Báo cáo " DETERMINING THE ISOMERIC RATIO OF NUCLEAR REACTION 46 Ti (γ, pn)44 Sc BY EXPERIMENT " docx

VNU. JOURNAL OF SCIENCE, Mathematics - Physics. T.XXI, N
0
1 - 2005
DETERMINING THE ISOMERIC RATIO OF NUCLEAR
REACTION
46
T
i
(γ,pn)
44
Sc BY EXPERIMENT
Tran Tri Vien, Doan Quang Tuyen, Nguyen Trung Tinh
College of Science, VNU
Abstract.
The bremsstrahlung beam with energy end point of 65MeV createdwhenthe
e
−
beam with energy of 65MeV irradiated to thin wolfram target was used to irradiate
to TiO
2
sample in order to make the
46
T
i
(γ, pn)
44m,g
Sc reaction. The gamma spectrum
of Sc
44m,g
was analyzed by the gammavision spectrometry with HPGe detector at linear
accelerator laboratory in POSTECH, Korea. As the result, the isomeric ratio

Υ
m
/Υ
g
of
the reaction is presented.
1. Introduction
The isomeric ratio data of nuclear take an important role in nuclear structure re-
search and nuclear reaction mec h anism, that why, there are many laboratories in the
world studying these. In our experiment , the beam of bremsstrahlung radiations is cre-
ated when e
−
current with energy of 65MeV irradiating to thin wolfram - target, then the
bremsstrahlung beam irradiating to TiO
2
sample of 99.99% pure degree. After 2 hours
of irradiation, the sample disintegrates in a period of time depending on the sample ra-
dioactivity. The sample is measured by the geometric arrangement fixed for minimizing
the error.
The
44
Sc is created by reaction as follows
γ +
46
Ti →
44
Sc + n + p.
After being produced,
44
Sc nuclei is in excited states. However, the life-time of

these states is very short(< 10
−10
sec). Then the nuclei jump into the lower energy states,
and at the end, they jump to the isomeric state or ground state. On the other hand,
44
Sc
is a radioactive nuclear. It disintegrates to
44
Ca from isomeric state and ground state.
The gamma spectrum of
44
Sc created from two parts, one is due to
44
Sc transferred from
isomeric state in to ground state, and the other is due to
44
Ca transferred from higher
energy excited states to the lower one or to the ground state (Fig.1).
2. Calculating the essential parameters of reaction
In this paper the following symbols are used: t
1
is time for irradiating to TiO
2
target, t
2
is the disintegrating time (the period of time from radiation stop to spectral
measurement) and t
3
is time spectral measurement.
The equation representing the irradiating at sample is as follows

dN
m
dt
=N
0
σ
m
φ(t) − λ
m
N
m
(2.1)
Typeset by A
M
S-T
E
X
51
52 Tran Tri Vien, Doan Quang Tuyen, Nguyen Trung Tinh
dN
g
dt
=N
0
σ
g
φ(t) + P
m,g
N
g

− λ
g
N
g
, (2.2)
where σ
m
and σ
g
are cross-sections of the metastable and the ground state, respectively,
λ
m
and λ
g
are the decay constants of these states, P
m,g
is the branching ratio for the
decay of metastable to ground state, N
0
is the number of target nuclei, φ(t)istheflux of
beam per 1cm
2
of bremsstrahlung irradiated in to the sample, N
m
and N
g
are the number
of nuclei in the metastable and the ground state.
Figure 1. Production and deca y of the metastable and the ground state
In gamma spectra, the area (number of count) of peak with energy E

γ
is determined
as follows:
S=f
γ

t
3
8
0
A(t)dtC
f
γ
: intensity of photopeak
:detectionefficiency of gamma spectrometry
For gamma spectrum of
44
Sc
m
, the spectral peak area with energy E
γ
calculated
as follows:
S
m
=N
m
=f
m
γ


m
t
2
+t
3
8
t
2
λ
m
N
m
dtC
m
=f
m
γ

m
N
0
φ
0
σ
m
λ
m
(1 − e
−λ

m
t
1
)e
−λ
m
t
2
(1 − e
−λ
m
t
3
)C
m
(2.3)
Determining the isomeric ratio of nuclear reaction 53
Similarly, the area of spectral peaks caused by the disintegration of nuclei
44,g
Sc is
S
g
=N
g
=f
g
γ

g
N

0
φ
0
^
P
m,g
σ
m
λ
g
λ
m
(λ
g
− λm)
(1 − e
−λ
m
t
1
)e
−λ
m
t
2
(1 − e
−λ
m
t
3

)

