Bubble chamber tracks analysis

PHY 4822L (Advanced Laboratory):

Analysis of a bubble chamber picture

Introduction In this experiment you will study a reaction between “elementary particles” by analyzing their tracks in a bubble chamber. Such particles are everywhere around us [1,2]. Apart from the standard matter particles proton, neutron and electron, hundreds of other particles have been found [3,4], produced in cosmic ray interactions in the atmosphere or by accelerators. Hundreds of charged particles traverse our bodies per second, and some will damage our DNA, one of the reasons for the necessity of a sophisticated DNA repair mechanism in the cell.

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Figure 1: Photograph of the interaction between a high-energy π--meson from the Berkeley Bevatron accelerator and a proton in a liquid hydrogen bubble chamber, which produces two neutral short-lived particles Λ0 and K0 which decay into charged particles a bit further.

Figure 2: illustration of the interaction, and identification of bubble trails and variables to be measured in the photograph in Figures 3 and 4. The data for this experiment is in the form of a bubble chamber photograph which shows bubble tracks made by elementary particles as they traverse liquid hydrogen. In the experiment under study, a beam of low-energy negative pions (π- beam) hits a hydrogen target in a bubble chamber. A bubble chamber [5] is essentially a container with a liquid kept just below its boiling point (T=20 K for hydrogen). A piston allows expanding the inside volume, thus lowering the pressure inside the bubblechamber. When the beam particles enter the detector a piston slightly decompresses the liquid so it becomes "super-critical'' and starts boiling, and bubbles form, first at the ionization trails left by the charged particles traversing the liquid. The reaction shown in Figure 1 shows the production of a pair of neutral particles (that do not leave a ionized trail in their wake), which after a short while decay into pairs of charged particles:

π - + p → Λo + Ko,

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where the neutral particles Λo and Ko decay as follows:

Λo → p + π-, Ko → π+ + π-. In this experiment, we assume the masses of the proton (mp = 938.3 MeV/c2) and the pions (mπ+ = mπ- = 139.4 MeV/c2) to be known precisely, and we will determine the masses of the Λ0 and the K0, also in these mass energy units.

Momentum measurement In order to “reconstruct” the interaction completely, one uses the conservation laws of (relativistic) momentum and energy, plus the knowledge of the initial pion beam parameters (mass and momentum). In order to measure momenta of the produced charged particles, the bubble chamber is located inside a magnet that bends the charged particles in helical paths. The 1.5 T magnetic field is directed up out of the photograph. The momentum p of each particle is directly proportional to the radius of curvature R, which in turn can be calculated from a measurement of the “chord length” L and sagitta s as:

r = [L2/(8s)] + [s/2] , Note that the above is strictly true only if all momenta are perfectly in the plane of the photograph; in actual experiments stereo photographs of the interaction are taken so that a reconstruction in all three dimensions can be done. The interaction in this photograph was specially selected for its planarity. In the reproduced photograph the actual radius of curvature R of the track in the bubble chamber is multiplied by the magnification factor g, r = gR. For the reproduction in Figure 3, g = height of photograph (in mm) divided by 173 mm. The momentum p of the particles is proportional to their radius of curvature R in the chamber. To derive this relationship for relativistic particles we begin with Newton's law in the form: