Table of experimental nuclear ground state charge radii: An update

https://doi.org/10.1016/j.adt.2011.12.006Get rights and content

Abstract

The present table contains experimental root-mean-square (rms) nuclear charge radii R obtained by combined analysis of two types of experimental data: (i) radii changes determined from optical and, to a lesser extent, Kα X-ray isotope shifts and (ii) absolute radii measured by muonic spectra and electronic scattering experiments. The table combines the results of two working groups, using respectively two different methods of evaluation, published in ADNDT earlier. It presents an updated set of rms charge radii for 909 isotopes of 92 elements from 1H to 96Cm together, when available, with the radii changes from optical isotope shifts. Compared with the last published tables of R-values from 2004 (799 ground states), many new data are added due to progress recently achieved by laser spectroscopy up to early 2011. The radii changes in isotopic chains for He, Li, Be, Ne, Sc, Mn, Y, Nb, Bi have been first obtained in the last years and several isotopic sequences have been recently extended to regions far off stability, (e.g., Ar, Mo, Sn, Te, Pb, Po).

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 (e) 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” rkeαr, nevertheless the results are quoted also in terms of r2 [3], [4]. Optical and Kα 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 δr2. The KαX 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 μ atoms and electron scattering e, 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 R-tabulation, the paper [7] does not give numerical values of R’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 — R and δr2. 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 Z and N 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 R2(A)=R2(A)+δr2AA links the data on rms radii R(R=r21/2) of a stable reference isotope A with the radius change δr2AA=r2Ar2A between A and a radioactive isotope A, giving the R(A) value of any isotope A in a long isotopic sequence. The extraction of R according to this simple equation meets with serious statistical and computational problems in cases where there exist data on R(A) for many isotopes and

Radii changes from optical isotope shift

In the algorithms of Refs. [12], [13], the sources of data on nuclear parameters λ and δr2 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 δr2. 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 δr2 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 N and proton number Z 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.

References (50)

  • H. de Vries et al.

    At. Data Nucl. Data Tables

    (1987)
  • E.G. Nadjakov et al.

    At. Data Nucl. Data Tables

    (1994)
  • I. Angeli

    At. Data Nucl. Data Tables

    (2004)
  • J. Libert et al.

    Nuclear Phys. A

    (2007)
  • P. Aufmuth et al.

    At. Data Nucl. Data Tables

    (1987)
  • F. Boehm et al.

    At. Data Nucl. Data Tables

    (1974)
  • G.G. Simon et al.

    Nuclear Phys. A

    (1980)
  • I. Sick

    Phys. Lett. B

    (2003)
  • D. Borisyuk

    Nuclear Phys. A

    (2010)
  • M.O. Distler et al.

    Phys. Lett. B

    (2011)
  • A. De Rujula

    Phys. Lett. B

    (2011)
  • U.D. Jentschura

    Ann. Phys.

    (2011)
  • U.D. Jentschura

    Ann. Phys.

    (2011)
  • O. Sorlin et al.

    Prog. Part. Nucl. Phys.

    (2008)
  • R. Hofstadter et al.

    Phys. Rev.

    (1953)
  • R. Engfer et al.

    At. Data Nucl. Data Tables

    (1974)
  • G. Friecke et al.

    At. Data Nucl. Data Tables

    (1995)
  • E.W. Otten
  • H.-J. Kluge

    Hyperfine Interact.

    (2010)
  • I. Angeli et al.

    J. Phys. G

    (2009)
  • I. Angeli, Recommended values of nuclear charge radii, 2008,...
  • Yu. Gangrsky, K. Marinova, Nuclear charge radii, 2008....
  • Database of the Lomonosov Moscow State University, Skobeltsyn Institute of Nuclear Physics....
  • I. Angeli, K. Marinova, Nuclear charge radii–2010, A newsletter of the Nuclear Data Section (NDS) Issue No. 50, 2010, 3...
  • G. Fricke et al.
  • Cited by (0)

    View full text