physics report
COLLEGE
PHYSICS LAB REPORT
STUDENTS NAME
ANALYSIS OF A BUBBLE CHAMBER PICTURE
SUPERVISED BY:
19/05/2020
1. Introduction
A bubble chamber is a vessel filled with a superheated transparent liquid (most often liquid hydrogen) used to detect electrically charged particles moving through it. It was invented in 1952 by Donald A. Glaser, for which he was awarded the 1960 Nobel Prize in Physics.
A convenient way to study the properties of the fundamental subatomic particles is through observation of their bubble trails, or tracks, in a bubble chamber. Using measurements made directly on a bubble chamber photograph, we can often identify the particles from their tracks and calculate their masses and other properties. In a typical experiment, a beam of a particular type of particle is sent from an accelerator into a bubble chamber, which is a large liquid-filled vessel. To simplify the analysis of the data, the liquid used is often hydrogen, the simplest element. The use of liquid hydrogen, while it simplifies the analysis, complicates the experiment itself, since hydrogen, a gas at room temperature, liquefies only when cooled to -246◦C. For charged particles to leave tracks in passing through the chamber, the liquid must be in a “super-heated” state, in which the slightest disturbance causes boiling to occur. In practice, this is accomplished by expanding the vapor above the liquid with a piston a few thousandths of a second before the particles enter the chamber.
2. Methods
2.1 Materials needed:
1. student worksheet per student
2. Ruler
3. Scissors
4. Glue stick
5. Pocket calculator
2.2 Procedures
2.2.1 Calculation of the X Particle’s Mass.
Make measurements on each of the photographs. In particular, for each of the circled events measure these four quantities:
· `Σ - The length of the Σ track,
· θ - the angle between the Σ− and π− track,
· s - the sagitta of the π− track,
· `π - The chord length of the π− track.
Your values for the event should be close to those given in the sample input. Run the program using each set of measurements, and tabulate the computed X0 mass from each event. Compute an average of the calculated masses and find the average deviation, expressing your result as Mx ±∆Mx.
Compare your final result with some known neutral particles listed below and identify the X0 particle based on this comparison.
Particle mass (in MeV/c2)
π0 135
K0 498
n 940
Λ0 1116
Σ0 1192
Ξ0 1315
2.2.2 Determination of the Angle θ .
The angle θ between the π− and Σ− momentum vectors can be determined by drawing tangents to the π− and Σ− tracks at the point of the Σ− decay.
We can then measure the angle between the tangents using a protractor. We can show an alternative method which does not require a protractor. Let AC and BC be the tangents to the π− and Σ− tracks respectively. Drop a perpendicular (AB) and measure the distances AB and BC. The ratio AB/BC gives the tangent of the angle 180◦ −θ. It should be noted that only some of the time will the angle θ exceed 90◦.
2.2.3 Determination of Momentum from Range.
We cannot determine the momentum of the Σ− track from its radius of curvature because the track is much too short. Instead, we make use of the known way that a particle loses momentum as a function of the distance it travels. In each event in which the K− comes to rest before interacting, energy conservation applied to the process requires the Σ− particle to have a specific momentum of 174 MeV/c. The relatively massive Σ− particle loses energy rapidly, so its momentum at the point of its decay is appreciably less than 174 MeV/c even though it travels only a short distance. It is known that a charged particle’s range, d, which is the distance it traveled before coming to rest, is approximately proportional to the fourth power of its initial momentum, i.e., d ∝ p4. For a Σ− particle traveling in liquid hydrogen, the constant of proportionality is such that a particle of initial momentum 174 MeV/c has a range of 0.597cm. Next we find the “residual range,” which is the difference between the maximum range d0 and the Σ− track length `Σ. Note that when `Σ = 0.597 you get pΣ = 0 as you would expect.
2.2.4 Calculation of the Sigma Lifetime.
The Σ− lifetime can be approximately determined using the measured values of the Σ− track lengths. The average momentum of the Σ− particle can be found from its initial and final values:
p ¯ Σ = 1/2(174 + pΣ), where pΣ is found from , using the measured track length `Σ.
The length of time that the Σ− lives (the time between its creation and decay) is t = `Σ /v , where `Σ is the length of the Σ− track and v is the average velocity of the Σ− particle.
Write a program that calculates the amount of time that each Σ− lives, and determine an average lifetime. The accepted value is 1.49×10−10 seconds. Since all our photographs are less than life-size, the computed times must be multiplied by the scale factor 1.71. This method of finding the Σ− lifetime can only be expected to give a very approximate result because (a) only four events are used and (b) we have ignored the exponential character of particle decay.
