Nuclear Charge Radii Research Articles

Effects of the pairing energy on nuclear charge radii

Atomic masses of various radionuclides around the Z = 82 shell closure were determined with the ISOLTRAP mass spectrometer. This particular mass region is characterized by strong nuclear structure effects, like, e.g., shape coexistence. In this contribution results derived from mass spectrometry and laser spectroscopy are examined for a possible correlation between mass values and nuclear charge radii.

Measurement of the nuclear charge radii of 8, 9Li

Nuclear charge radii of 6, 7, 8, 9Li have recently been measured at the GSI on-line mass separator using high-resolution resonance ionization mass spectroscopy. We give a brief description of the experimental method. The results for the charge radii are compared with different theoretical predictions.

Isotope shifts and nuclear radius measurements for helium and lithium

It is now well established that accurate relative values of the rms nuclear charge radius for light atoms can be extracted from a comparison between high-precision theory and experiment for the isotope shift in atomic transition frequencies. Results are available for isotopes of helium and lithium. This paper reviews and updates the interpretation of earlier measurements for 3He relative to 4He, and 6Li relative to 7Li. New results are presented for the quantum electrodynamic recoil corrections. Recent measurements for the halo nucleus 6He, and the short-lived nuclei 8Li, and 9Li are discussed. The derived nuclear charge radii of 2.054(14), 2.30(4), and 2.24(4)~fm, respectively, are compared with the predictions of various nuclear structure models.PACS Nos.: 31.15.Pf, 31.30.Jv, and 32.10.Hq

Precision measurements of fine and hyperfine structure in lithium I and II

Recent advances in modeling Li I and II in conjunction with improved experimental techniques have enabled precise tests of quantum electrodynamics. For Li+, the hyperfine intervals of the 1s2s 3S1 and 1s2p 3P0,1,2 states are in excellent agreement with theory. A recent measurement of the 1s2p 3P1,2 fine-structure interval also agrees well with the calculated value and resolves a discrepancy found by two prior experiments. For neutral lithium, discrepancies exist among the results of various experiments for the 6,7Li D1 isotope shift and the 2P fine structure. However, all of the fine-structure measurements are several MHz larger than the theoretical value. Prospects for future experiments to improve the determination of the fine-structure constant and the relative 6,7Li nuclear charge radii are discussed. PACS Nos.: 32.10.Fn, 31.30.Gs, 42.62.Fi

Hyperfine structure of the metastable level in hydrogen-like atoms

Precision methods for measuring the hyperfine splitting EHFS(2S) of the metastable level in light hydrogen-like systems such as hydrogen, deuterium, and the 3He+ ion are considered. These measurements open up a new possibility for precise testing of quantum electrodynamics (QED) of bound states in hadronic systems. While the direct calculation of the energy levels in such systems runs into the problem of the uncertainty of the nuclear charge radius, the contribution of energy corrections appearing in the calculation of the parameter D21 = 8EHFS(2S) - EHFS(1S) taking the finite size of the nucleus into account becomes smaller. The results of calculations of D21 are presented and compared with experimental values. The approach considered in the paper allows the testing of some bound-state QED corrections to the hyperfine splitting energy at a level of 10-7, which is comparable with the results of precision QED tests based on the study of the hyperfine splitting in leptonic systems.

Erratum: Nuclear Charge Radii ofLi8,9Determined by Laser Spectroscopy [Phys. Rev. Lett.93, 113002 (2004)

Erratum: Nuclear Charge Radii of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">L</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:mrow><mml:mprescripts /><mml:none /><mml:mrow><mml:mn>8</mml:mn><mml:mo>,</mml:mo><mml:mn>9</mml:mn></mml:mrow></mml:mmultiscripts></mml:math>Determined by Laser Spectroscopy [Phys. Rev. Lett.<b>93</b>, 113002 (2004)

A systematic study of neutron magic nuclei with N = 8, 20, 28, 50, 82 and 126 in the relativistic mean-field theory

We perform a systematic study of all the traditional neutron magic nuclei with N = 8, 20, 28, 50, 82 and 126, from the neutron drip line to the proton drip line. We adopt the deformed relativistic mean-field theory as our framework and treat pairing correlations by a simple BCS method with a zero-range δ-force. Remarkable agreement with the available experimental data is obtained for the binding energies, the two- and one-proton separation energies, and the nuclear charge radii. The calculated nuclear deformations are compared with the available experimental data and the predictions of the FRDM mass formula and the HFBCS-1 mass formula. We discuss, in particular, the appearance of sub-shell magic nuclei by observing irregular behaviour in the two- and one-proton separation energies.

