PHYSICAL REVIEW A 88, 062507 (2013) Electron-correlation trends in the hyperfine A and B constants of the Na isoelectronic sequence Narendra Nath Dutta and Sonjoy Majumder Department of Physics and Meteorology, Indian Institute of Technology-Kharagpur, Kharagpur-721302, India (Received 6 June 2013; published 10 December 2013) In this paper, we have described electron-correlation trends in the calculations of the hyperfine A and B constants for a few elements belonging to the Na isoelectronic sequence. The hyperfine A and B/Q values of the ground state 3s 2 S 1/2 and the excited states 3p 2 P 1/2 ,3p 2 P 3/2 ,3d 2 D 3/2 , and 3d 2 D 5/2 of the ions from Si 3+ to V 12+ are presented. The influence of the Breit interaction in the unretarded approximation to these hyperfine values is reported briefly. With increasing atomic number of this sequence, the variations of the different correlation contributing terms such as core correlations, core polarizations, and pair correlations are discussed in the framework of the relativistic coupled-cluster theory. The electron-correlation effect relative to the Dirac-Fock value in the hyperfine A constants of the 3d 2 D 3/2,5/2 states follows unusual trends with increasing ionization. The relative pair-correlation effect influences the hyperfine constants of the fine-structure states of a term in an identical way at each species of this sequence. The presented relativistic coupled-cluster results are found to agree excellently with the other available results for a few ions. DOI: 10.1103/PhysRevA.88.062507 PACS number(s): 31.30.Gs, 31.15.V−, 31.15.bw I. INTRODUCTION Elements belonging to the isoelectronic sequences of lighter and heavier atoms are being considered as ideal species to investigate the electron-correlation trends with increasing ionization in different atomic properties [1–9]. In particular, research on the isoelectronic sequences of alkali-metal atoms is a subject of considerable interest to observe the correlation ef- fects on the hyperfine properties in various levels of ionization [3–6]. In the calculations of the hyperfine fields or hyperfine constants, it was noticed earlier that the electron correlation relative to the single-particle approximation decreases rapidly for the first few elements with increasing atomic number (Z) in an isoelectronic sequence [2–6]. The linked-cluster many-body perturbation theory was applied in relativistic (RLCMBPT) and nonrelativistic (LCMBPT) forms to analyze these correlation effects in some Li-like [3,6] and K-like systems [4]. In their work, they gave detailed descriptions of the different correlation mechanisms such as exchange core polarization and other many-body effects with respect to the single-particle approximation in the hyperfine properties of these systems [3,4,6]. Calculations on the ground-state hyper- fine constants of a few Li-like species were also performed by the relativistic many-body perturbation theory (RMBPT) [5]. This work included the estimations of Dirac-Fock contribution, complete polarization, and first- and higher-order correlations to these constants [5]. The hyperfine calculations associated with the LCMBPT, RLCMBPT, and RMBPT were carried out mainly on the ground states of the species considered there [3–6]. There are some calculations on a few excited states of Li-like F 6+ only [6]. However, the correlations in the hyperfine calculations of the excited states of the elements that are isoelectronic to alkali-metal atoms are very interesting. In particular, the A constants of 2 D 5/2 states of such singly ionized ions are abnormally correlated, as observed in some earlier calculations [10,11]. For the alkali-metal-like singly ionized ions, it was demonstrated earlier by Mani et al. and Sahoo et al. that the relativistic coupled-cluster (RCC) theory has the potential to exhaust even such an abnormal correlation in the most accurate way [10,11]. This theory has been used successfully to analyze the correlation contributions to the hyperfine A constants of a few low-lying states of these ions [10–12]. The correlations arising from the different coupled-cluster terms were discussed there extensively [10–12]. But, to the best of our knowledge, using the coupled-cluster theory, there are no discussions on the correlation trends for a series of species which are isoelectronic to an alkali-metal atom. In the work of Mani et al., the discussions were aimed at the hyperfine A constants only [10]. Also, with 2 S 1/2 states as the ground states of Li-like and K-like systems, there was no scope in the LCMBPT, RLCMBPT, and RMBPT calculations to understand the correlation trends in the hyperfine B constants, as their values are zero there [13]. The work of Sahoo et al. presented the exhaustiveness of the electron correlations in the hyperfine B constants of 2 D 5/2 states using the RCC theory through several singly ionized alkali-metal-like ions [11]. In this work, more than 150% correlation contribution is observed for the B constant of the Na-like 25 Mg + [11]. However, no work has been done yet on the isoelectronic trend in the B constants to the best of our knowledge. The stripped ions of the Na isoelectronic sequence are very important elements in various astronomical bodies. The ultraviolet emission lines of these ions from the solar atmosphere, transition regions, and coronae of active stars have been identified using advanced high-resolution spectroscopy [14–16]. With the availability of wavelengths [17] and oscilla- tor strengths [18] from the literature, the analysis of these high-resolution spectra requires the inclusion of hyperfine splitting for proper modeling of line profiles [19]. Hence, one can get a more accurate picture of abundance analysis [19,20]. Therefore, it is necessary to provide more hyperfine data in the literature for such ions. Hyperfine data for stripped ions can be considered as an excellent benchmark comparison between experiment and theory [3,6,21]. Also, these data may be used for nuclear quadrupole moment estimations using experimental techniques such as laser spectroscopy [22]. In the present work, we use RCC theory in a nonlinear form [12,23,24] to study the correlation trends in the hyperfine A and B constants of a few elements of the sodium isoelectronic 062507-1 1050-2947/2013/88(6)/062507(9) ©2013 American Physical Society