ガンマ線強度関数法によるアプローチ H. Utsunomiya (Konan University) Outline 1.Methodology of the  SF method 2.Applications to unstable nuclei along the valley of  -stability 3. comments on a versatile application based on Coulomb dissociation experiments 2011 年度核データ研究会プログラム 2011 年 11 月 16 日 ( 水 ) – 17 日 ( 木 ) 日本原子力研究開発機構テクノ交流館リコッティ Approach by the  -ray strength function method

Collaborators H. Utsunomiya a), H. Akimune a), T. Yamagata a), H. Toyokawa c), H. Harada d), F. Kitatani d), Y. -W. Lui e), S. Goriely b) I. Daoutidis b), D. P. Arteaga f), S. Hilaire g), and A. J. Koning h) a)Department of Physics, Konan University, Japan b)Institut d’Astronomie et d’Astrophysique, ULB, Belgium c) National Institute of Advanced Industrial Science and Technology, Japan d) Japan Atomic Energy Agency, Tokai, Naka-gun, Ibaraki , Japan e) Cyclotron Institute, Texas A&M University, USA f) Institut de Physique Nucléaire, Université Paris-Sud, France g) CEA,DAM, DIF, Arpajon, France h) Nuclear Research and Consultancy Group, The Netherlands

Radiative neutron capture cross sections for unstable nuclei in nuclear engineering and nuclear astrophysics Direct measurements at CERN n-TOF, LANSCE-DANCE, Frankfurt-FRANZ and J-Parc ANNRI facilities can target some of unstable nuclei along the valley of  -stability if samples can be prepared. ---> s-process Indirect experimental method is called in for unstable nuclei along the valley of  -stability ---> s-process, neutron-rich region ---> r-process surrogate reaction technique ANY OTHER?

follows the statistical model of the radiative neuron capture in the formation of a compound nucleus and its decay by using experimentally-constrained  SF.  -ray strength function method H. Utsunomiya et al., PRC80 (2009) n + A X A+1 X E, J,  A X(n,  ) A+1 X Radiative neutron capture continuum  SF NLD decay process

Total  transmission coefficient  - ray strength function nuclear level density X=E, M =1, 2, …  SF method neutron resonance spacing low-lying levels source of uncertainty Hauser-Feshbach model cross section for A X(n,  ) A+1 X After integrating over J and π

 -ray strength function: nuclear statistical quantity interconnecting (n,  ) and ( ,n) cross sections in the HF model calculation n+ A X A+1 X E, J,  A X(n,  ) A+1 X A+1 X( ,n) A X Photoneutron emission Radiative neutron capture Brink Hypothesis continuum

SnSn GDR PDR, M1 Structure of  -ray strength function Primary strength E1 strength in the low- energy tail of GDR Extra strengths 6 – 10 MeV

SnSn ( ,n) GDR Methodology of  SF method STEP 1 Measurements of ( ,n) c.s. near Sn A-1 A A ( ,n)  SF STEP 1

SnSn Methodology of  SF method STEP 2 Normalization of  SF Extrapolation of  SF by models SnSn ( ,n) GDR A-1 A A ( ,n)  SF STEP 1

JUSTIFICATION BY REPRODUCING KNOWN (n,  ) C.S. Methodology of  SF method STEP 2 known (n,  ) SnSn SnSn ( ,n) GDR A-1 A A ( ,n)  SF STEP 1

neutron capture by unstable nucleus Methodology of  SF method STEP 3 (n,  ) to be determined A+1 A+2 ( ,n) STEP 3 A+1 X(n,  ) A+2 X known (n,  ) A-1 A A ( ,n) STEP 1 STEP 2 Extrapolation is made in the same way as for stable isotopes. ( ,n) GDR SnSn STEP 1 STEP 2  SF

6 6 Sn h d y 108 Pd y d 96 Zr y 80 Se d d Applications LLFP (long lived fission products) nuclear waste Astrophysical significance Present ( ,n) measurements Existing (n,  ) data H.U. et al., PRC82 (2010) H. Utsunomiya et al., PRC80 (2009) H.U. et al., PRL100(2008) PRC81 (2010) To be published F. Kitatani et al. (n,  ) c.s. to be deduced

