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

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 components 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 preliminary 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 components 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 previous 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?;. The Q-values used in the calculations were from the preliminary JNDC Library. The results are shown by solid line in Figs. 2(a)-(e).. All the data points from the preliminary JNDC Library (open circles) were derived from published decay schemes by DHEWG. Note that a large part of the Eg and E, values of ENDFIB-M and of Tasaka's library are based on theoretical or empirical estimation. The overall agreement between the present calculations and the data from the existing libraries. seems to be good for the Ep values. In the case of the E, values, the agreement is less. satisfactory. This is partly due to the fact that the calculated 7-energies are more sensitive to the assumed value of Q,, than the ,%energy. It should also be noted that the E, values, both the present and the other values, scatter from nuclide to nuclide more widely than the Ej values, and that the values derived by DHEWG from published decay schemes (preliminary JNDC Lib., open circle) are generally smaller than the other E: values. Later on, we will relate the latter observation with the nature of the measured ?-ray spectra.

N. ESTIMATION OF UNKNOWN DATA Short-lived (or, high Q-value) FP's in the JNDC Library are classified into the following three categories : Class I : Nuclides with Q-values larger than 5MeV; Both half-life and decay scheme are known. (85 nuclides) * Class U : Half-life is measured but decay scheme is not known. (98 nuclides) Class IU : Neither half-life nor decay scheme is known. (254 nuclides) For the Class I nuclides the preliminary JNDC Library contains the values of Ep and E, derived by DHEWG from recent publications of decay scheme^"^'. Later on we will come back to discuss these data of Class I. Preceding the estimation for the unknown data of the Class L[ and 1II nuclides, we must find the Q-value (total $.decay energy) of each nuclide. For this purpose, an atomic mass formula given by Uno & Yamada'I8' has been employed, because this formula makes full use of the recent fruits of atomic mass measurements and

* Yttrium-96, an important contributor to short cooling-time decay heat, is excluded, for this nuclide needs special consideration due to its feature in decay ~cheme"~'. mol., Vol. 18, No. 6 (June 1981)

Qoo. A : ES~Y/B-rr Q... V: Tasska (1979) 4 : A and Vovcrlapped i Beta Energy (MeV) Gamma Energy (MeV) . E, : ta

~iy: ' rith As- 7 8 om . Ge-79 (9.. .As-80 'om Ge-81 As-81 of .~s-82' 'he 'As-82 ies. $ Br-82 As-83 3SS. . ive.

3%. ed. IY ' he.

0' 0' !z

r e f

v I i Fig. 2(a) The solid Line corresponds to the calculation described in Chap. E. For nuclides with solid circle (Class I nuclides), the calculated valuer are finally adopted. Fig. W-(e) Averaged 3- and r-energies released per one disintegration of fission product vo 396 3. Ar?rrl. Sci. Technol.,

3 2 1 0 0 1 2 3

rC*

v A

Fig. Zib) i

sol., Vol 18, No. 6 (June 1981)

Fig. 2(c) Riucl. Sci. Technol., J. V,

Fig. 2:d) nol.. Vol. 18, No. 6 (June 1981) 401

Fig. 2(e)

