (pCp) and based on thiophene. The structures of these macrocycles have been confirmed through X-ray crystallographic analysis. Our investigation centers on their electronic properties across various redox states, with a specific focus on potential through-space electronic coupling and global aromaticity. Experimental measurements, including UV-vis-NIR electronic absorption, NMR, ESR spectra, and X-ray diffraction, combined with theoretical calculations, reveal that both the neutral compounds and their tetracations exhibit a closed-shell ground state. However, their dications manifest as diradical dications with a subtle magnetic exchange interaction. Consequently, the through-space electronic coupling facilitated by the pCp unit in their respective ground states appears to be weak.

Diffusion probabilistic models enhance variational autoencoder for crystal structure generative modeling

The crystal diffusion variational autoencoder (CDVAE) is a machine learning model that leverages score matching to generate realistic crystal structures that preserve crystal symmetry. In this study, we leverage novel diffusion probabilistic (DP) models to denoise atomic coordinates rather than adopting the standard score matching approach in CDVAE. Our proposed DP-CDVAE model can reconstruct and generate crystal structures whose qualities are statistically comparable to those of the original CDVAE. Furthermore, notably, when comparing the carbon structures generated by the DP-CDVAE model with relaxed structures obtained from density functional theory calculations, we find that the DP-CDVAE generated structures are remarkably closer to their respective ground states. The energy differences between these structures and the true ground states are, on average, 68.1 meV/atom lower than those generated by the original CDVAE. This significant improvement in the energy accuracy highlights the effectiveness of the DP-CDVAE model in generating crystal structures that better represent their ground-state configurations.

Spin-statistics relation and Abelian braiding phase for anyons in the fractional quantum Hall effect

Quasihole excitations in fractional quantum Hall (FQH) systems exhibit fractional statistics and fractional spin, but how the spin-statistics relation emerges from many-body physics remains poorly understood. Here we prove a spin-statistics relation using only FQH wave functions, on both the sphere and disk geometry. In particular, the proof on the disk generalizes to all quasiholes in realistic systems, which have a finite size and could be deformed into arbitrary shapes. Different components of the quasihole spins are linked to different conformal Hilbert spaces (CHS), which are nullspaces of model Hamiltonians that host the respective FQH ground states and quasihole states. Understanding how the intrinsic spin of the quasiholes is linked to different CHS is crucial for the generalized spin-statistics relation that takes into account the effect of metric deformation. In terms of the experimental relevance, this enables us to study the effect of deformation and disorder that introduces an additional source of Berry curvature, an aspect of anyon braiding that has been largely neglected in previous literature.

Direct high-precision mass spectrometry of superheavy elements with SHIPTRAP

Direct mass measurements in the region of the heaviest elements were performed with the Penning-trap mass spectrometer SHIPTRAP at GSI Darmstadt. Utilizing the phase-imaging ion-cyclotron-resonance mass-spectrometry technique, the atomic masses of No251 (Z=102), Lr254 (Z=103), and Rf257 (Z=104) available at rates down to one detected ion per day were determined directly for the first time. The ground-state masses of No254 and Lr255,256 were improved by more than one order of magnitude. Relative statistical uncertainties as low as δm/m≈10−9 were achieved. Mass resolving powers of 11 000 000 allowed resolving long-lived low-lying isomeric states from their respective ground states in No251,254 and Lr254,255. This provided an unambiguous determination of the binding energies for odd-A and odd-odd nuclides previously determined only indirectly from decay spectroscopy.Received 24 June 2022Accepted 28 September 2022DOI:https://doi.org/10.1103/PhysRevC.106.054325Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBinding energy & massesNuclear structure & decaysPropertiesA ≥ 220TechniquesMass spectrometryPenning trapsRadioactive beamsNuclear Physics

Low-lying level structures in the transuranic n -rich Z=93 nuclei Np243 and Np244

