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Excitation functions of alpha-particle induced nuclear reactions on natural ytterbium
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NIM B Beam Interactions with Materials & Atoms
Nuclear Instruments and Methods in Physics Research B 266 (2008) 3919–3926 www.elsevier.com/locate/nimb
Excitation functions of alpha-particle induced nuclear reactions on natural ytterbium B. Kira´ly a,*, F. Ta´rka´nyi a, S. Taka´cs a, A. Hermanne b, S.F. Kovalev c, A.V. Ignatyuk c a
Institute of Nuclear Research of the Hungarian Academy of Sciences (ATOMKI), 4026 Debrecen, Bem ter 18/c, Hungary b Cyclotron Laboratory, Vrije Universiteit Brussel (VUB), 1090 Brussels, Belgium c Institute of Physics and Power Engineering (IPPE), Obninsk 249020, Russian Federation Received 18 December 2007; received in revised form 1 July 2008 Available online 10 July 2008
Abstract Excitation functions of the reactions natYb(a,xn)170,171,173,175,177m2Hf, natYb(a,x)171g,172g,177g,178mLu and natYb(a,x)169g,177gYb have been measured up to 39 MeV, among them seven (170,171,173,177m2Hf, 177g,178mLu, 177gYb) are reported for the first time. The experimental excitation functions are compared to the theoretical calculations based on the model code ALICE-IPPE and to the only data-set found in the literature. Yields of different production routes of the therapeutically relevant 177Lu are compared. Ó 2008 Elsevier B.V. All rights reserved. PACS: 25.55.e; 27.70.+q Keywords: Ytterbium target; Alpha-particle irradiation; Excitation function; Cross section;
1. Introduction In the frame of a systematic investigation of production routes of radioisotopes used in medicine for radiotherapy excitation functions of a-induced nuclear reactions on natural Yb target have been measured. Cross sections nat for the reactions Yb(a,xn)170,171,173,175,177m2Hf, nat 171g,172g,177g,178m Yb(a,x) Lu and natYb(a,x)169g,177gYb are reported here up to 39 MeV. Among the possible reaction products 177Lu and 169Yb are the most important in medical practice.
*
Lu (b decay) has excellent properties for applications in therapy and the emitted photons are also ideally suited for imaging and localization with gamma cameras. Its production using deuteron beams was studied in [1].
177
Corresponding author. Tel.: +36 52 509 200; fax: +36 52 416 181. E-mail address: [email protected] (B. Kira´ly).
0168-583X/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2008.07.002
177
Lu;
169
Yb
169
Yb (EC = 100%) is an almost pure Auger-electron and X-ray emitter and has been gaining interest in brachytherapy, it has also found application in medical diagnostics, especially in cisternography. Its production routes in a reactor via the 168Yb(n,c) reaction and with a cyclotron via the 169Tm(p,n) reaction were compared in [2]. Other possible routes like 169Tm(d,2n) and natEr(a,x) are discussed in [3,4].
Knowledge of these cross sections is also important for reliable activation analysis of samples containing rare earth elements. This study furthermore allows checking the capability of nuclear models to describe complex reactions on medium mass nuclei and the predictive value and accuracy of codes based on these models. The only earlier results for alpha-particle induced nuclear reactions on natural ytterbium target were presented by Romo et al. [5] in 1992. Their renormalized data for 175Hf, 171gLu, 172gLu and 169gYb are compared with ours.
B. Kira´ly et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 3919–3926
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Preliminary results of this study for the reactions Yb(a,x)177gLu and natYb(a,x)169gYb were presented at the International Conference on Nuclear Data for Science and Technology in Nice, in 2007 [6].
3. Data processing
nat
2. Experimental procedure Two stacks of ytterbium targets were irradiated with the external 39 MeV alpha-particle beam of CGR-560 cyclotron at the Vrije Universiteit Brussel, Belgium, in 2006. Stack1 and stack2 contained ten and eight high purity ytterbium foils (Goodfellow), respectively, interloaded with Ti monitor foils. An Al degrader was placed at the front of stack2 to ensure a small energy shift in the successive Yb foils of the two stacks. The thicknesses of the foils were: Yb 30 lm, Ti 12 lm and Al 25.5 lm. The beam-currents were 137 and 128 nA, both irradiations continued for approximately 90 min. No chemical separation was performed. The gamma spectra of the irradiated foils were registered with a PC-coupled HPGe detector system. The efficiency was determined by placing standard sources in sample holders at different distances from the detector. The distance between the ytterbium sample and the detector crystal was in all cases carefully chosen to avoid dead time corrections, pile-up effects and coincidence losses. The data acquisition started 0.5 h after the end of bombardment and continued for almost a month measuring each ytterbium foil three times, enabling separation of radioisotopes having the same gamma-lines but different half lives and following cumulative processes. The high purity Ti foils inserted in the stacks served both as energy degraders and as beam monitors to correct the given nominal alpha-particle energy and beam current if needed. The whole excitation function of the nat Ti(a,x)51Cr monitor reaction was re-measured and adjusted to the curve recommended in the IAEA TECDOC-1211 [7] (Fig. 1).
Cross section (mb)
600
Monitor reaction nat 51 Ti(α,x) Cr
400
Stack1
The recorded gamma spectra were analyzed with an automatic peak searching program. The nuclear data for the evaluation of cross sections of the different radioisotopes were taken from [8] and are tabulated in Table 1. The mean energy of the alpha-particle beam in the successive target foils was calculated using the polynomial approximation of Ziegler [9]. The energy uncertainty at the first foil in the stack was estimated to be ±0.3 MeV increasing up to ±1.5 MeV at the last foil due to the energy straggling and the uncertainty on the target thickness. The uncertainty on the cross sections was determined in the standard way according to the guidelines of [10]. The linearly contributing independent processes were taken into account by extracting the square root of quadratically summed relative uncertainties, namely: number of the bombarding particles (7%), number of the target nuclei (3%), decay data (3%), detector efficiency (7%) and peak area (1–10%).
4. Theoretical calculations The measured experimental data were compared to and analyzed with theoretical calculations based on the model code ALICE-IPPE. The ALICE code family was developed by Blann [11] and is based on the hybrid, the geometry dependent hybrid (GDH) or the hybrid Monte Carlo simulation (HMS) pre-equilibrium models and the Weisskopf– Ewing evaporation formalism. The ALICE-IPPE code [12] is a version of the ALICE-91 code [13] modified by the Obninsk Group to include the generalized superfluid level density model and pre-equilibrium cluster emission. Corrections were made, among others, for gamma-emission and optical model parameters. Angular distribution and refraction were not taken into account. The lack of angular momentum and parity treatments in the Weisskopf–Ewing formalism used makes independent treatment of isomeric states impossible, only total production cross sections can be calculated. The theoretical curves were determined using one recommended input data-set without any optimization or adjustment of parameters to the individual reactions or stable target isotopes. The results of the reaction products of interest in this study were weighted and summed according to the abundance of the target isotopes and to the cumulative processes.
Stack2 IAEA recommended [7] 200
5. Results and discussion 0 0
10
20
30
40
Alpha-particle energy (MeV)
Fig. 1. Excitation function of
nat
Ti(a,x)51Cr monitor reaction.
50
As the ytterbium foils used in these measurements had already been irradiated with deuterons in a previous experiment [1] less than 1.5 years before, only those radioisotopes which could not be produced at that time (i.e.
