  The unified method for total electron-ion recombination is extended to study
the dielectronic satellite (DES) lines. These lines, formed from radiative
decay of autoionizing states, are highly sensitive temperature diagnostics of
astrophysical and laboratory plasma sources. The computation of the unified
recombination rates is based on the relativistic Breit-Pauli R-matrix method
and close coupling approximation. Extending the theoretical formulation
developed earlier we present recombination rate coefficients for the 22
satellite lines of KLL complexes of helium-like Fe XXV and Ni XXVII. The
isolated resonance approximation, commonly used throughout plasma modeling,
treats these resonances essentially as bound features except for dielectronic
capture into, and autoionization out of, these levels. A line profile or cross
section shape is often assumed. On the other hand, by including the coupling
between the autoionizing and continuum channels, the unified method gives the
intrinsic spectrum of DES lines which includes not only the energies and
strengths, but also the natural line or cross section shapes. A formulation is
presented to derive autoionization rates from unified resonance strengths and
enable correspondence with the isolated resonance approximation. While the
rates compare very well with existing rates for the strong lines to <20%, the
differences for weaker DES lines are larger. We also illustrate the application
of the present results to the analysis of K ALPHA complexes observed in
high-temperature X-ray emission spectra of Fe XXV and Ni XXVII. There are
considerable differences with previous results in the total KLL intensity for
Fe XXV at temperatures below the temperature of maximum abundance in coronal
equilibrium. (Abbreviated Abstract)
