Photoneutron cross section measurements on 208 Pb

. Photoneutron reactions on 208 Pb in the Giant Dipole Resonance (GDR) energy range have been investigated at the γ -ray beam line of the NewSUBARU synchrotron radiation facility in Japan. Making use of quasi-monochromatic laser Compton scattering (LCS) γ -ray beams and of a novel ﬂat-e ﬃ ciency neutron detection system along with associated neutron-multiplicity sorting method, total and partial ( γ ,xn) photoneutron cross sections with x = 1 to 4 have been measured for 208 Pb in a broad energy range covering the neutron threshold up to 38 MeV.


Introduction
The double magic 208 Pb is a benchmark case for theoretical modeling of electric dipole response in nuclei [1,2]. It has been extensively investigated through photonuclear reactions [3,4] as well as through inelastic hadron scattering experiments [5][6][7][8]. However, there are unresolved systematic discrepancies [9] between the total and partial (γ,n) and (γ,2n) photoneutron cross sections obtained at the Saclay and Livermore positron in flight annihilation facilities: the Saclay results [3] for the (γ,abs) and (γ,n) cross sections are systematically higher than the Livermore ones [4], while Livermore (γ,2n) cross sections overestimate the Saclay ones. We note that the evaluations adopted in the 1999 and 2019 IAEA Photonuclear Data Libraries [10] follow the recommendation of Berman et al. [11] of lowering the Saclay data by 7% and increasing the Livermore results by 22%, although a single renormalization factor fails to simultaneously solve the inconsistencies for both the (γ,n) and (γ,2n) channels.
New measurements of photoneutron reactions on 208 Pb in the Giant Dipole Resonance (GDR) energy range have been performed at the γ-ray beam line of the NewSUB-ARU synchrotron radiation facility in Japan [12,13]. Total and partial (γ,xn) photoneutron cross sections with x = 1 * e-mail: ioana.gheorghe@nipne.ro to 4 have been measured for 208 Pb in a broad energy range covering the neutron threshold up to 38 MeV.
The investigations made use of a novel high-and-flat efficiency moderated neutron detection array (FED) and the associated neutron-multiplicity sorting methods [14,15]. The FED has a 36.5 ± 1.6 % efficiency averaged on the (0.01 -5.00) MeV neutron kinetic energy range and consists of 31 3 He counters arranged in three concentric rings and embedded in a polyethylene block.
In Section 2, we present the experimental technique and methodology, with focus on diagnostics of the incident LCS γ-ray beams and on the neutron multiplicity sorting procedure based on a statistical treatment of multiple firing coincidence events. Preliminary cross section results are given in Section 3. A summary and outlook are given in Section 4.

Experimental technique and methodology
A diagram of the NewSUBARU LCS γ-ray beamline BL01 and of the experimental setup is shown in figure 1.
After passing through the collimation system, the LCS γ-ray beams irradiated the isotopically enriched metallic 208 Pb targets placed at the center of the FED. Large volume NaI(Tl) and LaBr 3 :Ce detectors were used for monitoring the γ-ray beam flux and, respectively,   the incident spectra. The laser triggering signal, the time and amplitude of the NaI(Tl) and LaBr 3 :Ce signals, the arrival time and the firing ring of the neutron induced signals in the 3 He counters were collected in triggerless list mode, using an 8 parameter 25 MHz digital data acquisition system.

