When I had finished my second year at the Uppsala University School of
Engineering I was accepted for a traineeship in the Czech Republic at the
Nuclear Physics Institute of Academy of Science of the Czech Republic at Řež. My trainee-ship started July 7 and ended August 20. The first couple of weeks I worked on a program that simulates the neutron absorption in tungsten target. It was a computer-simulation of the work made by the previous trainee Evgenia
Michelioudaki (Study of spallation for nuclear waste transmutation). I also made an experiment studying the neutron field around a cyclotron.
1.1 Accelerator driven transmutation of nuclear waste
Nuclear power produces a large amount of highly radioactive materials which have a long lifetime. This is one of the most relevant problems concerning nuclear power and scientists is now trying to find a way to transmute them into shortlived or stable isotopes. Then deep underground storage would not be necessary.
The intensive neutron flux is necessary for effective transmutation. Such neutron flux is possible to produce using spallation reactions which are induced by high energy ( ~ 1 GeV) protons. We simulated distribution of neutrons produced in thick heavy target using semi-empirical model.
2.1 The Model
An intensive beam of protons is injected into the tungsten target. The target has the shape of a cylinder with radius = 1 cm and length = 60 cm. The intensity of the beam is decreasing along its way through the target according to

Ie
  x
I where ‘  ’ is the absorption coefficient and ‘x’ is the position. Absorption coefficient ’  ’ for tungsten is calculated to be 0.0919 cm -1 . A number of neutrons are generated as the proton beam is injected into the target. The number is calculated using the empirical formula [1]
N = (0.121+0.0469*ln(E))*A where ‘E’ is the energy of the protons in keV and ‘A’ is the mass number of the target. In this case the target is tungsten and A = 184.
The total number of neutrons is then calculated by multiplying the intensity with the number of neutrons. The neutron-flux inside the target is symmetric i.e. all directions for the neutrons have the same probability.

2.2 The Program
The simulation of the neutron absorption in tungsten target is written in the language C++ using a UNIX-computer.
Since we are interested in how the neutrons are spread inside the target, the target is described as an array with 30 boxes. Each box represents 2 cm of the target and it will hold the number of the neutrons in that area.
To know how many neutrons that are generated at each position we need to know the energy of the proton beam and its intensity at each position. From the data obtained from the experiment made by Evgenia Michelioudaki (Study of spallation for nuclear waste transmutation) we could use extrapolation to calculate the energy in each position. This is done in the function prot_energ(int).
The calculated energy is then used in the function number_neutron which calculates the number of neutrons at a specified position. This function does not depend on the intensity of the proton beam. The intensity I is calculated using the first equation above. The total number of neutrons is obtained in the function “number_of_neutrons” where the intensity is multiplied with the result obtained in the function “number_neutron”.
The program first calculates the probability of which direction the neutron will have. This is done by using a random generator, which generates number between 0 and 2  . The function "where" uses this when it calculates where the neutron will hit the target.
The number of neutrons that are generated at that position is calculated and multiplied by the probability of the different direction and then we will have the number of neutrons at different places in the target. This is repeated each
2 cm starting with 1 cm up to 59 cm.
2.3
Results
The spatial distribution of neutrons produced in reactions of 1.5 GeV protons with a 60 cm long tungsten target with diameter 2.0 cm was calculated using our
Program. Table shows for each position in the target the energy and the intensity of the proton beam, the number of produced neutrons, the actual number of produced neutrons (i.e. the number of produced neutrons multiplied with the intensity of the proton beam) and the number of neutrons that are absorbed at each position in the target.
1
3
5
Position Energy
(cm) (MeV)
1.4780
1.4180
1.3580
Intensity Number Actual of protons of neutrons number
Flow of neutrons through target produced produced surface
0.912196 25.6355 23.38460
0.759041 25.2779 19.18690
0.631599 24.9048 15.72980
7.51821
8.70061
8.90774
1.3155 0.525555 24.6304 12.94460 8.59938 7
9
11
13
1.2805
1.2350
1.1850
0.437316 24.3977 10.66950
0.363891 24.0855 8.764490
0.302795 23.7288 7.184960
7.94325
7.05098
6.24098
1.1525 0.251956 23.4888 5.918160 5.46964 15
17
19
21
23
25
1.1275
1.0780
1.0180
0.209653 23.2996 4.884830
0.174453 22.9121 3.997090
0.145163 22.4180 3.254250
4.76165
4.10932
3.57029
0.9650 0.120790 21.9566 2.652140 3.05738
0.9150 0.100510 21.4974 2.160700 2.63986

