E.Vagena. S.Stoulos and M.Manolopoulou Average cross section measurement for 162Er(γ,n) reaction validated with theoretical calculations using TALYS E.Vagena. S.Stoulos and M.Manolopoulou Nuclear Physics Lab., School of Physics, Aristotle University of Thessaloniki, Greece

Introduction A method to calculate the effective cross-section of the photonuclear reaction 162Er(γ,n), using the experimental results from a photoactivation experiment at a medical Linac. No value for the 162Er(γ,n) reaction in EXFOR. The photonuclear cross-section of the heavy p-nuclei 162Er in the energy range near the neutron threshold is of particular interest in astrophysical studies. Why is the photonuclear cross-section data of 162Er important?

Description of the experiment SSD (source to surface distance) = 1 m Medical Linac head -rays Electron beam @ 15 MeV isocenter Target (W+Re) 1 mm University Hospital of Larisa: Elekta SL medical linac Eight metals are placed at the isocenter (SSD=1 m from the target). We studied one reaction per material. Reactions : 7 + 1 (197Au,75As,191Ir,55Mn,73Se,112Sn, 162Er) Duration of irradiation ~ 60 min  Photon dose 155 Gy. Endpoint of bremsstrahlung photons = 14 MeV. Δεσμη ε- 15 μεβ πεφτουν σε στοχο 1μμ W+Re + χανουν ενεργεια που εκπεμπεται με τη μορφη φωτονιων (ακτινοβολια πεδησης). End point energy?? διαμορφωση της δεσμης (παταω κουμπι) Ειδικοί κατευθυντήρες διαμορφώνουν τη γεωμετρία της εξερχόμενης δέσμης και ειδικά φίλτρα διαμορφώνουν την ποιότητα της εξερχόμενης ηλεκτρομαγνητικής ακτινοβολίας. Παραγωγη νετρονιων Οι αντιδρασεις τοσο των ηλεκτρονιων οσο κ των φωτονια με τα υλικα του επιταχυντη, απελευθερωνουν νετρονια. Για την παραγωγη νετρονιων απαιτειται ενεργεια φωτονια πανω απο καποιο κατωφλι, συνηθως για τα περισσοτερα μεταλλα ειναι > 5 MeV. Τα φωτονια που απαρτιζουν την θεραπευτικη δεσμη + τα παραγομενα νετρονια απο (γ,ν) αντιδρασεις, κατευθυνονται προς το ισοκετρο. Ο αριθμος γ>> αριθμο νετρονιων. Στο ισοκεντρο (δλδ σε αποσταση 100 ψμ απο το στοχο) τοποθετουνται οι στοχοι που εχουμε επιλεξει να ακτινοβοηθουν. Χρόνος ακτινοβόλησης ~ 60 min Δόση φωτονίων 155 Gy.

EXFOR cross-sections in the GDR region Photon fluence using photonuclear reactions We exploit the different threshold values of the photonuclear reactions (γ, n). The threshold values vary from 8.02 to 12.22 MeV EXFOR cross-sections in the GDR region Ir-191(γ,n) Προσδιορισαμε (9) αντιδρασεις νετρονιακης αρπαγης (ν,γ), απο οπου κ υπολογισαμε τη ροη νετρονιων για καθε αντιδραση. Για τον υπολογισμο της ροης χρησιμοποιησαμε την διορθωσμενη ενεργη διατομη λογω τπου ss effect. (ΣΧΗΜΑ) Σφαλματα Τα σφαλματα που υπεισερχονται στους υπολογισμους ειναι τα ¨...... Ni-58(γ,n)

γ-spectrometry measurements Aluminum cap Active Ge volume Inactive Ge volume γ-ray activity of the natEr target HPGe detector Due to the variety of the geometry of the thick targets, the photo-peak efficiency was calculated using GEANT4. Photon self-absorption and the True Coincidence Summing effect are considered. After ????

Bremsstrahlung spectrum at the isocenter Photon fluence using (γ,n) reactions Activity : Photon fluence : Effective cross section: Φ(Ε) is calculated with GEANT4 A detailed geometry of the ELEKTA SL medical accelerator is simulated The extra photon source from secondary photons is found negligible (<1 %) Linear fitting of the photon spectrum for E>8MeV Bremsstrahlung spectrum at the isocenter

Photon fluence using (γ,n) reactions The effective cross-section (σeff) is taken from: The EXFOR Library Gives cross-section for 197Au, 191Ir, 55Mn, 75As, 112Sn, 73Se, 58Ni 162Er is unknown The TALYS 1.6 model (we calculated the cross-section for all reactions) Nuclear physics input (γ-ray strength functions, ground state properties, nuclear level densities (default: Fermi-gas model), optical potential (default: Koning and Delaroche). The γ-ray strength function is the most important for the γ,n reactions (Khan et al.2005, Mei et al. 2015). γ-ray strength function: Five different approaches Kopecky-Uhl (Generalized Lorentzian) Brink-Axel (Default, Standard Lorentzian) Hartree-Fock-BSC Hartree-Fock-Bogolyubov Goriely’s hybrid model ] Khan, E., Goriely, S., & Allard, D., et al, Astropart. Phys. 23 (2005) 191 https://arxiv.org/pdf/1507.04916.pdf As shown in Fig. 4, the (p, γ) cross section is sensitive to the γ-ray strength function from about 2 MeV to very high energies and differences between cross sections predicted by TALYS using different γ-ray strength functions are particularly large at energies above 5 MeV.