Laser Compton-scattered γ-ray beams
Gamma-ray beams were produced at the NewSUBARU facility by head-on collisions of 1064 nm and 532 nm wavelength laser beams and electron beams circulating in the storage and acceleration ring. The energy of the electrons was varied between 629 and 1050 MeV, generating LCS γ-ray beams with energies between 7 and 38 MeV.
The absolute value for the maximum energy of the incident γ-ray beam is directly determined from the laser and electron beams energies. The NewSUBARU electron beam energy has been calibrated by means of low-energy LCS γ-ray beams produced using CO 2 laser photons [16], with a relative uncertainty in the order of 10 −5 . Figure 2 shows the LCS γ-ray energy range available using 1064 and 532 nm wavelength lasers, as well as the probing energies for the 208 Pb photoneutron reactions in the present study.
A double collimation system of 3 mm and 2 mm aperture shown in figure 1 has been used to obtain quasimonochromatic γ-ray beams. The eliLaBr Monte Carlo  simulation code for LCS γ-ray sources [17][18][19] has been used to reproduce the experimental monitor LaBr 3 :Ce detector responses and thus obtain the spectral distribution of the incident γ-ray beams shown in figure 3. The (γ, n) measurements below two-neutron emission threshold S 2n made use of the 1064 nm INAZUMA laser and 4.31 g/cm 2 targets, while the high-energy (γ, xn) ones of the 532 nm Talon laser and 10.87 g/cm 2 targets. The incident spectra are shown in figure 3 as L(E γ , E m ) distributions, defined as the average path length per unit energy traveled through the target by a E γ photon in a LCS γ-ray beam of E m maximum energy. Thus, the L(E γ , E m ) distributions contain also the secondary photons generated in the target by electromagnetic interactions of the incident photon beam, as described in Ref. [18]. We notice that the low energy, secondary photon contribution is increasing with the incident beam energy and with the increase in the target thickness. The NewSUBARU electron beam bunches have a 500 MHz frequency (2 ns interval) and 60 ps width. The Q-switch mode operated lasers produced photon pulses 40 to 60 ns wide. Thus, the pulsed time structure of the γ-ray beam follows the one of the laser beam. The Poisson fitting method [20] associated to pulsed beams has been used for precise determination of incident LCS γ-ray beam flux, with characteristic uncertainties between 1 % and 3 %, also for time dependent incident flux [21]. The incident flux on the 208 Pb targets was of ∼10 5 γ/s below S 2n and ∼10 4 γ/s above S 2n .

Neutron detection and multiplicity sorting
Neutron-multiplicity sorting experiments involve the recording of neutron coincidence events, where by i-fold coincidence neutron events we refer to events of detecting i neutrons during a given LCS γ-ray beam interval. In order for the neutrons detected in the same interval to have been emitted in reactions induced by the same γ-ray pulse, it is necessary that the time interval between two γray pulses be of the order of the neutron die-away time in the detector. Thus, based on simulation and experimental investigations [14,15,22], the time interval between consecutive pulses was set to 1 ms by operating the laser at a low 1 kHz frequency.
Based on the number of i-fold events (n i ), we extract the primary experimental quantities, which are the i-fold where n T is the concentration of target nuclei, N γ is the incident photon number and ξ = [1 − exp(−µL)]/µ is a thick target correction factor given by the target thickness L and attenuation coefficient µ. The experimental i-fold cross sections for the 208 Pb(γ, xn) reactions are shown in figure 4. In low reaction rate conditions, one can disregard events in which multiple reactions are induced in the target by the same photon pulse. In such a single-firing approximation, the σ γ, xn cross sections for the (γ, xn) photoneutron reactions can be obtained through the direct neutronmultiplicity sorting method [14], which basically involves solving directly the following set of equations: where N is the highest neutron emission multiplicity order, ε is the constant neutron detection efficiency and x C i is the binomial coefficient. However, the γ-rays multiplicity follows the Poisson distribution, with a typical mean number of ∼10 photons per pulse. Thus, multiple-firing events can't be completely eliminated. Their contribution depends on the partial cross sections, areal density of target material and number of incident photons per pulse. Multiple firings are visible in figure 4(c) from the non-zero N 3 cross sections below the three neutron separation energy S 3n . Such 3-neutron coincidence events originate from combinations of (γ, n) and (γ, 2n) reactions induced by the same γ-ray pulse.
Thus, we applied a statistical treatment of neutron coincidence events [15], which models the multiple-firing of all available combinations of photoneutron (γ, xn) reactions. Using the minuit package of ROOT, a χ 2 minimization procedure is performed to determine the multiplefiring corrected 208 Pb(γ, xn) cross sections and average photoneutron energies from the measured i-fold cross sections (N i ) and average energies (E i ). We note that the ringratio method is separately applied on i-fold coincidence events to obtain the corresponding E i average energies. The 208 Pb(γ, xn) cross sections and average neutron ener-  γ, 4n). The present preliminary results (black) are compared with the TENDL2019 evaluation and with existing positron in flight annihilation data of Saclay [3] (red) and Livermore [4] (blue), LCS γ-ray beam data of Teras [24] (yellow) and bremmstrahlung data [25] (green). gies represent the free parameters in the minimization procedure, while the target characteristics (n T , ξ), the multiplicity distribution of incident LCS γ-rays and the number of incident multi-photon γ-ray pulses are fixed to experimentally determined values.
Despite the good energy resolution of the incident LCS γ-ray beams and the concentration of spectral density in the maximum energy region of the spectra, the measured cross section is in fact the convolution, or folding, between the true excitation function and the energy distribution of the incident beam shown in figure 3. The experimental 208 Pb(γ, xn) excitation functions were thus obtained by unfolding the measured multiple-firing corrected cross sections, following the iterative procedure described in Ref. [23].