B. Kira´ly et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 3919–3926
3921
Table 1 Decay data of radioisotopes [8], the possible contributing reactions and their threshold energies [14] Radionuclide 170
Hf
Half life 16.01 h
Spin, parity 0+
Ec (keV)
Ic (%)
620.7
18
Reactiona
Threshold energyb (MeV)
168
19.2 34.9 11.6 27.3 34.1 10.8 17.6 25.8 32.3 40.0 2.5 10.7 17.2 24.8 37.8 2.3 9.9 22.9 8.8 15.8 22.6 30.8 37.3 11.6 27.3 34.1 15.1 15.4 23.7 30.2 37.8 9.6 13.9 15.4 25.3 14.2 14.0 8.7 15.4 23.6 30.2 37.8 16.4 32.1 38.9 29.2 15.4 25.3
Yb(a,2n) Yb(a,4n) 168 Yb(a,n) 170 Yb(a,3n) 171 Yb(a,4n) 170 Yb(a,n) 171 Yb(a,2n) 172 Yb(a,3n) 173 Yb(a,4n) 174 Yb(a,5n) 171 Yb(a,c) 172 Yb(a,n) 173 Yb(a,2n) 174 Yb(a,3n) 176 Yb(a,5n) 173 Yb(a,c) 174 Yb(a,n) 176 Yb(a,3n) 168 Yb(a,p) 170 Yb(a,t) 171 Yb(a,tn) 172 Yb(a,t2n) 173 Yb(a,t3n) 168 Yb(a,n)171Hf? 170 Yb(a,3n)171Hf? 171 Yb(a,4n)171Hf? 170 Yb(a,d) 171 Yb(a,t) 172 Yb(a,tn) 173 Yb(a,t2n) 174 Yb(a,t3n) 174 Yb(a,p) 176 Yb(a,t) 176 Yb(a,3He)177Yb? 176 Yb(a,3p)177Tm ? 177Yb? 176 Yb(a,d) 168 Yb(a,3He) 170 Yb(a,an) 171 Yb(a,a2n) 172 Yb(a,a3n) 173 Yb(a,a4n) 174 Yb(a,a5n) 168 Yb(a,t)169Lu? 170 Yb(a,t2n)169Lu? 171 Yb(a,t3n)169Lu? 168 Yb(a,3n)169Hf ? 169Lu? 176 Yb(a,3He) 176 Yb(a,3p)177Tm? 170
171
12.1 h
(7/2+)
469.3 662.2
173
23.6 h
1/2
123.7 139.6 297.0
83 12.7 33.9
5/2
343.4
84
51.4 min
37/2
277.3 606.5
78 11.9
Hf
Hf
175
Hf
177m2
Hf
70 d
100c 266c
171g
Lu
8.24 d
7/2+
667.4 739.8
11.04 47.8
172g
Lu
6.70 d
4
810.1 900.7 1093.7
16.63 29.8 62.5
177g
Lu
6.734 d
7/2+
208.4
11
Lu Yb
23.1 min 32.026 d
(9) 7/2+
426.4 177.2 307.7
97 22.16 10.05
Yb
1.911 h
(9/2+)
150.4
20.3
178m 169g
177g
a nat b c
Yb: 168Yb 0.13%, 170Yb 3.05%, 171Yb 14.3%, 172Yb 21.9%, 173Yb 16.12%, 174Yb 31.8%, 176Yb 12.7%. If the outgoing particles are pn, p2n, 2pn and 2p2n instead of d, t, 3He and a, add 2.3, 8.7, 7.8 and 28.9 MeV, respectively, to the threshold energy. Relative intensity.
activation by (a,xn) reactions) or with half lives short enough to decay out completely by the time of this experiment were investigated. Tables 2 and 3 represent the numerical values of cross sections and the uncertainties. The measured excitation functions are shown in Figs. 2–12 together with the curves of ALICE-IPPE calculations and the data found in the literature.
The only cross section measurements for a-induced reactions on natural ytterbium targets were reported by Romo et P al. in 1992 [5]. Their data must be multiplied by i ai Ai ¼ 173:1 to get production cross sections, where ai and Ai are the abundance and the atomic weight of the ith isotope of natural ytterbium. Natural ytterbium consists of seven stable isotopes (see Table 1) so excitation functions show complex shapes
170
E (MeV)
DE (MeV)
r (mb)
7.8 16.6 17.4 20.3 21.0 23.7 24.3 26.7 27.3 29.6 30.1 32.3 32.8 34.8 35.3 37.2 37.7
1.5 1.0 1.0 0.9 0.9 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.4 0.4 0.3 0.3
173
Hf
0.35 1.03 1.28 1.63 1.84 1.72 2.00 1.81 1.87 1.82 1.38 1.24
Yb(a,xn)170,173,175,177m2Hf,
nat
Yb(a,x)171g,172g,177g,178mLu and
175
Hf
Hf
Dr (mb)
r (mb)
Dr (mb)
0.16 0.24 0.27 0.28 0.39 0.34 0.62 0.44 0.43 0.52 0.52 0.38
0.20 1.11 17.5 42.0 85.0 107 129 148 165 195 233 267 291 300 329 346
0.03 0.13 2.1 5.1 9.9 13 15 17 19 22 28 31 34 35 39 41
Ind
r (mb)
r (mb)
Dr (mb)
8.84 51.2 84.1 122 144 165 211 287 347 410 454 480 479 480 454
177m2
0.99 5.7 9.5 14 16 19 24 32 39 46 51 54 54 54 51
0.18 0.37 0.83 1.25 2.08 2.57 3.56 3.57
Cum
Dr (mb)
r (mb)
171g
0.05 0.28 0.63 0.54 0.49 0.32 0.44 0.49 2.73 9.5 18.1 29.0 34.8 44.7 53.0
0.07 0.09 0.16 0.22 0.29 0.39 0.46 0.45
Yb(a,x)169g,177gYb
Lu
Cum
Dr (mb)
r (mb)
0.02 0.06 0.13 0.11 0.09 0.08 0.09 0.23 0.55 1.3 2.2 3.4 4.1 5.1 6.0
0.12 0.44 1.00 1.12 2.23 2.12 5.04 5.1 9.9 9.4 14.5 10.3 18.5 16.4
172g
Lu
Cum
Dr (mb)
0.06 0.17 0.16 0.25 0.29 0.34 0.69 1.1 1.4 1.2 1.7 1.3 2.3 2.1
177g
178m
Lu
Ind
r (mb)
Dr (mb)
r (mb)
0.06
0.03
0.05
0.09
0.47 1.04 1.75 2.38 2.81 3.11 3.71 3.40 4.78 4.07 6.18 6.74
0.10 0.27 0.22 0.38 0.47 0.56 0.77 0.56 0.76 0.65 0.89 0.94
0.24 0.34 0.43 0.67 0.82 0.81 0.97 1.02
Lu
Cum
Dr (mb)
0.04 0.05 0.06 0.10 0.10 0.13 0.11 0.12
169g
177g
Yb
Cum
r (mb)
Dr (mb)
r (mb)
Dr (mb)
0.46
0.17
0.19
0.12
1.18 0.89 1.58 2.46 2.49
0.85 0.42 0.71 0.67 0.73
0.22 0.29
0.18 0.15
0.23
0.11
Yb
Dr (mb)
Hf
171
Yb(a,xn)171Hf
nat
r (mb)
Table 3 Measured cross sections of the reaction
DE (MeV)
0.030 0.073 0.064 0.20 0.043
Alpha-particle
E (MeV)
0.226 0.265 0.350 0.44 0.186
0.088 0.41 0.78 1.6 2.1 2.8 3.5 3.9
Hf
170
40
0.389 1.92 6.42 12.8 18.2 23.6 29.9 34.4
Yb(α,xn)
30
40
1.5 1.0 1.0 0.9 0.9 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.4 0.4 0.3 0.3
nat
Stack1
Stack2
20
Alpha-particle energy (MeV)
ALICE-IPPE, 170Hf
10
Hf
171
35
Yb(a,xn)170Hf reaction.
nat
Yb(α,xn)
30
7.8 16.6 17.4 20.3 21.0 23.7 24.3 26.7 27.3 29.6 30.1 32.3 32.8 34.8 35.3 37.2 37.7
3.0
2.0
1.0
0.0 0
nat
Fig. 2. Excitation function of
Stack1
Stack2
25
Alpha-particle energy (MeV)
ALICE-IPPE, 171Hf
20
The relative gamma intensities were multiplied by 0.055 [15] in the evaluation process.
