Determining Dose Rate with a Semiconductor Detector - Monte Carlo Calculations of the Detector Response

SE9900106 FOA-R--99-01035-861 --SE February 1999 FOA ISSN 1104-9154 DEFENCE RESEARCH Technical Report ESTABLISHMENT

Charlotte Nordenfors Determining dose rate with a semiconductor detector - Monte Carlo calculations of the detector response

Division of NBC Defence SE-901 82 UMEA DEFENCE RESEARCH ESTABLISHMENT FOA-R--99-01035-861-SE Division of NBC Defence February 1999 SE-901 82 UMEA ISSN 1104-9154 SWEDEN

Charlotte Nordenfors Determining dose rate with a semiconductor detector - Monte Carlo calculations of the detector response

Distribution: SkyddS, SSI Issuing organization Document ref. No., ISRN Defence Research Establishment FO A-R--99-01035-861 -SE Division of NBC Defence Date of issue Project No. SE-901 82 UMEA February 1999 E415 SWEDEN Project name (abbrev. if necessary)

Author(s) Initiator or sponsoring organization FOA Charlotte Nordenfors Project manager Torbjorn Nylen Scientifically and technically responsible Thomas Ulvsand Document title Determining dose rate with a semiconductor detector - Monte Carlo calculations of the detector response

Abstract To determine dose rate in a gamma radiation field, based on measurements with a semiconductor detector, it is necessary to know how the detector effects the field. This work aims to describe this effect with Monte Carlo simulations and calculations, that is to identify the detector response function. This is done for a germanium gamma detector owned by the department of Nuclear Weapon Issues and Radiaton Science at the Swedish National Defence Research Establishment in Umea. The detector is normally used in the in-situ measurements that is carried out regularly at the department. After the response function is determined it is used to reconstruct a spectrum from an in-situ measurement, a so called unfolding. This is done to be able to calculate fluence rate and dose rate directly from a measured (and unfolded) spectrum.

The Monte Carlo code used in this work is EGS4 (Electron Gamma Shower, version 4) developed mainly at Stanford Linear Accelerator Center. It is a widely used code package to simulate particle transport with

The results of this work indicates that the method could be used as-is since the accuracy of this method compares to other methods already in use to measure dose rate. Bearing in mind that this method provides the nuclide specific dose it is useful, in radiation protection, since knowing what the relations between different nuclides are and how they change is very important when estimating the risks.

Keywords Dose rate,semiconductor detector, Monte Carlo methods, gamma ray spectromety, EGS4 Further bibliographic information Language English

ISSN 1104-9154 ISBN Pages 77 p. Price Ace. to pricelist

Distributor (if not issuing organization) Dokumentets utgivare Dokumentbeteckning, ISRN Försvarets forskningsanstalt FOA-R-99-01035-861--SE Avdelningen för NBC-skydd Dokumentets datum Uppdragsnummer 901 82 UMEÅ Februari 1999 E415 Projektnamn (ev förkortat)

Upphovsman(män) Uppdragsgivare FOA Charlotte Nordenfors Projektansvarig Torbjörn Nylén Fackansvarig Thomas Ulvsand Dokumentets titel i översättning Dosratsbestämning med halvledar-detektor - Monte Carlo beräkning av detektor respons

Sammanfattning För att bestämma dosrat i ett gammastrålfält baserat på mätningar med en halvledardetektor måste man känna till hur detektorn påverkar strålfältet. Målet med det här arbetet är att beskriva denna påverkan med hjälp av Monte Carlo simulering och beräkning d.v.s. ta fram detektorns responsfunktion. Detta görs för en germanium gammadetektor som ägs av institutionen för kärnvapenfrågor och strålningsvetenskap vid Försvarets forskningsanstalt i Umeå. Detektorn används normalt vid de in-situ mätningar som görs regelbundet vid institutionen. Då responsfunktionen är känd används den för att rekonstruera ett uppmätt spektrum. När detta är gjort kan fluensrat och dosrat beräknas direkt från det uppmätta (och rekonstruerade) spektrumet.

Monte Carlo-koden som används i arbetet är EGS4 (Electron Gamma Shower, version 4) som utvecklats huvudsakligen vid Stanford Linear Accelerator Center. Det är ett ofta använt programpaket för simulering av partikeltransport.

Resultaten pekar på att metoden kan användas som den är eftersom noggrannheten kan jämföras med metoder som redan används för att mäta dosrat. Med tanke på att denna metod ger den isotopspecifika dosen är den användbar, i strålskyddssammanhang, eftersom det är viktigt att känna till relationerna mellan olika isotoper och hur dessa ändras då riskuppskattningar görs.

Nyckelord Dosrat, halvledardetektor, Monte Carlo-metoder, EGS4, gamma spektrometri

Övriga bibliografiska uppgifter Språk Engelska

ISSN 1104-9154 ISBN

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Distributör (om annan än ovan) V.1.1 Contents

Preface vii

1 Introduction 1

2 Gamma-ray spectrometry 3 2.1 Photon interactions 3 2.1.1 Photoelectric absorption 3 2.1.2 Compton scattering 4 2.1.3 Pair production 5 2.2 Contributions to the detector response .... 6 2.2.1 The very large detector 7 2.2.2 The very small detector 7 2.2.3 The real detector 8 2.2.4 Summing up the detector response . . 9 2.3 Semiconductor detectors 10 2.3.1 The portable high purity germanium detector 11

3 The theory of unfolding the response function 15 3.1 The unfolding 15 3.2 How to find the inherent response function . . 17

4 EGS4 - The Monte Carlo package 19 4.1 A summary of capabilities and features .... 19 4.2 How to use EGS4 20 4.3 PEGS4 - data preparation 21 4.4 DOSRZ - a User Code 22

5 Calculations 25 5.1 The detector model 25 5.2 Input parameters 30 vi CONTENTS

5.3 The output 32

6 Results of the unfolding 35 6.1 The procedure 35 6.2 Comparison with point source measurements . 35 6.3 In-situ measurements and angular dependence 36 6.4 Discussion 37

7 Conclusions 39 7.1 Further developments 39

References 40

A Detector data 43

B Input and output from EGS4 49 B.I .egs4inp 49 B.2 .egs41st 53 B.3 .egs4eff 58 C Calculations 61 C.I DOSRZ - the regions of the detector model . 61 C.2 Empirical values of the efficiency 62

D Unfolding 63 D.I Point source 63

E Wave programs 65 E.I The point source unfolding 65 E.2 The in-situ unfolding 66 E.3 Fixing the vector with the measured spectrum 68 E.4 Making the matrix 69 Preface

This work is a master thesis within the Physical Engineering program at Umea University and is done at the department of nuclear weapon issues and radiation science within the Na- tional Defence Research Establishment (FOA) in Umea. Su- pervisor is Thomas Ulvsand together with Goran Agren and Kenneth Lidstrom. The examinator is Lennart Olofsson, department of radiation physics at Umea University. The author likes to thank all of the above for the help with this work and Hans Holmstrom for patience and help with UNIX and computer related questions.

vn Chapter 1

Introduction

There is a need for efficient methods to determine radioactiv- ity in the environment e.g. after nuclear accidents or for large area surveys. One such method is gamma-ray spectrometry performed in the contaminated environment, so called in-situ spectrometry. The measurements are done near the radioactive source and usually one meter above the ground. This kind of spectrometry is used to determine the activity levels in the ground or in the air. The method of in-situ gamma-ray spectrometry has been widely used after the reactor accidents at Three Mile Island (USA, 1979) and Chernobyl (USSR, 1986). Especially the latter convinced many of the necessity for quick and reliable methods to determine radionuclide contamination. Perhaps even more important for the spread of the method is the de- velopment of portable high purity germanium detectors that are easy to handle and available at a reasonable cost. A de- scription of these detectors is found in section 2.3 below. To judge the biological effect the radiation has on for example humans it is of interest to find the radionuclide specific as opposed to the total dose rate in an area. So in some applications of radiation protection it would desirable to measure the radionuclide specific dose rate distribution directly by in-situ gamma-ray spectrometry. The result of a measurement with a germanium detector is a pulse-height distribution which represents the spectral distribution of the energy deposition events in its active volume. A substantial fraction of these events corresponds to photons that only deposited a fraction of their incoming energy. Also, the detector dis-

1 CHAPTER 1. INTRODUCTION turbs the measurements due to interaction between the incoming photons and the detector housing and cooling system. This leads to a superposition of counts coming from full energy deposition of radiation scattered in the environment with counts corresponding to partial energy deposition events (section 2.2). All this has to be taken in to account in order to obtain the photon fiuence rate spectrum and consequently the dose rate spectrum. By applying an unfolding procedure to the measured pulse- height distribution, in which the partial energy deposition events are subtracted, a conversion to fiuence is made. This unfolding procedure requires an accurate and detailed knowledge of the response of the detector to monoenergetic photons of energies in the range of the spectrum. The theoretical background to the unfolding and how the response function can be calculated using Monte Carlo methods is described in chapter 3. The goal of the present work is to determine the response function, for one of the two germanium detectors in use at department 41, and to unfold a measured spectrum. One widely used general purpose Monte Carlo package is EGS4, (Electron Gamma Shower version 4), and it is described in chapter 4 together with the usercode DOSRZ that is used in this work to sample the pulse-height distribution in a model of the detector. Chapter 5 describes the calculations, choice of input parameters, how the model of the detector evolved, etc. Chapter 6 describes the actual unfolding where comparisons are made with some indoor measurements of a point source and with an in-situ measurement. It also includes a discussion on the angular dependence of the response function. The conclusions are in chapter 7 and also a discussion on how this method can be used and how this work can be further developed. Chapter 2

Gamma-ray spectrometry

2.1 Photon interactions

The detection of any ionizing particle or radiation depends upon the ionization and excitation produced in the detector material. Charged particles produce a signal within a detector by directly ionizing and exciting the detector material. Since photons are uncharged gamma-ray detection depends on interactions which transfer the gamma-ray energy to electrons which then can ionize the detector material. Gamma-rays interact with the material through elastic (coherent) scattering and through inelastic processes. Only the latter contribute to absorption of energy when energy transfers to the material via energetic electrons and positrons. The inelastic processes are: • photoelectric absorption - total absorption of the gamma energy possibly followed by flourescent X-rays, • Compton scattering - a partial absorption of the energy, • pair production - total absorption followed by possible total or partial loss of annihilation quanta. In [8] and [10] detailed descriptions of these interactions are given.

2.1.1 Photoelectric absorption The photoelectric absorption, PE, originates from interaction between the gamma photon and one of the bound electrons in CHAPTER 2. GAMMA-RAY SPECTROMETRY

Figure 2.1 Photoelectric absorption (PE)

the material. The electron is thrown out from its shell with

the kinetic energy Ee given by

Ee = E~y — Eb (2-1)

where Ey is the photon energy and Et, is the binding energy of the electron (fig. 2.1). The probability, per atom, that the photon will undergo photoelectric absorption can be expressed as a cross section, a and depends heavily on the atomic number of the absorbing material. In fact a oc Zn (2.2)

where n varies between 4 and 5.

2.1.2 Compton scattering

Photons interact with an electron and the energy is partially transfered according to

F — F — F1 (0 %\

or rather

v\\ 57 I (2-4) i i is-,(l —cost/) I \ / 1 + meC2 / where 6 is the scattering angle, E' is the energy of the scat- 2 tered photon and mec is the electron rest energy (511 keV). This interaction is called Compton scattering, CS (fig. 2.2). The probability for CS per atom increases linearly with Z. 2.1. PHOTON INTERACTIONS

Figure 2.2 Compton scattering (CS) E,

2.1.3 Pair production

Pair production, PP, (fig. 2.3) occurs in the strong Coulomb field close to the nucleus and leads to the creation of an electron-positron pair. The gamma energy must be at least twice the electron rest energy (2 x 511 keV) for this to occur but in practice it has to be much higher than that. The energy that exceeds the combined electron and positron mass is

Figure 2.3 Pair production (PP)

E. 7511

7511 CHAPTER 2. GAMMA-RAY SPECTROMETRY

split between them (eq. 2.5).

2 Ee- + Ee+ = £7 - 2 x mec (2.5)

The slowed down positron will eventually meet an electron and they annihilate. This will free two so called annihilation photons, each with the energy 511 keV, which are emitted in opposite directions. The probability for PP per nucleus varies approximately as the square of Z.

2.2 Contributions to the detector response

These interactions all contribute in different ways to the detector response which means that they add different features to the measured spectrum.

Figure 2.4 A very large detector where all the energy is absorbed.

/\r- 2.2. CONTRIBUTIONS TO THE DETECTOR RESPONSE

Figure 2.5 Absorption of all the incident energy results in a full energy peak Counts All events corresponding to that per f energy. channel

Detector response (energy absorbed)

2.2.1 The very large detector If the detector is large enough, i.e. the size of the volume is large compared with the mean free path of the photons (in the relevant energy range), maybe three to four decimeters, the incident gamma energy will be totally absorbed. In figure 2.4 some representative course of events are illustrated. Within the time scale of the detector all of these events take place instantaneously and the result is a full energy peak corresponding to the incident photon energy (fig 2.5).

