Xi Tao CNDC/CIAE - KNUanrdw-3.knu.ac.kr/resources/PDF/32-VII.5_aprml_Xi_Tao.pdf · 1 Xi Tao (...
Transcript of Xi Tao CNDC/CIAE - KNUanrdw-3.knu.ac.kr/resources/PDF/32-VII.5_aprml_Xi_Tao.pdf · 1 Xi Tao (...
11
Xi Tao(CNDC/CIAE) Chonghai Cai (Naikai University)
Qingbiao Shen( CNDC/CIAE) E-mail:[email protected]
2012.08.29
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Outline
APRML code Background Introduction of APRML code R-matrix theory in APRML
n+6Li reaction Reaction channel Input files and parameters Results
Summery
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Background
International 1936, Breit G. and Wigner E. P R, r-matrix theory, describe resonance. 1958, Lane A. M. and Thomas R. G. , a class paper for r-matrix theory. SAMMY(1980-Now), resonance parameters. EDA: The Energy Dependent Analysis code,developed by D.
Dodder, G. Hale and K. Witte at Los Alamos. n+12C, minus energy level.
In China Chengjiu Zhu(朱诚久)、Guochn Qiu(丘国春)、Weili Sun(孙伟力)、
Zhenpeng Chen(陈振鹏)、Hongwei Wang(王宏伟) RAC code: Zhenpeng Chen(陈振鹏) ,used for light nuclei
CNDC LUNF can calculate light nuclei reaction cross section and double
differential cross section, but can not deal with resonance cross section.
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Introduction of APRML
Adjusting Parameters of R-Matrix for Light nuclei in 1p-shell. Chonghai Cai(Nankai University), Qingbiao
Shen(CNDC/CIAE), Xi Tao(CNDC/CIAE) Base on R-matrix theory Light nuclei in 1p-shell Cross section of 2-bodys reaction Angular distribution (n,tot),(n,el),(n,non),(n,γ),(n,inl),(n,p),(n,t),(n,3He),(n,α),(n,d),(n,5He),(n,X)
Auto adjusting parameters
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Theory 《低能和中能核反应理论》
Low and moderate energy nuclear reaction theory 《高等量子力学讲义》
Advanced quantum mechanics 《中子引发轻核反应的统计理论》
Neutron induced nuclear reaction statistics theory in light nuclei 申老师和蔡老师的报告
Reports of professor Qingbiao Shen and Chonghai Cai
Structure of APRML Codes:APRML.for, plot.for, compiled by fortran Input files:APRMLk.dat ,APRMLi.dat Output files: APRML.dat, APRMLo.dat, APRMLs.dat,APRMsa.dat plot.dat, plot.gnu
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S-matrix
Total wave function after reaction:
Integral cross section formula:
Neutron injected
⎭⎬⎫
+⎩⎨⎧ −
+=Ψ
∑
∑
'''''''''',''''
0)(
)('
1)(1
12
jln
JMjlnll
Jnljjln
JMnljll
iJMIMjm
jmiml
ljJM
t
iFGSv
iFGv
eCClkri
l
Ii
i
i
ααααα
σ
ϕϕ
π
-
2
,'''',''''''
2222,''
ˆˆˆ
1 Jnljjlnnljjln
Jjljlnn SJ
Iik αααααα δπσ −= ∑
( )∑ −=ljJ
Jljt SJ
Ik)Re(1ˆ
ˆ2
22
πσ
∑ ∑ −=ljJ jl
Jljjlljjlel SJ
Ik ''
2
,'',''2
22ˆ
ˆ2δπσ )||1(ˆ
ˆ22
'',''
222
)( ∑∑ −=jl
Jljjl
ljJ
nne SJ
Ikπσ
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R-matrix
Element of S-matrix:
Minus energy level used:
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
−+−++= ∑+−
λλλλ
λλφφ
Γ∆
ΓΓδ
2
21
21
' ,','
)(0'' iEE
ieSS cccc
icccc
cc
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
Γ−−
ΓΓ+= ∑+−
λλλ
λλφφ δ
2
21
21
' ,','
)(' iEE
ieS cccc
icc
cc
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Parameters in element of S-matrix: Phase of hard sphere scattering
Resonance width matrix
⎟⎟⎠
⎞⎜⎜⎝
⎛=
c
cc G
Farctanφ
)( ccc kaFF = )( ccc kaGG =
)( 3/13/1Tpcc AAra +=
2)(2 ccc EP λλ γ=Γ 2 2( ) cc
c c
kaP EG F
=+
Adjusting parametersAdjusting parametersAdjusting parametersAdjusting parameters
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Formula of angular distribution
Ω+
Ω+
Ω=
Ω dd
dd
dd
dd )3(
,'')2(
,'')1(
,'','' nnnnnnnn αααααααα σσσσ
nnnnCnn
vzZef αααα
αα δθµ
δθσ
,''4
2
2
2
,''2
)2(,''
2cosec
2)(
dd
⎟⎟⎠
⎞⎜⎜⎝
⎛==
Ω
( )] )(cos 1Reˆ
2cosec
2ˆˆdd
2sinln
2)(2
2
22
2
22,''
)3(,''
20
θ
θµ
δσ
θη
πσσ
αααα
lJlj
iii
ljJ
nnnn
PSeJ
vzZe
kIi
l
−⎢⎢⎣
⎡
=Ω
⎟⎠⎞
⎜⎝⎛+−−
∑
∑∞
=
+=Ω 0
)1(,'' )(cos)12(
41
dd
LLL
nn PBL θπ
σ αα
( ) ( )[ ]*,'''',''''
)(,'''',''''
)(
2121212121212
''''
122
'
2
2
22222222
'221
11111111
'11
2222211111
Re
)'';''''''();()12()12(ˆˆ)1(
Jjnljlnjnljln
iJjnljlnjnljln
i
JjljlJjljl
IiIi
L
SeSe
LIiJJjjllAiILJJjjllAJJIik
B
llllαααα
σσαααα
σσ δδ
π
−−
++−
=
+−+
−−+
∑
coherent of coulomb and reaction
Coulomb part
Reaction part
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APRML(characteristic) APRML considers all reaction channels. Total width is equal to the sum of all channels.
