1. A typical case of SD structure at high spin in 194Hg! sig_tot = 1barn Atarget = 186, thikness = 0.5mg/cm 2 beam intensity = 5pnA, N = 3.12. 10 10 which gives a reaction rate of R = 5.10 4 /s the probability of any given particle to induce a reaction is P = R/N = 1.6 10 -6 Assuming a beam pulse frequency of 10 MHz, i.e. t = 100ns There are n = 3.12 10 10 pps/ 10 7 = 3.1 10 3 particles in every pulse! The probability to have x reactions within a the beam pulse is p x = (P. n) x e –(P.n) /x! In our case P.n = 0.005 thus, the probability to have 0 reaction in a pulse = 0.995 the probability to have 1 reaction in a pulse = 0.005 the probability to have 2 reactions in a pulse = 10 -5 If we increase the beam by a factor 10 i.e, 50pnA (100pnA) P.n = 0.05 (0.1) thus, the probability to have 0 reaction in a pulse = 0.95 (0.9) the probability to have 1 reaction in a pulse = 0.05 (0.09) the probability to have 2 reaction in a pulse = 10 -3 (5 10 -3 )

2. As you can see here up to 100pnA intensity and 10MHz beam pulsing the probability of 2 reactions per beam pulse is < 1%! One could go to 50MHz beam pulsing (as typical Ge detectors have a 20ns time resolution) and be able to use up to 500pnA with the same probability of double reaction per beam pulse Note: that if recoils are detected in coincidence in a focal plan of a spectrometer this sets an additional limitation i.e. time distribution of the recoils around 50ns! This means the fastest beam pulsing would be 20 MHz!

3. BUT in reality : the limitation will be set already by the individual counting rates of the Ge detectors 10Khz! going to Agata (digital electronics) a factor 5 to 10 gain is expected ! The overall gains will allow to use beams with intensities not higher than 100pnA

4. Multiple reactions per beam pulse ( in general cases)! the probability of two reaction in a pulse seems to be already 10% for a value of P.n = 0.5! P.n = R/N. N/HF = R/HF R : reaction rate N : nombre of particle/s in the incident beam HF: beam frequency Taking a HF= 10MHz, P.n = R. 10 -7 That means that at a reaction rate of 5.10 6 the limit is reached! in barn). I (in pps) = 10 12 For a target of mass A=100 and thickness of 1mg/cm2 For 1barn, the limit is 10 12 pps (of the order of 500pnA) For 0.1 barn the limit is 10 13 pps (of the order of 5p A) For 0.01 barn the limit is 1014 pps (of the order of 50p A)