Report about Evaluation of gamma spectra of proton irradiatedAluminum and Copper foils at NPI
Řež
By
Ines Hartwig
Student of Computational Science Bachelors
ChemnitzUniversity of Technology
Germany
e-mail:
Table of Contents:
1. Introduction
2. Data about the experiment and aims of evaluation
3. Work steps and overview over calculations
4. Results in extracts
5. Conclusions and remaining problems
1. Introduction
For the great experience of a practical training at the Nuclear Physics Institute in Řež, Czech Republic though only being in my second year at university I want first of all to thank my supervisor and colleagues here who were enduring and answering my questioning with such kind patience and, of course, my appreciations also go to the IAESTE Czech and German National Committees as well as the DAAD.
During my seven weeks work period at the institute I did, besides several very interesting excursions to the different research departments, analysis of gamma spectra by a computer program called DEIMOS32. The obtained data will be used in further calculations necessary for profound research on spallation reactions and their usage for transmutation of nuclear waste.
2. Data about the experiment and aims of evaluation
The analyzed metal foils were irradiated in the following experiment:
“Neutron production inside complex setup consisting of lead target and uranium blanket irradiated by protons withenergy 0.7 GeV”
Datum:27. – 28. 6. 2004
Beam start: 17:07
Beam end: 01:58
Accelerator: Nuclotron
Beam: protons with energy 0.7 GeV
Beam integral (maximum): 5.19e13 protons
I have been analyzing Copper and Aluminum foils which were used to examine the proton beam in this way:
The proton beam with protons of energy 0.7 GeV first had to pass through big Copper and Aluminum foils (size 8cm*8cm, thickness 0.0481mm (Al), 0.0 245mm (Cu)), separated by paper so as to avoid the produced radioactive nuclei to spread from one foil to another. This setup should provide data to determine the total number of protons in the beam (The beam integral above provides only the upper limit).
Placed some centimeters behind the big foils in the beam were several multipart beam monitors (size 6cm*6cm), each composite of 9 small foils (size 2cm*2cm, thickness ~0.6mm (Al), ~0.2mm (Cu)) arranged as shown in the picture below (with the proton beam flowing away from the contemplator):
1 / 2 / 34 / 5 / 6
7 / 8 / 9
The aim of this latter arrangement is to obtain the beam position and its density distribution,enabling to conclude ondistribution and location of the radiation hitting the target.
All these metalfoils were then measured using a gamma ray detector and my task was to analyze part of them, meaning one big Copper and Aluminum as well as one multipart Copper and one multipartAluminum monitor.
3. Work steps and overview over calculations
The measured raw data was first evaluated using the program DEIMOS32 doing Gaussian fit to the peaks leading to peak areas, statistical error percentages of their fitting and, of course, the energies of the peaks. Having assigned the radioactive nuclei by their characteristic gamma line energies to the diverse peaks in the measured spectra, I started on doing calculations with anassorted selection of these (e.g. the spectra also contained several lines of , a calibration isotope not at all involved in experimental results), a table of which is given beneath:
Isotope / Line / Gamma line energy (keV) / Half-life (h) / Intensity of the line (%) / Cross section (mbarn)Copper
44m-Sc-1 / 271.13 / 58.6 / 68.3 / 4.00
46-Sc-1 / 889.277 / 2010.96 / 99.984 / 5.28
46-Sc-2 / 1120.545
47-Sc-1 / 159.377 / 80.3808 / 68.3 / 2.25
48-V-1 / 944.104 / 383.364 / 7.76 / 11.51
48-V-2 / 983.517 / 99.98
48-V-3 / 1312.096 / 97.5
51-Cr / 320.0824 / 664.86 / 10 / 26.68
52-Mn-1 / 744.233 / 134.184 / 90 / 9.89
52-Mn-2 / 935.538 / 94.5
52-Mn-3 / 1434.068 / 100
54-Mn-1 / 834.848 / 7495.2 / 99.976 / 18.83
56-Co-1 / 846.771 / 1854.48 / 100 / 10.20
56-Co-2 / 1037.84 / 13.99
56-Co-3 / 1238.282 / 67.6
57-Co-1 / 122.0614 / 6522.96 / 85.6 / 26.38
57-Co-2 / 136.4743 / 10.68
58-Co-1 / 810.775 / 1700.64 / 99 / 42.70
60-Co-1 / 1173.237 / 46177.46 / 99.9736 / 12.41
60-Co-2 / 1332.501 / 99.9856
Aluminum
7-Be / 477.595 / 1274.88 / 10.52 / 5.69
22-Na / 1274.53 / 22792.644 / 99.944 / 13.79
During my calculations it became clear, that at least part ofis a leftover from detector calibration, too, and thus not to be taken into account.