Cross section (mb) 40
30
20
10
0 15
Fig. 3. Excitation function of natYb(a,xn)171Hf reaction. The relative gamma intensities were multiplied by 0.055 [15] in the evaluation process.
Cross section (mb)
Hf
nat
B. Kira´ly et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 3919–3926
Alpha-particle
nat
3922
Table 2 Measured cross sections of the reactions
B. Kira´ly et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 3919–3926 1.E+04
400
nat
300
Hf
200 Stack1 Stack2 100
ALICE-IPPE, 173Hf
171g
Yb(α,x) Lu cumulative
173
Yb(α,xn)
Cross section (mb)
Cross section (mb)
nat
1.E+02
1.E+00
Stack1 Stack2 ALICE-IPPE, 171Hf + 171m+gLu ALICE-IPPE, 171Hf Romo 1992 [5]
1.E-02
1.E-04
0 0
10
20
30
0
40
20
40
Fig. 4. Excitation function of
60
80
100
Alpha-particle energy (MeV)
Alpha-particle energy (MeV) nat
Yb(a,xn)173Hf reaction.
nat
Yb(a,x)171gLu reaction.
Fig. 7. Excitation function of cumulative
600
250 nat
Yb(α,xn)
175
Hf
nat
400 Stack1 Stack2 ALICE-IPPE, 175Hf Romo 1992 [5]
200
172g
Yb(α,x) Lu cumulative
200
Cross section (mb)
Cross section (mb)
3923
150 Stack1 Stack2
100
ALICE-IPPE, 172m+gLu Romo 1992 [5] 50
0
0 0
20
40
60
80
0
100
20
40
Alpha-particle energy (MeV)
Fig. 5. Excitation function of
60
80
100
Alpha-particle energy (MeV)
nat
Yb(a,xn)175Hf reaction.
Fig. 8. Excitation function of cumulative
nat
Yb(a,x)172gLu reaction.
8
1.E+03 Stack1
nat
Cross section (mb)
Cross section (mb)
1.E+02
ALICE-IPPE, 177m1+m2+gHf
1.E+01 nat
1.E+00
177m2
Yb(α,xn) Hf independent
177g
Yb(α,x) Lu independent
Stack2 6
4 Stack1 Stack2 ALICE-IPPE, 177m+gLu 2
ALICE-IPPE, 177m+gYb
1.E-01 0 0
0
10
20
30
20
30
40
40
Alpha-particle energy(MeV)
Fig. 6. Excitation function of independent
Fig. 9. Excitation function of independent
nat
Yb(a,x)177gLu reaction.
nat
Yb(a,xn)177m2Hf reaction.
reflecting the contributions of reactions taking place on the different stable isotopes. The possible reactions producing the given radioisotope and their threshold energies [14] are given in Table 1. 5.1. Cross sections nat
10
Alpha-particle energy (MeV)
1.E-02
Yb(a,xn)170Hf process. Our measured points with relatively high uncertainties follow the shape of the
ALICE-IPPE curve and are slightly above it (Fig. 2). The theoretical calculation clearly shows the contributions of the (a,2n) and (a,4n) reactions in the investigated energy range with respective threshold energies of 19.2 and 34.9 MeV. nat Yb(a,xn)171Hf process. The gamma intensities of this reaction product given in [8] are relative and no absolute values are available in the literature. The latest recommendation found in the Nuclear Data Sheets [15] says that the relative intensities (see Table 1) should be multiplied by
B. Kira´ly et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 3919–3926
3924 6
Cross section (mb)
nat
178m
Yb(α,x) Lu independent
4
Stack1
2
Stack2 ALICE-IPPE, 178m+gLu
0 0
10
20
30
40
Alpha-particle energy (MeV)
Fig. 10. Excitation function of independent
nat
Yb(a,x)178mLu reaction.
Cross section (mb)
1.E+03 Stack1 Stack2 ALICE-IPPE, 169Hf + 169m+gLu + 169m+gYb A-I, 169Hf A-I, 169m+gLu A-I, 169m+gYb Romo 1992 [5]
1.E+02
1.E+01
nat
1.E+00
169g
Yb(α,x) Yb cumulative
1.E-01 0
20
40
60
80
100
Alpha-particle energy (MeV)
Fig. 11. Excitation function of cumulative
nat
Yb(a,x)169gYb reaction.
1.2
Cross section (mb)
nat
177g
Yb(α,x) Yb cumulative
0.8 Stack1 Stack2 ALICE-IPPE, 177m+gYb 0.4
0.0 0
20
40
60
80
Alpha-particle energy (MeV)
Fig. 12. Excitation function of cumulative
nat
Yb(a,x)177gYb reaction.
0.055 to get absolute intensities if one made an assumption that the ground state of 171Lu is not fed by beta decay. We used this factor in the cross section evaluation process. The results are tabulated in Table 3 and shown in Fig. 3. As Figs. 2, 4 and 5 show the predictions of ALICE-IPPE calculations seem very good in the case of (a,xn) processes (i.e. hafnium isotopes) so we can trust that this is valid in the case of 171Hf as well. This means that the assumption given above is not far from the truth. According to the theoretical calculation the (a,n) reaction taking place on 168Yb has a high maximum (530 mb at 23 MeV) but as the abun-
dance of this isotope is very low (0.13%), the curve shows a grazing shape up to 29 MeV. The rising part of the excitation function is drawn by the (a,3n) and (a,4n) processes. nat Yb(a,xn)173Hf process. The measured data coincide with the theoretical calculation (Fig. 4). The nearly monotonous increasing curve with small breaks indicates that it is a sum of several excitation functions of (a,xn) reactions taking place on four different stable isotopes of ytterbium. nat Yb(a,xn)175Hf process. The long half life and the strong gamma line of 175Hf allows long acquisition times resulting in lower statistical uncertainty. The agreement with the prediction of the ALICE-IPPE code is very good (Fig. 5). The contribution of the (a,c) reaction is negligible, the first rise with the small plateau is the sum of the (a,n) and (a,2n) reactions, the maximum is caused by the (a,3n) reaction and the peak at higher energy measured by Romo et al. [5] is the result of the (a,5n) reaction taking place on 176Yb. However, no explanation is found for the discrepant low cross section value at 48 MeV or for the upward tendency above 80 MeV. nat Yb(a,xn)177m2Hf independent process. The stable nuclide 177Hf has two metastable states in addition to the ground state. Only cross sections for the longer lived and higher lying m2 state could be measured. The excited state 177m2 Hf is not fed by b decay of any of the two isomeric states of 177Lu (177gLu 7/2+, 177mLu 23/2) so independent cross sections are determined and plotted in Fig. 6. As the ALICE-IPPE code cannot calculate the excitation functions of different isomeric states separately we can only conclude that the contribution of the excitation of the m2 state to the total cross section is lower by one to three orders of magnitude than the contribution of the other two states together. nat Yb(a,x)171gLu cumulative process. This cumulative cross section includes the contributions of 171Hf (T1/2 = 12.1 h, (7/2+)) and the metastable state (T1/2 = 79 s, 1/2) of 171Lu after their total decay in addition to the independent formation of the ground state. Although the reactions resulting in formation of 171Lu are energetically possible the comparison of the experimental cumulative cross section with the prediction of the ALICE-IPPE code for production of 171Hf shows that the indirect route is the nearly only contributor to formation of 171gLu (see Fig. 7). Romo’s [5] data (excluding their first three points) and ours both fit to the theoretical curve. nat Yb(a,x)172gLu cumulative process. This cumulative cross section includes the contribution of 172mLu (T1/2 = 3.7 min, 1) after its total decay in addition to the independent formation of the ground state but does not include any contribution from 172Hf (T1/2 = 1.87 y, 0+) because the number of decaying nuclei was negligible during the acquisition of the gamma spectra. The sum of the excitation functions of reactions taking place on different stable isotopes of ytterbium results in a monotonously rising curve as shown by Romo’s [5] and our measured points (Fig. 8). The ALICE-IPPE code which calculates the sum of the excitation functions of the two isomeric states, so
B. Kira´ly et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 3919–3926
Yield (MBq / μAh)
1.E+02
177m2
1.E+00
Hf
178m
Lu
170
Hf
173
Hf 175
Hf
1.E-02
171
Hf
177g
Yb
1.E-04 169g
Yb
171g
177g
Lu
172g
Lu
Lu
1.E-06 15
20
25
30
35
40
Alpha-particle energy (MeV)
Fig. 13. Integral yields calculated on the basis of our fitted experimental data.