Low-lying level structures of the neutron-rich transuranic $Z$=93 isotopes, namely, odd-mass $^{243}\mathrm{Np}$ and its odd-odd neighbor $^{244}\mathrm{Np}$, are investigated with a view to characterize the respective ground state (gs) and to identify any long-lived isomer (LLI). For $^{243}\mathrm{Np}$ levels, we critically examine all the available information from three sources, namely, experimental, systematics from isotopic and isotonic neighbor, and theoretical results from microscopic Nilsson model calculations. Our investigations conclude $^{243}\mathrm{Np}$ gs ${\mathrm{J}}^{\ensuremath{\pi}}$ and configuration to be 5/2${}^{\ensuremath{-}}[523\ensuremath{\downarrow}$] on all counts. For the odd-odd $^{244}\mathrm{Np}$, we employ our well-tested three-step two-quasiparticle rotor model (TQRM) to identify and evaluate excitation energies of low-lying (${E}_{x}\phantom{\rule{4pt}{0ex}}\ensuremath{\le}$ 400 keV) 2qp bands and respective I(I$+$1) rotational levels. These calculations yield $^{244}\mathrm{Np}$ gs to have ${\mathrm{J}}^{\ensuremath{\pi}}$ and 2qp configuration as 2${}^{+}${p:5/2${}^{\ensuremath{-}}[523]\ensuremath{\bigotimes}$ n:${9/2}^{\ensuremath{-}}$[734]} while confirming the earlier reported ${7}^{\ensuremath{-}}${p:5/2${}^{+}[642]\ensuremath{\bigotimes}$ n:${9/2}^{\ensuremath{-}}$[734]} 2.29 m high-spin isomer (HSI) to be an excited state placed around ${E}_{x}\phantom{\rule{4pt}{0ex}}\ensuremath{\sim}100$ keV. We also briefly discuss the earlier reported $^{244}\mathrm{Np}\phantom{\rule{4pt}{0ex}}\ensuremath{\beta}$-decay branches of the ${\mathrm{K}}^{\ensuremath{\pi}}$=7${}^{\ensuremath{-}}$ isomer and the admissible main $\ensuremath{\beta}$ branches of ${\mathrm{K}}^{\ensuremath{\pi}}$=2${}^{+}$ gs to the various levels in $^{244}\mathrm{Pu}$.

Nuclear Structure and Decay Data for A=149 Isobars

Experimental nuclear structure and decay data are evaluated for all the 17 known nuclides of mass 149 (Xe, Cs, Ba, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb). Detailed compiled and evaluated spectroscopic information is presented for each reaction and decay dataset, and recommended values are provided for level properties, α, β and γ radiations, and other spectroscopic parameters, based on an evaluation of all the available experimental data for A=149 isobaric nuclides. Although large amounts of nuclear spectroscopic data are available for nuclides of A=149, yet large gaps in knowledge exist, as described below. For the lowest atomic number nuclide 149Xe, only the isotopic identification has been made, with no data for its ground-state half-life. For 149Cs, 149Tm and 149Yb information is available for only the respective ground states. For 149Ba, 149La and 149Er, limited data exist for excited states. Many of the decay schemes of radioactive nuclei of A=149 are considered as incomplete, either due to large energy differences between the highest observed excited states in daughter nuclides and the respective Q-values, or due to the lack of confirmed γ-ray data, as listed below: 149Cs → 149Ba, 149Ba → 149La, 149La → 149Ce, 149Ce → 149Pr, 149Pr → 149Nd, 149Tb(4.17 min) → 149Gd, 149Ho(21.0 s and 56 s) → 149Dy, 149Er(4 s and 9.6 s) → 149Ho, and 149Tm → 149Er. No data exist for the decay of 149Yb to 149Tm. Data for half-lives of the excited states in this mass chain are generally lacking as given below by the number of excited levels of known half-life / approximate number of known levels in a nuclide: 2/17 for 149Ba, 0/18 for 149La, 3/53 for 149Ce, 3/44 for 149Pr, 17/110 for 149Nd, 9/90 for 149Pm, 10/210 for 149Sm, 2/125 for 149Eu, 6/270 for 149Gd, 5/200 for 149Tb, 3/80 for 149Dy, 3/90 for 149Ho, and 3/14 for 149Er. This work supersedes earlier evaluations of A=149 nuclides published by 2004Si16, 1994Si18, 1985Sz01 and 1976Ho17.