Laser Spectroscopic Determination of theH6eNuclear Charge Radius

We have performed precision laser spectroscopy on individual 6He (t(1/2)=0.8 s) atoms confined and cooled in a magneto-optical trap, and measured the isotope shift between 6He and 4He to be 43 194.772+/-0.056 MHz for the 2(3)S1-3(3)P2 transition. Based on this measurement and atomic theory, the nuclear charge radius of 6He is determined for the first time in a method independent of nuclear models to be 2.054+/-0.014 fm. The result is compared with the values predicted by a number of nuclear structure calculations and tests their ability to characterize this loosely bound halo nucleus.

Helium. Relativity and QED

A large body of work to calculate nonrelativistic energies, relativistic corrections, and quantum electrodynamic (QED) energy shifts in helium is reviewed and compared with experiment. Of particular significance are measurements of the QED (Lamb) shift for the low-lying S-states of helium, where the accuracy rivals the best measurements in the corresponding He + hydrogenic ion. Applications of high precision spectroscopy to measurements of the fine structure constant α, and to measurements of the nuclear charge radius from the isotope shift are discussed.

Helium. Relativity and QED

A large body of work to calculate nonrelativistic energies, relativistic corrections, and quantum electrodynamic (QED) energy shifts in helium is reviewed and compared with experiment. Of particular significance are measurements of the QED (Lamb) shift for the low-lying S-states of helium, where the accuracy rivals the best measurements in the corresponding He + hydrogenic ion. Applications of high precision spectroscopy to measurements of the fine structure constant α, and to measurements of the nuclear charge radius from the isotope shift are discussed.

Bethe logarithm for the lithium atom from exponentially correlated Gaussian functions

The calculation of Bethe logarithm for the ground state of the lithium atom is presented. The Bethe logarithm is the main QED effect coming from the electron self-interaction, which has not been obtained yet. Both results for the infinite nuclear mass, $\mathrm{ln}{k}_{0}=5.17817(3),$ and the mass polarization correction, $\ensuremath{\Delta}\mathrm{ln}{k}_{0}=0.114(3),$ significantly improve the hitherto theoretical values for the lithium ground-state energy. They allow from one side to test the theory against precise measurements of transition frequencies and from the other side, to improve the accuracy of determination of the difference in the square of nuclear charge radii from the isotope-shift measurements. The applied calculational method is based on the well adapted explicitly correlated Gaussian basis set and can be extended to other few-electron atoms and molecules.

Electronic properties of gold–aluminium intermetallic compounds

The intermetallic compounds in the Au–Al system were studied by 197Au Mössbauer spectroscopy. The observed isomer shifts and electric quadrupole splittings are compared with the electron densities and electric field gradients at the gold nuclei obtained by LAPW calculations using the WIEN97 computer code. This provides insights into the electronic structure of Au–Al alloys and yields values for the groundstate quadrupole moment of 197Au and for the change of the nuclear charge radius for the 77 keV transition of 197Au.

Hyperfine structure of heavy hydrogen-like ions

The hyperfine splittings of the 1s hydrogen-like ground level of two isotopes of thallium were measured using the SuperEBIT electron beam ion trap. The measurements allowed us to accurately infer a magnetization radius. The inferred radius exceeds the single particle estimate by about 10% and the nuclear charge radius by about 7%. Because two isotopes were measured, we were able to observe for the first time the interaction between the finite size of the nuclear magnetization distribution and the finite size of the charge distribution on the hyperfine anomaly. The measured isotope difference of 30.59±0.38 meV differs from the value of 31.04±0.01 meV inferred from neutral thallium using a point magnetic dipole approximation, but is in good agreement with the difference of 30.71±0.16 meV calculated by using an extended magnetic dipole.