1.E+02 Hermanne [1] Yb(d,p)177Yb -> 177Lu
177
176
Lu
Yield (MBq / μAh)
it is comparable with our results, predicts a curve with a shift to higher energy by about 8 MeV and with higher absolute values. nat Yb(a,x)177gLu independent process. This cross section may contain contributions of decays of 177Tm (T1/2 = 85 s, (1/2+)), 177mYb (T1/2 = 6.41 s, (1/2)), 177gYb (T1/2 = 1.911 h, (9/2+)) in addition to independent formation of the ground state but contribution from 177mLu (T1/2 = 160.4 d, 23/2) is negligible as presence of its strong gamma-lines in the spectra could not be proved. The ALICE-IPPE prediction says that 177Tm and 177Yb do not play roles in this energy region (Fig. 9) so the only processes responsible for the shape of this excitation function up to 39 MeV are 176Yb(a,p2n)177Lu and 174Yb(a,p)177Lu. The former dominates above and the latter below 36 MeV but their sum underestimates our measured values. nat Yb(a,x)178mLu independent process. As 178Yb (0+) does not decay into the metastable state of 178Lu, an independent cross section for 178mLu formation could be measured. Weak gamma-lines of 178gLu (T1/2 = 28.4 min, 1(+)) were not found in the spectra. 178mLu can only be formed on 176Yb via (a,d) or (a,pn) process. The ALICE-IPPE calculation shows that the contribution of the ground state to the total cross section is higher than that of the metastable state (Fig. 10). nat Yb(a,x)169gYb cumulative process. This cumulative cross section may contain contributions of 169Hf (T1/2 = 3.24 min, (5/2)), 169mLu (T1/2 = 160 s, 1/2), 169gLu (T1/2 = 34.06 h, 7/2+) and 169mYb (T1/2 = 46 s, 1/2) after their total decay in addition to the independent formation of the ground state 169gYb. As Fig. 11 shows the model code predicts that among them 169Lu has no effect on the cross section of the measured reaction below 39 MeV. Our data have relatively high statistical uncertainties because of the weak gamma-lines and are a factor of two lower than the values published by Romo et al. [5]. nat Yb(a,x)177gYb cumulative process. This cumulative cross section may contain the contributions of 177Tm (T1/2 = 85 s, (1/2+)) and 177mYb (T1/2 = 6.41 s, (1/2)) after their total decay in addition to independent formation of the ground state 177gYb but according to the model code results the role of 177Tm is negligible in this energy region. Only four points were determined with large uncertainty because of the poor counting statistics and there is a considerable difference between the measured and calculated results as can be seen in Fig. 12.
3925
1.E+00
Hermanne [1] Yb(d,n)177Lu
176
1.E-02 This work Yb(α,x)177Lu
nat
1.E-04
1.E-06 0
10
20
30
40
Particle energy (MeV)
Fig. 14. Comparison of integral yields of different routes of production.
177
Lu
177
Lu while the (d,p) reaction leads to mother nucleus Yb that decays into 177Lu by b decay. The figure shows that among the charged particle induced production routes 176Yb(d,n) is more productive when compared to the recently investigated a-route. However, the possible batch yield of the (n,c) process near high flux reactors is higher by orders of magnitude and remains the production route of choice. As 169Yb cannot be produced from Yb targets without carrier being present, a more detailed discussion and comparison with charged particle production routes resulting in non carrier added end-product is not relevant. 177
5.2. Integral yields
6. Conclusion
On the basis of our fitted experimental data integral yields were calculated and are shown in Fig. 13. Because of the medical importance of 177Lu integral yields of its different production routes via charged particle induced nuclear reactions are compared in Fig. 14. Hermanne et al. [1] reported yield curves as results of calculations from cross section measurements of deuteron induced reactions on 176Yb. The (d,n) reaction produces
Experimental cross sections for eleven alpha-particle induced nuclear reactions on natural ytterbium target have been measured up to 39 MeV, seven of them for the first time. The reliability of our results is ensured by the monitor reaction which was re-measured over the whole energy range. In general reasonable agreement with values predicted by the ALICE-IPPE code and with the results of Romo et al. [5] is observed.
3926
B. Kira´ly et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 3919–3926
The yield deduced from our fitted excitation curve shows that for the production of 177Lu the alpha-particle induced route on natYb target is not competitive. The production of medically interesting radioisotopes 177 Lu and 169Yb via alpha-particle irradiation of natural Yb target is not of practical but of academic interest. References [1] A. Hermanne, S. Taka´cs, M.B. Goldberg, E. Lavie, Yu.N. Shubin, S. Kovalev, Deuteron-induced reactions on Yb: measured cross sections and rationale for production pathways of carrier-free, medically relevant radionuclides, Nucl. Instr. and Meth. B 247 (2006) 223. [2] I. Spahn, S. Taka´cs, Yu.N. Shubin, F. Ta´rka´nyi, H.H. Coenen, S.M. Qaim, Cross-section measurement of the 169Tm(p,n) reaction for the production of the therapeutic radionuclide 169Yb and comparison with its reactor-based generation, Appl. Radiat. Isotopes 63 (2005) 235. [3] F. Ta´rka´nyi, A. Hermanne, S. Taka´cs, F. Ditro´i, I. Spahn, S.F. Kovalev, A.V. Ignatyuk, S.M. Qaim, Activation cross sections of the 169 Tm(d,2n) reaction for production of the therapeutic radionuclide 169 Yb, Appl. Radiat. Isotopes 65 (2007) 663. [4] B. Kira´ly, F. Ta´rka´nyi, S. Taka´cs, A. Hermanne, S.F. Kovalev, A.V. Ignatyuk, Excitation functions of alpha-induced nuclear reactions on natural erbium, Nucl. Instr. and Meth. B. 266 (2008) 549. [5] A.S.M.A. Romo, A.A. Sonzogni, D.A. Rodriguez Sierra, S.J. Nassiff, Nuclear reactions induced by alpha-particles on natural ytterbium, Radiochim. Acta 57 (1992) 57.
