The useful energy released in the fission of 232Th 233U, 234U, 236U, 237Nr, 238Pu, 240Pu and 242Pu

Journal of Nuclear Energy, Vol. 25, pp. 513 to 523. Pergamon Press 1971. Printed in Northern Ireland

THE USEFUL 232Th,

233U

ENERGY ,

234u,

236U

RELEASED IN THE FISSION OF , 237N P, 238Pu, 240Pu AND 242Pu

M. F. JAMES Fast Reactor Physics Division, Atomic Energy Establishment, Winfrith, Dorchester, Dorset, England (Received 30 March 1971) Abstract-This paper extends an earlier study (JAMES, 1969) of the useful energy released from fission to other heavy nuclides. The total effective energy released is calculated from atomic mass excesses, and a detailed discussion is given of a method of interpolation that has to be used when data on fission product yields are sparse or non-existent. A comparison is made between calculated values and the few experimental measurements that have been made for the nuclides under consideration and reasonable agreement is obtained, although the discrepancy between time-of-flight and solid state detector measurements of fission fragment kinetic energies is again noted. The recommended values for the useful energy released from fission, and for the total useful energy per fission in a thermal neutron reactor, including contributions from neutron capture, are respectively : zaaTh 184.2 f 0.9 MeV/f; 192.8 +c 1.0 MeV/f ZSSU 190.0 * O-5 MeV/f; 199.1 f 0.6 MeV/f 231U 188.9 & I.0 MeV/f; 199.2 & 1.3 MeV/f zseU 191.4 h 0.9 MeV/f; 201.8 + 1.1 MeV/f 237N 193.6 + 1.0 MeV/f; 205.1 f 1.2 MeV/f P 238Pu 196.9 f 0.8 MeV/f; 208.5 + 1.0 MeV/f =aopu 196.9 h 1.0 MeV/f; 210.4 & 1.3 MeV/f zazPu 200.0 f 1.9 MeV/f; 213.1 f 2.4 MeV/f. The values for 2s3Uand 23sPuare for fission induced by thermal neutrons; for the other nuclides the incident neutrons are assumed to have the spectrum of fission neutrons from *asU. 1. INTRODUCTION

IN A PREVIOUS paper (JAMES, 1969; which we shall refer to as I) an evaluation was made of the useful energy released by thermal neutron fission of 235U 23gPuand 241Pu, and by fission of 238Uinduced by fission spectrum neutrons. Althoigh a study of all the available experimental information was made in I, it was shown that the most accurate method of calculating the total energy released was not by adding all the separate contributions, but by using the mass excesses of the target nuclide and of the stable fission products : this method was first used by WALKER (1968). In this present note, we use mass excesses to calculate the energy released through thermal neutron fission of 233U and 238Pu, and through fission of 232Th, 234U, 236U, 237Np, 240Pu and 242Puby fission spectrum neutrons. We should be forced to use this method, even if it were not the more accurate, because of the dearth of experimental measurements of the separate contributions to the total energy for all these nuclides, excepting 233U. However, the application of the method is less straightforward than in I, because, data on the mass yields of the fission again excepting 233U, there are insufficient products of the nuclides being considered. Consequently, the mean mass excesses of the fission products have to be found by interpolation. However, it has already been noted in I, that such an interpolation may be somewhat inaccurate, and so care is necessary. In Section 3, the method of interpolation that we use is outlined. In I, it is shown that the total effective energy release Qi,, is given by: Qiot = m(A, Z) -

mL 513

Kz, -

(ct -

l)m,,

(1)

514

M. F. JAMES

where m(A, 2) is the mass excess in MeV of the target nucleus (A, Z), and (light)

*L=

7

(heavy)

Yimi

and

SH =

7

Yimi

are the mean mass excesses of the light and heavy fission products; the sums are over all light and heavy products respectively, and y, is the yield and mi the mass excess (light)

in MeV of the i-th fission product.

