Microsoft PowerPoint - 共鳴チュートリアルv.ppt
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1 共鳴公式とパラメータ評価 原研リニアックと ORELA での経験 平成 18 年 月 1 日核データ チュートリアル原子力機構先端基礎交流棟大会議室 原子力機構水本元治 1
2 講義内容 1. 中性子反応断面積と中性子共鳴とは. 中性子共鳴断面積の測定実験 3. 共鳴パラメータ ( ブライト ウィグナーの公式 ) 4. 共鳴パラメータの解析例 5. まとめ
![反応の収量 Y ab dl [ ] 1 s N dl n σ cm x 毎秒標的核 1](/docs-images/82/86785331/images/3-4.jpg "個当たりに起こる反応の数断面積 σ ab 毎秒 1cm 当たりに入射する粒子の数面積の次元")
3 中性子反応と断面積 a + X Y + b X ( a, b) Y 弾性散乱 非弾性散乱核変換 ( 捕獲 吸収 分裂 ) a: 入射粒子 X: 標的核 Y: 残留核 b: 放出粒子 n a a b σ N ab x 反応の前後で保存エネルギー ( 質量を含む ) 運動量 角運動量 電荷 核子数 パリティー 反応の収量 Y ab dl [ ] 1 s N dl n σ cm x 毎秒標的核 1 個当たりに起こる反応の数断面積 σ ab 毎秒 1cm 当たりに入射する粒子の数面積の次元 (cm ) を持つ 通常 10-4 cm ( バーン ) a ab 3
4 水素 (Hydrogen) σ s 0.491±0.014b σ γ 0.336±0.0007b 水素 炭素 鉄の中性子反応断面積 (JENDL3.3) 炭素 (Carbon) 鉄 (Ion) E H 850keV t303 (s33,p14,d18) E L MeV ~0 resonances σ s 4.740±0.005b σ γ 3.50±0.07mb D o 17±keV D 1 4.0±0.4keV σ s 1.46±0.49b σ γ.59±0.14b 4
5 149 Sm とウランの中性子断面積 Sm E H 50eV 158 resonances σ s 9.38±0.09b σ γ.680±0.019b σ s 197b σ γ ±600b D o.±kev nat U 35 U 38 U D o 0.44±0.06eV D o 0.9±1.16eV D 1 7.±0.4eV E H.5keV 3165 resonances E H 10keV s473,p119 resonances 5
6 Cross Section (b) 中性子捕獲断面積 37 Np JENDL-3.3 熱中性子領域 JENDL-3.3 ENDF/B-VI, JEFF-3 Stupegia+('67) Lindner+('76) Weston+('81) Trofimov+('83) Buleeva+('88) Buleeva+('88) Kobayashi+('93) Smith+('57) Tattersall+('60) 共鳴領域 Resonance Region Neutron Energy (ev) Cross Section (b) 連続領域 Np Capture JENDL-3.3 JENDL-3.3 Point Weston+('81) Neutron Energy (ev) 37 Np の捕獲断面積
7 中性子反応 E n n + A X E n D 10 ev σ Sn H:.5MeV 1 C: 4.946MeV 56 Fe: 7.646MeV 149 Sm: 7.985MeV 35 U: 6.546MeV 38 U: 4.806MeV ターゲット核 (Target Nucleus) S n 4~10 MeV α γ 線を出して崩壊 D 100 kev Fission 中性子結合エネルギー (Neutron Binding Energy) A+1 X 複合核 (Compound Nucleus) 7
8 共鳴理論 Breit-Wigner 公式 G. Breit and E.P. Wigner Phys. Rev., 49, 519 (1936). σ n, x ( E) π k 共鳴パラメータ J と L ごとに E, Γ n, Γ x g J l J r ( E を評価 Γ E r nr ') Γ xr Γ r 8
9 Eugene Paul Wigner (November 17, 190 January 1, 1995) was a Hungarian physicist and mathematician who received the Nobel Prize in Physics in 1963 "for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles". In 1939 and 1940, Dr. Wigner played a major role for a Manhattan Project. In 1946, Wigner accepted a job as director of research and development at Clinton Laboratory (now Oak Ridge National Laboratory) in Oak Ridge, Tennessee. Wigner returned to teaching and research at Princeton University. Eugene Wigner Gregory Breit (July 14, 1899 September 11, 1981) was an Russian-born American physicist, professor at universities in New York, Wisconsin, Yale, and Buffalo. Together with Eugene Wigner he gave a description of particle resonant states. During the early stages of the war, Breit was chosen to supervise the early design of the first atomic bomb during an early phase in what would later become the Manhattan Project. Gregory Breit Gregory_Breit 9
