A measurement of the branching ratio for the∑ + →pγ decay

We have measured the weak radiative decay branching ratio (∑ ⁺ →pγ)/(∑ ⁺ →pπ⁰). The experiment was carried out at Brookhaven National Laboratory using a low-energy separatedK ^? beam stopping in liquid hydrogen. The∑ ⁺ was tagged by observing the pion fromK ^? K ⁺ p→∑ ⁺π^? in a range telescope, and the gamma was detected in a segmented NaI detector. The result is (2.81±0.39 _?0.43 ^+0.21 )×10^?3, which is consistent with previous measurements. This corresponds to a branching ratio for (∑ ⁺ →pγ)/(∑ ⁺ → all) of (1.45±0.20 _?0.22 ^+0.11 )×10^?3, where the quoted errors are statistical and systematic, respectively. A total of 408 signal events were observed, doubling the previous world total.     

Computer extended series solution for unsteady flow in a contracting or expanding pipe

Unsteady flow in a semi-infinite contracting or expanding pipeis reinvestigated using long series analysis. The proposed seriesmethod is useful in analysing the problem for a moderately largeconstant ( = aa/, where a = a(t), the radius of the pipe isa function of time, a(t) is the velocity of the wall, and iskinematic viscosity). For positive values of (expansion ofthe pipe) accuracy of the series representing shear stress andpressure gradient is increased from = 2.89 to = 6.0 by extractingthe singularity followed by completion of the series. For negativevalues of (contraction of the pipe), we revert the series whichresults into the increase of the region of validity of the transposedseries from = -25.0 to = -2.89. Later we use Padé approximantsfor summing them. Also, the asymptotic solution for large valuesof is obtained and it agrees closely with pure numerical valuesof shear stress at the wall and pressure gradient.