Relativistic calculation of dielectronic recombination on theC4+ground state

Abstract

The measurement of the dielectronic recombination (DR) cross section of ${\mathrm{C}}^{4+}$ with a high resolution [S. Mannervik et al., Phys. Rev. A 55, 1810 (1997)] provides a rigorous test case for various theoretical methods. In the earlier work, the relativistic multichannel theory was applied to the DR process on the ${\mathrm{He}}^{+}$ ion for both the $\ensuremath{\Delta}N=1$ and $\ensuremath{\Delta}N=2$ transitions with a principal quantum number of the outermost electron up to 5. In principle, that method can be applied to resonances with any high principal quantum numbers. Practically, however, the calculations become very time consuming. In the present work, the method is extended by incorporating the Bell-Seaton theory. The DR cross sections of ${\mathrm{C}}^{4+}$ for the resonances with $2<~n<~25$ are calculated. The results are in good agreement with those of the experiment except for the $n=6$ and $7$ resonances. According to the present calculation, the Rydberg cutoff due to field ionization could be about ${n}_{\mathrm{max}}=25$ instead of ${n}_{\mathrm{max}}=16$ to take into account the effect of the radiative decay during the time of flight. A sudden decrease is observed between the $n=7$ and $8$ resonances due to the opening of the $1s2s{}^{1}S\ensuremath{\epsilon}l$ continuum. From the agreement with experiment, it would appear that the present method is applicable to both the low-$n$ and high-$n$ resonances.