Upon turon OFF there is a one nano farad capacitor that stays charged with 8000 volts until it slowly self discharges.
my question is how to calculate and what should be the cal/cm2 value for such case as long as the capacitor is charged?

We are not talking about a lot of energy here. Unless I've missed a few zeros, it sounds like fractions of a calorie, even over 2 seconds.

The shock hazard may be the more serious concern here.

you are absulutly right. the energy stored in the capacitor is a fraction of a calorie.
yet, i am asked to calculate the cal/cm2 and I do not know how to approach it.

In free air, the incident energy at a distance of r would be your stored energy over the surface area of a sphere of radius r.

thank you. this is clear.
just to make sure - for 1nF capacitor charged at 8000V the stored energy is 1/2CV^2 = 1/2 * 1nF * 8000^2 = 0.032 Joule = 0.0076 cal.
The only question left is what should I use as r in my case to get the arc flash value?

I believe the r is arbitary. How far do you want to be? 1 inch, 20 ft, 2 miles, etc. It is what you decide to be the distance of interest.

r would be your distance to the worker, usually determined by voltage level and working rules (rubber glove or hot stick).

Perhaps another approach would be to turn it around, and determine what r will result in 1.2 cal/cm^2.

r is distance from arc to worker. Area is 4·pi·r², so your IE is negligible for any distance. For 1 cm, IE = 0.0076/(4·pi·1²) = 0.0006 cal/cm².