Nuclear Instruments and Methods in Physics Research B 296 (2013) 14–21
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Nuclear Instruments and Methods in Physics Research B
journal homepage: www.elsevier.com/locate/nimb
Excitation functions of (d,x) nuclear reactions on natural titanium up to 24 MeV
Mayeen Uddin Khandaker a,⇑, Hiromitsu Haba b, Jumpei Kanaya b, Naohiko Otuka c
a
Department of Physics, University of Malaya, 50603 Kuala Lumpur, Malaysia
Nishina Center for Accelerator-based Science, RIKEN, Wako, Saitama 351-0198, Japan
c
Nuclear Data Section, Division of Physical and Chemical Sciences, Department of Nuclear Sciences and Applications, International Atomic Energy Agency, A-1400 Vienna, Austria
b
a r t i c l e
i n f o
Article history:
Received 23 October 2012
Received in revised form 29 November 2012
Available online 20 December 2012
Keywords:
Excitation functions
nat
Ti(d,x) reactions
24-MeV deuteron
Thick target yields
TALYS calculations
Deuteron-induced cross-section database
a b s t r a c t
Excitation functions of the natTi(d,x)48V and natTi(d,x)43,44m,44g,46,47,48Sc nuclear reactions were measured
up to a 24-MeV deuteron energy by using a stacked-foil activation technique combined with c-ray spectrometry with a high-purity germanium detector at the AVF cyclotron of the RIKEN RI Beam Factory,
Wako, Japan. An overall good agreement is found between the measured cross-sections and the literature
ones, whereas partial agreements are obtained for the theoretical calculations based on the TALYS code.
Physical thick target yields, i.e., induced radioactivities per unit fluence of the 24-MeV deuteron were also
deduced, and they were compared with the directly measured ones in the literature. The present results
will have an important role in enrichment of the literature database of the deuteron-induced reactions on
natural titanium leading to various applications.
Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction
Light-charged-particle-induced production cross-sections of
residual radionuclides from various targets find remarkable attention to the nuclear data community due to their increasing applications in nuclear medicine, accelerator and nuclear technology, and
testing of nuclear reaction theories. Availability of variable energy
cyclotrons throughout the world made it possible to measure
cross-sections via light-charged-particle irradiations on different
elements. In reality, optimum production parameters of a particular radionuclide leading to practical applications could be determined only if cross-sections via different induced channels like
proton, deuteron, and alpha are sufficient in the literature. However, measured cross-sections of the (d,x) processes for different
elements are scanty relative to (p,x). Owing to this fact, we initiated systematic studies to report new experimental cross-sections
via deuteron irradiations on different elements relevant to various
practical applications. In this work, we measured excitation functions for the natTi(d,x)48V and natTi(d,x)43,44m,44g,46,47,48Sc reactions
up to a 24-MeV deuteron energy using the AVF cyclotron of the RIKEN RI Beam Factory (RIBF), Wako, Japan.
Titanium (Ti), a high-strength, lustrous, durable, and light white
metal finds wide applications in industrial, aerospace, recreational,
and emerging markets. It is widely used as a refractory and corrosion resistant metal. Due to its non-toxicity and biocompatibility,
titanium and its alloys such as Ti-6Al-4V are useful in a wide range
⇑ Corresponding author. Tel.: +60 1115402880; fax: +60 379674146.
E-mail address: [email protected] (M.U. Khandaker).
0168-583X/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.nimb.2012.12.003
of structural, chemical, petrochemical, marine, and biomaterial
applications. Moreover, titanium is a potential target material for
the production of medical radionuclides such as 43Sc, 44gSc, 46Sc,
and 47Sc. The suitable decay properties of 43Sc (T1/2 = 3.891 h;
total
Ec = 372.9 keV, Ic = 22.5%; Emax
bþ = 1198.8 keV, Ibþ = 88.1%) made it
promising to be used in vivo dosimetry [1]. 44gSc (T1/2 = 3.97 h;
total
Emax
bþ = 1473.5 keV, I bþ = 94.27%; Ec = 1157.02 keV, Ic = 99.9%) is
one of the most interesting radionuclide for nuclear medical imaging using a b+-c coincidence technique [2]. Moreover, both 43Sc and
44g
Sc find applications as PET surrogates for the therapeutic isotope
47
Sc and possibly for 177Lu [3]. 47Sc (T1/2 = 3.3492 d) shows a promising interest in radio-immunotheraphy [4] due to its favorable b
emission
(Emax
= 440.9 keV,
Ib1 = 68.4%;
Emax
= 600.3 keV,
b
b
1
2
47
Ib2 = 31.6%). Sc could be also used in an imaging procedure due
to its primary c-ray of 159.381 keV (Ic = 68.3%). The long-lived
46
Sc (T1/2 = 83.79 d) was applied as a labeled microsphere for investigation of myocardial blood flow measurements [5]. 46Sc was also
successfully applied as a radiotracer to analyze lungs by Wehner
et al. [6]. Furthermore, Inoue and Komura [7] demonstrated the potential use of 46Sc as a cosmogenic radionuclide for an investigation
of the evolution history of chondrites after separation from their
parent body. In addition to the wide use of the natTi(d,x)48V
reaction in monitoring of beam intensity and energy [8–10], 48V
was investigated as an alternative of 68Ga to use as a calibration
source for PET cameras [11]. 48V is also a well-known radiotracer
in many research areas from biology [12,13] to material science
[14,15]. 48V was used as a thermoluminescence dosimetry source
for intravascular brachytherapy (IVBT) due to its relatively
ease production scheme, a minimum of 30-days shelf-life, and
15
M.U. Khandaker et al. / Nuclear Instruments and Methods in Physics Research B 296 (2013) 14–21
2. Experimental
The irradiation technique, the radioactivity determination, and
the data evaluation procedures were similar to our previous works
[27–32]. A well established stacked-foil activation technique combined with c-ray spectrometry with a high-purity germanium
(HPGe) detector was employed to determine production cross-sections of residual radionuclides by irradiating deuterons on titanium metallic foils.
