Fission Product Yield Data for the Transmutation of Minor Actinide ...

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FIG. III.6. Dependence of chain yield on energy for the right hand side of the heavy peak. (for E n £ 20 MeV) or 3 (for E n ≥ 20 MeV) Gaussian functions: I Â 1 yi i= ( A- A+ D i ) Y( A) = exp - 2 2ps 2s i where I = 5 (E n £ 20 MeV) or 3 (E n ≥ 20 MeV) and A — = (A F – n – )/2 (A F is the mass of the fissioning nucleus). Due to the symmetry of the distribution, there are altogether 9 (for 5 Gaussians) or 6 (for 3 Gaussians) adjusted parameters: D 1 , (D 2 ), g 1 , (g 2 ), g 3 , s 1 , (s 2 ), s 3 , A — . The optimum parameters were obtained from a non-linear least squares fit using iteration procedures: ( k+ 1) C = C k ( k) T -1 ( k) -1 ( k) T -1 ( k) = C + ( F V F ) F V ( Y -Y ) V = ( F V C ( kT ) Y -1 ( k) 1 Y F ) - ( k+ 1) ( k) ( k) ( k) Y = Y = F C + Y V = F V F Y ( k) ( kT ) C where F is the sensitivity matrix of yield Y to parameters C. The initial values Y (0) were calculated according to the Wahl equations [III.10]. Although the iteration should proceed until convergence is reached, this point of termination was not always achieved. Experimental data have to be normally smoothed over several data points. Zöller data were generally smoothed over 7 points (in special cases over 9 points) in order to obtain i 2 Y FIG. III.7. Dependence of linear fit coefficients on mass A. convergence. Since the search for optimal multi-parameter values is a complex process, the solution is not always unique. The parameters must be chosen from several possible solutions to maintain the systematic behaviour for each parameter at different energy points and require extensive and sometimes complicated calculations. Reduced c 2 for the final fit is smaller than 1.0 for all energy points. (2) Each parameter was fitted at different energy points by the least squares method with a second order function y = a + bx s1 + x s2 , where s can be either ‘+’ or ‘–‘, to reduce c 2 . The 9 parameters were fitted in the energy region from 0 to 20 MeV, and 6 parameters from 20 to 200 MeV. Results are given in Figs III.9–III.17 for 0–20 MeV, and in Figs III.18–III.23 for 20– 200 MeV. (3) Experimental mass distribution data measured by means of the kinetic energy method (on which our systematics is based) have been compared with the data calculated using adjusted and systematics parameters, and are given in Figs III.24–III.39. The latter can generally reproduce the former, except for some differences at 50 and 63 MeV. (4) Comparisons of various experimental mass distribution data measured with the radiochemical method and the data calculated with adjusted and systematics parameters are given in Figs III.40–III.47. Some systematic differences can be seen to occur. Mass distributions calculated with systematics at the two wings are normally narrower, especially the right side of the heavy mass peak, that can be attributed to a systematic difference between 325
