Evaluation of delayed neutron yields and time spectra from photofission of 238 U induced by Bremsstrahlung photons below 9 MeV

. Few data exist regarding the yields and time spectra of delayed neutrons from the photofission reaction on actinides. In this paper, we report the characteristics of both six-group and eight-group delayed neutron time models for the photofission of 238 U induced by a Bremsstrahlung photon spectrum with an end-point energy at 9 MeV. This study was conducted using a 9 MeV linear electron accelerator housed at the SAPHIR platform located at CEA Paris-Saclay, France. A reference sample of depleted uranium was positioned inside a neutron detection block, previously designed and optimized by Monte Carlo simulation, made of high-density polyethylene covered by cadmium and including ten one meter-long 3 He proportional counters. Based on the consistent set of half-lives proposed by Spriggs et al. as early as 1999 for neutron-induced fission, our description in eight delayed neutron groups for 238 U at 9 MeV is the first published for photofission. These new results bring valuable information to the scarce data available in the literature and represent useful inputs for the development of photofission-based nuclear measurement systems as they meet a significant interest in the fields of nuclear data, radioactive waste package characterization and for security-related applications.


Introduction
The reaction in which the fission of an atomic nucleus is induced by a high-energy photon is known as photofission [1,2]. Both fissile actinides ( 235 U, 239 Pu, etc.) and fertile actinides ( 238 U, 240 Pu, etc.) can undergo photofission. The energy threshold of this reaction is around 6 MeV for all actinides. The applications of photofission range from security at borders to radioactive waste package characterization. To implement this technique, the high-energy photon beam is usually produced by Bremsstrahlung in the conversion target of a linear electron accelerator. Moreover, a strong interest has emerged in the recent years for the use of electron accelerators operated below 10 MeV in order to develop photofission mobile systems [3,4]. Both the design of these measurement stations and the evaluation of their performance require Monte Carlo simulation studies and post-processing calculations, which justifies the need for the most reliable nuclear data concerning the photofission reaction in the energy range of interest.
A six-group multi-exponential theoretical description was originally provided by Keepin et al. in 1957 for delayed neutrons from thermal or fast neutroninduced fission of several isotopes [5] [8,9]. In 2009, Macary et al. provided data for the photofission of 235 U and 237 Np for a couple of end-point energies below 20 MeV [10].
From a theoretical point of view, each delayed neutron group is characterized by a half-life time ( 1/2 ) or an equivalent decay constant and a relative yield . Following an irradiation of duration irr , the delayed neutron signal decays over time and can be described by Eq. 1 considering a number of groups noted .
In this paper, we evaluate the delayed neutron yields and time spectra for the photofission of 238 U induced by Bremsstrahlung photons below 9 MeV. First, we show the experimental setup, determine the irradiation times and describe our nuclear data extraction algorithm. Then, we present and discuss the results obtained. In addition to the description in six delayed neutron groups, based on the consistent set of half-lives proposed by Spriggs et al. as early as 1999 for neutron-induced fission [11,12], our description in eight groups for 238 U at 9 MeV is the first published for photofission.

Experimental setup
The experiments were conducted at the SAPHIR platform located at CEA Paris-Saclay, France. This facility houses a linear electron accelerator, Linatron® M9A manufactured by Varex Imaging Corp., which was operated at 9 MeV and 200 Hz. The neutron detection block, designed and optimized beforehand by the authors of this paper using Monte Carlo simulation with the MCNP6 code [13], consists of ten 3 He-filled gas proportional counters (150NH100, 4 bars) embedded in high-density polyethylene surrounded on its outer and inner surfaces by a 1 mm-thick cadmium layer. A 241 g reference sample of depleted uranium was positioned and laser-aligned at the centre of the neutron detection block. The delayed neutron signal was acquired using new digital readout electronics developed at our laboratory, which will be presented in detail in a dedicated paper. Fig. 1 shows an overview of the experimental setup whereas Fig. 2 focuses on the neutron detection block.

