Laser-atomic-beam spectroscopy in Sm: Isotope shifts and changes in mean-square nuclear charge radii

A systematic investigation of the isotope shifts of all natural Samarium isotopes was performed in 15 lines of the Sm I spectrum using the laser-atomic-beam technique. The observed lines correspond to transitions between the ground configuration 4f ⁶6s ² and the upper configurations 4f ⁶6s6p and 4f ⁵5d6s ². In one line a contribution of hyperfine-structure second-order effects to the isotope shift of the odd isotopes could be demonstrated. The measured isotope shifts have been separated in all lines into field shift and mass shift contributions assuming the specific mass shift to be zero in pures ²-sp transitions. From the field shift of the pures ²-sp transitions the changes in mean-square nuclear charge radii, δ<r ²>, have been evaluated for all natural Sm isotopes (in fm²): [144, 148] 0.517(27); [148, 150] 0.303(16); [150, 152] 0.423(22); [152, 154] 0.230(12); [147, 148] 0.152(8); [148, 149] 0.092(5). There is good consistency with recent muonic x-ray measurements of the changes in the Barrett nuclear charge radii,δR _k , of the even Sm isotopes.     

Optical isotope shifts of146Sm and151Sm

We have measured the optical isotope shifts of¹⁴⁶Sm and¹⁵¹Sm by laser resonance fluorescence. From these measurements the changes in the mean square nuclear radii are: Δ〈r²〉 (A=144 to 146)=0.266(10) fm², and Δ〈r²〉 (A=151 to 152)=0.262(10) fm². These results, together with those of the stable isotopes, show that the average nuclear expansion of samarium can be accounted for by the liquid drop model with deformations.     

Isotope shift in the Ca I resonance line and changes in mean-square nuclear charge radii of the stable Ca isotopes

The isotope shift of all stable Ca isotopes was studied in the Ca I resonance line. Enriched isotopes were used in an atomic beam, passing through the center of a spherical Fabry-Perot interferometer. The measured isotope shifts were separated into mass shift and field shift by comparing the optical isotope shift with δ〈r ²〉 values derived from recent muonic x-ray measurements. The results are discussed together with known data on the isotope shift in the Ca I intercombination line and data from Hartree-Fock calculations. The following mean values are obtained for the change in nuclear charge distribution δ〈r ²〉 [fm²]∶ [40, 42] 0.23(3); [40, 43] 0.13(3); [40, 44] 0.28(4); [40, 46] 0.14(7); [40, 48] 0.00(2).     

Isotope shift in molybdenum

The isotope shift in molybdenum has been studied in 16 lines of the arc and 6 lines of the spark spectrum for all stable isotopes by means of a photoelectric recording Fabry-Perot spectrometer with digital data processing. Mass shift and field shift were separated by two independent methods and were compared with the results of Hartree-Fock calculations. In the field shift large crossed-second-order effects ind ⁵ s ⁷ S and⁵ S were observed, which could be explained quantitatively by theory. The changes in mean square nuclear charge radii were evaluated from three 5s-5p transitions between different multiplets. The relativeδ〈r ² 〉 values are: [92, 94] 1; [94, 96] 0.854(3); [96, 98] 0.665(4); [98, 100] 1.003(5); [95, 97] 0.703(5);. [94, 95] 0.270(4); [96, 97] 0.119(5). The absolute values can be obtained withδ〈r ² 〉 ^{92, 94}=0.226(19)fm².     

Optical isotope shifts in neodymium

Isotope shifts have been measured in Nd II from which the shifts between pure configurations 4f ⁴ 6s and 4f ⁴ 5d can be determined. The specific mass shift for such a “transition” was estimated to be + 3 mK for a change of two neutrons. By comparison with electronic X-ray isotope shifts the following values were obtained for the change in the nuclear charge distributionδ〈r ²〉 [fm²]: (142, 144) 0.277; (144, 146) 0.257; (146, 148) 0.286; (148, 150) 0.381; (142, 143) 0.130; (144, 145) 0.111. Field shifts in several optical transitions have been compared with values of ¦ψ(0)¦² obtained from Hartree-Fock wave functions; agreement is good. Other specific mass shifts have been estimated 4f ⁴ 6s? 4f ⁴ 6p, ?1 mK; 4f ⁴ 6s? 4f ³ 5d ², ?30 mK. These values are in good agreement with calculated values of ?1.1 and ?30.6 mK.     

