We present an ab initio method of calculation of isotope shift and relativistic shift in atoms with a few valence electrons. It is based on an energy calculation involving combination of the configuration interaction method and many-body perturbation theory. This work is motivated by analyses of quasar absorption spectra that suggest that the fine structure constant, alpha, was smaller at an early epoch. Relativistic shifts are needed to measure this variation of alpha, while isotope shifts are needed to resolve systematic effects in this study. The isotope shifts can also be used to measure isotopic abundances in gas clouds in the early universe, which are needed to study nuclear reactions in stars and supernovae and test models of chemical evolution. This paper shows that isotope shift in magnesium can be calculated to very high precision using our new method.
We calculate field isotope shifts for nobelium atoms using nuclear charge distributions which come from different nuclear models. We demonstrate that comparing calculated isotope shifts with experiment can serve as a testing ground for nuclear theories. It also provides a way of extracting parameters of nuclear charge distribution beyond nuclear RMS radius, e.g. parameter of quadrupole deformation $β$. We argue that previous interpretation of the isotope measurements in terms of $δ\langle r^2 \rangle$ between $^{252,254}$No isotopes should be amended when nuclear deformation is taken into acco…
X-Ray transition energies and isotope shifts in heavy atoms are evaluated. The energy levels with vacancies in the inner shells are calculated within the approximation of the average of nonrelativistic configuration employing the Dirac-Fock-Sturm method. The obtained results are compared with other configuration-interaction theoretical calculations and with experimental data.
We report on the isotope shift between ${}^{88}$Sr and ${}^{87}$Sr on the ${}^1S_0 - {}^3P_0$ clock transitions. The interleaved operation of an optical lattice clock with two isotopes allows the canceling out of common perturbations, such as the quadratic Zeeman shift, the clock-light shift, and the blackbody radiation shift. The isotope shift is determined to be 62 188 134.004(10) Hz, where the major uncertainty is introduced by the collisional shift that is distinct for each isotope. Our result allows us to determine the frequency of $^{88}$Sr-$^{87}$Sr optical lattice clocks with a fractio…
Relativistic calculations of the isotope shifts of energy levels in highly charged Li-like ions are performed. The nuclear recoil (mass shift) contributions are calculated by merging the perturbative and large-scale configuration-interaction Dirac-Fock-Sturm (CI-DFS) methods. The nuclear size (field shift) contributions are evaluated by the CI-DFS method including the electron-correlation, Breit, and QED corrections. The nuclear deformation and nuclear polarization corrections to the isotope shifts in Li-like neodymium, thorium, and uranium are also considered. The results of the calculations …
Theory of the isotope shift of the centroid energies of light few-electron atoms is reviewed. Numerical results are presented for the isotope shift of the $2^3P$-$2^3S$ and $2^1S$-$2^3S$ transition energies of $^3$He and $^4$He. By comparing theoretical predictions for the isotope shift with the experimental results, the difference of the squares of the nuclear charge radii of $^3$He and $^4$He, $δR^2$, is determined with high accuracy.