TABLE III.1. LINEAR–LINEAR FIT COEFFICIENTS a, Da AND b, Db AND c 2 , y = a + bE Mass A Coeff b × 100 Uncertainty of b × 100 Coeff a Uncertainty of a c 2 80 4.4132E–01 1.0115E–01 5.6516E–02 6.5807E–03 1.65 82 5.6911E–01 6.3240E–02 1.7571E–01 1.4361E–02 2.02 84 1.4603E+00 1.7245E–01 3.0392E–01 1.4381E–02 1.44 86 1.9988E+00 2.0858E–01 6.2864E–01 2.0406E–02 3.47 88 1.6561E+00 2.3028E–01 1.2312E+00 2.8319E–02 6.27 90 2.7170E+00 2.7671E–01 2.0500E+00 3.5437E–02 5.18 92 2.9007E+00 3.0633E–01 3.1690E+00 4.2809E–02 4.23 94 1.5419E+00 3.1440E–01 4.5368E+00 5.0596E–02 4.19 96 –7.7440E–01 3.1551E–01 5.9457E+00 5.7003E–02 6.85 98 –4.2976E+00 3.0693E–01 6.9091E+00 6.0986E–02 2.52 100 –8.0050E+00 2.9082E–01 7.2704E+00 6.2008E–02 0.98 102 –8.5889E+00 2.8456E–01 6.6210E+00 5.9408E–02 5.92 104 –7.0673E+00 2.6536E–01 5.1893E+00 5.4007E–02 3.67 106 –3.0285E+00 2.4897E–01 3.3087E+00 4.5019E–02 4.08 108 1.9644E–01 2.3865E–01 1.7823E+00 3.4151E–02 5.19 110 3.7744E+00 2.4096E–01 6.0791E–01 2.2114E–02 5.51 112 5.8563E+00 2.7011E–01 8.1563E–02 1.1849E–02 6.57 114 5.2108E+00 2.5001E–01 –6.4665E–02 6.8609E–03 18.17 116 4.3468E+00 2.3856E–01 –5.0020E–02 4.7802E–03 14.28 118 4.6524E+00 2.4572E–01 –3.5454E–02 4.4867E–03 25.48 120 5.2324E+00 2.6143E–01 –3.0769E–02 5.1275E–03 14.33 122 5.4493E+00 2.8323E–01 9.0936E–03 7.0759E–03 4.86 124 5.8781E+00 2.9366E–01 1.4210E–01 1.2195E–02 3.62 126 8.1932E+00 3.4988E–01 3.7731E–01 1.7625E–02 1.23 128 9.7178E+00 3.5540E–01 1.3911E+00 2.9412E–02 0.90 130 8.1890E+00 3.5279E–01 3.0181E+00 4.2131E–02 1.55 132 3.7598E+00 3.3305E–01 4.9461E+00 5.2346E–02 10.81 134 –1.8240E+00 3.1795E–01 6.4860E+00 5.8729E–02 4.39 136 –7.1292E+00 2.9066E–01 7.2812E+00 6.2137E–02 2.19 138 –9.4191E+00 4.0504E–01 7.0728E+00 5.5668E–02 1.79 140 –1.0385E+01 2.5022E–01 6.2269E+00 5.9467E–02 5.48 142 –8.9264E+00 2.2096E–01 4.8041E+00 5.3829E–02 4.51 144 –7.7906E+00 1.7982E–01 3.4683E+00 4.6910E–02 1.78 146 –5.6127E+00 1.4270E–01 2.2820E+00 3.9816E–02 4.58 148 –3.4833E+00 1.1200E–01 1.3802E+00 3.2122E–02 5.46 150 –1.3995E+00 9.5925E–02 7.0814E–01 2.3825E–02 2.34 152 –5.9363E–01 8.0314E–02 3.6077E–01 1.7377E–02 2.26 154 –2.7922E–01 5.8022E–02 1.6458E–01 1.2399E–02 2.51 Note: Average c 2 for all mass A is 5.32. 326
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Fission Product Yield Data for the
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AFGHANISTAN ALBANIA ALGERIA ANGOLA
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COPYRIGHT NOTICE All IAEA scientifi
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CONTRIBUTING AUTHORS Denschlag, J.-
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3.2.1. Introduction . . . . . . . .
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6. BENCHMARK EXERCISE . . . . . . .
