According to Paul Indelicato

transition 3P1 -> 3P0  in 78Kr32+ : 

A	2.48E+08	1/s   "transition rate" 
t	4.03E-09	s     "lifetime 3P1" 
dv	3.95E+07	Hz    "natural line width" 
dE	1.63E-07	eV    "width in eV" 

Now, if we assume a final dp/p (after electron cooling) of the ion beam of ~1E-5, 
this corresponds to a longitudinal temperature of ~16000 K (~1.4 eV). 
This implies a Doppler width of ~26 GHz (ION frame). 

This is broader than the width of the laser pulse in the ION frame (between 4.4 and 23.4 GHz). 

This, in turn, implies that we should "see" the transition if we make 0.0024 nm steps in the UV (LAB frame). 
The transition would then be something like 2-3 steps wide. 

If we use this stepsize, and scan from 257.175 nm to 257.675 nm (LAB frame), we need 207 steps. 

If one step takes 1 minute (using 1 ESR cycle and fixed laser wavelength per cycle), one scan takes ~3.5 hours ! 
I think that is too long. 

For this procedure, the ESR cycle (injection -> next injection) must be faster. 
Also the time for the laser to change the wavelength must be fast, but that should be OK. 
We should try to get to sth. like 1 hour per scan.