The electron affinities eA(S) are measured for the two isotopes 32S and 34S (16752.9753(41) and 16752.9776(85) cm-1, respectively). The isotope shift in the electron affinity is found to be positive, eA(34S)-eA(32S) = +0.0023(70) cm-1, but the uncertainty allows for the possibility that it may be either "normal" (eA(34S) > eA(32S)) or "anomalous" (eA(34S) < eA(32S)). The isotope shift is estimated theoretically using elaborate correlation models, monitoring the electron affinity and the mass polarization term expectation value. The theoretical analysis predicts a very large specific mass shift…
We have measured the hyperfine structure and isotope shifts of the 402.0 nm and 399.6 nm resonance lines in 229Th+. These transitions could provide pathways towards the 229Th isomeric nuclear state excitation. An unexpected negative isotope shift relative to 232Th+ is observed for the 399.6 nm line, indicating a strong Coulomb coupling of the excited state to the nucleus. We have developed a new all-order approach to the isotope shift calculations that is generally applicable to heavy atoms and ions with several valence electrons. The theoretical calculations provide an explanation for the neg…
The present work reports results from systematic multiconfiguration Dirac-Hartree-Fock calculations of electronic isotope shift factors for a set of transitions between low-lying states in neutral zinc. These electronic quantities together with observed isotope shifts between different pairs of isotopes provide the changes in mean-square charge radii of the atomic nuclei. Within this computational approach, different models for electron correlation are explored in a systematic way to determine a reliable computational strategy and to estimate theoretical error bars of the isotope shift factors…
Energy levels, normal and specific mass shift parameters as well as electronic densities at the nucleus are reported for numerous states along the beryllium, boron, carbon, and nitrogen isoelectronic sequences. Combined with nuclear data, these electronic parameters can be used to determine values of level and transition isotope shifts. The calculation of the electronic parameters is done using first-order perturbation theory with relativistic configuration interaction wave functions that account for valence, core-valence and core-core correlation effects as zero-order functions. Results are c…
The present work reports results from systematic multiconfiguration Dirac-Hartree-Fock calculations of electronic isotope shift factors for a set of transitions between low-lying states in neutral aluminium. These electronic quantities together with observed isotope shifts between different pairs of isotopes provide the changes in mean-square charge radii of the atomic nuclei. Two computational approaches are adopted for the estimation of the mass- and field shift factors. Within these approaches, different models for electron correlation are explored in a systematic way to determine a reliabl…
Isotope shifts and hyperfine structure of tungsten were studied in the near UV range. We have used laser induced fluorescence spectroscopy on a pulsed supersonic beam to probe the 5D0 -> 5F1 transition at 384.9 nm, 7S3 -> 7P4 transition at 400.9 nm, and 7S3 -> 7P3 transition at 407.4 nm. Three new magnetic hyperfine constants are reported for 7P3,7P4, and 5F1 states. The isotope shifts of the 384.9 nm transition are presented for the first time, and the isotope shifts of 400.9 nm and 407.4 nm transition are measured with an order of magnitude higher precision compared to the previous measureme…
Isotope shift spectroscopy with narrow optical transitions provides a benchmark for atomic structure calculations and has also been proposed as a way to constrain theories predicting physics beyond the Standard Model. Here, we have measured frequency shifts of the ${^1}S_0 \rightarrow {^3}P_1$ and ${^1}S_0 \rightarrow {^3}P_0$ transitions between all stable isotopes of strontium relative to ${^{88}}$Sr. This includes the first reported measurements of the ${^1}S_0 \rightarrow {^3}P_0$ isotope shift of ${^{88}}$Sr-${^{86}}$Sr and ${^{88}}$Sr-${^{84}}$Sr. Using the isotope shift measurements of …
The present work reports results from systematic multiconfiguration Dirac-Hartree-Fock calculations of isotope shifts for several well-known transitions in neutral magnesium. Relativistic normal and specific mass shift factors as well as the electronic probability density at the origin are calculated. Combining these electronic quantities with available nuclear data, energy and transition level shifts are determined for the $^{26}$Mg$-^{24}$Mg pair of isotopes. Different models for electron correlation are adopted. It is shown that although valence and core-valence models provide accurate valu…