Cross-section data: sensitivity to γ-ray strength function EXFOR vs TALYS 197Au,191Ir, 75As, 55Mn (γ,n) reactions are best described B-A model. 112Sn(γ,n) reaction is best described with the Hartree-Fock BSC (H-F). 74Se(γ,n) is best described with Hartree-Fock Bogolyubov (H-F-B). 58Ni(γ,n) reaction follows the approach Kopecky-Uhl &/or Goriely model (GLO). Odd-even nuclei (197Au, 191Ir, 75As, 55Mn) follow the Brink-Axel SLO model Even-even nuclei (112Sn, 74Se, 58Ni) are described by different models.

Photon fluence ± error (x 108 γ.cm-2s-1) Photon fluencies from (γ,n) reactions Photon fluencies calculated using experimental and modeled σeff Photon fluence ± error (x 108 γ.cm-2s-1) Reaction TALYS EXFOR 191Ir(γ,n)190Ir 1.998 0.103 1.669 0.099 197Au(γ,n)196Au 1.748 0.079 1.827 0.105 55Mn(γ,n)54Mn 0.503 0.032 0.627 0.044 75As(γ,n)74As 0.497 0.607 0.056 112Sn(γ,n)111Sn 0.198 0.027 0.205 74Se(γ,n)73Se 0.026 0.007 0.004 58Ni(γ,n)57Ni 0.028 0.003 0.022 Uncertainties Efficiency of the HPGe detector (3%) Peak area determination (< 8%) Half-life ( < 1%) γ-ray abundance ( < 1%) effective cross-section (~ 3 – 13%) Which is logical, since we calculated the TALYS cross section data based on the corresponding experimental cross-sections Good agreement between the two set of photon flux

Er-162 Photon fluence and effective cross section of Er-162 The photon fluence for the cut-off energy of Er-162 (9.2 MeV) is calculated by fitting a linear regression model . Photon fluence vs cut-off threshold Er-162 TALYS EXFOR Total photon fluence 1.19 (± 0.26) x108 162Er(γ,n) TALYS: σeff,calc = 93 (±21) mb Total photon fluence : 1.35(± 0.31) x108 162Er(γ,n) EXFOR: σeff,calc = 83 (±18) mb σTALYS,DIRECTLY = 87 (±4) mb

Photon fluence vs cut-off threshold Validation for known cross-sections Calculation of the σeff of the reactions 197Au(γ,n) (8.08 MeV) and 55Mn(γ,n) (10.23 MeV) Photon fluence vs cut-off threshold TALYS 197Au(γ,n) Effective cross-section (mb) TALYS Reactions Our method EXFOR 197Au(γ,n)196Au 160 ± 35 148 ± 7 55Mn(γ,n)54Mn 8.4 ± 1.8 7.5 ± 0.4 55Mn(γ,n)

7+1 targets are irradiated with an ELEKTA SL medical linac. Summary 7+1 targets are irradiated with an ELEKTA SL medical linac. Known cross-sectionfor the 7 targets are taken from TALYS and EXFOR. Unknown cross-section of 162Er (γ, n) is calculated from a linear fit between fluence and threshold energies. The average effective cross-section for 162Er (γ, n) for energy interval from 9.2 - 14 MeV is = 88 (±18) mb . Medical Linac, is an excellent photon source for photon nuclear experiments due to its excellent stability and reproducibility of the beam. the medical Linac, is an excellent photon source for photon nuclear experiments due to its excellent stability and reproducibility of the beam of medical Linac are good prerequisites for such experiments.

Calculation of the effective cross-section data - TALYS 1.6 Prediction regarding the (γ,n) reactions of the even-even nuclei:40Ca ,56Fe, 94Mo, 82Se, 154Sm, 120Sn Possible explanation for the differences occurring in even-even nuclei: Neutron-to-proton ratio 58Ni: neutron-to-proton ratio ≅ 1 -> K-U (GLO model) 112Sn: neutron-to-proton ratio = 1.3 -> H-F model 74Se: neutron-to-proton ratio = 1.3 -> H-F-B model To test the validity of the above assumption several even-even nuclei are tested. 40Ca: neutron-to-proton ratio = 1-> K-U 56Fe: neutron-to-proton ratio = 1.1-> K-U 94Mo: neutron-to-proton ratio = 1.3 -> H-F and/or H-F-B 82Se: neutron-to-proton ratio = 1.4 -> K-U 154Sm: neutron-to-proton ratio = 1.4 -> K-U 120Sn: neutron-to-proton ratio = 1.4 -> K-U

Erbium theoretical cross-section data Theoretical cross-sections calculations of each Er isotope (γ,n) 162, 164, 166, 167, 168, 170Er isotopes have been calculated using the TALYS 1.6 code. The five γ-strength functions have been considered. Comparison of the theoretical data with the only available experimental cross section set of natEr (γ,n). Since the 77% of natEr is even-even nuclei with neutron-to-proton ratio = 1.4, the For the 166Er (most abundant isotope), the B-A and K-U fits the data, as well. The H-F-B, B-A and K-U describes the 162Er(γ,n) reaction

odd-even nuclei

odd-even nuclei Possible explanation: neutron-to-proton ratio Mo-100: n/p = 1.4 Sn-120: n/p = 1.4 Possible explanation: neutron-to-proton ratio n/p ~ 1 -> SLO model n/p ~ 1.2-1.3 -> B-A model n/p ≥ 1.4 GLO model