A theory, called the weakest bound electron potential model theory, is empl
oyed in a study of the transition probabilities of C-1, C-II, C-III, and C-
IV. A coupled equation that relates energy epsilon and radial expectation v
alue (r)(NL) of the weakest bound electron is proposed for determining the
parameters used in the calculation of the transition probability. The resul
ts presented are in agreement with the accepted values, and the agreement w
ith is within experimental uncertainties. (C) 2001 Optical Society of Ameri
ca.