of studies on its systematics. Applicability of this formula to isotopes far off stability-line was studied and the uncertainty associated with the Q-value prediction was estimated to be mostly within k0.5 MeV and k1 MeV at most(IS). 1. Estimation of Ep and for Class Il Nuclides For Class D[ nuclides (75Zr-1S%d), the key parameter Q,, of each nuclide was fixed with the aid of the measured half-life in the same manner as the 170 nuclides described in the preceding chapter. BY use of this Q,,-value, Eg and E, were calculated. Among the nuclides included in this category, 89Br, 04Rb, lo'Nb, iatZr, IotNb, 'Wb, lo3M0,l0*Nb ,, lS9I "%a and la6La are relatively important in decay heat calculations of short cooling-time. The contributions from these nuclides amount to nearly 15% of the total decay heat at the cooling-time of 10s after a burst irradiation on 'V, for instance. 3 2. Estimation of gp, and T,,,for Class IU Nuclides The key parameter Q,, for these nuclides was determined in the following two methods, namely, (a) The Qao-value was fixed to 1.0 MeV for all the nuclides. (b) Systematic behavior of the values of Q~owas examined for each mass region and each even-odd category, and the QOO value was extrapolated to each nuclide of Class IU. By use of the Q,,-values determined in the above methods, Eg, E, and T,,, were calculated. There was, however, no essential difference between the two decay heat curves correspond- ing to the above two methods. This is due to a fact that the contribution from Class IU nuclides is minor in the calculated decay heat even at very short cooling-time. In practice, we stored the is,Er and TLIZdata based on the method (b) in the JNDC Library. Details of the data estimation method will be described in Ref. (ZO), where the numerical data of Eg, ,!?; and TL12are tabulated. 402 J. Nucl. Sci. Technol., VG

The decay heat after an instantaneous irradiation of thermal neutron on ?3'U was calculated by use of the preliminary version of the JNDC Library (status: October, 1980) and Tasaka's library. The former contains the experimental data of Ej and e': for Class I nuclides and the theoretical data calculated for Class D and Ill nuclides. The computer code used here is DCHAIN made by Tasaka"". The a- and pray components of the calculated decay heat are displayed in Figs. 3(a) and (b), respectively, in comparison with the integral measurement of Oak Ridge:" and others:2?>-<24~. It is easy to see that the preliminary JNDC Library (thin solid line with a letter @) overestimates the a-energy release, and largely underestimates the penergy release. These figures also show the decay heat curves calculated with Tasaka's library(6) (broken line) and with ENDFIB-I\' (dot-dot-dash line). The latter curves were taken from the paper by Dickens et al.!" As far as the short cooling-time (less than several hundred seconds) is concerned, the agreement of the Tasaka's and the ENDF/B-nT curves with the measure- mentsis not satisfactory except the r-energy release. after about 20s. Even in comparison with these curves, the underestimation with the JNDC preliminary library in the ;-energy re!ease is obvious between 5-200s of cooling-time. On the other hand, the thick solid curves with a letter 5 reproduce the measurements (especially of Oak Ridge) very well both in the a- and 7-energy releases. These are the results of calculations based on a modified version of the JNDC Library in which all the values of Eg and E, of Class I nuclides were replaced by theoretical values. The Class I nuclides are indicated by solid circle in Figs. 2. (a)-(e) The theoretical values of Ej and E, adopted here correspond to the solid line in this figure. The improvement of the agreement with the measurements is quite drastic as is seen in Figs. 3(a) and (b). It is interesting to see if the full use of the theoretical values of Ej and g; reproduces also well the integral measurements for other fissile nuclides. Figures 4(a) and (b) show the 8- and 7-ray components of *3sP~and 2riPu decay heat after an instantaneous irradiation of thermal-neutron. The calculation reproduces quite well the measurements by Dickens et again. Figures 5(a) and (b) show the decay heat curyes calculated with the modified JNDC Library (after the introduction of theoretical values) for '"'U and '3SU, for which experimental data of decay heat are quite scarce. The large change mentioned here suggests that the contribution from the Class I nuclides are predominant in the cooling-time range up to several hundred seconds. Among the important nuclides producing the above change, there are '3Rb, "Sr, "Y, I3jTe, '""I , Y, my 2 e, '"G, "'Cs, "'La and "'La. We have been concentrating on the examination of the effect of the data for the Class I nuclides until now. In fact, the contribution from the Class II nuclides is of minor importance except in the cooling-time range less than 20 s. The contribution from the Class IU nuclides is much less important than Class II nuclides.