2.2.2 The very small detector A small detector is a detector where the dimensions are much smaller then the photon mean free path, typically a couple of centimeters. One contribution to the spectrum is the Comp- ton edge and continuum that originates from single Compton events where the scattered photons leave the detector (fig. 2.6). From the pair production there is the double escape peak 2 (at E = hv — 2mec ) due to the fact that both of the annihila- CHAPTER 2. GAMMA-RAY SPECTROMETRY

Figure 2.6 The small detector, only photoelectric absorption per contributes to the full channel energy peak. Other PP double escape PE interactions take place once and emitted photons 7511 escape.

7511 Detector response (energy absorbed)

tion photons will escape the detector. The full energy peak is the result of photoelectric absorption only, sometimes called the photo peak, and it is less intense than the full energy peak in the large detector case.

2.2.3 The real detector A real detector is somewhere in between in size, around five to ten centimeters normally, and this fact creates a spectrum with a mixture of features from the large and small detectors with some additions. A pair production event can now lead to a double escape peak, as above, but can also lead to a so called 2 single escape peak (at E — hv — raec )because only one of the annihilation photons escapes. Multiple Compton events can occure and this leads to a filling in of the area between the Comptom edge and the full energy peak (fig. 2.7). The gamma ray can also interact with the detector surroundings such as the casing and this adds even further to the detector response. Compton events where the photon is scattered at a large angle, between 120° and 180°, result in a backscatter peak around 200 keV (eq. 2.6).

hv (2.6)

The annihilation peak att E = 511 keV appears because of pair production interactions outside of the detector where one of the annihilation photons is emitted towards and then absorbed by the detector. 2.2. CONTRIBUTIONS TO THE DETECTOR RESPONSE

Figure 2.7 The real detector with the two escape peaks and the PE 7 CS filling in between the PP pp Compton edge and the full 1 pp single escape energy peak. double escape

7511 Detector respons (energy absorbed)

Figure 2.8 is a spectrum, from the calculations which are part of this work, where the incident photons have the energy 2 MeV. Here all the features described above can be seen. From left to right; the backscatter peak, the annihilation peak, the double escape and the single escape peaks, the Compton edge and last the full energy peak. Also clearly visible is the Compton continuum and the filling in between the Compton edge and the full energy peak, the latter due to multiple scattered photons.

2.2.4 Summing up the detector response

An ideal, very large detector's response would contain full energy peaks only corresponding to the energies emitted by the source. In a real detector incomplete absorption of the gamma energies leads to other features appearing in the spectrum. The loss of an exact amount of energy leads to peaks like the escape peaks while random losses give rise to a continuum. The degree of incomplete absorption depends on the physical size of the detector and on the energy of the incident gamma radiation. A large detector offers more space for multiple scattering and a low gamma ray energy leads to a greater probability for complete absorption via photoelectric absorption. 10 CHAPTER 2. GAMMA-RAY SPECTROMETRY

Figure 2.8 All the features of the detector response function. The width of the peaks is full energy 10.0 (hi/) due to the discrete 10 keV intervals (bins) in the calculations. single escape pepeak; 1 (hv — 511 ke'

ublc escape peak *\ | . c 1.0

j il 500 1000 1500 2000 Energy [keV]

2.3 Semiconductor detectors

As described above there are several interactions which transfers energy from the gamma-ray to the electrons. These particles loose their kinetic energy by scattering within the detector, creating ionized atoms and ion pairs. This population of secondary entities forms the basis of the detector signal. There are a few requirements for an ideal detector [8]: • Output should be proportional to gamma-ray energy

• Good efficiency (high absorption coefficient)

• Easy mechanism for detector signal collecting

• Good energy resolution

• Good stability over time, temperature and operating parameters • Reasonable cost and size

Good efficiency means a reasonable probability of complete absorption and in principle this is true if the detector is large 2.3. SEMICONDUCTOR DETECTORS 11

enough but in practice we want complete absorption within an achievable size. As described in section 2.1 the cross section for the photoelectric absorption is very dependent on the atomic number of the material used in the detector. The probability for both Compton scattering and pair production increases with the atomic number, although not as strongly, so this would suggest that a high atomic number material should be used for the detector [8]. Having absorbed the gamma-ray and created many charged particles the detector material must allow the charge to be col- lected in some manner and presented as an electrical signal. This can be done with a reversed biased diod. In the diod there is a depletion area where there are no free carriers, i.e. no current. But when the gamma-ray interacts with the material it is ionized and free carriers are created and therefor current that can be detected. This is the basis of the semiconductor detector.

2.3.1 The portable high purity germanium detector Germanium is the most common detector material. Its rel- atively high atomic number (32) makes it suitable for the detection of high energy gamma radiation. The drawback is

Figure 2.9 Common Ge-detector types. 7-ray

coaxial coaxial well p-type n-type p-type n planar contact contact active volume 12 CHAPTER 2. GAMMA-RAY SPECTROMETRY

that the germanium detector has an operating temperature of 77K and because of that a container with liquid nitrogene, or an electric cooling device, has to be added to the detector to cool it during use. There are other materials that operate at room temperature but germanium has other advantages such as a small band gap and high electron and hole mobility (ref. [4], [8] and [10]). Germanium detectors are available in a number of different configurations to suit particular applications. In figure 2.9 some common detector types are shown. At low energies the gamma-ray absorption coefficient is very high and high efficiency is expected but this is limited by absorption of the photons before they reach the detector itself. We can expect absorption in the detector cap and in the contact layer on the side of the detector facing the incoming radiation. The typical lithium n+ contact produces a dead layer of impure germanium about 700 ^m thick. In contrast the dead layer caused by the ion-implanted p+ contact is only 0.3 /um thick (see for example the data sheet in apendix A). As seen in figure 2.9 the thick n+ contact is on the outer surface of the p-type detector. If the n+ contact is on the inside of the detector and the very thin p+ contact, which can be made by ion-implantation of boron, is on the outside then the detector is known as reverse electrode detector. This is also called an n-type detector. The closed-end p-type coaxial detector, mounted in a aluminum cap, could be called a standard configuration. This type of detector, with its outer 700 fjm n+ contact, cannot be used much below 40 keV [8]. The detector concerned in this

Figure 2.10

The weak regions are weak regions bullet shape removed giving the detector its bullet like shape. 2.3. SEMICONDUCTOR DETECTORS 13

work is of this type. The n-type detector has advantages over the p-type but is much more expensive. Originally these closed-end coaxial detectors were manu- fatured with a complete cylindrical shape but it was realized that in such detectors there were regions of especially low field. Particular problems were recognized in the corner regions on the detector face. The practical solution to this is to remove those regions giving the detector its bullet like shape (fig. 2.10). 14 CHAPTER 2. GAMMA-RAY SPECTROMETRY Chapter 3

The theory of unfolding the response function

3.1 The unfolding

The relation between the pulse height distribution and the incident photon fluence is described by the response function, RhlE-y), of the detector. This is defined as the probability per unit pulse height that a photon fiuence incident with the energy E^ will produce a pulse of height h. In general, the response function RhiE-y) can be expressed as an integration

= J D{E, E^)Gh{E)dE (3.1) where D is the probability that photons with energy E1 deposits the energy E in the detector crystal, per unit energy (E) and per incident fluence. Gh(E) is the probability per unit pulse height that a deposited energy E will give rise to a pulse of height h (fig. 3.1). The resolution function Gh(E) is a measure of the efficiency and statistics of the signal collec- tion and processing in the detector and can be approximated by a Gaussian distribution [4]. In this work it is assumed that Gh{E) is a narrow (practically a delta function) Gaussian of the form

where s is the standard deviation, h is the pulse height and hp(E) the peak height for the energy E. hp(E) is calibrated

15 16 CHAPTER 3. THE THEORY OF UNFOLDING THE RESPONSE FUNCTION

from each spectrum using peaks of known photon energy (e cesium - 662 kEv).

Figure 3.1 a) The absorbed energy in the detector leads to b) a registered pulse of a height E1 h that has c) a certain /W\/» probability Gh- I '-•> kp(E)

a) c)

Procedures for spectrum unfolding are based on the relationship between the measured pulse height distribution and the distribution of the photon fluence ^>{Ey) in energy

Nh = I Rh{E1)

dEi (3.4)

hp(E.) Nhdh (3.5)

and (3.6)

then equation 3.3 becomes

(3.7)

The summation extends over the number of energy bins of the spectrum. The j-th column of the response matrix, i?,j, represents the response, distributed over n bins, to photons whose energy corresponds to the j-th bin of the spectrum (fig. 3.2). ifj is the photon fluence in the j-th energy bin. 3.2. HOW TO FIND THE INHERENT RESPONSE FUNCTION 17

Figure 3.2 Building the response matrix

From equation 3.7 the photon fiuence can be determined directly by matrix inversion

(3.8)

This method can be applied if the respons functions have been determined with sufficient precision and the statistical uncer- tainties in the data are small. Otherwise it can lead to large oscillations, and eventually significant negative components, of the derived spectrum.

3.2 How to find the inherent response function

Detector response functions for selected energies can be obtained by using monoenergetic gamma-ray sources. However, these measurements can only be made for a limited number of energies so that a procedure for interpolating between and extrapolating from the measured response function is needed in order to obtain the full set of response functions necessary for the unfolding. One problem in the experimental determination of the detector response function is the presence of contributions to the response coming from photons that have scattered in the material of the source and its encapsulation, as well as surroundings of the place of measurements. 18 CHAPTER 3. THE THEORY OF UNFOLDING THE RESPONSE FUNCTION

Alternatively, the response functions can be calculated by Monte Carlo simulation of the particle transport in the detector. The calculations can be made for as many photon energies as necessary, so that there is no need to determine response functions by interpolation. For Nal-detectors and Ge(Li)-detectors the limited knowledge of the true shape of the sensitive volume, due to dead layers, leads to uncertain- ties in the calculated efficiencies unless the sensitive volume is determined by experiments. However, for high purity germanium detectors dead layers are present only at the n-f- contact the thickness of which can be specified fairly well by the manufacturers. Therefore, particularly for the n-type detectors, where this layer is in the hole inside of the detector crystal, the detector response function can be calculated with a good degree of accuracy by Monte Carlo simulation of the photon transport [4]. To do this its essential to know the precise shape and dimension of the detector crystal. The housing and cryo- stat of the detector should be included in the simulation too ([11] and [7]). The peak response (counts in the full-energy peak divided by the particle fluence) depends on the angle of incidence of the radiation on the detector. Furthermore, the partial energy deposition events of the response function depend on the incidence direction too. For detectors with a length-to-diameter ratio much different from unity, an even larger dependence of the response function of the angle of incidence is to be expected. This dependence has to be taken into account when determining the set of response functions to be used for the unfolding. In this work the unfolding procedure is used with response functions calculated with Monte Carlo methods. Chapter 4 EGS4 - The Monte Carlo package

The EGS4 (Electron Gamma Shower version 4) Code System [13] is a general purpose package for the Monte Carlo simulation of the coupled transport of electrons and photons in an arbitrary geometry for particles with energies above a few keV up to several TeV. It has been extensively benchmarked against experimental data.

4.1 A summary of capabilities and features

The radiation transport of electrons or photons can be sim- ulated in any element, compound or mixture. That is, the data preparation package, PEGS4, creates data to be used by EGS4, using cross section tables for elements 1 through 100. The following are some of the physics processes that are taken into account by the EGS4 Code System:

• Bremsstrahlung production.

• Positron annihilation in flight and at rest (the annihilation quanta are followed to completion).

• Moller (electron-electron) and Bhabha (positron-electron) scattering. Exact rather than asymptotic formulae are used.

19 20 CHAPTER 4. EGS4 - THE MONTE CARLO PACKAGE

• Pair production.

• Compton scattering.

• Photoelectric effect.

4.2 How to use EGS4

There must be a User Code. This code is a MAIN program including the subroutines HOWFAR and AUSGAB to determine geometry and output respectively. Additional auxiliary subprograms can be included according to the needs of the user. Usually MAIN will perform any initialization needed for the geometry routine, HOWFAR, and will set the values of certain EGS COMMON variables specifying things like the name of the media to be used, the desired cutoff energies and the distance units to be used (e.g. inches, centimeters, radiation length, etc.). MAIN then calls the subroutine HATCH which "hatches EGS" by doing once only initializations and reading material data from sets created by PEGS. MAIN will then call SHOWER and each such call will result in the gener- ation of one history. The arguments to SHOWER specify the parameters (e.g. charge, position, energy etc.) of the incident particle initiating the cascade, one such user code is DOSRZ described in section 4.4 below.

