I. INTRODUCTION
Doping is an important method to change the properties of materials. For example, the substitutions of some atoms in organic semi-conductors promote the charge transport and stability greatly [1, 2]. The general method for doping is chemical synthesis which introduces new elements into the original material. Actually, neutron activation is an important method to make doping in material, which can even change one element to other one, directly or after the decay of unstable isotopes produced by activation. In this situation, different to the chemical doping, different doping effects can be expected.
It is well known that for different nuclei, there are different threshold energy values for specific channels in neutron induced reactions [3]. For material having different elements, the different threshold energy values for neutron reactions provide a chance for specific activation if the neutron energy is selected in experiments.
In this article, the neutron induced reactions on stable carbon, nitrogen, and oxygen isotopes will be investigated by using a Talys toolkit. The energy windows between the different isotopes will be analyzed. The theory is briefly discussed in Sec. II. The results are discussed in Sec. III, and a summary is presented in Sec. IV.
II. METHODS
The optical model can describe the neutron induced reaction well in a wide range of incident energies. In Talys1.4, the ECIS-06 is implanted as a subroutine to deal with the optical model calculations [4]. The description of Talys1.4 and the implanted functions can be found in the user manual [5, 6].
In statistical models for predicting cross sections, nuclear level densities are used at excitation energies where discrete level information is not available or incomplete. Several models are implanted to describe the level density in Talys, which range from phenomenological analytical expressions to tabulated level densities derived from microscopic models. The constant temperature and Fermi-gas model is set as the default parameter of level density at low excitation energy region, while the Fermi-gas model is used in the high excitation energy region [6].
Due to the threshold energy exists for different channels in the neutron induced reaction on a nucleus, one channel can only happen if the incident energy of the neutron is above the threshold, which potentially provides energy windows only one channel can happen while the other channels are prohibited. In this work, the incident energy of the calculated reactions ranges from 0.20 MeV to 85.00 MeV, and the default parameters in Talys1.4 are adopted. The main reaction channels include (n, np), (n, p), (n, α), (n, 2n) and (n, γ). The calculated results are compared to the measured data, which are extracted from the EXFOR library provided by the National Nuclear Data Center (NNDC) [7]. All the natural abundance data and the half-life time of isotopes are taken from Wikipedia [8].
III. RESULTS AND DISCUSSION
A. Neutron induced reactions on carbon isotopes
The C element has two stable isotopes, 12C and 13C, with natural abundances of 98.93% and 1.07%, respectively. Only the n+12, 13C reactions are calculated.
1. n + 12C reactions
The 12C(n, p)12B, 12C(n, α)9Be, and 12C(n, 2n)11C channels have been measured previously. 12B is an unstable nucleus, which decays to 12C via electron emission with a half-life time of 20.20 ms. 9Be is a stable isotope. 11C is also unstable, which decays to 11B via positron emission with a relative long half-life time of 20.334 min. Thus the 12C(n, 2n)11C and 12C(n, np)11B channels are the main channels which result in element changes with the same final products, 11B. The results are plotted in Fig. 1.
First, for the 12C(n, α)9Be channel, the Talys1.4 results are consistent with the measured results when En<11.00 MeV [9], while the Talys1.4 results differ largely with the results measured by Stevens et al. [10] in the range of 18.65 MeV<En<21.46 MeV. In the energy range of 20.00 MeV<En<60.70 MeV, the Talys1.4 results are also much larger than the calculated results by Dimbylow et al. [11]. Above En>11.00 MeV, the results of the 12C(n, α)9Be channel have large difference, which suggests that further experiment should be performed for a systematic understanding.
Second, for the 12C(n, p)12B channel, the measured results by Kreger et al. [12] and Rimmer et al. [13] coincide when En<16.00 MeV, but differ when En is higher. The Talys1.4 results agree well with the measured results when En<16.00 MeV, but overestimate the measured results by Kreger et al. [12] in the range of 16.00 MeV<En<22.00 MeV. The calculated results of 12C(n, p)12B in the range of 20.00 MeV<En<60.70 MeV by Dimbylow et al. [11], which also uses the optical model, prefer the measured results by Kreger et al. [12]. Meanwhile, the Talys1.4 predicts similar results between 12C(n, p)12B and 12C(n, np)11B reactions when En<20.00 MeV.