We report new precision measurements of the $^{20}$Ne--$^{22}$Ne isotope shift for several transitions, as well as state-of-the-art, \textit{ab initio} field-shift calculations. Our results are combined with historical measurements in a global fit to obtain the isotope shifts of all fifty low-lying neon levels with high precision. These level shifts show a wealth of electronic, nuclear, and relativistic phenomena. Relying on the analogy between mass shift and fine-structure operators, we explain this plethora of neon level-shifts utilizing a small number of effective parameters in a global par…
The present work deals with a set of problems in isotope shifts of neutral barium spectral lines. Some well known transitions ($6s^2~^1S_0-6s6p~^{1,3}P^o_1$ and $6s^2~^1S_0-6p^2~^3P_0$) are first investigated. Values of the changes in the nuclear mean-square charge radius are deduced from the available experimental isotope shifts using our ab initio electronic factors. The three sets $\{ δ\langle r^2\rangle^{A,A'}\} $ obtained from these lines are consistent with each other. The combination of the available nuclear mean-square radii with our electronic factors for the $6s5d~^3D_{1,2} -6s6p~^{1…
The isotope effects in Si$^-$ bound levels are studied using the multi-configuration Hartree-Fock ab initio approach. Large scale calculations are carried out for the $3p^3\ ^4S^o,\, ^2D^o$ and $^2P^o$ multiplets of Si$^-$ and the $3p^2\ ^3P$ multiplet of Si. We predict an anomalous isotope shift on the electron affinity, dominated by the specific mass shift, with a value of $IS(^e\!\!A)= -0.66(6)$ m$^{-1}$ for the ($30-28$) isotope pair. We also report hyperfine structure parameters for the studied multiplets. Finally, we provide the values of level electric field gradients at the nucleus tha…
By combining a recent precise measurement of the ionization energy of $^{87}$Rb with previous measurements of electronic and hyperfine structure, an accurate value for the $^{85}\textrm{Rb}-^{87}\textrm{Rb}$ isotope shift of the 5$^2S_{1/2}$ ground state can be determined. In turn, comparison with additional spectroscopic data makes it possible for the first time to evaluate isotope shifts for the low-lying excited states, accurate in most cases to about 1 MHz. In a few cases, the specific mass shift contribution can be determined in addition to the total shift. This information is particularl…
Background: Atomic spectral lines from different isotopes display a small shift in energy, commonly referred to as the line isotope shift. One of the components of the isotope shift is the field shift, which depends on the extent and the shape of the nuclear charge density distribution. Purpose: To investigate how sensitive field shifts are with respect to variations in the nuclear size and shape and what information of nuclear charge distributions that can be extracted from measured field shifts. Methods: Nuclear properties are obtained from nuclear density functional theory calculations base…
The hyperfine structure and isotope shifts of the 3s23p2 3P2 to 3s3p3 3Do3 transition in silicon have been measured. The transition at 221.7 nm was studied by laser induced fluorescence in an atomic Si beam. For 29Si, the hyperfine A constant for the 3s23p2 3P2 level was determined to be -160.1+-1.3 MHz (1 sigma error), and the A constant for the 3s3p3 3Do3 level is -532.9+-0.6 MHz. This is the first time that these constants were measured. The isotope shifts (relative to the abundant isotope 28Si) of the transition were determined to be 1753.3+-1.1 MHz for 29Si and 3359.9+-0.6 MHz for 30Si. T…
We report measurements of the isotope shifts of the 3d6 4s2 a 5D3 - 3d6 4s4p z 5F4o FeI resonance line at 373.7 nm between all four stable isotopes 54Fe, 56Fe, 57Fe and 58Fe, as well as the complete hyperfine structure of that line for 57Fe, the only stable isotope having a non-zero nuclear spin. The field and specific mass shift coefficients of the transition have been derived from the data, as well as the experimental value for the hyperfine structure magnetic dipole coupling constant A of the excited state of the transition in 57Fe : A(3d6 4s4p z 5F4o) = 68.21(69) MHz. The measurements were…
State-of-the-art relativistic multiconfiguration Dirac-Hartree-Fock calculations have been performed to evaluate the electronic field and mass isotope shift factors of the Cu~I resonance line at $λ= 324.8$~nm. A linear correlation between the mass factors and the transition energy is found for elaborate correlation models, allowing extrapolation to the observed frequency limit. The relativistic corrections to the recoil operator reduces the transition mass factor by 5~\%.
