Evaluation of excitation function for 186 W ( d , 2 n ) 186 Re reaction

The excitation function of the 186W(d,2n)186Re reaction was evaluated and the thick target yield (TTY) of the therapeutic radioisotope 186Re was calculated. The available experimental data from the EXFOR library and literature were analyzed and corrected with the g-ray branching ratio, radioactive decay constant and standard cross sections. The excitation function of the 186W(d,2n)186Re reaction was recommended below 50 MeV on basis of the least-squares fit with polynomial and the theoretical calculation with TALYS code. The TTY was calculated using the recommended excitation function of the 186W(d,2n)186Re reaction.


Introduction
The charged particle excitation functions are the important part of the nuclear data, applied to the activation analysis, nuclear medicine investigation, nuclear theory, calculation of integral thick target yield, and so on.
Rhenium-186 is an important medically radionuclide, and regarded very suitable for radiotherapy and radioimmunotherapy due to its attractive properties which include emission of high-energy β-rays 1.07 MeV, low-abundance (9.42%) gamma emission at 137 keV, and 90.64 h half-life.
The 186 Re has been produced using nuclear reactors through 185 Re(n,γ ) 186 Re reaction, but the specific activity is medium, not in no-carrier-added form.In order to radiolabel antibodies more efficiently, production of nocarrier-added 186 Re with high specific activity is required.There are two major routes for the production of nocarrier-added 186 Re by cyclotron, namely 186 W(p,n) 186 Re and 186 W(d,2n) 186 Re.
In the present work, the excitation function of 186 W(d,2n) 186 Re reaction was evaluated.The available experimental data include the latest reports [1,2] that are not considered in previous works [3,4] were analyzed and corrected.The nuclear model calculation was done using TALYS [5].The TTY of 186 Re was calculated using the recommended excitation function of 186 W(d,2n) 186 Re reaction, and compared with the TTY from 186 W(p,n) 186 Re reaction [6].

Evaluation of experimental data
The activation method and stacked foil technique are often used in the charged particle excitation functions measurement.The formula [7] of charged particle excitation functions is as follows: • 10 24 (b) (1) Where, M is the target molecular weight, nis the target nucleus number in a molecule, ε denotes the detection a e-mail: jmwang@ciae.ac.cn efficiency of detector at full energy peak, p is the g-ray branching ratio, a denotes the isotope abundance, N 0 is the Avogadro constant, c/tis the accounting g-ray number at full energy peak in a unit time, χ denotes the target weight in a unit area, t i denotes the irradiation time, Qis the total integrated beam current (in Coulomb), t d denotes the cooling time (start from stop irradiation) and λ is the radioactive decay constant.
From the mentioned-above formula, the cross sections are proportional to the radioactive decay constant, and inversely proportional to the g-ray branching ratio.Moreover, if the experiment is relative measurement, the cross sections are proportional to the standard cross sections.According to these relations, σ can be corrected by the new p, λ and standard cross sections.
In the measurement of Tao Zhenlan et al. [7], the g-ray branching ratio of 137.16 keV are 0.092, and the new value is 0.0942 [13].The sample was WO 3 powder, enriched to 99% in 186 W, so the corrected factor is 0.9813.The experimental data after normalization and correction are shown in Fig. 2.

Nuclear model calculations
Several nuclear model code have been developed, in the evaluation of data are very helpful.In the process of evaluation, the parameters of the nuclear model   code need to be adjusted to reproduce the experimental data.
In this work, the cross sections were calculated using TALYS, a nuclear model code, developed by Koning et al. [5].The nuclei were considered non-spherical in shape.The compound nucleus contribution was considered in the frame of Moldaner model.The contributions of direct reactions were taken into account by ECIS.The back-shifted Fermi gas model (BFM) was used for level densities (ldmodel 2).The OM parameters were adjusted,

Fitting of experimental data
After normalization and correction, the experimental data are consistent besides the partial data of S.J. Nassiff et al. [9] and S. Manenti et al. [1].S.J. Nassiff et al. reported six cross section values from 7.3 to 16.7 MeV, but the errors not given.The data are higher than the calculated values using TALYS and those reported by other authors between 10 to 20 MeV.The data of S. Manenti et al. are highter than the results of calculation and other measurements at 11.76, 12.38, 12.54 and 13.14 MeV.F.W. Pement et al. [8] reported nine data points but not given the errors also.So these data were neglected in fitting of experimental data.
On basis of least-squares fit with polynomial, the evaluated experimental data were fitted from threshold to 14 MeV and from 14 to 50 MeV.The curves of fitting are shown in Fig. 4 and Fig. 5.

Results and discussion
The excitation function for 186 W(d,2n) 186 Re reaction was recommended from threshold energy to 50 MeV after comprehensive evaluation, take into account the results of calculation and fitting.The recommended curve is given in Fig. 6, together with the results of M. Hussain et al. [3] and IAEA TRS 473 [4].The recommended excitation function of 186 W(d,2n) 186 Re reaction are agree with the experimental data, the maximum value is slightly higher than the value of IAEA TRS 473, and little lower than the value of M. Hussain et al.
The thick target yield (TTY) of 186 Re was calculated using the recommended excitation function of 186 W(d,2n) 186 Re reaction, and compared with the TTY from 186 W(p,n) 186 Re reaction [6], together with the measurements [1,14,15] are shown in Fig. 7.The TTY of 186 W(d,2n) 186 Re reaction are much higher than the value of 186 W(p,n) 186 Re reaction above 15 MeV.So the 186 W(d,2n) 186 Re reaction may be more suitable for production of no-carrier-added 186 Re for medical application, if the deuteron beams are available by cyclotron and the energy is high enough.

Figure 2 .
Figure 2. The experimental data after normalization and correction.

Figure 3 .
Figure 3.The results of nuclear model calculation using TALYS.

Figure 4 .
Figure 4.The results of fitting from threshold to 14 MeV.

Figure 5 .
Figure 5.The results fitting from 14 to 50 MeV.

Figure 6 .
Figure 6.The recommended excitation function for 186 W(d,2n) 186 Re reaction, compared with experimental data and results published earlier.

Figure 7 .
Figure 7.The TTY of 186 W(d,2n) 186 Re reaction, compared with the TTY of 186 W(p,n) 186 Re reaction.