I am running a CFA and getting good fit indices (CFI = .99, RMSEA = .01) for a uni-dimensional scale. However, when I test for internal consistency, I get poor Cronbach's $\alpha$s ($\alpha = .6$). I have tried everything from removing outliers, to dropping items and still end up with the same problem.
I am wondering if there is anything in SEM that shows that the measure is reliable?
I know that there is some debate about whether Cronbach's $\alpha$ (or internal consistency) even measures reliability but since my field requires Cronbach's $\alpha$ to be reported as a measure of psychometric goodness, I need to find a way to show internal consistency as being adequate for this measure.