- Email: [email protected]
Calculated beta-ray spectra from decay of fission products produced by thermal-neutron fission of 235U
Volume 113B, number 3
PHYSICS LETTERS
17 June 1982
CALCULATED BETA-RAY SPECTRA FROM DECAY OF FISSION PRODUCTS PRODUCED BY THERMAL-NEUTRON FISSION OF 235U
J.K. DICKENS Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA Received 29 January 1982 Revised manuscript received 22 March 1982
Beta-ray spectra from decay o f fission products created by thermal-neutron fission o f :~3sU have been calculated using summation techniques and using an independently created beta:ray data file. The calculated beta-ray spectra are in very good agreement for E# -- 1 to 8 MeV with recently measured spectra o f beta rays for two very different exposure and counting time conditions: (a) an "instantaneous" spectrum following a 1.5 day exposure, and (b) an 8 s counting-time spectrum obtained 1.7 s following a 1 s exposure o f 235U by thermal neutrons.
_
Recently Schreckenbach et al. [1] at the Institute Laue Langevin (ILL) obtained experimentally the/3ray spectrum from decay of fission products produced during a 1.5 day exposure of 235U by thermal neutrons. The reported [ 1] experimental data were obtained primarily to provide an experimental basis for the determination of the associated antineutrino spectrum. For such determination the reported [1 ] ~-ray spectrum can be considered a de facto "benchmark" data set, such that computations of a reactor-produced antineutrino spectrum should also provide a reactorproduced/3-ray spectrum in agreement with the experimental data. For any such calculations the quality of agreement of the computed/3-ray spectrum with the "benchmark" data should be indicative of the reliability of a computed antineutrino spectrum, which might be applied, for example, to recent measurements [2,3] of antineutrino-induced reactions and the interpretations of these experiments. In the present report the ILL data [1] are compared with predictions using a summation computer code and files of basic nuclear data recently assembled by the author [4] ,1. In fig. 1 the data [1] are compared with spectra calculated for three conditions: (a) the triangles (zx) represent the predicted spectrum for/~ rays following decay of 278 fission products for ,1 The data file is available from the ORNL Radiation Shielding Information Center (RSIC) u p o n request.
0 031-9163182/0000-00001502.75 © 1982 North-Holland
~°°
4o -~
I
I
~
I
I
~
_
z o
4°-z --
C---
~ to-3 = _~ B
-
7-- t0-4
N
= -~0-5
4o-O
0
nTHERMAL EXPOSURETIME =t.5 days ~\~ ÷ EXPERIMENT (IL-L,~981) [ ~ PRESENT CALCULATIONS [ORNL, 1984) / [I ~i TOTAL SPECTRUM, 500 FISSION PRODUCTS [ PARTIAL SPECTRUM. 278 FISSloi~ PRODUCTS / - - - - PARTIAL SPECTRU[¢. 84As ,
I
I
'~
2
3
-
a
5
6
7
8
9
40
BETA-RAY ENERGY [MeV)
Fig. 1. Beta-ray spectra following a 1.5 day exposure o f 23SU by thermal neutrons. The solid points represent the data o f Schreckenbach et al. (ref. [ 1 ]). The lines and the open triangles (zx) indicate results o f present calculations. The solid line is the total predicted spectrum, while the triangles represent the portion due to 278 nuclides for which #-ray spectral information is known. Although not indicated as such, the triangles follow the dashed curve for E# > 8 MeV. The dashed curve represents the portion due to decay o f 84As, the dominant nuclide decay for large E#. All calculations use the R i d e r - M e e k evaluation o f fission-product yields (ref. [ 17 ]).
