PhE - Momentum & Track Curvature

Find the momentum of the particle

Lorenzo Galante

Under Construction

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EVALUATE THE MOMENTUM FROM THE CURVATURE OF THE TRACKS

This is a picture of a collision between a negative pion and an Helium nucleus. You can see three tracks of the particles involved in the process: the incoming pion (from the left), the pion scattered upward after the collision and the nucleus scattered downward.

You have to determine the momentum of the three particles involved in the interaction and, as usual in nuclear physics, express them in eV/c. The picture is embedded in a Geogebra app which gives you a set of tools that should help you in fulfilling the task.

If the app does not fit your display open it from Here.

Repeat the same procedure for the scattered pion (orange circle) and the Helium nucleus (green circle).
In order to transform the gGU in meters you can use the length of the segment CD which is expressed both in gGU and meters.
The magnetic field B is perpendicular to the picture and its value is appears on the left of the picture
The magnetic field B is perpendicular to the picture and its value is appears on the left of the picture
From the magnetic force relation you can derive the momentum p of each particle as a function of the radius of curvature R, the magnetic field B and the charge q ( p=RqB ).
After you have determined the momentum in SI Units, determine the conversion factor in order to express momenta in eV/c (if any problem, read this Help).
You can make a Copy of this worksheet in order to perform your evaluations.

HOW THE APP WORKS

Click on the "Show Pion IN Circle" and move the point J to fit the incoming pion track.
WARNING: the radius is really sensitive to small changes in the position of J. So be careful and do your best to pass through the points shown in the picture below!

When the best fit is reached, take note of the radius of the circle (expressed in Geogebra Units: gGU) on the top.

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