Field Isotope Shift Research Articles

Nuclear deformation as a source of the nonlinearity of the King plot in the Yb+ ion

We perform atomic relativistic many-body calculations of the field isotope shifts and calculations of corresponding nuclear parameters for all stable even-even isotopes of Yb$^+$ ion. We demonstrate that if we take nuclear parameters of the Yb isotopes from a range of the state-the-art nuclear models which all predict strong quadrupole nuclear deformation, then calculated non-linearity of the King plot, caused by the difference in the deformation in different isotopes, is consistent with the non-linearity observed in the experiment (Ian Counts {\em et al}, Phys. Rev. Lett. {\bf 125}, 123002 (2020)). The changes of nuclear RMS radius between isotopes extracted from experiment are consistent with those obtained in the nuclear calculations.

Using isotope shift for testing nuclear theory: The case of nobelium isotopes

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 $\beta$. We argue that previous interpretation of the isotope measurements in terms of $\delta \langle r^2 \rangle$ between $^{252,254}$No isotopes should be amended when nuclear deformation is taken into account. We calculate isotope shifts for other known isotopes and for hypothetically metastable isotope $^{286}$No for which the predictions of nuclear models differ substantially.

Sensitivity of the isotope shift to the distribution of nuclear charge density

It is usually assumed that the field isotope shift (FIS) is completely determined by the change of the averaged squared values of the nuclear charge radius $\langle r^2\rangle$. Relativistic corrections modify the expression for FIS, which is actually described by the change of $\langle r^{2 \gamma}\rangle$, where $\gamma=\sqrt{1 - Z^2 \alpha^2}$. In the present paper we consider corrections to FIS which are due to the nuclear deformation and due to the predicted reduced charge density in the middle of the superheavy nuclei produced by a very strong proton repulsion (hole in the nuclear centre). Specifically, we investigate effects which can not be completely reduced to the change of $\langle r^2 \rangle$ or $\langle r^{2 \gamma}\rangle$.

Calculation of isotope shifts for cesium and francium

We perform ab initio calculations of isotope shifts for isotopes of cesium (from $A=123$ to $A=137$) and francium (from $A=207$ to $A=228$). These calculations start from the relativistic Hartree-Fock method and make use of several techniques to include correlations. The field (volume) isotope shift is calculated by means of an all-order correlation potential method and within the singles-doubles--partial-triples linearized coupled-cluster approach. Many-body perturbation theory in two different formulations is used to calculate the specific mass shift. We discuss the strong points and shortcomings of the different approaches and implications for parity nonconservation in atoms. Changes in nuclear charge radii are found by comparing the present calculations with experiment.

Field isotope shifts in the 6s-6p and 4f-5d transitions from the 4f^6 6s^2 ^7F_J ground multiplet of Sm I

Multiconfiguration Dirac-Fock (MCDF) calculations are used to interpret the field shift contributions to isotope shifts of Sm I in visible and near-UV transition lines. The investigated lines correspond to the transitions between the ground configuration 4f^6 6s^2 and the excited configurations 4f^6 6s6p and 4f^5 5d6s^2. For the 6s-6p transition the field shift is negative as a result of the reduced 6s electron occupation, whereas for the 4f-5d transition the field shift is positive because of the decreased screening of 6s and inner-shell electrons. MCDF calculations for the electron charge density at the origin that include the configuration mixing effect agree well with the electronic factor ratios derived from experimental data with the exception of a few cases of 6s-6p transitions.

Relativistic calculations of isotope shifts in highly charged ions

The isotope shifts of forbidden transitions in Be- and B-like argon ions are calculated. It is shown that only using the relativistic recoil operator can provide a proper evaluation of the mass isotope shift, which strongly dominates over the field isotope shift for the ions under consideration. Comparing the isotope shifts calculated with the current experimental uncertainties indicates very good perspectives for a first test of the relativistic theory of the recoil effect in middle-$Z$ ions.

Charge radii in francium isotopes

Nuclear distributions affect many aspects of atomic spectra, making atomic physics a useful tool to study also nuclear properties. Relativistic coupled-cluster calculations for the 7s and 7p states in Fr are presented and applied to binding energies, and to electronic factors for the field isotope shift. The result, F

Field isotope shift ratios in argon

Multiconfiguration Dirac-Fock (MCDF) calculations have been made for the field isotope shift ratio of the 3p5(4p-5d) and 3p5(4s-4p) transitions in argon, in an attempt to account for a seeming anomaly in the existing experimental values.

Reanalysis of the isotope shift and nuclear charge radii in radioactive potassium isotopes

Accurate ab initio calculations are presented of the electronic factor F for the field isotope shift in the resonance line in K and for the hyperfine structure of the states involved. The relation between the authors' calculated F value and that obtained from experimental hyperfine structure data is discussed. The isotope shift data by Touchard et al for the chain 38(sup)-or+4 7K are reanalysed and revised values for delta (r2) are presented and compared with corresponding results for neighbouring Ca isotones.

Crossed-second-order effects of the isotope shift in the Er II groundconfiguration 4f 126s

In the Er II groundconfiguration 4f126s the level isotope shift (IS) between the isotopes166Er and170Er in the terms2H and4H was determined by high-resolution computer-supported interference spectroscopy. On the grounds of a parametric description of the level IS the crossed-second-order-parametersg3(4f,6s)=−4.5(9) MHz andz4f=+56(2) MHz were evaluated. By normalizing these parameters for comparison with other lanthanide elements, in respect of the field isotope shift and different finestructure Slater integrals, the following quotients can be stated:g3/(δ〈r2〉·G3)=−3(1)·10−6·fm−2 andz4f/(δ〈r2〉·ζ4f)=3.65(60)·10−6·fm−2. They are of the same order of magnitude as those presently obtained in other lanthanide elements.

