BETA PARTICLE ABSORPTION

Table of Contents

Discussion

When one considers the motion of beta particles through any material, two phenomena dominate the evaluation of the process:

• the energy spectrum of the incident betas, and
• the straggling path of the betas.

First, when considering an isotopic source, it becomes apparent that the energy of the beta emitted is not held to a unique value (as in the case of a gamma ray) due to energy-sharing with the anti-neutrino. While the decay schemes show the maximum energy available to the beta, the average is roughly 1/3 of the maximum.

We are not dealing with a monoenergetic source.

Secondly, as a beta particle moves through a material, its collisions impart an erratic, constantly changing direction to the particle. This "straggling" is accompanied by absorption of some energy of the particle at each collision site, ultimately reducing its velocity to zero. The erratic path is characteristic of beta motion.

Modeling of the transmission of betas under such boundary conditions would not seem to lend itself to a simple model. However, the combination of these two independent phenomena produces observed results which tend to fit an exponential curve which may be described by:

where:

• I_o is the intensity of the beta beam impinging upon the absorber [/cm²/s],
• I is the intensity of the beta beam [/cm²/s] at a depth x into the material,
• µ = mu is the beta mass absorption coefficient of the material [cm2/mg],
• x is the absorber thickness to the point of interest [cm], and
• p = rho is the absorber density [mg/cm³].

Defining the mass thickness: t_d= p*x [mg/cm²], we get :

If the data are plotted on a semi-log scale, two straight lines should result: one describing the attenuation of the beta rays through the material, and the second describing the region beyond the reach of all beta particles (i.e. background radiation). The intersection of these two straight lines defines the range of the beta particles studied.
 

Object

To measure the beta mass absorption coefficient of a material and the range of beta rays.
 

Procedure

The experimental determination of µ depends on the evaluation of the absorption which takes place in all materials between the source and detector. The constant value of the mass thickness of the detector window and of the air gap for each absorber must be added to the mass thickness of each absorber. The collimator serves to control the scattered radiation which reaches the detector.

A Geiger detector should be used for this experiment and the manufacturer's specification of window mass thickness noted.

1. Determine the Geiger plateau and set the H.V.
2. Take a background count with no source or absorber.
3. Select a source which has a single beta (no gamma), place it in position, and take a count.
4. Place a calibrated absorber in place and take a count. A calibrated absorber is one whose composition (usually a pure metal) is known and whose thickness has been accurately determined. These absorbers are very thin and special care must be taken to prevent damage to the absorber.
5. Repeat, increasing absorber thickness, until the count recorded has reached background.
6. Continue adding absorber thickness and taking background counts to determine background level.

NOTE: Select count times so as to provide reasonable counting statistics.

Report

1. Determine the total absorber mass thickness (window, air, and material) for each step.
2. Plot the data (cpm vs total absorber mass thickness) on semi-log paper. Does the data generate straight lines? If not, why not?
3. From your plot, determine the mass absorption coefficient for the material at the beta energy used.
4. Does the value agree with that calculated by empirical equations?
5. Calculate the maximum range of the beta particle in the material and compare it to your measured data.
6. What is the maximum distance the beta particle will travel in this material?