Measurement of (n, f ) and (n, xn) cross sections with surrogate reaction method

Surrogate reaction method is an important approach to overcome the difficulties meet in the direct measurement of neutron induced nuclear reaction. The current existing surrogate reactions generally employ the peripheral reactions such as inelastic excitation and transfer reaction where the involved angular momenta are much larger than the neutron capture reaction, which causes a difficulty in theoretical correction of spin of compound nucleus. We proposed to use capture reaction of light charged particle as the surrogate reaction, thus the spin distributions of compound nucleus in two reactions are quite similar and therefore the spin correction is not strongly desired. Based on this idea, the 239Pu(n, f ) and (n, 2n) cross sections were successfully extracted by using 236U(α, f ) and (α, 2n) reactions as the surrogate reactions. The well coincidence of the present results with the data of ENDFB7 within the error bars shows the reliability of the proposed surrogate capture reaction


Introduction
Nuclear power today makes a significant contribution to electricity generation, providing about 10% of global electricity supply. The design of advanced nuclear reactors for power supply and nuclear waste transmutation calls for some key nuclear data urgently, especially the neutron induced reaction data.However, due to the limited energies for the neutron beams, the short-lived target nuclides and strong radioactivity, many neutron induced reaction data are very difficult to measure directly. Especially for (n, 2n) reaction which plays an essential role in nuclear waste transmutation, the direct measurement is even harder due to the interference caused by the background neutrons from scattering and fission, etc. The surrogate reaction method (SRM) overcomes the difficulties meet in the direct measurement for the neutron induced reaction cross sections effectively.

surrogate reaction method
SRM refers to an indirect method which uses an surrogate reaction with a more experimentally accessible or preferable combination of projectile "d" and target "D" in measuring the target neutron "a" induced reaction cross sections,as shown in Figure 1 [1]. The basic principle is that the same compound nucleus (CN) "B" with the same excitation energy (E x ) can be formed by selecting a suitable reaction channel, based on the idea for the equilibrated compound nucleus that the formation phase is independent of the decay phase (if omitting the small difference for the angular momentum). SRM was proposed in the early 1970s by Cramer J D and Britt H C, who used (t, p f ) two-neutron transfer reaction as the surrogate reaction in the measurement of the (n, f ) cross sections of the actinide nuclei [2]. For example, 230,232 Th, 234,236,238 U and 240,242 Pu(t, p f ) were used as the surrogate reactions for 231,233 Th, 235,237,239 U and 241,243 Pu(n, f ) respectively, through a simple formula: σ n f (E n ) and σ C (E n ) are respectively the neutron induced fission cross section and the neutron capture cross section at the energy E n , and P exp (t,p f ) (E n ) is the experimental measured fission probability of the surrogate reaction at the corresponding neutron energy E n , N p and N f are the proton counts from transfer reaction and the fission counts, respectively. After decades of development, especially the blowout type development after 2000 [3][4], now SRM has different forms like surrogate ratio method [3], surrogate capture reaction method and so on.

Surrogate Ratio Method
Surrogate ratio method obtains the reaction cross section by measuring the ratio of the cross section of the desired reaction channel to that of a well-measured reaction channel, which means that the higher data accuracy the selected reference reaction channel has, the better data the target reaction channel can be obtained. According to the difference of the reference reaction channels, surrogate ratio method can be divided into the two types of internal ratio method [3] and external ratio method [4]. The internal ratio method obtains the cross sections by measuring the ratio of reaction cross section between different de-excitation channels of the same compound nucleus. The external ratio method obtains the cross sections by measuring the ratio of reaction cross section of the same exit channel between different compound nuclei. Burke J T et al. [4] studied the 237 U(n, f ) cross section by comparison with the well-measured 235 U(n, f ) cross section. With 238 U(α, α ′ f ) and 236 U(α, α ′ f ) as the surrogate reactions, the cross section ratio between 237 U(n, f ) and 235 U(n, f ) was measured, then the 237 U(n, f ) cross section was obtained by comparing with the perfect data of 235 U(n, f ). This greatly reduces the systematic and theoretical calculation errors that exist in the direct surrogate reaction method [5].