Third, for the 12C(n, 2n)11C channel, which have been measured by many groups, the measured data agree well when En<27.00 MeV. The results can be divided into two groups in the range of 27.00 MeV<En<40.00 MeV, of which the upper group was measured by Welch et al. [14], Anders et al. [15], and Kim et al. [16]; and the bottom group by Brill et al. [17], Uno et al. [18], Brolley et al. [19], and Soewarsono et al. [20]. The calculated results by Dimbylow et al. [11] prefer the upper group results when En<35.00 MeV. Kim et al. [16] measured the results in the energy range from 55.00 MeV to 64.00 MeV. The calculated results by Talys1.4 largely overestimate the measured ones when En<50.00 MeV, but agree with the measured results by Kim et al. [16]. The calculated results by Dimbylow et al. [11] underestimate the measured results by Kim et al. [16].
The threshold energies of the 12C(n, α)9Be, 12C(n, p)12B, 12C(n, np)11B and 12C(n, 2n)11C channels increase, which are about 6.18 MeV, 13.64 MeV, 14.89 MeV and 20.30 MeV, respectively. The 12C(n, γ)13C channel happens in the whole energy range, but have a much smaller probability compared to other channels.
2. n + 13C reactions
No measured data for the neutron induced reactions on 13C is found. The Talys1.4 calculated results are plotted in Fig. 2. The threshold energy values increase with the (n, α), (n, 2n), (n, p) and (n, np) channels, with the values 4.13 MeV, 5.33 MeV, 13.64 MeV and 16.50 MeV, respectively. The (n, γ) channel has no lowest energy threshold. The (n, γ) and (n, p) channels have relatively low probabilities compared to the other channels. In the whole energy range calculated, when En<15.00 MeV, the main channel is 13C(n, α)10Be, in which 10Be decays to 10B by electron emission with a very long half-life time 1.39×106 years; when En>15.00 MeV, the dominant channel is 13C(n, np)12B, in which 12B mainly decays to 12C with a half-life time 20.20 ms.
B. Neutron induced reactions on nitrogen isotopes
The N element has two stable isotopes, 14N and 15N, with a natural abundance of 99.64% and 0.36%, respectively. Only the n+14, 15N reactions are calculated.
1. n + 14N reactions
The calculated channels for the n+14N reaction are 14N(n, np)13C, 14N(n, p)14C, 14N(n, α)11B, 14N(n, γ)15N, and 14N(n, 2n)13N reactions, respectively. The nuclei 13C, 15N, and 11B are stable, while 14C and 13N are unstable. 13N decays to 13C by positron emission with a half-life time 9.965 min. The (n, np), (n, p), (n, 2n), and (n, α) channels are the main ones which will result in element changes.
The results of the n+14N reaction are plotted in Fig. 3. For clarity, the results are plotted in different panels. The 14N(n, α)11B and 14N(n, p)14C have small threshold energies, which are very similar. The 14N(n, α)11B channel has been measured by different groups [21-25], and the 14N(n, p)14C has also been measured [21, 23-25]. For the two channels, the data measured by different groups is consistent. The Talys1.4 results agree with the measured data in the low incident energies, but overestimate the measured results when the En increases.
For the 14N(n, 2n)13N channel, the measured results [26-30] are consistent when En<19.00 MeV. When En>24.00 MeV, the measured results by Brill et al. [17] and Yashima et al. [31] are relatively consistent, and the calculated results by Dimbylow et al. [11] also agree with the measured data but have relatively large errors. The predicted threshold energy value by Talys1.4 is En 11.00 MeV, but the Talys1.4 cross sections overestimate the measured results in the whole energy range, which increases fast with En and reaches maximum at En=24.00 MeV and decreases with En when En > 24.00 MeV. Since 13N decays to 13C, the final production is the same as the 14N(n, np)13C channel. The 14N(n, np)13C channel has a low threshold energy value of about 6.00 MeV, and the cross section of the channel increase fast with En, which peaks at about En=14.00 MeV.
The threshold energies increase in the order of (n, α), (n, np), and (n, 2n), which are about 0.13 MeV, 5.67 MeV and 11.27 MeV, respectively. The (n, γ) and (n, p) channel happens in the whole En range and forms a peak around 19.00 MeVand 9.50 MeV with a wide width, but the cross sections are very small compared to other channels.