In short the user communicates with EGS through

1. Subroutines

• HATCH - to establish media data • SHOWER - to initiate the cascade • HOWFAR - to specify the geometry • AUSGAB - to score and output the result 2. COMMON blocks - by changing values of variables

3. Macro definitions - redefinition of predefined features. 4.3. PEGS4 - DATA PREPARATION 21

Figure 4.1 EGS4 flow chart. Information ^\ I Control ) ( Exttacted ] From Shower y

( Block *\ Dala ) (Dotauh) y

4.3 PEGS4 - data preparation PEGS4 is a stand alone data preprocessing code consisting of twelve subroutines and 85 functions. The output is in a form for direct use in EGS4. To be able to run EGS4 the elements (or compounds or mixtures) to be used must be specified in the user code or in some input to it. Either already existing data files can be used or PEGS4 has to be run to create the necessary datafiles. In general the user need to use PEGS4 only once to obtain the media data files required by EGS4. To create a data file with the cross section data for a particular element, compound or mixture a PEGS4 input file is made. The following is an example from this work and it is the input file for liquid nitrogen 22 CHAPTER 4. EGS4 - THE MONTE CARLO PACKAGE

COMP &INP NE=2,RH0=0.808,PZ=l,l,IAPRIM=l &END NITROGENLIQUID N N EMER &INP AE=0.521,UE=55.511,AP=0.01,UP=55. &END PWLF &INP &END DECK &INP &END

where a compound is specified (COMP). Next line gives, for example, the number of elements and their densities, and line four gives the symbol for each element which of course here is only nitrogene. On line six the upper and lower cut-off energies are specified. How to use PEGS4 is described in detail in reference [12] and [13].

4.4 DOSRZ - a User Code

This code simulates the passage of an electron or photon beam in a cylindrical geometry. It can score pulse height distri- butions in an arbitrary volume made up of any number of regions. The energy deposited within various user defined regions is scored and analyzed statistically following the simulation. The user

• defines the geometry of the target via the input of a number of planar and cylindrical coordinates which di- vide the cylinder into a number of regions, each region composed of a user specified material (fig. 4.2),

• specifies in which regions the pulse height distribution is to be scored,

• selects either the energy, if a monoenergetic beam is to be used, or specifies an energy spectrum,

• selects the source of radiation from amongst parallel beam and point sources originating from the side or 4.4. DOSRZ - A USER CODE 23

front or isotropically raditing sources embedded in the cylinder,

selects the number of histories, the time limit and statistical limit,

selects transport controls such as the fractional energy loss per charged particle step, the maximum step size, particle energy cutoffs and range rejection parameters,

Figure 4.2 The first region is outside the gridsystem that starts NR ((NR-1) ((NR-1) ((NR-1) with region no 2 in the left NR*NZ *NZ)+2 *NZ)+3 *NZ)+4 bottom corner. NZ: the ... NR*NZ +1 number of planar slabs. NR: the number of radii

NZ+2 NZ+3 NZ+4 2NZ 2NZ+1 1

2 3 4 NZ NZ+1

When "scoring the pulse height distribution" is selected, in DOSRZ, the size of the energy bins (intervals) in the output has to be chosen. Either all bins are equal (default is 10 keV) or the the bins are indiviually specified with the top of each bin. For the statistical analysis of the peak efficiencies a AE can be chosen (default is 5 keV). The number of histories chosen is divided into ten batches to make statistical analysis possible e.g. 20 million histories means 10 batches of 2 million histories each. All of these parameters are set in a input file called X.egs4inp. When the calculations are done the output is spread out onto different files the two important ones in this work being the 24 CHAPTER 4. EGS4 - THE MONTE CARLO PACKAGE

files with the extensions .egs4lst, which lists the run - its various inputs and output in a verbose way, and .egs4eff which holds the actual pulse height distribution calculated, together with the total efficiency. There is a .egs4inp, .egs41st and a .egs4eff for every run (every incident energy) made. In appendix B the three file types are listed for an incident energy of 2 MEv. Chapter 5 Calculations

5.1 The detector model

As mentioned above DOSRZ works with a cylindrical geometry which is suitable when modelling a portable high purity germanium detector. The detector used in this work is a p-type with 50% relative efficiency (Pop-Top from EG&G ORTEC). To be able to describe the detector accurately it is X-rayed, and a data sheet is obtained from the manufacturers giving the dimensions and the material used for the detector and housing. All detail on the detector is found in appendix A. There is no detailed data sheet obtainable for the liquid nitrogen container but a simple model is made based on the inner and outer volume and a general knowledge (ref. [8] and

Figure 5.1 A simple model of the liquid nitrogen container and the cooling rod.

vaccuum copper liquid nitrogen I aluminum

25 26 CHAPTER 5. CALCULATIONS

Figure 5.2 Above: the simple germanium cylinder 10 detector and the spectrum it gives rise to. Below: The spectrum when a aluminum disc is added behind the cylinder.

200 400 600 Energy [keV]

germanium cylinder with aluminum disc

200 400 600 Energy [keV]

[10]) of how these containers are built (fig. 5.1). The first very simple model of the detector is only a solid germanium cylinder. After that an aluminum disc is added behind the detector. As soon as the disc is introduced a 5.1. THE DETECTOR MODEL 27

Figure 5.3 The geometric model (above) of the detector, used in the calculations, compared with the real detector (below) where the bullet shape can be seen

germanium mylar aluminum

lithium copper stainless steel

CCmtM.CONTACT PS

backscatter peak appears just below 200 keV (incident energy is 662 keV) (fig. 5.2). Similar observations have been made by several research teams e.g. in [11], [7] and [14]. A more complex model of the detector is now built. In figure 5.3 the difference between the model and the real detector is shown. The real germanium crystal has a bullet form whereas the model is a right cylinder. Also behind the 28 CHAPTER 5. CALCULATIONS

Figure 5.4 Trial runs are made with a point source at five different angles, one meter from a reference point just inside the germanium.

-O 90°

\ s \

60°

45° o o 30° 0°

detector part there is a more complicated, not symmetrical, geometry in the real detector. Here is the molecular sieve, some electronics, screws etc. All these things are just ignored in the model. What the geometry used in DOSRZ actually looks like, with all the numbered regions, is shown in appendix C. Five runs are done with a point source of 662 keV at five different angles from the detector. The angles chosen are 0°, 30°, 45°, 60° and 90° (fig. 5.4). In figure 5.5 the response from the five runs are plotted in the same graph. The angular dependence of the backscatter peak is clearly visible. There 5.1. THE DETECTOR MODEL 29

Figure 5.5 The backscatter peaks originating from the five Bockscotter, onqular dependence different angles. Inserted is a zoomed out view of the spectra.

0.5 0.2 0.4 Energy [MeV]

is a sharp peak when the source is straight in front of the detector face which is flattening out as the source is moved to the side. These calculations are done with 20 million histories.

An indoor measurement is performed at department 41, FOA Umea, by Thomas Ulvsand and Kenneth Lidstrom using a Cs-137 point source. The point source is mounted in a case that is part of the Swedish Armed Force's test equipment (dose rate meter 1-25) and the uncertainty is given as "approximately 1.5 MBq" (appendix D). The distance between the source and a point just inside the germanium is one meter. The peak response is calculated for the model and compared with the empirical values (fig. 5.6). The calculated values are higher by around 10 %. This is possibly due to that the dead layer of the p-type detector is not exactly known, and also that the model needs to be described in more detail e.g. with the bullet shape added. Details of the empirical values are in appendix C. 30 CHAPTER 5. CALCULATIONS

Figure 5.6 Comparison between peak response from the 1 1 1 1 1 1 1 ' ' 1 ' 1 calculations (diamond shapes) with empirical values (triangles). The calculated values are 1x10 - 0 between 5-10 % higher © O than the empirical. 1

A A A -

-5 3x10 1 1 1 0.0 0.5 1.0 1.5 Angle [rad]

5.2 Input parameters

The matrix of respons functions is built up in steps of 10 keV for the energies 10 keV to 2 MeV and for the four different angles; 0°, 30°, 45° and 60°. 90° is left out here because of the situation in a normal in-situ measurement where the radioactive source is spread out on the ground beneath the detector (fig. 5.7). 30 million histories is chosen that gives a statistical uncertainty of less than 0.5 % in the full energy peak and below 2 % for the rest of the respons function. The source is "Point source off axis", one of the available in DOSRZ. This choice makes it possible to place the source anywhere around the detector as seen in figure 5.4. The distance from the z-axis and the perpendicular distance from the face of the detector are used as input. The idea behind using the point source is to have as pure response functions as possible; one monoenergetic point source for each run building up a "finger print" for that particular detector, then repeating this for a number of different angles for comparison. DOSRZ is set to sample the pulse height distribution in 5.2. INPUT PARAMETERS 31

Figure 5.7 This is the normal detector set-up for an in-situ measurement. The detector is facing downwards one meter above the ground.

the germanium regions of the model. Other options such as the transport control variables are set to the EGS4 default. 32 CHAPTER 5. CALCULATIONS

5.3 The output

For one incident gamma energy the total count in the detector can be expressed as the product between the fluence, tp, and the total probability, Dtot-, that an incident photon causes an event in the detector, like this

N = Dtat

Dtot{E7) = / ** D(E,E~)dE (5.2) Jo where E1 is the energy of the incident photons. For a point source, with activity A at a distance r from the detector, the fluence is

so that

N = Dtot-^-2 p (5.4) 4nr2 where p is the abundance, that is the fraction of the decay that leads to the emission of a photon. One of the outputs from DOSRZ is the total efficiency, 77, defined as the probability that a photon leaving the source will cause an event. With the notation introduced above;

Combining this with eq. 5.4 yields

2 Dtot = Vr (5.6) The other output from DOSRZ is the normalized probability that photons with the incident energy E^ deposits the energy E in the detector crystal

^ (5.7) utot that is = 1. (5.8) Jo 5.3. THE OUTPUT 33

In other words, D is the detector respons that where sought after and is given as a histogram with a bin width that is determined in the input to DOSRZ. For one energy bin the following is true (compare this with eq. 3.3) N(E)= D(E,EJtp(EJdE^ (5.9) JE where tp(E^) is a delta function which only has a value at the incident energy, this and eq. 5.6 and eq. 5.7 now gives

N(E) = / Dr2-q(E^{E^)dE^ (5.10) JE Following the discussion in chapter 3 the response matrix will take the form

2 RZJ = r r], /' TJ(E,Ey)dE. (5.11) J E%—\ Equation 5.8, the fact that

¥> = —. (5.13) V 34 CHAPTERS. CALCULATIONS Chapter 6 Results of the unfolding

6.1 The procedure

The unfolding in this work is done with PV-WAVE (Visual Numerics). The different spectra are read from the DOSR.Z output files and written to a separate file. The spectrum to be unfolded is read into a vector with dimensions and energy bins corresponding to the calculated matrix. The matrix is inverted, using the function INVERT in WAVE (which uses the Gaussian elimination method), and the measured vector is multiplied with the inverse. A vector with the total efficiencies from each run, each incident photon energy, is created and the result from the matrix multiplication is divided (scalarly) with these efficiencies. What is left now is the unfolded measured spectrum from which fluence rate and dose rate can be calculated.

6.2 Comparison with point source measurements

The procedure described above was applied to the cesium-137 point source measurement. The activity of the cesium used was 1.5 MBq and should yield a fluence rate of

y = -A-0.85 = L5Xl°60.85 = 1.01 x lO^-V1 (6.1) Airr2 Arc where r2 = 1 and 0.85 stems from the fact that only 85 % of the cesium decay results in the characteristic 662 keV (the

35 36 CHAPTER 6. RESULTS OF THE UNFOLDING

abundance). The result of the unfolding is 1 (p = 1.06 x K^m-V (6.2) which is around 5 % higher. The uncertainty in the point source activity is much larger (see appendix D). In fig. 6.1 the measured spectrum together with the unfolded can be seen. The peaks are normalized to the fluence rate of the unfolded spectrum. It is clear that most of the backscatter peak has vanished with the unfolding. The remaining peak is due to the fact that the source is mounted in a little case.