Irradiation times
The six or eight groups being characterized by half-lives ranging from ~50 s to a few tens of ms, the irradiation time can be adapted to the delayed neutron group whose parameters are to be extracted. In order to determine the most adapted irradiation times to be used in our measurement protocol, we plotted the relative delayed neutron yields of each group as a function of irradiation time irr thanks to Eq. 2.
As a first approach, the relative delayed neutron yields and the decay constants for 238 U were taken from Nikotin et al. [2] and the maximum counting time max was set at 300 s. Fig. 3 presents the results obtained. However, for this type of study, the delayed neutron groups are usually matched in pairs and three different irradiation times are chosen [6][7][8][9][10]. Fig. 4 presents the updated results. Finally, the irradiation times chosen to "stimulate" preferentially groups two by two are: 300 s, 10 s and 1 s. Whatever the irradiation time, as soon as an irradiation sequence is completed, the neutron detection system is switched on and acquires the signal for a duration of 300 s. For statistics purposes, these measurements -based on 300 s, 10 s and 1 sirradiation times -were repeated respectively: 5, 50 and 100 times. Regarding groups 5 and 6, irradiation times below 1 s raise questions about beam stability and measurement reliability, which from the point of view of the authors of this paper is the case for experimental protocols followed in previous studies [6][7][8][9][10].

Nuclear data extraction algorithm
To determine the twelve parameters of delayed neutrons from photofission of 238 U at 9 MeV according to the sixgroup model: • the first step consists in extracting 1 and 2 from the 300 s-irradiation data; • the second step consists in extracting 3 and 4 from the 10 s-irradiation data; • the third step consists in extracting 5 and 6 from the 1 s-irradiation data; • running again steps 1 to 3 through an iterative process enables to fine-tune all the parameters ; • the last step consists in taking the 300 s-irradiation data (all groups at equilibrium), fixing the six decay constants to their previously determined values, and extracting the six relative yields .
To determine the parameters of delayed neutrons from photofission of 238 U at 9 MeV according to the eight-group model, we took the consistent set of eight half-lives proposed by Spriggs et al. for neutron-induced fission [11,12], which following the recommendations from the NEA/WPEC-6 report [14] was later used by the JEFF evaluation, since version JEFF-3.1 [15]. The eight remaining relative yields to be determined are obtained using the 300 s-irradiation data fitted with an eight-group multi-exponential.
Furthermore, whatever the number of delayed neutron groups (six or eight), the uncertainties associated to the parameters determined experimentally are evaluated using the series of repeated measurements and under the assumption of a Poisson distribution.

Results and discussion
An example of time spectrum of delayed neutrons from photofission of 238 U at 9 MeV, acquired following a 300 s-irradiation, is shown in Fig. 5. Although the total counting time is equal to 300 s, this figure focuses on the first 60 s of counting.

Six-group model
The parameters obtained for the six-group model of delayed neutrons from photofission of 238 U at 9 MeV are gathered in Table 1. We can note in particular that the half-life of group 1 is lower than that assessed by Nikotin and Petrzhak for 238 U at 15 MeV (56.2 ± 0.8 [6]), while the relative yield of group 6 is more in agreement with Nikotin and Petrzhak (16.1 −5.0 +2.0 % [6]) than Doré et al. (8.5 ± 0.8 % [8]). As both the half-lives [ 1/2 ] and the relative yields vary simultaneously through the nuclear data extraction algorithm, it is however difficult to be conclusive when comparing with parameters determined by other authors working on photofission delayed neutrons with a six-group model.  Table 2 gathers the parameters obtained for the eightgroup model of delayed neutrons from photofission of 238 U at 9 MeV. As a reminder, the consistent set of halflives comes from neutron-induced fission [11,12]. These values could be used as a comparison basis for future evaluations of delayed neutrons from photofission according to an eight-group model.

Conclusions and perspectives
In this paper, we reported a six-group time model for delayed neutrons from photofission of 238 U induced by a Bremsstrahlung photon spectrum with an end-point energy at 9 MeV. Moreover, based on the consistent set of half-lives proposed by Spriggs et al. as early as 1999 for neutron-induced fission, we also provided a description in eight groups, which is the first one published for photofission. These results should constitute a valuable contribution considering the scarce data available in the literature for time models of delayed neutrons from photofission, i.e., three peerreviewed articles and two proceedings papers in more than 50 years. The next step of this study would consist in carrying out additional measurements at both 6 MeV -i.e., just above the energy threshold of the photofission reaction -and 9 MeV as well as for other radionuclides such as 235 U and 239 Pu. Furthermore, complementary Monte Carlo simulations would enable to quantify the impact of neutron-induced fission reactions in the samples during these photofission measurements. The logical follow-up of this work would also include the determination of the absolute yields for delayed neutrons from photofission for the various radionuclides of interest at the two Bremsstrahlung spectrum endpoint energies. These new measurements would allow comparison between the different results obtained and in particular enable to draw conclusions regarding the influence of the Bremsstrahlung photon spectrum endpoint energy on the absolute and relative yields.