C
g
+f
g
γ

g
N
0
φ
0
^
1
λ
g
w
σ
g
− P
m,g
σ
m
λ
g
λ
g
− λm
W

(1 − e
−λ
g
t
1
)e
−λ
g
t
2
(1 − e
−λ
g
t
3
)

C
g
,
(2.4)
where f
m
γ
and f
g
γ
is intensity of gamma ray corresponding with the state of
44,m
Sc and

44,g
Sc,

γ
is detection efficiency of gamma spectrometry at spectral peak with energy E
γ
,C
m
and
C
g
are the self-absorption correction c oefficient of radiated sources, C
m
a 1, C
g
a 1.
With the result of equations (2.3), (2.4) the isomeric ratio can be determined
IR =
σ
m
σ
g
=
^
λ
g
(1 − e
−λ
m
t

1
)e
−λ
m
t
2
(1 − e
−λ
m
t
c
)
λ
m
(1 − e
−λ
g
t
1
)e
−λ
g
t
2
(1 − e
−λ
g
t
c
)

w
C
m
N
m
f
m
γ

m
C
g
N
g
f
g
γ

g
−
P
m,g
λ
g
λ
g
-λ
m
W
+

P
m,g
λ
m
λ
g
− λ
m

−1
(2.5)
And the error
∆IR
IR
=

w
∆N
m
N
m
W
2
+
w
∆N
g
N
g
W

2
+
w
∆
m

m
W
2
+
w
∆
g

g
W
2
, (2.6)
in which
C
m
C
g
istherateofcorrectioncoefficients and has value of around 1.
3. Experiment
3.1. Experime ntal arrangement
The experimental flowchart is arranged as fig.2.
Figure 2. Experimental arrangement.
Gamma spectrum of
44

Sc from Ti(γ, pn)Sc reaction is measured by HPGe gamma
spectrometry. The measurement scheme is presented in fig.3, and the gamma spectrum of
44
Sc presented in Fig.4.
54 Tran Tri Vien, Doan Quang Tuyen, Nguyen Trung Tinh
.
Figure 3. Scheme of analytical system for gamma spectrum of reaction preduction
Figure 3. Gamma spectrum of
44
Sc measured by Gammavision Spectrometry
3.2. Calculation of typical peak area
In the gamma spectrum of
44
Sc, there are two spectral peaks with energies of
271keV created due to
44
Sc transferring from metastable to ground state and of 1157keV
created when the
44
Sc nuclei in both metastable and ground state disintegrate to
44
Ca.
With
44m
Sc, relative intensity of gamma ray with energy E
γ
= 271keV and with energy
E
γ
= 1157keV is 86.7:1.31. So that, the count of peak with 271keV energy of metastable

state is equal the area of spectral peak of 271keV energy. But, the count number of
1157keV energy peak of ground state is not equal the area of 1157 keV energy peak. It is
determined as follows
N
m
=S
271
(3.1)
N
g
=S
1157
−
1.31
g
86.7
m
N
m
, (3.2)
where S
271
is the area of 271 keV energy peak and S
1157
is the area of 1157 keV one.
Determining the isomeric ratio of nuclear reaction 55
3.3. Isomeric ratio
The detection-efficiency of gamma spectrometry with energy of 271 keV and of
1157 keV has been determined in the paper ” Surveying the HPGe gamma detector abso-
lute efficiency”, and their value is as follows: at 271 keV energy 

m
=0.01068 ± 0.00029;
at 1157 keV energy: 
g
=0.00291 ± 0.00007
According to the part mentioned above, we can determine the values of N
m
and
N
g
. Substituting the parameters int o formula (2.5),wecalculatetheisomericratioof
46
Ti(γ, n)
44
Sc reaction:
IR = 0, 112
The error of isomeric ratio calculated according to the formula(2.6) and it’s value is:
IR = 0.011
So, the isomeric ratio of reaction
46
Ti(γ, pn)
44m,g
Sc is:
IR = 0, 112 ± 0.011
4. Conclusion
Using the beam of bremsstrahlung with energy end point of 65MeV from the ac-
celerator in POSTECH - South Korea, we ha ve determined the isomeric ratio (IR) of the
reaction
46
Ti(γ, pn)

44m,g
Sc as follows:
IR = 0.112 ± 0.011
In order to compare this data with the others, we have consulted a lot of published
data and those from in the Internet. But, we could not get any data that is similar to this
reaction. Consequently, the result of our experiment can be considered as the new result
that may contribute to d atabase of isomeric ratio of nuclear reaction.
Acknowledgements: This work is supported by the Science Researc h Program provided
by Vietnam National Universit y, Hanoi QG-04-02.
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45
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56 Tran Tri Vien, Doan Quang Tuyen, Nguyen Trung Tinh
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