Figure 6.1 Point source spectrum 1.2x10 together with unfolded 1.0x10 - spectrum. Normalized to the calculated full energy 8.0x10' peak. The measured spectra - dotted line, the 6.0x10 - unfolded spectra - solid line. 2 4.0x10 -

2.0x10 -

0 ^

-2.0x10 200 400 600 800 I 000 Energy [keV]

6.3 In-situ measurements and angular dependence

In-situ measurements were done in Finland 1995 [5] and one spectrum was chosen (shell 2, point 5) to be unfolded. In fig. 6.2 the result can be viewed. To calculate the dose rate A . Men JJ = if (6.3) P is used where ^^ is the energy absorption coefficient of air and hu is the energy in that particular interval. Calculating 6.4. DISCUSSION 37

Incidence from front. Doserote = 2.29429e-007 Gy/h Figure 6.2 , 1 , , , 1 , ^—, , , , , , ,—u— In-situ measurements from Finland 1995 together with 4.0X1CT - ; the unfolded spectrum. Normalized to the calculated full energy peak. 3.0x10 The measured spectra - dotted line, the unfolded 2.0x10 spectra - solid line.

l.Oxio4 i-

200 400 600 800 1000 Energy [keV]

the dose rate in this way yields the dose rate 0.21 /uGy/h using the matrix for the 45° angle and 0.23 fxGy/h for 0°. Dose rate measurements were done at the same place with a GM-tube equipped dose rate meter (RNI10) which is calibrated to show ambient dose equivalent. The relationship between doserate and ambient doserate equivalent (for cesium-137) is

1 Gy/h = 1.2 Sv/h (6.4)

(reference [1] and [3]). The mean of the readings in Fin- land is 0.20/j,Sv/h which corresponds to 0.17/uGy/h for Cs-137 gamma radiation. This means that the dose is overestimated by about 35 % when the radiation is incident from the front and 24 % at a 45° angle.

6.4 Discussion Since the uncertainty in the measurements of the equivalent dose, in Finland, is as high as 20 % and the uncertainty in the activity of the point source is about as high it is very difficult to verify the results of the calculations. It would be interesting to try to test these results against some other measurements as well to evaluate them further. CHAPTER 6. RESULTS OF THE UNFOLDING Chapter 7 Conclusions

The result of this work indicates that the efficiencies are overestimated and that, in turn, should mean that the fluence and dose should be underestimated but, as seen above, this is not the case. It is not possible, from the two tests, to say whether or not the results are good or bad. Despite this, the method could be used as-is since the accuracy of this method compares to methods already in use. Bearing in mind that this method gives the nuclide specific dose it could still be useful, in radiation protection, since knowing how the relations between different nuclides are and how they change is very important when estimating the risks.

7.1 Further developments

Suggested developments that would make this method better and more accessible: • The angular dependence should be further investigated and probably used somehow in the unfolding procedure.

• Some sort of statistical weighting might be useful, an- other Gh approximation (see chapter 3). • A user friendly program for unfolding measured spectra and calculate dose is needed.

• Perform the calculations for any other detector in use.

39 40 CHAPTER 7. CONCLUSIONS Bibliography

[1] Determination of dose equivalents from external radiation sources-part 2. Technical Report 43, ICRU - Inter- national Commision on Radiation Units and Measure- ments, ICRU Publications, Maryland, USA.

[2] Radiation quantities and units. Technical Report 33, ICRU - International Commision on Radiation Units and Measurements, ICRU Publications, Maryland, USA, 1980.

[3] Beta, X and gamma radiation dose equivalent and dose equivalent rate meters for use in radiation protection. Technical Report CEI/IEC 846, Norme interna- tionale/International standard, 1989.

[4] Gamma-ray spectrometry in the environment. Technical Report 53, ICRU - International Commision on Radia- tion Units and Measurements, ICRU Publications, Mary- land, USA, 1994.

[5] Resume 95 - Rapid Environmental Surveying Using Mo- bile Equipment. Technical report, Nordic Nuclear Safety Research, Copenhagen, 1997.

[6] A.J. Cook. Mortran3 user's guide. Technical report, SLAC Computation Research Group Technical Memo- randum CGTM-209, 1983.

[7] Georg Fehrenbacher [Reinhard Meckbach] [Peter Jacob]. Unfolding of the respons of a Ge detector used for in- situ gamma-ray spectrometry. Nuclear Instruments & Methods in Physics Research, A383:454-462, 1996.

41 42 BIBLIOGRAPHY

[8] Gordon Gilmore [John Hemingway]. Practical Gamma- ray Spectrometry. John Wiley & Sons, 1995.

[9] J.R. Hook [H.E. Hall]. Solid state physics. John Wiley h sons, 2nd edition, 1991.

[10] Glenn F. Knoll. Radiation detection and measurement. John Wiley k Sons, 1979.

[11] R Meckbach [P. Jacob]. Unfolding of Ge-detector response by Monte Carlo simulation and applications in radiation protection. Progress in Nuclear Energy, 24:321- 326, 1990.

[12] W.R. Nelson. PEGS4 - data sets for different media. Stanford linear accelerator center - lecture notes.

[13] Walter R. Nelson [Hideo Hirayama] [David W. 0. Rogers]. The EGS4 code system. Technical report, Stanford Linear Accelerator Center — SLAC-Report-265, 1985.

[14] D.W.O. Rogers. More realistic Monte Carlo calculations of photon detector response functions. Nuclear Instru- ments and Methods, 199:531-548, 1982. Appendix A Detector data

43 44 APPENDIX A. DETECTOR DATA

Figure A.I Data sheet from the manufacturers, EG&G ORTEC 45

Figure A.2 Quality assurance data sheet 'r Si

wsrModes; Ms.

sm9Smw^Sk::::.'.'... j. JV^V;'-'::':'-.-.;.;:;:-:-::':"-'

Jfysts! • %st ' f •

vr^m^M^^^

W&i *•?*%&*:?.

1000 v5 46 APPENDIX A. DETECTOR DATA

Figure A.3 Exploded view of the same type detector as in this work 47

Figure A.4 X-ray image of the detector. The image is inverted. 48 APPENDIX A. DETECTOR DATA Appendix B Input and output from EGS4

B.I .egs4inp

2 HoV photons from 30 degress (HBO 3JC10«»7 histories 0, 0, 0, 1, 1, 0 30000000., 97, 33, 12.99, 2, 0.01, 0 0 27 0.0 0.10 0.50 0.5025 O.S050 0.5750 1.7950 6.3650 10.2650 10.5850 10.9050 11.5450 11.8650 13.1650 16.8310 18.3910 19.7170 24.6310 25.9310 27.9310 28.9310 30.9310 31.9310 53.0 65.9310 66.9310 68.9310 69.9310 16 0.3150 0.490 0.5840 1.0530 1.650 3.4250 3.4950 3.5450 3.8950 3.9950 4.1250 4.150 7.250 8.250 10.250

49 50 APPENDIX B. INP UT AND 0 UTP UT FROM EGS4

11 .250 1, 1. 1 , 1 7 GERHAHIUH ALUHIDUK COPPER HYLAR LIIHIUH NITROGEII.LIQUID STEEL.SIAIKLESS 0, 3, 3 0, 12. 12 0, 14. 14 0, 27, 27 0, 30, 30 0, 35, 36 0, 39, 39 0, 41, 41 0. 54. 54 0, 57. 57 0, 63, 63 0, 66. 66 0, 68. 68 0. 81. 81 0, 84. 84 0. 90, 90 0, 93. 93 0, 95, 97 0, 99. 99 0, 103, 103 0, 108, 108 0, 111, 111 0, 117, 118 0, 120, 120 0, 122, 124 0, 126, 126 0, 130, 130 0. 135, 135 0, 138, 138 0, 144, 145 0. 147, 147 0, 149, 151 0, 153, 153 0, 157, 157 0, 162, 162 0, 165, 165 0, 171. 172 0, 174. 174 0 , 176, 178 0. 180, 180 0, 182, 182 0. 184, 184 0, 189, 189 0, 192, 192 0, 201, 201 0, 203, 205 0, 207, 207 0, 209, 209 0, 211, 211 0, 216. 216 0, 219, 228 0, 230, 232 0, 234, 234 0, 236, 236 0, 238, 238 0, 243, 243 0, 246, 259 0 , 261, 261 0. 263, 263 0, 265, 265 0, 270, 270 0, 290, 290 0, 292, 292 0, 297,, 297 0, 299,, 312 0, 317 , 317 0. 319 , 319 0. 324 , 324 0, 326 . 344 0, 346 . 346 0, 351 . 351 0. 353 , 371 0, 373 , 373 B.I. .EGS4INP 51

0, 378, 378 0, 380. 398 0, 400, 405 0, 407, 425 1, 7, 7 1, 34, 34 1, 61, 62 1, 88. 89 1. 115, 116 1, 142, 143 2, 2, 2 2. 5, 5 2, 11, 11 2, 13, 13 2. 26, 26 2, 28, 29 2, 32, 32 2. 38, 38 2, 40, 40 2. 53. 53 2, 55. 56 2, 59. 59 2, 65. 65 2, 67. 67 2, 80. 80 2, 82, 83 2, 86, 86 2, 92, 92 2, 94, 94 2, 100, 102 2. 104, 104 2. 107, 107 2, 109, 110 2. 113. 113 2. 119, 119 2, 121, 121 2, 127, 129 2, 131. 131 2, 134, 134 2, 136, 137 2, 140, 140 2, 146, 146 2, 148, 148 2, 154. 156 2, 158. 158 2, 161. 161 2, 163, 164 2. 167. 167 2. 173, 173 2, 175. 175 2, 181. 181 2. 183, 183 2, 185. 185 2. 18S. 188 2, 190, 191 2, 194, 200 2, 202, 202 2, 208, 208 2. 210, 210 2, 212, 212 2. 215, 216 2, 217, 218 2, 229, 229 2. 235, 235 2, 237, 237 2, 239, 239 2, 242, 242 2, 244. 245 2, 262, 262 2, 264, 264 2, 266, 266 2, 269, 269 2. 271, 289 2, 291, 291 2, 293, 293 2, 296, 296 2, 298, 298 2, 313,. 316 2, 318, 318 2, 320, 320 2, 323, 323 2, 325,, 325 2, 345 , 345 52 APPENDIX B. INPUT AND OUTPUT FROM EGS4

2, 347, 347 2, 350, 350 2, 352, 352 2, 372, 372 2, 374. 377 2, 379 . 379 2, 399 , 399 2, 406 , 406 2, 426 , 433 3, 8, 10 3, IE, 24 3, 37, 37 3, 42. 51 3, 64, 64 3, 69, 78 3, 91, 91 4, 4, 4 31, 31 58, 58 85, 85 112. 112 139, 139 166, 166 193, 193 5, 6, 6 S, 33, 33 B, 60, 60 5. 87, 87 5. 114, 114 5. 141. 141 5. 168. 170 6. 25, 25 6, 52, 52 6, 79, 79 6, 105, 106 6. 132, 133 6, 159, 160 6, 186 . 187 6, 213. 214 6, 240, 241 6, 267. 268 6, 294. 295 6, 321 , 322 6, 348, 349 7, 98, 98 7, 125 . 125 7, 152 . 152 7, 179 . 179 7, 206, 206 7, 233 , 233 7, 260. 260 0, 0, 0 7 34 61 62 8£ 89 115 116 142 143 0 0.01000, 0.00500 0, 12, 50.0. 85.60, 0.0, 0.0 0 2.0 0.0. 0 .0, 0.521, 0.010, 0. 0, 0, 2.0, 0 0.0, 0 .0, 0.0 0. 0, 0 0, 0 1 1 1 3 0 0 0, 0, 0, 0, 0.0 B.2. .EGS4LST 53

B.2 .egs4lst

2 HeV photons fron 30 degrees (WBC) 3X10**7 histories

HBOC CALCULATION USING D0SRZCEOS4) DOSRZ V2KSID 1.23) 02 Jan 1997 OK DEC-0SF1/DEC3000/800AXP 11:00:24 Har 21 1998

KOKIE CARLO, rSAKSPaRT. AKD SCATTER COJTROLS

HAX » OF HISTORIES TO RUH 30000000 HAX » OF HISTORIES TO ANALYZE 30000000 IICIDEUT CHARGE 0 INCIDENT XIItETIC ENERGY 2.000 (HoVj FRACTIONAL ELECTRON ENERGY/STEP 1.000 HAXIHUH GLOBAL ELECTROII STEP SIZE 1.000E-HO GLOBAL ELECTRON TRAHSPORT CUT-OFF 0.S21 (HeV) GLOBAL PHOTOH TRANSPORT CUT-OFF O.01O (HeV) PHOTON FORCE INTERACTION SWITCH OFF RANGE REJECTIOH SHITCH OFF REDUCE CALLS TO HOUFAR USIHG DNEAR HAXIHUR CPUTIHE ALLOHED 12.99 (HRS) STATS IN PEAK REGION OBJECTIVE 0.01 X 1ST IIITIAL RAUDOK NUHBER SEED 97 2ND IIITIAL RANDOK NUHBER SEED 33 DISCARD ALL ELECTRODS BELOW: 2.000 IF TOO FAR FROB CLOSEST BOU»DRY » ZONES ELEC ENERGY LOSS/STEP ALTERED NONE « ZONES HAX ELEC STEP SIZE ALTERED NORE KORHAL ELECTRO* TRANSPORT UITH DISCRETE IKTERACTIOIS FLUORESCENT X-RAYS ARE DISCARDED

