Thank you James!

Are you suggesting that her abdomen is like a huge storage tank full of Sunflower oil?

The "storage tank" is obviously full or almost so, but the actual contents of the crop is another matter. Although less likely, a mere coincidence (e.g. a worker full of honeydew traveling on the sunflower) cannot be excluded - that's why I wrote "maybe".
The answer to your other question: yes, worker ants are always of the female gender, contrary to many termite groups.

I should have mentioned that there were several of these worker ants on the same Sunflower and they were moving around slowly as if foraging. I read somewhere that these workers will hang from a cave ceiling almost motionless for a long time until the food is needed at which time they will regurgitate the honeydew or oil as needed to feed their larvae or their queen. Is that this particular ant's purpose and does she die at such time or does she get to repeat the process more than once? Thanks again...

you read about occur only in two genera in North-America: the widespread false-honey Ant Prenolepis imparis, and the several Honeypot Ants (Myrmecocystus sp.) of the arid South-West.
In both cases, the crop - and the inter-segmental membranes - of these specialized young workers soon get so enlarged that a return to a "normal" worker lifestyle is no more possible. Most don't even see the outside for their whole lifespan. Nonetheless, as the volume of stored fluids can vary to a large extant, it can be said that the process can be repeated several times. But this is indeed a "particular purpose".
The Formica worker you posted is no true "replete", but simply a lucky forager who has filled her crop to the biggest possible volume. But this inflating process is still quite reversible.