Surrogate Capture Reaction Method
The existing SRM generally chooses the peripheral reactions of inelastic excitation or transfer reaction [1] as surrogate reaction, such as (α, α ′ f ) [6], (d, p f ) [7], ( 3 He, t f ) [8], ( 18 O, 16 O f ) and so on. The angular momentum brought by peripheral reaction is generally dozens of . While the central reaction of the neutron capture reaction is in the low-angle momentum region, and the angular momentum of the compound nucleus is generally merely a few . As a result, the theoretical correction for the angular momentum, which is always essential for SRM, causes great difficulty in data analysis.
In view of this, we choose the capture reaction of light charged particle as the surrogate reaction, and use the compound nucleus as a bridge to obtain the neutron induced reaction cross sections, that is the surrogate capture reaction method (SCRM). As mentioned above, the angular momentum of the compound nucleus formed by light charged particle capture reaction is very low and close to that of the compound nucleus formed by neutron capture, therefore the deviation caused by the spin correction will be reduced. For example, to select 236 U(α, 2n) as the surrogate reaction of 239 Pu(n, 2n) to generate the same compound nucleus 240 Pu, the average spins of the compound nucleus formed in α+ 236 U and n+ 239 Pu were calculated with PACE4 [9] and ECIS programs [10] [11] respectively, as shown in Figure 2. It can be seen that the spin difference of the compound nucleus formed by the two pathways is small at the same excitation energy (E x ). The difference of the average spin ∆<J> is also shown. In the excitation energy region of interest the spin difference is only ±2 and little correction is expected (correction is ignored in the following analysis.).   ergy by using α+ 236 U fusion as in neutron capture n+ 239 Pu can be obtained by selecting the corresponding α energy, which is shown in Figure 2. In the decay stage 238 Pu is formed from the 2n evaporation channel. The 2n evaporation cross section of 240 Pu is obtained by measuring the α decay of 238 Pu, then the 239 Pu(n, 2n) cross section can be calculated: σ cap n is the neutron capture cross section, which is basically a geometric cross section and changes slowly with energy and can be accurately calculated using the ECIS program [10] [11], σ cap α is the fusion cross section for α + 236 U that can be accurately calculated using CC-FULL [12].
In addition, as the by-products of the (n, 2n) cross section, (n, f ), (n, 1n) and (n, 3n) cross sections also can be extracted using SCRM. If the reaction cross section of a certain reaction channel like (n, f ) is already well measured, it can be used as a reference for further improving the data accuracy with the internal ratio method.
2 The application of SCRM -use 236 U(α, 2n) as the surrogate reaction of 239 Pu(n,2n) Based on the HI-13 tandem accelerator at the China Institute of Atomic Energy, 236 U(α, 2n) were performed as the surrogate reaction of 239 Pu(n, 2n). The experiment can be divided into three steps: 1) The on-line experiment for measuring the angular distributions of elastic scattering and fusion-fission fragments of α+ 236 U, then the optical potential and the fission excitation function can be obtained, which are helpful in constraining the α capture reaction cross section calculation and improving the accuracy; 2) The on-line irradiation of the 236 U targets, where 18 236 U targets were irradiated with α beam at the same energies as in step 1; 3) Offline α radioactivity measurement, where α radioactivity of 238 Pu was measured to deduce the yield of 2n evaporation residual nucleus. 236 U target with a diameter of ϕ5) mm was electroplated onto 2 µm thick aluminum foil. 2 thick targets of 5.0 µg/cm 2 were made for on-line experiment and 18 thin targets of 1.0 µg/cm 2 were made for on-line irradiation and off-line measurement.

The on-line experimental setup for α+ 236 U
In the on-line experiment, eight ϕ8 mm Si(Au) detectors were used with a rotatable base for the angular distribution measurement of elastic scattering and fission fragments. At each energy point, the base plate was rotated in a step of 5 • for three times, the elastic scattering and fission angular distribution can be obtained at totally 32 angles between 15 • ∼ 162.8 • . In addition, four Si(Au) detectors were placed symmetrically at the forward angle of 25 • for monitoring the beam quality and cross section normalization. The α beam intensity was about 100 ∼ 200 enA.

The on-line irradiation of the 236 U targets
For the on-line irradiation, 18 uranium targets were divided into three groups for the higher, medium and lower energy α beams, corresponding α particle energies for all the 18  The α beam intensity for the on-line irradiation was about 1.0 eµA, and it was monitored by a water-cooling Faraday cup. In addition, a thin Au target (about 70 µg/cm 2 ) was placed behind the uranium targets for relatively normalizing the cross section and cross-check the beam energy at the last target.