Inverse Compton Scattering  = E e /mc 2 “photon accelerator” Laser Compton scattering  -ray beam

=1064, 532 nm AIST (National Institute of Advanced Industrial Science and Technology)

Detector System Triple-ring neutron detector 20 3 He counters (4 x 8 x 8 ) embedded in polyethylene

6 6 Sn h d Applications 7 H. Utsunomiya et al., PRC, in press (2011) H. Utsunomiya et al., PRC80 (2009)

STEP 1 Measurement of ( ,n) cross sections Sn isotopes

HFB+QRPA E1 strength supplemented with a pygmy E1 resonance in Gaussian shape E o ~ 8.5 MeV,  ~ 2.0 MeV,  o ~ 7 mb ~ 1% of TRK sum rule of GDR STEP 2 – Extrapolation of  SF to the low-energy region HFB+QRPA + PDR

STEP 2 – Justification of the extrapolated  SF

STEP 3 – Statistical model calculations of (n,  ) cross sections for radioactive nuclei 121 Sn[T 1/2 =27 h] 123 Sn[T 1/2 =129 d] Uncertainties: 30-40% Uncertainties: a factor of 3

93 Zr[T 1/2 =1.5×10 6 y] Results for Zr isotopes long-lived fission product nuclear waste

95 Zr[T 1/2 =64 d] s-process branching 30-40% uncertainties

107 Pd[T 1/2 =6.5×10 6 y] long-lived fission product nuclear waste 30-40% uncertainties stem from NLD

Coulomb dissociation in the  SF method (n,  ) to be determined by  SF method A A A+1 ( ,n) by Coulomb dissociation s-process branching nucleus

s-process branching nuclei F. Käppeler et al., Rev. Mod. Phys. 83, 157 (2011)

Coulomb dissociation experiments s-process branching nucleihalflife(yr)Coulomb dissociation (n,  ) data 134Cs,135Cs2.0652, 2.3× Cs,135Cs,134Cs133Cs 152Eu* Eu, 152Eu151Eu 154Eu,155Eu8.593, Eu,155Eu,154Eu153Eu 160Tb Tb,160Tn159Tb 163Ho Ho,166Ho165Ho 170Tm,171Tm0.352, Tm,171Tm,170Tm169Tm 179Ta Ta,182Ta181Ta 204Tl Tl,204Tl203Tl 11 branching nuclei 18 Coulomb dissociations F. Käppeler et al., Rev. Mod. Phys. 83, 157 (2011)

Ambitious application of the  SF method to the r-process The astrophysical significance is controversial ！ BUT this would be the first application to a very neutron-rich nucleus. A pioneering work is in progress. 1) A systematic study of the  SF for Sn isotopes 116Sn,…., 124Sn (7 stable) → → → 132Sn 132Sn( ,n) data: GSI Coulomb dissociation data for 132Sn 131 Sn(n,  ) 132 Sn cross sections in the r-process nucleosynthesis

Summary  SF method: (n,  ) c.s. for unstable nuclei 1. Nuclear Physics Experiment: ( ,n) c.s. measurements real photons for stable nuclei virtual photons for unstable nuclei (CD) 2. Nuclear Theory: models of  SF models of NLD primary strength: low-energy E1 of GDR extra strengths: PDR, M1 3. Coulomb dissociation experiments play a key role in a versatile application of the  SF method. SAMURAI + RIKEN-RIBF ALADIN +

Neutron beam Photon beamRI beam Determination of (n,  ) CS for unstable nuclei 直接測定 ガンマ線強度関数法 ( ,n) (n,  ) 原子力核データ、宇宙核物理（ s-process ） along the valley of  -stability 宇宙核物理 r-process p-process far from stability

Comparison with the surrogate reaction technique Forssèn et al., PRC75, (2007) 93Zr(n,  )94Zr 95Zr(n,  )96Zr 1. The surrogate reaction technique gives larger cross sections by a factor of ~ 3 than the  SF method. The surrogate reaction technique gives similar cross sections to those given by the  SF method provided that a choice is made of the Lorentian type of  SF. Zr isotopes