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However, this CRP entered an entire
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‘Provisional masses’ are determ
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Three scientists were invited to pa
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8 (d) Prompt or delayed neutron emi
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[2.1.40] ITKIS, M.G., OGANESSIAN, Y
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[2.1.96] PATE, B.D., et al., Distri
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[2.1.152] JACOBS, E., et al., Produ
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16 2.2. MEASUREMENTS OF THE ENERGY
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FIG. 2.2.3. 94 Sr: best experimenta
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FIG. 2.2.15. 132 Te: best experimen
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FIG. 2.2.27. 146 Ba: best experimen
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3. EVALUATIONS 3.1. ACTINIDE NUCLEO
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3.1.2. Statistical model At least t
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J Â K=-J 2 2 2 ^ sym Krot ( U, J)
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nuclei with N > 144. However, for h
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neutron number. The observed fissio
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FIG. 3.1.6. 235 U(n,f) fission cros
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FIG. 3.1.10. 237 Np(n,f) fission cr
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from higher fission chances [3.1.43
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[3.1.48] DUSHIN, V.N., et al., Stat
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where Y S is our new standard, and
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TABLE 3.2.2. EVALUATED REFERENCE FI
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TABLE 3.2.2. EVALUATED REFERENCE FI
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TABLE 3.2.3. EVALUATED REFERENCE YI
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TABLE 3.2.3. EVALUATED REFERENCE YI
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The comparisons of our evaluated da
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TABLE 3.2.4. COMPARISON OF RECOMMEN
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TABLE 3.2.8. COMPARISON OF THE UNCE
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REFERENCES TO SECTION 3.2 [3.2.1] I
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where N C , N U are the modified an
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activities were recorded with a pro
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3.3.4. Results and discussion The r
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FIG. 3.3.10. Li Ze et al. data: com
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96 Annex 3.3.1 EVALUATED EXPERIMENT
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Li Ze et al. [3.3.8] Thierens et al
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100 Annex 3.3.3 EVALUATED DATA SET
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The range of target nuclides availa
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condensation of cross-sections by t
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(h) REFERENCE (C,80KIEV,171,1980) i
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uncertainties of the calculation. T
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4. SYSTEMATICS AND MODELS FOR THE P
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FIG. 4.1.2. 235 U total cross-secti
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FIG. 4.1.9. Total and mode separate
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4.2. SYSTEMATICS OF FISSION PRODUCT
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A - = (PA - NT)/2 (4.2.1b) 4.2.2.3.
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FIG. 4.2.4(a). 238 U + 5.5 MeV n, L
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FIG. 4.2.8(a). U238 + 300 MeV p, LS
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TABLE 4.2.1. EQUATIONS FOR SYSTEMAT
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values (points) and the derived fun
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distributions. Values of N(A) seldo
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FIG. 4.2.19. Systematic Z P paramet
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FIG. 4.2.21. Systematic Z P paramet
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FIG. 4.2.23. Nuclear charge displac
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FIG. 4.2.24. Number of protons emit
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epresenting model values and thus s
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FIG. 4.2.36. n T(A) for CF249T. FIG
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FIG. 4.2.41. U235T, line: model; po
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The FAST subroutine in the CYFP pro
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[4.2.28] BELHAFAF, D., et al., Kine
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4.3. FIVE GAUSSIAN SYSTEMATICS FOR
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Derived from measured data Fitted r
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FIG. 4.3.7. Mass distribution of 23
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FFIG. 4.3.12. Mass distribution of
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4.4. PHENOMENOLOGICAL MODEL FOR FRA
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where = 2mE is the wavelength, E
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FIG. 4.4.4. Fragment mass distribut
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fragment mass distributions are des
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FIG. 4.4.10. Fragment mass distribu
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P LD È Ê * E - 44. 7ˆ ˘ = Í1 +