[6] B. Kira´ly, F. Ta´rka´nyi, S. Taka´cs, A. Hermanne, S.F. Kovalev, A.V. Ignatyuk, Excitation functions of alpha-induced nuclear reactions on natural erbium and natural ytterbium targets, in: International Conference on Nuclear Data for Science and Technology, 22-27 April 2007, Nice, France, p. 1371, doi:10.1051/ndata:07255. [7] F. Ta´rka´nyi, S. Taka´cs, K. Gul, A. Hermanne, M.G. Mustafa, M. Nortier, P. Oblozinsky, S.M. Qaim, B. Scholten, Yu.N. Shubin, Z. Youxiang, Beam monitor reactions (Chapter 4), in: Charged Particle Cross-Section Database for Medical Radioisotope Production: Diagnostic Radioisotopes and Monitor Reactions, IAEA-TECDOC-1211, Vienna, 2001, p. 49, Available from:. [8] L.P. Ekstro¨m, R.B. Firestone, WWW Table of Radioactive Isotopes, Database Version 2/28/99 from URL . [9] J.F. Ziegler, Helium – Stopping powers and ranges in all elemental matter, Volume 4 of the Stopping and Ranges of Ions in Matter, Pergamon Press, 1977, ISBN 0-08-021606-4. [10] Guide to the Expression of Uncertainty in Measurement, International Organization for Standardization, Geneva, 1995, ISBN 92-6710188-9. [11] M. Blann, LLNL Report, UCRL-JC-109052, 1991. [12] A.I. Dityuk, A.Yu. Konobeyev, V.P. Lunev, Yu. N. Shubin, Report INDC(CCP)-410, International Atomic Energy Agency, Vienna, 1998. [13] M. Blann, Report PSR-0146, Available from: . [14] T-2 Nuclear Information Service, Los Alamos, Available from:
NIM B Beam Interactions with Materials & Atoms
Nuclear Instruments and Methods in Physics Research B 266 (2008) 3919–3926 www.elsevier.com/locate/nimb
Excitation functions of alpha-particle induced nuclear reactions on natural ytterbium B. Kira´ly a,*, F. Ta´rka´nyi a, S. Taka´cs a, A. Hermanne b, S.F. Kovalev c, A.V. Ignatyuk c a
Institute of Nuclear Research of the Hungarian Academy of Sciences (ATOMKI), 4026 Debrecen, Bem ter 18/c, Hungary b Cyclotron Laboratory, Vrije Universiteit Brussel (VUB), 1090 Brussels, Belgium c Institute of Physics and Power Engineering (IPPE), Obninsk 249020, Russian Federation Received 18 December 2007; received in revised form 1 July 2008 Available online 10 July 2008
Abstract Excitation functions of the reactions natYb(a,xn)170,171,173,175,177m2Hf, natYb(a,x)171g,172g,177g,178mLu and natYb(a,x)169g,177gYb have been measured up to 39 MeV, among them seven (170,171,173,177m2Hf, 177g,178mLu, 177gYb) are reported for the first time. The experimental excitation functions are compared to the theoretical calculations based on the model code ALICE-IPPE and to the only data-set found in the literature. Yields of different production routes of the therapeutically relevant 177Lu are compared. Ó 2008 Elsevier B.V. All rights reserved. PACS: 25.55.e; 27.70.+q Keywords: Ytterbium target; Alpha-particle irradiation; Excitation function; Cross section;
1. Introduction In the frame of a systematic investigation of production routes of radioisotopes used in medicine for radiotherapy excitation functions of a-induced nuclear reactions on natural Yb target have been measured. Cross sections nat for the reactions Yb(a,xn)170,171,173,175,177m2Hf, nat 171g,172g,177g,178m Yb(a,x) Lu and natYb(a,x)169g,177gYb are reported here up to 39 MeV. Among the possible reaction products 177Lu and 169Yb are the most important in medical practice.
*
Lu (b decay) has excellent properties for applications in therapy and the emitted photons are also ideally suited for imaging and localization with gamma cameras. Its production using deuteron beams was studied in [1].
177
Corresponding author. Tel.: +36 52 509 200; fax: +36 52 416 181. E-mail address: [email protected] (B. Kira´ly).
0168-583X/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2008.07.002
177
Lu;
169
Yb
169
Yb (EC = 100%) is an almost pure Auger-electron and X-ray emitter and has been gaining interest in brachytherapy, it has also found application in medical diagnostics, especially in cisternography. Its production routes in a reactor via the 168Yb(n,c) reaction and with a cyclotron via the 169Tm(p,n) reaction were compared in [2]. Other possible routes like 169Tm(d,2n) and natEr(a,x) are discussed in [3,4].
Knowledge of these cross sections is also important for reliable activation analysis of samples containing rare earth elements. This study furthermore allows checking the capability of nuclear models to describe complex reactions on medium mass nuclei and the predictive value and accuracy of codes based on these models. The only earlier results for alpha-particle induced nuclear reactions on natural ytterbium target were presented by Romo et al. [5] in 1992. Their renormalized data for 175Hf, 171gLu, 172gLu and 169gYb are compared with ours.
B. Kira´ly et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 3919–3926
3920
Preliminary results of this study for the reactions Yb(a,x)177gLu and natYb(a,x)169gYb were presented at the International Conference on Nuclear Data for Science and Technology in Nice, in 2007 [6].
3. Data processing
nat
2. Experimental procedure Two stacks of ytterbium targets were irradiated with the external 39 MeV alpha-particle beam of CGR-560 cyclotron at the Vrije Universiteit Brussel, Belgium, in 2006. Stack1 and stack2 contained ten and eight high purity ytterbium foils (Goodfellow), respectively, interloaded with Ti monitor foils. An Al degrader was placed at the front of stack2 to ensure a small energy shift in the successive Yb foils of the two stacks. The thicknesses of the foils were: Yb 30 lm, Ti 12 lm and Al 25.5 lm. The beam-currents were 137 and 128 nA, both irradiations continued for approximately 90 min. No chemical separation was performed. The gamma spectra of the irradiated foils were registered with a PC-coupled HPGe detector system. The efficiency was determined by placing standard sources in sample holders at different distances from the detector. The distance between the ytterbium sample and the detector crystal was in all cases carefully chosen to avoid dead time corrections, pile-up effects and coincidence losses. The data acquisition started 0.5 h after the end of bombardment and continued for almost a month measuring each ytterbium foil three times, enabling separation of radioisotopes having the same gamma-lines but different half lives and following cumulative processes. The high purity Ti foils inserted in the stacks served both as energy degraders and as beam monitors to correct the given nominal alpha-particle energy and beam current if needed. The whole excitation function of the nat Ti(a,x)51Cr monitor reaction was re-measured and adjusted to the curve recommended in the IAEA TECDOC-1211 [7] (Fig. 1).
Cross section (mb)
600
Monitor reaction nat 51 Ti(α,x) Cr
400
Stack1
The recorded gamma spectra were analyzed with an automatic peak searching program. The nuclear data for the evaluation of cross sections of the different radioisotopes were taken from [8] and are tabulated in Table 1. The mean energy of the alpha-particle beam in the successive target foils was calculated using the polynomial approximation of Ziegler [9]. The energy uncertainty at the first foil in the stack was estimated to be ±0.3 MeV increasing up to ±1.5 MeV at the last foil due to the energy straggling and the uncertainty on the target thickness. The uncertainty on the cross sections was determined in the standard way according to the guidelines of [10]. The linearly contributing independent processes were taken into account by extracting the square root of quadratically summed relative uncertainties, namely: number of the bombarding particles (7%), number of the target nuclei (3%), decay data (3%), detector efficiency (7%) and peak area (1–10%).
4. Theoretical calculations The measured experimental data were compared to and analyzed with theoretical calculations based on the model code ALICE-IPPE. The ALICE code family was developed by Blann [11] and is based on the hybrid, the geometry dependent hybrid (GDH) or the hybrid Monte Carlo simulation (HMS) pre-equilibrium models and the Weisskopf– Ewing evaporation formalism. The ALICE-IPPE code [12] is a version of the ALICE-91 code [13] modified by the Obninsk Group to include the generalized superfluid level density model and pre-equilibrium cluster emission. Corrections were made, among others, for gamma-emission and optical model parameters. Angular distribution and refraction were not taken into account. The lack of angular momentum and parity treatments in the Weisskopf–Ewing formalism used makes independent treatment of isomeric states impossible, only total production cross sections can be calculated. The theoretical curves were determined using one recommended input data-set without any optimization or adjustment of parameters to the individual reactions or stable target isotopes. The results of the reaction products of interest in this study were weighted and summed according to the abundance of the target isotopes and to the cumulative processes.
Stack2 IAEA recommended [7] 200
5. Results and discussion 0 0
10
20
30
40
Alpha-particle energy (MeV)
Fig. 1. Excitation function of
nat
Ti(a,x)51Cr monitor reaction.
50
As the ytterbium foils used in these measurements had already been irradiated with deuterons in a previous experiment [1] less than 1.5 years before, only those radioisotopes which could not be produced at that time (i.e.