As mentioned at the end of Chap. 117, a survey of Figs. 2 (a)-(e) leads to an observation that the E, values of short-lived FP's derived by DHEWG from recent publications of decay schemes are generally smaller than those from ENDFIB-IV and Tasaka's library. This seems to be closely related to the fact that these recent data for decay schemes of short-lived FP's are extensively adopted only in the new JNDC Library (and possibly in I '

?OL, Voi. 18, No. 6 (June 1981)

caE - - and .OWL (1980) Ref. (0 D (19M) ss 1 SRRC Ref. (221 - ter - :(a) ,ad - h a lse. ' en

'/ -+: Present (modified JNDC Lfb.) +: Jnoc Library (stmr: kt.. 19803 ---.-: Tarah's Library 11979)

----:Enows.lv. kf. (41

Its I 1 I I 1 l 1111 I I I , ,/,I! I 1 1 11111 :he 100 101 loz 1o3 .he Codling tine, t (i) s l (a) pray component G ,n t OWL (1990) Ref. (41 - o om1 (1962) Ref. (231 es o USL (19631 Ref. (241 IW a- 'Y

- 4- : Werent (modified JNCC Lib.) -4- : ~socrrs~~~, (status; act.. 19801 - - ---.-. Iarcka'r Libraw (1919) : EhOF,B-iV - I lcO 101 1cZ lo3 Coaling tine. t ($1 (b) pray component Calcularion after the replacement of Eg and Er values of Class I nuclides (thick solid line wirh a> is compared with the original library calculation (thin did line with @) and others. Fig. 3(a),(b) 8- and 7-ray components of decay heat following an I instantaneous rrradiation of thermal neutron on "U i J. Nud. Sci. Technol.,

1.0 I It8 8 tltl

(a) *.ray component

(b) pray component Pis. 4(a),ib) j- and ;-ray componenm of decay heat following an instantaneous irradiation of thermal neutron on *Pu and '"Pa 101.. Vol. 18, No. 6 (June 1981) 40.5

, ( , , , , , , , , , , , , , , , , ,I , , , , , 0 ' ' """ ' ' . , , , .,, , . , . , , ., loa 10' 10' do, ' 10' 10' 0' Cmfing lime. 11s) Cmiing 1~rne.llsl (a) p-ray component (b) pray component Fig. 5(a),(b) 8- and r.ray components of decay heat following an instantaneous irradiation of thermal neutron on PSSUand of fast neutron on

ENDFIB-V*). A large part of them were published after the completion of other libraries compared here. The use of these recent values of E, resulted in a large underestimation of the r-ray component of the decay heat at short cooling-time. The overestimation in 8-energy release is inseparably related to the underestimation in r-energy through the energy-conservation. In Chap. V, however, it was shown that the full use of the theoretical values of Eg and E, for FP's with high Q-values remedied these discrepancies. Based on this observation, we infer that the recently published decay schemes for these FP's may probably he inappropriate to use in calculations of E9 and 1,. It seems that there are following difficulties in constructing high Q-value decay schemes from experimental information. (1) Decay schemes of high Q-value FP's are generally constructed from the intensity balance of r-ray line spectra measured by Ge detectors coupled with on-line mass separator. In this situation, it is not a rare case that only a several intense ;'-rays of low energies are detected. Even if it is not the case, it is very probable that an appreciable fraction of the decay Prays are left unobserved. Hardy et al. performed a quite interesting numerical ex~eriment'~~',which sheds light on the situation mentioned above. They created numerically a complex p-r transition scheme of high Q- value decay of a fictional nuclide 'Pandemonium' using a statistical model. By analyz- ing the simulated detector response of the 7-rays associated with it, they concluded that much r-rays remained unobserved under normal experimental conditions. (2) Let us suppose a case where the quality of the measurement is relatively good and a lot of r-ray peaks are detected. Even in this case, it is likely that an appreciable amount of the detected ?-rays fail to he placed in right positions in the decay scheme and are excluded from it. These unplaced rs, whose intensity is weak, generally lack evident coincidence relationships with other T-ray peaks, which constitute a quite helpful information used in the construction of a decay scheme. * According to a letter from Dr. T.R. England '(~ec.8, 1980), calculated decay heal curves (preliminary) with ENDFIB-V decay data show very similar behavior as those of the preliminary JNDC Library. 406 J. Nucl. Sci. Technol.,

