Measurement of the delayed-neutron yield in the thermal neutron induced fission of 239 Pu

. This article presents an experimental effort to provide high-quality data to improve the evaluation of the 239 Pu delayed neutron yield in the thermal energy range. The set-up is composed of a long counter with sixteen 3 He tubes, a fast shutter system to produce irradiation cycles with short rising/falling times, and a miniature fission chamber containing 114µg of 239 Pu. The whole system was installed in the PF1B experimental zone of the Institut Laue-Langevin, which provides a cold neutron beam. The repetition of irradiation/decay cycles enables to saturate the delayed neutron precursors and to measure their yield through the observed activity, shortly after the beam-stop. The innovation of our measurement technique relies on the clear distinction between prompt and delayed neutron counting, thanks to boron absorbers, without the necessity to move the sample. In such a way, it is possible to normalize the counting of delayed neutron emission to the one of total neutron emission, based on the well-known value of the prompt neutron multiplicity. The present work provides a delayed neutron yield value of 𝜈 𝑑 = 0.642(5)%. The latter is in 1  agreement with the IAEA recommendation of 0.628(38)%, with a strongly reduced uncertainty thanks to our normalization technique.


Introduction
The accurate prediction of reactor dynamic relies on the well-established point kinetics equations. Among the different parameters that drive the calculation of the reactivity as a function of the neutron flux, the effective delayed neutron fraction plays an important role. We remind its expression below [1]: , and , are respectively the delayed and total neutron yields of fissile isotope j, , and , the corresponding neutron energy spectra, and + the forward and adjoint neutron fluxes. This parameter is a weighted mean of delayed neutron production over total (delayed+prompt) neutron production, summed over the various fissile isotopes.
While the fission cross section and prompt neutron multiplicity are now known with a precision better than 1% (1) thanks to an extensive experimental database, the delayed neutron yield remains poorly known, even for the most important isotopes like 239 Pu. An effort has been conducted by IAEA over the last decade to compile * Corresponding author: pierre.leconte@cea.fr recent theoretical and experimental works connected to beta-delayed neutron data [2]. For thermal neutrons, the delayed neutron yield of 239 Pu is reported at ±6% (1): = 0.628(38) %. This value is based on the evaluation by Tuttle in 1979 [3]. Since that time, no significant progress was reported, apart from one measurement by Borzakov in 2000 [4]: = 0.663(23)%. In 2018, in the framework of the PhD thesis of D. Foligno [5], CEA undertook the design of an experimental set-up in order to provide high-precision delayed neutron data for thermal-neutron induced fission (typically better than ±2%). The motivation was to cover a list of the most important isotopes involved in the kinetics of light water reactors (LWR), through a series of experiments performed at the High Flux Reactor of the Institut Laue Langevin (ILL). Two campaigns were performed in 2018 and 2019, focusing on the 235 U thermal fission [6,7].
The present paper exposes the work conducted in 2021 to measure the delayed neutron yield of 239 Pu [8]. The first part describes the method used to determine the delayed neutron yield, the second one presents the experimental set-up, the third one explains the data processing methodology, the last one discusses the measurement results in comparison with published data.

Method
The most common method for delayed neutron measurement, as used by Keepin et al. [7] for instance, involves the irradiation of a sample and its pneumatic transfer from its irradiation location to a neutron detector. Such transfer usually takes hundreds of milliseconds during which shortest-lived delayed neutron precursors may be lost.
In order to record delayed neutron emission starting a few tens of milliseconds after the irradiation, an innovative method was developed in order to avoid the displacement of the sample. Thanks to an appropriate design of the sample and neutron detector, it is possible to suppress background from thermal neutrons from the beam, while keeping prompt and delayed neutrons induced in the fission of the actinide. To do so, the neutron detector has to be shielded with a highly efficient neutron absorber, such as boron or cadmium. These materials prevent the direct detection of neutrons from the thermal neutron beam but are quite transparent to energies higher than 100 keV for delayed and prompt neutrons.
The measurement is split in two phases. The first one consists in the irradiation of the sample, in order to build-up delayed neutron precursors. The second one consists in the measurement of delayed neutron emission, when the neutron irradiation and the prompt neutron emission have stopped. In order to improve the counting statistics, these two phases are repeated a large number of times (typically hundred to thousand times).
The equations that drive the total neutron counting ( ) during these two phases, assuming an infinite repetition of cycles, are the following: -Beam-on phase: With the following definitions: 0 the fission rate during the irradiation phase (assumed to be constant), and , are the detection efficiency for respectively the prompt spectra and delayed neutron spectra associated to group k, and are the background counting rates for respectively the "beam on" and "beam off" situations. and are respectively the beam-on and beam-off duration times.
Averaging ( ) over an irradiation period , we get: Proceeding the same way for the decay phase, by averaging ( ) between two time bins [ ; +1 ], we get: Combining equations (4) and (5), we can remove the contribution of 0 and derive the value of  , based on the experimental observables ̅̅̅̅̅ and ̅̅̅̅ , and assuming a known value for  .
Thanks to an appropriate design of the detector so that its efficiency has a flat energy dependence over the range of delayed neutron emission (typically from 100 keV to 1 MeV), it is possible to remove the group dependant efficiency values , from the summations terms of Equation (4) and (5). Moreover, in the asymptotic situation very long irradiations ( → ) are followed by short beam interruptions ( → 0), equations (5) and (6) simplify in such a way that we can determine  without the knowledge of the delayed neutron group constants (k, ak).