B. Kira´ly et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 3919–3926
3921
Table 1 Decay data of radioisotopes [8], the possible contributing reactions and their threshold energies [14] Radionuclide 170
Hf
Half life 16.01 h
Spin, parity 0+
Ec (keV)
Ic (%)
620.7
18
Reactiona
Threshold energyb (MeV)
168
19.2 34.9 11.6 27.3 34.1 10.8 17.6 25.8 32.3 40.0 2.5 10.7 17.2 24.8 37.8 2.3 9.9 22.9 8.8 15.8 22.6 30.8 37.3 11.6 27.3 34.1 15.1 15.4 23.7 30.2 37.8 9.6 13.9 15.4 25.3 14.2 14.0 8.7 15.4 23.6 30.2 37.8 16.4 32.1 38.9 29.2 15.4 25.3
Yb(a,2n) Yb(a,4n) 168 Yb(a,n) 170 Yb(a,3n) 171 Yb(a,4n) 170 Yb(a,n) 171 Yb(a,2n) 172 Yb(a,3n) 173 Yb(a,4n) 174 Yb(a,5n) 171 Yb(a,c) 172 Yb(a,n) 173 Yb(a,2n) 174 Yb(a,3n) 176 Yb(a,5n) 173 Yb(a,c) 174 Yb(a,n) 176 Yb(a,3n) 168 Yb(a,p) 170 Yb(a,t) 171 Yb(a,tn) 172 Yb(a,t2n) 173 Yb(a,t3n) 168 Yb(a,n)171Hf? 170 Yb(a,3n)171Hf? 171 Yb(a,4n)171Hf? 170 Yb(a,d) 171 Yb(a,t) 172 Yb(a,tn) 173 Yb(a,t2n) 174 Yb(a,t3n) 174 Yb(a,p) 176 Yb(a,t) 176 Yb(a,3He)177Yb? 176 Yb(a,3p)177Tm ? 177Yb? 176 Yb(a,d) 168 Yb(a,3He) 170 Yb(a,an) 171 Yb(a,a2n) 172 Yb(a,a3n) 173 Yb(a,a4n) 174 Yb(a,a5n) 168 Yb(a,t)169Lu? 170 Yb(a,t2n)169Lu? 171 Yb(a,t3n)169Lu? 168 Yb(a,3n)169Hf ? 169Lu? 176 Yb(a,3He) 176 Yb(a,3p)177Tm? 170
171
12.1 h
(7/2+)
469.3 662.2
173
23.6 h
1/2
123.7 139.6 297.0
83 12.7 33.9
5/2
343.4
84
51.4 min
37/2
277.3 606.5
78 11.9
Hf
Hf
175
Hf
177m2
Hf
70 d
100c 266c
171g
Lu
8.24 d
7/2+
667.4 739.8
11.04 47.8
172g
Lu
6.70 d
4
810.1 900.7 1093.7
16.63 29.8 62.5
177g
Lu
6.734 d
7/2+
208.4
11
Lu Yb
23.1 min 32.026 d
(9) 7/2+
426.4 177.2 307.7
97 22.16 10.05
Yb
1.911 h
(9/2+)
150.4
20.3
178m 169g
177g
a nat b c
Yb: 168Yb 0.13%, 170Yb 3.05%, 171Yb 14.3%, 172Yb 21.9%, 173Yb 16.12%, 174Yb 31.8%, 176Yb 12.7%. If the outgoing particles are pn, p2n, 2pn and 2p2n instead of d, t, 3He and a, add 2.3, 8.7, 7.8 and 28.9 MeV, respectively, to the threshold energy. Relative intensity.
activation by (a,xn) reactions) or with half lives short enough to decay out completely by the time of this experiment were investigated. Tables 2 and 3 represent the numerical values of cross sections and the uncertainties. The measured excitation functions are shown in Figs. 2–12 together with the curves of ALICE-IPPE calculations and the data found in the literature.
The only cross section measurements for a-induced reactions on natural ytterbium targets were reported by Romo et P al. in 1992 [5]. Their data must be multiplied by i ai Ai ¼ 173:1 to get production cross sections, where ai and Ai are the abundance and the atomic weight of the ith isotope of natural ytterbium. Natural ytterbium consists of seven stable isotopes (see Table 1) so excitation functions show complex shapes
170
E (MeV)
DE (MeV)
r (mb)
7.8 16.6 17.4 20.3 21.0 23.7 24.3 26.7 27.3 29.6 30.1 32.3 32.8 34.8 35.3 37.2 37.7
1.5 1.0 1.0 0.9 0.9 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.4 0.4 0.3 0.3
173
Hf
0.35 1.03 1.28 1.63 1.84 1.72 2.00 1.81 1.87 1.82 1.38 1.24
Yb(a,xn)170,173,175,177m2Hf,
nat
Yb(a,x)171g,172g,177g,178mLu and
175
Hf
Hf
Dr (mb)
r (mb)
Dr (mb)
0.16 0.24 0.27 0.28 0.39 0.34 0.62 0.44 0.43 0.52 0.52 0.38
0.20 1.11 17.5 42.0 85.0 107 129 148 165 195 233 267 291 300 329 346
0.03 0.13 2.1 5.1 9.9 13 15 17 19 22 28 31 34 35 39 41
Ind
r (mb)
r (mb)
Dr (mb)
8.84 51.2 84.1 122 144 165 211 287 347 410 454 480 479 480 454
177m2
0.99 5.7 9.5 14 16 19 24 32 39 46 51 54 54 54 51
0.18 0.37 0.83 1.25 2.08 2.57 3.56 3.57
Cum
Dr (mb)
r (mb)
171g
0.05 0.28 0.63 0.54 0.49 0.32 0.44 0.49 2.73 9.5 18.1 29.0 34.8 44.7 53.0
0.07 0.09 0.16 0.22 0.29 0.39 0.46 0.45
Yb(a,x)169g,177gYb
Lu
Cum
Dr (mb)
r (mb)
0.02 0.06 0.13 0.11 0.09 0.08 0.09 0.23 0.55 1.3 2.2 3.4 4.1 5.1 6.0
0.12 0.44 1.00 1.12 2.23 2.12 5.04 5.1 9.9 9.4 14.5 10.3 18.5 16.4
172g
Lu
Cum
Dr (mb)
0.06 0.17 0.16 0.25 0.29 0.34 0.69 1.1 1.4 1.2 1.7 1.3 2.3 2.1
177g
178m
Lu
Ind
r (mb)
Dr (mb)
r (mb)
0.06
0.03
0.05
0.09
0.47 1.04 1.75 2.38 2.81 3.11 3.71 3.40 4.78 4.07 6.18 6.74
0.10 0.27 0.22 0.38 0.47 0.56 0.77 0.56 0.76 0.65 0.89 0.94
0.24 0.34 0.43 0.67 0.82 0.81 0.97 1.02
Lu
Cum
Dr (mb)
0.04 0.05 0.06 0.10 0.10 0.13 0.11 0.12
169g
177g
Yb
Cum
r (mb)
Dr (mb)
r (mb)
Dr (mb)
0.46
0.17
0.19
0.12
1.18 0.89 1.58 2.46 2.49
0.85 0.42 0.71 0.67 0.73
0.22 0.29
0.18 0.15
0.23
0.11
Yb
Dr (mb)
Hf
171
Yb(a,xn)171Hf
nat
r (mb)
Table 3 Measured cross sections of the reaction
DE (MeV)
0.030 0.073 0.064 0.20 0.043
Alpha-particle
E (MeV)
0.226 0.265 0.350 0.44 0.186
0.088 0.41 0.78 1.6 2.1 2.8 3.5 3.9
Hf
170
40
0.389 1.92 6.42 12.8 18.2 23.6 29.9 34.4
Yb(α,xn)
30
40
1.5 1.0 1.0 0.9 0.9 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.4 0.4 0.3 0.3
nat
Stack1
Stack2
20
Alpha-particle energy (MeV)
ALICE-IPPE, 170Hf
10
Hf
171
35
Yb(a,xn)170Hf reaction.
nat
Yb(α,xn)
30
7.8 16.6 17.4 20.3 21.0 23.7 24.3 26.7 27.3 29.6 30.1 32.3 32.8 34.8 35.3 37.2 37.7
3.0
2.0
1.0
0.0 0
nat
Fig. 2. Excitation function of
Stack1
Stack2
25
Alpha-particle energy (MeV)
ALICE-IPPE, 171Hf
20
The relative gamma intensities were multiplied by 0.055 [15] in the evaluation process.
