7 Li neutron-induced elastic scattering cross section measurement using a slowing-down spectrometer

. A new integral measurement of the 7 Li neutron induced elastic scattering cross section was determined in a wide neutron energy range. The measurement was performed on the LPSC-PEREN experimental facility using a heterogeneous graphite-LiF slowing-down time spectrometer coupled with an intense pulsed neutron genera-tor (GENEPI-2). This method allows the measurement of the integral elastic scattering cross section in a slowing-down neutron spectrum. A Bayesian approach coupled to Monte Carlo calculations was applied to extract natural C, 19 F and 7 Li elastic scattering cross sections. First experimental results obtained with heterogeneous graphite slowing down time spectrometers were presented: they provide integral elastic scattering cross section measurements in the 1–1000 eV neutron energy range. Using a Bayesian analysis, three complementary experiments have allowed the determination of the probability density functions of graphite and ﬂuorine elastic scattering cross sections. The ratio of 7 Li to 19 F elastic scattering cross sections was deduced from the experiments. We have obtained a new 7 Li integral cross section at low neutron energy range in agreement with the JEFF3.1and ENDF-BVII libraries. Thy`ebault, A. Nuttin for the discussions on reactor physics.


Motivation
In the past, Oack Ridge National Laboratory developed the molten salt reactor experiment MSRE [1] as a starting for molten salt reactor research plan [1]. Since few years the LPSC has improved this kind of system by developing the Molten Salt Fast Reactor (MSFR). In this concept, the fuel, in liquid phase, is also the neutron moderator and the coolant. This fuel is based on a liquid fluoride salt. It was demonstrated that the breeding potential of this concept depends strongly on the number of available neutrons in the core [2]. Consequently, to avoid neutron losses through 6 Li(n, t) capture reactions only 7 Li isotope has to be content in the salt. In the Thorium Molten Salt Fast Reactor concept (Th-MSFR), the fuel-coolant is defined as 7 LiF(0.775)-232 ThF 4 (0.20)-233 UF 4 (0.025) (mass proportion). A reaction cross section sensitivity analysis was performed which results are reported in the table 1 [3]. In regard to the sensitivity of K eff multiplication factor, the most important reactions are captures on 232 Th and 233 U and fission of 233 U. In regard to the moderation, the light nuclei were considered to define correctly the neutron spectrum.

Slowing-down time spectrometer set-up
We performed a measurement of an integral 7 Li elastic scattering cross section in a slowing-down time neutron spectrum in a heterogeneous graphite slowing-down time spectrometer. Classical slowingdown spectrometers are generally built with lead blocks as heavy elements allows a better energy resolution than lighter elements. From 1 eV up to 10 keV neutron energy range, the neutron slowingdown time is mainly due to elastic scatterings. At higher energies, inelastic scattering process is needed to describe correctly the time-energy correlation [4]. With light elements like graphite and low energy neutrons, we have only access to the mean slowing down time which is a function of the elastic scattering cross section. However, for graphite, inelastic reactions appear starting from 4.7 MeV. As a consequence, this reaction does not perturb the energy-time correlation for thermal and epithermal neutron

Presentation of PEREN facility
The graphite slowing down time spectrometer used in the PEREN facility is consists in a graphite cylinder of 1 m in diameter and height. Using the D(d, n)t reactions, a pulsed deuteron source of 220 keV provides intense neutron pulses of E n ∼ 3 MeV (GENEPI [12]). The titanium-deuterium target (TID) is placed in the middle of the graphite matrix. In the core of this spectrometer, we positioned a gamma detector (with a YAP scintillator) coupled to a resonant capture target, here in gold. The γ flash due to the interaction of deuteron pulse with the target backing (made of copper) gives the start for the acquisition and the gamma rays emitted by the 197 Au(n, γ) capture provides the slowing-down time (Fig. 1). Three configurations of the spectrometer were combined to extract the 7 Li elastic scattering cross section. The first configuration is a heterogeneous LiF-Graphite spectrometer. The mean value of the slowing down time corresponds to a combination of cross sections and densities of the all elements present in the spectrometer. A second configuration describes as a heterogeneous Teflongraphite spectrometer used to obtain the fluorine contribution in the slowing-down time spectrum. The last configuration is a pure graphite spectrometer to cross-check and validate the experimental set-up.  7 LiF ingots are synthesized in gloves boxes using a 7 LiF powder obtained by fluorination of 7 Li hydroxide provided by Cogema. Several preliminary fusions of the powder were performed to elaborate the blocks used for the final ingots melting. Solidification took place in a graphite crucible, in a three areas furnace with very slow temperature slope rate. Hollow ingot is molded in two pieces owing in order to minimize internal strain.

Experimental data analysis
The characteristic of a slowing down time spectrometer is the energy-time correlation described by the following relation [7]: where E 0 is the energy of source neutrons, T 0 the characteristic slowing down time function of the properties of the materials present in the spectrometer (cross sections and densities) and Tr the mean resonant time. In Fig. 2 a slowing down time spectrum is presented after subtraction of the background induced by the components of the YAP scintillator and photomultiplier. For each capture resonance of the gold target, we observe a peak in a time spectrum which position and shape are function of the integral (n,el) cross section from the source neutron energy, E 0 , down to the resonant energy E r . Monte Carlo calculations were performed using MCNP5.1 and MURE codes [8] to extract the 7 Li(n,el) cross section from the recorded time spectrum . We have taken into account the compositions of graphite, lithium fluoride and Teflon blocks, the geometry of the gold target and detector as well as the PEREN facility configuration and environment.