Simultaneous cooling by measuring one ancillary system

We present a simultaneous-cooling protocol for a double-resonator system via projective measurements on an ancillary $V$-type qutrit. Through repeated measurements on the ground state of the ancillary system, the two resonators can be cooled down to their respective ground states from thermal states. With respect to the measurement-based cooling, an optimized measurement-interval $\tau_{\rm opt}$ is analytically obtained for the first time, which is inversely proportional to the collective thermal Rabi frequency $\Omega_{\rm th}$ as a function of the resonators' average population of the last round. Under about only $20$ optimized measurements, the average population of the target resonators can be reduced by $6$ orders in magnitude. Our simultaneous or collective cooling protocol is scalable to the systems with more numbers of resonators and robust to the fluctuation in the resonator frequency.

Photoexcited Intramolecular Charge Transfer in Dye Sensitizers: Predictive In Silico Screening for Dye-Sensitized Solar Cell Devices.

Efficient photoinduced intramolecular charge transfer (ICT) from donor to acceptor in dye molecules is the functional basis and key property in the working of a dye-sensitized solar cell (DSSC). To understand the ICT process in photoexcited dye molecules, we analyze the electronic properties and structural parameters of a chosen set of experimentally synthesized donor–acceptor (D–A) and donor−π-spacer−acceptor (D−π–A) type dye molecules in their ground, excited, and cationic states. The correlation between structural modification and charge redistribution in different parts of the molecule helps to identify the extent of π-conjugation and spatial rearrangement of electron density localization along the molecular skeleton. We find that prominent twisting of several groups and the resulting molecular bond rearrangements in larger parts of the molecule promote efficient donor to acceptor ICT, such as in D–A type ADEKA1 and C275 dyes. Thus, based on the modest computation of structural and electronic properties of dye molecules in their respective ground, excited, and cationic states, we identify the desired structural changes that facilitate tunable intramolecular charge transfer to highlight a simple and direct prescription to screen out probable efficient dye molecules among many samples. Our approach complements recent experimental evidence of capturing the structural view of the excited-state charge transfer in molecules.

A two-dimensional magnetic carbon allotrope of hexagonally arranged fused pentagons

A two-dimensional magnetic carbon allotrope of hexagonally arranged fused pentagons is theoretically predicted through the copolymerization of benzene and spiro[4.4]nonatetraene. The hexagonal spiro-graphene has ferromagnetic and antiferromagnetic phases as its respective ground and metastable states, the two states being almost degenerate in energy because the Dirac band at the Fermi level is narrow. The polarized electron spin is distributed throughout a hexagonal network of three-fold coordinated C atoms surrounded by four-fold coordinated C atoms. The sheet of these coordinated C atoms also possesses an electrostatic polarization normal to the atomic layer because the atomic arrangement along this direction is asymmetric.

The activated reaction of dichlorocarbene with triplet molecular oxygen.

The well-known dichlorocarbene (CCl2, 1) is deemed to undergo an extremely facile addition reaction with triplet molecular oxygen (3O2) under formation of the corresponding singlet Criegee intermediate, phosgene O-oxide. This is unexpected, because the carbene possesses a singlet ground state with a large singlet-triplet gap and, typically, only triplet carbenes react swiftly with triplet dioxygen. Hence, we deployed a careful theoretical study of this reaction and computed the oxygen addition barrier at levels of electron correlation as high as CCSD(T) and BD(TQ) and basis sets as large as cc-pV5Z. Our results firmly establish the existence of a reaction barrier, and we estimate its height to amount to 8.8 kcal mol-1. Furthermore, the initially formed triplet dioxygen adduct is prone to facile O-O bond breaking rendering phosgene and triplet oxygen atoms likely products of the overall reaction. As a general conclusion, we find that carbenes are ambiphiles in oxygen additions and more electrophilic as well as that more nucleophilic carbenes show greater reactivity.

