Specific Mass Shift Research Articles

Optical isotope shifts of stable hafnium atoms in a resonance cell on-line with a heavy-ion accelerator.

Optical isotope shifts were measured on the 618-nm, ground-state transition of Hf i for the isotopes $^{174\mathrm{\ensuremath{-}}180}\mathrm{Hf}$. For the isotope pair 178-180, a specific mass shift of approximately -8 times the normal mass shift was deduced for this transition. The large size of this shift is consistent with other specific mass shifts that result from a broken d-shell electron pair. A transtion electronic factor of ${\mathit{E}}_{618}$=0.158\ifmmode\pm\else\textpm\fi{}0.012 was extracted from the data. Excited-state hyperfine coefficients for the odd isotopes $^{179}\mathrm{Hf}$ and $^{177}\mathrm{Hf}$ were also deduced. The values of mean-square-charge radii obtained for the isotopic chain agree well with previously published results.

Optical determination of the ^20,22Ne 3s–3p specific mass shift

By using a supersonic beam of metastable Ne* atoms and a single-mode dye laser we determine the 2p(5)3s-3p specific mass shift of the (20,22)Ne isotopes by means of optical spectroscopy. The resulting value, on the basis of a systematic measurement of transition isotope shifts at different transition energies between 15,300 and 17,000 cm(-1), is 473 +/- 2.5 MHz. This is ~ 50 MHz larger than the best-known theoretical value.

Experimental and MCHF isotope shifts of strongly perturbed levels in Ca I and Sr I

Theoretical and experimental isotope shifts for Ca I and Sr I levels are presented. The isotope shifts of the levels 4s6s 1S0, 4p2 1S0 and 4p2 1D2 of calcium have been measured between the isotopes 40, 42, 43, 44 and 48 in two-photon transitions from the Ca ground state using two lasers with different wavelengths. Results of ab initio mass and field shift calculations are presented for these levels as well as for a number of other strongly perturbed low-lying levels in calcium and strontium using the multiconfiguration Hartree-Fock method. The 'gradient' and the alternative 'Slater' forms of the specific mass shift operator have been tested; the latter is found to be unreliable with the MCHF expansions which are limited to valence correlation effects.

Calculations of isotope shifts in caesium and thallium using many-body perturbation theory

Ab initio many-body perturbation calculations are presented for the field and the specific mass isotope shifts for caesium and thallium. The calculations are fully relativistic and incorporate the random phase approximation core screening corrections together with the lowest order correlation corrections. For the specific mass shift certain higher order corrections are also included. For the Cs 6s1/2 ground state the authors obtain a field shift value which they believe is accurate to 3%. For Tl they find relatively poor agreement between the calculated field shift values at this level of approximation. Current experimental data are re-examined in the light of the results.

High-precision isotope-shift measurement of 2(3)S-2(3)P transition in helium.

The isotope shift for the ${2}^{3}$S-${2}^{3}$P transition between $^{3}\mathrm{He}$ and $^{4}\mathrm{He}$ has been measured with a laser-microwave spectroscopy technique to a precision of 1 ppm, or 30 kHz. Our result is 100 times more precise than previous measurements and is by far the most precise isotope-shift measurement ever made for a multielectron system. It provides, for the first time, not only a check for the specific mass shift, but also for the calculations of the nuclear volume shift, the relativistic corrections involving the coupling between electrons, and the QED contributions.

Optical isotope shift and hyperfine structure measurements of 152,154-158,160Gd.

Laser spectroscopic measurement of the optical isotope shifts of all the naturally occurring Gd isotopes have been made using a collimated atomic beam system. The isotope shift and hyperfine splitting of all the stable isotopes have been measured for five optical transitions of Gd I at 570.135, 574.466, 574.636, 575.188, and 579.138 nm. The data were combined with the available muonic and electronic x-ray isotope shift data to extract the specific mass shift and the field shift constant. The change in charge radii, \ensuremath{\lambda}\ensuremath{\approxeq}\ensuremath{\delta}〈${\mathit{r}}^{2}$〉, have been extracted and compared with droplet model predictions. The accuracy of the isotope shift measurements is 0.1% and the extracted charge radius changes have an uncertainty of about 3%.