10 複合核準位 λ が形成される確率振幅 F λ (E) 全系の波動関数準位 λの波動関数 F λ exp( iet / h) Ψ( E) exp( iwt / h)x λ 波動関数の時間によらない部分確率振幅 S ( E) α βα, res βα, res 0 ( E) F e λ e 複合核過程の断面積 π S k λ dt iet / h iw t / h h 1 1 ( E) k ( E E ) + Γ α ( E) 1 E W W E iγ ( Γ > 0 ) λ λ λ λ λ λ i 1 E W λ / 4 λ X λ, Ψ( E) λ Resonance Off-Resonance Sn 10
11 JENDL3.3 の共鳴順位のデータの例 ( nat Fe の全断面積 ) K.Shibata et al.,j.nucl.sci.technol.,39(00)115 11
12 JENDL3.3 Resonance Parameters of 109 Ag (Example) ZA AWR ABN (Abundance) NIS(No. of Isotopes) MT151 LRU Resolved resonance) NLS (No. of l) MF ZAI(Z,A) EL SPI EH AP (Radius) LRF(MLBW) NER NRO NRS 6*NRS ER i AJ i GT i GN i GG i GF i MAT (Material No.) i 以下略 1
13 Breit Wigner の一準位公式 ( 共鳴間 反応間の Interference( 干渉 ) がない場合 ) 散乱断面積 ( E Eλ )sinkr Γ λ ( 1 cos kr ) 4 sin kr + Γ λn ( E E + λ ) 1 / 4Γ λ σ n,n( E ) π D ( Γ λn ) ( E Eλ ) + 1 / 4Γ λ 捕獲断面積 Γ λnγ λx σ n,x ( E ) πd ( E Eλ ) + 1 / 4Γ λ 全断面積 σ E ) σ ( E ) + σ ( E ) n,t ( n,n n, γ + ピーク断面積 散乱 σ 0 n σ 0 σ 0 Γ Γ n 捕獲 6 gγ n. 608* 10 A + 1 4πD Γ E ( ev ) A 0 σ 0 γ σ 0 gγ Γ Γ Γ n λ 13
14 中性子強度関数 S-wave S l gγ l n ( l + 1)D l ( l 1 + 1) ΔE j g j Γ l nj S 0 g 0 Γ n D 0 Reduced Neutron Width Γ l nj 1eV Γ E V nj l 1eV Γ 0 nj Γ E g nj 0 j Γ nj E g jγ nj E S 0 D 0 Average level spacing D l Spin statistical weight factor g J + 1 J + 1 J ( i + 1)( I + 1) ( I + 1 ) 14
15 共鳴パラメータのコンピレーション 1. Said. F. Mughabghab et al.: Neutron Cross Sections, Vol. 1, Part A, Z1-60, Academic Press (1981). Neutron Cross Sections, Vol. 1, Part B, Z61-100, Academic Press (1984). S.I. Sukhoruchkin et al.: Low Energy Neutron Physics, Landolt-Börnstein (1998) 3. Said F. Mughabghab : Atlas of Neutron Resonances : Resonance Parameters and Thermal Cross Sections. Part A: Z1-50. Part B: Z51-100(HRD) /Publisher:Elsevier Published 006/03 ( 出版予定 ) US$ 参考書 J.A.Harvey ed., Experimental Neutron Resonance Spectroscopy, Publisher: Academic Press
16 JAERI LINAC Resonance Experiments Energy10MeV Flight path 40m, 55m, 190m Rep10-600pps Pulse width0ns-0us FP(Ag,Eu,Nd,Sm,Cs, 38 U 16
17 The Oak Ridge Electron Linear Accelerator (ORELA) (n.γ) 40 station Flight path #7 150 MeV e - linac. Δt 30 ns. P < 60 kw. Rate Hz. 11 Flight Paths. 8-18, 0, 35, 40, 85, 150, and 00 m flight stations. Transmission ORELA 06,07,08 Pb, Capt., Trans. 159 Tb, Capt. 136 Xe,Capt, Trans 17
18 全断面積の測定 L190m Neutron Source Sample Detector Start:T 0 Stop:T s E 1 mv 1 L 7. 3 m t t s L t0 L: Flight Path Length T: Flight time (T s -T 0 ) 18
19 全断面積 ( 透過率測定 Transmission)