20]
Volume 113B, number 3
PHYSICS LETTERS
which the file contains data obtained from the literature on the energy, intensity, and forbiddeness (E~, 1~, FO) for individual/3-decay modes of these fission products; (b) the dashed line indicates the high-energy portion of the spectrum from decay of 84As, a fission product having a dominant high-energy known/3-ray transition (E¢ = 9.8 MeV, I# = 51%, and FI3 probably first-forbidden non-unique [5]); and (c) the solid line is the predicted spectrum which includes the data from the above mentioned 278 fission products plus using partial experimental and/or postulated nuclear data for an additional ~225 short-lived fission products produced by thermal-neutron fission of 235U having fractional yields >10 -6. The total spectrum compares very favorably with the experimental data [1 ], particularly in the highest energy region Et~ > 6.5 MeV. In this energy region, also, the partial spectrum (zx in fig. 1) agrees well with the experimental data, illustrating that for 6.5 ~
17 June 1982
main nearly 200 radionuclides (the "unknowns") for which only an average/3-ray energy, (E~), is entered in the data file. For nuclides having (Eta) determined from experiments [11,12], the experimentally derived (EI~) were used in the file. For all remaining fission products (E#)was obtained from the US ENDF/B-IV evaluation [13]. To utilize the 0V#) data for the "unknown" nuclides to determine a/3-ray distribution, a simple prescription was used [ 14]. This prescription involved computing the decay of an "unknown" fission product as a single allowed transition having an end point (Ej3)max such that the average energy of this allowed transition is equal to the (E~) given in the file. Essentially, it is assumed that the important part of the Gamow-Teller strength for beta decay is localized to an excited state in the daughter having a large overlap with, and the same parity as, the/3-emitting state of the parent. It is evident that this prescription biases against possible ground-state transitions and produces a total fission-product/3-ray spectrum which agrees with tabulated/3-ray spectral results of Klapdor and Metzinger [10] but is a much softer/3-ray spectrum (i.e. fewer high-energy/3 rays) than the spectra of refs. [7-9]. The justification of the use of this prescription is based upon the following considerations: (a) nearly all of the cumulative fission yields for 235Ufission for the "unknown" radionuclides are very small, <0.1% per fission; (b) the lack of highest-energy/3-ray transitions is in agreement with recent more detailed calculations of Klapdor et al. [ 15] and (c) as is evident from fig. l, in fact, the "benchmark" data are even softer than the present calculations and those of ref. [10]. A ~-ray spectrum [16] ,2 for very different irradiation and counting conditions than the spectrum in fig. 1 is shown in fig. 2 along with two full calculations. The time periods for the spectrum in fig. 2 enhance the contributions from the short.lived fission products. The two calculations shown in fig. 2 are for two different, and widely used, sets of evaluated fissionproduct yields [17,18]. The calculated spectra shown in fig. 2 rely somewhat more heavily upon the contributions from the postulated partial decay schemes and also the (Et3) for the "unknown" nuclides, especially ,2 Spectral data are availablefrom the ORNL Radiation ShieldingInformation Center upon request.
Volume 113B, number 3 too _--
I
I
PHYSICS
I
I
I
I
-
~. t0 .2
~£
iqTHERMA L + 235 U B E T A - R A Y Texposure = t . 0 sec Twaii = 1.7 sec
~0-3
":~,~,,
SPECTRUM
~+' ~
'TT'
Tcoun t = 8 . 0 sec ~, E X P E R I M E N T ( O R N L , 1980) PRESENT CALCULATIONS - USING E N D F / B - V YIELDS - - . . . . DSING AERE ( 1 9 7 ? ) Y I E L D S
1o-4 0
1
1
t
2
1
I
I
3 4 5 BETA-RAY ENERGY ( M e V )
I
I
B
7
17 June 1982
encountered are reflected in the assigneduncertainties. An important point is that for the data shown in both figures, all o f the calculated values are equal to or larger than the experimental data for E# > 6.5 MeV indicating a paucity of real high-energy 13-ray transitions from decay of "unknown" nuclides. The present calculations do not seriously underestimate the highenergy portion of the spectrum, as suggested by the authors o f ref. [9]. In summary,/3-ray spectra have been computed for two very different exposure and counting intervals, and the computed p-ray spectra are in very good agreement with recently measured/3-ray spectra [1,16]. The quality of agreement lends credence to the calculational methods and the evaluated nuclear data file given in ref. [4].
