Table of experimental nuclear ground state charge radii: An update
Introduction
The nuclear charge radius is one of the most obvious and important nuclear parameters that give information about the nuclear shell model and the influence of effective interactions on nuclear structure. Experimental information on root-mean-square (rms) nuclear charge radii can be derived from different sources and has been published several times. The results from electron scattering () experiments are expressed in terms of the rms radius, and, for some nuclei, in parameters of the Fermi-distribution [1], [2]. Muonic X-ray energies are another source of information. These probe somewhat different moments of nuclear distribution, the so called “Barrett moments” , nevertheless the results are quoted also in terms of [3], [4]. Optical and X-ray isotope shifts are sensitive to the same nuclear parameters and provide an important source of complementary information on mean square (ms) radii changes . The X results are easier to interpret; however, these measurements can be performed only on stable isotopes since the experimental method requires several tens of milligrams of target. The same refers to experiments with atoms and electron scattering , while optical isotope shifts (OIS) can be measured with negligible quantities of radioactive atoms, inclusive single ones, with lifetimes down to 1 ms, and thus give access to long chains of radioactive isotopes extending far off stability [5], [6].
The four electromagnetic methods are sensitive to different properties of the nuclear ground-state charge distributions. For this reason, a combination of data from different experimental methods generally yields more detailed and accurate knowledge of the nuclear radii than is available from any single method alone.
Many new data on isotope shift measurements have been published in recent years; therefore, it is again the right moment to see another summary of facts and trends in the field. This is already done in the recent paper [7], which presents and discusses not only the isotopic trend of nuclear charge radii but also a full systematic of isotonic shifts extracted from the wealth of data. Special attention is paid to the structural evolution along the isotonic and isotopic chains around the “traditional” magic numbers 8, 20, 28, 50, 82 and 126 and to the appearance of new non-traditional magic numbers especially in the region of light nuclei. However, discussing the consequences of the -tabulation, the paper [7] does not give numerical values of ’s. The latter, together with short explanations, are accessible online in the database of the Lomonosov Moscow State University, Skobeltsyn Institute of Nuclear Physics and are presented as three different data sets (see Refs. [8], [9], [10]). A modified and updated version can be found in the site Data Library of NDS IAEA [11] as a single data set.
The purpose of this paper is to present in a compact form the numerical values of the experimental rms charge radii obtained by a combined treatment of the experimental data of both types — and . The results of two different methods of data evaluation [12], [13] are combined into a single data set (Table 1). This is for the benefit of data users, who generally prefer a single, unified data set to several separate tables. Also a few new data are added, due to the last achievements of laser spectroscopy (see references to Table 2). Therefore, the resulting tabulation of radii covers a broader range of and than most recently published tables [10], [11]: it contains 909 isotopes for 92 elements.
Section snippets
Evaluation procedures
The principle of a combined treatment is obvious: a simple relation links the data on rms radii of a stable reference isotope with the radius change between and a radioactive isotope , giving the value of any isotope in a long isotopic sequence. The extraction of according to this simple equation meets with serious statistical and computational problems in cases where there exist data on for many isotopes and
Radii changes from optical isotope shift
In the algorithms of Refs. [12], [13], the sources of data on nuclear parameters and published before 1989 are the compilations Refs. [5], [18]. Only a limited number of original papers after 1989 are used in Ref. [12], while the tables of Ref. [13] take into account a large amount of more recent results. The reference list to Table 2 of this work presents the updated data sources on . About 25% of the OIS data are published or found since the previous tables from 2004 covering 799
Global behaviour of rms nuclear charge radii
Transforming into absolute rms radii values, one receives a global overlook on the charge radii trend in an extended region of nuclei from He to Cm. The accuracy of the combined data is high compared to that of the directly measured radii values for the same element.
The dependences of the rms nuclear radii on neutron number and proton number are demonstrated in Fig. 2, Fig. 3, Fig. 4. Adding new data to that of Ref. [10] does not influence the global features of the isotopic (Fig. 2,
Acknowledgments
The authors are grateful to W. Nörtershäuser for providing data on Li charge radii before its publishing. Thanks are due to Yu. Gangrsky for the helpful suggestions.
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