Specific Mass Shift Research Articles

Optical pumping of 5s4d1D2 strontium atoms for laser cooling and imaging

We present a faster repumping scheme for strontium magneto-optical traps operating on the broad 5s21S0−5s5p1P1 laser cooling transition. Contrary to existing repumping schemes, we directly address lost atoms that spontaneously decayed to the 5s4d1D2 state, sending them back into the laser cooling cycle by optical pumping on the 5s4d1D2−5s8p1P1 transition. We thus avoid the ∼100µs-slow decay path from 5s4d1D2 to the 5s5p3P1,2 states that is part of other repumping schemes. Using one low-cost external-cavity diode laser emitting at 448nm, we show our scheme increases the flux out of a 2D magneto-optical trap by 60% compared to without repumping. Furthermore, we perform spectroscopy on the 5s4d1D2−5s8p1P1 transition and measure its frequency νSr88=(668917515.3±4.0±25)MHz. We also measure the frequency shifts between the four stable isotopes of strontium and infer the specific mass and field shift factors, δνSMS88,86=−267(45)MHz and δνFS88,86=2(42)MHz. Finally, we measure the hyperfine splitting of the 5s8p1P1 state in fermionic strontium and deduce the magnetic dipole and electric quadrupole coupling coefficients A=−4(5)MHz and B=5(35)MHz. Our experimental demonstration shows that this simple and very fast scheme could improve the laser cooling and imaging performance of cold strontium atom devices, such as quantum computers based on strontium atoms in arrays of optical tweezers. Published by the American Physical Society 2024

Refined theoretical values of field and mass isotope shifts in thallium to extract charge radii of Tl isotopes.

Electronic factors for the field and mass isotope shifts in the 6p 2P3/2 → 7s 2S1/2 (535nm), 6p 2P1/2 → 6d 2D3/2 (277nm), and 6p 2P1/2 → 7s 2S1/2 (378nm) transitions in neutral thallium were calculated within the high-order relativistic coupled cluster approach. These factors were used to reinterpret previous experimental isotope shift measurements in terms of charge radii of a wide range of Tl isotopes. Good agreement between theoretical and experimental King-plot parameters was found for the 6p 2P3/2 → 7s 2S1/2 and 6p 2P1/2 → 6d 2D3/2 transitions. It was shown that the value of the specific mass shift factor for the 6p 2P3/2 → 7s 2S1/2 transition is not negligible compared with the value of normal mass shift in contrast to what had been suggested previously. Theoretical uncertainties in the mean square charge radii were estimated. They were substantially reduced compared with the previously ascribed ones and amounted to less than 2.6%. The achieved accuracy paves the way for a more reliable comparison of the charge radii trends in the lead region.

Model-QED-operator approach to relativistic calculations of the nuclear recoil effect in many-electron atoms and ions

A model-operator approach to fully relativistic calculations of the nuclear recoil effect on energy levels in many-electron atomic systems is worked out. The one-electron part of the model operator for treating the normal mass shift beyond the Breit approximation is represented by a sum of semilocal and nonlocal potentials. The latter ones are constructed by employing the diagonal and off-diagonal matrix elements rigorously evaluated for hydrogenlike ions to first order in the electron-to-nucleus mass ratio. The specific mass shift beyond the lowest-order relativistic approximation has a form which can be directly employed in calculations. The capabilities of the method are probed by comparison of its predictions with the results of ab initio QED calculations. The proposed operator can be easily incorporated into any relativistic calculation based on the Dirac-Coulomb-Breit Hamiltonian.

Isotope shifts in the metastable a5F and excited y5Go terms of atomic titanium

We measure and analyze the isotope shifts the multiplet of transitions between the metastable a$^5$F and excited y$^5$G$^\circ$ terms of neutral titanium by probing a titanium vapor in a hollow cathode lamp using saturated absorption spectroscopy. We resolve the five $J\to J+1$ and the four $J\to J$ transitions within the multiplet for each of the the three $I=0$ stable isotopes ($^{46}$Ti, $^{48}$Ti, and $^{50}$Ti). The isotope shifts on these transitions allow us to determine the isotope-dependent variation in the fine-structure splitting of the a$^5$F and y$^5$G$^\circ$ levels themselves. Combined with existing knowledge of the nuclear charge radii of titanium nuclei, we derive the specific mass and field shifts, which arise from correlated electronic motion and electronic density at the nucleus respectively, and further observe a strong $J$-dependent variation in each. Our results yield insight into the electronic and nuclear structure of transition metal atoms like titanium, and also characterize optical transitions that may allow for optical manipulation of ultracold gases of transition metal species.