High precision calculations on the 2S ground state of the lithium atom

The results of a detailed variational calculation on the 2S ground state of the lithium atom are reported. The wave function was constructed using Hylleraas-type functions with extensive exponent optimization being employed. The calculated nonrelativistic ground state energy obtained was −7.478 059 53 a.u., which is the lowest upper bound estimate for this quantity obtained to date. The discrepancy with semi-empirical estimates of this quality is discussed. The hyperfine coupling constant for 7Li is calculated to be 401.795 MHz, which compares favorably with the experimental result of 401.752 043 3 MHz. Expectation values are reported for the individual energy components, as well as the electron density at the nucleus, and the specific mass shift operator. The transition isotope shift is also evaluated. The convergence characteristics of the calculations are discussed, along with the effect of retaining only one of the two possible spin eigenfunctions in the basis set.

J dependences of the isotope shift and hyperfine structure in Gd I 4f75d6s2 9D, 4f75d6s6p 9D, and 9F terms.

Isotope shifts of 16 transitions in 4${\mathit{f}}^{7}$5d6${\mathit{s}}^{2}$${(}^{9}$D)-4${\mathit{f}}^{7}$5d6s6p${(}^{9}$D${,}^{9}$F) of Gd i for the stable isotopes with A=152--160 were measured by atomic-beam laser spectroscopy. The hyperfine constants A and B of $^{155}\mathrm{Gd}$ and $^{157}\mathrm{Gd}$ in two $^{9}$D terms and the $^{9}$F term were determined. The single-electron hyperfine parameters ${\mathit{a}}_{4\mathit{f}}^{10}$ for the 4f electron and ${\mathit{a}}_{5\mathit{d}\mathit{s}}^{\mathit{k}}$${\mathit{k}}_{\mathit{l}}$,${\mathit{b}}_{5\mathit{d}\mathit{s}}^{\mathit{k}}$${\mathit{k}}_{\mathit{l}}$ for the 5d electron were deduced. The electric quadrupole moments Q of $^{155}\mathrm{Gd}$ and $^{157}\mathrm{Gd}$ were obtained to be 1.27(5)b and 1.36(6)b, respectively. The J dependences of the isotope shifts in two $^{9}$D terms and the $^{9}$F term were observed. The parameter ${\mathit{z}}_{5\mathit{d}}$ of the crossed-second-order effect for the $^{9}$D term of 4${\mathit{f}}^{7}$5d6${\mathit{s}}^{2}$ was derived, and the value of ${\mathit{z}}_{5\mathit{d}}$/\ensuremath{\lambda} was obtained to be 134(4) MHz/${\mathrm{fm}}^{2}$. We confirmed that the field shift is dominant in the crossed-second-order effect and the specific mass shift is negligible.

Optical isotope shift measurements using collinear ion beam laser spectroscopy and the configuration of the NdII(23537)9/20 level

The optical isotope shifts of five even isotopes of neodymium have been measured by using collinear ion beam laser spectroscopy (CIBLS). Isotopically pure NdII ions with energy of 30ke V from an isotope separator were collinearly interacted with light from a tunable dye laser and selectively excited from a metastable level of 4f4 5d6 K9/2 to the (23537)9/20 level by Doppler tuning technique. The resonant excitation frequency values for each Nd isotope with mass number of 142, 144, 146, 148 and 150 were obtained. After the separation of the normal and specific mass shift and the field shift from the experimentally measured isotope shift, the configuration of the (23537)9/20 level was decomposed into 4f4 6p, 4f3 5d2 and 4f3 5d6p, and their fractions, for the first time. were determined to be 0.12-0.13, 0.88-0.85 and 0-0.02, respectively.

Calculations on the 2S ground states of some members of the Li I isoelectronic series.

Extensive variational calculations using Hylleraas-type functions are carried out on the $^{2}\mathrm{S}$ ground states for the following members of the Li i isoelectronic series: Li i, B iii, C iv, N v, O vi, F vii, and Neviii. For each species, the nonrelativistic energy, the electronic density at the nucleus, the specific mass shift, the transition isotope shift, the Fermi contact interaction, the diamagnetic susceptibility, the nuclear magnetic shielding factor, moments of 〈${r}_{i}^{n}$〉 for n=-1, 1, 2, and 3 and of 〈${r}_{\mathrm{ij}}^{n}$〉 for n=-1, 1, and 2 are reported. The nonrelativistic energies obtained are lower than any previously published values for each member of the Lii series examined. The effect of one versus two spin eigenfunctions in the basis set is examined. The rates of convergence for both the one- and two-spin-eigenfunction basis sets are examined for each expectation value.

