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Decay Heat Calculations Based on Theoretical Estimation of Average Beta- and Gamma-Energies Released from Short-Lived Fission Products

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Decay Heat Calculations Based on Theoretical Estimation of Average Beta- and Gamma-Energies Released from Short-Lived Fission Products i NW- L-L~ - I Journal of NUCLEARSCIENCE and TECHNOLOGY,18161, PP. 393-407 (June 1981). 393 Decay Heat Calculations Based on Theoretical Estimation of Average Beta- and Gamma-Energies Released from Short-Lived Fission Products Tadashi YOSHIDA, NAIG Nuclear Research Laboratory, Nippon Atomic Industry Group Co., Ltd.* Ryuzo NAKASIMA Department of Physics, Hosei University** Received January 12, 1981 Fission product decay heat of was calculated for short cooling-time on the basis of a preliminary version of a new.decay data library recently completed by the Japanese Nuclear Data Committee. It was shown that a full adoption of recent publications of decay schemes to derive average energies of p- and :-rays, Eg and E,, leads to a large underestimation of the 7-ray component of the decay heat and to an overestimation of the ,+ray component. In order to remedy this, theoretical values of I?$ and Er were introduced for high Q-value decays, which were obtained with a gross theory of ?-decay. It improved remarkably the agreement between calculation and experiment not only for the 'W decay heat but for "9P~ and '"Pu as well. It was concluded that a large part of decay schemes recently published for high Q-value nuclides are inappropriate to use in calculations of I?? and Er, because they fail to reproduce the effect of ?-strengths at high excitations, which makes E,: small and E, large. The use of the gross theory.introduces this effect correctly into the . - values of Ej and E, and, hence, leads to a quite good prediction of both ,+ and r-ray com- ponents of the decay heat. KEYWORDS: decay heat, fission products, decay energy; beta decay, gross theory, short-liued, uranium 235, plutonium 239, plutonium 2d1, beta sfrength, ' 8 decay scheme, beta ray, gamma ray, Q value, half life, selection rule Recent several Years a lot of studies have been performed for the purpose of improving the prediction accuracy of nuclear decay heat, which is one of the important factors for nuclear facility design and its safety analysis. From the experimental side, results of high accuracy measurements have been published, which include calorimetric measurements by Yarnell & Bendt"', by Grossman et ol."', a total absorption scintillator measurement by Friesenhahn et al."', 8- and 7-s~ectroscopicmeasurements by Dickens et a[."', and by Akiyama"'. These experiments had been planned mostly to support the safety analysis of the hypothetical loss-of-coolant accident in a light water reactor. There exist several nuclear decay data libraries for summation calculations of decay heat. which include ENDFIB-N, /B-V, French"' and Enalish"' files. and Tasaka's librarv@'. * Ukishima-cho, Kawasaki-ku, Kawasaki 21 0. ** Fujimi, Chiyoda-ku, Tokyo 102. 391 J. Nucl. Sci. Technol., The most recent ones may be ENDF/B-V and Tasaka's new library'9'. The latter is a revision of the old library including the fruits of his study on estimation method of the average 9- and 7-ray energies Ej and E, released per one disintegration of data-unknown nuclides. In spite of these elaborations, the agreement between calculation and experiment is not satisfactory for short cooling-time range of 1-1,000s. Schmittroth & Schenter"O' pointed out the importance of certainty of the values Es and E,. Schmittroth estimated unknown Es and 3, based on measured j3 strength functions'"'. French and English files apply a relatively simple method to estimate these value^'^'^^'. One of the present authors developed an estimation method of Ej and E,"" on the basis of gross theory of as a part of the activity of the Decay Heat Evaluation Working Group (hereafter DHEWG) of the Japanese Nuclear Data Committee (JNDC). Very recently, DHEWG has completed a pre- liminary version of Fission Product Decay Data Library for summation calculations["'. This library contains the,complete set of basic data needed in the summation calculation for more than 1,100 fisiion product nuclides (hereafter FP's). Nearly a half of them are short-lived FP's with p-decay Q-values larger than 4-5 MeV, which play an important role in the decay heat of short cooling-time. In the present report, we describe the estimation method of Es and E, applied to data-unknown FP's in the JNDC Library, and then, try to fill the gap between calculation and measurement which is observed in p- and 7-ray com- ponents of the decay heat at short cooling-time with the