20 Transmission Experiment T trans ( ( I I in out Bkg Bkg in out ) / ) / mon mon in out exp( nσ t ) σ t 1 log( T n trans ) T trans : Transmission σ t : total cross section n:sample thickness I in : sample in counts I out :sample out counts Bkg in :Background (to sample in) Bkg out :Background (to sample out) mon: monitor counts 55 Mn(336eV) 59 Co(13eV) 109 Ag(5.19eV) 115 In(1.457eV) Thermal Bump Sample Changer to compensate the neutron fluctuation Black Resonance Filter Method for Background Determination 0
21 捕獲 散乱断面積測定 m 捕獲断面積測定装置 3500l LLSD 47m and 55m flight station 47m 散乱断面積測定装置 6 Li 検出器 1
![反応の収量 x a ab [ s ] 1 cm C ss C ms Y dl N dl n](/docs-images/82/86785331/images/22-2.jpg "σ C ss : Self-shielding Correction C ms :")
22 捕獲断面積測定 Sample thickness correction is necessary ab 反応の収量 x a ab [ s ] 1 cm C ss C ms Y dl N dl n σ C ss : Self-shielding Correction C ms : Multiple scattering correction C ss C ms
23 散乱断面積測定
24 核分裂断面積測定
25 Resolution Broadening E 1 mv 1 L 7. 3 m t t L m 938( MeV ) /(, ( m / s )) /(, ( m / s )) kg kg Target (Moderator) de / E ( dt / t ) + ( dl / L ) ) 1 / ) 1 / ( dt /( 7. 3* L )* E ) + ( dl / L ) n Sample (Detector) f Lc ( E ) Δ Lc Δ Lc 1 E 3 π de " ( E E ) exp ΔLc [( Δt / t ) + ( ΔL / L ) ] c " f ( E " ) 5
26 Doppler Broadening σ m : M : k T D : : ( E ) 4mEkT ΔD M mass of neutron, t Δ arg et Boltzmann' effective D 1 π mass, s de " cons tant, temperature exp of ( E n " Δ sample D E ) σ ( M material E Thermal Motion " ) 6
27 コード (SAMMY) によって 再現された 149 Sm 共鳴 σ 0 γ σ 0 Γ Γ λ σ 4πD 0 gγ Γ n A + 1 A. 608* 10 E ( ev ) gγ Γ n 0 6 g 0 j Γ nj E g jγ nj E S 0 D 0 7
28 Sm 共鳴パラメータ BNL-35 Γ γ : constant Γ n is proportional to Sqrt(En) 8
29 Sm and 149 Sm 共鳴解析 Nuclear Physics A357(1981)90 9
30 Pb 全断面積と捕獲断面積 ORELA Exp Phys. Rev. C19 (1979)
31 実験解析コード Atta-Harvey : Trans. Single Level B-W, Area Analysis, Atta-Harvey SIOB: Trans. Multi-Level B-W, Shape Analysis, de Saussure et al. TACASI: Trans, Capt., Self Indication, Single Level B-W, Shape&Area, Frohner LSFIT: Cap. Single Level B-W, Shape&Area, Macklin SAMMY: Trans. Capt. Fission etc., Reich Moore, Larson Resonance-resonance interference Resonance self-shielding Doppler broadening Multiple scattering Experimental resolution broadening Normalization, Background Fitting 31
32 Sammy R-M MLBW Reich-Moore 公式 C.W. Reich and M.S. Moore Phys. Rev., 111, 99 (1958) In the MLBW approximation, all off-diagonal elements of level matrix A are neglected. In the RM approximation, only those off-diagonal elements arising from photon channels are neglected. The MLBW formulation does not include level-level interference nor the multi channel features of RM For isolated resonances of non-fissile nuclei, the values for these parameters would be equal in the two cases. 3
33 Area Analysis 38 U 66.01eV 注意 Capture ker nel A A γ γ gγ /( 1+ gγ /( gγ )) γ < gγ γ A γ γ gγ Γ /( Γ n n γ n + Γ ) γ 原子力学会誌 Vol.3 (1981) 709 中川等 33
34 Area Analysis の例 M.Ohkubo J.Nucl.Sci.Technol.16(1979)701 34