We report on the measurement of the isotope shifts of the $3d^74s \,\, a \, {}^5\!F_5 - 3d^74p \,\, z \, {}^5\!G^o_6$ Fe~I line at 358~nm between all four stable isotopes ${}^{54}$Fe, ${}^{56}$Fe, ${}^{57}$Fe and ${}^{58}$Fe, as well as the hyperfine structure of that line for ${}^{57}$Fe, the only stable isotope having a nonzero nuclear spin. This line is of primary importance for laser cooling applications. In addition, an experimental value of the field and specific mass shift coefficients of the transition is reported as well as the hyperfine structure magnetic dipole coupling constant $A$…
We use the combination of configuration interaction and many-body perturbation theory method (CI+MBPT) to perform ab initio calculations the low-energy spectra of Cr II with high accuracy. It is found that second-order MBPT diagrams should be included in a consistent and complete way for the MBPT to improve the accuracy of calculations in this five-valence-electron system. This contrasts with previous ions with fewer valence electrons where it was found that single-valence-electron diagrams dominate the corrections. Isotope shifts and relativistic shifts (q-values) are calculated for use in as…
Precise calculations of the isotope shifts in berylliumlike thorium and uranium ions are presented. The main contributions to the field and mass shifts are calculated within the framework of the Dirac-Coulomb-Breit Hamiltonian employing the configuration-interaction Dirac-Fock-Sturm method. These calculations include the relativistic, electron-electron correlation, and Breit-interaction effects. The QED, nuclear deformation, and nuclear polarization corrections are also evaluated.
We report measurements of the isotope shifts of the $3d^64s^2 a ^5D_4 - 3d^64s4p z ^5F_5^o$ Fe I resonance line at 372 nm between all four stable isotopes $^{54}$Fe, $^{56}$Fe, $^{57}$Fe, and $^{58}$Fe, as well as the complete hyperfine structure of that line for $^{57}$Fe, the only stable isotope having a non-zero nuclear spin. The field and specific mass shift coefficients of the transition have been derived from the data, as well as the experimental value for the hyperfine structure magnetic dipole coupling constant $A$ of the excited state of the transition in $^{57}$Fe: $A(3d^64s4p z ^5F_…
Today, the electron affinity is experimentally well known for most of the elements and is a useful guideline for developing ab initio computational methods. However, the measurements of isotope shifts on the electron affinity are limited by both resolution and sensitivity. In this context, theory eventually contributes to the knowledge and understanding of atomic structures, even though correlation plays a dominant role in negative ions properties and, particularly, in the calculation of the specific mass shift contribution. The present study solves the longstanding discrepancy between calcula…
We have measured the isotope shift of the narrow quadrupole-allowed 5 2S1/2 - 4 2D5/2 transition in 86Sr+ relative to the most abundant isotope 88Sr+. This was accomplished using high-resolution laser spectroscopy of individual trapped ions, and the measured shift is Delta-nu_meas^(88,86) = 570.281(4) MHz. We have also tested a recently developed and successful method for ab-initio calculation of isotope shifts in alkali-like atomic systems against this measurement, and our initial result of Delta-nu_calc^(88,86) = 457(28) MHz is also presented. To our knowledge, this is the first high precisi…