Atomic spectroscopy studies of short-lived isotopes and nuclear isomer separation with the ISOLDE RILIS

The resonance ionization laser ion source (RILIS) at the ISOLDE on-line isotope separator is based on the selective excitation of atomic transitions by tunable laser radiation. Ion beams of isotopes of 20 elements have been produced using the RILIS setup. Together with the mass separator and a particle detection system it represents a tool for high-sensitive laser spectroscopy of short-lived isotopes. By applying narrow-bandwidth lasers for the RILIS one can study isotope shifts and hyperfine structure (HFS) of atomic optical transitions. Such measurements are capable of providing data on nuclear charge radii, spins and magnetic moments of exotic nuclides far from stability. Although the Doppler broadening of the optical absorption lines limits the resolution of the technique, the accuracy of the HFS measurements examined in experiments with stable Tl isotopes approaches a value of 100 MHz. Due to the hyperfine splitting of atomic lines the RILIS gives an opportunity to separate nuclear isomers. Isomer selectivity of the RILIS has been used in studies of short-lived Ag, Cu and Pb isotopes.

Systematic model calculations of the hyperfine structure in light and heavy ions

Systematic model calculations are performed for the magnetization distributions and the hyperfine structure (HFS) of light and heavy ions with a mass close to A ~ 6 208 235 to test the interplay of nuclear and atomic structure. A high-precision measurement of lithium-isotope shifts (IS) for suitable transition, combined with an accurate theoretical evaluation of the mass-shift contribution in the respective transition, can be used to determine the root-mean-square (rms) nuclear-charge radius of Li isotopes, particularly of the halo nucleus 11Li. An experiment of this type is currently underway at GSI in Darmstadt and ISOLDE at CERN. However, the field-shift contributions between the different isotopes can be evaluated using the results obtained for the charge radii, thus casting, with knowledge of the ratio of the HFS constants to the magnetic moments, new light on the IS theory. For heavy charged ions the calculated n-body magnetization distributions reproduce the HFS of hydrogen-like ions well if QED contributions are suppressed. Ab-initio calculations of the HFS of 209Bi80+ were performed to analyse this surprising result. Here, the boiling of the QED vacuum gives an important contribution to the HFS, thus modifying the theoretical results of other models. The investigations performed have initiated detailed studies of the structure of lithium-like ions heavier then bismuth, to obtain predictions for the experiments on uranium, which are proposed at PHELIX-XRL. PACS Nos.: 31.15Pf, 31.30Jv, 32.10Hq, 21.10GV, 21.10FT, 21.60-n, 21.60+n

Shell model description of isotope shifts in calcium

Isotope shifts in the nuclear charge radius of even and odd calcium isotopes are calculated within the nuclear shell model. The model space includes all configurations of nucleons in the $2s, 1d_{3/2}, 1f_{7/2}, {\rm and} ~2p_{3/2}$ orbits. The shell model describes well the energies of the intruder states in Sc and Ca, as well as the energies of the low-lying $2^+$ and $3^-$ states in the even Ca isotopes. The characteristic features of the isotope shifts, the parabolic dependence on $A$ and the prominent odd-even staggering, are well reproduced by the model. These features are related to the partial breakdown of the $Z = 20$ shell closure caused by promotion, due to the neutron-proton interaction, of the $ds$ shell protons into the $fp$ shell.

Isospin and Z1/3-dependence of the nuclear charge radii

Based on the systematic investigation of the data available for nuclei with A≥ 40, a Z 1/3-dependence for the nuclear charge radii is shown to be superior to the generally accepted A 1/3 law. A delicate scattering of data around R c/Z 1/3 is inferred as owing to the isospin effect and a linear dependence of R c/Z 1/3 on N/Z (or (N - Z)/2) is found. This inference is well supported by the microscopic Relativistic Continuum Hartree-Bogoliubov (RCHB) calculation conducted for the proton magic Ca, Ni, Zr, Sn and Pb isotopes including the exotic nuclei close to the neutron drip line. With the linear isospin dependence provided by the data and RCHB theory, a new isospin-dependent Z 1/3 formula for the nuclear charge radii is proposed.