All parameters correlate. Adjusting one parameter, and all cross section changed.
cc
λ λΓ = Γ∑
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Content
APRML code Background Introduction of APRML code R-matrix theory in APRML
n+6Li reaction Reaction channel Input files and parameters Results
Summery
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Reaction channels
Experimental data
Structure parameters
CalculationComparison
Results
Adjusting parameters
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Particles outgoing process of n+6Li reaction
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n+6Li reaction channels choosed
The 8th channel use a fake 2-bodys channel instead. The 8th channel use a fake 2-bodys channel instead. The 8th channel use a fake 2-bodys channel instead. The 8th channel use a fake 2-bodys channel instead. n+n+n+n+6666LiLiLiLi****The 1st channel include elastic scatteringThe 1st channel include elastic scatteringThe 1st channel include elastic scatteringThe 1st channel include elastic scattering
((((n,tot)(n,el)(nn,tot)(n,el)(nn,tot)(n,el)(nn,tot)(n,el)(n, , , , γ)(n,inl)(n,p)(n,t)(n,a)(n,nda)(n,inl)(n,p)(n,t)(n,a)(n,nda)(n,inl)(n,p)(n,t)(n,a)(n,nda)(n,inl)(n,p)(n,t)(n,a)(n,nda))))
n+6Li→7Li*→
γ+7Li 0
n+6Li 1
p+6He 2
d+5He 6 7
t+α 3 5
n+d+α 8
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Experimental data used
Cross section (n,tot) EXFOR (n,el) EXFOR(in high energy)
ENDF/B-VII.1(low energy) (n, γ) ENDF/B-VII.1 (n,inl) ENDF/B-VII.1 (n,p) EXFOR (n,a) EXFOR, used (n,t) instead (n,nda) d outgoing data in EXFOR
Angular distribution DA of (n,el), 1964 R.O.Lane DA of (n,a), 1974 J.C.Overley
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Elastic scattering distribution in EXFOREntry 年代 作者 文献 能点
10415 1961 R.O.Lane (J,AP,12,135,196102) 0.225,0.235,0.245,0.255,0.265,0.275MeV
10710 1979 H.D.Knox (J,NSE,69,223,197902) 4.08,4.26,4.57,4.83,5.05,5.29,5.54,5.74,6.05,6.37,6.66,6.94,7.32,7.50
10854 1980 P.W.LISOWSKI (R,LA-8342,8010)(P,NEANDC(E)-194,78)
5.96,9.83
10904 1982 A.B.SMITH (J,NP/A,373,305,8201)(R,ANL-NDM-52,8002)
1.50,1.59,1.72,1.82,1.87,2.00,2.10,2.30,2.40……3.70,3.817,3.90,4.00
10914 1979 H.KNOX,R.O.LANE (C,79KNOX,783,7910)(J,BAP,23,942(DC2),7811)
2.30,2.80,3.31,3.83,4.08
11092 1976 H.B.WILLARD (J,PR,101,765,56) 0.210,0.258,0.300
11153 1968 J.C.HOPKINS (J,NP/A,107,139,6801) 4.83,5.74,7.50
11170 1964 R.O.Lane (J,PR,136,B1710,1964) 0.20,0.25,0.30,0.32,0.35,0.40,0.45,0.50,0.60,0.70,0.80,0.90,1.00,1.10,1.20……2.0
20376 1967 H.H.KNITTER (R,EUR-3454E,6704) 1.0,1.1,1.2,1.33,1.4,1.5……2.00,2.09,2.19,2.30
20492 1973 F.DEMANINS (R,INFN/BE-73/2,7306) 1.98,2.24,2.49,2.74,2.98,3.2,4.1,4.64
20749 1977 H.H.KNITTER (R,EUR-5726E,1,7704) 0.233,0.248,0.266,0.296,0.323,0.338,0.353,0.390,0.450,0.500,0.550,0.600,0.650,0.700,0.750,0.800,0.850,0.900,0.950,1.00,1.10,1.20,1.33,1.4,1.5……2.00,2.09,2.19,2.30,2.50,2.60,2.70,2.80,2.90,3.00
21147 1963 R.BATCHELOR (J,NP,47,385,6309) 3.35,4.00,5.15,6.36,7.54
21276 1971 M.CANCE (P,EANDC(E)-140,115,7108) 6.00
21986 1985 S.Chiba (J,NST,22,(10),771,198510) 4.2,5.4,14.2
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Angular distribution of (n,t) in EXFOR年代作者 能点 参考文献 Entry
2007 M.Devlin+ 1.10e6--4.50e6 C,2007NICE,,(563),2007 14159
2006 Guohui Zhang+ 1.05e6 1.54e6 2.25e6 J,NSE,153,41,2006 32651
2003 Guohui Zhang+ 1.85e6 2.67e6 J,NSE,143,(1),86,200301 32646
2000 Guohui Zhang+ 3.67e6 4.42e6 J,NSE,134,312,2000 32544