27
29
31
33
35
37
39
41
43
45
47
0.8720 0.083634 21.0820 1.763180 2.25383
0.8320 0.069592 20.6768 1.438950 1.89592
0.7920 0.057908 20.2516 1.172730 1.66081
0.7520 0.048185 19.8044 0.954282 1.42650
0.7085 0.040095 19.2902 0.773443 1.22569
0.6635 0.033363 18.7239 0.624691 1.04964
0.6150 0.027761 18.0689 0.501621 0.89348
0.5650 0.023100 17.3371 0.400496 0.77054
0.4975 0.019222 16.2392 0.312149 0.65981
0.4225 0.015994 14.8290 0.237185 0.58684
0.3545 0.013309 13.3147 0.177208 0.49184
49
51
53
55
57
0.2895 0.011074 11.5667 0.128097 0.43427
0.2385 0.009215 9.89445 0.091179 0.36905
0.1935 0.007668 8.09007 0.062034 0.31844
0.1485 0.006380 5.80588 0.037044 0.27402
0.1035 0.005309 2.69048 0.014284 0.23777
59 0.0585 0.004417 0 0 0.21180
The main feature of neutron intensity spatial distribution is exponential decreasing. The calculated spatial distribution is compared with experimental data on Figure 1. The experimental data were obtained using accelerator at JINR
Dubna [2] and are normalised on simulated ones. The very good agreement is between experimental and simulated shape of spatial distribution. The differences are done not only by simplicity of used model but also by fact that experimental neutron field was measured only for energy higher than 6 MeV.
3.1
Introduction
One of the important aspects of studies of nuclear waste transmutation possibility is knowledge of neutron interaction, transport of neutrons through different materials a neutron radiation damage of different materials and devices. The neutron field is necessary for such studies. One of the possible source of neutrons is accelerator. It is possible to use accelerator as source of charged particles for neutron generator (for example deuterons and their reaction with Be target). In this case we have neutron field with well defined spectrum. It is also possible to use for simple studies neutron field produced around accelerator during irradiation for other purposes.
3.2
Experiment
The isochronous cyclotron U120 of nuclear Physics Institute at Řež is used for neutron studies. One possibility is a neutron generator using deuterons with energy 20 MeV from cyclotron and Be target. In this case we obtain homogenous neutron field with mean energy of neutrons 6 MeV. The second possibility is neutron field produced around cyclotron during its work. In this case it is necessary to determine intensity and energy of neutrons at specific places. The neutron field in different places around the cyclotron was studied in our experiment.
The neutron yields were determined using activation method. Neutrons interact with different nuclei and produced other isotopes. Some of them are radioactive, decay by beta decay and produce gamma ray. The probability of given reaction is done by energy of neutrons. The number of radioactive (activated) nuclei is done by number of neutrons and their energy. The intensity of gamma is done by number

of activated nuclei. We used foils of gold, copper and aluminium for activation.
Used radioisotopes and their production reactions are shown in Table.
Reaction Half life time (hours) Gamma lines (keV)
27 Al(n,  ) 24 Na
197 Au(n,  ) 198 Au
14.959
64.68408
1368.633
411.8 675.88
63 Cu(n,  ) 64 Cu 12.700 511.0 1345.8
These were placed at different positions from the cyclotron. The purpose was to study the intensity of neutrons at different positions and distances from the cyclotron. We also placed plastic between some of the foils and the cyclotron.
The set-up of the experiment is shown in Figure 2. Intensities of gamma lines from the decay of radioactive isotopes was measured using semiconductor HPGe detector.
3.2 Data analysis
Since the relative values of the intensity is needed it is not necessary to know the absolute efficiency of the detection. The areas of the lines were derived using the program DEIMOS, which made gaussian fitting. It is necessary to make some corrections to obtain comparable intensity:
Nuclei of radioactive isotope decay during the measurement and therefore it is necessary to make a correction on the time t.
The formula for decay
I