2.1. Targets and irradiations
A titanium foil (99.5% purity; 20 lm thickness; Nilaco Corp.,
Japan; Lot no.: 453212) having natural isotopic compositions
(46Ti 8.25%, 47Ti 7.44%, 48Ti 73.72%, 49Ti 5.41%, and 50Ti 5.18%
[33]) was used as the target material. Several foils of aluminum
(>99% purity; 100 lm thickness; Nilaco Corp., Japan; Lot no.:
013323) and natural iron (99.995% purity; 22 lm thickness; Rare
Metallic Co. Ltd., Japan; Lot no.: 60530-83-MI-R) were inserted in
between any two consecutive Ti foils throughout the whole stack.
The Al foil was used to cross-check the beam intensity determined
from the front positioned Ti foil. The Al and Fe foils were also used
to degrade the beam energy throughout the whole stack. The irradiation was carried out in a standard target holder that served as a
Faraday cup: the number of incident deuterons was estimated
from the collected charge with the Faraday cup. The stacked-foils
were irradiated for 2.0 h with a 24-MeV deuteron beam from the
AVF cyclotron with an average beam current of 215 nA. The beam
was collimated to 9-mm diameter. All of the monitor and target
foils were prepared with a size of 15 15 mm2 to ensure that
equal areas of the monitors and targets received the same beam
line.
2.2. Measurement of the radioactivity
After the irradiation, the samples were removed from the target
holder, and the activities of the produced radionuclides were measured using a high resolution c-ray spectrometer (1.85 keV at
FWHM at 1332.5 keV). The c-ray spectrometer was a p-type coaxial HPGe detector (ORTEC; GEM-25185P; Serial no. 33-TP10928B;
55.1-mm crystal diameter and 52.0-mm thickness; operating voltage: +2000 V) having an efficiency of 25% relative to a NaI(Tl)
detector of 7.62 cm diameter 7.62 cm thickness. The HPGe detector was coupled to a 4096 multi-channel analyzer with the associated electronics to determine the photopeak area of the c-ray
spectra. The spectrum analysis was done using a Gamma Vision
5.0 (EG&G ORTEC) computer program. The photopeak efficiency
curve of the Ge detector was determined with a multi-nuclide
point source having the specifications of the following radionuclides: 241Am (59.541 keV), 109Cd (88.040 keV), 57Co (122.061 keV;
136.474 keV), 139Ce (165.8575 keV), 203Hg (279.1952 keV), 113Sn
(391.698 keV), 85Sr (514.007 keV), 137Cs (661.657 keV), 88Y
60
(898.042 keV;
1836.063 keV),
and
Co
(1173.228 keV;
1332.492 keV). As shown in Fig. 1, the detection efficiencies as a
function of the photon energy were determined at the counting
distances of 2–35 cm from the end-cap of the detector to avoid
coincidence losses, to assure a low dead time (<10%), and a point
like geometry. The measured detection efficiencies were fitted by
using a polynomial function:
ln e ¼
5
X
ak ln ðEk Þ
k¼0
where e is the detection efficiency, ak represents the fitting parameters, and E is the energy of the photopeak. The fitting parameters
such as a0 to ak are presented in Table 1. The activity measurements
of the irradiated samples were started about 4 h after the end of
bombardment (EOB) to separate the complex c lines from the decay
of the undesired short-lived nuclides. The measurements of the
irradiated samples were repeated 5–6 times to follow the decay
of the radionuclides and thereby to identify the possible interfering
nuclides.
2.3. Data analysis
The IAEA recommended monitor reactions of 27Al(d,x)24Na
(Ed = 22.9 MeV, r = 57.84 mb) and natTi(d,x)48V (Ed = 23.44 MeV,
r = 225.5 mb) [10,34] were used to determine the beam intensity.
100
Detection Efficiency (%)
the mixed b+ and c emissions mechanism [16]. Arbabi et al. [17]
demonstrated the suitability of usefulness of 48V stent in renal artery brachytherapy. Due to its biochemical action in the body (e.g.,
insulin-like and anti-carcinogenic characteristics, and interaction
with ATP-ases), 48V was applied as a labeled compound for
in vivo studies [18]. Besides the aforementioned medical applications, 48V was utilized as a positron source to determine the Doppler broadening of 511-keV peak for different materials like copper,
lead, and indium at the U-120 cyclotron installations [19], and was
also suggested to use in an activation analysis of steel [8]. An accurate determination of production cross-sections for natTi(d,x)48V
and natTi(d,x)43,44m,44g,46,47,48Sc, therefore, shows great importances
in various practical applications.
A detailed survey of literatures reveals that various production
pathways have been investigated for the radionuclides of interest
in this work: e.g., 43Sc from 42Ca(p,c), 43Ca(p,n), 44Ca(p,2n),
42
Ca(d,n), and 46Ti(p,a); 44Sc from 44Ca(p,n), 41K(a,n), V,Ti(p,spall),
and 44Ti decay/generator; 47Sc from 48Ti(c,p), 47Ti(n,p), 50Ti(p,a),
nat
V(d,x), 45Sc(t,p), and 48Ti(t,a); 48Sc from 48Ca(p,n), 51V(n,a), and
50
Ti(d,a); 48V from 47Ti(p,c) and 45Sc(a,n). However, only a few
investigations were carried out for the (d,x) processes using natural or enriched Ti targets [8–10,14,20–25], and considerable discrepancies were found among the reported cross-sections.