In both cases, the 'lost' prays are originated presumably in highly excited states. When a decay scheme is constructed from the intensity balance of such a defective ray spectrum, the dense and complex structure of the high energy part of the scheme is open to an oversimplification. It is suggested by nuclear theorie~"~"~~'that the high enegy part plays an important role in ,@decay schemes having large Q-values. They predict an increasing trend of the P-strength function-a square of transition matrix multiplied by the final state density, see Chap. I[-with the increase of the energy (ei in Fig. 1). In the case of the Fermi and the Gamow-Teller transitions, for instance, the P-strength has a large peak at the isobaric analog state extremely high above the ground state, to which real ,%transitions are energetically prohibited. The @-strength increases its value toward this peak with the excitation energy. This trend is observed also in the P-strengths obtained from experiments specially deviced for the p~rpose'~~"~~'.Large P-strength high above the ground state leads to a decrease of Es and to an increase of I?,. This trend of the P-strengths is properly taken into account in the gross theory calculations applied here, and hence in the theoretical values of z3 and E;. The Es and E, values derived from the published decay schemes, on the contrary, do not probably reflect this increasing trend of the &strengths, since the high energy parts of them are oversimplified as is pointed out above. This will explain the overestimation of the ,!-ray component of the decay heat and the underestimation of the r-ray component as well as the remarkable improvement brought about by the introduction of the theoretical values of EB and !?,.

In the previous chapter it was suggested that high energy parts of the published decay schemes are open to an oversimplification because of the limitation of experimental information, and that they fail, hence, in reproducing correctly the real behavior of the 8- strengths high above the ground state. We conclude here that reliable values of Ej and I?: cannot be derived without taking account of the effect of the large ,!-strength at high excitation in a correct way. This can be accomplished by extensive use of the results of theoretical calculations as is done here, or probably by utilizing the fruit of the experimental study on $strength as is being carried out by Schmittroth"". .knother conclusion drawn here is that the fission yield, half-life and branching ratio data adopted in the JNDC Library would appear to be quite reasonable, since they reproduce the measured decay heat well, after the introduction of the theoretical values of e', and E'?, not only for 238U but also for 23nP~and $"Pu as well.