Bayesian approach
In this experiment, we measured the resonant time spectrum, T r , as a function of the elastic scattering cross sections and densities (ρ) of the spectrometer components: and we want to infer the 7 Li elastic scattering cross section as a function of data: 7 Li(n, el) = g(T r ; nat C(n, el); 19 F(n, el); 7 Li(n, el); ρ c ; ρ LiF ) To solve the equation (3), we have based our analysis on a Bayesian approach [9,10]: If where the "data" are the resonant time spectrum (T r ), "H i " the assumption on 7 Li(n, el) cross section plateau and η the nuisance parameters as graphite and fluorine cross sections and densities of the components. The probability of hypothesis "H i " given data and nuisances "η" is called the posterior probability. P(H i ) represents the knowledge on the parameter sought and is called prior. The probability of data given hypothesis and nuisances, P(data|H i , η), is proportional to the likelihood function. The normalisation by the probability of data, P(data), erases the proportionality between the likelihood function and the probability P(data|H i , η). For a Gaussian propagation of uncertainties, the likelihood function L is defined as [9]:

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with χ 2 being the least square function.

Homogeneous graphite spectrometer
Using a pure graphite spectrometer, we have measured three sets of data with a gold resonant target. First, we present the probability density function (PDF) of C(n,el) cross section in comparison to the JEFF3.1 evaluation in Fig. 3. We note a perfect agreement between these three measurements. Each point is the result of a MCNP calculation performed with different values of JEFF3.1 C(n,el) cross section plateau. The standard deviation of each measurement is around 1.7% and the final posterior of all data are defined by a mean value of 0.2% (compared to JEFF3.1) and a standard deviation of 1.2% taking into account a 0.5% standard deviation on the graphite density. This analysis with a constant prior gives the spectrometer resolution in regard to C(n,el) cross section: R(C(n,el))∼1.7%. In a second time, the precision on the available experimental data in the C(n,el) cross section plateau is around 2%. This resolution defines the prior knowledge on this cross section. Thus, a second calculation with a new prior led to the final measurement on graphite. The posterior density probability function is closed to JEFF3.1 assessment with a 0.1% mean value (in comparison to JEFF3.1 C(n,el) evaluation) and a 1%standard deviation considering the 0.5% standard deviation of graphite density. According to the time-energy correlation, the weight W(E n ) of neutron induced elastic scattering cross section at neutron energy E n , can be defined as the ratio of the differential "life time" of neutron at E n to the total slowing-down time. This weight represents the importance of the cross section value at 07005-p.4 neutron energy E n in the integral cross section measurement for a gold resonant target (E r = 4.9 eV) and a source neutron at E 0 = 3 MeV (fig. 4).

Heterogeneous graphite-Teflon and graphite-lithium fluoride spectrometers
Similar studies were performed for two heterogeneous spectrometer configurations. The first configuration considered here is the graphite-Teflon spectrometer with a gold resonant target. In this configuration, the resonant time, Tr, depends on both graphite and fluorine elastic scattering cross sections as well as densities (ρ) of graphite and Teflon blocks. To determine the probability density function of 19 F(n,el) cross section, we have included in the calculations the resolution of the spectrometer in regards of C(n,el) cross section: P( 19 F(n, el)|T r ; η) = P(T r | 19 F(n, el); η) · P( 19 F(n, el)) P(T r ) data are the resonant time spectrum with Teflon T r = N r (t) and η characterises the nuisance parameters: η = C(n,el); ρ c ; ρ Teflon . The resolution on C(n,el) cross section gives a limit on the precision on the mean resonant time value for the Teflon block. To take into account this uncertainty on the comparison between experimental spectrum and Monte-Carlo calculated spectra, we consider the least square given by: where statistical uncertainties of experiments (N exp ) and Monte Carlo calculations (N cal ) are added to the uncertainty on the mean resonant time given by: S Tr ; C(n,el) and R(C(n,el) are, respectively, the sensitivity of mean resonant time to the C(n, el) cross section and the resolution of the slowing down time spectrometer in regard to the C(n,el)  cross section. The probability density function of 19 F(n,el) cross section compared of JEFF3.1 (Fig. 5) were calculated with a 5% standard deviation on the prior probability, corresponding to the present knowledge of 19 F(n, el) cross section plateau. The preliminary result matches rather well the JEFF3.1 assessment with a mean deviation of 3.1 (±2.7)% compared to JEFF3.1. We can extract from this analysis the correlation between 19 F(n, el) and C(n,el) cross section measurements that is found equal to −0.25. For the heterogeneous Lithium fluoride -Graphite spectrometer configuration, the 19 F(n, el) and C(n, el) cross sections and the densities of components define the nuisance parameters η. Many cracks in the LiF block prevent from an exact determination of the lithium density. Presently, we have only determined the ratio of 7 Li(n, el) and 19 F(n, el) cross sections. For the JEFF3.1 assessment of 19 F(n, el) cross section, we obtain an elastic scattering cross section plateau at 1.04 ± 0.8 barn with a 5% standard deviation from the JEFF3.1 19 F(n, el) evaluation (Fig. 6). The result is in better agreement with JEFF3.1 and ENDF-BVII evaluations than with the JENDL library. However the resolution of our experiment cannot exclude the JENDL library values. Moreover, an integral measurement does not provide access to the structures of the 7 Li elastic scattering plateau as defined by JEFF3.1 and ENDF-BVII libraries.

Conclusion and perspectives
First experimental results obtained with heterogeneous graphite slowing down time spectrometers were presented: they provide integral elastic scattering cross section measurements in the 1-1000 eV neutron energy range. Using a Bayesian analysis, three complementary experiments have allowed the determination of the probability density functions of graphite and fluorine elastic scattering cross sections. The ratio of 7 Li to 19 F elastic scattering cross sections was deduced from the experiments. We have obtained a new 7 Li integral cross section at low neutron energy range in agreement with the JEFF3.1and ENDF-BVII libraries.