Total dielectronic recombination rate coefficient for Ar-like tungsten

Ab initio calculations of the total dielectronic recombination (DR) rate coefficient for Ar-like tungsten $\left({\mathrm{W}}^{56+}\right)$ are performed using the relativistic HULLAC code package based on the parametric potential method. The high efficiency of HULLAC compared to other codes enables us to perform extensive DR calculations for highly complex atomic systems such as Ar-like tungsten. The present work provides a general procedure for computing the DR rate coefficients for multielectron high-$Z$ ions. This procedure is applicable to DR computations for other Ar-like ions, as well as for ions in neighboring isoelectronic sequences. In the present work level-by-level calculations are performed for evaluating the contributions to DR through all the relevant K-like autoionizing inner-shell excited configuration complexes: ${3p}^5{4ln}^{\prime }{l}^{\prime }$ $(4\mathrm{}<~n^{\prime }<~17),$ ${3s3p}^6{4ln}^{\prime }{l}^{\prime }$ $(4\mathrm{}<~n^{\prime }<~12),$ ${3p}^5{3dn}^{\prime }{l}^{\prime }$ $(8\mathrm{}<~n^{\prime }<~18),$ ${3s3p}^6{3dn}^{\prime }{l}^{\prime }$ $(7\mathrm{}<~n^{\prime }<~18),$ ${2p}^5{3s}^2{3p}^6{3dn}^{\prime }{l}^{\prime }$ $(3\mathrm{}<~n^{\prime }<~8),$ ${2s2p}^6{3s}^2{3p}^6{3dn}^{\prime }{l}^{\prime }$ $(3\mathrm{}<~n^{\prime }<~5),$ and ${3p}^5{5l5l}^{\prime }.$ In addition, extrapolation methods are developed to calculate the contributions of even higher $n^{\prime }$ complexes along each complex series. In the case of ${3p}^5{3dn}^{\prime }{l}^{\prime },$ the usual complex-by-complex extrapolation method based on the $n^{\prime -3}$ scaling law is found to be inaccurate; thus, a more detailed level-by-level procedure is discussed. All calculations are carried out assuming no electron collisions occur after the initial electron capture. Although the dominant DR contributions come from ${3p}^5{4ln}^{\prime }{l}^{\prime }$ and ${3p}^5{3dn}^{\prime }{l}^{\prime },$ the contributions of the other complex series cannot be neglected. A comparison between the present results and the Burgess-Merts (BM) approximation shows that at low electron temperatures the BM approximation greatly underestimates the DR rate coefficients, whereas at high electron temperatures this approximation is fairly good.