The authors express their thanks to Mr. H. Ihara who cooperated in decay heat calculations, to Dr. Z. Matumoto for his comment on description about decay scheme, and to Dr. T. R. England for his information about his recent experience. Thanks are also due to Dr. K. Tasaka for his comment on calculated results, to Dr. R. E. Schenter for introduc- ing us interesting papers on the present field, and to Mr. S. Iijima for his continuous en- couragement. As to the knowledge on the integral experiment, the authors due much to bfr. bI. Akiyama. - i i Vol. 18, No. 6 (June 1981) 407 inol., t tates. r-ray YARSELL,J.L., BENDT, P. J. : Decay heat from products of thermal fission by fast-response open boil-off calorimetry, LA-NUGEG.6713. .~(1977). . G~oss*r.as.L. M., NUH, F.M., PRUSSIN,S.G., SCHROCK,V.E., SOCKALISGA~I,K.C.: P~oc.of II, rtant : Topical ~Lleetingon Thermal Reactor Safety, Vol. p. 207 (1977), ldaho State Univ. FRIESESHAHS,S. I., LURIE,N.A. : ibid., p. 163. f the i 1 DlCtiESS, J. K., LOVE, T.A., MCCONNELL,1. W., PEELLE,R. W. : Nucl. Sci. Eng., 74, 106 (1980). , see i AKIYI~IA.M. : TO be published; See also 1. At. Energy Soc. Jcpcn, (in Japanese), 22C63, 358 i the (1980). BLACHOT,J.. DE TOUREIL,R.: Bibliotheque de donnees nucleaires relatives aux produits de fis- baric , sion, CEA I\'-1526, (1972). are , 1 TOBIAS.A.: Data for the calculation of gamma radiation spectra and beta heating from fission i the ; products, RD/R/M 2669. (1973). U.K. Central Electricity Board. lents TASAKA.K., SASAMOTO,N.: NucI. Sci. Eng., 54, 177 (1974). TASXKA. K. : Nuclear data library of fission products for decay heat power calculation, ArUREGI leads~~. 1 CR-0705, (1979). - SCHMITTROTH,F.. SCHENTER,R. E: : Nucl. Sci. Eng., 63, 276 (1977). 'W, :tical SCH~IITTROTH,F.: Theoretical estimates of decay infdmation for non-experimental nuclides, Conf. on Sucl. Data Evaluation Methods and Procedures, (1980). BNL. S, on . YOSHID-I, T.: IVUCI.Sci. Eng., 63, 376 (1977). . high / TAK.~H.ISHI,K., YALIADA,M.: Progr. Theor. Phys., 41, 1470 (1969) ; KOYADIA,S., T.~K.AHMHI, the 1 K., YIDM : ibid., 44, 663 (1970). JNDC Fission Product Decay Data Library, to be released, Decay Heat Evaluation Working Group, the : Japanese Suclear Data Committee. (1981). See also Ref. Uli. TAKAH;ISHI,K., YALIADA, M., KONDOW,T.: At. Nuc~.Data Tcbles, 12, 101 (1973). Yosn1o.a. T.: JAERI-M 6313, (in Japanese), (1975). :lion YA~;uloTo,T., AKIYAMA, M., MATUMOTO,Z., NAKASIHA,R.: JAERI-M 9359, (1981). I ho, h.f., Y.I\IADA, M.: Contribution to 6th Int. Conf. on Atomic Masses, Michigan State Univ., (1979). j Y~slaD.1, 41. : Private communication, (1979). in- Yos~loA.T. : JAERIM Report, To be published; MATSU:MOTO,2.: JAERI-IM Report, To be i published. ? 8- ! TASAK-I, K.: DCHAIX code for analysis of build-up and decay of nuclides, JAERI 1250, (in and Japanese), (1977). r at MAcM-IHOS, T.D., WELLEM,R., WILSON,H.\I7.: J. Nucl. Epergy, 24, 493 (1970). PERR>-,.A. XI., MAIESSCHEIS,F. C., VOKDY,D. R. : Fission product after heat-a review of ex. -1s periments pertinent to the thermal-neutron fission of *'jU, ORNL.TM.4197, (1973). ex- FISCHER,P.C., ESGLE, L.B. : Phys. Ree., 134, 8796 (1964). DlcKESs, J.K.: Fission product decay heat for thermal reactors, Conf. on Nucl. Cross Sections for Technol., Knoxville. (1979). atio .' DICKEX. J. I<.. EMERY,J.F.. LOVE,T.A., ~,~cCOSSELL,J.W., NORTHCUTT,K.J., PEELLE.R.W., luce WEA~ER.H. : Fission product energy release for times following thermal neutron fission of ?jSPu E;, between 2 and 14,000 seconds, ORNL/NUREG.34, (1978). HARDY,J.C., CARRAZ,L.C., JOSSOS, B., HASSEX, P.G.: Phys. Left., 71B, 307 (1977). See for instance. HASSEX, P.G.: The beta strength function, Aduan. Nucl. Phus.,7, 159 (1975). ALEKLETT,K., NYMAS, G.. REDSTAM,G.: Nucl. Phys., A246, 425 (1975).

cal- 1 to due iuc- en- to