We report measurements of the isotope shifts of two transitions ($4f^46s\rightarrow [25044.7]^{\circ}_{7/2}$ and $4f^46s\rightarrow [25138.6]^{\circ}_{7/2}$) in neodymium ions (Nd$^+$) with hundredfold improved accuracy, using laser spectroscopy of a cryogenically-cooled neutral plasma. The isotope shifts were measured across a set of five spin-zero isotopes that spans a nuclear shape transition. We discuss the prospects for further improvements to the accuracy of Nd$^+$ isotope shifts using optical clock transitions, which could enable higher precision tests of King plot linearity for new phy…
We report on improved isotope shift measurements of the isotopes $^{40,42,44,48}$Ca in the $4s\,^2 \rm{S}_{\frac{1}{2}} \rightarrow 4p\,^2\rm{P}_{\frac{3}{2}}$ (D2) transition using collinear laser spectroscopy. Accurately known isotope shifts in the $4s\,^2 \rm{S}_{\frac{1}{2}} \rightarrow 4p\,^2\rm{P}_{\frac{1}{2}}$ (D1) transition were used to calibrate the ion beam energy with an uncertainty of $ΔU \approx \pm 0.25$ V. The accuracy in the D2 transition was improved by a factor of $5 - 10$. A King-plot analysis of the two transitions revealed that the field shift factor in the D2 line is ab…
We report a new determination of muonium 1S-2S transition frequency and its isotope shift with deuterium by recalibrating the iodine reference lines using an optical frequency comb. The reference lines for the muonium and deuterium 1S-2S transitions are determined with a precision of 2.4*10^-10 and 1.7*10^-10 respectively. A new muonium-deuterium 1S-2S isotope-shift frequency is derived from these references to be 11 203 464.9(9.2)(4.0) MHz, in agreement with an updated bound-state quantum-electrodynamics prediction based on 2010 adjustments of Committee on Data for Science and Technology and …
We present the theoretical calculations of the electronic isotope shift factors of the $5d^{7}6s^{2} \ ^{4}\!F_{9/2} \to (\mbox{odd},J= 9/2)$ line at 247.587 nm, that were recently used to extract nuclear mean square radii and nuclear deformations of iridium isotopes [Mukai $\textit{et al.}$ (2020)]. The fully relativistic multiconfiguration Dirac-Hartree-Fock method and the relativistic configuration interaction method were used to perform the atomic structure calculations. Additional properties such as the $\textit{sharing rule}$, Landé $g$ factors or $\textit{phase tracking}$ were employed …
We report measurements of isotope shifts for the five spinless Yb isotopes on the $6s^2\,^1\textrm{S}_0 \rightarrow 5d6s\,^1\textrm{D}_2$ transition using Doppler-free two-photon spectroscopy. We combine these data with existing measurements on two transitions in Yb$^+$ [Phys. Rev. Lett. 125, 123002 (2020)], where deviation from King-plot linearity showed hints of a new bosonic force carrier at the 3$σ$ level. The combined data strongly reduces the significance of the new-physics signal. We show that the observed nonlinearity in the joint Yb/Yb$^+$ King-plot analysis can be accounted for by th…
We have investigated $4s\;^2S_{1/2} \rightarrow 5p\;^2P_{1/2}$ transition ($D_1$ line) of the potassium isotopes $^{39}$K, $^{40}$K, and $^{41}$K using Doppler-free laser saturation spectroscopy. Our measurements reveal the hyperfine splitting of the $5p\;^2P_{1/2}$ state of $^{40}$K and we have determined the specific mass shift and the nuclear field shift constants for the blue $D_1$ line.
Isotope shifts of the 2$p_{3/2}$-2$p_{1/2}$ transition in B-like ions are evaluated for a wide range of the nuclear charge number: Z=8-92. The calculations of the relativistic nuclear recoil and nuclear size effects are performed using a large scale configuration-interaction Dirac-Fock-Sturm method. The corresponding QED corrections are also taken into account. The results of the calculations are compared with the theoretical values obtained with other methods. The accuracy of the isotope shifts of the 2$p_{3/2}$-2$p_{1/2}$ transition in B-like ions is significantly improved.