Therefore, the objective of the present study was to report new
cross-sections for the natTi(d,x)48V and natTi(d,x)43,44m,44g,46,47,48Sc
reactions to reduce the discrepancies among the literature data
and to validate the IAEA recommended cross-sections of the
nat
Ti(d,x)48V monitor reaction. The measured new cross-sections
also find significance in practical applications such as the productions of medical radionuclides, accelerator and target technology to
produce high energy or high intensity neutron fluxes for nuclear
waste transmutation, RI beam production with neutrons, fusion
energy application, and space applications [26].
d= 2 cm;
d= 12 cm;
10
d= 7 cm
d=24 cm
d=35 cm
1
0.1
0.01
1E-3
40
100
1000
2000
Photon Energy (keV)
Fig. 1. Detection efficiency of the HPGe detector as a function of photon energy
measured at different distances between the sample and the detector surface.
16
M.U. Khandaker et al. / Nuclear Instruments and Methods in Physics Research B 296 (2013) 14–21
Table 1
Coefficients of efficiency fitting curves for different source to detector distances.
Source to detector distance (cm)
2
7
12
24
35
Efficiency curves fitting coefficients
A0
A1
A2
A3
A4
A5
6.960668E+02
5.158505E+02
5.440220E+02
5.225504E+02
5.575685E+02
5.681181E+02
4.097168E+02
4.339063E+02
4.136920E+02
4.414771E+02
1.850238E+02
1.304289E+02
1.389568E+02
1.318505E+02
1.406984E+02
2.998082E+01
2.067239E+01
2.216439E+01
2.092522E+01
2.230375E+01
2.420308E+00
1.634519E+00
1.763862E+00
1.656513E+00
1.761378E+00
7.785421E02
5.156582E02
5.600938E02
5.231302E02
5.542251E02
Table 2
Decay data and contributing processes of the investigated radionuclides; italicized gamma lines were not used in activity determination. Only the major contributing reactions are
listed here.
Produced nuclei
Half-life, T1/2
Decay mode (%)
c-ray energy, Ec (keV)
c-ray intensity, Ic (%)
Contributing reactions
Q-value
(MeV)
Threshold
(MeV)
48
15.9735 d
EC (50.1); b+ (49.9)
7.87
99.98
98.2
22.5
47
4.6
7.02
15.16
5.29
14.18
4.4
19.4
23.9
4.5
16.1
4.40
19.4
23.9
4.48
16.10
3.8
12.7
3.97
19.9
4.2
15.1
0.0
7.3
15.8
5.5
17.8
0.0
20.3
24.9
4.6
16.8
0.0
20.3
24.9
4.6
16.8
3.9
13.2
0.0
20.7
4.3
15.7
2.0
13.7
6.5
21.8
4.5
5.4
13.6
3.8
20.1
2.1
14.2
0.0
22.7
4.6
5.6
14.1
0.0
20.9
V
3.891 h
EC (11.9); b+ (88.1)
944.13
983.525
1312.106
372.9
Sc
58.61 h
EC (1.20); IT (98.8)
271.241
86.7
44g
Sc
3.97 h
EC (5.73); b+ (94.27)
1157.020
99.9
46g
Sc
83.79 d
b (1 0 0)
889.277
1120.545
99.9840
99.9870
47
3.3492 d
b (1 0 0)
159.381
68.3
48
43.67 h
b (1 0 0)
175.361
983.526
1037.522
1312.120
7.48
100.1
97.6
100.1
43
Sc
44m
Sc
Sc
Specifically, the natTi(d,x)48V reaction was used to obtain the final
beam current whereas the 27Al(d,x)24Na reaction was used for
the purpose of cross checking. We found an excellent agreement
in the beam currents determined by the monitor reactions and obtained from the digital current integrator module (ORTEC 439)
coupled to the Faraday cup. The deuteron energy degradation
along the stacked foils was calculated by using a computer program SRIM-2003 [35]. The use of multiple monitor foils decreases
unknown systematic uncertainties during an activity determination. The beam intensity was considered as constant to deduce
cross-sections for each foil in the stack. Further, the natFe(d,x)56Co
reaction was utilized to monitor the energy scale throughout the
whole stack.
The cross-sections for the natTi(d,x) processes were determined
in the deuteron energy range of 2–24 MeV using a well-known
activation formula [28,29]. The decay data such as half-life
(T1/2 = ln2/k), c-ray energy (Ec), and c-ray emission probability
(Ic) used in the cross-section determination were taken from the
ENSDF evaluation [33,36–40] obtained from the NuDat-2.6 software [41], and they are summarized in Table 2. The Q-values and
threshold energies calculated on the basis of the atomic mass
Ti(d,n)
Ti(d,2n)
Ti(d,3n)
46
Ti(d,n + a)
47
Ti(d,2n + a)
46
Ti(d,a)
46
Ti(d,2d)
46
Ti(d,2n + 2p)
47
Ti(d,n + a)
48
Ti(d,2n + a)
46
Ti(d,a)
46
Ti(d,2d)
46
Ti(d,2n + 2p)
47
Ti(d,n + a)
48
Ti(d,2n + a)
46
Ti(d,2p)
47
Ti(d,n + 2p)
48
Ti(d,a)
48
Ti(d,2d)
49
Ti(d,n + a)
50
Ti(d,2n + a)
IT (100%) decay of
47
Ti(d,2p)
48
Ti(d,2p + n)
49
Ti(d,a)
49
Ti(d,2n + 2p)
50
Ti(d,n + a)
48
Ti(d,2p)
49
Ti(d,n + 2p)
50
Ti(d,a)
50
Ti(d,2d)
48
49
46m
Sc
evaluation by Audi and Wapstra [42] and the Q-tool system [43]
are also presented in Table 2. Intense and independent characteristic c-lines were used to quantify the radionuclides. In some cases,
two or more characteristic c-rays were used to cross-check the obtained results.