I
0
 e
 t /
 
I
0

2
 t / T
1 / 2 where  is the mean life time and T
1/2 half life time.
Different foils does not have the same weight (number of nuclei) and it will be necessary to make a weight-correction. We calculate the intensity per mass m:
I m
= I/m
We made measurements at two different moments and it was possible to determine decay time of isotopes 64 Cu and 198 Au to test correctness of our measurements.
5
6
7
8
1
2
3
4
Position I
1
T
1
I
2
T
2
 T T
1/2
10900(300) 5.17 930(40)
18300(500) 5.59 930(30)
50.15 44.98 12.71(27)
51.58 45.99 10.71(16)
15500(400) 8.76 1040(60) 51.78 43.02 11.04(26)
23500(600) 2.88 50.97 48.09
94600(2000) 5.4 4190(140) 52.18 46.78 10.40(13)
64100(1400) 6.68 3450(120) 52.75 46.07 10.94(15)
57100(1300) 6.3 3030(90) 52.38 46.08 10.88(14)
18400(500) 6.48 880(50) 52.57 46.09 10.50(20)
Our obtained values of halftime for isotope 64 Cu are slightly lower than at literature (12.70 hours).

1
4
5
6
7
8
Position I
1
T
1
I
2
T
2
 T T
1/2
2520000(4000) 50.37 11240(160) 389.87 339.5 64.6(3)
1667100(2200) 50.63 7340(90) 390.07 339.44 64.55(26)
353300(400)
689800(700)
301950(290)
50.82 1510(40)
51.0 2840(50)
51.2 1270(40)
390.25 339.43 64.7(5)
390.43 339.43 64.5(4)
390.62 339.42 64.4(5)
1329300(1800) 51.48 5660(80) 390.8 339.32 64.29(29)
Our obtained values of halftime for isotope 198 Au are with the perfect agreement with literature (64.68 hours)
Au Cu Al
I
01
[1000] I
02
[1000] Ratio
1 1928.4(19) 1921(27) 1.00(6)
2
3
I
01
[1000] I
02
[1000] Ratio
74(2) 74.5(3)
I
01
[1000]
1.00(5) 8.430(27)
128(30)
137(30)
80(3)
96(6)
1.60(7} 0.710(9)
1.42(9) 1.380(10)
4 1309.7(10) 1300(16) 1.01(4)
5 273.14(17) 273(70)
139(30)
1.00(4) 672(14)
6 515.3(32) 508(90)
7 236.6(14) 233(60)
1.01(3)
1.02(3)
8 110.5{30) 108.1(15) 1.02(4)
382(13)
482.4(10) 321(11)
413.5(10) 272(80)
138.2(30) 81(40)
1.550(11)
1.76(7) 30.10(60)
1.41(6) 9.800(40)
1.52(6) 10.30(40)
1.69(3) 8.900(90)
Obtained data about neutron field in different positions around the cyclotron are prepared for further detailed analysis.
The computer program simulated spatial distribution of neutron distribution around thick target irradiated by high energy protons. Spatial distribution around tungsten target irradiated by 1.5 GeV protons was calculated and good agreement in the shape of this distribution with experimental data was obtained.
The intensities of neutron field at different points around the cyclotron of
Nuclear Physics Institute at Rez were measured using activation method. The data are prepared for further more detailed analysis.
[1] J. Cugnon: Nucl. Phys. A625(1997)729
[2] V. Wagner: Acta Polytechnica 38(1998)53