Diode-laser hyperfine-structure spectroscopy of138,139La

With a beam of unenriched lanthanum, the hyperfine structure (hfs) of ${}^{138,139}\mathrm{La}$ has been measured for the transition from the ${5d6s}^{2}{}^{2}{D}_{3/2}$ ground state to the $5d6s6p{}^{4}{F}_{5/2}$ level at 675.304 nm by means of atomic-beam diode-laser spectroscopy. Magnetic-dipole (A) and electric-quadrupole $(B)\mathrm{hfs}$ constants of the 0.090% abundant ${}^{138}\mathrm{La},$ as well as those of ${}^{139}\mathrm{La},$ have been determined for the ${5d6s}^{2}{}^{2}{D}_{3/2}$ and $5d6s6p{}^{4}{F}_{5/2}$ levels; this serves as a measurement of hyperfine structure constants A and B for ${}^{138}\mathrm{La}.$ The isotope shift between ${}^{139}\mathrm{La}$ and ${}^{138}\mathrm{La}$ has been obtained for the 675.304-nm transition and change in mean-square nuclear charge radii $\ensuremath{\delta}〈{r}^{2}〉$ derived.

Isotope shifts and hyperfine structure in the transitions of gadolinium

High-resolution resonance ionization mass spectrometry has been used to measure isotope shifts and hyperfine structure in all (J = 2-6) and the transitions of gadolinium (Gd I). Gadolinium atoms in an atomic beam were excited with a tunable single-frequency laser in the wavelength range of 422-429 nm. Resonant excitation was followed by photoionization with the 363.8 nm line of an argon ion laser and resulting ions were mass separated and detected with a quadrupole mass spectrometer. Isotope shifts for all stable gadolinium isotopes in these transitions have been measured for the first time. Additionally, the hyperfine structure constants of the upper states have been derived for the isotopes 155, 157 Gd and are compared with previous work. Using prior experimental values for the mean nuclear charge radii, derived from the combination of muonic atoms and electron scattering data, field shift and specific mass shift coefficients for the investigated transitions have been determined and nuclear charge parameters for the minor isotopes 152, 154 Gd have been calculated.

Lithium isotope shifts as a measure of nuclear size

The isotope shifts for $2{}^{2}{P}_{J}$\char21{}$2{}^{2}S$ and $3{}^{2}S$\char21{}$2{}^{2}S$ transition energies in lithium are calculated variationally in Hylleraas coordinates, including nonrelativistic, relativistic, and QED terms up to $O(\ensuremath{\mu}/M),$ $O(\ensuremath{\mu}{/M)}^{2},$ $O({\ensuremath{\alpha}}^{2}\ensuremath{\mu}/M),$ and $O({\ensuremath{\alpha}}^{3}\ensuremath{\mu}/M)$ atomic units, and the lowest-order finite nuclear size correction. With high-precision isotope shift measurements, our results can potentially yield a precise determination of the nuclear charge radius for different isotopes of lithium, and especially for the exotic ${}^{11}$Li ``halo'' isotope. For the case of ${}^{7}\mathrm{Li}$-${}^{6}\mathrm{Li},$ using the nuclear charge radii from nuclear scattering data, our calculated isotope shifts for the $2{}^{2}{P}_{1/2}$\char21{}$2{}^{2}S,$ $2{}^{2}{P}_{3/2}$\char21{}$2{}^{2}S,$ and $3{}^{2}S$\char21{}$2{}^{2}S$ transitions are $10534.31(61)(6)$ MHz, $10534.70(61)(6)$ MHz, and $11454.31(39)(5)$ MHz, respectively, where the first brackets indicate the uncertainties due to the nuclear charge radii, and the second brackets indicate the computational uncertainties. The experimental isotope shifts are inconsistent with each other and with theory for these transitions.