The uncertainty of the deuteron energy for each representing
energy point in the stack depends on the irradiation circumstances
and the position of the foil in the stack. These are due to the initial
beam energy uncertainty (<1%), the target thickness and homogeneity, and the beam straggling. The estimated uncertainties of a
representing energy point in the excitation function range from
±0.4 MeV to ±0.8 MeV, which are shown in tables and figures.
In this measurement, uncertainties due to c-ray countings were
0.5–8%. In addition, the following uncertainties were assumed or
considered: uncertainties due to determination of the beam flux
(5%), detector efficiency (4%), sample thickness (1%), and cray intensity (1%). All these uncertainties were considered as
independent, and consequently, they were quadratically added
according to the laws of error propagation to obtain the total
uncertainties. The overall uncertainties of the measured cross-sections were then in the range of 6.5–10.4%.
17
M.U. Khandaker et al. / Nuclear Instruments and Methods in Physics Research B 296 (2013) 14–21
3. Model calculations
10
nat
Cross Section (mb)
8
43
Ti(d,x) Sc
6
4
Takacs et al., '97 (Norm.)
This work
Talys-1.4 (TENDL-2011)
2
0
8
10
12
14
16
18
20
22
24
Deuteron Energy (MeV)
Fig. 3. Excitation function for the
nat
26
28
30
Ti(d,x)43Sc nuclear reactions.
8
Cross Section (mb)
A number of model code systems such as ALICE-IPPE [44],
TALYS [45], and EMPIRE [46] for calculating charged-particle-induced reaction cross-sections were developed by the nuclear data
community in the recent time. However, there are some difficulties
to predict deuteron-induced reaction cross sections by means of
conventional reaction models [47,48]: first, the weak binding energy of the deuteron makes a variety in reaction channels such
as elastic A(d,n + p)Ag.s. and inelastic A(d,n)B⁄ ? x + C or
A(d,p)B⁄ ? x + C break-up reactions as well as stripping (d,p) and
(d,n) reactions. Second, currently there is no global deuteron optical potential which can reproduce a wide range of target nuclei and
incident deuteron energies [48]. Under this situation, Avrigeanu
and Avrigeanu [48] performed a detailed analysis for experimental
d + 27Al [49] and d + 63,65Cu [50] activation cross sections. It has
been known that experimental (d,p) reaction cross sections are often underestimated by the reaction models [47,48]. To resolve this
difficulties, Ignatyuk et al. [51,52] determined an energy dependent phenomenological enhancement factor K based on the general relations for nuclear transfer reaction in the continuum [53]
and introduced the factors to the ALICE-IPPE, GNASH [54] and EMPIRE model code systems.
Under this situation, it is also meaningful to compare experimental data with model calculation without any adjustment of
model parameters so that we may reveal the deficiencies of various
reaction mechanisms in conventional reaction models. In this
work, therefore, we compare our experimental production crosssections with the TENDL-2011 library [55] which compile production cross-sections based on the nuclear model code TALYS [45]
Ver. 1.4. Note that there is no production cross-section where the
(d,p) or (d,n) stripping reaction is expected to be dominant among
reactions discussed in this article.
Takacs et al., '97 (Norm.)
Hermanne et al., '00
Takacs et al., '07
Gagnon et al., '10
This work
Talys-1.4 (TENDL-2011)
6
4
nat
2
44m
Ti(d,x)
Sc
2
8
0
0
4
6
10 12 14 16 18 20 22 24 26 28 30
Deuteron Energy (MeV)
Fig. 4. Excitation function for the
10
nat
nat
Ti(d,x)44mSc nuclear reactions.
44g
Ti(d,x) Sc
work, the cross-sections for the natTi(d,x)48V,43,44m,44g,46,47,48Sc reactions were measured via a deuteron irradiation on the natural titanium targets in the 2–24 MeV energy
region. The excitation functions of the investigated radionuclides
48
V and 43,44m,44g,46,47,48Sc are shown in Figs. 2–8 together with
the experimental data available in the EXFOR database [56], and
also with the predicted data compiled in the TENDL-2011 library
by the TALYS code. The numerical data with statistical and other
errors are presented in Table 3. Thick target yields were also deduced using the measured cross-sections by taking into account
that the total energy is absorbed in the target, and they are shown
in Figs. 9 and 10.
this
4
Takacs et al., '97 (Norm.)
Gagnon et al., '10
This work
Talys-1.4 (TENDL-2011)
2
0
2
nat
Jung '91
West et al., '93 (Norm.)
Takacs et al., '97 (Norm.)
Takacs et al., '01
Takacs et al., '07
Gagnon et al., '10
This work
IAEA recommendation
Talys-1.4 (TENDL-2011)
48
Ti(d,x) V
400
300
200
4
6
8
10 12 14 16 18 20 22 24 26 28 30
Deuteron Energy (MeV)
Fig. 5. Excitation function for the
60
500
Cross Section (mb)
6
0
nat
Ti(d,x)44gSc nuclear reactions.
Takacs et al., '97 (Norm.)
Takacs et al., '07
This work
50
Cross Section (mb)
In
Cross Section (mb)
8
4. Results and discussion
Hermanne et al., '00
Gagnon et al., '10
Talys-1.4 (TENDL-2011)
40
30
20
100
10
0
0
nat
0
10
20
Deuteron Energy (MeV)
Fig. 2. Excitation function for the
nat
30
Ti(d,x)48V nuclear reactions.
40
46
Ti(d,x) Sc
0
2
4
6
8
10 12 14 16 18 20 22 24 26 28 30
Deuteron Energy (MeV)
Fig. 6. Excitation function for the
nat
Ti(d,x)46Sc nuclear reactions.
18
M.U. Khandaker et al. / Nuclear Instruments and Methods in Physics Research B 296 (2013) 14–21
20
Takacs et al., '97 (Norm.)