Cross section (mb) 40
30
20
10
0 15
Fig. 3. Excitation function of natYb(a,xn)171Hf reaction. The relative gamma intensities were multiplied by 0.055 [15] in the evaluation process.
Cross section (mb)
Hf
nat
B. Kira´ly et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 3919–3926
Alpha-particle
nat
3922
Table 2 Measured cross sections of the reactions
B. Kira´ly et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 3919–3926 1.E+04
400
nat
300
Hf
200 Stack1 Stack2 100
ALICE-IPPE, 173Hf
171g
Yb(α,x) Lu cumulative
173
Yb(α,xn)
Cross section (mb)
Cross section (mb)
nat
1.E+02
1.E+00
Stack1 Stack2 ALICE-IPPE, 171Hf + 171m+gLu ALICE-IPPE, 171Hf Romo 1992 [5]
1.E-02
1.E-04
0 0
10
20
30
0
40
20
40
Fig. 4. Excitation function of
60
80
100
Alpha-particle energy (MeV)
Alpha-particle energy (MeV) nat
Yb(a,xn)173Hf reaction.
nat
Yb(a,x)171gLu reaction.
Fig. 7. Excitation function of cumulative
600
250 nat
Yb(α,xn)
175
Hf
nat
400 Stack1 Stack2 ALICE-IPPE, 175Hf Romo 1992 [5]
200
172g
Yb(α,x) Lu cumulative
200
Cross section (mb)
Cross section (mb)
3923
150 Stack1 Stack2
100
ALICE-IPPE, 172m+gLu Romo 1992 [5] 50
0
0 0
20
40
60
80
0
100
20
40
Alpha-particle energy (MeV)
Fig. 5. Excitation function of
60
80
100
Alpha-particle energy (MeV)
nat
Yb(a,xn)175Hf reaction.
Fig. 8. Excitation function of cumulative
nat
Yb(a,x)172gLu reaction.
8
1.E+03 Stack1
nat
Cross section (mb)
Cross section (mb)
1.E+02
ALICE-IPPE, 177m1+m2+gHf
1.E+01 nat
1.E+00
177m2
Yb(α,xn) Hf independent
177g
Yb(α,x) Lu independent
Stack2 6
4 Stack1 Stack2 ALICE-IPPE, 177m+gLu 2
ALICE-IPPE, 177m+gYb
1.E-01 0 0
0
10
20
30
20
30
40
40
Alpha-particle energy(MeV)
Fig. 6. Excitation function of independent
Fig. 9. Excitation function of independent
nat
Yb(a,x)177gLu reaction.
nat
Yb(a,xn)177m2Hf reaction.
reflecting the contributions of reactions taking place on the different stable isotopes. The possible reactions producing the given radioisotope and their threshold energies [14] are given in Table 1. 5.1. Cross sections nat
10
Alpha-particle energy (MeV)
1.E-02
Yb(a,xn)170Hf process. Our measured points with relatively high uncertainties follow the shape of the
ALICE-IPPE curve and are slightly above it (Fig. 2). The theoretical calculation clearly shows the contributions of the (a,2n) and (a,4n) reactions in the investigated energy range with respective threshold energies of 19.2 and 34.9 MeV. nat Yb(a,xn)171Hf process. The gamma intensities of this reaction product given in [8] are relative and no absolute values are available in the literature. The latest recommendation found in the Nuclear Data Sheets [15] says that the relative intensities (see Table 1) should be multiplied by
B. Kira´ly et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 3919–3926
3924 6
Cross section (mb)
nat
178m
Yb(α,x) Lu independent
4
Stack1
2
Stack2 ALICE-IPPE, 178m+gLu
0 0
10
20
30
40
Alpha-particle energy (MeV)
Fig. 10. Excitation function of independent
nat
Yb(a,x)178mLu reaction.
Cross section (mb)
1.E+03 Stack1 Stack2 ALICE-IPPE, 169Hf + 169m+gLu + 169m+gYb A-I, 169Hf A-I, 169m+gLu A-I, 169m+gYb Romo 1992 [5]
1.E+02
1.E+01
nat
1.E+00
169g
Yb(α,x) Yb cumulative
1.E-01 0
20
40
60
80
100
Alpha-particle energy (MeV)
Fig. 11. Excitation function of cumulative
nat
Yb(a,x)169gYb reaction.
1.2
Cross section (mb)
nat
177g
Yb(α,x) Yb cumulative
0.8 Stack1 Stack2 ALICE-IPPE, 177m+gYb 0.4
0.0 0
20
40
60
80
Alpha-particle energy (MeV)
Fig. 12. Excitation function of cumulative
nat
Yb(a,x)177gYb reaction.
0.055 to get absolute intensities if one made an assumption that the ground state of 171Lu is not fed by beta decay. We used this factor in the cross section evaluation process. The results are tabulated in Table 3 and shown in Fig. 3. As Figs. 2, 4 and 5 show the predictions of ALICE-IPPE calculations seem very good in the case of (a,xn) processes (i.e. hafnium isotopes) so we can trust that this is valid in the case of 171Hf as well. This means that the assumption given above is not far from the truth. According to the theoretical calculation the (a,n) reaction taking place on 168Yb has a high maximum (530 mb at 23 MeV) but as the abun-
dance of this isotope is very low (0.13%), the curve shows a grazing shape up to 29 MeV. The rising part of the excitation function is drawn by the (a,3n) and (a,4n) processes. nat Yb(a,xn)173Hf process. The measured data coincide with the theoretical calculation (Fig. 4). The nearly monotonous increasing curve with small breaks indicates that it is a sum of several excitation functions of (a,xn) reactions taking place on four different stable isotopes of ytterbium. nat Yb(a,xn)175Hf process. The long half life and the strong gamma line of 175Hf allows long acquisition times resulting in lower statistical uncertainty. The agreement with the prediction of the ALICE-IPPE code is very good (Fig. 5). The contribution of the (a,c) reaction is negligible, the first rise with the small plateau is the sum of the (a,n) and (a,2n) reactions, the maximum is caused by the (a,3n) reaction and the peak at higher energy measured by Romo et al. [5] is the result of the (a,5n) reaction taking place on 176Yb. However, no explanation is found for the discrepant low cross section value at 48 MeV or for the upward tendency above 80 MeV. nat Yb(a,xn)177m2Hf independent process. The stable nuclide 177Hf has two metastable states in addition to the ground state. Only cross sections for the longer lived and higher lying m2 state could be measured. The excited state 177m2 Hf is not fed by b decay of any of the two isomeric states of 177Lu (177gLu 7/2+, 177mLu 23/2) so independent cross sections are determined and plotted in Fig. 6. As the ALICE-IPPE code cannot calculate the excitation functions of different isomeric states separately we can only conclude that the contribution of the excitation of the m2 state to the total cross section is lower by one to three orders of magnitude than the contribution of the other two states together. nat Yb(a,x)171gLu cumulative process. This cumulative cross section includes the contributions of 171Hf (T1/2 = 12.1 h, (7/2+)) and the metastable state (T1/2 = 79 s, 1/2) of 171Lu after their total decay in addition to the independent formation of the ground state. Although the reactions resulting in formation of 171Lu are energetically possible the comparison of the experimental cumulative cross section with the prediction of the ALICE-IPPE code for production of 171Hf shows that the indirect route is the nearly only contributor to formation of 171gLu (see Fig. 7). Romo’s [5] data (excluding their first three points) and ours both fit to the theoretical curve. nat Yb(a,x)172gLu cumulative process. This cumulative cross section includes the contribution of 172mLu (T1/2 = 3.7 min, 1) after its total decay in addition to the independent formation of the ground state but does not include any contribution from 172Hf (T1/2 = 1.87 y, 0+) because the number of decaying nuclei was negligible during the acquisition of the gamma spectra. The sum of the excitation functions of reactions taking place on different stable isotopes of ytterbium results in a monotonously rising curve as shown by Romo’s [5] and our measured points (Fig. 8). The ALICE-IPPE code which calculates the sum of the excitation functions of the two isomeric states, so
B. Kira´ly et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 3919–3926
Yield (MBq / μAh)
1.E+02
177m2
1.E+00
Hf
178m
Lu
170
Hf
173
Hf 175
Hf
1.E-02
171
Hf
177g
Yb
1.E-04 169g
Yb
171g
177g
Lu
172g
Lu
Lu
1.E-06 15
20
25
30
35
40
Alpha-particle energy (MeV)
Fig. 13. Integral yields calculated on the basis of our fitted experimental data.
