# KJM-FYS 5920 Lab Exercise 2 - Student Report

KJM-FYS 5920 Lab Exercise 2 report (Autumn 2010):

## Setting up a HPGe gamma-spectroscopy system

Participating students (authors): Tomas Kvalheim Eriksen, Alexander Mauring, Therese Renstrøm, Inger Eli Ruud, Pejman Mansouri Samani, Martin Ytre-Eide, Sindre Øvergaard.

Teachers: Prof. Jon Petter Omtvedt and Hilde-Therese Nyhus (lab assistant)

University of Oslo 1st October 2010

#### Introduction

(Written by: Jon Petter Omtvedt)

#### Detector and Preamplifier Signals

(Written by: Pejman)

#### Spectroscopy Amplifier Setup & Signals

(Written by: Martin)

ADC (or A/D) means analog to digital converter. The ADC is a fundamental link between analog and digital electronics as it converts information in an analog signal to an equivalent digital form. This happens by the ADC accepting input pulses of 0-10V and converting these to digital numbers ranging from 0-8195. (The ranges here are from the device used in the experiment, the voltage- and digital number range may differ from model to model.) E.g for this device an input pulse of 2.0V would be converted to the digital number 1639.

MCA means multi-channel analyzer. Together with the ADC it forms a unit which sorts out and keeps count of the different pulses, and stores the count of each pulse in a multi-channel memory. The memory channel adress corresponds to the digitized value of the signal. In this way the pulses received from the detector system are sorted out and counted according to pulse height (voltage), which is proportional to the gamma energy. The total number of channels into which the voltage range is digitized is known as the conversion gain, and it determines the resolution of the MCA.
It can be connected to a computer, or another output device, in order to view the acquired spectre (Counts per channel).

Basic architecture of a MCA

The SA is connected to the ADC/MCA for conversion of the enhanced pulses. The next step is to adjust the gain, we want 0.5keV per channel. 137Cs has a gamma peak at 662keV, this energy then corresponds to channel number 1324. What voltage should the incoming pulses have? The answer is channel number divided by total channel number times the maximum voltage in the range of the ADC, here (1324/8195)*10V=1.62V.
With 137-Cs in front of the detector, we adjust the gain until we see pulses about 1.62V on the oscilloscope. The gain is then 10.348 and the MCA should now have a resolution of 0.5keV per channel.
Now the ADC/MCA unit is ready for connection to a computer to view the acquired spectre, and for further calibration.

Analog to digital conversion. The channel number given by the ADC is proportional to the amplitude of the incoming pulse.

(Written by: Tomas)

#### Calibration

The electrical signal from the Ge-detector has now propagated through many components that has both shaped and enhanced the pulse. The energy of interest is of course that deposited by the gamma in the detector. The Gaussian-like pulse produced in the main amplifier will have an amplitude proportional to the gamma-energy. The signals from the main amplifier are analysed by the ADC/MCA unit. Information from the MCA is received by the lab-computer in the form of a histogram; number of counts pr energy bin. We use the spectrum analysis program MAESTRO to look at the resulting spectra. Since the detector has an approximately linear response, we have that:

E_gamma = a * channel nr + b, where we ignore higher order terms.

To determine the two unknowns, a and b, we need two equations. We need two known gamma energies and their corresponding channel number. Co-60 has two prominent peaks, one at 1173 keV and one at 1332 keV. Using the peak-finding function in MAESTRO, we find the channel number of the two peaks. The radioactive isotope Co-60 provides excellent calibration for energies in the region between 1-1.5 MeV. We recognize that the energy separation between the two peaks; delta_E = (1332 - 1173) keV = 159 keV, is small compared to the uncertainties connected to determination of peaks and detector resolution. A small error in the determination of a and b will give a large mistake for energies far from the calibration region (1173 - 1332 keV).

In the spectrum of Co-60 we observed three strong peaks in the interval between 1 and 1.5 MeV, but we expected only two . The unknown peak appeared to come from the considerable concentration of K-40 in the concrete walls of the lab. Table of Isotopes gives one gamma energy for K-40, E_gamma = 1460 keV. This peak would correspond to the highest of the three detected peaks. We also tested this theory by removing the Co-60 source from in front of the Ge-detector. The two peaks with the lower energy disappeared as expected. The reason why the background line was so strong, was that we did not shield the source with lead blocks. A rough calibration was performed with Co-60 giving poor results for low energy gammas.

We need an additional calibration-point at lower energy to get a more accurate calibration for low gamma energies. Co-57 has clear, separable peak at E_gamma = 122 keV. We finally decided to use the 122 keV peak from Co-57 and the 1332 keV peak from Co-60 as calibration points. The energy-separation between these peaks are: delta_E = (1332-122)keV = 1210 keV. These points certainly gave a  better calibration for lower energy gammas and still good results for higher energies.

Still the spectrum showing in MAESTRO needed improvements. E_gamma = 0 keV should correspond to channel nr 0. But in our case we had a negative energy in channel 0. We tuned the ADC until we got it right. New calibration was performed whenever we changed voltage. We also noticed that the energy pr bin was a bit over the pre set width of 0.5 keV. Increasing the amplification decreased the width of the bins to ca 0.5 keV.

At this point in the experiment we were ready to look at spectra in MAESTRO and seeing correct energies of the peaks.

(Written by: Therese and Inger Eli )

#### Detector Performance

(Written by: Alexander and Sindre)

#### Experimental setup and results

The above figure shows the experimental setup used for this part of the exercise. The 662 keV line from a radioactive Cs-137 source was used to measure the total FWHM. The result was FWHM = ΔE = 2.22 keV. In order to measure the contribution to the FWHM from the associated electronics the radioactive source was replaced by a produced signal from a pulse generator at 673 keV. The resulting FWHM was = 1.83 keV. The contribution from the detector is then

Knowing that the energy resolution is given as ΔE/E we can write

Solving this equation for F yields

Inserting values into the right hand side of this equation gives us an experimental value of the Fano factor

The nominal value of F is 0.13 which means our experiment gave a good estimate of the Fano factor.

(Written by: )