PRESTA INPUTS ••••* NEW PRESTA PATH-LENGTH CORRECTIOt USED BOUNDARY CROSSIXG ALGORITHK INVOKED BLCHI«= 2.327 LATERAL CORRELATION ALGORITHM INVOKED >EH THXS CALCULATION USED

PRESTA CALCULATED HIPCIHUK STEP SIZES FOR HAXIHUH ENERGY ELECTRONS KEDIUH NO. t,prime,Bin for E=E»ax= 1 0.224E-03 cm 2 0.4S8E-03 c« 3 0.130E-03 ci 4 0.986E-03 en 5 0.331E-02 c» 6 0.167E-02 c» 7 0.142E-03 c«

•>>•« END OF PRESTA INPUTS •••••

HATERIAL SUHHARY 7 HATERIALS USED

II HATERIAL DENSITY(g/c.«»3) AE(U°V) APOIeV) UE(HeV) UP(HeV)

1 GERHA* 5.360E+00 0.521 0.010 55.511 55.000 2 ALUHm 2.702E*00 0.521 0.010 55.511 55.000 3 COPPER 8.933E+00 0.521 0.010 55.511 55.000 4 HYLAR 1.38OE+0O 0.521 0.010 55.511 55.000 5 LITHIU 5.340E-01 0.521 0.010 55.511 55.000 $ NITROG 8.080E-01 0.E21 0.010 55.511 55.000 7 STEEL_ 8.060E*00 0.521 0.010 55.511 55.000

SOURCE PARAHETERS

POINT SOURCE OFF AXIS, RADIAL COORDINATE 50.000 PERPENDICULAR DISTAUCE OF SOURCE FROH FRONT FACE 54 APPENDIX B. INPUT AND OUTPUT FROM EGS4

PULSE HEIGHT DISTRIBUTIOM IS SCORED III THOSE RECIOtS DEIOTED WITH I 1 HO). 2(0), 3(0), 4(0) 5(0), 6(0), 7(1) 8(0) 9(0), 10(0) 11(0), 12(0), 13(0), 14(0) . 15(0), 16(0), 17(0) . 18(0), 19(0), 20(0) 21(0), 22(0), 23(0), 24(0) . 25(0), 26(0), 27(0) , 28(0), 29(0), 30(0) 31(0), 32(0), 33(0), 34(1) . 35(0). 36(0), 37(0) , 38(0), 39(0). 40(0) 41(0), 42(0), 43(0), 44(0) . 45(0), 46(0), 47(0) . 48(0), 49(0), 50(0) 51(0), 52(0), 53(0), 54(0) , 55(0), 56(0), 57(0) . 58(0), 59(0), 60(0) 61(1) , 62(1), 63(0), 64(0) . 65(0), 66(0). 67(0) . 68(0), 69(0), 70(0) 71(0), 72(0), 73(0), 74(0) . 75(0). 76(0), 77(0) . 78(0), 79(0). 80(0) 81(0), 82(0), 83(0), 84(0) , 85(0). 86(0), 87(0) , 88(1), 89(1). 90(0) 91(0), 92(0), 93(0), 94(0) . 95(0). 96(0). 97(0) , 98(0). 99(0), 100(0) 101(0), 102(0) , 103(0) , 104(0) , 105(0). 106(0), 107(0) , 108(0), 109(0), 110(0) 111(0), 112(0), 113(0), 114(0) , 115(1). 116(1), 117(0) , 118(0), 119(0), 120(0) 121(0), 122(0), 123(0), 124(0) , 125(0). 126(0), 127(0) , 128(0), 129(0), 130(0) 131(0), 132(0), 133(0). 134(0) , 135(0). 136(0), 137(0) , 138(0), 139(0), 140(0) 141(0), 142(1), 143(1). 144(0) , 145(0). 146(0). 147(0) , 148(0), 149(0), 150(0) 151(0), 152(0). 153(0), 154(0) , 155(0), 156(0) , 157(0) , 158(0), 159(0). 160(0) 161(0), 162(0). 163(0), 164(0) , 165(0), 166(0). 167(0) , 168(0), 169(0). 170(0) 171(0), 172(0). 173(0), 174(0) , 175(0), 176(0), 177(0) . 178(0), 179(0). 180(0) 181(0), 182(0). 183(0). 184(0) , 185(0). 186(0). 187(0) . 188(0). 189(0). 190(0) 191(0) , 192(0), 193(0). 194(0) . 195(0). 196(0), 197(0) . 198(0). 199(0), 200(0) 201(0), 202(0). 203(0), 204(0) , 205(0), 206(0), 207(0) . 208(0), 209(0). 210(0) 211(0), 212(0), 213(0), 214(0) , 215(0). 216(0), 217(0) , 218(0). 219(0). 220(0) 221(0) , 222(0). 223(0), 224(0) , 225(0), 226(0), 227(0) , 228(0), 229(0). 230(0) 231(0) , 232(0), 233(0). 234(0) , 235(0). 236(0), 237(0) , 238(0), 239(0), 240(0) 241(0) , 242(0), 243(0). 244(0) . 245(0). 246(0), 247(0) , 248(0), 249(0), 250(0) 251(0), 252(0), 253(0), 254(0) , 255(0), 256(0), 257(0) , 258(0), 259(0), 260(0) 261(0), 262(0), 263(0), 264(0) , 265(0), 266(0), 267(0) , 268(0), 269(0). 270(0) 271(0) , 272(0), 273(0), 274(0) . 27S(0), 276(0), 277(0) , 278(0), 279(0), 280(0) 281(0), 282(0), 283(0), 284(0) , 285(0). 286(0), 287(0) , 288(0), 289(0), 290(0) 291(0), 292(0), 293(0), 294(0) , 295(0). 296(0), 297(0) , 298(0), 299(0), 300(0) 301(0) , 302(0), 303(0). 304(0) , 305(0), 306(0) , 307(0) . 308(0). 309(0) , 310(0) 311(0), 312(0), 313(0), 314(0) , 315(0). 316(0). 317(0) . 318(0). 319(0) , 320(0) 321(0). 322(0), 323(0), 324(0) , 325(0), 326(0). 327(0) , 328(0), 329(0) . 330(0) 331(0), 332(0), 333(0), 334(0) , 335(0). 336(0), 337(0) . 338(0), 339(0). 340(0) 341(0), 342(0), 343(0), 344(0) , 345(0). 346(0). 347(0) , 348(0), 349(0) . 350(0) 351(0), 352(0), 353(0), 354(0) , 355(0). 356(0), 357(0) . 358(0), 359(0), 360(0) 361(0), 362(0), 363(0) , 364(0) , 365(0). 366(0), 367(0) , 368(0), 369(0), 370(0) 371(0), 372(0), 373(0) , 374(0) , 375(0). 376(0), 377(0) , 378(0), 379(0). 380(0) 381(0), 382(0), 383(0). 384(0) . 385(0). 386(0) . 387(0) . 388(0). 389(0), 390(0) 391(0), 392(0), 393(0) , 394(0) . 39S(0). 396(0). 397(0) , 398(0), 399(0). 400(0) 401(0) , 402(0), 403(0), 404(0) . 405(0). 406(0). 407(0) , 408(0), 409(0). 410(0) 411(0), 412(0). 413(0), 414(0) , 415(0), 416(0). 417(0) , 418(0). 419(0), 420(0) 421(0), 422(0). 423(0), 424(0) , 425(0). 426(0), 427(0) , 428(0), 429(0), 430(0) 431(0) , 432(0), 433(0). \f 2 HeV Dhotons from 30 decrees (HBO 3X10«*7 histories

»ROC CALCULATION USING D0SR2(EGS4) DOSRZ V2KSID 1.23) 02 Jan 1997 OH DEC-0SF1/DEC3000/800AIP 11:00:24 Har 21 1998

EXECUTION IHFORHATIOH AND HARMING HESSAGES

USIHG D0SRZ(EGS4) DOSRZ V2KSID 1.23) 02 Jan 1997

.....,,., VEW IMPUT FILE

...... DESIRED STATISTICAL ACCURACY OF 0.010S MOT REACHED. STATS I» DOSE REGIO»= 99.900 X AFTER 10 BATCHES

at...... FI»AL RAMDOH MUHBER SEEDS: 35 68 ......

FINISHED SIKULATia«S:TIHE ELSAPSED,CPUTIHE.RATIO= 9378.3 9204.7(= 2.56HR) 1.02

CPUTIHE PER HISTORY - 0.00031 SEC. HUUBER OF HISTORIES PER HOUR = 11733125. \f 2 HeV photons fron 30 degrees (U8C) 3X10**7 histories Har 21 1998 13:21:20

SUHHARY OF PULSE HEIGHT DISTRIBUTIOH

30000000 HISTORIES AMALYSED B.2. .EGS4LST 55

EBIM J TOP PDST CUHULJITIVE 0.0100 0.0031 ( 2.639%) 0.0031 ( 2.639%) 0.0200 0.0033 ( 1.261%) 0.0064 ( 1.119%) 0.0300 0.0033 ( 2.754%) 0.0097 ( 1.244%) 0.0400 0.0032 ( 1.068%) 0.0129 ( 0.987%) 0.05O0 0.0031 ( 1.332!!) 0.0160 ( 0.814%) 0.0600 0.0032 ( 2.454%) 0.0191 ( 0.664%) 0.0700 0.0032 ( 1.968%) 0.0224 ( 0.582%) 0.0800 0.0032 ( 2.519%) 0.0256 ( 0.671%) 0.0900 0.0032 ( 1.848%) 0.0288 ( 0.638%) 0.1000 0.0032 ( 2.541%) 0.0320 ( 0.536%) 0.1100 0.0033 ( 1.932%) 0.0354 C 0.490%) 0.1200 0.0032 ( 2.434%) 0.0386 ( 0.497%) 0.1300 0.0032 ( 1.505%) 0.0417 ( 0.526%) 0.1400 0.0032 ( 2.753%) 0.0449 ( 0.566%) 0.15OO 0.0031 ( 1.534%) 0.0480 ( 0.543%) 0.1600 0.0031 ( 1.288%) 0.0511 ( 0.528%) 0.1700 0.0031 ( 1.607%) 0.0542 ( 0.547%) 0.1800 0.0031 ( 1.863%) 0.0573 ( 0.567%) 0.1900 0.0033 ( 1.754)!) 0.0606 ( 0.588%) 0.2000 0.0032 ( 1.656%) 0.0638 ( 0.5711) 0.2100 0.0032 ( 1.668%) 0.0670 ( 0.531%) 0.2200 0.0033 ( 2.385%) 0.0702 ( 0.567%) 0.2300 0.0037 ( 2.118«) 0.0739 ( 0.526%) 0.2400 0.0046 ( 1.194%) 0.0785 ( 0.482%) 0.2500 0.0043 ( 1.457%) 0.0828 ( 0.432%) 0.2600 0.0038 ( 1.575%) 0.0867 ( 0.457%) 0.2700 0.0035 ( 1.198%) 0.0902 < 0.429%) 0.2800 0.0032 ( 1.975%) 0.0934 ( 0.422%) 0.2900 0.0032 ( 1.942%) 0.0966 ( 0.411%) 0.3000 0.0031 ( 1.969%) 0.0997 ( 0.381%) 0.3100 0.0031 ( 2.020%) 0.1028 ( 0.404%) 0.3200 0.0031 ( 2.306%) 0.1058 < 0.416%) O.3300 0.0031 ( 1.493%) 0.1089 < 0.416%) 0.3400 0.0030 ( 1.404%) 0.1119 ( 0.379X) 0.3500 0.0029 ( 2.646%) 0.1148 ( 0.345%) 0.3600 0.0028 ( 2.264%) 0.1176 ( 0.351%) 0.3700 0.0029 ( 1.541%) 0.1204 ( 0.343%) 0.380O 0.0028 ( 2.472%) 0.1232 ( 0.335%) 0.3900 0.0028 ( 2.873%) 0.1260 ( 0.296%) 0.4000 0.0028 C 2.113%) 0.1288 < 0.321%) 0.4100 0.0029 ( 3.314%) 0.1317 ( 0.299%) 0.4200 0.0028 ( 2.667%) 0.1345 ( 0.275%) 0.4300 0.0029 ( 2.008%) 0.1374 < 0.283%) 0.4400 0.0028 ( 2.134%) 0.1401 ( 0.270%) O.4500 0.0028 < 1.513%) 0.1429 ( 0.273%) 0.4600 0.0028 C 2.564%) 0.1457 ( 0.284%) 0.4700 0.0028 ( 1.565%) 0.1485 ( 0.275%) O.4800 0.0028 ( 1.599%) 0.1513 ( 0,266%) 0.4900 0.0027 ( 1.858%) 0.1540 ( 0.272%) 0.5000 0.0028 ( 2.767%) 0.1567 ( 0.292%) 0.5100 0.0028 ( 2.048%) 0.1595 ( 0.283%) 0.5200 0.0033 C 1.734%) 0.1629 ( 0.260%) 0.5300 0.0028 ( 1.819%) 0.1657 ( 0.253%) 0.5400 0.0027 ( 2.601%) 0.1684 t 0.242%) 1 0.5500 0.0027 ( 1.471%) 0.1711 ( 0.252%) 0.5600 0.0028 ( 2.647%) 0.1740 { 0.239%) 0.5700 0.0028 < 2.509%) 0.1767 ( 0.223%) 0.5800 0.0027 ( 2.690%) 0.1795 ( 0.250%) 0.5900 0.0029 ( 1.919%) 0.1823 ( 0.251%) 0.6000 0.0027 C 2.014%) 0.1850 ( 0.253%) 0.6100 0.0028 ( 2.110%) 0.1878 ( 0.267%) 0.6200 0.0027 ( 2.883%) 0.1906 ( 0.268%) 0.6300 0.0028 ( 1.786%) 0.1934 ( 0.269%) 0.6400 0.0027 ( 2.381%) 0.1961 ( 0.261%) I 0.6500 0.0028 ( 2.708%) 0.1988 ( 0.256%) 0.6600 0.OO27 ( 2.161%) 0.2015 ( 0.247%) I 0.6700 0.0029 ( 3.443%) 0.2044 ( 0.273%) 0.6800 0.0028 < 2.204%) 0.2072 ( 0.274%) 0.6900 0.0029 ( 2.954%) 0.2101 ( 0.292%) 0.7000 0.0028 ( 2.508%) 0.2128 ( 0.280%) 0.7100 0.0028 ( 2.084%) 0.2156 ( 0.294%) 0.7200 0.0028 ( 2.532%) 0.2184 ( 0.293%) 1 0.7300 0.0028 ( 1.671%) 0.2212 < 0.286%) 1 0.7400 0.0027 ( 2.082%) 0.2240 ( 0.290%) 0.7500 0.0029 ( 2.330%) 0.2269 ( 0.283%) 0.7600 0.0030 ( 2.475%) 0.2298 ( 0.262%) 1 0.7700 0.0030 ( 2.415%) 0.2328 ( 0.255%) 1 0.7800 0.0028 ( 2.637%) 0.2356 C 0.253%) 1 0.7900 0.0028 ( 2.102%) 0.2384 ( 0.244%) I 0.8000 0.0028 ( 2.642!!) 0.2411 ( 0.230%) 0.8100 0.0028 C 2.325%) 0.2440 ( 0.239%) 56 APPENDIX B. INPUT AND OUTPUT FROM EGS4

0.820O 0.0028 ( 1.538%) 0.2468 ( 0.233%) 0.8300 0.0028 ( 2.5467.) 0.2495 ( 0.220%) 0.84DO 0.0028 ( 2.046X) 0.2523 ( 0.222%) 0 8500 0.0029 ( 2.143%) 0.2552 ( 0.226%) 0.860O O.0O28 ( 2.019%) 0.2580 ( 0.240%) 0.8700 0.0030 ( 1.639%) 0.2610 ( 0.233%) 0.8800 0.0028 ( 1.646%) 0.2638 ( 0.232%) 0.8900 0.0029 ( 2.296%) 0.2667 ( 0.227%) 0.9000 0.0029 ( 1.824%) 0.2696 ( 0.226%) 0.9100 0.0029 ( 2.462%) 0.2725 ( 0.235%) 0.9200 0.0029 ( 1.613%) 0.2754 C 0.233%) 0.9300 0.0029 ( 2.454%) 0.2783 ( 0.225%) O.9400 0.0030 ( 2.465%) 0.2813 ( 0.227%) 0.9500 0.0029 ( 2.210X) 0.2842 ( 0.222%) 0.9600 0.0031 ( 1.923X) 0.2873 ( 0.214%) 0.9700 0.0030 ( 1.545X) 0.2903 ( 0.216%) 0.9800 0.0084 ( 1.768X) 0.2988 ( 0.228%) 0.9900 0.0033 ( 2.587%) 0.3020 ( 0.228%) 1.0000 0.0034 ( 1.605%) 0.3054 ( 0.228%) 1.0100 0.0033 ( 2.199X) 0.3087 ( 0.226%) 1.0200 0.0034 ( 1.811%) 0.3121 ( 0.226%) 1.0300 0.0033 ( 2.436%) 0.3154 ( 0.221%) 1.0400 0.0034 ( 1.691X) 0.3188 ( 0.218%) 1.0500 0.0034 ( 1.786X) 0.3222 ( 0.211%) 1.0600 0.0034 ( 1.786%) 0.3256 ( 0.212%) 1 1.0700 0.0035 ( 2.298%) 0.3290 ( 0.200%) 1.0800 0.0036 ( 1.303X) 0.3326 ( 0.200%) 1.0900 0.0035 ( 1.758%) 0.3361 ( 0.199%) 1.1000 0.0036 ( 1.716X) 0.3397 ( 0.197%) 1.1100 0.0036 ( 1.870X) 0.3432 ( 0.193%) 1 1.1200 0.0035 ( 1.544X) 0.3467 ( 0.201%) 1 1.1300 0.0036 ( 2.278%) 0.3503 ( 0.192%) 1 1.1400 0.0035 ( 1.763%) 0.3539 ( 0.194%) 1 1.1500 0.0036 ( 2.002%) 0.3574 ( 0.188%) 1 1.1600 0.0037 ( 3.018%) 0.3611 ( 0.191%) : 1.1700 0.0038 C 2.028%) 0.3649 ( 0.191%) 1 1.1800 0.0036 ( 1.801%) 0.3686 ( 0.188%) 1 1.1900 0.0038 ( 2.340%) 0.3723 ( 0.187%) 1 1.2000 0.0038 ( 2.708%) 0.3761 ( 0.187%) 1.2100 0.0039 ( 1.812%) 0.3799 ( 0.193%) 1 1.2200 0.0039 ( 1.839X) 0.3839 ( 0.199%) 1 1.2300 0.0038 ( 1.996%) 0.3877 C 0.211%) 1 1.2400 0.0039 ( 1.684%) 0.3916 t 0.199%) 1 1.2500 0.0041 ( 1.605%) 0.3957 ( 0.194%) 1 1.2600 0.0039 ( 1.814X) 0.3996 ( 0.197%) 1 1.2700 0.0041 ( 1.426%) 0.4038 ( 0.196%) 1 1.2800 0.0041 ( 1.580%) 0.4078 ( 0.191%) 1 1.2900 0.0042 t 1.611%) 0.4120 ( 0.196%) 1 1.3000 0.0042 C 1.681%) 0.4162 ( 0.188%) 1 1.3100 0.0042 ( 2.246%) 0.4205 ( 0.172%) 1 1.3200 0.0043 ( 1.264%) 0.4248 ( 0.168%) 1 1.3300 0.0042 ( 1.999%) 0.4290 ( 0.171%) 1 1.3400 0.0043 ( 1.617%) 0.4332 ( 0.170%) 1 1.3500 0.0043 ( 1.275%) 0.4375 ( 0.167%) 1 1.3600 0.0044 ( 1.785%) 0.4418 ( 0.159%) 1 1.3700 0.0044 ( 1.210%) 0.4462 ( 0.150%) 1 1.3800 0.0044 ( 1.978%) 0.4506 ( 0.140%) 1 1.3900 0.0044 ( 2.242%) 0.4550 ( 0.139%) 1 1.4000 0.0045 ( 2.033%) 0.4595 ( 0.143%) 1 1.4100 0.0044 ( 2.225%) 0.4639 ( 0.145%) 1 1.4200 0.0046 ( 1.518%) 0.4685 ( 0.134%) 1 1.4300 0.0046 ( 1.834%) 0.4731 ( 0.131%) 1 1.4400 0.0046 ( 1.805%) 0.4777 ( 0.134%) 1 1.4500 0.0047 ( 2.212%) 0.4824 ( 0.124%) 1 1.4600 0.0048 C 1.696%) 0.4872 C 0.121%) 1 1.4700 0.0049 ( 2.542%) 0.4921 ( 0.123%) 1 1.4800 0.0051 C 1.223%) 0.4972 ( 0.129%) 1 1.4900 0.0152 ( 0.861%) 0.5124 ( 0.126%) 1 1.5000 0.0054 < 1.248%) 0.5178 ( 0.131%) 1 1.5100 0.0055 ( 2.038%) 0.5233 ( 0.133%) 1 1.5200 0.O056 ( 1.263%) 0.5288 t 0.132%) 1 1.5300 0.0058 ( 1.390%) 0.5346 ( 0.120%) 1 1.5400 0.0058 ( 1.052%) 0.5404 ( 0.126%) 1 1.5500 0.0059 ( 1.788%) 0.5464 ( 0.113%) 1 1.5600 0.0061 ( 1.252%) 0.5525 ( 0.108%) 1 1.5700 0.0063 < 1.548%) 0.5588 ( 0.097%) 1 1.5800 0 0064 < 1.203%) 0.5652 ( 0.103%) 1 1.5900 0.0065 ( 1.155%) 0.5717 ( 0.097%) 1 1.6000 0.0066 ( 1.678%) 0.5783 ( 0.101%) 1 1.6100 0.O069 ( 2.037%) 0.5852 < 0.096%) 1 1.6200 0.O071 ( 1.513%) 0.5923 < 0.097%) 1 1.6300 0.0073 ( 1.294%) 0.5996 ( 0.094%) 1 1.6400 0.0075 ( 1.022%) 0.6071 ( 0.097%) B.2. .EGS4LST 57

.6500 0.0077 ( 1.768%) 0.6148 ( 0.098%) 1.6600 0.0079 ( 1.934%) 0.6228 0.091%) 1.6700 0.0083 ( 1.627%) 0.6311 0.086%) 1.6800 0.0085 ( 1.269%) 0.6396 0.098%) 1.6900 0.0089 ( 1.826%) 0.6484 0.088%) 1.7000 0.0092 ( 1.020%) 0.6577 0.089%) 1.7100 0.0096 ( 1.149X) 0.6672 0.091%) 1.7200 0.0101 ( 0.872%) 0.6773 0.092%) 1.7300 0.0105 ( 1.291%) 0.6878 0.087%) 1.7400 0.0108 ( 1.099%) 0.6986 0.083%) 1.7500 0.0115 ( 0.821%) 0.7102 0.086%) 1.7600 0.0122 ( 0.908%) 0.7223 0.077%) 1.7700 0.0127 ( 0.846%) 0.7350 0.082%) 1.7800 0.0094 ( 1.493%) 0.7444 0.079%) 1.7900 0.0071 ( 1.846%) 0.7515 0.082%) 1.8000 0.0067 ( 1.207%) 0.7582 0.079%) 1.8100 0.0064 ( 1.705%) 0.7646 0.080X) 1.8200 0.0060 ( 1.661%) 0.7706 0.074%) 1.8300 0.0056 ( 1.067%) 0.7761 ( 0.073%) 1.840O 0.0051 ( 1.199%) 0.7812 < 0.073%) 1.8500 0.0046 ( 1.793%) 0.7858 ( 0.067%) 1.8600 0.0039 ( 1.382%) 0.7897 ( 0.066%) 1.8700 0.0032 ( 2.217%) 0.7929 ( 0.064%) 1.8800 0.0025 ( 2.169%) 0.7954 ( 0.063%) 1.8900 0.0018 ( 2.830%) 0.7972 0.067%) 1.90OO 0.0013 ( 4.422%) 0.7984 0.068%) 1.9100 0.0009 ( 2.720%) 0.7993 0.068%) .9200 0.0006 ( 7.304%) 0.7999 0.064%) .9300 O.0OO5 ( 4.991%) 0.8004 0.063%) .9400 0.0004 ( 4.887%) 0.8008 0.062%) .9500 0.0004 ( 6.132%) 0.8012 0.062%) .9600 0.0004 < 6.653%) 0.8016 0.062%) .9700 0.0003 < 3.187%) 0.8020 0.060%) .9800 O.OO04 ( 5.614%) 0.8023 0.061%) .9900 0.0003 ( 6.248%) 0.8026 0.062%) .0000 0.1974 C 0.254%) 1.0000 0.015%)

PLOT NORMALIZED TO PEAK OF OWE, PDST IS NORHALIZED TO UNIT AREA

PEAK EFFICIEHCIES PER COUIT I» SPECTRUH

FULL EKERCY PEAK 0.197H*- 0.249%) SINGLE ESCAPE PK 0.0126C+- 1.368%) DOUBLE ESCAPE PK 0.0070C*- 2.247%) 511 KEV PK 0.0019(«- 3.369%)

SOLID ANGLE SUBTENDED BY DETECTOR HOUSING » 6.402E-02C 0.0%)

FRACTION OF PARTICLES INTO 4-PI WHICH CAUSE A PULSE « 2.220E-04( 0.1%)

FRACTION OF PARTICLES IKCIDEHT OK HOUSING WHICH CAUSE A PULSE " 4.356E-02( 0.1%)