3. Results and Discussion
The bubble chamber is similar to a cloud chamber, both in application and in basic principle. It is normally made by filling a large cylinder with a liquid heated to just below its boiling point. As particles enter the chamber, a piston suddenly decreases its pressure, and the liquid enters into a superheated, metastable phase. Charged particles create an ionization track, around which the liquid vaporizes, forming microscopic bubbles. Bubble density around a track is proportional to a particle's energy loss.
Bubbles grow in size as the chamber expands, until they are large enough to be seen or photographed. Several cameras are mounted around it, allowing a three-dimensional image of an event to be captured. Bubble chambers with resolutions down to a few micrometers (μm) have been operated.
The entire chamber is subject to a constant magnetic field, which causes charged particles to travel in helical paths whose radius is determined by their charge-to-mass ratios and their velocities. Since the magnitude of the charge of all known charged, long-lived subatomic particles is the same as that of an electron, their radius of curvature must be proportional to their momentum. Thus, by measuring their radius of curvature, their momentum can be determined. A careful quantitative analysis of measurements made on tracks in bubble chamber photographs can reveal much more than can a simple visual inspection of the photographs.
First, while reactions can often be unambiguously identified by their topology, such identification can be confirmed if we make measurements of the length, direction, and curvature of each track, and then analyze these data by computer. Second, through such a procedure we can determine whether an unseen neutral particle was present. Third, we can determine properties of an unseen neutral particle. In each of the photographs there are one or more events. The circled event in each photograph is the one of particular interest because all of its tracks lie very nearly in the plane of the photograph and this considerably simplifies the analysis. Such “almost coplanar” events are a rare occurrence since all directions are possible for the particles involved. For events that are more non-coplanar we must analyze at least two stereoscopic photographs of each event in order to completely describe its three dimensional kinematics. For each of the circled events we will first determine three quantities:
(a) The momentum of the π− particle (pπ);
(b) The momentum of the Σ− particle (pΣ) at the point of its decay; and
(c) The angle θ between the π− and Σ− tracks at the point of decay
On their way through the liquid, particles constantly loose energy because of the ionization processes and Bremsstrahlung. A lower momentum corresponds to a smaller track radius in a magnetic field: In the bubble chamber; The Lorentz force 𝐹𝐿 = 𝑞 ∙ 𝑣 ∙ 𝐵
acts as centripetal force 𝐹𝑐 = 𝛾 ∙ 𝑚 ∙ 𝑣 2 𝑟 (with 𝛾 = 1 √1− 𝑣 2 𝑐 2 for relativistic particles).
Therefore: 𝑞 ∙ 𝑣 ∙ 𝐵 = 𝛾 ∙ 𝑚 ∙ 𝑣 2 𝑟 ⇒ 𝑟 = 𝛾∙𝑚∙𝑣 𝑞∙𝐵 = 𝑝 𝑞∙𝐵 or 𝑝 = 𝑞 ∙ 𝑟 ∙ 𝐵.
Where; q= electric charge of particle in C 𝑣= speed of particle in m/s
𝑐=speed of light in vacuum in m/s 𝐵= Magnetic field strength in T
𝑚=mass of particle in kg 𝑟= radius of curvature of the particle track in m
𝑝= (relativistic) momentum of the particle
3.1 Energy loss
A fast charged particle traversing the bubble chamber liquid loses continuously energy by interactions with the atoms of the medium, which become ionized. At low momenta the losses are large and have a dependence of the type 1/v2; the losses for v=c tend to a constant value of about 0.27 MeV/cm in liquid hydrogen. The losses are furthermore proportional to the square of the particle charges; all elementary particles have charge +1 or -1 times the proton charge. An electron with more than few MeV has always a velocity close to the velocity of light; it loses a relatively small energy by ionization and more by radiating photons (the bremsstrahlung process). A fast electron thus yields a track with slightly less than 10 bubbles per centimeter and which spirals because of the large energy loss by radiation.
How can we be sure that the event is really an elastic event? This can be done by checking if energy and momentum are conserved.
I) Conservation of energy: (Total energy of the K+) + (mass energy of a stationary proton) is equal to (Total energy of the outgoing K+) + (total energy of the outgoing proton)
II) Conservation of linear momentum. (Momentum of incident K+) + (0) is equal to (momentum of outgoing K+) + (momentum of outgoing proton)
Although bubble chambers were very successful in the past, they are of limited use in modern very-high-energy experiments for a variety of reasons:
· The need for a photographic readout rather than three-dimensional electronic data makes it less convenient, especially in experiments which must be reset, repeated and analyzed many times.
· The superheated phase must be ready at the precise moment of collision, which complicates the detection of short-lived particles.
· Bubble chambers are neither large nor massive enough to analyze high-energy collisions, where all products should be contained inside the detector.
· The high-energy particles may have path radii too large to be accurately measured in a relatively small chamber, thereby hindering precise estimation of momentum.