Parameters of Isotope Shifts for 2s2p 3,1P1 → 2s2 1S0 Transitions in Heavy Be-Like Ions**Supported by the National Natural Science Foundation of China under Grant Nos 11874090, 11604385, 91536106 and 11204374, and the Research Project of National University of Defense Technology under Grant No ZK17-03-11.

The field shift and mass shift parameters of the 2s2p 3,1P1 → 2s2 1S0 transitions in Be-like ions (70 ≤ Z ≤ 92) are calculated using the multi-configuration Dirac–Hartree–Fock and the relativistic configuration interaction methods with the inclusion of the Breit interaction and the leading QED corrections. We find that the mass shift parameters of these two transitions do not change monotonously along the isoelectronic sequence in the high-Z range due to the relativistic nuclear recoil effects. A minimum value exists for the specific mass shift parameters around Z = 80, especially for the 2s2p 3P1 → 2s2 1S0 transition. In addition, the field shifts and mass shifts of these two transitions are estimated using an empirical formula, and their contributions are compared along the isoelectronic sequence.

QED theory of the specific mass shift in few-electron atoms

The quantum electrodynamics formalism to treat the interelectronic-interaction correction of first order in $1/Z$ to the two-electron part of the nuclear recoil effect on binding energies in atoms and ions is developed. The nonperturbative in $\alpha Z$ calculations of the corresponding contribution to the energies of the $1s^2$ state in He-like and the $1s^2 2s$ and $1s^2 2p_{1/2}$ states in Li-like ions are performed in the range $Z=5-100$. The behavior of the two-electron part of the nuclear recoil effect beyond the lowest-order relativistic approximation as $Z$ grows is studied.

Hyperfine structure and isotope shift measurements on spin-forbidden transitions of atomic gadolinium

We present the first measurements of the [Xe]4f75d16s6p$\;^{11}{F_J}$11FJ excited state hyperfine coefficients and isotope shifts of spin-forbidden transitions of atomic gadolinium (Gd) at 726 and 743 nm in a hollow cathode gas discharge. In addition, we performed a King Plot analysis to determine specific mass shift and field shift constants for these lines. Moreover, we observed King Plot nonlinearity for the 743 nm transition, which is an effect recently proposed to aid in searches for hypothetical new light bosons. Spectroscopic results obtained from this study will facilitate the development of more efficient isotope separation techniques, enable narrowband laser cooling of Gd for novel dipolar physics investigations, and foster technological advances in high precision atomic clocks and quantum enhanced metrology.

Nuclear Charge Radii of ^{229}Th from Isotope and Isomer Shifts.

The isotope ^{229}Th is unique in that it possesses an isomeric state of only a few electron volts above the ground state, suitable for nuclear laser excitation. An optical clock based on this transition is expected to be a very sensitive probe for variations of fundamental constants, but the nuclear properties of both states have to be determined precisely to derive the actual sensitivity. We carry out isotope shift calculations in Th^{+} and Th^{2+} including the specific mass shift, using a combination of configuration interaction and all-order linearized coupled-cluster methods and estimate the uncertainty of this approach. We perform experimental measurements of the hyperfine structure of Th^{2+} and isotopic shift between ^{229}Th^{2+} and ^{232}Th^{2+} to extract the difference in root-mean-square radii as δ⟨r^{2}⟩^{232,229}=0.299(15) fm^{2}. Using the recently measured values of the isomer shift of lines of ^{229m}Th, we derive the value for the mean-square radius change between ^{229}Th and its low-lying isomer ^{229m}Th to be δ⟨r^{2}⟩^{229m,229}=0.0105(13) fm^{2}.

GRASP2018—A Fortran 95 version of the General Relativistic Atomic Structure Package

The present Grasp2018 is an updated Fortran 95 version of the recommended block versions of programs from Grasp2K Version 1_1 for large-scale calculations Jönsson et al. (2013). MPI programs are included so that all major tasks can be executed using parallel computers. Tools have been added that simplify the generation of configuration state function expansions for the multireference single- and double computational model. Names of programs have been changed to accurately reflect the task performed by the code. Modifications to the relativistic self-consistent field program have been made that, in some instances, greatly reduce the number of iterations needed for determining the requested eigenvalues and the memory required. Changes have been made to the relativistic configuration interaction program to substantially cut down on the time for constructing the Hamiltonian matrix for configuration state function expansions based on large orbital sets. In the case of a finite nucleus the grid points have been changed so that the first non-zero point is Z-dependent as for the point nucleus. A number of tools have been developed to generate LaTeX tables of eigenvalue composition, energies, transition data and lifetimes. Tools for plotting and analyzing computed properties along an iso-electronic sequence have also been added. A number of minor errors have been corrected. A detailed manual is included that describes different aspects of the package as well as the steps needed in order to produce reliable results. Program summaryProgram Title:Grasp2018Program Files doi:http://dx.doi.org/10.17632/x574wpp2vg.1Licensing provisions: MIT licenseProgramming language: Fortran 95.Nature of problem: Prediction of atomic properties – atomic energy levels, isotope shifts, oscillator strengths, radiative decay rates, hyperfine structure parameters, specific mass shift parameters, Zeeman effects – using a multiconfiguration Dirac–Hartree–Fock approach.Solution method: The computational method is the same as in the previous Grasp2K [1,2] version except that only the latest recommended versions of certain routines are included.Restrictions: All calculations are for bound state solutions. Instead of relying on packing algorithms for specifying arguments of arrays of integrals, orbitals are designated by a “short integer” requiring one byte of memory for a maximum of 127 orbitals. The tables of reduced coefficients of fractional parentage used in this version are limited to sub-shells with j≤9∕2 [3]; occupied sub-shells with j>9∕2 are, therefore, restricted to a maximum of two electrons. Some other parameters, such as the maximum number of orbitals are determined in a parameter_def_M.f90 file that can be modified prior to compile time.Unusual features: Parallel versions are available for several applications.References•[[1]] P. Jönsson, X. He, C. Froese Fischer, and I. P. Grant, Comput. Phys. Commun. 176, 597 (2007).•[[2]] P. Jönsson, G. Gaigalas, J. Bieroń, C. Froese Fischer, and I. P. Grant, Comput. Phys. Commun. 184, 2197 (2013).•[[3]] G. Gaigalas, S. Fritzsche, Z. Rudzikas, Atomic Data and Nuclear Data Tables 76, 235 (2000).

Relativistic full-configuration-interaction calculations of magic wavelengths for the 2 3S1→2 1S0 transition of helium isotopes

A large-scale full-configuration-interaction calculation based on Dirac-Coulomb-Breit (DCB) Hamiltonian is performed for the $2\,^1S_0$ and $2\,^3S_1$ states of helium. The operators of the normal and specific mass shifts are directly included in the DCB framework to take the finite nuclear mass correction into account. High-accuracy energies and matrix elements involved n (the main quantum number) up to 13 are obtained from one diagonalization of Hamiltonian. The dynamic dipole polarizabilities are calculated by using the sum rule of intermediate states. And a series of magic wavelengths with QED and hyperfine effects included for the $2\,^3S_1\rightarrow2\,^1S_0$ transition of helium are identified. In addition, the high-order Ac Stark shift determined by the dynamic hyperpolarizabilities at the magic wavelengths are also evaluated. Since the most promising magic wavelength for application in experiment is 319.8 nm, the high-accuracy magic wavelength of 319.815 3(6) nm of $^4$He is in good agreement with recent measurement value of 319.815 92(15) nm [Nature Physics (2018)/arXiv:1804.06693], and present magic wavelength of 319.830 2(7) nm for $^3$He would provide theoretical support for experimental designing an optical dipole trap to precisely determine the nuclear charge radius of helium in future.

