Measurement of elastic scattering in antiproton-proton collisions at 52.8 GeV centre-of-mass energy

We measured the differential cross section for p?p and pp elastic scattering in the momentum-transfer range 0.01 <|t| < 1.0 GeV² at the CERN Intersecting Storage Rings with center-of-mass energy $\text{s}\text{= 52.8}\text{GeV}$. Fitting the differential cross section with an exponential [Aexp (bt)], we found $\text{b}\text{p}\text{p = 13.92 ± 0.59}\text{GeV}{}^{\mathrm{?2}}$ for |t| < 0.05 GeV², whilst for |t| > 0.09 GeV², $\text{b}\text{p}\text{p = 10.68 ± 0.26}\text{GeV}{}^{\mathrm{?2}}$. Using the optical theorem, we obtained for the total cross section $\text{σ}{}_{\mathrm{<mtext>tot</mtext>}}\text{(}\text{p}\text{p)= 44.86 ± 0.78}\text{mb}$ and, by integrating the differential cross section, we obtained for the total elastic cross section $\text{σ}{}_{\mathrm{<mtext>el</mtext>}}\text{(}\text{p}\text{p) = 7.89 ± 0.28}\text{mb}$. Calculations of σ_tot combining elastic-rate and total-rate measurements are also given. All of these measurements were also performed for pp scattering at the same energy, and the results for both reactions are compared.     

Conservative methods for the Toda lattice equations

We are concerned with the numerical integration of the Todalattice equations by using different conservative methods. Numericalexperiments suggest that the global error for isospectral schemesdecreases exponentially with time but it is almost constantfor either symplectic or more general integrators. We providea theoretical explanation for these experimental findings.