2. n + 15N reactions
No measured data for the n+15N reaction is found. Only the Talys1.4 calculated results are plotted in Fig. 4. The calculated results for the (n, np) and (n, α) channels have almost the same values when En<12.00 MeV and the (n, np) channel has much larger values than that of the (n, α) channel. At the same time, the cross sections of (n, p) and (n, 2n) channels only have small difference when En>17.00 MeV. The (n, np), (n, α), (n, p), and (n, 2n) channels have relatively similar threshold energy values, which are about 8.57 MeV, 8.09 MeV, 9.55 MeV and 11.56 MeV, respectively. The cross sections of the (n, γ) channel are much smaller compared to the other channels. When En>40.00 MeV, large fluctuations are found in the results of the (n, p) and (n, γ) channels.
C. Neutron induced reactions on oxygen isotopes
The O element has three stable isotopes, 16O, 17O, and 18O, with a natural abundance of 99.75%, 0.0038%, and 0.205%. Only the n+16,18O reactions are calculated.
1. n + 16O reactions
In Fig. 5, the results of the n+16O reactions are plotted. The channels include 16O(n, α)13C, 16O(n, p)16N, 16O(n, 2n)15O, 16O(n, np)15N, and 16O (n, γ) 17O. 16N decays to 16O by emitting electron with a half-life time of 7.13 s. Thus the main channels which make the element change are 16O(n, α)13C and 16O(n, np)15N.
For the 16O(n, α)13C channel, the Talys1.4 calculated results are consistent with these measured by Johnson et al. [32], and Seitz et al. [33] except those by Divatia et al. [34] when En is smaller than 5.00 MeV. When En>7.00 MeV, the measured results by Dickens et al. [35], Bormann et al. [36], and Dandy et al. [37] are consistent, but the Talys1.4 calculated results are unable to reproduce measured data well.
For the 16O(n, p)16N channel, the measured results by Martin et al. [38], Bormann et al. [39], and Seeman et al. [40] agree well. The measured results by Subashi et al. [41] and DeJuren et al. [42] also agree with those results but have relatively large difference. The Talys1.4 calculated results largely underestimate the measured results but have similar trend to the measured ones.
For the 16O(n, 2n)15O channel, the measured results by Yashima et al. [33] and Brill et al. [17] are in different energy ranges, but for the overlapping range of En, the results have some difference. The Talys1.4 results overestimate the measured ones when En<40.00 MeV, but underestimate the measured ones when En>40.00 MeV.
The 16O(n, np)15N and 16O(n, γ)17O channels have not been measured. For the 16O(n, np)15N channel, the probability increases fast above the threshold energy of 10.57 MeV and has a maximum value around En=20.00 MeV. The 16O(n, γ)17O channel happens in the whole En range but have much smaller values.
The Talys1.4 calculated threshold energies of the (n, α), (n, p), (n, np) and (n, 2n) channels for 16O are 2.36 MeV, 10.25 MeV, 10.57 MeV and 16.65 MeV, with peaks form at around 10.00 MeV, 14.50 MeV, 26.00 MeV and 28.00 MeV, respectively.
2. n + 18O reactions
The main channels that the n+18O reactions cover are 18O(n, α)15C, 18O(n, np)17N, 18O(n, p)18N, 18O(n, 2n)17O, and 18O(n, γ)19O. 17N can decay to 16O and 17O with a half-life time of 4.173 s; 18N can decay to 18O, 14C, or 17O with a half-life time of 622 ms, which are all stable nuclei (14C has a very long half-life time).
In Fig. 6, the calculated results for the channels are plotted. The thresholds of the (n, α), (n, 2n), (n, p), and (n, np) channels are 5.29 MeV, 8.49 MeV, 13.85 MeV and 14.49 MeV, and the peaks form at around 10.00 MeV, 17.00 MeV, 18.00 MeV and 49.50 MeV, respectively. When En> 33.00 MeV, the yield of the (n, p) channel has large fluctuations with En.
