Report from a summer job at Nuclear Physics Institute AS CR

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Report from a summer job a
t Nuclear Physics Institute AS CR

Author:

Øystein H. Færder

Time:

Summer 2010

Location:

Rez, Czech Republic

Field:

Data analysis in nuclear physics

Introduction

Before we start using a fissile fuel, it is important to know how
feasible the fuel is. In this
case, we will study

the feasibility of

235
U as a fissile fuel.

The technical part of this experiment has been done before me, and it goes like this: a beam of
protons strikes a lead target; neutrons are then produced as an ou
tgoing beam by spallation;
the spallation neutrons hits a sample of
235
U; the sample is then undergoing different
reactions, mainly fission, but also alpha decay, beta decay and neutron decay, and therefore
many new isotopes are produced from the sample. A
ll of the isotopes emit photons due to beta
decay and electron transitions in the atoms. The photons are then detected by spectrographs
such that photons with different energy are registered in different channels. Finally the
spectrum is import to a comput
er by an ADC converter.

Goal

My task is to use the spectra to find out how much which was produced of each isotope, hence
also how much neutrons were produced in the spallation.

These data are important because we
need to know the efficiency of this fuel (
number of neutrons produced per proton per foil
mass), and because we want to know what kind of nuclear waste which will be produced.

Equipment

-

DEIMOS, a computer program used to evaluate spectra

-

Spectra from two different samples of
235
U, referred to as
sample no. 5 and no. 6. We
got 11 measurements from each sample, taken at different times and different
positions at the spectrograph

-

The website
http://nucleardata.nuclear.lu.se/nu
cleardata/toi/index.asp

for nuclear data,
in this text referred to as “the nuclear database”

Execution

To evaluate the spectra, we use a program called DEIMOS.
The first thing to do after loading
in a spectrum was to check that the calibration was OK. We k
now that we should expect a
huge peak centered
about

energy

of 511 keV, because this is the energy of photons created in
annihilation of electrons and positrons.

Looking at the spectra from the first measurement

of
sample 5
, wh
ich was taken at position no. 8 at time 51 minutes after end of irradiation, I found
that peak very quickly, and it DEIMOS calculated the peak to be centered at
510.8

keV. Thus,
the annihilation peak is where it should be, with an error less than 1 keV. He
nce, the
calibration
cannot

be too bad.

I continued focusing on sample no. 5, and started measuring the areas under each peak of the
spectrum from measurement 1, that is to say, the area between the peak and the continuum
curve in the spectrum
.


Then it wa
s time to look at some of the peaks and see if I could figure out which isotope
which the line corresponds to. I started with a peak at 846.9 keV with area
9701.4
, which was
a relatively high area in this measurement. I used the nuclear database to search
for gammas

with an energy close to this in a range of 1 keV.

Things to keep in mind while looking for a proper mother isotope: This first measurement is
taken at 51 minutes after end of irradiation, at the spectrograph position with the lowest
efficiency a
nd the lowest measurement time


.

Therefore, if the half
-
life
,




,

of the
mother isotope is shorter than 10 min, there will probably not be much left of the isotope, and
we would not see any great line from the isotope. If






is

in the order of years or higher, it
will probably radiate so slowly that we won’t obtain much photons from it. This is not always
true, but if we locate a line where we can’t find any proper mother isotope in this range, we
will skip that line and come ba
ck to it later, after evaluating the other measurements of the
same sample. We will also use a “probability curve” that tells us the probability of creating a
specific isotope from
235
U as a function of the atomic mass. In that way we have an idea about
wh
ich isotopes we can expect there will be produced a lot of. With these criteria in mind, we
should first of all check if there we can see other lines from the same isotope. Second: for
small energy variations, in distances of 1
-
300 keV, the area of the lin
e divided by the relative
intensity



should almost constant

if the lines are from the same isotope
. For high
er

ranges

this fraction will decrease with the energy, because the efficiency decreases with energy.

Back to the peak at
846.9 keV (with area
97
01.4
), I found several matches on the database
following the above mentioned criteria, but in the end I concluded that it had to be a line from
134
I with
energy 847.
0

keV and relative intensity 95.4.