1988 S.Shirato+ 1.41e7 C,88MITO,,249,198805 22361
1988 A.Trzcinski 1.81e7 T,Trzcinski,1988 30943
1986 C.M.Bartle 2.16e6 1.37e7 J,RE,95,331,1986 30918
1982 H.G.Knox+ 2.00e6 3.50e6 J,BAP,27,703(DE12),8209 12974
1982 S.Higuchi+ 1.41e7 J,NP/A,384,(1),51,198208 21694
1981 J.C.Engdahl+ 2.28e4 J,NSE,78,44,198105 10755
1979 C.M.Bartle 2.16e6 9.66e6 J,NP/A,330,1,197910 10446
1977 E.Rosario-Garcia+ 4.71e6 7.25e6 J,NP/A,275,453,1977 10632
4.37e6 7.27e6 10632
1977 R.E.Brown+ 8.70e4 3.98e5 J,PR/C,16,513,7708 10866
1974 J.C.Overley+ 1.00e5 1.90e6 J,NP/A,221,573,197403 10382
1.00e5 1.90e6 10382
1967 D.Rendic+ 2.70e6 1.44e7 R,ZFK-130,143,196712 30193
1965 G.Robaye+ 2.50e5 3.90e5 6.00e5 C,65ANTWERP,,500(18),6507 20262
1963 Y.Baudinet-Robinet+ 1.90e5 J,JPR,24,803,6311 20196
1960 V.P.Perelygin+ 2.15e6 J,AE,9,(6),488,6012 40455
1959 S.J.Bame Jr+ 1.50e5 5.65e5 J,PR,114,1580,59 11103
1954 G.M.Frye Jr 1.41e7 J,PR,93,1086,195403 11071
1954 J.B.Weddell+ 1.10e6 1.50e6 2.00e6 J,PR,95,117,5407 11076
1953 L.E.Darlington+ 2.70e5 4.00e5 6.00e5 2.00e5 J,PR,90,1049,5306 11065
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Resonance energy level
-2.2175 -1.3967 -0.5758 0.245 1.82 3.18 3.51 3.57 5.17 5.9908 6.8117 7.6325
1minmax
−−
=∆N
EEE
Fake
Real
Fake
Fake energy level formula
EEEEEEEEEEEEEEEEEE
N
N
N
∆+=∆+=∆+=∆−=∆−=∆−=
+
+
+
32
23
min6
min5
min4
min3
min2
min1
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Parameters used in calculation
ridus 4 (n,el) non threshold, 9 (n, γ) non threshold , 9 (n,inl) 2.186MeV, 4 (n,p) 3.183MeV, 3 (n,a) non threshold , 9 (n,nda) 1.721MeV, 5
Total parameters: 43
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1st input file
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2nd input file
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Total cross section
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Total cross section
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Elastic scattering cross section
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Elastic scattering cross section
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Cross section of (n,t)
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Cross section of (n,p)
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Cross section of (n,dx)
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200keV 250keV
350keV
450keV
Elastic angular distribution
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600keV 800keV
1.5MeV 2.0MeV
Elastic angular distribution
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(n,a) angular distribution
100keV
150keV
260keV
1.00MeV
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(n,a) angular distribution
1.5MeV 1.7MeV
1.8MeV 1.9MeV
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Summary
APRML is a nuclear reaction code for calculating and fitting light nuclei cross sections, developed at CNDC and NanKai University.
APRML was compiled and adjusted less than a year, many mistakes and bugs have been fixed. The code has been compiled and some functions are under debugging and testing.
APRML is used to calculate and fit n+6Li reaction. Preliminary result is given. The shapes of cross sections roughly agree with experimental data, but the angular distribution result is not well.
In future, We will deal with the problems and fix bugs, and we hope this code will be used for light nuclei reaction evaluation.
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