I
o_ _m u_
LETTERS
8
Fig. 2. Beta-ray spectra for a 1 s exposure of 23SUby thermal neutrons and a 1.7 s interval from the end of the irradiation to the start of an 8 s counting period. The solid points represent data obtained at ORNL (ref. [3]). The lines indicate results of present calculations, with the solid line indicating results using the Rider-Meek evaluation of fission-product yield (ref. [17]) and the dashed line indicating results using the Crouch evaluation of fission-product yields (ref. [18]).
for E~ > 6 MeV, than do the spectra shown in fig. 1, and so the agreement obtained tends to substantiate the decay characteristics postulated in the present data rifle. The half lives in the data file of the radionuclides contributing to the calculated spectra of fig. 2 are from experimental measurements; those half lives in thedata file which had to be obtained from theoretical estimates are all sufficiently short that the corresponding fission products substantially decay away during the 1.7 s waiting period following the irradiation. One may note similarities in calculated curves vis-avis both sets of experimental data [1,16]. As shown in both figures, the calculation is somewhat too large for E# ~ 3 to 3.5 MeV and somewhat too small for E# ~ 5 to 6 MeV. It seems likely that the sources of these small differences will be related to errors in the • nuclear data due to errors in original experiments. For E# > 6.5 MeV in fig. 2, experimental difficulties
F.C. Maienschein and P.H. Stelson (ORNL), P. Vogel (CalTech), R. Wilson (Harvard), and K. Schreckenbach (ILL) have been extremely helpful and their contributions are appreciated. This research was sponsored by the US Department of Energy, Office of Energy Research, under contract W-7405eng-26 with Union Carbide Corporation.
References [1] K. Scltreckenbach et al., Phys. Lett. 99B (1981) 25. [2] F. Boehm et al., Phys. Lett. 97B (1980) 310. [3] F. Reines, H.S. Sobel and E. Pasierb, Phys. Rev. Lett. 45 (1980) 1307. [4] J.K. Dickens, ORNL report no. ORNL/TM-8285 (1982), in preparation. [5 ] C.M. Lederer and V.S. Shirley, eds., Table of isotopes, 7th Ed. (Wiley, New York, 1978). [6] P. Hoff, K. Aleklett, E. Lund and G. Rudstam, Z. Phys. A300 (1981) 289. [7] F,T. Avignone III and Z.D. Greenwood, Phys. Rev. C22 (1980) 594. [8] B.R. Davis, P. Vogel, F.M. Mann and R.E. Schenter, Phys. Rev. C19 (1979) 2259. [9] P. Vogel, G.K. Schenter, F.M. Mann and R.E. Schenter, Phys. Rev. C24 (1981) 1543. [10] H.V. Klapdor and J. Metzinger, Phys. Rev. Lett. 48 (1982) 127. [11] K. Aleklett and G. Rudstam, Nucl. Sci. Eng. 80 (1982) 74. [12] C.W. Reich and R.L. Bunting, Intern. Nucl. Data Comm. Report no. INDC(NDS)-87/GO + Sp (May 1978), unpublished, p. 245. [13] P.F. Rose and T.W. Burrows, BNL report no. BNLNCS-50545 (1976), unpublished, Vols. I, II. 203
Volume 113B, number 3
PHYSICS LETTERS
[14] J.K. Dickens, Phys. Rev. Lett. 46 (1981) 1061. [ 15] H.V. Klapdor, T. Oda, J. Metzinger, W. Hillebrandt and F.K. Thielemann, Z. Phys. A299 (1981) 213. [16] J.K. Dickens et al., ORNL report no. NUREG/CR-0162, ORNL/NUREG-39 (1978), unpublished.
204
17 June 1982
[17] B.F. Rider and M.E. Meek, General Electric Company report no. NEDO-12154-2(E) (1978). [18] E.A.C. Crouch, At. Data Nucl. Data Tables 19 (1977) 419.