D. Comparison between main channels of n+C/N/O isotopes
The differences between the threshold energies of the different channels make it possible to change one element to another. To change the element in organic materials specifically, the incident energy of the neutron should be selected to fit the energy window, as has been illustrated in the results above. The comparison between the thresholds of the main channel inducing element changes will show the En window more clearly.
For 12C, both the final production of 12C(n, np)11B and 12C(n, 2n)11C are 11B since 11C decays to 11B via positron emission with a half-life time of 20.30 ms. The threshold energy of 12C(n, α)9Be is about 6.18 MeV. When En>7.00 MeV, 12C can be changed to 9Be. The threshold energy of 12C(n, np)11B is about 14.89 MeV. When En>16.00 MeV, 12C can be changed to 9Be and 11B. This provides actual application of neutron activation on C isotopes. The chemically synthesized compound, in which a C atom is substituted by a B atom, demonstrates a novel molecular engineering concept of organic semiconductors [43]. For 14N, the most important channel is (n, 2n), which happens at very low neutron incident energy. Since the final yields in the n+14, 15N reactions are mainly carbon isotopes, we do not discuss the energy window for these channels. For 16O, the main channels are 16O(n, α)13C and 16O(n, np)15N when En<15.00 MeV, with the production of 13C and 15N, respectively. There is also an En window between the two channels in the range from 4.00 MeV to 11.00 MeV. With larger En, the 16O(n, 2n)15O channel is opened. 15O decays to 14N by emitting a positron with a half-life time of 70.60 s, i.e., 16O is changed to 14N finally.
For a better understanding of the energy windows, the energy above the Talys calculated threshold energy for each channel is plotted in Fig. 7. The numbers from 1 to 24 represent the channels and the alphabet from a to w represent the values of the threshold energies, of which are also listed as follows (the unit is MeV): 1, En=0 for the 14N(n, p)14C and (n, γ) channel of C/N/O; 2, 14N(n, α)11B (a=0.13); 3, 16O(n, α)13C (b=2.36); 4, 13C(n, α)10Be (c= 4.13); 5, 18O(n, α)15C(d=5.29); 6, 13C(n, 2n)12C (e=5.33); 7, 14N(n, np)13C (f=5.67); 8, 12C(n,α)9Be (g=6.18); 9, 15N(n, α)12B (h=8.09); 10, 18O(n, 2n)17O (i=8.49); 11, 15N(n, np)14C (j=8.57); 12, 15N(n, p)15C (k=9.55); 13, 16O(n, p)16N (l=10.25); 14, 16O(n, np)15N (m=10.57); 15, 14N(n, 2n)13N (n=11.27); 16, 15N(n, 2n)14N (o=11.56); 17, 13C(n, p)13B (p=13.635); 18, 12C(n, p)12B (q=13.645); 19, 18O(n, p)18N (r=13.85); 20, 18O(n, np)17N (s=14.49); 21, 12C(n, np)11B (t=14.89); 22, 13C(n, np)12B (u=16.49); 23, 16O(n, 2n)15O (v=16.65); 24, 12C(n, 2n)11C (w=20.30). Though the energy windows are clearly shown in Fig. 8, it should be carefully analyzed when the neutron is used to activate special compounds, including different elements.
IV. CONCLUSION
In this article, the neutron induced reactions on the stable C, N, and O isotopes are investigated by using the Talys1.4 toolkit, which calculates the reactions in the framework of optical model. On the one hand, it is found that for 12C and 14N, the Talys1.4 results agree with the experimental data, while for 16O, the parameters in Talys1.4 should be adjusted for a better prediction. On the other hand, a systematic comparison among the main channels of n+C/N/O reactions which induce element change are performed to find En windows among the original C, N, and O stable isotopes (by considering the final production of the channel, i.e., direct change or indirect change through decay to a different element isotope). In these En windows, specific elements can be activated to a different one while leaving the other element unchanged. The results may help to study material modification by using neutron induced doping techniques such as in organic materials like the organic semiconductor.
Notes on ECIS94, CEA Saclay Report No. CEA-N-2772
, 1994.User Manual of Talys-1.4
. (http://www.talys.eu/_leadmin/talys/user/docs/talys1.4.pdf).JAERI-M Reports, No. 92, 027, 354
, 1992.Oak Ridge National Lab. Reports, No. 4743, 37
, 1972.Aldermaston Reports, No. 60/68
, 1968.