Laser excitation spectroscopy of the A and B states of jet-cooled copper dimer: Evidence for large electronic isotope shifts

Fluorescence excitation spectra recorded for the A–X system of jet-cooled Cu2 show conclusive evidence of a ΔΛ=0 transition, and the A state is thereby definitively assigned as 1Σ+u. A previous assignment of the B state as 1Σ+u is confirmed, but the vibrational levels of this state are complicated by the presence of a perturbation at v′=0. The perturbing state does not, however, appear to be either of the two optically accessible electronic states in this spectral region. Anomalously large electronic isotope shifts are observed for the A and B states, and this behavior is discussed in terms of the correspondingly large ‘‘specific mass shifts’’ observed in the optical spectra of atomic copper for transitions that couple states differing in the number of d electrons. Due to the large spin-orbit coupling constants in the ‘‘d-hole’’ configurations, it is proposed that the low-energy-excited molecular states of Cu2 derived from these configurations should be described by Hund’s case (c) coupling. Dynamical effects observed in the gas phase and in solid matrices are briefly discussed in terms of this bonding scheme.

Parametric analysis of the isotope shift and hyperfinestructure in the Eu I configuration 4f 7 5d 6s

With doppler-reducedintermodulatedoptogalvanicsaturation laserspectroscopy (IMOGS) in Eu I the isotope shift (IS) and hyperfine structure (hfs) of the remainingb8D term of the configuration 4f7 5d 6s was investigated. With the help of former measurements in our group (a6,10D) and by other authors (a8,10D) the IS of the now complete configuration (20 levels) was analysed with wavefunctions by J.-F. Wyart. From the parametric description of the IS resulted the necessity also to include the often neglected small parameterg1(g1(4f, 5d)=9.3(3) MHz), which is mainly due to the specific mass shift. The IS of all 20 levels can be well described by further crossed-second-order parametersg2(5d, 6s)=−401(5) MHz andg3(4f, 6s)=−27(1) MHz and one commonJ-dependent parameterz5d=40.4(4.1) MHz. — With effective one-electron parametersa kl ,b kl an interpretation of the magnetic and electric hfs (except for a few disturbed levels) could also be carried out.

Calculations on the 2S ground state of Be II.

Extensive variational calculations on the $^{2}\mathrm{S}$ ground state of ${\mathrm{Be}}^{+}$ are reported. Using a 401-term expansion of Hylleraas-type functions, the nonrelativistic ground-state energy is determined to be -14.324 760 a.u., which is the lowest upper bound to the ground-state energy reported to date for this system. The Fermi contact interaction is determined to be 12.4980 a.u., which is in very close agreement with the experimental value of 12.503 88 a.u. The nuclear-magnetic shielding factor and the molar diamagnetic susceptibility are evaluated to be \ensuremath{\sigma}=1.415401 \ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$ a.u. and \ensuremath{\chi}=-5.154 43\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}6}$ ${\mathrm{cm}}^{3}$ ${\mathrm{mol}}^{\mathrm{\ensuremath{-}}1}$, respectively. The electron density at the nucleus, the moments 〈${r}_{i}^{n}$〉, n=-1, 1, 2, and 3, and 〈${r}_{\mathrm{ij}}^{n}$〉, n=-1, 1, and 2, are also reported. The specific mass shift (mass polarization contribution) is determined to be 2.758\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$ a.u. The rate of convergence of the calculation is discussed. The role of one versus two spin eigenfunctions in the basis set is discussed with respect to its bearing on the calculation of the Fermi contact interaction.

Reformulation of the theory of the mass shift

The conventional division of the mass shift in atomic spectra into normal and specific mass shift is shown to lead to cancellation between the two terms in heavy atoms. It is suggested that the evaluation of the NMS in terms of the binding energy of a level is potentially unreliable, and certainly complicates unnecessarily the relativistic corrections to the mass shift. A mass shift Hamiltonian is derived, including relativistic corrections to order 1/c2, and the physical significance of the terms discussed. The Hamiltonian is given in two equivalent forms, for use with non-relativistic and relativistic wavefunctions. The implications for parametric analysis of isotope shifts are discussed.