1.E+02 Hermanne [1] Yb(d,p)177Yb -> 177Lu
177
176
Lu
Yield (MBq / μAh)
it is comparable with our results, predicts a curve with a shift to higher energy by about 8 MeV and with higher absolute values. nat Yb(a,x)177gLu independent process. This cross section may contain contributions of decays of 177Tm (T1/2 = 85 s, (1/2+)), 177mYb (T1/2 = 6.41 s, (1/2)), 177gYb (T1/2 = 1.911 h, (9/2+)) in addition to independent formation of the ground state but contribution from 177mLu (T1/2 = 160.4 d, 23/2) is negligible as presence of its strong gamma-lines in the spectra could not be proved. The ALICE-IPPE prediction says that 177Tm and 177Yb do not play roles in this energy region (Fig. 9) so the only processes responsible for the shape of this excitation function up to 39 MeV are 176Yb(a,p2n)177Lu and 174Yb(a,p)177Lu. The former dominates above and the latter below 36 MeV but their sum underestimates our measured values. nat Yb(a,x)178mLu independent process. As 178Yb (0+) does not decay into the metastable state of 178Lu, an independent cross section for 178mLu formation could be measured. Weak gamma-lines of 178gLu (T1/2 = 28.4 min, 1(+)) were not found in the spectra. 178mLu can only be formed on 176Yb via (a,d) or (a,pn) process. The ALICE-IPPE calculation shows that the contribution of the ground state to the total cross section is higher than that of the metastable state (Fig. 10). nat Yb(a,x)169gYb cumulative process. This cumulative cross section may contain contributions of 169Hf (T1/2 = 3.24 min, (5/2)), 169mLu (T1/2 = 160 s, 1/2), 169gLu (T1/2 = 34.06 h, 7/2+) and 169mYb (T1/2 = 46 s, 1/2) after their total decay in addition to the independent formation of the ground state 169gYb. As Fig. 11 shows the model code predicts that among them 169Lu has no effect on the cross section of the measured reaction below 39 MeV. Our data have relatively high statistical uncertainties because of the weak gamma-lines and are a factor of two lower than the values published by Romo et al. [5]. nat Yb(a,x)177gYb cumulative process. This cumulative cross section may contain the contributions of 177Tm (T1/2 = 85 s, (1/2+)) and 177mYb (T1/2 = 6.41 s, (1/2)) after their total decay in addition to independent formation of the ground state 177gYb but according to the model code results the role of 177Tm is negligible in this energy region. Only four points were determined with large uncertainty because of the poor counting statistics and there is a considerable difference between the measured and calculated results as can be seen in Fig. 12.
3925
1.E+00
Hermanne [1] Yb(d,n)177Lu
176
1.E-02 This work Yb(α,x)177Lu
nat
1.E-04
1.E-06 0
10
20
30
40
Particle energy (MeV)
Fig. 14. Comparison of integral yields of different routes of production.
177
Lu
177
Lu while the (d,p) reaction leads to mother nucleus Yb that decays into 177Lu by b decay. The figure shows that among the charged particle induced production routes 176Yb(d,n) is more productive when compared to the recently investigated a-route. However, the possible batch yield of the (n,c) process near high flux reactors is higher by orders of magnitude and remains the production route of choice. As 169Yb cannot be produced from Yb targets without carrier being present, a more detailed discussion and comparison with charged particle production routes resulting in non carrier added end-product is not relevant. 177
5.2. Integral yields
6. Conclusion
On the basis of our fitted experimental data integral yields were calculated and are shown in Fig. 13. Because of the medical importance of 177Lu integral yields of its different production routes via charged particle induced nuclear reactions are compared in Fig. 14. Hermanne et al. [1] reported yield curves as results of calculations from cross section measurements of deuteron induced reactions on 176Yb. The (d,n) reaction produces
Experimental cross sections for eleven alpha-particle induced nuclear reactions on natural ytterbium target have been measured up to 39 MeV, seven of them for the first time. The reliability of our results is ensured by the monitor reaction which was re-measured over the whole energy range. In general reasonable agreement with values predicted by the ALICE-IPPE code and with the results of Romo et al. [5] is observed.
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The yield deduced from our fitted excitation curve shows that for the production of 177Lu the alpha-particle induced route on natYb target is not competitive. The production of medically interesting radioisotopes 177 Lu and 169Yb via alpha-particle irradiation of natural Yb target is not of practical but of academic interest. References [1] A. Hermanne, S. Taka´cs, M.B. Goldberg, E. Lavie, Yu.N. Shubin, S. Kovalev, Deuteron-induced reactions on Yb: measured cross sections and rationale for production pathways of carrier-free, medically relevant radionuclides, Nucl. Instr. and Meth. B 247 (2006) 223. [2] I. Spahn, S. Taka´cs, Yu.N. Shubin, F. Ta´rka´nyi, H.H. Coenen, S.M. Qaim, Cross-section measurement of the 169Tm(p,n) reaction for the production of the therapeutic radionuclide 169Yb and comparison with its reactor-based generation, Appl. Radiat. Isotopes 63 (2005) 235. [3] F. Ta´rka´nyi, A. Hermanne, S. Taka´cs, F. Ditro´i, I. Spahn, S.F. Kovalev, A.V. Ignatyuk, S.M. Qaim, Activation cross sections of the 169 Tm(d,2n) reaction for production of the therapeutic radionuclide 169 Yb, Appl. Radiat. Isotopes 65 (2007) 663. [4] B. Kira´ly, F. Ta´rka´nyi, S. Taka´cs, A. Hermanne, S.F. Kovalev, A.V. Ignatyuk, Excitation functions of alpha-induced nuclear reactions on natural erbium, Nucl. Instr. and Meth. B. 266 (2008) 549. [5] A.S.M.A. Romo, A.A. Sonzogni, D.A. Rodriguez Sierra, S.J. Nassiff, Nuclear reactions induced by alpha-particles on natural ytterbium, Radiochim. Acta 57 (1992) 57.
[6] B. Kira´ly, F. Ta´rka´nyi, S. Taka´cs, A. Hermanne, S.F. Kovalev, A.V. Ignatyuk, Excitation functions of alpha-induced nuclear reactions on natural erbium and natural ytterbium targets, in: International Conference on Nuclear Data for Science and Technology, 22-27 April 2007, Nice, France, p. 1371, doi:10.1051/ndata:07255. [7] F. Ta´rka´nyi, S. Taka´cs, K. Gul, A. Hermanne, M.G. Mustafa, M. Nortier, P. Oblozinsky, S.M. Qaim, B. Scholten, Yu.N. Shubin, Z. Youxiang, Beam monitor reactions (Chapter 4), in: Charged Particle Cross-Section Database for Medical Radioisotope Production: Diagnostic Radioisotopes and Monitor Reactions, IAEA-TECDOC-1211, Vienna, 2001, p. 49, Available from: