Ecm = 1000GeV, N=2.019 x 10^{10}/bunch, sigma_y / sigma_x = 3.077nm / 372nm beta_x/beta_y = 0.12356mm / 24.62mm and headon collision.

For total numbers of generated pairs ( 5MeV < E_e < 500GeV), ABEL has about 20% less pairs than CAIN and GP, while CAIN agrees very well with GP(pair_q2=0, i.e. Q^2=m^2). There are three processes of LL (Landau-Lifshitz), BH (Bethe-Heitler) and BW (Breit-Wheeler) in incoherent pair creation. Among them, BH of ABEL was apparently less than those of CAIN and GP.

The three programs have two effects in processes with virtual photons; that is, (1) beam size effect and (2) external field effect. In order to study this discrepancy, pairs were generated without the two effects. For LL and BW, ABEL's numbers were 1.8 and 1.5 times higher than those of CAIN/GP, respectively, while BH pairs were same for the three. Since the absolute number of BW is two order of magnitudes less than LL and BH, the difference in BW was not seen in total. Next, the beam size effect was studied, where only the beam size effect was taken account of. The suppression factors in LL(BH) were 0.33 (0.37), 0.52 (0.47) and 0.51 (0.46) for ABEL, CAIN and GP, respectively. So the ABEL's factor was 0.63 (0.78) of those of CAIN and GP. Additional effects due to the external field were very similar for them, whose suppression factors in LL (BH) were 0.80 (0.99), 0.75 (1.0), 0.77 (1.0) for ABEL, CAIN and GP, respectively. With all effects, the LL of ABEL has 1.8 (generation) x 0.63 (beam size) x 1.05 (external field) = 1.19 and the BH of ABEL has 1.0 (generation) x 0.78(beam size) x 0.99 (external field) =0.77 relative to CAIN and GP. Since the generated number of BH pairs is dominant, the total generated number of ABEL was 20% less than those of CAIN and GP as mentioned before.

ds 56*(a*re)**2 --- = -------------*2*log(1/x)*log(s/m**2*x) (1) for LL dx 9*pi * x, (m/E1 << x << 1) , where , x=(E_e of final e+ or e-)/E1 , s=4*E1*E2 (E1,E2=beam energy (E0) ) (dependence on E2 ignored. replaced by E0), a=fine str.const., re=classical electron radius, m=rest mass, and see a reference paper of E.A.Kraev et al, Sov.J.Nucl.Phys.23(1976)85 , and

ds 16*a*re**2 s*x*(1-x) --- = -----------*(x**2-x+ 3/4)*(log---------- - 1/2 ) (2) for BH dx 3 2*m**2,(m/Ephoton < x < 1), where x=(E of final e+ or e-)/Ephoton , s=4*E1*Ephoton (E1=initial electron energy). Then, the patch factors were 0.70, 0.92 and 0.50 for LL, BH and BW, respectively. Actually, an integration of Eq. (1) is 1.55 times that of CAIN/GP for (0.005 < E_e<500GeV) while an integration of Eq.(2) is the same as them. Therefore, ABEL over-estimated the LL cross section by 1.55 at least.

With the updated patch factors, ABEL generated almost the same numbers of BH and BW as CAIN/GP, while the number of LL was 1.18 times of them. The difference of 18% is considered to be due to further approximations employed in ABEL. This amount is within an accuracy of real photon approximation such as Q^2 scale ambiguity. A small correction in the LL cross section was applied too in order to correct the energy distribution at high energy. Now, we understand the 1.8 factor in the LL-calculation by 1.55 (energy function) x 1.18 (ABEL/BASES). The 1.5 factor in the BW was reduced to unity by a change of the patch factor from 0.5 to 0.92.