Predictions of nuclear charge radii

In this study,we improve the relations of the charge-radius difference of two isotopes by considering a term that relates to the proton number and the parity of the neutron number.The correction reduces the root-meansquared deviation to 0.0041 fm for 651 nuclei with a neutron number larger than 20,in comparison with experimental data compiled in the CR2013 database.The improved relations are combined with local relations consisting of the charge radii of four neighboring nuclei.These combination...     

New nuclear charge radii database

Several large relational databases (DBs) containing various atomic nucleus parameters and nuclear reaction features were produced at the Centre for Photonuclear Experiments Data (Centr Dannyh Fotoyadernykh Eksperimentov (CDFE)) of the Skobeltsyn Institute of Nuclear Physics, Moscow State University). The sources are numerical data founds maintained by International Nuclear Data Centers Network of the International Atomic Energy Agency (IAEA) and produced by CDFE. The original CDFE product is the electronic “Chart of Quadrupole Nuclear Deformations” which includes ∼2000 sets of data on nuclei quadrupole moments Q and quadrupole deformation parameters β₂ for ∼1500 nuclei. At last time, in the frame of joint research with the Joint Institute for Nuclear Research (JINR) that electronic Chart was supplemented with the data on nuclear mean-root-square (MRS) charge radii (∼900 isotopes of 90 elements (Z = 1–96, N = 0–152)) and therefore transformed into the “Chart of Nucleus Shape and Size Parameters”—complete collection of data under discussion. New Chart allows one to investigate the isotopic and isotonic behavior of nuclei quadrupole moments, parameters of quadrupole deformation and charge radii, and study the R(Z, N) surface structure and R(A) dependence of the fine structure. Original Russian Text ? I.N. Boboshin, V.V. Varlamov, Yu.P. Gangrsky, B.S. Ishkhanov, S.Yu. Komarov, K.P. Marinova, 2009, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2009, Vol. 73, No. 6, pp. 857–862.     

关于原子核电荷半径的研究

结合原子核电荷半径实验数据, 对885个中子数N≥8和质子数Z≥8的核电荷半径做了系统的研究. 对于单参数核电荷半径公式, Z^1/3律公式计算的结果优于A^1/3律的结果, 而对于两参数和三参数公式, Z^1/3律和A^1/3律的结果基本相当. 考虑到壳效应及奇偶摆动现象, 在原有的三参数公式基础上提出了加入Casten因子项和δ项的核电荷半径新公式. 利用该公式计算得到的核电荷半径理论值和实验值符合得非常好, 均方根偏差仅为σ=0.0266 fm, 此值比常用的三参数公式的结果下降了近50%, 理论计算值能更好地反映出壳效应及核电荷半径奇偶摆动的变化趋势.     

Nuclear charge radii,nuclear moments,and nuclear structure

New and systematic measurements of nuclear charge radii and nuclear moments are providing a deeper insight into properties of nuclei. In this article, the implications of these new measurements on our understanding of collective properties of nuclei are discussed.     

Isotonic and isobaric dependencies of nuclear charge radii for rare-earth nuclei

Isotonic and isobaric dependencies of nuclear charge radii in the region between Z=54 and Z=70 are obtained from the analysis of isotope shift data r² and muonic and electron scattering data on r². They are compared with the predictions of the droplet model and the Hartree-Fock calculations. The isobaric dependencies of r² have proven to be especially sensitive to the choice of an effective nucleon-nucleon interaction.     

Evolution of nuclear charge radii in copper and indium isotopes

Systematic trends in nuclear charge radii are of great interest due to universal shell effects and odd-even staggering (OES). The modified root mean square (rms) charge radius formula, which phenomenologically accounts for the formation of neutron-proton (np) correlations, is here applied for the first time to the study of odd-Z copper and indium isotopes. Theoretical results obtained by the relativistic mean field (RMF) model with NL3, PK1 and NL3^* parameter sets are compared with experimental data. Our results show that both OES and the abrupt changes across begin{document}$ N = 50 $end{document} and 82 shell closures are clearly reproduced in nuclear charge radii. The inverted parabolic-like behaviors of rms charge radii can also be described remarkably well between two neutron magic numbers, namely begin{document}$ N = 28 $end{document} to 50 for copper isotopes and begin{document}$ N = 50 $end{document} to 82 for indium isotopes. This implies that the np-correlations play an indispensable role in quantitatively determining the fine structures of nuclear charge radii along odd-Z isotopic chains. Also, our conclusions have almost no dependence on the effective forces.     

Odd-even staggering in nuclear charge radii of neutron-rich europium isotopes

Nuclear magnetic dipole and electric quadrupole moments and changes in mean square charge radii for the neutron-rich^155–159Eu isotopes have been measured using resonance ionization spectroscopy at the IRIS facility. It has been found that the isotopes withN>92, unlike the isotopes with 89≦N≦92, have an ordinary character of odd-even staggering in nuclear charge radii. This means that the octupole deformation attributed previously to the europium nuclei around¹⁵⁴Eu does not display itself in the charge radii of heavier europium isotopes.     

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.     

An analysis of nuclear charge radii based on the empirical formula

Several nuclear charge radii had been calculated based on the law of A^1/3 and isospin dependence Z^1/3 formula which had been used to describe the charge radii data. It is achieved that the isospin dependence Z^1/3 formula is superior to the generally accepted A^1/3 law through mean root square deviation analysis, that is, the Z^1/3 formula is more effective to describe the charge radii data.     

The odd-even staggering of the nuclear charge radii of Pb isotopes

Previous laser-spectroscopic studies of the hyperfine structure splittings and isotope shifts of the (6p^{2 3}P₀-6p7s ³P₁; 283.3 nm) PbI resonance line have been extended to further radioactive Pb nuclides: ^{196, 197, 197m, 211, 214}Pb Using an improved theoretical result for the specific mass shift, we recalibrate the isotope shifts of the full series (A = 196–214) of measured isotope shifts in terms of the nuclear parameter and determine the odd-even staggering parameters. The variation of the nuclear charge radii of the Pb nuclides exhibits distinct shell effects, and the odd-even staggering shows a conspicuous trend, being more pronounced for neutron-deficient Pb isotopes.     

An analysis of nuclear charge radii based on the empirical formula

Several nuclear charge radii had been calculated based on the law of A1/3 and isospin dependence Z1/3 formula which had been used to describe the charge radii data. It is achieved that the isospin dependence Z1/3 formula is superior to the generally accepted A1/3 law through mean root square deviation analysis, that is, the Z1/3 formula is more effective to describe the charge radii data.     

Optimal channels of the Garvey-Kelson mass relations in extrapolation

Garvey-Kelson mass relations connect nuclear masses of neighboring nuclei within high accuracy, and provide us with convenient tools in predicting unknown masses by extrapolations from existent experimental data. In this paper we investigate optimalchannels of the Garvey-Kelson relations in extrapolation to the unknown regions, and tabulate our predicted masses by using these optimized channels of the Garvey-Kelson relations.     

Quark model relation for kaon charge radii

We derive the equation r_E²(K⁰)/r_E²(K⁺) = m_s² − m_n²))/(2m_s² + m_n²) relating the kaon electric charge radii and the strange (m_s) and non-strange (m_n) quark masses in the nonrelativistic quark model, and suggest an inequality which we expect to hold in the presence of relativistic corrections. New data for these charge radii are presently being analysed by two experimental groups.     

Quark model relation for kaon charge radii

We derive the equation r²_E(K⁰)/r²_E(K⁺) = -(m²_s ? m²_n)/(2m²_s + m²_n) relating the kaon electric charge radii and the strange (m_s) and non-strange (m_n) quark masses in the nonrelativistic quark model, and suggest an inequality which we expect to hold in the presence of relativistic corrections. New data for these charge radii are presently being analysed by two experimental groups.     

Systematics of nuclear charge radii of the stable molybdenum isotopes from muonic atoms

The results of precise measurements of the energies of the $\text{2}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{?1}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{and}\text{2}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{?1}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ muonic X-ray transitions of ⁹²Mo, ⁹⁴Mo, ⁹⁵Mo, ⁹⁶Mo, ⁹⁷Mo, ⁹⁸Mo and ¹⁰⁰Mo are reported. The data were analyzed in terms of the Barrett moments 〈r^ke^?αr〉 of the nuclear charge distributions from which the equivalent nuclear radii R_k and the differences ΔR_k between neighboring isotopes were computed. Systematic shell effects have been observed at the neutron numbers N = 50 and N = 56.     

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 r² deduced from our studies in 5806.05 Å (f¹² s²-f¹² sp) transition is in excellent agreement with muonic X-ray value. With negligible specific mass shift (SMS) in 5806.05 Å 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.     

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.