In a second step, a few first calculations were done: Because, e.g., of the time passing between irradiation and measurement, it is necessary to do corrections on the area of the peaksevaluated by DEIMOSprimarily,signifying the number of nuclei at measurement time, and so to recalculate the total number of radioactive nuclei produced during irradiation which finally carries on to the total number of protons going through the different foils, our desired result.
Here are the equations used:
to obtain the decay constant of the nuclei from the tabulated half-life;
to obtain the total amount of nuclei produced during irradiation;
respectively, with ,
to finally obtain the total number of protons going through the foils.
Where the symbols signify:
Symbol / Used names in the Excel files / Description/ yield / Number of produced radioactive nuclei
/ n.o.p. / number of protons / Number of protons going through the foil
/ intensity (of the line) / intensity of the gamma line
/ detector efficiency / detector efficiency detector at energy E
/ cross section / Cross section for proton reaction at 0.7 GeV
/ treal / duration of the measurement
/ tlive / ‘online’ time of detector during measurement
/ t0 / time span between beam end and begin of measurement
/ tirr / duration of irradiation
/ decay constant / decay constant of the isotope
/ half-life / half life of the isotope
/ foil mass / foil mass
/ foil thickness / foil thickness
/ foil area / area of the foil
/ density / density of the foil material (Copper / Aluminum)
/ atomic mass number / Atomic mass number of Copper / Aluminum
/ Avagadro’s number
Besides the determination of the yield and proton numbers I also did some standard deviationestimation, based on statistical errors made by DEIMOS (aerr (%)) and approximated cross section errors,using weighted averages.
All the evaluation data and results of the calculations can be found in 4 Excel files, located in the directory C:\Meins\Excel\, named:
Crosssections.xls containing the data for estimation of the cross sections
Efficiency.xls containing the data for calculation of detector efficiencies
Copper.xls containing the data for the big and multipart Copper monitor
Aluminium.xls containing the data for the big and multipart Aluminum monitor.
In the latter two, extracts of which are given in the next section, I made a few comments on the data and marked problematic points in red text.
4. Results in extracts
Copper:
As for one, these are the calculations done for the big Copper monitor. Similar tables exist for all the other copper foils.
filenamemcu_r1
“good isotopes”
line / energy (keV) / yield/gram / n.o.p. / gram / absolute error n.o.p. / wghtd. avrg. n.o.p.
44m-Sc-1 / 270.84 / 1.7E+07 / 2.07E+13 / 9.69E+12 / 6.11E+12
46-Sc-1 / 889.26 / 7.8E+06 / 9.69E+12 / 9.10E+11
46-Sc-2 / 1120.38 / 1.4E+07
47-Sc-1 / 159.17 / 4.5E+06 / 9.66E+12 / 2.89E+12 / sum n.o.p. for the multipart monitor foils
48-V-1 / 944.00 / 1.4E+07 / 6.28E+12 / 4.02E+11 / 1.08E+13
48-V-2 / 983.47 / 1.5E+07
48-V-3 / 1312.09 / 1.5E+07
51-Cr-1 / 320.06 / 3.2E+07 / 5.76E+12 / 6.16E+11 / abs. error wghtd. avrg.
52-Mn-1 / 744.12 / 1.1E+07 / 5.47E+12 / 5.43E+11 / 2.89E+11
52-Mn-2 / 935.43 / 1.1E+07
52-Mn-3 / 1434.10 / 1.2E+07
54-Mn-1 / 834.87 / 2.8E+07 / 7.23E+12 / 7.01E+11
56-Co-1 / 846.75 / 1.4E+07 / 6.61E+12 / 6.48E+11
56-Co-2 / 1037.84 / 1.4E+07
56-Co-3 / 1238.24 / 1.7E+07
57-Co-1 / 121.90 / 4.3E+07 / 7.67E+12 / 6.80E+11
57-Co-2 / 136.38 / 3.2E+07
58-Co-1 / 810.70 / 3.7E+07 / 4.15E+12 / 5.68E+11
Where the “good isotopes” that turned out to be the most reliable are,, and also . From the first three, which show indeed very high concistency especially when comparing the obtained yield values for their different lines, I calculated the weighted average proton numbers for each foil. Logically, the sum of proton numbers for all the nine small foils of the multipart monitor should be smaller than the total amount of protons going through the big foil, which is apparently not the case as can be seen in the above table and requires further investigation.
The good thing is, though, that for all the isotopes the line of weighted average appears to lie within a range of three times the standard deviation error bars:
Concerning the analysis of the multipart foil, I prepared some charts for comparison of the proton flux through the different foils, to illustrate the density distribution:
The upper one shows the total number of protons respective to the foil number (experimental setup see part 2), whereas the lower one contains a parabolic fit of the beam density (Gaussian fit would reflect nature better). For this, I calculated the relative proton flux through the foils, normalizing the flux by assigning100% to the middle foil, no.5. For the fit I took the three values for foils no.5 (position 0cm from the center), no.2 (2cm) and no.1 (2.83cm).