Spontaneous magnetic order and spin and charge entanglement of a coupled spin-electron model on a decorated square lattice composed from trigonal bipyramids

A coupled spin-electron model on a decorated square lattice formed by interconnected trigonal bipyramids is exactly solved by imposing two mobile electrons per each triangular plaquette with the help of a generalized decoration-iteration transformation, which establishes a precise mapping correspondence with the effective Ising model on a square lattice with temperature-dependent interaction. The investigated spin-electron model exhibits two different macroscopically degenerate ground states. The residual entropy of the first ground state, which shows a spontaneous ferromagnetic or ferrimagnetic long-range order depending on character of the exchange coupling, arises from chiral degrees of freedom of the mobile electrons. In contrast, the second ground state is disordered due to a kinetically driven frustration of the localized Ising spins triggered by the hopping term of the mobile electrons. The outstanding reentrant phase transitions connected with temperature induced formation of the spontaneous ferromagnetic or ferrimagnetic order can be found if the spin-electron model is driven sufficiently close to the ground-state phase boundary, but the disordered frustrated phase is the respective ground state. It is verified that the bipartite fermionic entanglement between two mobile electrons within the spontaneously ordered ferromagnetic or ferrimagnetic phase predominantly comes from their charge degrees of freedom, while the one within the disordered frustrated phase comes from both charge and spin degrees of freedom of these particles.

Finite and infinite matrix product states for Gutzwiller projected mean-field wave functions

Matrix product states (MPS) and `dressed' ground states of quadratic mean fields (e.g. Gutzwiller projected Slater Determinants) are both important classes of variational wave-functions. This latter class has played important roles in understanding superconductivity and quantum spin-liquids. We present a novel method to obtain both the finite and infinite MPS (iMPS) representation of the ground state of an arbitrary fermionic quadratic mean-field Hamiltonian, (which in the simplest case is a Slater determinant and in the most general case is a Pfaffian). We also show how to represent products of such states (e.g. determinants times Pfaffians). From this representation one can project to single occupancy and evaluate the entanglement spectra after Gutzwiller projection. We then obtain the MPS and iMPS representation of Gutzwiller projected mean-field states that arise from the variational slave-fermion approach to the $S=1$ Bilinear-Biquadratic (BLBQ) quantum spin chain. To accomplish this, we develop an approach to orthogonalize degenerate iMPS to find all the states in the degenerate ground-state manifold. We find the energies of the MPS and iMPS states match the variational energies closely indicating the method is accurate and there is minimal loss due to truncation error. We then present the first exploration of the entanglement spectra of projected slave-fermion states exploring their qualitative features and finding good qualitative agreement with the respective exact ground state spectra found from DMRG.

Nuclear Data Sheets for A=233

The present evaluation of the known A=233 nuclides (233Fr, 233Ra, 233Ac, 233Th, 233Pa, 233U, 233Np, 233Pu, 233Am, 233Cm) and 233Bk represents an update and revision, after 15 years of the previous evaluation of A=233 published by B. Singh and J.K. Tuli (2005Si15). Laboratory identification of 233Bk nuclide is still considered as tentative. Various decay and reaction data are evaluated and compared. Adopted data, levels, gammas, level half-lives, spins, parities, and configuration assignments are provided. For 233Fr, 233Ra, 233Ac, 233Pu, 233Am and 233Cm, information is available for the respective ground states only. The decay schemes from β− decays of 233Fr and 233Ra, and from ε decay of 233Am and 233Cm are unknown, while those from β− decay of 233Ac, and from ε decay of 233Np are considered incomplete. The α decay of 237Np to 233Pa has been studied in detail by many investigators, yet the decay scheme is considered incomplete as several very low-energy transitions are involved, without the knowledge of their intensities, resulting in mismatch of directly measured α feedings and those deduced from γ-transition intensity balances. The decay schemes from α decays of 237Am, 237Cm and 237Cf to respective A=233 daughters are considered incomplete. Particle-transfer and high-spin data are available for 233Th, 233Pa and 233U nuclei, which remain the most extensively studied in this mass chain. However, data for half-lives for the excited states are available only for one level in 233Pa, and for five levels in 233U, thus limiting the knowledge of reduced transition probabilities in this mass chain.