aid of the gross theory. Chapter I1 reviews the gross theory very briefly. Chapters ill and nr describe the data-estimation method for nuclides with no experimental information. Decay heat will be calculated in Chap. 1' by use of the preliminary version of the JNDC library and by a modified veision in which theoretical values of and E, are fully used for FP's with high Q-values. Since the framework of the gross theory of @-decay has been reviewed in the pre- vious report"", we describe the theory here to the minimal extent. Figure 1 schemat- ically shows a @-decay of a nucleus (Z, ;\:) to its daughter nucleus (Z+1, l\'-ij. In this case, the decay constant and the average j- and 7-ray energies per one disintegration can be written as a sum of contribution from each partial decay to the i-th final state of enercrv c; as follows-: - " L'" i E;=Y --Ei. (3) I ,to 2 __I------------ --?" I i' (2.N) (Zc1.N-1) In Eq. (2 ), C:" denotes the ratio of the av- Ej, .I?,.and E, are average j-,;- and erage electron kinetic energy-associated with antineutrino-enereirr.-. resoecrivelv. a transition to,the i-th state-to the maximum Fis. 1 Typical decay scheme of electron kinetic energy Q-en. The partial high Q-value nuclide * The ;-rays from a nucleus (2.N) mean the ;s fallowing a ;?.decay of (Z,:\') LO (Z+l,i\i-l). Yol. 18. NO. 6 Uune 1981) 395 ld.. is a decay constant 2'" is related to the branching ratio a$ in % as ar=1002i"/2 P. The ,=* the expression (1) can be reduced to further fundamental form using the ,&transition matris- own element, which is conventionally written as (Yi, on, not lted Iwn where f is the integrated Fermi function and Ei=Q-at-1, the maximum energy available for the emitted electron including rest mass. The symbol J2 stands for the transition ya jped. .operator, and go is the coupling constant. The starting point of the gross theory lies in replacement of the summation over the final levels i by an integration with respect to the .S a. , the. level energy on an assumption that the final levels are dense enough to allow this change. The gross theory expression of the total decay constant is Pre- 10 :c14'- # i=?{ X1g~l'.Ihl~(E,!I~f(-E,+ljdE,. (5) :ion 2s -QQ are Instea2 of E, in the expression ( 2 1. ve take :he par~ialdecav energy as 3,=-(E,-l) aie accord:>g to LI convention used in the xiginal paper^"^"'^'. The symbol iilf@,)? repre :ion sents a square of fhe trzxitioxmatrix demer-c multiplied by ihe level densiry of the final to states. This qrantit.], the rrzos: fundamental one in the gross thexy, is cal:ed the 8. ~ ~1- strength hnction and cil be evaluated with the aii of the fo.lonrir,g sum rules and 2 .re!atively simple wxlear m~del. the be . a ith re- where Vis the wave function of the initial state, and H stands for ehe Hamiltonian of the If- whole system. A close procedure with the decay constant leads to the gross theory.~ .. expres. sions for the averagep- and f-ineigies, of where F stands for the Ferrni function, and P for the electron momentum. As the types of the &transitions, the Fermi, the Garnow-Teller and the first-forbidden transitions are &ken into account in the computer codegJ' used in the present work. in the present purpose of the estimation of the average 8- and 7-energies, the effect of the selection rules applied to decays to low-lying levels plays a &tical role, because the pro- hibition of the decay to the ground and the lowestseveral levels appreciably increases the 7-energy and decreases the ,+energy (see Fig. I). TOintroduce this effect into the values af l?p and E,, the calculated ,%strengths were modified to be zero below the lowest level which is actually fed by a direct #-&ansition. The energy position of this level-denoted as QBOhereafter-is not known for nuclides which necessitate the estimation of E, and &, 396 J. Nucl. Sci. Technoi., The integral of the as-calculated strengths was assumed to be accumulated at energy Q,,, the upper end of the prohibited energy range. A recipe to determine the parameter Q,,. was described in Ref. (12) and we will follow it in the present calculations. In principle we adopted a method proposed in Ref. (12) to estimate the Ej and E7 values. The key parameter Q,, was found within the following energy range so as ta give a calculated half-life which agreed best with the measured one for each nuclide. 0.0 MeViQoo12.0MeV for odd-odd nuclides 0.5 MeVlQoo12.0MeV for others. Then, the average p- and 7-energies f?? and E, were calculated by use of this value of Q,,, which was expected to reflect the effect of. the selection rules as was discussed in Ref. (12). The calculations were performed for about 170 short-lived FP's (Q-value,3MeV) with. experiment-based values of f?? and b?;.
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