PHYSICS LETTERS
17 June 1982
CALCULATED BETA-RAY SPECTRA FROM DECAY OF FISSION PRODUCTS PRODUCED BY THERMAL-NEUTRON FISSION OF 235U
J.K. DICKENS Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA Received 29 January 1982 Revised manuscript received 22 March 1982
Beta-ray spectra from decay o f fission products created by thermal-neutron fission o f :~3sU have been calculated using summation techniques and using an independently created beta:ray data file. The calculated beta-ray spectra are in very good agreement for E# -- 1 to 8 MeV with recently measured spectra o f beta rays for two very different exposure and counting time conditions: (a) an "instantaneous" spectrum following a 1.5 day exposure, and (b) an 8 s counting-time spectrum obtained 1.7 s following a 1 s exposure o f 235U by thermal neutrons.
_
Recently Schreckenbach et al. [1] at the Institute Laue Langevin (ILL) obtained experimentally the/3ray spectrum from decay of fission products produced during a 1.5 day exposure of 235U by thermal neutrons. The reported [ 1] experimental data were obtained primarily to provide an experimental basis for the determination of the associated antineutrino spectrum. For such determination the reported [1 ] ~-ray spectrum can be considered a de facto "benchmark" data set, such that computations of a reactor-produced antineutrino spectrum should also provide a reactorproduced/3-ray spectrum in agreement with the experimental data. For any such calculations the quality of agreement of the computed/3-ray spectrum with the "benchmark" data should be indicative of the reliability of a computed antineutrino spectrum, which might be applied, for example, to recent measurements [2,3] of antineutrino-induced reactions and the interpretations of these experiments. In the present report the ILL data [1] are compared with predictions using a summation computer code and files of basic nuclear data recently assembled by the author [4] ,1. In fig. 1 the data [1] are compared with spectra calculated for three conditions: (a) the triangles (zx) represent the predicted spectrum for/~ rays following decay of 278 fission products for ,1 The data file is available from the ORNL Radiation Shielding Information Center (RSIC) u p o n request.
0 031-9163182/0000-00001502.75 © 1982 North-Holland
~°°
4o -~
I
I
~
I
I
~
_
z o
4°-z --
C---
~ to-3 = _~ B
-
7-- t0-4
N
= -~0-5
4o-O
0
nTHERMAL EXPOSURETIME =t.5 days ~\~ ÷ EXPERIMENT (IL-L,~981) [ ~ PRESENT CALCULATIONS [ORNL, 1984) / [I ~i TOTAL SPECTRUM, 500 FISSION PRODUCTS [ PARTIAL SPECTRUM. 278 FISSloi~ PRODUCTS / - - - - PARTIAL SPECTRU[¢. 84As ,
I
I
'~
2
3
-
a
5
6
7
8
9
40
BETA-RAY ENERGY [MeV)
Fig. 1. Beta-ray spectra following a 1.5 day exposure o f 23SU by thermal neutrons. The solid points represent the data o f Schreckenbach et al. (ref. [ 1 ]). The lines and the open triangles (zx) indicate results o f present calculations. The solid line is the total predicted spectrum, while the triangles represent the portion due to 278 nuclides for which #-ray spectral information is known. Although not indicated as such, the triangles follow the dashed curve for E# > 8 MeV. The dashed curve represents the portion due to decay o f 84As, the dominant nuclide decay for large E#. All calculations use the R i d e r - M e e k evaluation o f fission-product yields (ref. [ 17 ]).