Electron-impact excitation of W40+–W43+ ions: Cross-section and polarization

Electron-impact excitation of tungsten ions [Formula: see text] has been studied using the fully relativistic distorted wave (RDW) theory. The excitation cross-sections of selected electric dipole allowed transitions of these ions to be determined for the incident electron energies from the excitation threshold to 20 keV. Further, the calculated cross-section results are fitted with an analytical expression for direct applications in plasma modeling. In addition, using the density matrix theory, the linear polarization of the photons emitted from the excited tungsten ions when decay to their respective ground states is presented.

Global Calculations of Beta-Decay Properties Based on the Fayans Functional

An effective approximation to a fully self-consistent global description of beta-decay properties of nuclei within the theory of finite Fermi systems is presented. It is based on describing the ground state properties within the energy density functional proposed by Fayans and coauthors (DF3) and on the continuum quasiparticle random-phase approximation (CQRPA). The accuracy of global DF3 $$+$$ CQRPA calculations is analyzed. For more than 200 (quasi)spherical nuclei with $$Z=18$$ to 51 having half-lives in the range of $$T_{1/2}<5$$ s, the experimental half-lives and delayed neutrons emission probabilities are described within a factor of two and three, respectively. A comparison is performed with the results of similar calculations based on state-of-the-art self-consistent models : the relativistic spherical RHB $$+$$ RQRPA approach and deformed finite-amplitude method (FAM) and HFB $$+$$ QRPA approaches, as well as the interacting shell model. A detailed analysis of beta-decay properties in the nickel isotopic chain that were obtained in various calculations allows us for determining basic mechanisms responsible for the sudden shortening of the half-lives that was found experimentally at RIKEN for isotopes heavier than the doubly magic $${}^{78}$$ Ni nucleus. These are the contributions of first-forbidden (FF) transitions and multiphonon configurations and spin inversion of the respective ground states. The acceleration effect in question is highly sensitive to the balance of the contributions of Gamow–Teller (GT) and FF transitions to the total beta-decay rate. It is shown that, in nickel isotopes, the ratio of these contributions takes different values before and after the neutron-shell crossing at $$N=50$$ .

Mechanisms of the photodissociations of single isolated methanol

The mechanisms of the photodissociation of single isolated methanol (CH3OH) molecules in the lowest singlet-excited (S1) state were systematically studied using the complete active-space second-order perturbation theory (CASPT2) and transition state theory (TST). This theoretical study focused on the nonradiative relaxation processes that transform the S0 → S1 vertically excited molecule to the products in their respective electronic ground states. The results confirmed that O–H dissociation is the predominant exothermic process and that the formation of formaldehyde (CH2O), in which the O–H dissociated species are the precursors for the reaction in the S0 state, is the second most favorable process. For C–O dissociation, the theoretical results suggested a thermally excited precursor in a different Franck–Condon region in the S0 state, from which vertical excitation leads to a transition structure in the S1 state and spontaneously to the [CH3]· and [OH]· products in their electronic ground states. The CASPT2 and TST results also revealed the possibility of [CH3OH] → [CH2OH2] isomerization dissociation, in which another thermally excited precursor is vertically excited, and C–O dissociation and intermolecular proton transfer lead to the singlet and triplet [CH2]–[H2O] H-bond complexes in their electronic ground states. Although sufficient thermal energy to generate the precursors in the S0 state is available and the reactions are kinetically feasible at high temperatures, the strongly kinetically controlled O–H dissociation predominates the C–O and [CH3OH] → [CH2OH2] isomerization dissociations. The present results verified and confirmed the reported theoretical and experimental findings and provided insights into the thermal selectivity and interplay between thermal excitation and photoexcitation.

Photolytic mechanisms of hydroxylamine.