Experimental set-up
The measurement system is made of three elements: a neutron shutter for periodic irradiations of a fissile target, a detection system for prompt and delayed neutrons, called LOENIEv2, a fissile target in the form of a miniature fission chamber. In the next sections, we detail each of these elements.

Beam shutters for periodic irradiations
One of the key elements of the set-up is the beam shutter used to shape periodic irradiations. The system has to be fast enough to produce square irradiation with transient times as short as possible. It has to be efficient enough to avoid significant background from the beam during the delayed neutron counting.
A rotary system was designed to meet these requirements. It is composed of two screens of B4C lined with a cadmium foil, mounted in parallel on a motorized support (Fig.1). The screens can be put parallel to the beam, so that the neutrons fly freely in between the screens, or perpendicular to it, so that neutrons are absorbed. The thickness of the B4C was calculated to attenuate the neutron beam by >10 7 . The system was measured to rotate between the two positions in about 4 ms, which is fast enough regarding the half-life of the 8 th group of delayed neutrons (200 ms).

Delayed neutron long-counter LOENIEv2
Our detector is an enhancement of a previously designed long counter for Pn (neutron probability) measurement at ILL, in the framework of a postdoctoral work by L. Mathieu [10].
This new version, called LOENIEv2, is composed of sixteen proportional counters (PCs) filled with 10 bars of 3 He, placed in a cylindrical high density polyethylene (HDPE) matrix, covered by a 1 cm layer of boron rubber. The system was mounted at the exit of the beam line and surrounded by concrete blocks for biological protections (see Fig. 2). The PEHD matrix has a central hole, covered with boron rubber as well, in which the fissile target was installed for irradiation.

Fig. 2. LOENIEv2 long counter during its installation; only one half of the detector is presented
The arrangement of the sixteen proportional counters (PC) in the PEHD matrix was designed so that the total detection efficiency varies by less than 1.5% over the neutron energy range [0.1 -1 MeV]. The efficiency was calibrated with different neutron sources, covering an energy range from 500 keV to 5 MeV. The total efficiency is close to 20%. The 3 He PCs were plugged to charge sensitive preamplifiers (CSPA) which shaped the short current pulses delivered by the detectors into integrated and exponential tailed voltage pulses. The latter were fed to two synchronized digitizer cards (CAEN V1724), running a real time digital pulse processing embedded program to process the data flow, detect events and output their arrival time and energy (i.e. the amplitude of the pulses). Raw data buffers are stored into binary files in "list mode" for further data processing. The whole system is controlled by the ILLdeveloped NOMAD [11]. A server performs the local acquisition, and its user interface allows for monitoring remotely the acquisition.