Isotope shift in Ni I and changes in mean-square nuclear charge radii of the stable Ni isotopes

The isotope shift in the Ni I spectrum was studied in 17 lines for all stable isotopes by means of a photoelectric recording Fabry-Perot spectrometer with digital data processing. The measured isotope shifts were separated into mass shift and field shift by comparing the optical isotope shift with model-independent δ〈r ²〉 values derived from a combined elastic electron scattering and muonic x-ray data analysis. The ratios of the observed field shifts in different types of transitions could be explained quantitatively by Hartree-Fock calculations. The relative changes in mean-square nuclear charge radii were found to be: [58, 60] 1.293(15); [60, 62]1; [62, 64] 0.641(16); [60, 61] 0.382(9). The absolute value δ〈r ²〉^60,62=0.170(35) fm² was derived using fine structure as well as hyperfine structure data for the determination of the change in the electron charge density at the nucleus in 4s-4p transitions.     

Changes in nuclear mean square charge radii of stable Krypton isotopes

The isotope shifts of stable even Kr isotopes (A=78 throughA=86) in the optical transitions at 432 nm and 557 nm were measured by means of polarization laser spectroscopy. The observed shifts are consistent with earlier results for other transitions. From the isotope shifts the changes in the nuclear mean square charge radiiδ〈r ²〉 were inferred using preliminary muonic isotope shift data. Starting from⁷⁸Kr, a monotonic decrease of 〈r ²〉 with increasing mass number is found throughout theg _9/2 neutron shell. The effect onδ〈r ²〉 of nuclear deformations as well as possible contributions due to changes in the skin thickness of the nuclear charge distribution are discussed.     

A muonic X-ray study of the charge distribution of 144, 148, 150, 152, 154Sm

We report the measurement of the energies of the 4f → 3d, 3d → 2p and 2p → Is muonic atomic transitions in separated isotopes of ^{144, 148, 150, 152, 154}Sm, and that of the 2s → 2p transitions of ¹⁵²Sm as well. Using these transition energies as well as the hyperfine splittings of the 2p levels, we have interpreted our data in terms of a deformed Fermi distribution for the charge density and obtained good fits. A model independent analysis of the isotope shifts in terms of generalized R_h moments has been made and is in good agreement with electronic X-ray and optical isotope shifts. The static quadrupole moments and the isomer shifts of the first excited state of ^{152, 154}Sm have been determined from the 2p hyperfine structure.     

Changes in mean-square nuclear charge radii in Er from optical isotope shifts by laser-atomic-beam spectroscopy

High-resolution laser-atomic-beam spectroscopy has been applied to investigate transitions 4f ¹² 6s ²?4f ¹¹ 5d6s ² and transitions starting from metastable states of the configuration 4f ¹¹ 5d6s ² of Er I. Precise values for the transition isotope shifts and for the hyperfine constants of 10 levels belonging to the configuration 4f ¹¹ 5d6s² and 9 levels belonging to high lying even-parity levels have been determined. From the isotope shift data relative changes of mean-square nuclear charge radiiδ 〈r ²〉 for all the stable Er isotopes have been deduced: ¦168,170¦ 1, ¦166,168¦ 0.984(15), ¦164,166¦ 0.984(15), ¦162,164¦ 1.198(18), ¦166,167¦ 0.3357(50). Absoluteδ 〈r ²〉 values have been obtained by calibrating the optical data with a value from muonic x-ray spectroscopy: ¦168,170¦ 0.121 (10) fm². The odd-even staggering parameter for¹⁶⁷Er has been determined: 0.683(10). Our results are compared with experimental data from electronic x-ray spectroscopy and data from calculations with the extended liquid-drop and the droplet model.     

Shape evolution for Sm isotopes in relativistic mean-field theory

The evolution of shape from the spherical to the axially deformed shapes in the Sm isotopes is investigated microscopically in relativistic mean-field theory. The microscopic and self-consistent quadrupole deformation constrained relativistic mean-field calculations show a clear shape change for the even-even Sm isotopes with N = 82-96. The potential surfaces for ¹⁴⁸Sm, ¹⁵⁰Sm and ¹⁵²Sm are found to be relatively flat, which may be the possible critical-point nuclei. By examining the single-particle spectra and nearest-neighbor spacing distribution of the single-particle levels, one finds that the single-particle levels in ¹⁴⁸Sm , ¹⁵⁰Sm, and ¹⁵²Sm distribute more uniformly.     