Hermanne et al., '00
Takacs et al., '07
Gagnon et al., '10
This work
Talys-1.4 (TENDL-2011)
Cross Section (mb)
16
12
8
nat
47
Ti(d,x) Sc
4
0
0
2
4
6
8
10 12 14 16 18 20 22 24 26 28 30
Deuteron Energy (MeV)
Fig. 7. Excitation function for the
nat
Ti(d,x)47Sc nuclear reactions.
14
Takacs et al., '97 (Norm.)
Hermanne et al., '00
Takacs et al., '07
Gagnon et al., '10
This work
Talys-1.4 (TENDL-2011)
Cross Section (mb)
12
10
8
nat
Ti(d,x)43Sc processes
6
4.2.
4
The relatively short-lived radionuclide 43Sc (T1/2 = 3.891 h) decays to the stable 43Ca with a b+ emission (88.1%) and an EC process
(11.9%). Only one characteristic c-ray of 372.9 keV was used to
identify this radionuclide. The measured cross-sections of 43Sc
are shown in Fig. 3 together with only one earlier measurement
by Takács et al. (1997) [8] and the theoretical data extracted from
the TENDL-2011 library. As shown in Fig. 3, we confirmed the
renormalized cross-sections of Takács et al. (1997) [8] for the first
time. The populations of 43Sc are due to the direct nuclear reactions
of 46Ti(d,na) (Q = 5.29 MeV) and 47Ti(d,2n + a) (Q = 14.18 MeV)
as presented in Table 2. A relatively low cross-sections of 43Sc
are due to the low abundances of the contributing target isotopes
46
Ti (8.25%) and 47Ti (7.44%) in the investigated energy region. The
coulomb barrier effect in the exit channel may inhibit the contributions of the 46Ti(d,na) reaction immediately after its threshold energy (EThres = 5.5 MeV). The model code TALYS is unable to
reproduce the measured excitation function for the natTi(d,x)43Sc
reactions.
2
nat
48
Ti(d,x) Sc
0
0
2
4
6
8 10 12 14 16 18 20 22 24 26 28 30 32 34
Deuteron Energy (MeV)
Fig. 8. Excitation function for the
4.1.
[23]. The natTi(d,x)48V cross-sections were measured by Takács
et al. (1997) [8] based on the 27Al(d,x)24Na (Ed = 21 MeV;
r = 54 mb) monitor reaction in the energy region of 2.95–
21.26 MeV. Therefore, we corrected the cross-sections using the
updated monitor cross-sections recommended by IAEA (Ed = 21 MeV; r = 50.8 mb), and the corrected values agree well with our
measured ones. The reported data by Jung [22] at 9.8–13.3 MeV
show a disagreement in both shape and magnitudes. A downward
energy shift of about 1 MeV could make an agreement of the crosssections by Jung [22] with our measurements. An excellent agreement is obtained with the IAEA recommended excitation function
for the whole investigated energy region, and this fact confirms the
reliability and accuracy of our measured cross-sections for the
nat
Ti(d,x)43,44m,44g,46,47,48Sc reactions. The model code TALYS produces a similar shape of the excitation function with an overestimation. Three direct reactions 47Ti(d,n) (Q = +4.6 MeV), 48Ti(d,2n)
(Q = 7.02 MeV), and 49Ti(d,3n) (Q = 15.16 MeV) contribute to
the formation of 48V in the present energy region. The TALYS code
reveals that the maximum cross-sections around 17 MeV are due
to the contribution of the 48Ti(d,2n) reaction on the abundant
48
Ti nuclide.
nat
Ti(d,x)48Sc nuclear reactions.
nat
Ti(d,x)48V processes
The long-lived radionuclide 48V (T1/2 = 15.9735 d) completely
decays to the stable nuclide 48Ti followed by an EC process
(50.1%) and a b+ emission (49.9%). On the other hand, the relatively
short-lived radionuclide 48Sc (T1/2 = 43.67 h) also decays to 48Ti via
a b emission (100%). The intense c-rays of 983.525 keV and
1312.106 keV from excited states of 48Ti are the common c lines
for 48V and 48Sc. An unambiguous identification of 48V could be
done in two ways: using a less intense but an independent c line
of 944.13 keV (7.87%) for 48V or using the spectra obtained after
a sufficient cooling time of more than 450 h. In this work, we attempted both the ways, and found a very good agreement between
them. The measured excitation function of 48V is shown in Fig. 2
together with the data available in the literature, and the theoretical data extracted from the TENDL-2011 library. Numerous
authors investigated the natTi(d,x)48V reactions due to its importance in the beam monitoring applications. West et al. [23]
reported isotopic cross-sections for the 47Ti(d,n)48V and
48
Ti(d,2n)48V reactions in the energy regions of 1.85–7.1 MeV and
7.13–34.56 MeV, respectively. The reported excitation functions
were summed to obtain elemental cross-sections taking into account the isotopic abundances of natural titanium (47Ti: 7.28%
and 48Ti: 73.72%). Although the (d,3n) and (d,4n) processes on
49
Ti (5.41%) and 50Ti (5.18%), respectively, may contribute to the
production of 48V at higher deuteron energies, West et al. [23] neglected the contribution of these two processes in their reported
data. Note that to keep the consistency in the renormalized excitation function, three scattered cross-sections of 48Ti(d,2n)48V
(EThres = 7.3 MeV) around it’s threshold energy region (7.13–
8.24 MeV) were excluded from the renormalization process. An
overall good agreement is found with the reported data by Gagnon
et al. [25], Takács et al. (2007) [10], Takács et al. (2001) [9] except
one point at 11.4 MeV, and by the renormalized data of West et al.