This isotope has a half
-
life at 52.5
min, which is
close to the time from end of irradiation to the time of measurement(






), and the atomic weight is near the top of the probability curve, which makes it highly
probable that we should see lines from this isotope. The isotope also has lines

884.1 ke
V and
1072.6 keV with rel. int.

at

64.9 and 14.9, respectively, in agreement with observed peaks at
884.0

keV and 1072.5 keV with areas 6488.0 and 1310.6, respectively. This looked very
promising, and we managed to locate more than 20 lines from this isoto
pe in the spectrum, I
can with very high certainty say that this isotope has been produced in the fissions of the
sample during the irradiation of neutrons.

The energy difference between all of these lines and
the corresponding theoretical
134
I
-
lines were
less than 1 keV, which also makes us more sure
that the calibration is good. The area of each of these lines also agreed good with the relative
intensity, except for a few lines which had too high area, but that may be due to blending with
another line wit
h almost same energy.

I managed to find a lot of other isotopes using this easy method, but there still remained a lot
of strong lines which I had trouble finding a proper mother isotope to. There were some good
mother isotope candidates for these lines t
oo, but one problem was that these “candidates”
only had one or two strong lines, and it wasn’t possible to tell which candidate which was the
right one
by using this simple method. I needed to obtain more information from the other
spectra.

So, the next
step was starting evaluating the other measurements from the same sample. The
n

I could compare the area of a specific line at two different measurements and try to
estim
ate
the half
-
life of the mother isotope.

To estimate the half
-
life, we’ll do some computations: We know that the amount
N

of an
isotope at a time
t

is given by









where



is the number of the isotope at



, and










is the decay constant. If the
measurement begins at



an
d ends at


, we have












(











)



(









(





)
)








(







)

From now on, I’ll change the names such that



becomes


, which often is referred to as the
cooling time, and



becomes


, the time of the

measurement.

To take the “dead time” in
to consideration, we should also include the fraction




, where



is the live time of the
measurement. But we will neglect it in this estimation, since it doesn’t make a big error.

With
so
me rough approximation, the area of a peak goes as







(

)



where


(

)

is the effi
ci
ency of the spectrograph position as a function of energy, and



is
the relative intensity of the line.

When comparing to different measurements, we should then
have











(


)








(


)









(









)


(


)








(









)


(


)




When looking at the same line (at different measurements) the fraction







cancels out. I
implemented this equation into a MATLAB code where I could estimate the half
-
life




by
solving this equation for


graphically. I also imported a program code from Dubna to
calculate the effi
ci
ency for a given position and a given ener
gy. It was originally written for
another programming language but was easy to translate into MATLAB.

First I had to try out this method on some of the lines which I had decided the mother isotope
by the simple method which I used first. For the three stro
ngest lines of the
134
I
-
isotope
mentioned above, I got half
-
lives at 69.3, 69.0 and 71.6 min, which is not too far away from
the actual half
-
life at 52.5 min. For an assumed
92
Sr
-
line at 1383.9 keV, I found the half
-
life to
be at 190 and 176.5 min by comparing measurement 1 and 2 and comparing meas. 2 and 3,
respectively. And the actual half
-
life of
92
Sr is 162.5, so the error is

still

not too big.

We
managed to detect several n
ew isotopes by using this method. E.g. an unknown line at 743
keV seemed to have a half
-
life at 340 min by comparing meas. 1 & 2

and between 900 and
1200 min by different comparisons of meas. 2 to 8. I concluded that the isotope
97
Zr with a
half
-
life of 16
.9 h (1014 min) was the main contributor to this line at long cooling times, but
at short cooling times, there also got to be a more short
-
lived contributor (together with
97
Zr)
.

Some of the lines which we used this method on seemed to come from mother is
otopes with
half
-
life which could be anything between 5000 min and infinity. Looking at the database, all
of these seemed to have mother isotopes with half
-
lives at the magnitude of thousands of
years or higher. Because of the high half
-
life, the error is

very, very huge.