Ris 4: A program for relativistic isotope shift calculations

Spectral lines from different isotopes display a small separation in energy, commonly referred to as the line isotope shift. The program ris 4 (Relativistic Isotope Shift) calculates normal and specific mass shift parameters as well as field shift electronic factors from relativistic multiconfiguration Dirac–Hartree–Fock wave functions. These quantities, together with available nuclear data, determine isotope-dependent energy shifts. Using a reformulation of the field shift, it is possible to study, in a model-independent way, the atomic energy shifts arising from changes in nuclear charge distributions, e.g. deformations. Program summaryProgram title: ris 4Program Files doi: http://dx.doi.org/10.17632/8vjpf69zch.1Licensing provisions: MITProgramming language: Fortran 77 and Fortran 90Journal reference of previous version: Comput. Phys. Comm. 184 (2013) 2187Does the new version supersede the previous version?: YesSubprograms used: grasp 2K VERSION 1_1Nature of problem: Prediction of level and transition isotope shifts in atoms using four-component relativistic wave functions.Solution method: The nuclear mass shifts and field shifts are treated using first order perturbation theory. The electron density and the normal and specific mass shift parameters can be expressed as ∑μ,νcμcν〈Φ(γμPJMJ)|Vˆ|Φ(γνPJMJ)〉, where Vˆ is the relevant operator and Ψ(γPJMJ)=∑ν=1McνΦ(γνPJMJ) is the configuration state expansion, where P, J and MJ are the parity and angular quantum numbers, respectively. The matrix elements, in turn, can be decomposed as sums over radial integrals multiplied by angular coefficients. The angular coefficients are calculated using routines from the grasp2K version 1_1 package [1].Reasons for new version: This new version calculates field shift electronic factors resulting from non-constant (varying) electron densities inside the nucleus.Summary of revisions: This new version uses an expression of the field shift that through a polynomial expansion of the electron density contains higher order radial moments and thus takes the varying electron density within the nuclear volume into account.Restrictions: The complexity of the cases that can be handled is entirely determined by the grasp2K package [1] used for the generation of the electronic wave functions.Unusual features: Using a reformulation of the field shift, it is possible to study the atomic energy shifts arising from changes in nuclear charge distributions, e.g. deformations.

Isotope shifts in the spectrum of the neutral titanium atom

An investigation of 53 saturated absorption lines of titanium at wavelengths ranging from 695 to 1005 nm is performed. In addition, transitions 3d34sa5FJ → 3d34py5FJ(J = 3,4,5) in the ultraviolet range are measured. The isotope lines of 46Ti, 48Ti, and 50Ti are clearly observed for 53 transitions. A facing target sputtering system containing a magnetic field is used as a sample cell of titanium in this experiment. The Zeeman effect in a hyperfine structure is calculated for the condition of an intermediate field approximation to determine the unperturbed line positions in the odd mass isotopes 47Ti and 49Ti. For all observed transitions, the King plot analysis is performed to determine the electronic factors of the field shift and specific mass shift.

Charge radii and electromagnetic moments of At195–211

Hyperfine-structure parameters and isotope shifts of At195-211 have been measured for the first time at CERN-ISOLDE, using the in-source resonance-ionization spectroscopy method. The hyperfine structures of isotopes were recorded using a triad of experimental techniques for monitoring the photo-ion current. The Multi-Reflection Time-of-Flight Mass Spectrometer, in connection with a high-resolution electron multiplier, was used as an ion-counting setup for isotopes that either were affected by strong isobaric contamination or possessed a long half-life; the ISOLDE Faraday cups were used for cases with high-intensity beams; and the Windmill decay station was used for short-lived, predominantly α-decaying nuclei. The electromagnetic moments and changes in the mean-square charge radii of the astatine nuclei have been extracted from the measured hyperfine-structure constants and isotope shifts. This was only made possible by dedicated state-of-the-art large-scale atomic computations of the electronic factors and the specific mass shift of atomic transitions in astatine that are needed for these extractions. By comparison with systematics, it was possible to assess the reliability of the results of these calculations and their ascribed uncertainties. A strong deviation in the ground-state mean-square charge radii of the lightest astatine isotopes, from the trend of the (spherical) lead isotopes, is interpreted as the result of an onset of deformation. This behavior bears a resemblance to the deviation observed in the isotonic polonium isotopes. Cases for shape coexistence have been identified in At197,199, for which a significant difference in the charge radii for ground (9/2-) and isomeric (1/2+) states has been observed.