Die Isotopieverschiebung von151Eu,152Eu,153Eu,154Eu und die Kernmomente der radioaktiven Isotope152Eu und154Eu

The isotope shift of the stable¹⁵¹Eu,¹⁵³Eu, and the radioactive¹⁵²Eu,¹⁵⁴Eu isotopes and the hyperfine splitting of the¹⁵²Eu isotope was investigated using a digital recording Fabry-Perot-spectrometer. From isotope shift measurements on the line λ 5 765 Å (4f ⁷ 6s 6p z⁶P_7/2-4f ⁷ 6s² a⁸S_7/2) the relative isotope shift was derived:¹⁵¹Eu:0;¹⁵²Eu: 0.923(8);¹⁵³Eu: 1;¹⁵⁴Eu: 1.197(8). The results show that there is a strong increase in the change of the mean square nuclear charge radius δ〈r²〉 when only one neutron is added to the 88 neutrons of the¹⁵¹Eu nucleus, whereas the change of δ〈r²〉 between¹⁵²Eu and¹⁵³Eu is of the same order of magnitude as that between¹⁵³Eu and¹⁵⁴Eu. From the hyperfine splitting of the radioactive isotope¹⁵²Eu in the line δ 6865 Å (4f ⁷ 6s 6p z ¹⁰ P _9/2-4f ⁷ 6s² a⁸S_7/2) the sign of the magnetic dipole moment μ_I(¹⁵²Eu) was found to be negative, and with this result and earlier experimental data the signs of the nuclear quadrupole momentsQ(¹⁵²Eu) andQ (¹⁵⁴Eu) could be determined to be positive.     

Measurements ofE4 matrix elements in152Sm and154Sm

TheE4 transition matrix element from the ground state to the 4⁺ state has been measured in¹⁵²Sm and¹⁵⁴Sm, by comparing relative thick targetγ-ray intensities following Coulomb excitation with 12 MeV⁴He, 24–30 MeV¹⁶O, and 35–40 MeV³²S projectiles. Values for 〈0⁺∥?(E4)∥4⁺〉 of (+0.31 _?0.20 ^+0.12 ) barn in¹⁵²Sm and (+0.50 _?0.12 ^+0.09 ) barn in¹⁵⁴Sm are found.     

Isotope shifts and hyperfine splitting in HfI changes in nuclear charge radii of stable isotopes and182Hf

Isotope shifts and hyperfine structures in three optical transitions of HfI are investigated. Magnetic dipole coupling constant A and electric quadrupole coupling constant B of four atomic levels for both stable odd-even isotopes¹⁷⁷Hf and¹⁷⁹Hf are determined. Nuclear charge radii changesδ〈r ²〉 of the stable Hf isotopes and¹⁸² Hf (T _1/2=9×10⁶ y) are extracted using the standard semiempirical procedure. Strong deviation from muonic atom data onδ〈r ²〉 is observed. The course of theδ〈r ²〉 dependence on mass number indicates changes in nuclear deformation at A=174 and influence of higher order deformations on nuclear shape in this region.     

Isotope shifts in transitions between low-lying levels of Sr I by laser-atomic-beam spectroscopy

High-resolution laser-atomic-beam spectroscopy has been used to determine isotope shifts in five transitions between low-lying states of Sr I. With these results and existing data a parametric analysis of level isotope shifts has been performed. The transition isotope shifts have been separated into field shift and mass shift contributions with a King-plot procedure using model-independent nuclear charge equivalent radiiR _k from muonic x-ray measurements. Values for the mean-square nuclear charge radiiδ〈r ₂ 〉 have been calculated from the field shifts in the optical transitions 5s ^{2 1} S ₀-5s5p ³ P ₁ and 5s5p ³ P ₀-5s6s ³ S ₁ and compared with correspondingδ〈r ² 〉 values evaluated from muonic x-ray data.     