The off-line measurement of α radioactivity
The radioactivity of the irradiated target samples were measured off-line. For the off-line measurement of α radioactivity, 18 target-detector measurement systems were manufactured. With the target-detector distance method, that is to measure the relationship between the counting rate and the target-detector distance, the absolute efficiency of each detector system can be calibrated to further improve the measurement accuracy.
In the off-line measurement, mainly the amount of 238 Pu generated through the 2n evaporation of CN was determined. 238 Pu has a half-life of 87.7 years and the decay α energies are 5.456 MeV (28.98 %) and 5.499 MeV (70.91 %), which are higher than the 236 U decay α energies of 4.445 MeV (26 %) and 4.494 MeV (74 %).
The off-line measurement energy spectra show two distinct peaks as shown in Fig. 4, corresponding to the α particles from 236 U and 238 Pu, respectively. The energy spectra prove that the purity of 236 U was extremely high and there's no interference from other radioactive impurity. The ratio of the two peak areas changes clearly with the α beam energy.  Figure 5 shows the experimental results of the fission fragment angular distributions and the fitted results by using the saddle point transitional state theory [13] for the total 16 energy points between 17.93 ∼ 36.00 MeV. The fission excitation function can be obtained by integrating the angular distribution and then be used to verify the calculation result of CCFULL to improve the accuracy, since more than 90% CN de-excite by fission.

α+ 236 U data analysis
From the offline measured α radioactivity of 238 Pu, the total number of 238 Pu nuclei generated by (α, 2n) reaction can be obtained by using the exponential decay law for radioactivity. The number of 238 Pu can be taken as constant during the offline measurement considering the relatively long half-life. Combining the 236 U target thickness with the incident α particle number, the 2n evaporation cross section can be calculated:  here N( 236 U) is the number of 236 U nuclei per unit area and N( 4 He) is the total number of the incident α particles. Figure 6 shows the fission excitation functions and 2n evaporation channel of α+ 236 U system, the error bars are only the statistical errors. The dots represent the experimentally measured (α, f ) cross sections, the solid line represents CCFULL calculation result for fusion, and the diamond points are the measured (α, xn) cross sections which contain 3n evaporation component at the higher energy region. It can be seen that the experimental measurement is in good agreement with the theoretical (α, 2n) cross sections of PACE4 [9] (dashed line) at the intermediated energy region of E α = 22 ∼ 27 MeV.   calculated with SCRM. The (n, f ) (dots) and (n, 2n) (diamonds) cross sections obtained with the present SCRM are shown in Figure 7. The data of ENDFB7 [14][15] [16] is also plotted. It can be seen that the present results are consistent with both the evaluated nuclear data and the result by Lougheed R W et al. [17] within the error bars.

Extraction of
For 239 Pu(n, 2n), the evaluated nuclear data of ENDF differ greatly between the different versions. We chose the B5, B6, and B7 libraries and also the data of the related experiments 239 Pu(n, 2n) [15,16] for comparison, as shown in Figure 8. Lougheed R W et al. [17] measured 239 Pu(n, 2n) with 14 MeV neutrons, and after more than 30 years tracking measurement of the α radioactivity of the residual nuclei, they obtained a more accurate (n, 2n) cross section. It can be seen that our result is in good agreement with not only the data of B7 library, but also the more accurate (n,2n) cross section data around 14 MeV [17]. At the peak region of the (n, 2n) cross section, i.e. E n is about 11 ∼ 12 MeV, the accuracy for the present data is better than 25%, at low energies (E n < 8 MeV) the data accuracy becomes poor with the increasing statistical error.

Conclusion
The SCRM proposed here chooses the capture reaction of the light charged particles as the surrogate reaction for neutron capture. By employing the reaction cross section measurement of 236 U(α, f ) and 236 U(α, 2n), the excitation functions of 239 Pu(n, f ) and 239 Pu(n, 2n) reactions at E n = 5 ∼ 20 MeV energy region were obtained. The 239 Pu(n, f ) and (n, 2n) cross sections extracted indirectly by SCRM are consistent with that of ENDF within the error bars, demonstrating that SCRM is a powerful method for measuring the neutron reaction data of transuranium nuclei.