Extensive and accurate relativistic calculations of atomic data on the 83Kr I spectrum

We provide an extensive, accurate and complete new spectroscopic data set for many levels belonging to the intermediate perturbing Rydberg series ns[K]J (5 ≤ n ≤ 8), nd[K]J (4 ≤ n ≤ 7) and the autoionizing Rydberg series np[K]J (5 ≤ n ≤ 7) and nf[K]J (4 ≤ n ≤ 5) relative to the ground state 4p6 1S0 for neutral krypton-83 isotope. The data set is composed of the energy levels, the oscillator strengths the radiative transition rates the Landé g-factors, the magnetic dipole and electric quadrupole hyperfine constants. The values of these spectroscopic parameters are calculated in the multiconfiguration Dirac-Hartree–Fock (MCDHF) framework. The calculations are carried out in the active space where the electron correlation effects, contributions from relativistic configuration interaction (RCI), the quantum electrodynamics (QED) effects with transverse photon Breit interaction and vacuum photon polarization, specific mass shift and self-energy corrections are included. In addition, we provide the oscillator strengths and transition rates in Coulomb and Babushkin gauges for the 4p5(2P)4d–4p5(2P)5p, 4p5(2P)5s–4p5(2P)5p, 4p5(2P)6s–4p5(2P)5p, 4p5(2P)4d–4p5(2P)44f, 4p5(2P)5d–4p5(2P)4f, 4p5(2P)5d–4p5(2P)6p, 4p5(2P)7s–4p5(2P)6p, 4p5(2P)4d–4p5(2P)5f, 4p5(2P)5d–4p5(2P)5f, 4p5(2P)6d–4p5(2P)5f, 4p5(2P)7p–4p5(2P)6d and 4p5(2P)8s–4p5(2P)7p transition arrays. Extensive comparisons with other experimental and theoretical data from the reference databases are carried out in order to judge the reliability of our data. These comparisons indicate that our results are accurate. The present spectroscopic data may be useful for line identification in observed spectra as well as modelling and diagnostics of astrophysical and fusion plasmas.

DeltaMS: a tool to track isotopologues in GC- and LC-MS data.

Stable isotopic labeling experiments are powerful tools to study metabolic pathways, to follow tracers and fluxes in biotic and abiotic transformations and to elucidate molecules involved in metal complexing. To introduce a software tool for the identification of isotopologues from mass spectrometry data. DeltaMS relies on XCMS peak detection and X13CMS isotopologue grouping and then analyses data for specific isotope ratios and the relative error of these ratios. It provides pipelines for recognition of isotope patterns in three experiment types commonly used in isotopic labeling studies: (1) search for isotope signatures with a specific mass shift and intensity ratio in one sample set, (2) analyze two sample sets for a specific mass shift and, optionally, the isotope ratio, whereby one sample set is isotope-labeled, and one is not, (3) analyze isotope-guided perturbation experiments with a setup described in X13CMS. To illustrate the versatility of DeltaMS, we analyze data sets from case-studies that commonly pose challenges in evaluation of natural isotopes or isotopic signatures in labeling experiment. In these examples, the untargeted detection of sulfur, bromine and artificial metal isotopic patterns is enabled by the automated search for specific isotopes or isotope signatures. DeltaMS provides a platform for the identification of (pre-defined) isotopologues in MS data from single samples or comparative metabolomics data sets.

Isotopic shift of the ground state of neon from the experimental results concerning the absorption of 0.63-μm laser radiation

Isotopic shifts of the 3s[3/2]10–2р6(1S0) and 3s'–2р6(1S0) transitions, equal, respectively, to 417 ± 20 and–98 ± 20 MHz, have been measured using the 0.63-μm radiation of a helium–neon laser and opto-magnetic resonances induced by the interference of the reactive components of fields in overlapping areas of the emissions of isotopic atoms. Combining these results with the absolute specific mass shift of the 3p[5/2]2 level (–647 MHz), the isotopic mass shift of the ground state of neon equal to 3223 ± 30 MHz, and its specific mass shift equal to–9782 ± 30 MHz have been determined.

