Photoneutron Reaction Data for Nuclear Physics and Astrophysics

We discuss the role of photoneutron reaction data in nuclear physics and astrophysics in conjunction with the Coordinated Research Project of the International Atomic Energy Agency with the code F41032 (IAEA-CRP F41032). 1 PHOENIX Collaboration for the IAEACRP F41032 The Coordinated Research Project of the International Atomic Energy Agency with the code F41032 (IAEACRP F41032) was launched in 2016 as a 5-years project. The goal of the project is to publish two compilations of an updated photonuclear data library and a reference database of photon strength functions in 2020. We have established an experimental collaboration called the PHOENIX (PHOto-Excitation and Neutron emIssion cross [X] sections) Collaboration for the IAEA-CRP in the -ray beam line GACKO (GAmma Collaboration hutch of KOnan university) of the NewSUBARU synchrotron radiation facility in Japan [1]. The PHOENIX Collaboration is hosted by the Konan University; the collaboration involves the University of Oslo, ELI-NP (Extreme Light Infrastructure – Nuclear Physics), Moscow State University, Shanghai Institute of Applied Physics, Texas A&M University, Technische Universität Darmstadt, Université Libre de Bruxelles, and University of Hyogo. In this collaboration, we are measuring (,xn) cross sections with x=1–4 for the first compilation (photonuclear data) and (,1n) cross sections near oneneutron threshold for the second compilation (photon strength functions). A list of nuclei to be measured in the PHOENIX Collaboration is given in Table 1. Table 1. Nuclei covered by the PHOENIX Collaboration. Photonuclear data Photon strength functions 2015 Bi, Be Tl, Tl, Y 2016 Au, Tm, Y Os, Re, Ba, Ba, Ni, Ni, Ni, Ni, C 2017 Ta, Ho, Co W, W, W, Zn, Zn, Zn 2018 Tb, La, Rh Gd, Gd, Gd, Gd We provide (,xn) cross section data to resolve the long-standing discrepancy between the Livermore and Saclay data of partial photoneutron cross sections. In many cases, Saclay provided larger cross sections for (,1n) reactions than Livermore and vice versa for (,2n) reactions [2]. The ratio of the Saclay data to the Livermore data of integrated total cross sections, R S /L , varies from 0.65 to 1.35 over 19 nuclei from V to U. As shown in Fig. 1, the ratio for © The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/). EPJ Web of Conferences 178, 06003 (2018) https://doi.org/10.1051/epjconf/201817806003

integrated partial cross sections averaged over the 19 nuclei is very different; it is  R int (1n)  =1.07 and  R int (2n)  = 0.84 for the (,1n) and (,2n) reactions, respectively [3].We also provide (,1n) cross section for specific nuclei near the one-neutron threshold for an absolute normalization of the photon strength function below neutron threshold obtained with the Oslo method [4].Figure 2 shows the resulting photon strength function for 117 Sn constructed experimentally, showing the presence of an extra strength over the neuron threshold at 6.94 MeV that is attributed to a pygmy E1 resonance [5].We also provide (,1n) cross sections systematically over an isotopic chain to reach a unified understanding of (,n) and (n,) cross sections with the -ray strength function method [6,7].This method effectively deduces (n,) cross sections for radioactive nuclei involved in the isotopic chains as a result of this unified and comprehensive approach.
The PHOENIX Collaboration will continue after the IAEA-CRP.Nuclei for which (,xn) cross sections will be measured after 2018 may include 112 Sn, 116 Sn, 120 Sn, 124 Sn, 208 Pb, 232 Th, and 238 U.