Isomerieverschiebung im Eu151

The isomer shift of the 21.7 keVγ transition in Eu¹⁵¹ has been studied for various divalent and trivalent europium compounds using the Mössbauer technique. Theγ energy is lower by up to 1.1·10^?6 eV in divalent compounds than in trivalent compounds. Using data from atomic spectroscopy it is estimated that the electron density at the nucleus is larger by about 1.9·10²⁶cm^?3 for the configuration 4f ⁶ than for 4f ⁷ due to different shielding of thes ² shells. The difference of the mean square radii of the 21.7 keV state and the ground state is thenδ〈r²〉=+0.03 fm². The measured isomer shift between trivalent and metallic europium and the relatives-electron densities in the rare earth metals measured by the positron annihilation rates are used to establish a calibration scheme for isomer shifts in rare earth metals. This calibration scheme is used to deduce a changeδ〈r ²〉=+0.005₅ fm² between the 26 keV state and the ground state of Dy¹⁶¹.     

Isotope shifts in the atomic spectrum of xenon and nuclear deformation effects

Optical isotope shifts of four lines in the atomic spectrum of xenon have been measured using enriched samples of all stable xenon isotopes. The spectrograms were recorded with the aid of a pressure-scanned Fabry-Pérot interferometer and analysed by digital data techniques. The measured isotope shifts are shown to be self-consistent by means of a King plot. An estimate of the specific mass effect is given and the changesδ 〈r ²〉 of the mean square radius of the nuclear charge distribution are extracted from the measured shifts. These changesδ 〈r ²〉 are discussed in terms of the nuclear deformation parameterβ ². The results for the deformation of the stable even xenon isotopes are shown to be in good agreement with the systematic of deformation found for the neighbouring elements from Coulomb excitation experiments.     

Hyperfine structure and isotope shift of the neutron-rich barium isotopes139–146Ba and148Ba

The hyperfme structure and isotope shift in the 6s ² S _1/2?6p ²P_3/2 line of Ba II (455.4 nm) have been measured by collinear fast-beam laser spectroscopy for the neutron-rich isotopes^139–146Ba and¹⁴⁸Ba. Nuclear moments and mean square charge radii of these isotopes have been recalculated. The isotope shift of the isotope¹⁴⁸Ba (T_1/2=0.64 s) could be studied for the first time, yieldingδ〈r²〉^138,148=1.245(3) fm².     

Isomer shifts and changes of the nuclear charge radii in99Ru and101Ru

The recoilless nuclear gamma resonance of the 127 keV γ-rays of¹⁰¹Ru was observed in ruthenium metal, RuO₂ and [Ru(NH₃)₄(HSO₃)₂]. By comparison of the isomer shifts observed in these materials for the 127 keV absorption line with the corresponding shifts of the 90keV γ-rays of⁹⁹Ru one obtains δ〈r ²〉 [127 keV]/ δ〈r ²〉 [90 keV]=1.78±0.26 for the ratio of the changes of the mean square nuclear charge radii between the first excited and the ground states in these nuclei. An estimate of electron density differences based on free-ion relativistic self-consistent field calculations yields δ〈r ²〉[90keV]≈+1.4·10^?3 for⁹⁹Ru and δ〈r ²〉/〈r ²〉 [127 keV]≈+2.4·10^?3 for the¹⁰¹Ru case. These results are discussed in terms of the core excitation model.     

Isotope shift measurements in the atomic spectrum of lanthanum (LaI)

Using the reactor-produced lanthanum isotope ₅₇ ¹³⁷ La, the highly enriched rare ₅₇ ¹³⁸ La and the stable ₅₇ ¹³⁹ La, the isotope shift has been measured in five lines of the La I-spectrum with the aid of a pressure-scanned Fabry-Pérot interferometer. The isotope shift data obtained show surprisingly large specific mass effects, arising from configuration mixing of levels with a 4f electron involved. The changes in mean square charge radiusδ〈r ²〉 of these nuclei extracted from the experimental isotope shift constants C_exp are compared with the corresponding values for the isotonic barium nuclei, where similar anomalies in the isotope shifts occur.     

Coupled channel analysis of asymmetry measurements for low-lying states of Sm and Sm by inelastic proton scattering

Asymmetries and differential cross sections have been measured for elastic and inelastic scattering of 24.5 MeV polarized protons from the spherical nucleus ¹⁴⁸Sm. The comparison with the results of an asymmetry measurement at the same proton energy on the rotational nucleus ¹⁵²Sm shows significant differences for the first 2⁺ states. A coupled-channels analysis for the first 2⁺ and 3⁻ states in ¹⁴⁸Sm and for the 2⁺ and 4⁺ states of the ground-state rotational band in ¹⁵²Sm fits the experimental data very well.