Theoretical calculations on isotope shifts of Mg I by using relativistic multiconfiguration Dirac-Hartree-Fock method

The isotope shift parameters for the atomic transitions 1S0-1P1 and 1S0-3P1 of Mg are calculated by the relativistic multiconfiguration Dirac-Hartree-Fock (MCDHF) method, including the normal mass shift (NMS) coefficients, the specific mass shift (SMS) coefficients and the field shift (FS) factors. The detailed calculations of the isotope shifts for the three stable isotopes 24Mg, 25Mg and 26Mg are also carried out, in which the GRASP2K package is used together with another modified relativistic isotope shift computation code package RIS3. The two-parameter Fermi model is used here to describe the nuclear charge distribution in order to calculate the field shift by the first-order perturbation. A restricted double excitation mode is used in our calculations, one electron is excited from the two electrons in the 3s shell (3s2), another electron is excited from the eight electrons in the 2s or 2p shells (2s22p6), and the two electrons in the 1s shell (1s2) are not excited. The active configurations are expanded from the occupied orbitals to some active sets layer by layer, each correlation layer is numbered by the principal quantum numbers n (n= 3, 4, 5, …) and contains the corresponding orbitals s, p, d, …. The active configurations with the mixing coefficients in the added layer can be optimized by the MCDHF calculations. In this work, the atomic state functions are optimized simultaneously by the self-consistent field method and the relativistic configuration interaction approach in which the Breit interaction is taken into account perturbatively as well. The maximum principal quantum number n equals 10 and the largest orbital quantum number lmax is g. In our calculations, the NMS coefficients are -576.8 and -359.9 GHz·u, the SMS coefficients are 133.9 and -479.6 GHz·u, and the FS factors are -62.7 and -78.0 MHz·fm-2 for the 1S0-1P1 and 1S0-3P1 transitions of Mg, respectively. The difference between our isotope shift calculations and the previous experimental measurements is in a range from 6 MHz to 20 MHz with the relative error range from 0.6% to 1.3%, which shows that our results are in good agreement with experimental values. Our calculations are also coincident with other theoretical results. The isotope shift parameters provided here can be applied to the quick calculations of isotope shifts for the short-lived Mg isotopes, including 20-23Mg and 27-40Mg, and can be referred to for the corresponding isotope shift experiments. The methods used here canbe applied to calculating the isotope shifts and the atomic spectroscopic structures for other Mg-like ions with twelve extranuclear electrons.

Subtyping of Campylobacter jejuni ssp. doylei Isolates Using Mass Spectrometry-based PhyloProteomics (MSPP).

MALDI-TOF MS offers the possibility to differentiate some bacteria not only at the species and subspecies level but even below, at the strain level. Allelic isoforms of the detectable biomarker ions result in isolate-specific mass shifts. Mass spectrometry-based phyloproteomics (MSPP) is a novel technique that combines the mass spectrometric detectable biomarker masses in a scheme that allows deduction of phyloproteomic relations from isolate specific mass shifts compared to a genome sequenced reference strain. The deduced amino acid sequences are then used to calculate MSPP-based dendrograms. Here we describe the workflow of MSPP by typing a Campylobacter jejuni ssp. doylei isolate collection of seven strains. All seven strains were of human origin and multilocus sequence typing (MLST) demonstrated their genetic diversity. MSPP-typing resulted in seven different MSPP sequence types, sufficiently reflecting their phylogenetic relations. The C. jejuni ssp. doylei MSPP scheme includes 14 different biomarker ions, mostly ribosomal proteins in the mass range of 2 to 11 kDa. MSPP can in principle, be adapted to other mass spectrometric platforms with an extended mass range. Therefore, this technique has the potential to become a useful tool for strain level microbial typing.

Isotope Shifts of Nitrogen around 800 nm

The Doppler-limited absorption spectra of 14N and 15N atoms were measured around 800 nm using concentration modulation spectroscopy to study their isotope shifts. The nitrogen atoms were generated by discharging molecular nitrogen buffered with helium in a home-made discharge tube. The isotope shifts of four multiplets (3s4PJ→3p4DoJ, 3s4PJ→3p4PoJ, 3s2DJ→5p2DoJ, and 3p2PoJ→5s2PJ) were measured and their J-dependent specific mass shifts were observed and discussed.

Isotope shifts in Sb I

The isotope shifts of eight lines of Sb I covering the UV–NIR spectral range have been measured. We used two different experimental techniques: high-resolution emission spectroscopy and optogalvanic absorption spectroscopy with a tunable dye ring laser system. Recurring to pseudo-relativistic Hartee–Fock estimates, the field and specific mass shifts of numerous configurations were evaluated. The comparison between experimental and ab initio line shift values is very satisfactory.