Direct Neutron-Multiplicity Sorting with a Flat-Response Detector
We have long used a high-efficiency neutron detector of Livermore type to measure (,1n) cross sections near the one-neutron threshold.This detector consisting of three rings of total twenty 3 He proportional counters embedded in a polyethylene moderator has a strong dependence of the detection efficiency on neutron kinetic energies.We use the so-called ring-ratio (RR) technique developed at Livermore [8] to determine the mean kinetic energies of neutrons.However, because of the RR technique, we limited ourselves to (,1n) cross section measurements below the two-neutron threshold, where the number of detected neutrons is equal to the number of (,1n) reactions.In the one-neutron channel, the ring ratio can surely determine the mean kinetic energies of neutrons produced in the (,1n) reaction.However, when we go above the two-neutron threshold, we immediately encounter an essential problem with the RR technique because there is no way to know in what reaction neutrons are produced and detected.
Let us consider measurements of (,xn) cross sections with neutron-multiplicity x=1-3 with a neutron detector of Livermore type by using a pulsed -ray beam.The frequency of the pulsed beam is typically 1ms because of the long neutron-moderation time of the polyethylene.During the 1ms time-interval between two successive ray pulses, we detect neutrons.According to the number of detected neutrons (n), let us name neutron events as single (N s ), double (N d ), and triple (N t ) events corresponding to n=1, 2, and 3, respectively.The neutron events are expressed as follows.  Here N x (x=1,2,3) is the number of (,xn) reactions induced by -ray pulses and E ij is the kinetic energy of the j-th neutron emitted in the (,in) reaction.Note that the neutron detection efficiency (   ) depends on the neutron kinetic energy.
In the triple neutron event, obviously all of the first-, second-, and third-emitting neutrons are detected when the (,3n) reaction takes place.The second term of the double neutron event means that the first-and secondemitting neutrons are detected, while the third-emitting neutron is undetected when the (,3n) reaction takes place.The single neutron event consists of six terms in which the third term means that the second-emitting neutron is detected, while the first-emitting neutron is undetected when the (,2n) reaction takes place.Note that kinetic energy of the j-th emitting neutron is, in principle, different from that of the k-th (  k  j) emitting neutron.Thus, the RR technique, which is applied to the experimental quantities, N s , N d , and N t , does not work to determine neutron kinetic energies.
One can immediately see that the only solution to determine the number of (,xn) reactions is to make the neutron detection efficiency (  ) independent of neutron kinetic energies.In this case, the neutron events are expressed as follows.  Now one can solve a set of Eqs. ( 4), ( 5), and ( 6 We have developed a flat-response neutron detector (FRD) for (,xn) cross section measurements in the IAEA-CRP [9].The detector consists of three concentric rings of 4, 9, and 18 3 He counters embedded in a 46 cm (horizontally) x 46 cm (vertically) x 50 cm (along the beam axis) polyethylene moderator at the distances of 5.5, 13.0 and 16.0 cm from the -ray beam axis, respectively.Figure 3 shows a photograph of the flatresponse detector.
The total and partial detection efficiencies of the FRD are shown in Fig. 4 along with results of the calibration with a 252 Cf source and GEANT4 simulation.
The emission rate of the 252 Cf source was calibrated at the National Metrology Institute of Japan.Results are plotted at the average energy (3/2) of the 252 Cf neutron spectrum corresponding to the temperature  =1.42 MeV [10], where the fission spectrum is given by the Maxwell-Boltzmann distribution, () ∝  1∕2 ⋅ exp(−∕).The GEANT4 simulation was performed for monochromatic neutrons (dotted lines) and neutronevaporation spectra (solid lines) expressed by () ∝  ⋅ exp(−∕) with the Weisskopf-Ewing model [11].Results for the evaporation spectra are shown at the average neutron energy (2).The total efficiency for the evaporation spectra average over the energy range of 0.01 -5.0 MeV is 36.5 % with one standard deviation of 1.6%.The neutron energy range was investigated for 209 Bi(,xn) reactions at 40 MeV by means of a Monte Carlo statistical model calculation [12].The calculation shows that the mean neutron energy for the (,xn) channel with x=2-5 lies within the energy range.The neutron angular distribution effect on the detection efficiency was investigated for isotropic s-and anisotropic p-wave neutrons with respect to the linear polarization of the laser Compton-scattering -ray beam.It was confirmed that the FRD has nearly identical efficiencies for s-and p-wave neutrons, where the strong spatial anisotropy in the p-wave neutron emission is smeared out during the thermalization of neutrons in the moderator.This is a common feature of moderationbased neutron detectors of the Livermore type.
Figure 5 shows distributions of the arrival-time of neutrons at the FRD for single, double, and triple neutron events in the 209 Bi(,xn) reaction at 34 MeV.Time distributions of the 1 st -and 2 nd -arriving neutrons and the 1 st -, 2 nd -, and 3 rd -arriving neutrons are also shown for the double and triple neutron events, respectively.It was found that the sum distribution is EPJ Web of Conferences 178, 06003 (2018) https://doi.org/10.1051/epjconf/201817806003CGS16 best fitted with a linear combination of two exponential functions with time constants, ~10s for the fast component and ~100s for the slow component, respectively.One can see that the major part of the 1 starriving neutrons is well characterized by the fast component, while the 2 nd and 3 rd components by the slow component.The fast component may represent neutron detection with the first ring located at 5.5cm, while the slow component neutron detection with the second and third rings at 13 and 16cm.The arrival-time distribution is a good subject to investigate by a Monte Carlo simulation.