Analysis of the electronic structure, hyperfine structure, and volume isotope shifts in the low lying states of Ba I and Ba II

Relativistic multi-configuration Dirac Fock (MCDF) wavefunctions coupled to good angular momentum J have been calculated for low lying states of Ba I and Ba II. These wavefunctions are compared with semi-empirical ones derived from experimental atomic energy levels. It is found that significantly better agreement is obtained when close configurations are included in the MCDF wavefunctions. Calculations of the electronic part of the field isotope shift lead to very good agreement with electronic factors derived from experimental data. Furthermore, the slopes of the lines in a King plot analysis of many of the optical lines are predicted accurately by these calculations. However, the MCDF wavefunctions seem not to be of sufficient accuracy to give agreement with the experimental magnetic dipole and electric quadrupole hyperfine structure constants.

A reformulation of the theory of field isotope shift in atoms

The theory of the field isotope shift (FS) in atomic spectra is discussed critically and the results are presented in a form which is more straightforward than the expressions traditionally used to interpret experimental data. First-order perturbation theory is applied within the single-particle framework to the case of an s or p1/2 electron outside closed shells. Parameters to take account of many-body effects are subsequently included. The nuclear and electronic dependences of the FS are separately discussed. In a generalisation of the work of Seltzer (1986), it is shown that the former can be represented as a series of even charge moments: the coefficients of the first three terms for an s electron are given. The difference between the series for an s and a p1/2 electron is shown to be generally insignificant. The electronic dependence enters through the (relativistic) probability density N of the electron at the origin; for the case of an s electron. They relate N to the magnetic hyperfine splitting factor alpha s. A table which allows N to be found from a measurement of alpha s is given. Second-order field shifts are of the order of 10-3-10-4 of the first-order shifts for a two-neutron change.

Calculation of hyperfine splitting constants fors-electrons: a clarification

It is shown that two different methods of normalization have been used in previous work on calculating the hyperfine structure parameteras ofs-electrons leading to different values ofas for the case of heavy atoms. The normalization used in calculatingas by means of the exact Dirac radial functions of the one electron problem is discussed in detail. For the ratio between the field isotope shift constant and the hyperfine splitting parameter the two methods yield nearly identical values.

Field shift and generalised moments of nuclear charge distribution

It is shown that the use of realistic charge distribution leads to odd moment dependence of the nuclear field isotope shift. Our expression for field isotope shift reduces to the familiar result of Seltzer for low and moderateZ, Z denoting atomic number.

Field shift and generalised moments of nuclear charge distribution

It is shown that the use of realistic charge distribution leads to odd moment dependence of the nuclear field isotope shift. Our expression for field isotope shift reduces to the familiar result of Seltzer for low and moderateZ, Z denoting atomic number.

Field shift crossed second-order effects in dNsp configurations

In configurations containing open s subshells, far-configuration mixing ('crossed second-order effects') leads to different electron change densities at the nucleus for the various Russell-Saunders terms and thus to different field isotope shifts. For ndN(n+1)s (n+1)p configurations (n=3, 4, 5; N=1-10) the electron charge densities D of pairs of terms belonging to parents with the same multiplicity calculated using the Hartree-Fock computer code of Froese Fischer (1978). Usually, the term with the higher multiplicity has the larger density. The density difference Delta D increases linearly with the number of d electrons up to the half-filled shell and then decreases. The terms belonging to the parent with the higher multiplicity show larger values of Delta D than those belonging to the parent with the lower multiplicity. The effect increases with the principal quantum number n; it depends on the spins of the parent and grandparent terms but not on their angular momenta. The Hartree-Fock results of Delta D were used to calculate field shift differences between the corresponding terms. The comparisons of calculated and experimental field shift differences shows that the non-relativistic Hartree-Fock method correctly predicts their sign and order of magnitude.

Improved calculation of field isotope shift constants for optical spectral lines

Following the approach of previous investigations improved formulae for the field isotope shift constantCunif of optical spectral lines have been derived assuming a uniform nuclear charge distribution. From these formulaeCunif may be evaluated forselectrons with an accuracy of better than 1%. After considering the effect of the different normalization procedures the results obtained by different methods of approach are in good agreement.

A re-evaluation of isotope shift constants

The field isotope shift constantCunif for a uniform nuclear charge distribution has been re-evaluated fors-electrons for elements with 10≦Z≦ 95. A table is given which permitsCunif to be found for any isotope pair.

Refined MCHF evaluations of field isotope shift and hyperfine structure in the calcium atom

In the calcium atom, the MCHF method has been applied for evaluating the field-shift electronic parts of both 4s2-4s4p lines, and the hyperfine-structure electronic effective parameters of the 4s4p3P2 and1P1 levels. For the hyperfine structures, the far-configuration mixing corrections have been computed with the assumption that the lower state is itself a two-componentsp+dp state in close-configuration mixing.

Experimental and theoretical isotope shifts of strontium levels subject to very strong configuration mixing

The isotope shifts of the levels 5p2 1D2, 1S0 and 5sns 1S0(n=7, 8) of strontium have been measured between the isotopes 84, 86, 87 and 88 in two-photon transitions from the ground state using two lasers with different wavelengths. These levels occur below the beginning of the Rydberg series, and are known to exhibit very strong configuration mixing. Mass and field isotope shifts are calculated ab initio by means of the MCHF method for these levels and 5s4d 1D2, 5s6s 1S0. The qualitative agreement between theory and experiment confirms the necessity of taking into account the mixing (up to 50%) with both the 5p2 and 4d2 perturbers in the wavefunction expansions.