The coupled-cluster approach to non-relativistic and relativistic many-body calculations

A review is given of the atomic many-body theory in the coupled-cluster approach or exponential-Ansatz formulation. Explicit equations and corresponding graphical representations are given in the pair-approximation, where the one- and two-body parts of the cluster (exponent) operator are considered. Also the effect of a small, additional perturbation is considered. The technique of evaluating diagrams by means of one- and two-particle functions, satisfying inhomogeneous differential equations, is reviewed. Illustrative numerical results are given for the electron correlation energy, electron binding energy, hyperfine separation and specific mass shift of simple atomic systems. The extension of the non-relativistic procedure to the relativistic regime is discussed by considering the effect of the exchange of one and two virtual, transverse photons between the electrons. In lowest order this leads to the "no-virtual-pair approximation".

Isotope shift of the 3s 2S [formula omitted] and 3p 2P J levels in 6,7Li

Applying the method of resonant Doppler-free 2-photon laser spectroscopy, the isotope shift of the 6.7Li 2S-3P-17S and 2S-2P-3S transitions have been measured with a thermionic detector. Because the residual isotope shift of the 17S level is negligible, the shift of the 3P level could be derived directly from the first transition. Taking into account the level isotope shift of the 2S ground state, as measured recently in our laboratory, the isotope shift of the 3S level was determined from the second transition. Including precise experimental isotope shift data for 2S, 4S and 2P, approximate scaling formulas for the specific mass shift of the nS and nP level series can be given.

Evaluation of changes in mean-square nuclear charge radii of stable isotopes of erbium

Isotope shifts involving all the stable even-A isotopes of erbium have been studied in four transitions using optical technique and highly enriched isotopes. The value of change in mean-square charge radii δ〈r2〉 deduced from our studies in 5806.05 A (f12 s2-f12 sp) transition is in excellent agreement with muonic X-ray value. With negligible specific mass shift (SMS) in 5806.05 A line, the SMS and field shifts in other lines are compared via King-Plot. In transitions involving change of 4f-electron (e.g., f12s2-f11ds2), large negative SMS value is obtained which is very close to the theoretically predicted value.

Many-body calculations of spectroscopic properties of the 3s3p3P and 3s3d3D states in Mg

Many-body perturbation theory within the algebraic approximation has been applied to compute properties of the double open-shell states 3s3p 3P and 3s3d 3D in Mg. The computed results are based on a complete perturbation expansion to third order, and even a few fourth-order core polarisation diagrams have been considered. The properties considered are the specific mass shift and field shift contributions to the 26Mg-24Mg isotope shifts in the transitions 3s2 1S-3s3p 3P and 3s3p 3P-3s3d 3D, the fine structure and isotope shift in the fine structure of the 3s3p 3P state, and finally the magnetic hyperfine structure of the 3s3p 3P state. Good or reasonable agreement with experiments was obtained in all cases, except for the isotope shift in the fine structure where only a qualitative agreement was obtained.

Specific mass shift for the sup2S ground state of the lithium atom.

The absolute specific mass shifts for the $^{2}\mathrm{S}$ ground state of the lithium atom are calculated using a 352-term Hylleraas-type wave function. The specific mass shifts for $^{7}\mathrm{Li}$ and $^{6}\mathrm{Li}$ are 5.180 and 6.042 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, respectively, using first-order perturbation theory, and 5.177 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ ${(}^{7}$Li) and 6.039 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ ${(}^{6}$Li) from a nonperturbative approach. With use of Pekeris's accurate values for the specific mass shifts of ${\mathrm{Li}}^{+}$, the transition isotope shift of Li relative to ${\mathrm{Li}}^{+}$ is calculated to be 1.101 GHz, using first-order perturbation theory, and 1.071 GHz from a nonperturbative procedure. The calculated shift is in very close agreement with the experimental value of 1.111\ifmmode\pm\else\textpm\fi{}0.006 GHz obtained by Lorenzen and Niemax.

Laser-induced fluorescence measurement of6,7lithium isotope shift

Values of frequency splittings in the lithium isotopes have been determined with the aid of laser-induced fluorescence in a supersonic beam, perpendicularly irradiated by a CW ring dye laser. The residual 2s-2p isotope shift has been found to be 4721.8±2.0 MHz, leading to a specific mass shift for the 2p level of −3610.8±5 MHz.