PHYSICAL REVIEW C 87, 024310 (2013) Nuclear charge radii of heavy and superheavy nuclei from the experimental α-decay energies and half-lives Dongdong Ni, 1,* Zhongzhou Ren, 1,2,3,† Tiekuang Dong, 4 and Yibin Qian 1 1 Department of Physics, Nanjing University, Nanjing 210093, China 2 Center of Theoretical Nuclear Physics, National Laboratory of Heavy-Ion Accelerator, Lanzhou 730000, China 3 Kavli Institute for Theoretical Physics China, Beijing 100190, China 4 Purple Mountain Observatory, Chinese Academy of Science, Nanjing 210008, China (Received 10 December 2012; revised manuscript received 18 January 2013; published 13 February 2013) The radius of a nucleus is one of the important quantities in nuclear physics. Although there are many researches on ground-state properties of superheavy nuclei, researches on charge radii of superheavy nuclei are rare. In this article, nuclear root-mean-square (rms) charge radii of heavy and superheavy nuclei are extracted from the experimental α-decay data. α-decay calculations are performed within the generalized density-dependent cluster model, where α-decay half-lives are evaluated using quasibound state wave functions. The charge distribution of daughter nuclei is determined in the double-folding model to reproduce the experimental α-decay half-lives. The rms charge radius is then calculated using the resulting charge distribution. In addition, a simple formula is also proposed to calculate nuclear charge radii with the experimental α-decay energies and half-lives. The formula is directly derived from the Wentzel-Kramers-Brillouin barrier penetration probability with some approximations. The two different methods show good agreement with the experimental data for even-even nuclei, and the deduced results are consistent with other theoretical models. Moreover, nuclear radii of heavy and superheavy nuclei with Z = 98–116 are extracted from the α-decay data, for which α decay is a unique tool to probe nuclear sizes at present. This is the first result on nuclear charge radii of superheavy nuclei based on the experimental α-decay data. DOI: 10.1103/PhysRevC.87.024310 PACS number(s): 21.60.Gx, 23.60.+e, 21.10.Ft, 21.10.Tg I. INTRODUCTION One of the fundamental properties of a nucleus is its size (i.e., the radius of the nucleus). At an early stage in the study of nuclear structure, evidences on the size of the nucleus and the matter distribution in it were obtained from α-decay half-lives and scattering cross sections of α particles on light nuclei [1]. Until the 1950s, electron scattering on nuclei had been used to probe nuclear charge and/or matter distributions [2,3]. Subsequently, other particles (p, π ± , μ, ...) scattering on nuclei with appropriate energy were also employed to probe nuclear density distributions. The deduced nuclear charge distributions confirmed the conclusion obtained from α-particle scattering and α decay; that is, nuclei are characterized by an approximately constant density within a volume that increases roughly in proportion to the mass number [1]. Although electron scattering was proved as one of the most appropriate methods for investigating nuclear densities of stable nuclei [4,5], it is hard to use it to obtain charge radii of superheavy nuclei because these nuclei are produced by experiments and exhibit short lifetimes so that they are not available as target nuclei. In the following years, it is difficult to obtain information on nuclear densities and sizes for them by electron scattering. In this case, it is desired to pave a new way for researches of nuclear sizes. Theoretically, one of the pioneering works in early nuclear physics is the quantum mechanical explanation of α decay as a tunneling effect [6]. In this explanation, it was assumed * dongdongnick@gmail.com † zren@nju.edu.cn that the α particle moves in a potential well. The half-life was sensitive to the range R of the potential rather than the depth V 0 . The yielded R values from α-decay half-lives were within about 10% of each other. At that time this proved the existence of nuclear radii and implied that R was the nuclear radius [7,8]. But such rough evaluations could not be regarded to give a precise value of nuclear radii. Along with the development of nuclear physics, α-decay data have accumulated with improved accuracy and α-decay calculations have made considerable progress due to the wide and deep impact of α decay on nuclear physics. Very impressively, the superheavy elements up to Z = 118 have been successfully synthesized by fusion-evaporation reactions and identified by observation of α-decay chains in laboratories [9–13]. The available α-decay models can be divided into three groups, namely, the phenomenological analysis of α-decay half-lives, the Wentzel-Kramers-Brillouin (WKB) barrier penetration probability, and the quasibound solution to Schr¨ odinger equa- tions. The first group is famous for its simplicity such as the Geiger-Nuttall law [14], the Viola-Seaborg formula [15], and some new laws for α decay and cluster radioactivity [16–18]. The second group is easy to see the physical meanings [19], where various α-nucleus potentials have been used such as the double-folding potential [20–24], the Woods-Saxon shape potential [25], the proximity potential [26], and the fissionlike theory [27]. The third group is consistent with the quantum nature of α decay [28–30]. The generalized density- dependent cluster model (GDDCM) belongs to this category and reproduces the experimental α-decay half-lives within a factor of two [28]. Moreover, the α-decay process is also well described in the collective coordinates where the cluster 024310-1 0556-2813/2013/87(2)/024310(9) ©2013 American Physical Society