New 209 Bi(,xn) data
The technique of the direct neutron-multiplicity sorting was first used to measure 209 Bi(,xn) cross sections [13] in the IAEA-CRP.Figure 6 shows partial photoneutron cross sections obtained in the new measurement in comparison with the TALYS [14] calculation of the giant-dipole resonance (GDR) and quasi-deuteron component [15,16].The GDR cross section was obtained within the Hartree-Fock-Bogolyubov plus quasiparticle random phase approximation approach on the basis of the D1M Gogny interaction both for the E1 [17] and M1 [18] components.See Ref. [13] for details.

Fig. 1
Fig. 1 The ratio of the Saclay data to the Livermore data of integrated cross sections, R int  S int / L int , for (,1n) (open squares) and (,2n) (solid triangles) reactions.

Fig. 2 (
Fig. 2 (color online) Photon strength function for 117 Sn constructed from the photoneutron data and the data of the Oslo method.
) to determine N 1 , N 2 , and N 3 , the numbers of (,xn) reactions (x=1,2,3) induced by the -ray beam from the experimental quantities, N s , N d , and N t .Note that   is now a constant.It is straightforward to determine (,xn) cross sections (   xn ) by  xn  N x /(N   N T ) with the number of -rays (  N  ) incident on target nuclei (  N T ) per unit area.

Fig. 4
Fig. 4 Total and partial detection efficiencies of the flatresponse neutron detector for neutron-evaporation spectra (solid lines) and monochromatic neutrons (dotted lines).

Fig. 5 (
Fig. 5 (color online) Arrival-time distributions of neutrons detected with the flat-response detector for single (a), double (b), and triple (c) neutron events in the 209 Bi(,xn) reactions at 34 MeV.For the double neutron events, the arrival-time distribution is shown for the 1 st -(blue) and 2 nd -arriving (green) neutrons as well as the sum neutrons.Similarly, for the triple neutron events, the arrival-time distribution is shown for the 1 st -(blue), 2 nd -(green), and 3 rd -arriving (orange) neutrons as well as the sum neutrons.The best fits to the single (a), double sum (b), and triple sum events (c) are shown by the red lines.

Fig. 6 (
Fig. 6 (color online) Comparison with the present partial photoneutron cross sections with the TALYS calculation with the default preequilibrium parametrization (solid lines), the modified Levinger parameter L=20 with (dotted lines) and without (dashed lines) surface effects (E surf = 1 MeV).

3. 1
Puzzle of the 209 Bi(,1n) cross sectionWhile the (,xn) cross sections with x=2, 3, and 4 are reasonably well reproduced by the TALYS calculation with the default preequilibrium parametrization (solid lines), the large (,1n) cross section above 25 MeV is highly puzzling.The standard statistical model predicts small (,1n) cross sections (3-4 mb) in this energy range.Furthermore, it is kinematically considered that kineticenergies of neutrons emitted in the (,1n) channel are very large; they are outside the energy range (0.01 -5.0