4.3.
nat
Ti(d,x)44mSc processes
The relatively long-lived, high spin, and meta-stable radionuclide 44mSc (T1/2 = 58.61 h; 6+) directly decays to the 3285.0-keV
energy level of the same spin state of 44Ca following an EC process
(1.2%). Meanwhile, this isomeric state (44mSc) decays to its shortlived, and unstable low-spin state 44gSc (T1/2 = 3.97 h; 2+) via an
IT (98.8%) process by emitting an intense c-ray of 271.241 keV.
44g
Sc further decays to the 1157.02-keV level of the same spin state
of 44Ca followed by an EC process and a b+ emission with a branching ratio of 98.95%. The remaining 44gSc nuclei decays to the
2656.48-keV (0.112%) and 3301.35-keV (0.014%) energy levels of
the same spin state of 44Ca via an EC process. In this work, the
strong and independent characteristic c line of 271.241 keV was
used to obtain cross-sections of 44mSc, and the excitation function
of the natTi(d,x)44mSc reaction is shown in Fig. 4 together with the
literature data and the theoretical data extracted from the TENDL2011 library. We found a good agreement of our data with the recently measured ones by Gagnon et al. [25] and Takács et al. (2007)
[10] at the low energy region. The data reported by Hermanne et al.
[24] and the renormalized ones of Takács et al. (1997) [8] also
show an agreement to our data within the error limits. The
TALYS code produces a better fitted excitation function to the
19
M.U. Khandaker et al. / Nuclear Instruments and Methods in Physics Research B 296 (2013) 14–21
Table 3
Production cross-sections of the investigated radionuclides for the
Deuteron
energy (MeV)
2.7 ± 0.8
4.80 ± 0.62
6.66 ± 0.55
8.22 ± 0.51
9.59 ± 0.49
10.84 ± 0.47
12.00 ± 0.45
14.93 ± 0.42
17.49 ± 0.40
19.79 ± 0.38
21.91 ± 0.37
23.44 ± 0.36
nat
Ti(d,x) nuclear processes.
Measured cross-sections (mb) ðr Drstatistical Drothers Þ
48
43
V
1.03 ± 0.01 ± 0.07
16.44 ± 0.05 ± 1.08
18.56 ± 0.05 ± 1.22
24.68 ± 0.06 ± 1.62
90.42 ± 0.24 ± 5.93
166.1 ± 0.3 ± 10.9
222.8 ± 0.4 ± 14.6
303.6 ± 0.7 ± 19.9
325.5 ± 0.7 ± 21.3
304.3 ± 0.7 ± 20.0
255.9 ± 0.4 ± 16.8
224.7 ± 0.4 ± 14.7
44m
Sc
–
–
–
–
–
–
0.10 ± 0.09 ± 0.01
1.15 ± 0.11 ± 0.08
2.96 ± 0.20 ± 0.19
4.03 ± 0.15 ± 0.26
4.82 ± 0.18 ± 0.32
4.77 ± 0.20 ± 0.31
44g
Sc
–
0.067 ± 0.006 ± 0.005
0.31 ± 0.01 ± 0.02
0.62 ± 0.01 ± 0.04
0.92 ± 0.02 ± 0.06
1.24 ± 0.03 ± 0.08
1.53 ± 0.14 ± 0.10
2.43 ± 0.16 ± 0.16
2.81 ± 0.15 ± 0.18
3.13 ± 0.23 ± 0.24
3.58 ± 0.24 ± 0.28
3.75 ± 0.15 ± 0.29
0.029 ± 0.001 ± 0.002
1.23 ± 0.01 ± 0.08
2.94 ± 0.02 ± 0.19
4.25 ± 0.04 ± 0.28
5.05 ± 0.05 ± 0.33
5.14 ± 0.09 ± 0.34
5.03 ± 0.09 ± 0.33
5.15 ± 0.09 ± 0.34
6.13 ± 0.10 ± 0.40
6.61 ± 0.11 ± 0.43
6.80 ± 0.11 ± 0.45
6.60 ± 0.11 ± 0.43
5
48
V
48
V
ke
V
44
g
Sc
48
Sc
g
Sc
46
48
V
1
51
44
46
g
Sc
4
Counts (#)
48
Sc
m
43 Sc
Sc
47
Sc
10
10
3
10
Energy: 17.49 MeV
Counting time: 1200 s
Cooling time: ~5 days
Irradiation time: 7200 s
2
10
1
10
0
300
600
900
Photon Energy (keV)
1200
1500
Fig. 9. A typical c-ray spectrum from the activities induced in the natural titanium
with an exposure of 17 MeV deuteron.
5
10
Energy < 2 MeV
Counting time: 1200 s
Cooling time: ~5 days
Irradiation time: 7200 s
4
0.11 ± 0.01 ± 0.01
3.79 ± 0.05 ± 0.25
12.67 ± 0.08 ± 0.83
21.04 ± 0.10 ± 1.38
29.39 ± 0.31 ± 1.93
35.99 ± 0.42 ± 2.36
39.47 ± 0.33 ± 2.59
33.04 ± 0.62 ± 2.17
27.04 ± 0.51 ± 1.77
24.74 ± 0.50 ± 1.62
23.87 ± 0.35 ± 1.57
23.70 ± 0.37 ± 1.55
47
48
0.067 ± 0.002 ± 0.004
0.34 ± 0.01 ± 0.02
0.87 ± 0.01 ± 0.06
1.43 ± 0.01 ± 0.09
1.97 ± 0.02 ± 0.13
2.43 ± 0.06 ± 0.16
2.90 ± 0.09 ± 0.19
4.29 ± 0.16 ± 0.28
6.13 ± 0.20 ± 0.42
7.65 ± 0.18 ± 0.50
9.30 ± 0.20 ± 0.61
11.65 ± 0.22 ± 0.77
0.046 ± 0.002 ± 0.004
0.15 ± 0.01 ± 0.01
0.38 ± 0.01 ± 0.03
0.76 ± 0.02 ± 0.06
0.99 ± 0.04 ± 0.08
1.15 ± 0.05 ± 0.09
1.35 ± 0.16 ± 0.10
2.08 ± 0.15 ± 0.16
3.26 ± 0.15 ± 0.25
4.99 ± 0.21 ± 0.39
6.99 ± 0.21 ± 0.54
7.69 ± 0.18 ± 0.60
Sc
Sc
of 46Ti(d,a) (Q = +4.40 MeV), 47Ti(d,na) (Q = 4.48 MeV), and
48
Ti(d,2na) (Q = 16.10 MeV), and via an IT (98.80%) transition
from the relatively long-lived isomer 44mSc (T1/2 = 58.61 h). Therefore, the 1157.020-keV photopeak area of 44gSc includes a contribution of 44gSc formed as a decay daughter of 44mSc. However, it
is possible to evaluate an interference free area for 44gSc in the
1157.020-keV photopeak by using the spectra having a cooling
time of around 40 h or more, i.e., more than 10 half-lives of
44g
Sc; the detected area is due to the 44mSc via an IT process
(98.80%). By using a typical decay curve analysis, the contribution
of 44mSc in the 1157.020-keV was subtracted, and the independent
cross-sections were determined for 44gSc. The measured excitation
function for 44gSc is shown in Fig. 5. We found a good agreement of
our data with the recently measured ones by Gagnon et al. [25]. An
overall agreement within the error limit is also obtained with the
renormalized data of Takács et al. (1997) [8] in the whole investigated energy region. The TALYS code reproduces a similar shape of
the excitation function to the measured ones but overestimates it
in absolute values. An analysis of the excitation function reveals
that the gradual increasing trend of the cross-sections from
3 MeV to 12 MeV are due to the contribution of 46Ti(d,a)
(Q = +4.40 MeV) and 47Ti(d,na) (Q = 4.48 MeV), whereas the flat
maximum around 22 MeV is mostly due to the 48Ti(d,2n + a)
(Q = 16.10 MeV) reaction.
4.5.
46
1
10
0
300
600
900
Photon Energy (keV)
nat
46
48
V
1
51
47
Sc
g
Sc
48
V
2
10
1200
1500
Fig. 10. A typical c-ray spectrum from the activities induced in the natural titanium
with an exposure of <2 MeV deuteron.
experiments in the whole investigated energy region. Absence of
any clear maximum indicates that a complex system of reactions
on different target isotopes 46,47,48Ti would be involved in the formation of 44mSc within the present investigated energy region (see
Table 2). Additionally, the contribution of major isotopes in the
formation of 44mSc were checked with the TENDL-2011 library,
and found supportive evidence for the aforementioned statement.
4.4.
Sc
3
10
ke
V
Counts (#)
10
46g+m
Sc
nat
Ti(d,x)44gSc processes
The relatively short-lived and ground state radionuclide 44gSc
(T1/2 = 3.97 h) is formed via two processes: via the direct reactions
Ti(d,x)46Sc processes
Sc has two states, a long-lived but unstable ground state 46gSc
(T1/2 = 83.79 d) and a very short-lived isomeric state 46mSc
(T1/2 = 18.75 s). 46mSc completely decays to its ground state by an
IT process (100%) at the time of our measurements: the measured
cross-sections of 46Sc are defined as the cumulative ones. The
excellent agreement between the cross-sections determined from
two intense c lines of 889.277 keV and 1120.545 keV confirmed
the accuracy of our measurements. The measured excitation function of 46Sc is shown in Fig. 6. The literature data reported by Gagnon et al. [25] and Takács et al. (2007) [10] at the low energy region
agree well with the present measurements. A downward energy
shift of the excitation function by Hermanne et al. [24] could make
an agreement with the present results. The renormalized data of
Takács et al. (1997) [8] show a slightly larger cross-sections
throughout the whole investigated energy region. The TALYS code
reproduces a shape of the measured excitation function but underestimates it in magnitudes. As listed in Table 2, all of the target isotopes of natural Ti contribute to the formation of 46Sc via complex
particle emissions in the energy region of interest. However, an
analysis of the excitation function reveals that the sharp maximum
around 12 MeV reflects the contribution of an abundant target isotope 48Ti via the 48Ti(d,a) (Q = +3.97 MeV) reaction. This is because
M.U. Khandaker et al. / Nuclear Instruments and Methods in Physics Research B 296 (2013) 14–21
the other possible contributing reaction 46Ti(d,2p) (Q = 3.8 MeV)
may find coulomb barrier effect in the exit channel, hence cannot
contribute immediately after its threshold energy. Additionally,
the possible contribution from the 46Ti(d,2p) (Q = 3.8 MeV) as
well as 47Ti(d,n2p) (Q = 12.7 MeV) reactions were cross checked
using the data from the TENDL-2011 library which confirmed the
aforementioned statement.
4.6.
nat
Ti(d,x)47Sc processes
10
48
0.1
44m
This work ( Sc)
44m
Dmitriev et al. ( Sc)
0.01
46
This work ( Sc)
46
Dmitriev et al. ( Sc)
47
Sc (T1/2 = 3.3492 d) decays to the stable nuclide 47Ti via a
b emission (100%). The intense and independent c line of
159.38 keV was used to identify this radionuclide. The measured
excitation function of 47Sc is shown in Fig. 7. The data measured
by Gagnon et al. [25] and Takács et al. (2007) [10] at the low energy
region show a very good agreement with the present results. An
overall good agreement is also obtained between the corrected
data of Takács et al. (1997) [8] and the present results in the whole
investigated energy region. The cross-sections reported by Hermanne et al. [24] show an agreement to the present results by
slightly shifting the excitation function downwards, though a good
agreement is seen above 20 MeV. The TALYS code reproduces a
shape of the experimental excitation function but overestimates
it above 15 MeV.
1E-3
4.7.
This work ( Sc)
47
This work ( Sc)
47
Dmitriev et al. ( Sc)
1
Yield (MBq/µ A-h)
20
Ti(d,x)48Sc processes
0
2
4
6
8
10 12 14 16 18 20 22 24 26 28 30
Deuteron Energy (MeV)
Fig. 11. Physical thick target yields for the
48,47,46,44m
Sc radionuclides.
45
44g
This work ( Sc)
43
This work ( Sc)
48
This work ( V)
48
Dmitriev et al. ( V)
48
Valikova et al. ( V)
Yield (MBq/µA-h)
40
30
20
10
nat
48
0
-2
48
Sc (T1/2 = 43.67 h) decays to the stable nuclide Ti by releasing a b particle (100%). 48Sc is formed only by the direct nuclear
reactions listed in Table 2. The most intense c lines 983.526 keV
and 1312.120 keV were not used to identify 48Sc due to the interferences of 48V as mentioned above. Thus, the independent c line of
1037.522 keV (Ic = 97.6%) was used to assess the radioactivity of
48
Sc. The assessed radioactivity of 48Sc was also confirmed with another c line of 175.361 keV (Ic = 7.48%). The excitation function of
48
Sc is shown in Fig. 8. No clear peak is seen in the measured excitation function in the investigated energy region. We found a good
agreement between our data and the earlier ones by Gagnon et al.
[25], Takács et al. (2007) [10], Hermanne et al. [24], and the renormalized ones of Takács et al. (1997) [8]. The TALYS code cannot
reproduce the distorted excitation function as shown in Fig. 8.
4.8. Contributions from secondary neutrons
Secondary neutrons from elastic break-up of deuterons may
also contribute to the production of the investigated scandium
radionuclides via (n,x) reactions, though it is difficult to evaluate
this effect in the complex c-ray spectra. However, this effect was
evaluated to be negligible for all radionuclides of interest in this
work by irradiating two extra foils at the back side of the stack
where the induced deuteron energy was ranged out (below
2 MeV). To understand this situation more clearly, two experimental c-ray spectra having exposed energy of 17 MeV and <2 MeV are
presented in the Figs. 9 and 10, respectively. Additionally, by considering the present experimental conditions such as the total
thickness of the irradiated stack (1.09 mm), covered deuteron energy range (low energy irradiation environment 2–24 MeV),
observing a very much negligible area only for few long-lived
radionuclides for the foil with an exposed energy of <2 MeV (See
counts in Fig. 10 relative to the corresponding nuclei in Fig. 9)
etc., the estimated effect of the neutrons were neglected. Similarly,
the contribution of secondary protons was also considered to be
negligible.
0
2
4
6
8
10 12 14 16 18 20 22 24 26 28 30
Deuteron Energy (MeV)
Fig. 12. Physical thick target yields for the
48
V and
44g,43
Sc radionuclides.
5. Thick target yields
Physical thick target yields (physical yields [34]) were deduced
for all of the investigated radionuclides 48V, 43Sc, 44mSc, 44gSc, 46Sc,
47
Sc, and 48Sc using the measured cross-sections and the electronic
stopping power of natTi over the energy range from a respective
threshold to the initial deuteron energy by taking into account that
the total energy is absorbed in the target. A detailed explanation
about the deduction of the yield is available elsewhere [28]. The
deduced yield is expressed as MBq/lA-h, i.e. the radioactivity corresponding to the yield of radionuclides produced by beam particles with electric charge of 1 lA 1 h (=3.6 mC). The deduced
yields are shown in Figs. 11 and 12 as a function of the deuteron
energy with the directly measured thick target yield in the literature. Dmitriev et al. [57] reported the thick target yields for the
production of 48V, 44mSc, 46Sc and 47Sc by irradiating a thick natural
titanium target with a 22-MeV deuteron beam. Their target was
thick enough to cover the energy range from a threshold to
22 MeV. The present thick target yields show an excellent agreement with the directly measured ones for 46Sc and 48V by Dmitriev
et al. [57]. However, 47Sc yield reported by Dmitriev et al. [57] was
not confirmed by the present investigations. The physical thick target yields reported for 48V by Vakilova et al. [58] in the energy region of 4 to 12 MeV also agree well with the present ones as shown
in Fig. 12.
6. Conclusions
functions for the formation of 48V and
Sc via the natTi(d,x) nuclear reactions were
measured in the energy range of 2–24 MeV using a stacked-foil
Excitation
43,44m,44g,46,47,48
M.U. Khandaker et al. / Nuclear Instruments and Methods in Physics Research B 296 (2013) 14–21
activation technique with an overall uncertainty of about 11%.
Measured data were critically compared with the available literature data and found an overall good agreement, whereas partial
agreements were obtained with the theoretical calculations based
on the TALYS code. The physical thick target yields for the investigated radionuclides were also deduced using the measured crosssections, and found a good agreement with the directly measured
thick target yields in the literature. The shape of the IAEA recommended monitor cross-sections for natTi(d,x)48V reaction was verified. Above all, the measured cross-sections of the 48V, 43Sc, 44mSc,
44g
Sc, 46Sc, 47Sc, and 48Sc via deuteron irradiation on natural titanium targets could play an important role in enrichment of the literature database leading to various practical applications. In most
cases, it has been reported that TENDL-2011 cannot reproduce the
measured excitation functions properly, and we confirmed that the
adopted nuclear reaction models and parameter set in TALYS-1.4
for the production of TENDL-2011 are not sufficient enough to describe the investigated reactions precisely.
Acknowledgements
This work was performed at the RI Beam Factory operated by
RIKEN Nishina Center and CNS, University of Tokyo. The authors
would like to express their sincere thanks to the staffs of the AVF
cyclotron for an excellent beam operation. The work was partially
supported by the University of Malaya Research Grant (RG13911AFR).
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