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FIG. 4.4.13. Pre-neutron emission m
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FIG. 4.4.15. Post-neutron emission
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FIG. 4.4.17. Post-neutron emission
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fragment mass and charge distributi
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of the energy dependence of the fus
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4.5. MODAL APPROACH TO THE DESCRIPT
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This information was used for the p
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two neighbouring isotopes at differ
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FIG.4.5.2. Experimental relative ma
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Frequently, the yields Y i (M) are
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the nine optimum description parame
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TABLE 4.5.6. RELATIVE CONTRIBUTIONS
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TABLE 4.5.8. RELATIVE CONTRIBUTIONS
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Extracted values of s 2 M,S demonst
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FIG. 4.5.10. Fission fragment charg
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FIG. 4.5.12. Unchanged charge densi
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FIG. 4.5.16. Mass yield variance fo
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FIG. 4.5.20. Experimental mass yiel
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[4.5.24] GOVERDOVSKII, A.A., MITROF
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TABLE 4.6.1. FISSION PRODUCT YIELD
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TABLE 4.6.2. FIT PARAMETER VALUES O
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FIG. 4.6.2. Charge distributions fo
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model which is elucidated elsewhere
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the agreement is better. The observ
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inner barrier is much lower than th
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e determined in a self-consistent m
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FIG. 4.6.11. Overview of the coupli
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cross-section also has to be incorp
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FIG. 4.6.16. Same as Fig. 4.6.15, b
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FIG. 4.6.20. Pre-neutron emission m
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present have a reasonable contribut
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TABLE 4.6.5. ACCURACIES OBTAINED FR
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[4.6.7] BEIJERS, J.P.M., et al., Se
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5. NEW MODELS AND SYSTEMATICS: DEFI
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therefore his benchmark calculation
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mass distributions and practically
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5.2. BENCHMARK EXERCISE 5.2.1. Benc
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thorough and detailed analysis of t
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the fissioning nucleus and the numb
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should be undertaken — such a stu
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experimental method in order to der
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256 Valley heights and peak-to-vall
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FIG. 6.2.3. Benchmark exercise, par
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260 Wahl uncert. margins Wahl uncer
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262 Wahl uncert. margins Wahl uncer
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264 Wahl uncert. margins (adj. Wahl
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Wahl (1.6-160 MeV): Distributions a
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TABLE 6.2.2. 238 U PRE-NEUTRON EMIS
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as most features are very similar t
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FIG. 6.2.14. Benchmark exercise, pa
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Page 289 and 290: 278 REFERENCES TO SECTION 6 [6.1] B
Page 291 and 292: As mentioned above, the mass distri
Page 293 and 294: I.3.2.6. Liu Conggui et al. [I.8] M
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Page 297 and 298: 286 Zöller (1995) 89-110 MeV, post
Page 299 and 300: (1) Data were linearly interpolated
Page 301 and 302: 1. 290 Annex to Appendix I RECOMMEN
Page 303 and 304: 1.2. E n = 5.5 MeV 292 Nagy et al.
Page 305 and 306: 1.3. E n ª 8 MeV 294 Chapman (1978
Page 307 and 308: 1.5. E n = 14-15 MeV 296 Daroczy et
Page 309 and 310: 1.7. E n = 27.5 (22-33) MeV, Zölle
Page 311 and 312: 1.9. E n = 99.5 (89-110) MeV, Zöll
Page 313 and 314: 3. 302 239 Pu NEUTRON INDUCED FISSI
Page 316 and 317: Appendix II DATA ADJUSTMENT FOR MAS
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Page 320 and 321: Annex 1 to Appendix II ADJUSTED DAT
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Page 324 and 325: E n = 50 (45-55) MeV Post-neutron e
Page 326 and 327: Äystö et al. (1998) [II.9] E p =
Page 328 and 329: E n = 1.60 MeV Pre-neutron emission
Page 330 and 331: E n = 27.5 (22-33) MeV Post-neutron
Page 332 and 333: E n = 99.5 (89-110) MeV Post-neutro
Page 334 and 335: Appendix III FISSION YIELD SYSTEMAT
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Page 340 and 341: FIG. III.14. Dependence of paramete
Page 342 and 343: FIG. III.26. Comparison of the mass
Page 344 and 345: FIG. III.38. Comparison of the mass
Page 346 and 347: TABLE III.3. QUADRATIC FUNCTION FIT
Page 348 and 349: Uncertainty ratio or uncertainty Ad
Page 350: CONTENTS OF THE CD-ROM The attached
Page 353: This publication reports on a coord
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