ENERGY DEPOSITED I« DETECTOR PER IHITIAL PARTICLE: 0.00000 H«V (t-99.900%) \f 2 HeV photons froB 30 degress (UBC) 3X10**7 histories Har 21 1998 13:21:20

SUKHARY OF DOSE REGIOK RESULTS

TOTAL » CHARGED PARTICLE STEPS 147016224 •/- 0.046% TOTAL * OF TIDES HSCAT SWITCHED OFF 1359218*/- 0.085% RATIO 0.OO9 •/- 0.080%

» CHARGED PARTICLE STEPS III DOSE REG. 0 •/-99.900% • TIKES HSCAT SWITCHED OFF IK DOSE REG. 0 17-99.900% RATIO 0.000 +/-99.900X

Z» : GEOHETRICAL 20HE HUHBER P» : PLANAR ZONE NUHBER C» : CTLRDRICAL ZOVE KUHBER T : TOTAL DOSE (GRAYS/(INCIDENT FLUENCE)) T-S: TOTAL DOSE HIKUS STOPPERS

T T-S

Har 21 1998 13:36:43 58 APPENDIX B. INPUT AND OUTPUT FROM EGS4 B.3 .egs4eff

2 tlev photons froa 30 dogre«s: (HBO 3X10>>7 histories 200 IIUHBER OF ENERGY BINS TO FOLLOW 0. 1000E-01. 0.3113E*00, 0. 2639E+01, 0. 2OO0E-O1, 0.3272E+00, 0. 1261E+01, 0. 3000E-01, 0.3297E+00, 0. 27S4E+01, 0. 4000E-01, 0.3186E*00, 0. 1068E*01, 0. 5000E-01, 0.3086E^00, 0. 1332E+01. 0. SOOOE-01, 0.3178E^00. 0. 2454E*01, 0. 7000E-01, 0.3220E^0O, 0. 1968E+01. 0. 8000E-01, 0.3199E»00, 0. 2519E+01, 0. 9000E-01, 0.3248E*00, 0. 1848E*01, 0. 1000E-•00, 0.3239E*00, 0. 2541E+01, 0. 1100E+00. 0.3322E+00, 0. 1932E*01. 0. 1200E<•00. 0.321EE+00. 0. 2434E+01. 0. 1300E<•00, 0.3169E+00, 0. 1E0SE+01, 0. 1400E-I OO, 0.31B7E+00, 0. 2753E+01, 0. 1SO0E+O0, 0.309SE+00, 0. 1534E*01, 0. 1600E+00, 0.3098E*00, 0. 1288E+01. 0. 1700E'•00, 0.3102E+00, 0. 1607E+01, 0. 1800E< OO, 0.3107EÔO. 0. 1863E»01, 0. 1900E'•00, 0.3308E+00, 0. 17E4E*01, 0, 2000E*•OO, 0.31E3E+00, 0. 16E6E*01, 0. 2100E-"•00, 0.3217E^00. 0. 1S68E+01, 0 2200E<•00, 0.3261E^0O. 0. 2385E*01, 0.2300E*•00, 0.3678E^0O. 0. 2118E+0I, 0 2400EH•00, 0.4E91E^00, 0 . 1194E*01, 0 2500E<•00, 0.4308E»00, 0 14E7E*01, 0 2600E1•oo. 0.3846E*00. 0. 157EE+O1, 0.2700E+00, 0.3E2EE*00, 0 .1198E*01, 0 2800E<•00, 0.3221E^00, 0. 197SE+01, 0 .2900E<•00, 0.3190E+00, 0 1942E+01, 0 .3000EH•00, 0.3103E*00, 0 . 1969E+01, 0 3100E<•00, O.3074E+OO. 0 2020E*01, 0 3200E<•00, O.30E8E+OO, 0. 2306E+01, 0 3300E<•00, 0.3061EÔO. 0 1493E+01. 0 . 3400E<•00, 0.3004E*00. 0. 1404E+01, o 3E00E<•00, 0.2906E+00, 0. 2646E*01, 0 3600E<•00, 0.2754E^00. 0.2264E+01, 0 37OOE*O0, 0.2864E^0O, 0. 1541E+01, 0 3800E<•00, 0.2772E^00, 0.2472E-01, 0 . 3900E<•00, 0.2831E^00. 0 .2873E+01, 0 ,4000E*00, 0.2803EÔO, 0 .2113E+01. 0 .4100E*00, 0.290EE+00, 0 .3314E+01, 0 .42OOE*O0, 0.27S4E+00, 0 .2667E*01. 0 . 4300EH•00, 0.2882E*00, 0 .2008E+01, 0 .4400E<•00, 0.2760E+00, 0 .2134E*01. 0.4500E+00, 0.2780E«0, 0 .1E13E*O1, 0 .4600E*00, 0.2771E*00, 0 .2E64E+01, 0 .4700E<• 00, 0.2796E^00, 0 .1E6SE*O1, 0 .4800E+00, 0.2784E+00, 0 .1599E*01, 0 .4900E1• 00, 0.2698E+00, 0 .1858E*01, 0 .5000E*00, 0.2761E+00, 0 .2767E*01, 0 .5100E+00, 0.2815E*00, 0 .2048E+01. 0.5200E'•00. 0.3338E+00. 0 .1734E+01, 0 .E300E"•00. 0.2801E*00, 0 .1819E*01. 0 .S400E-•00. 0.2715E*00, 0 .2$01E*01, 0 .SSOOE*• 00, 0.2736E+00, 0 -1471E*01, 0 .S600E-•oo. 0.2831E*00, 0 .2647E*01. 0 .E700E-• 00, 0.2792E+00, 0 -2S09E*01, 0 .E800E-•00, 0.2706E*00, 0 .2690E+01, 0 .E900E*0O, 0.2865E+00, 0 .1919E+01, 0 .6000E-• 00, 0.2704E+00, 0 .2014E*01, 0 .6100E-• 00, 0.2812E*00, 0.2110E*01, 0 .6200E-• 00. 0.2732E*00, 0 .2883E+01, 0 .6300E-•00, 0.2801E*00, 0 . 1786E+01, 0 .6400E-•00, 0.2711E*00, 0 .2381E->01. 0 .6500E'• 00, 0.27S9E*00, 0 .2708E*01, 0 .6600E-• 00, O.2657E*O0. 0.2161E*01. 0 .6700E-• 00, 0.28S4E»00, 0 .3443E*01, 0 . 680OE-• 00, 0.283EE*00. 0.2204E-01. 0 6900E • 00, 0.28E6E*00, 0 .29S4E*01, 0 .7000E-•00, 0.2758E*00, 0.25O8E*01. 0 .7100E-• 00, 0.2793E+00. 0 .2084E*01. 0.7200E • 00, 0.2820E»00. 0.2S32E*01, 0 .7300E • 00, 0.2820E*00, 0 .1671E+01, 0 .7400E • 00, 0.2734E*00, 0 .2082E+01, 0 .7E00E • 00, 0.2878E*00, 0 .2330E*01, 0 .7600E • 00, 0.29E9E*00, 0 .2475E*01, 0 .7700E • 00, 0.29E6E+00, 0 .2415E*01. 0 .7800E • 00, 0.2778E+00, 0.2637E+01. B.3. .EGS4EFF 59

0.7900E*00, 0.2809E+00, 0 .2102E+01 0.8000E+00, 0.2769E*00, 0.2642E+01 0.8100E*00, 0.283EE*00, 0.2325E+01 0.8200E*00, 0.2807E+00, 0.1538E+01 0.8300E+00, 0.2759E*00, 0.2S46E-01 0.8400E*00, 0.2808E+00, 0.2046E+01 0.8500E*00, 0.2886E*00, 0.2143E+01 0.8600E+00, O.281OE*O0, 0.2019E+01 0.8700E-HX), 0.2979E*00, 0.1639E+01 0.8800E*00, 0.281SE*00, 0.1646E+01 0.8900E+00, 0.2863E+00, 0.2296E+01 0.9000E*00, 0.2910E*00. 0.1824E+01 0.9100E+00, 0.2924E+00, 0.2462E*01 0.9200E+00, 0.2907E*00, 0.1613E*01 0.93O0E*00, 0.2867E+00, 0.2454E*01 0.9400E*00, 0.3037E*00, 0.2465E+01 0.9S00E*0O, 0.2886E*00, 0.2210E*01 0.9600E+00, 0.3097E+00, 0.1923E*01 0.9700E+00, O.3OllE*00, 0.154SE*01 0.9800E+00, 0.8434E*00, 0.1768E*01 0.9900E*00, 0.32E7E+00, 0.2587E*01 0.IOOOE'01, 0.3419E+00, 0.1605E+01 0.1010E*01, 0.32E9E*00, 0.2199E+01 0.1020E+01, 0.3390E*00, 0.1811E+01 0.1030E*01, 0.332SE+00, 0.2436E*01 0.1040E*01, 0.336SE*00, 0.1691E+01 0.1050E+01, 0.3396E+00, 0.1786E+01 0.1060E+01, 0.3375E1-00, 0.1786E*01 0.1070E+01. 0.348SE*00, 0.2298E*01 0.1080E+01, 0.3E84E+00, 0.13O3E»(H 0.1090E+01, 0.34E0E+00, 0.1758E+01 0.1100E*01, 0.3E91E+00, 0.1716E*01 0.1110E+01, 0.35S3E*00. 0.1870E*01 0.1120E+01, 0.3502E*00, 0.1544E+01 0.1130E+01, 0.3S96E-KJ0, 0.2278E1-01 0.1140E+01, 0.3E37E+00, 0.1763E+01 0.IISOE'01, 0.3S65E+00. 0.2002E+01 0.1160E+01, 0.368SE*00, 0.3018E+01 0.1170E*01, 0.3843E+00, 0.2028E+01 0.1180E*01, 0.3617E+00, 0.1801E+01 0.1190E*01, 0.3761E+00, 0.2340E*01 0.12O0E+01. 0.3761E+00, 0.2708Et01 0.1210E+01, 0.3861E+00. 0.1812E-1-01 0.1220E+01, 0.3948E+00, 0.1839E+01 0.1230E*01, O.3846E+00, 0.199SE+01 0.1240E+01, 0.3874E*00, 0.1684E*01 0.1250E+01, 0.4084E*00, 0.160EE+01 0.1260E+01, 0.3944E+00, 0.1814E+01 0.1270E+01, 0.4108E*00. 0.1426E+01 0.1280E*01, 0.4057E*00, 0.1S80E-HH 0.1290E+01. 0.4220E+00, 0.16I1E+01 0.1300E*01, 0.421OE+OO, 0.1681E+01 0.1310E*01, 0.4238E+00, 0.2246E*01 0.1320E*01, 0.4274E*00, 0.1264E+01 0.1330E+01, 0.4203E+00, 0.1999E+01 0.1340E*01, 0.4263E+00, 0.1617E+01 0.13S0E«01, 0.4279E+00, 0.1275E*01 0.1360E»01, 0.43EOE+00, 0.1785E+01 0.1370E*01, 0.4362E+00, 0.12IOE+OI 0.1380E*01, 0.4397E+00. 0.1978E+01 0.1390E+01, 0.436SE+00, 0.2242E*01 0.1400E*01, 0.4S31E+00, 0.2033E+01 0.1410E*01, 0.4431E*00, 0.2225E+01 0.1420E*01, 0.4551E*00, 0.1S18E+01 0.1430E+01, O.4641E*00, 0.1834E*01 0.1440E+01. O.46O2E*0O. 0.1805E*01 0.1450E*01, 0.4704E+00, 0.2212E+01 0.1460E*01, 0.4786E+00, 0.1696E*01 0.1470E+01, 0.4928E+00, 0.2542E*01 0.1480E+01, 0.5074E+00, 0.1223E+01 0.1490E+01, 0.1S17E+01, 0.8615E+O0 0.1S00E+01, O.S420E*00, 0.1248E+01 0.1510E+01, 0.5471E*00, 0.2038E-KJ1 0.1520E*01, 0.5558E*00, 0.1263E+01 0.1530E*01, 0.5794E+00, 0.1390E+01 0.I540E*01, 0.E808E+00, 0.10E2E-KJ1 0.1550E*01, 0.5944E+00, 0.1788E*01 0.1E6OE*O1, 0.6129E*00, 0.12S2E<-01 0.1E70E-KH, 0.6275E+00. 0.1548E*01 0.1580E+01, 0.6449E*00, 0.1203E+01 0.1B9OE*O1, 0.6466E+00, 0.1155E*01 0.1600E*01, 0. S608E-tOO. 0.1678E+01 0.1610E+01. 0.6903E*00. 0.2037E*01 60 APPENDIX B. INPUT AND OUTPUT FROM EGS4