After using this method for a while, I had located lines from both
131
I,
133
I and
134
I, so I
expected that we should have some lines from
132
I, since this isotope have a half
-
life of 2.295
hours, which is within the range of half
-
lifes su
ch as the lines should be obtainable.
I actually
found some lines which seemed to be the strongest lines of this isotope, but from my half
-
life
-
estimation method, it seemed like the half
-
life was about 3
-
4 days.
After some research, I
realized that
132
I is being produced by beta
-
decay of
132
Te, which have a half
-
life of 3.204
days, and that looks like a good explanation why this lines yielded a half
-
life of 3
-
4 days.
Actually, both
131
I,
132
I,
133
I and
134
I is produced from this chain:
X
Sn


X
Sb


X
Te


X
I,
where X is the atomic mass. But for these masses, Sn and Sb have so short half
-
life that they
won’t affect the yielded half
-
life mention
-
worthly much (though
131
Sb have just long enough
half
-
life so that its lines are barely visible in the first measu
rement).
It’s also the same with
131
Te and
133
Te.
134
Te have a half
-
life of 41.8 min and produces
134
I in a rate such that the
yielded half
-
life from its lines in the 1
st

and 2
nd

measurement is about 70 min, while the real
half
-
life is 52.5 min. These four

above
-
mentioned isotopes of I decays further on to Xe, which
is stable.

Now I had obtained a bit more knowledge about these isotopes and how they are produced,
which leaded me to the final and maybe most efficient way to localize lines. This method goes
l
ike this: Looking systematically through isotopes of all masses between 80 and 150 (masses
outside this range are not probable to be produced from
235
U, nor
238
U)
; for each mass, start
with the first isotope which have a high enough half
-
life (minimum 20 m
in); from the half
-
life
you should be able to see which measurement where you are most probable to see the
strongest lines; see if you can locate the lines; estimate the half
-
life by the above
-
mentioned
method; make a conclusion! You’ll do the same with th
e next isotopes with same mass until
you come to a stable isotope, or an isotope with too high half
-
life.

And remember, if one
isotope have a much higher half
-
life than the next isotope in the beta
-
decay chain, the yielded
half
-
life from the different measurements will be affected by that. By doing this, I was able to
locate really many different isotopes. No
w, let’s go to the final step in this analysis, the yield
calculation!

To compute the number of produced nuclei of an isotope, we use the following equation:






(

)


(

)


(

)









(


)


(



)



(




)







(




)

where



is the number produced of the mother isotope of the line with energy
E

during
the whole period of irradiation divided by mass of the acti
vation detector and proton flux,
from now on, only referred to as the
yield

of an isotope.


(

)

is the area of the line,
measured from the spectra, COI is a
correction

factor which we here approximate to 1,
m

is
the foil mass,

(


)

is the proton flux
,



is the total time of irradiation by the spallation
neutrons, and the other are as mentioned earlier.

By inserting numbers into the equation from different measurements of different lines of the
same isotope, I got several yields for each isotope. For diff
erent measurements of the
same

line, the yield seemed not to be too different, and after some yield calculations, I decided not
to calculate yields from many measurements of the same line, but rather look at different lines
from the measurement where the l
ines of the specified isotope are strongest. For the different
lines (which are not blended by another line), there were some notable variations in the yield,
and the variation was systematic: the yield seems to increase with the line energy. This issue
ca
n have different explanation: there could be a systematic error in the calculated efficiencies,
or there could be a notable correction
factor (
COI)

which increases
with energy. The
variations are though only within one order of magnitude.

A list of all loc
ated isotopes and some yields are included on a separate Excel file.

At some of
the yields which are different from other yields of the same isotopes, I have been able to
figure out the reason, and I have wrote it down as note (look for a small red triangl
e in upper
right corner of some of the cells)
.

Conclusion

I have been able to locate many isotopes produced from neutron radiation of
235
U, and I’ve
got some yields for some of these isotopes, telling me how much of it that’s produced per
proton per foil
mass. I thereby hope the results of my analysis will be helpful for the scientists
who will continue the feasibility study.