Preliminary GDR cross sections for 208 Pb
The present preliminary 208 Pb(γ, n) cross sections shown in figure 5(a) are in good agreement with the positron in flight annihilation data of Saclay [3] (red triangles) on the entire GDR energy region. A good agreement is found also with the LCS γ-ray beam data taken at Teras [24] (yellow triangles) using a high-efficiency moderated neutron detection array and the associated ring-ratio method. Our preliminary 208 Pb(γ, n) cross sections are higher than the Livermore ones (blue diamonds) in the GDR energy region between 11 and 17 MeV. In the low energy region close to the neutron separation energy, the Livermore cross sections are in agreement with the present ones and with the other existing data. The present preliminary 208 Pb(γ, 2n) cross sections shown in figure 5(b) are systematically higher than the Saclay ones. A better agreement is found with the Livermore results below the ∼18 MeV. Above ∼18 MeV, it is difficult to make a comparison because of the large statistical fluctuations of the Livermore results. Figure 5(c) shows the present preliminary 208 Pb(γ, 3n) cross sections, which slightly overestimate the Saclay results, the only existing (γ, 3n) data set. The present 208 Pb(γ, 4n) cross sections in the energy region up to 38 MeV are shown in figure 5(d).

Summary
We have measured the (γ, n), (γ, 2n), (γ, 3n) and (γ, 4n) cross sections for 208 Pb in the energy region between the neutron emission threshold and 38 MeV. The measurements made use of quasi-monochromatic LCS γ-ray beams produced at the NewSUBARU synchrotron radiation facility and of a high-and-flat efficiency moderated neutron detection array of 3 He counters. The neutron multiplicity sorting was performed with an associated statistical treatment of multiple-firing neutron coincidence events. The dedicated eliLaBr Monte Carlo LCS simulation code was used to reproduce the experimental response functions of the monitor LaBr 3 :Ce detector and thus obtain the energy spectra of the incident photon beams. Considering the spectral density of the incident photon beams, an energy unfolding procedure was applied to the measured cross sections.
The present preliminary 208 Pb(γ, xn) cross sections were compared with existing data. The (γ, n) cross sections are in good agreement with the Saclay results, while the (γ, 2n) cross sections reproduce the Livermore ones. A similar trend was observed also in the recent photoneutron cross sections measurements performed for the International Atomic Energy Agency (IAEA) coordinated research project on Updating the Photonuclear Data Library (CRP F41032) [10]. We plan to further investigate the resonant structure in the (γ, n) channel through an additional energy unfolding procedure based on the Taylor expansion method, which has been routinely used in the analysis of low energy LCS γ-ray beam photoneutron measurements in the vicinity of the S n [26,27].
This work was supported by a grant of the Ministry of Research, Innovation and Digitization, CNCS -UE-FISCDI, project number PN-III-P1-1.1-PD-2021-0468, within PNCDI III.