0.1620E«01, 0.7090E*00 , 0.1513E*01, 0.1630E*01, 0.7253E*00 , 0.1294E«-01, 0.1640E+01, 0.7S41E*00 . 0.1022E+01, 0.1650E*01, 0.7721E+00 , 0.1768E+01, 0.1660E+01, 0.7941E+00 , 0.1934E+01. 0.1670E*01. 0.8333E+00 , 0.1627E*01. 0.1680E+01, 0.8466E+00 . 0.1269E*01, 0.1690E*01. 0.8866E*00 , 0.1826E+01, 0.1700E+01, 0.9240E*00 , 0.1020E*01, 0.1710E*01, 0.9584E+00 , 0.1149E*01. 0.1720E+01, 0.1008E»01 , 0.8718E*00, 0.1730E*01, 0.1049E+01 , 0.1291E*01. O.1740E»01, O.IO83E*O1 , 0.1099E+01. 0.1750E+01, 0.1153E+01 . 0.8205E-MJ0, 0.1760E-I-01, 0.1217E*01 , 0.9078E*00, O.177OE+O1, 0.1269E+01 , 0.8462E+00, 0.1780E*01, 0.9403E*00 , 0.1493E-HH, 0.1790E*01, 0.7085E*00 , 0.1846E+01, 0.1800E*01, 0.6712E+00 , 0.1207E1-01. 0.1810Et01, 0.6367E+00 , 0.1705E+01. 0.1820E*01, 0.5979E*00 , 0.1661Et01. 0.1830E+01, 0.B552E+00 , 0.1067E+01. 0.1840E-KJ1, 0.5084E*00 , 0.1199E+01, 0.1850E*01, 0.4610E+00 , 0.1793E+01, 0.186OE*01, 0.3863E*00 , 0.1382E»01, 0.1870E+01, 0.3203E*00 , 0.2217E+01, 0.1880E+01, 0.2493E+00 , 0.2169E+01, O.189OE+O1, 0.1787E»00 0.2830E+01, 0.1900E*01, 0.1261E»00 , 0.4422E+01, 0.1910E+01, 0.8802E-01 , 0.2720E+01, O.l92OE*01, 0.5719E-01 , 0.7304E*01, 0.1930E+01, 0.4663E-O1 , 0.4991E+01, 0.194OE+01, 0.4463E-01 , 0.4887E+01, O.195OE+O1, 0.4373E-01 , 0.6132E+01, 0.1960E*01. 0.4081E-01 , 0.66E3E+01, 0.1970E+01, 0.3322E-01 , 0.3187E»01. 0.1980E+01, 0.3537E-01 , 0.5614E+01, 0.1990E*01. 0.3083E-01 , 0.6248E*Ol, 0.2000E+01, 0.1974E+02 , 0.2B42E+00, >0H INDIVIDUAL PEAK «»D TOTAL EFFICIEIICIES O.1971E+0O 0.2491E+00 O.126OE-01 0.1368E*01 0.7013E-02 0.2247E*01 0.1862E-02 0.3369E*01 0.2789E-02 0.9126E-01 Appendix C Calculations

C.I DOSRZ - the regions of the detector model

Figure C.I

61 62 APPENDIX C. CALCULATIONS

C.2 Empirical values of the efficiency

Measurements has been made by Kenneth Lidstrom and Tor- bjorn Nylen, in Stockholm, to determine the efficiency of the detector. It was decided to use the expression (ref. [10])

V = (C.I)

where E is the incident energy and 8 the angle of incidence. The uncertainty in the source was 1.5 % and the statistical uncertainty 2.5 %.

Values

A1 = 0.00139 A2 = -0.0004 Bx = 0.712 B2 = -0.0181 Appendix D Unfolding

D.I Point source

From "Instruction manual intensimeter 25 dose rate meter calibration fixture" (Nuclear Research Corporation, Warrington, PA, USA): The Dose Rate Meter Calibration Fixture contains approximately 40 yuCi (1.5 MBq) of Cesium-137. The radioactive material is contained in a lead shield to lower the radiation level on the outside of the carrying case. The radiation level on the outside of the carrying case is below 0.005 mSv/h. The label mounted on the inside of the fixture will give the average calculated dose rates (in mSv/h) for the given year. The following is the information that appears on the label:

YEAR AVERAGE READING in mSv/h 1993-96 0.092-0.153 1997-00 0.083-0.139 2001-04 0.076-0.126 2005-08 0.069-0.115 2009-12 0.063-0.105

63 64 APPENDIX D. UNFOLDING Appendix E

Wave programs

E.I The point source unfolding

PRO labb ;««ee««««cfl««e«fl«6<«occc«eece«c

65 66 APPENDIX E. WAVE PROGRAMS

; print, fullpath ; status = dc_read_free(fullpath, tenpresp, /Colu«n, get_column = 2, HsJcip = 2) ; p», teaipresp ; if (x eq 0) then begin ; respons = teapresp ; endif else begin ; respons - [[respons], [teapresp]] ; endelse ;endfor ;pmf, 3, respons ;close, 3 ;cecc«««c«e««oc«ecccce«««««e««c«Qcco«««eco««««eo openr, 3, 'H:\»ontecarlo\wbc_binlO_front\wbc_front_respons ' rmf, 3, respons, 100, 100 close, 3 ;COCOO«OCCOOCCCCOOCOCCOCOCCCCOCtOOCCCCQQ, inverse.respons result = inverse.respons S histo toteff = fltarr(lOO) status a dc_read_free('H:\nontecarlo\wbc_binlO_front\Hbc_eff_front_10 .dat' , toi /Coluan, Get_Colunns = [l]) print, toteff final_result = result / toteff print, result print, final_result print, histo print, total(histo) factor = final_result(66)/histo(66) !X.style = 1 !Y.range = 0 !X.range = [50,1000] set_plot, 'ps' device , filename *H :\montecarlo\gaanal .ps ' plot. E. final.result, Background = 255, Color=O. Xtitle = 'Energy EkeV] ', $ Ytitle = 'Fluence rate', linestyle*O oplot, E. factor*histo. Background = 255, Color=O, linestyle=l device , /close set.plot. 'Win32' endif else begin = print F 'deterninanten 0 ' endelse plot, E, final_result, Background = 255, Color=0, Xtitle = 'Energy [keV]', $ Ytitle = 'Fluence rate [per square aeter per second]', linestyle=O oplot, E, histo. Background = 255, Color=O, linestyle=l

E.2 The in-situ unfolding

PRO finland COCOOCOCCOOCOOCOCOCCCOCQOCOCOOCOOCQOCOflCCCCQCOOC energyvec = fltarr(2119) countsvec = fltarr(2119) status = dc_read_free('H:\nontecarlo\wbc_finland_2_5.prn', energyvec, co ;for i = 0,1400, 100 do begin ; print, energyvec(i) ; print, countsvec(i) ;endfor ;COCfiCOCCCOC«OCCOO«CCCOCOCCCCfiOCCQCCCCOC«OCOOCOCC energyvec = energyvec * 0.001 bin - 0.01 histo = fltarr(lOO) for j « 1, 2117 do begin Elow = Cenergyvec(j-l) + energyvec(j)> / 2 Ehi = (energyvecCj+1) + energyvec(j)) / 2 delta = (energyvec(j+1) - energyvec(j-1)) / 2 k_lon = fixtElok / bin) ; print, k_low k_hi = fix(Ehi / bin) if (delta eq 0) then begin delta = 1.0 endif if (k_loH eq k_hi) then begin histo(k_low) = histo(k_low) + (countsvec(j) / delta) * (delta / bin) endif else begin delta_low = Elow - bin » k_low E.2. THE IN-SITU UNFOLDING 67

histo(k_low) = histo(k^lon) + (countsvectj) / delta) • (delta.lov / bin) delta.hi = Ehi - bin * k_hi histo(k_hi) = histo(k_hi) + (countsvec(j) / delta) • (delta_hi / bin) endelse endfor histo = histo / 900 E = fltarr(lOO) nun = 10 for 1 = 0, 99 do begin E<1) = nun nun = nun + 10 print, histo(l), E{1) endfor

openr, 3, 'H:\aontecarlo\nbc_binlQ_6Odeg\wbc_6Odeg_respons' raf, 3, respons, 100, 100 close, 3

deter = determ(respons) if (deter ne 0) then begin print, deter inverse_respons = invert(respons) ; pM, inverse_respons result = inverse.respons t histo toteff = fltarr<100) status = dc_read_free ('H:\«ontecarlo\Hbc_binlO_60deg\Hbc_eff_60d«g_10.dat', totexf , $ /Column, Get.Colunns = [1]) print, toteff final.result = rasult / toteff print, result print, final.result print, histo print, total(histo) factor = final_result(S6)/histo(66) fi_re = fltarr(10) hi = fltarr(lO) for ii = 0, 9, 1 do begin for jj = ii*10, ii*10+9, 1 do begin fi_r«(ii) » fi_re(ii) + final_result(jj) hi(ii) = hi(ii) + factor*histo(jj) endfor endfor

openr, 3,'H:\montecarlo\«u_en.prn' rmf, 3, Bu_«n, 10, 1 close, 3 ;«OBC«eo«««cccccceecceeecoccc«ficcccceeeeoeoccoeoecec openr, 3 , 'H:\«ont«carlo\ejoule.prn' nof, 3, E.joule, 10, 1 close, 3 ;COCCOCOO«CCOflOeCOCOOCOCCCC(lOCflCCC<)60C€0«COOCCCOOOfiC doserate a fltarr(10) doserate = fi_re*BU_en*E_joula •ockdose = hi*au_en*E.joule totmockdose = total(nockdose)*3600 totaldose * total

E.3 Fixing the vector with the measured spectrum

PRO measured_vector energyvec = fltarr(1476) countsvec - fltarr(1476) status = dc_read_free(*C:\mont9carlo\wbc_«easure_front.prn', energyvec, countsvec, /Colunn) ;for i = 0,1400. 100 do begin ; print, energyvec(i) ; print, countsvec(i) ;endfor energyvec = energyvec • 0-001 bin = 0.05 histo = fltarr(14) for j =1, 1474 do begin Blow = (energyvec(j-l) + energyvec(j)) / 2 Ehi = (energyvec(j + 1) + energyvec(j)) / 2 delta = (energyvec(j+l) - energyvec(j-1)) / 2 k.low = fix(Elow / bin) ; print, k_low k_hi = fixCEhi / bin) ; print, k^hi if (k_low eq k_hi) than begin histo(k_low) = histo(k_low) + (countsvec(j) / delta) • (delta / bin) endif else begin delta_lou = EIOM - bin * k_low histo(k_low) = histo(k_low) + (countsvec(j) / delta) • (delta.low / bin) delta_hi = Ehi - bin * k_hi histoCk^hi) = histo(k_hi) + (countsvec(j) / delta) • (delta^hi / bin) endalse endfor histo = histo / 1800 E « fltarr(l4) num = 50 for 1=0, 13 do begin E(l) = nun nuK = num + 50 print, histo(l), E(l) endfor path = 'H:\nontecarlo\wbc_front_' endp = '.dat' respons = fltarr(l4) teapresp = fltarr(14) openw, 1 , 'H:\nontecarlo\tfbc_front_respons' for x =0, 13, 1 do begin y = 50 * (x + 1) y_str = stringty, format; - "(14)") y_trim = strtrin(y_str, 2) ; print, y_tri« fullpath = path + y_trin + andp print, fullpath status = dc_read_free (fullpath, teapresp, /Colunn, get_colunn • 2, Ifskip = 2) ; pn, tempresp if (x eq 0) then begin respons = tenpresp endif else begin respons = [Crasponsj, [te»presp!]3 andelse andfor paf, 1, respons close, 1 ;p>, respons deter = determ(respons) print, deter if (deter ne 0) then begin inverse_respons = invert(respons) ; p», inverse.respons final_result = inverse_respons # histo openr, 2, 'H :\»ontecarlo\efftot.dat' rmf. 2, efftot, 14, 1 the_final_result = final_rasult / efftot print, final_result, the_final.result integral = total(the_final^rasult) print, histo, integral print, total(histo) E.4. MAKING THE MATRIX 69

plot, E, the.final.result, Background = 255, Color=0 oplot, E, 42.8 *histo, Background = 255, Color=0 close , 2 endif END

E.4 Making the matrix

PRO maJce.Batrix

endp = ' .dat* respons = fltarr(lOO) tempresp = fltarr(lOO) openw, 1, »H:\»ontecarlo\wbc_binl0_3Odeg\wbc_30deg_respons' for x = 0, 99, 1 do begin y = 10 * (x + 1) y_str « string(y, format = "(14)") y_tri» = strtrim(y_str, 2) print. y_trim fullpath = path + y_trim + «ndp print, fullpath status = dc_read_free(fullpath, teapresp, /Colu«n, get_colu«n = 2, Hskip = 2) ; pm, tempresp if (x eq 0) then begin respons = tempresp endif else begin respons = CCrespons], [tdmpresp]] endelse endfar pnf, 1, rdspons close, 1

END