35 SIOB Analysis( サンプルの厚さによる効果 ) gγ n 5.6meV Γγ3.5meV gγ n 4.meV gγ n 0.83meV 35
36 SIOB Analysis for 107 Ag and 109 Ag For analyses, Γγ130meV for 107 Ag Γγ140meV for 109 Ag are assumed 36
37 Cumulative Level Fig. 4a. gγ n0 versus energy for levels in 147 Sm. The slope gives the s-wave strength function. Fig. 4b. gγ n0 versus energy for levels in 149 Sm. The slope gives the s-wave strength function. The dotted line shows a simple average. 37
38 S- 波強度関数 図 s- 波中性子強度関数の実験と理論の比較 実験と波線はそれぞれ変形 球形核光学モデルの計算による 38
39 P- 波強度関数 図 P- 波中性子強度関数の実験と理論の比較 実験と波線はそれぞれ変形 球形核光学モデルの計算による A160 近傍にある小さなピークは Buck と Perey によって予想された 4P 巨大共鳴の回転分離による 39
40 Level Missing for 107 Ag and 109 Ag Moore procedure for missing resonances using the moments of the reduced neutron width distribution. truncated Porter Thomas distribution 0 0 ( ω )( ω gγ ) / ( ω gγ ) i i ni i ni ( ) Weight ω i for -wave contribution is calculated by Bayes theorem D0eV for 107 Ag D0eV for 109 Ag 40
41 Porter Thomas Distribution Measured at 55m flight path P ( x ) 1 π x e x x Γ Γ n 0 n 0 Chi-squared distribution with the degree of freedom ν1 Fig. 5b. Histograms of observed (gγ n0 MeV) 1/ values for 149 Sm The results for two choices of upper limits are shown. NP, A357(1981)90 41
42 Wigner Distribution Measured at 190m flight path P( D ) π D D e D π D The behavior of the eigenvalues of a symmetric matrix with random Gaussian distribution 原子力学会誌 Vol3(1981)64 4
43 S- 波中性子平均放射幅の質量依存性 実線は実験データをなぞる S- 波平均放射幅 x e x ) x, P( 1 ν ν ν ν Γ π ν 放射幅の分布
44 P- 波の平均放射幅 P- 波中性子平均放射幅の質量依存性 44
45 D- 波平均放射幅 D- 波中性子平均放射幅の質量依存性 実線は計算値 45
46 Different sample thickness SIOB 148 Sm m flight path Maximum energy 8.4keV JAERI memo (1986) 46
47 Tb Capture Cross Section With LSFIT Phys.Rev.C17(1978)5 47
48 136 Xe 93.6% enrich Transmission of 136 Xe+n SAMMY Analysis (a) The resonance near 18.4 kev is not larger than the resolution of 0.1%. The curve shows a p l/ assignment and gives a better fit than p 3/. The 134 Xe resonance near 17.7 kev has a width exceeding the resolution. The peak cross section is proportional to the statistical weight factor which gives a unique p3/ assignment. (b) The strong resonance near 480 kev could not be fitted with a single p 3/ resonance. (c) It was necessary to introduce a p 1/ resonance with the same energy to obtain the reproduction of the transmission dip. Phys. Rev. C31 (1985) 041 The 137 Xe neutron resonances can be excited through beta decay from 137 I. 48
49 Sammy R-M MLBW 49
50 共鳴領域の核分裂断面積 Cross Section (b) U(n,f) JENDL-3. (R-M) JENDL-3.1 (B-W) 84 Weston+ 88 Schrack Neutron Energy (ev) 50
51 まとめ共鳴測定の今後の課題 BGO サプレッサ 高精度化放射性核種の測定 ( 微少サンプル 高中性子束 バックグランドの低減 ) Minor Actinide クラスター検出器 クローバー検出器 全立体角型多重ガンマ線検出装置 LLFP Long Lived Fission Product 8530y,3x10 6 y 51
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