The electric dipole polarizabilities and hyperpolarizabilities for the lithium isotopes $^6$Li and $^7$Li in the ground state $2^2S$ and the excited states $2^2P$ and $3^2D$, as well as the leading resonance and dispersion long-range coefficients for the Li($2^2S$)--Li($2^2S$) and Li($2^2S$)--Li($2^2P$) systems, are calculated nonrelativistically using variational wave functions in Hylleraas basis sets. Comparisons are made with published results, where available. We find that the value of the second hyperpolarizability of the $2^2S$ state is sensitive to the isotopic mass due to a near cancel…
We study the electron correlation effects in the calculations of isotope shifts in Na and Mg+ using the relativistic coupled-cluster method. The trends of the correlation effects are explicitly discussed and comparison of the present results with the previously reported results are given. We also present the fine structure constant variation coefficients for many states in the above systems. From these results, it is possible to find out suitable transition lines those can be used as anchor and probe lines in finding possible variation in the fine structure constant.
Isotope shifts of 6s5d $^3$D-states in neutral Barium
对钡原子的低激发态$^1$ P和$^3$ D进行了激光光谱研究。这项工作大大有助于发展一个有效的激光冷却和重碱土金属元素的陷阱，特别是为了更好地了解这些系统的原子波函数的目的。同位素位移和超精细结构是探测原子核位置波函数的理想探针。这是必不可少的输入的基本对称性破缺性质，如永久电偶极矩的敏感性的理论评估。我们首次报道了$^3$ D $_{1,2}$ - $^1$ P $_1$跃迁的同位素位移测量。已观察到King图偏离其预期行为。此外，我们已经光学解决了超精细结构的$^3$ D $_{1,2}$状态。
Changes in the mean-square nuclear charge radii along the lithium isotopic chain were determined using a combination of precise isotope shift measurements and theoretical atomic structure calculations. Nuclear charge radii of light elements are of high interest due to the appearance of the nuclear halo phenomenon in this region of the nuclear chart. During the past years we have developed a new laser spectroscopic approach to determine the charge radii of lithium isotopes which combines high sensitivity, speed, and accuracy to measure the extremely small field shift of an 8 ms lifetime isotope…
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. C…
Atomic spectral lines for different isotopes are shifted, revealing a change in the properties of the nucleus. For spinless nuclei such isotope shifts for two distinct transitions are expected to be linearly related, at least at leading order in a change of the nuclear mass and charge distribution. Looking for a breaking of linearity in so-called King plots was proposed as a novel method to search for physics beyond the standard model. In the light of the recent experimental progress in isotope shift spectroscopy, the sensitivity of these searches will become limited by the determination of th…
We report measurements of the isotope shifts of the (3s3p)$^3$P$_{0,1,2}$ - (3s4s)$^3$S$_1$ Mg I transitions for the stable isotopes $^{24}$Mg (I=0), $^{25}$Mg (I=5/2) and $^{26}$Mg (I=0). Furthermore the $^{25}$Mg $^3$S$_1$ hyperfine coefficient A($^3$S$_1$) = (-321.6 $\pm$ 1.5) MHz is extracted and found to be in excellent agreement with state-of-the-art theoretical predictions giving A($^3$S$_1$) = -325 MHz and B($^3$S$_1$) $\simeq 10^{-5}$ MHz. Compared to previous measurements, the data presented in this work is improved up to a factor of ten.
Violation of linearity of the King plot is investigated for a chain of partially stripped argon isotopes. The nonlinearity originates within the Standard Model from subtle contributions to the isotope shifts from next-to-leading order effects, which have never been systematically studied so far. In light atoms these nonlinear effects are dominated by the quadratic nuclear recoil ($\propto 1/M^2$ where $M$ is the nuclear mass). Large-scale relativistic calculations of the linear and quadratic mass shift and the field shift are performed for the $2P$ fine-structure transitions in Be-like, B-like…
Isotope shift of atomic spectra is considered as a probe of new interaction between electrons and neutrons in atoms. We employ the method of seeking a breakdown of King's linearity in the isotope shifts of two atomic transitions. In the present work, we evaluate the magnitudes of the nonlinearity using relativistic wave functions and the result is compared with that of nonrelativistic wave functions in our previous work. It turns out that the nonrelativistic calculation underestimates the nonlinearity owing to the new interaction in the mass range of the mediator greater than 1 MeV. Further, w…