The two charts show clearly that the maximum beam intensity was not exactly located in the middle of the arrangement but shifted somewhat (about 0.8 cmfrom the center, according to my estimation) upward to foil no. 2 and to the left in the direction of foil no.1.
Aluminum:
As for Copper, there are luckily enough different isotopes to be able to do more or less sure conclusions, but in the Aluminum spectra I could only find 2 useful characteristic lines. The obtained results for the two isotopes and a comparison between them follow now:
For
file / yield / abs. error / number of protons/gram / abs. err. n.o.p. / pctg. proton flux / relative errormal_41 / 1.52E+07 / 4.26E+06 / 7.60E+11 / 2.74E+11 / 8.5% / 3.1%
mal_42 / 2.72E+07 / 4.79E+06 / 1.37E+12 / 3.51E+11 / 15.4% / 3.9%
mal_43 / 9.53E+06 / 3.57E+06 / 4.66E+11 / 2.12E+11 / 5.2% / 2.4%
mal_44 / 1.25E+07 / 3.66E+06 / 6.21E+11 / 2.32E+11 / 7.0% / 2.6%
mal_45 / 2.73E+07 / 3.05E+06 / 1.34E+12 / 2.57E+11 / 15.0% / 2.9%
mal_46 / 1.36E+07 / 5.40E+06 / 6.70E+11 / 3.19E+11 / 7.5% / 3.6%
mal_47 / 8.85E+06 / 2.37E+06 / 4.41E+11 / 1.53E+11 / 4.9% / 1.7%
mal_48 / 1.15E+07 / 1.57E+06 / 5.64E+11 / 1.22E+11 / 6.3% / 1.4%
mal_49 / 8.03E+06 / 6.91E+06 / 4.10E+11 / 3.86E+11 / 4.6% / 4.3%
sum multipart n.o.p. / 6.64E+12 / 74.5%
mal_r1 / 1.47E+07 / 1.90E+06 / 8.92E+12 / 1.86E+12 / 100.0% / 20.9%
For
file / yield / abs. error / number of protons/gram / abs.err. n.o.p. / pctg. proton flux / relative errormal_41 / 7.09E+07 / 1.51E+07 / 1.47E+12 / 4.15E+11 / 11.0% / 3.1%
mal_42 / 8.03E+07 / 1.59E+07 / 1.67E+12 / 4.47E+11 / 12.5% / 3.3%
mal_43 / 4.86E+07 / 9.61E+06 / 9.81E+11 / 2.63E+11 / 7.3% / 2.0%
mal_44 / 6.18E+07 / 1.01E+07 / 1.27E+12 / 2.96E+11 / 9.5% / 2.2%
mal_45 / 8.91E+07 / 9.35E+06 / 1.81E+12 / 3.16E+11 / 13.5% / 2.4%
mal_46 / 5.59E+07 / 1.25E+07 / 1.14E+12 / 3.33E+11 / 8.5% / 2.5%
mal_47 / 4.71E+07 / 6.02E+06 / 9.67E+11 / 1.91E+11 / 7.2% / 1.4%
mal_48 / 6.69E+07 / 4.48E+06 / 1.35E+12 / 1.85E+11 / 10.1% / 1.4%
mal_49 / 4.68E+07 / 7.48E+06 / 9.86E+11 / 2.27E+11 / 7.4% / 1.7%
sum multipart n.o.p. / 1.16E+13 / 87.1%
mal_r1 / 5.34E+07 / 6.67E+06 / 1.34E+13 / 2.60E+12 / 100.0% / 19.5%
Here, in contrast to the Copper foils, the relative proton flux has been calculated respective to the total amount of protons going through the big foil, which is possible because for Aluminum the sum of proton numbers is, reasonably, smaller than the total value detected by the big monitor.
For easier comparison, I plotted some results: The upper chart contains the total proton numbers of Beryllium and Sodium with standard deviation error bars:
I, too, calculated weighted average proton numbers for each foil and, to overcome troubles with foil no.9 caused by a big error in the determination of the Beryllium peak area, normalized the average values; a plot of these latter values respective to the foil numbers is below:
5. Conclusions and remaining problems
1. Beam integral:
The total proton numbers monitored by the big Copper and Aluminum foils show differences, which I cannot now explain, unfortunately. But as mentioned before, the big Copper foil requires further attention because of the disagreement between the sum of protons passing the multipart and the big monitor. At least, the order of the beam integral,,is right.
2. For Aluminum foils, the proton numbers obtained for are about twice as high as the appropriate values for, but still the differences are within a range of three times the standard deviation. I figure that the discrepancy is due to the very unequal half-lives of the two isotopes.
3. The characteristics of the multipart number of protons charts of Copper and Aluminum are very similar, though not exactly the same. For overview, I will here give another chart showing the proton flux through the multipart monitors.
Again, the difference lies within the range of three times the standard deviation error bars.