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.     

Nuclear compressibility and its effect on nuclear binding energies from the study of muonic atoms

The variation of nuclear parameter with mass number elicits information about nuclear compressibility. Analysis of muonic x-ray transitions provides an elegant method to investigate the behaviour of the nuclear parameterr ₀. It is observed from the behaviour ofr ₀ that nuclei in the regionA⩽70 are highly compressible while those in the regionA∼210 are almost incompressible. The behaviour ofr ₀ is incorporated into the semi-empirical mass formula through the Coulomb energy term. From the modified mass formula thus obtained binding energies of about 440 spherical nuclei have been calculated. The results suggest that nuclear compressibility imposes certain relationship between excess binding energies (E _exp−E _cal) and neutron. proton number. The present study also points out that shell effects exhibited by nuclear binding energies cannot be accounted for by simply varying the coefficients of the mass formula: on the other hand extra terms are necessary to explain them.     

Effects of nuclear polarizability on isotope shifts in electronic atoms

The isotope shift in electronic atoms is calculated in second order perturbation theory. We consider multipole ordersλ=0, 1 and 2 forZ=20–82 nuclei. To a good approximation it is directly proportional to the electron density at the nucleus. We study whether the polarization effect modifies the extraction ofδ〈r ²〉 values from isotope shifts measurements and find it to be small but not always negligible. Relative to the volume effect, the polarizability is of the same order of magnitude for electronic as well as muonic atoms.     

Pushing the limits of nuclear stability

Reaching the limits of nuclear stability offers unique opportunities to understand basic nuclear properties. New shell structures close to the driplines can change the existence of neutron-rich nuclei. A new search for ¹⁶Be confirmed the previous limit for particle stable Be isotopes at A=14. Single proton knock-out reactions offer the potential for more sensitive searches of very weakly bound nuclei. In order to extend the knowledge of the neutron dripline beyond Z=8 requires new accelerator developments. The proposed new rare isotope accelerator has the potential to push the limit of the neutron dripline to at least Z=25.     

Rearrangements in neutron shell closures far from stability

A survey of experimental results obtained at GANIL (Caen, Prance) on the study of the properties of very neutron-rich nuclei (Z = 6–20, A = 20–60) near the neutron drip line and resulting in an appearance of further evidence for the new magic number N = 16 is presented. Very recent data on mass measurements of neutron-rich nuclei at GANIL and some characteristics of binding energies in this region are discussed. Nuclear binding energies are very sensitive to the existence of nuclear shells and together with the measurements of instability of doubly magic nuclei ¹⁰He and ²⁸0 they provide information on changes in neutron shell closures of very neutron-rich isotopes. The behaviour of the two-neutron separation energies S_2n derived from mass measurements gives a very clear evidence for the existence of the new shell closure N = 16 for Z = 9 and 10 appearing between 2s_1/2 and ld_3/2 orbitals. This fact, strongly supported by the instability of C, N and O isotopes with N > 16, confirms the magic character of N = 16 for the region from carbon up to neon while the shell closure at N = 20 tends to disappear for Z ≤ 13. Decay studies of these hardly accessible short-lived neutron-rich nuclei from oxygen to silicon using the in-beam γ-ray spectroscopy are also reported.     

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.     

Some characteristics of nuclear densities

We propose a simple expression for nuclear densities, which brings out the following important nuclear properties: (i) shell effects in proton and neutron central densities, (ii) approximate global constancy of neutron central densities, (iii) approximate constancy ofRN ^?1/3 and R_pZ^?1/3 whereR is the nuclear half-density radius andR _p is the rms radius of the proton density, (iv) larger surface thickness and rms radius for neutron density as compared to those for proton density.     

Relation of contact densities with Mössbauer isomer shifts for 35.46 keV M1 transition of125Te

The internal conversion electron and Mössbauer isomer shifts associated with the 35.46 keV M1 transition of¹²⁵Te were observed for different metal samples into which radioactive¹²⁵I as probe atoms were introduced by means of ion-implantation. From the correlation between the Mössbauer isomer shifts and intensity ratios of O shell to N_I shell conversion electrons, a relation between 5s-electron contact densityp _5s(0) in a.u. and isomer shift δ in mm/s was deduced to bep _5s(0)=106+30.3 δ±4.3[(δ?0.30)²+0.069]^1/2, where δ was measured relative to ZnTe in mm/s. The change of the nuclear charge radius in the 35.46 keV M1 transition of¹²⁵Te was found to be ΔR/R=(0.85±0.12)×10^?4 (corresponding to Δ<r ²>=(3.7±0.5)×10^?3 fm²) when a theoretical 4s-electron contact density of 928 a.u. was used.     

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.     

Binding energies and radii of α-cluster-type nuclei from calculations based on the strictly restricted dynamics model

The properties of α-cluster-type nuclei with 4≤A≤80 are studied by employing the microscopic strictly restricted dynamics model (SRDM). The SRDM parameter set found via a fit to the experimental and theoretical values of nuclear binding and excited-level energies, classified according to the ground-state SU ₃ configurations, includes a nuclear-radius parameter r ₀ entering into the expression R=r ₀ A ^1/3 [fm], as well as the parameters of the effective central NN-interaction potential. The use of the microscopic SRDM allows one to obtain additional information about nuclei along the Z=N line, including binding energies, radii, and spectra of low-lying levels. The calculated nuclear binding energies and nuclear root-mean-square radii 〈r ²〉^1/2 are in reasonable agreement with their experimental counterparts.     

Isotope shift studies in the spectrum of boron monosulphide

The spectrum of boron monosulphide has been excited in microwave discharge and photographed at moderate dispersion. TheC ²Π _r ?X ²Σ⁺,B ²Σ⁺?A ²Π _i andA ²Π _i ?X ²Σ⁺ band systems extending from 2100–9000 Å have been obtained for B³²S and B³⁴S species. Isotope shifts for all these band systems have been measured. Comparison of the observed isotope shifts with the theoretically calculated isotope shifts confirms the emitter as well as the vibrational assignments of all these band systems.     

Electric monopole transitions from low energy excitations in nuclei

Electric monopole (E0) properties are studied across the entire nuclear mass surface. Besides an introductory discussion of various model results (shell model, geometric vibrational and rotational models, algebraic models), we point out that many of the largest E0 transition strengths, ϱ²(E0), are associated with shape mixing. We discuss in detail the manifestation of E0 transitions and present extensive data for single-closed shell nuclei, vibrational nuclei, well-deformed nuclei, nuclei that exhibit sudden ground-state changes, and nuclei that exhibit shape coexistence and intruder states. We also pay attention to light nuclei, odd-A nuclei, and illustrate a suggested relation between ϱ²(E0) and isotopic shifts.     

Nuclear moments and optical isotope shifts of108m Ag and110m Ag

The hyperfine structure of the resonance lines of^108m Ag and^110m Ag has been investigated by means of optical interference spectroscopy. The metastable isotopes were produced by neutron irradiation in a reactor. From the measureda- andb-values we derive the value for the nuclear magnetic dipole moment of^108mAgμ _I (108m)=3.577 (20)μ _n and the values for the electric quadrupole momentsQ _I (108m)=1.52(8) bQ _I (110m)=1.65(10) b (without Sternheimer correction). The measured isotope shifts allow the determination of the changes in the mean square charge radii of the nuclei involved:δ 〈r ²〉(108m-107)=0.022(3)fm² δ 〈r ²〉(110m-109)=0.029(2)fm². The isotope positions show odd-even staggering comparable with those of neighbouring isotonic nuclides.     

Isotope shift measurements and charge radii of152–158Yb

Isotope shifts have been measured for the neutron deficient even Yb isotopes up to the neutron shell closure at N=82. The isotope shifts were measured using the 556-nm atomic resonance transition from the¹ S ₀ ground state to the³ P ₁ level. The heavier isotopes of Yb have been investigated by Buchinger et al./1/. The change in (r ²) observed for Yb isotopes with N=82–90 has considerably different behavior than for the lighter rare earths.     

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.     

The formation of,and the γ-radiation from,the p-shell hypernuclei

The physical factors relevant for the production of various low-lying Λ-hypernuclear states ${}_{\mathrm{\Lambda }}{}^{\mathrm{A}}\text{Z}{}^1$ through the K^? → π^? and K^? → π⁰ reactions, in flight or from rest, on the corresponding target nuclei ^AZ and ^A(Z + 1) are discussed, on the basis of the shell model for these nuclei and hypernuclei, together with the characteristics of the dominant γ-transitions resulting from the excited states thus produced. Detailed consideration is given for a number of hypernuclei of specific interest, including the cases of _Λ⁷He, _ΛLi for A = 7, 9 and 10, _ΛBe for A = 9 and 10, _ΛB for A = 10, 11, and 12, _ΛC for A = 12, 13, 14, and 15, _ΛN for A = 14 and 15, and _Λ¹⁶O. The importance of (γ, π^?) correlation studies for the determination of hypernuclear spin values is stressed, with the discussion of several examples.     

Die Kernradiusänderung beim Einbau eines Protons

The change of therms radius of the nuclear charge distribution on addition of one proton is derived for 25 nuclides between ₁₉ ³⁹ K and ₈₂ ²⁰⁸ Pb. For this purpose, results of the muonic 2p-1s transition energies are used together with the optical isotope shifts. The uncertainties of the procedure are discussed. Corresponding results from elastic electron scattering are included for three pairs of nuclides. — For heavy nuclei, the average increase in radius per proton exceeds considerably that per neutron, as expected. Although the individual values are associated with rather large errors, shell effects seem to be noticeable atZ=28 andZ=50.     

Die Coulomb-Energien leichter Atomkerne

A compilation of the known data on Coulomb energy differences of isobaric doublets and isobaric triplets is given. Plots of the Coulomb energy differences versus¯Z/A ^1/3 with¯Z=(Z ₁+Z ₂)/2 show an analogous shell structure behaviour for the three series with 2¯Z=A?1,A andA+1 (T=1, 1/2 and 1), i.e. discontinuities at the closed shells atA=4, 16 and 40 and the closed subshell atA=32 and oscillations mainly being due to Coulomb proton-proton pairing energy. A positive energy shift of the lowest states withT=1 of all self-conjugate nuclei withA=4n+2 seems to be indicated by the experimental data. A semi-empirical formula is given that describes the data.     

Crystal field in the CeAl3 heavy-fermion compound

An analysis of inelastic neutron scattering in the CeAl₃ heavy fermion compound is presented. Using single-crystal magnetic-susceptibility and inelastic neutron scattering data, an unambiguous solution for the set of parameters of the electric crystal field Hamiltonian is obtained: B ₂ ⁰ = (5.8 ± 0.2) × 10^?2 meV and B ₄ ⁰ = (2.3 ± 0.1) × 10^?2 meV. The energy level scheme for the ground-state multiplet of the Ce³⁺ ion in CeAl₃ consists of the ground level Γ₉?±3/2〉 and two doublets Γ₈?±5/2〉 and Γ₇?±1/2〉 having close energies of ～6.3 meV at a temperature of 20 K. As follows from comparing the crystal-field parameters in the RAl₃ series (R = Ce, Pr, Nd), the fact that the parameters A ₂ ⁰ 〈r ²〉 and A ₄ ⁰ 〈r ⁴〉 in CeAl₃ differ significantly in value from the respective parameters in PrAl₃ and NdAl₃ cannot be explained in terms of the lattice constants of these isostructural compounds being different but rather is due to the enhanced hybridization of the localized 4f electrons of cerium with conduction electrons.     

Nuclear compression modulus and isotope shifts of Pb nuclei

Isotope shifts of Pb nuclei are studied by taking into account giant monopole and quadrupole resonance by a perturbative method. Giant monopole states are calculated by the HF + RPA response function method using three parameter sets of the Skyrme interactions SGI, SGII and SIII which give the compression moduli K_∞ = 269 MeV, 217 MeV and 356 MeV, respectively. Our calculations reproduce the kink of the observed isotope shifts at ²⁰⁸Pb, while the second-order effect due to the giant quadrupole resonances is not enough to explain the observed odd-even staggering. The Skyrme force SGII having K_∞ = 217 MeV shows the best quantitative agreement among three forces in comparison with the experimental data of the isotope shifts of Pb nuclei. The effect of the effective mass is also discussed.