20]
Volume 113B, number 3
PHYSICS LETTERS
which the file contains data obtained from the literature on the energy, intensity, and forbiddeness (E~, 1~, FO) for individual/3-decay modes of these fission products; (b) the dashed line indicates the high-energy portion of the spectrum from decay of 84As, a fission product having a dominant high-energy known/3-ray transition (E¢ = 9.8 MeV, I# = 51%, and FI3 probably first-forbidden non-unique [5]); and (c) the solid line is the predicted spectrum which includes the data from the above mentioned 278 fission products plus using partial experimental and/or postulated nuclear data for an additional ~225 short-lived fission products produced by thermal-neutron fission of 235U having fractional yields >10 -6. The total spectrum compares very favorably with the experimental data [1 ], particularly in the highest energy region Et~ > 6.5 MeV. In this energy region, also, the partial spectrum (zx in fig. 1) agrees well with the experimental data, illustrating that for 6.5 ~
17 June 1982
main nearly 200 radionuclides (the "unknowns") for which only an average/3-ray energy, (E~), is entered in the data file. For nuclides having (Eta) determined from experiments [11,12], the experimentally derived (EI~) were used in the file. For all remaining fission products (E#)was obtained from the US ENDF/B-IV evaluation [13]. To utilize the 0V#) data for the "unknown" nuclides to determine a/3-ray distribution, a simple prescription was used [ 14]. This prescription involved computing the decay of an "unknown" fission product as a single allowed transition having an end point (Ej3)max such that the average energy of this allowed transition is equal to the (E~) given in the file. Essentially, it is assumed that the important part of the Gamow-Teller strength for beta decay is localized to an excited state in the daughter having a large overlap with, and the same parity as, the/3-emitting state of the parent. It is evident that this prescription biases against possible ground-state transitions and produces a total fission-product/3-ray spectrum which agrees with tabulated/3-ray spectral results of Klapdor and Metzinger [10] but is a much softer/3-ray spectrum (i.e. fewer high-energy/3 rays) than the spectra of refs. [7-9]. The justification of the use of this prescription is based upon the following considerations: (a) nearly all of the cumulative fission yields for 235Ufission for the "unknown" radionuclides are very small, <0.1% per fission; (b) the lack of highest-energy/3-ray transitions is in agreement with recent more detailed calculations of Klapdor et al. [ 15] and (c) as is evident from fig. l, in fact, the "benchmark" data are even softer than the present calculations and those of ref. [10]. A ~-ray spectrum [16] ,2 for very different irradiation and counting conditions than the spectrum in fig. 1 is shown in fig. 2 along with two full calculations. The time periods for the spectrum in fig. 2 enhance the contributions from the short.lived fission products. The two calculations shown in fig. 2 are for two different, and widely used, sets of evaluated fissionproduct yields [17,18]. The calculated spectra shown in fig. 2 rely somewhat more heavily upon the contributions from the postulated partial decay schemes and also the (Et3) for the "unknown" nuclides, especially ,2 Spectral data are availablefrom the ORNL Radiation ShieldingInformation Center upon request.
Volume 113B, number 3 too _--
I
I
PHYSICS
I
I
I
I
-
~. t0 .2
~£
iqTHERMA L + 235 U B E T A - R A Y Texposure = t . 0 sec Twaii = 1.7 sec
~0-3
":~,~,,
SPECTRUM
~+' ~
'TT'
Tcoun t = 8 . 0 sec ~, E X P E R I M E N T ( O R N L , 1980) PRESENT CALCULATIONS - USING E N D F / B - V YIELDS - - . . . . DSING AERE ( 1 9 7 ? ) Y I E L D S
1o-4 0
1
1
t
2
1
I
I
3 4 5 BETA-RAY ENERGY ( M e V )
I
I
B
7
17 June 1982
encountered are reflected in the assigneduncertainties. An important point is that for the data shown in both figures, all o f the calculated values are equal to or larger than the experimental data for E# > 6.5 MeV indicating a paucity of real high-energy 13-ray transitions from decay of "unknown" nuclides. The present calculations do not seriously underestimate the highenergy portion of the spectrum, as suggested by the authors o f ref. [9]. In summary,/3-ray spectra have been computed for two very different exposure and counting intervals, and the computed p-ray spectra are in very good agreement with recently measured/3-ray spectra [1,16]. The quality of agreement lends credence to the calculational methods and the evaluated nuclear data file given in ref. [4].
