Measuring a Cross-section
In principle, measuring a cross-section is a very simple thing. One measures the yield of a reaction, and then extracts certain factors, leaving one with the cross-section. Yield is given by the simple equation:
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where n is the number of target atoms per unit area, I is the incident beam flux, and A is the area of integration.
This being the case, there are two approaches to measuring the yield, and therefore two methods to extracting a cross-section.
Method 1: Area of beam << Area of target.
Method 2: Area of beam >> Area of target.
The first is to have a finely focused beam and a large target. Since the beam strikes only a tiny fraction of the target dI can be considered to not vary with dA for purposes of the integral and pulled out. Trivially performing the integral then leaves:
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This leaves the tasks of measuring the total beam current well and producing a uniform target. Producing a uniform target is not normally a concern, but when the target material is radioactive, as is the case for 7Be, this becomes an issue. In fact, in previous measurements of the cross-section this has been the dominating uncertainty. For this reason we have decided to use a different method in the measurement here at the NPL.
If a target is manufactured to be much smaller than the beam then dn can now be considered to be non-varying with dA and removed from the integral. This yields another simple relation:
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In this case the total number of target atoms must be known, and a uniform beam flux is required.
The Apparatus
With this in mind our target chamber and experimental apparatus was designed to allow us to produce and measure a uniform beam flux, count the amount of 7Be in our target, and measure the yield of 8B from the reaction.
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The total amount of 7Be is measured using a Ge detector to count activity. The goal is to measure this to an accuracy of 2% or better.
To create a uniform beam a pair of magnets raster the beam in two dimensions, spreading a well focused beam into a large square area. To be sure that uniformity is achieved the beam is passed through different sized apertures and the flux through each is compared.
The strength of the sweeping fields is increased until the flux is uniform through all apertures, indicating that the beam flux is uniform over an area larger than the target.
Because the bombardment of the target creates a high background of scattered particles the Si detectors used to measure the a particles from the decay chain of the 8B are removed from the irradiation position of the target.
An arm attached to a servo motor moves the arm between the irradiation position and the counting position. When the arm is in the counting position we are simultaneously counting alpha particles as well as the amount beam passing through an aperture to same size as the target.
Repeating this over many cycles gives us a spectrum of alpha particles to determine the yield, and a measure of the incident beam.
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last modified: 6/6/00
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