Dear Djamel, You can write the formulae two ways either as you do B.L' / sin(th1-th2)/2) where L' is the non-constant difference OR as BL/(sin(th1)+sin(th2)) with th1 and th2 being the matching angle as used in the code. The two methods may have slightly different error propagation but are identical in the ideal case So you have another home-work problem So back to the drawing board. ------------------------------------------------------ Flemming Videbaek Physics Department Brookhaven National Laboratory tlf: 631-344-4106 fax 631-344-1334 e-mail: videbaek@bnl.gov ----- Original Message ----- From: "Djamel Ouerdane" <ouerdane@nbi.dk> To: <brahms-l@bnl.gov> Sent: Saturday, October 27, 2001 1:58 PM Subject: Momentum determination > Dear friends, > > Regarding the momentum problem (dAng vs P) that we've been talking for a > long time, I think I've found the problem or at least a part of it. > As always, this kind of problem is in fact quite easy to solve if you > seek the simplest explanation!! :) > I looked at the module matching tracks, and it's simply a geometrical > problem: starting from the equation P = qBr, you can easily derive r in > function of the bending angle. And you then find out that you should not > simply write P = Bdl/sin(theta). In the code, dl and theta are not right: > > first: Bdl is a constant in the code, it should not be at all since dl > depends on where the incoming and outgoing tracks point to the effective > egde planes. So the bigger bending angle, the bigger dl. > > second: the approximation written in the code for P_xz is: > > P_xz = Bdl/(sinTheta1 - sinTheta2) > > It should be: > > P_xz = B * (dl/2) / sin( (theta1 - theta2)/2 ) > > The approximation is maybe valid for very small angles: > (see below) > > For low momentum particles, this does not hold anymore. > > And you can really guess that the lower the momentum, the bigger the > deviation (in the plot dAng vs P) > > I cannot show some plots now since I'm at home on a windows machine but > I'll send some plots tomorrow. > > Ciao > Djam > > ------------------------------------ > > approximation: > > > sin (theta1 - theta2)/2 ~ (theta1 - theta2)/2 therefore: > > P_xz ~ B * (dl/2) / (theta1 - theta2)/2 > P_xz ~ B * dl / (theta1 - theta2) > P_xz ~ B * dl / (sin theta1 - sin theta2) > > provided that you have the right dl !!!! > > > Djamel Ouerdane ------------------------------------------o > | Niels Bohr Intstitute | Home: | > | Blegdamsvej 17, DK-2100 Ø | Jagtvej 141 2D, | > | Fax: +45 35 32 50 16 | DK-2200 Copenhagen N | > | Tel: +45 35 32 52 69 | +45 35 86 19 74 | > | http://www.nbi.dk/~ouerdane | > | ouerdane@nbi.dk | > o---------------------------------------------------------o >
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