The photodissociation of small molecules has been extensively studied because of the increase in environmental problems related to the atmosphere of the Earth. In this work, the photodissociation mechanisms of hydroxylamine (NH2OH) as a model molecule in its lowest singlet-excited (S1) state were systematically studied using the complete active space second-order perturbation theory (CASPT2) and transition state theory (TST). In particular, this study focused on nonradiative relaxation processes that convert the S0 → S1 excited-state molecule to its products in their respective electronic ground states. The potential energy curves obtained from relaxed scans suggest that O–H dissociation is the preferred process in the S1 state. For the N–O and N–H dissociation pathways, thermally excited precursors were hypothesized to form in the S0 state to circumvent O–H dissociation. Thus, S0 → S1 vertical excitations lead to transition structures in the S1 state, which fragment to their respective electronic-ground-state products. The thermodynamic and kinetic results confirmed the precursor hypothesis, showing that the exothermic energy caused by the formation of HNO and H2 is sufficient to generate such precursors in the S0 state. Additionally, the TST confirmed that unimolecular isomerization–dissociation is a two-step process that generates products effectively by direct photolysis of the corresponding covalent bonds. In particular, the process consists of O–H bond dissociation, followed by spontaneous isomerization and formation of H2 in its electronic ground state, resulting in the high quantum yield observed in the UV absorption experiments in the preferential formation of HNO and H2. The configuration interaction coefficients of the characteristic structures on the potential energy curves revealed considerable changes in the multiconfigurational character of the wavefunctions, especially for the transition structures. These are characterized by the development of Rydberg orbitals, being produced at the intersection of the S0 and S1 states. The present study highlights the effects of thermal selectivity and the multiconfigurational character of the wavefunctions on photodissociation. Because detailed information on the photolytic mechanisms of isolated NH2OH is limited both theoretically and experimentally, these results provide fundamental insight into unimolecular photodissociation, posing ground for future studies on related systems.

Ab Initio Molecular Orbital Study of the First Four Si/C Alternately Substituted Annulenes.

The ground and low-lying excited states of four alternating Si/C annulenes, H nSi n/2C n/2 with n = 4, 6, 8, and 10, have been investigated by ab initio molecular orbital methods and compared to those of their all-carbon and all-silicon analogues. In the ground state, all of the Si/C-mixed annulenes, except for the largest 10-membered annulene (H10Si5C5), assume equal-bond-length structures by adopting a closed-shell electronic structure in the possible highest symmetry. For the largest H10Si5C5, the trend of the bond delocalization still remains but the circular structure is considerably distorted and nonplanar due to severe angle strain. In the low-lying singlet (S1) and triplet (T1) states, the geometry of the compounds tends to be nonplanar as the excitations produce silyl radical character. Relative energies of the T1 and S1 states of the 6-membered ring, compared to those of the respective ground states (S0), are higher than those of the 4- and 8-membered rings, suggesting a special stability for H6Si3C3. The planar rhombus shape of the formally antiaromatic H4Si2C2 suggests that a synthetic effort is merited. Bonding analyses are given to support the conclusions reached on the basis of geometric structures and excited-state energetics.

Electron-impact excitations of highly charged tungsten ions and polarization study of their successive photon decay

Fully relativistic distorted wave theory has been utilized to study the electron-impact excitation of highly charged tungsten ions viz. Y-like (W35+), Sr-like (W36+), Rb-like (W37+) and Br-like (W39+). Electric dipole transitions pertaining to n = 4 → n′ = 4 states have been considered in these four ions. The electron excitation cross-sections are calculated for these ions in the wide range of electron-impact energies from excitation threshold to 20 keV. The required relativistic bound states wave functions for the initial and excited states of the ions are obtained using GRASP2k code. The accuracy of the computed wave functions is ascertained by comparing the calculated energies and oscillator strengths for the considered transitions with the available theoretical and experimental results. For the direct application of the cross-sections to the plasma modelling our calculated cross-sections are fitted to suitable analytical expressions. Further, the degree of linear polarization of the emitted photons due to the decay of the electron from the excited tungsten ions to their respective ground states is also calculated using density matrix theory. There are no previous calculations available for the cross-sections and polarizations to compare with our results of these ions.