Measurement of the branching ratios of the decays Xi0 --> Sigma+ e- nubar and anti-Xi0 --> anti-Sigma+ e+ nu

From 56 days of data taking in 2002, the NA48/1 experiment observed 6316 Xi0 --> Sigma+ e- nubar candidates (with the subsequent Sigma+ --> p pi0 decay) and 555 anti-Xi0 --> anti-Sigma+ e+ nu candidates with background contamination of 215+-44 and 136+-8 events, respectively. From these samples, the branching ratios BR(Xi0 --> Sigma+ e- nubar)= (2.51+-0.03stat+-0.09syst)E(-4) and BR(anti-Xi0 --> anti-Sigma+ e+ nu)= (2.55+-0.14stat+-0.10syst)E(-4) were measured allowing the determination of the CKM matrix element |Vus| = 0.209+0.023-0.028. Using the Particle Data Group average for |Vus| obtained in semileptonic kaon decays, we measured the ratio g1/f1 = 1.20+-0.05 of the axial-vector to vector form factors.