I
o_ _m u_
LETTERS
8
Fig. 2. Beta-ray spectra for a 1 s exposure of 23SUby thermal neutrons and a 1.7 s interval from the end of the irradiation to the start of an 8 s counting period. The solid points represent data obtained at ORNL (ref. [3]). The lines indicate results of present calculations, with the solid line indicating results using the Rider-Meek evaluation of fission-product yield (ref. [17]) and the dashed line indicating results using the Crouch evaluation of fission-product yields (ref. [18]).
for E~ > 6 MeV, than do the spectra shown in fig. 1, and so the agreement obtained tends to substantiate the decay characteristics postulated in the present data rifle. The half lives in the data file of the radionuclides contributing to the calculated spectra of fig. 2 are from experimental measurements; those half lives in thedata file which had to be obtained from theoretical estimates are all sufficiently short that the corresponding fission products substantially decay away during the 1.7 s waiting period following the irradiation. One may note similarities in calculated curves vis-avis both sets of experimental data [1,16]. As shown in both figures, the calculation is somewhat too large for E# ~ 3 to 3.5 MeV and somewhat too small for E# ~ 5 to 6 MeV. It seems likely that the sources of these small differences will be related to errors in the • nuclear data due to errors in original experiments. For E# > 6.5 MeV in fig. 2, experimental difficulties
F.C. Maienschein and P.H. Stelson (ORNL), P. Vogel (CalTech), R. Wilson (Harvard), and K. Schreckenbach (ILL) have been extremely helpful and their contributions are appreciated. This research was sponsored by the US Department of Energy, Office of Energy Research, under contract W-7405eng-26 with Union Carbide Corporation.
References [1] K. Scltreckenbach et al., Phys. Lett. 99B (1981) 25. [2] F. Boehm et al., Phys. Lett. 97B (1980) 310. [3] F. Reines, H.S. Sobel and E. Pasierb, Phys. Rev. Lett. 45 (1980) 1307. [4] J.K. Dickens, ORNL report no. ORNL/TM-8285 (1982), in preparation. [5 ] C.M. Lederer and V.S. Shirley, eds., Table of isotopes, 7th Ed. (Wiley, New York, 1978). [6] P. Hoff, K. Aleklett, E. Lund and G. Rudstam, Z. Phys. A300 (1981) 289. [7] F,T. Avignone III and Z.D. Greenwood, Phys. Rev. C22 (1980) 594. [8] B.R. Davis, P. Vogel, F.M. Mann and R.E. Schenter, Phys. Rev. C19 (1979) 2259. [9] P. Vogel, G.K. Schenter, F.M. Mann and R.E. Schenter, Phys. Rev. C24 (1981) 1543. [10] H.V. Klapdor and J. Metzinger, Phys. Rev. Lett. 48 (1982) 127. [11] K. Aleklett and G. Rudstam, Nucl. Sci. Eng. 80 (1982) 74. [12] C.W. Reich and R.L. Bunting, Intern. Nucl. Data Comm. Report no. INDC(NDS)-87/GO + Sp (May 1978), unpublished, p. 245. [13] P.F. Rose and T.W. Burrows, BNL report no. BNLNCS-50545 (1976), unpublished, Vols. I, II. 203
Volume 113B, number 3
PHYSICS LETTERS
[14] J.K. Dickens, Phys. Rev. Lett. 46 (1981) 1061. [ 15] H.V. Klapdor, T. Oda, J. Metzinger, W. Hillebrandt and F.K. Thielemann, Z. Phys. A299 (1981) 213. [16] J.K. Dickens et al., ORNL report no. NUREG/CR-0162, ORNL/NUREG-39 (1978), unpublished.
204
17 June 1982
[17] B.F. Rider and M.E. Meek, General Electric Company report no. NEDO-12154-2(E) (1978). [18] E.A.C. Crouch, At. Data Nucl. Data Tables 19 (1977) 419.