Physics307L:People/Wilkinson/Rough

= Shielding of Background Radiation Using Lead Bricks =

Author: Dan Wilkinson

''Experimentalists: Dan Wilkinson

Junior Lab, Department of Physics & Astronomy, University of New Mexico

Albuquerque, NM 87131

dnby89@unm.edu 

Abstract
The background radiation in the UNM Physics and Astronomy building was measured using a scintillation counter under various shielding arrangements of lead bricks. The data was analysed and is shown to obey a Poisson distribution. The fact that this process is a Poisson process means that there is a predictable number of events that will occur in a certain time interval even though these events are random and independent of one another. I show that there is a significant decrease in radiation counts before and after the lead bricks were added to the configuration. Using this data the cross section of the lead was also computed and equals $$11.(3) \times 10^{-24} cm^2 $$. 

Introduction
Understanding and quantifying background radiation has much practical importance. Most background radiation is produced by natural processes including cosmic rays, radon gas, and other naturally occurring radioactive isotopes. Understanding these fundamental sources is important for many practical applications. For example, in the hunt for dark matter, physicists must bury labs thousands of feet underground to shield their apparatus from cosmic radiation [1]. Cosmic radiation is produced when high energy particles expelled by the sun are incident on the Earth's atmosphere. Measuring and recording the abundance of this radiation can give information about the solar cycle, the earth's local magnetic field strength, and shielding effects of various materials [2].

Theory
The number of ionization events detected by the scintillator is equal to the number of radioactive events and can therefore be compared to the background radiation in the lab. This data was fit to a Poisson distribution. The probability on an event happening in one measured period is $$\Pr = \frac{e^{-\lambda} (\lambda)^k}{k!}$$ Here $$\lambda$$ is the expected value (the average value) and $$k$$ is the number of observed events. The flux of particles through a material is defined as [5] [6] [7] [8]
 * $$\frac{dN}{dx}= -N n \sigma$$

Solving for $$\sigma$$
 * $$\sigma = \frac{dN}{dx} \frac{-1}{N n}$$

Here $$\frac{dN}{dx}$$ is the number flux of particles through the material, N is the number of particles that are allowed to penetrate the material, and n is the number of absorbing molecules per unit volume of the material. For lead [4] $$n = 3.29 \times 10^{22} \frac{particles}{mL}$$

Methods
A Tracor Norther Model TN-1222 scintillator was used to detect ionizing radiation. As an ionization event occurs the a photon is created in the scintillator that interacts with a photomultiplier held at a given potiential. The PMT registers a voltage for the event and this voltage is read by the SPECTECH Universal Spectrometer UCS 30 and recorded by the UCS 30 software. Each ionization event registers as a count in a predetermined time interval. Each run consisted of 2049 data points of time intervals ranging from 20ms to 400ms. The measurements were also taken under the cover of 8cm of lead Figure 2 and with no lead cover Figure 3. See supplemental section for MATLAB code and explanation.



Results and Discussion


Initial background data has shown that background radiation can be predicted to a fairly good degree of accuracy Figure 3 ie the percent difference between the standard deviation of the data compared to the standard error of the fit was less than 3%. Since the data and the Poisson fit were almost identical I concluded that the process that generated the data is Poisson. This realization means that the calculated averages of data sets can be used to predict the average values of future background radiation events (within a reasonably small time period ie a few minutes to a few hours later).

Since the background radiation is predictable the cross section of lead can be calculated. I calculated the difference in average background counts per time period for both covered and uncovered data sets Figure 4. These differences are shown to be linear with time and therefore the percent difference between them is independent of time. I observed a 36(2)% decrease in counts when the lead bricks were placed on top of the scintillator Figure 5. This not only shows that the process is Poisson it allows for predictions to be made and an estimate of the effective cross section of the lead to the background radiation of the laboratory to be computed i.e. because the difference of means is linear with time then the cross section of lead must be a constant value that can be calculated using the above formula.

The cross section of the lead for background radiation in the UNM Physics Laboratory is $$11.(3) \times 10^{-24} cm^2 $$. Because of the geometry of the setup it is appropriate to assume that the decrease in radiation events resulted from shielding cosmic radiation. Energy scans were also ran with the various lead brick configurations. A calibration curve was generated using a Cesium 137 source and a Cobalt 60 source. Looking at Figure 6 the only significant change in energy flux density happens between windows 15 and 20. At around window 20 Cesium 137 has the first emission peak at window twenty. This first peak is corresponds to an energy of 32.19keV [3]. Without further analysis it can be said that the lead is more efficient at screening out particles with energies lower that 32.19keV ie over 32.19keV energies particles are still screened but not as efficiently. 



Acknowledgements
I want to thank Brian Josey for helping with this lab. Also Prof. Koch and Katie Richardson. Katie was instrumental in my understanding of some of the physics in this experiment.

Supplemental Data and Code
This data represents the fact that the background radiation fits a Poisson distribution. This is shown by comparing the standard deviations and computing percent difference between the two. 

An initial series of scans of background radiation were taken at 10,40,100,400,and 1000ms.  function [P,x1,y,sy,sP,error] = Poisson(X) x=X(:,3); x1=x; mu=mean(x); P=exp(-mu)*(mu.^x1)./(factorial(x1)); for i=1:max(x1)+1; ind1=find(x1==i-1); x1(ind1(1:end-1))=[]; P(ind1(1:end-1))=[]; end [x1,IX]=sort(x1); P=P(IX); length(x1); y=zeros(1,length(x1)); for j=1:length(x1); y(j)=length(find(x1(j)==x)); end y=y./sum(y); sy=std(y./sum(y)); sP=std(P); error=100*abs((sy-sP)/sy); end This MATLAB program loads the raw experimental data and generates a Poisson fit to the data. It also generates the standard deviation of the data/fit and the percent difference between the data and the fit. diffmean=[m20o-m20c,m40o-m40c,m80o-m80c,m100o-m100c,m200o-m200c,m400o-m400c]; dt=[20,40,80,100,200,400]; P=polyfit(dt,diffmean,1) t=linspace(20,400,200); fit=(P(1)*t)+P(2); plot(dt,diffmean,'*',t,fit),xlabel('Time Interval'),ylabel('Difference of Means'),legend('Difference of Means between covered and uncovered data','Linear    Fit'),title('Difference of Means') figure,plot(x20mso,p20mso,x20msc,p20msc,x40mso,p40mso,x40msc,p40msc,x100mso,p100mso,x100msc,p100msc,x400mso,p400mso,x400msc,p400msc) % hold on    % plot(x20msc,p20msc,'*',x40msc,p40msc,'*',x100msc,p100msc,'*',x400msc,p400msc,'*') blocked=diffmean./[m20o,m40o,m80o,m100o,m200o,m400o] sigma=blocked/(3.29*10^22) mean(sigma) std(sigma)/sqrt(length(blocked)) This code compares the data taken with a lead cover to the data with no lead cover by computing a percent difference in means between the two data sets per time interval. The percent differences were averaged and then used to compute the cross section of the lead.