239 Pu fission target and vacuum chamber
The fissile target was a miniature fission chamber (MFC) crafted by CEA (CFP12 type). It was composed of a Ti backing disk of diameter 8 mm, on which 239 Pu was electro-deposed. This deposit is embedded in a Ti body of 12 mm outer diameter. A miniature coaxial connector of 4 mm in diameter made it possible to plug the detector onto a coaxial cable The 239 Pu mass in the fissile deposit was chosen so that the maximum counting rate in a PC (due to prompt neutrons) does not reach more than 2.10 4 c/s, in order to minimize the dead time corrections. Gamma spectroscopy was used prior to irradiation to measure the activity of the 375-keV gamma-ray from 239 Pu decay and thus control the mass of the actinide. An activity of 261.1(55) kBq was obtained, which corresponds to 113.7(24) µg of 239 Pu. With such a low mass per cm², the intrinsic detection efficiency of the fission chamber is estimated to be 0.97 (1).
The MFC was placed under depression in a closed tubing system, which acted as a safety barrier, monitored thanks to a pressure gauge. It is made of an aluminum pipe and tore joint links which allows connecting the elements (pump and pressure gauge). The signal transmission cable from the fission chamber is connected to an airtight BNC feedthrough (see Fig. 3).

Data processing
The overall detection rate issued by the 16 3 He counters is the main physical quantity of interest taken as observable in the analytical models. Basically, the data reduction consists in processing the numerous raw signals so as to produce a time series proportional to the PC's neutron detection rate. It includes the following steps: 1. Conversion of the binary files into a (n x 3) matrix (events stored in rows, time stamp, energy and channel number in columns); 2. Synchronization of time stamps of each run using a photodiode signal indicating the closure of the beam as reference time (t = 0); 3. Energy rescaling and background removal by applying a region of Interest (ROI) in the energy range; 4. Calculation of the neutron detection rates versus time (by taking the histograms of the events arrival times) of each channel and for each run; 5. Correction for counts loss (pile-up and dead time) using an analytical non-extendable dead time model for each channel and for each run with  = 7.61 (7)  6. Calculation of total and quadrant detection rates for each run; 7. Calculation of means and standard deviations of the detection rates over all runs. The final decay curves are fed to the CONRAD nuclear data evaluation tool [12] to fit the delayed neutron yield expressed as parameters in the theoretical model based on Equations (4) and (5).

Results
Repetition cycles of duration 3.155(10)s irradiation + 0.253(10)s decay were performed over a time period of 10 hours. This time sequence was optimized to reach a quasi-saturation of delayed neutron precursors and to maximize the statistics for delayed neutron yield evaluation. The total counting rate, corrected for dead time, and averaged over the 10160 recorded cycles, is plotted in Fig. 4. In the figure, note that the high count rate below 30ms comes from neutrons that are arriving after the closing of the shutter because of their time of flight. This fission tail is responsible for an uncertainty in the reference time t = 0 estimated to be 5 µs.
The time window chosen for the fit ranged from 30 ms to 200 ms. It was chosen as a compromise between higher counting statistics and lower contribution of the model correction to account for (i, ai) parameters in the determination of d.
The delayed neutron yields were separately fitted by CONRAD by group of detectors (see Table 1). The results given by quadrants 1, 2 and 4 are found to be very consistent with each other, with a dispersion of 0.001% comparable to the calculated uncertainty of 0.002%. the value given by the third quadrant falls well below the other three values. The reason for that lies in an incorrect background level associated to quadrant 3. During the background measurements, it was found afterwards that some 3 He tubes were incorrectly positioned inside the HDPE matrix. As it was not possible to correct for that effect, it was decided to discard the result associated to this group of detectors.
In conclusion, the best estimate was obtained from the average of the three consistent quadrants. The result is the following: d[ 239 Pu] = 0.642(5) % The final uncertainty of 0.005 % (0.8 % in relative) is dominated by the systematic error associated to the prompt neutron multiplicity. The uncertainty breakdown, as issued by CONRAD is as follows: prompt neutron multiplicity (0.5%), efficiency ratio (0.3%), reproduction of cycle and irradiation times as well the reference time t = 0 (0.3%), model correction for t → 0 extrapolation (0.1%), This new estimation is in agreement with the IAEA recommended value of 0.628(38)%. It also compares well with the most recent measurement by Borzakov [4]: = 0.663(23)%. The strong uncertainty reduction of our work was obtained thanks to our normalization method that relies on the prompt neutron emission measurement. In this way, it was possible to avoid a complex determination of the absolute fission rate generally based on the absolute detection efficiency known with a poor uncertainty higher than 3% in other similar experiments.
Furthers works will include the analysis of various long-irradiation cycles (5 to 150 s irradiation times), in order to fit the delayed neutrons groups abundances. In 2023, the next experimental campaign at ILL will focus on 241 Pu.