They, are normalized so that

(heavy)

C yi =

z

yi

= 1. ?1 is the mean number of prompt and delayed neutrons per fisiion, and A, = S-07144 MeV is the neutron mass excess. All mass excesses were obtained from the tables of MATTAUCH et al. (1965). It is clear from equation (1) that we need to know it reasonably accurately: an uncertainty of kO.1 in & implies an uncertainty of f0.8 MeV in Qi,,. In the next. section we briefly discuss the values of ct. 2. THE

AVERAGE

NUMBER

OF

NEUTRONS

PER

FISSION

Since + is approximately a linear function of incident neutron energy, it is first necessary, for the nuclides that only undergo fast fission, to calculate the mean energy of the incident neutrons causing fission, Ei. This is: Ei = s0

mEq(E)+(E)

dE

is

%(E)+(E)

dE,

(2)

0

where o,(E) is the fission cross-section, and 4(E) is the neutron spectrum, which we take to be that of 235U fission neutrons represented by a Watt-Cranberg formula (CRANBERG et al. 1956) with a mean energy of 1.98 MeV. Ei has been computed using the fission cross-sections in the UK Nuclear Data Library, and the results are given in column 3 of Table 1. Column 2 gives the Data File Number (DFN) of each nuclide in the Nuclear Data Library (NORTON, 1969). The uncertainty in Ei has been estimated as &to*1 MeV. TABLE l.-MEAN

Nuclide %=Th X%U 134U 23lXU 28,N P ZSSPU 24OPu =4VU

DFN in UK Nuclear Data Library 332 334 336 337 340 342

INCIDENTNEUTRONENERGIESAND VALUESOF 2it AND i$ Mean incident neutron energy CM%)* 3.39 + O,l Thermal 2.36 i 0.1 2.82 f 0.1 2.37 f 0.1 Thermal 2.39 f 0.1 2.32 & 0.1

%(Ei) 2.412 2.487 2.684 2.706 2.89 2.90 3.22 3.14

+ f f f f f + f

0.023 0.007 0.090 0.06 0.03 0.03 0.07 0.20

Refs. (1) (2) (1) (3) (4) (5) (1) (6)

Refs.

*Ii 0.0496 0.0066 0.010 0.021 0.01 OW4 0.0088 0.021

k + + f & f f +

0.0020 0.0003 0.001 0.002 0.001 0.001 0.0006 O+lO2

By By By By

(7) (7) interpolation interpolation interpolation interpolation

(7) By interpolation

* The uncertainty of f0.1 MeV is estimated. (1) FILLMORE(1968) (renormalized). (2) HANNA et al. (1969). (3) HOLMBERGand CONDE (1970). (4) LEBEDEVand KAI.ASHNIKOVA(1962); measurement in a fast spectrum. (5) JAFFEYand LERNER(1970); ZAMJATNINet al. (1970). (6) Estimated from the empirical formula of GORDEEVAand SMIRENKIN(1963), revised by JAFFEY and LERNER(1970); dl?/dE assumed to be 0.14(MeV)-1. (7) KEEPIN(1968).

The useful energy released in a38Th, *YJ, WJ,

236U, *37Np, arsPu, zaoPu and zazPu

515

Columns 4 and 5 of the table give the values of s,(EJ that we use, and the references from which they were obtained. Most of the measurements were of the number f, of prompt neutrons only, so we give values of the number of delayed neutrons for each nuclide, with the appropriate reference. The only nuclide for which no measurements off appear to be available is 242Pu; for this nuclide a value has been estimated from the semi-empirical formula of GORDEEVAand SMIRENKIN(1963), revised in the light of more recent data by JAFFEYand LERNER(1970) : F,(O) = 0.18212 + 0*0088/t - 16.34 + 0.09T

(3)

where T = -1 for a target nuclide such as 242Pu with even numbers of protons and neutrons. All the t values have been normalized to ?t(252Cf) = 3.765, or 1,(235U) = 2.4229 (HANNA et al. 1969). 3. THE

CALCULATION OF THE MEAN MASS STABLE FISSION PRODUCTS

EXCESS

iii OF THE

For 233U, the fission product yields of RIDER et al. (1967) have been used to calculate the mean mass excesses (L)

Eiii, =

2 yimi i

and (Ii) mH = T Yimi of the light and heavy peaks respectively. Good yield data are not available for the other nuclides, although there are sufficient data for 232Th and 237Np for fairly good estimates to be made of the mean mass numbers KL and AH of the light and heavy peaks, and of the widths of the peaks. Except for 233U,it is therefore necessary to use some method of interpolation and extrapolation to deduce rii for the nuclides under consideration. But it was noted in Section 2 of I that a simple interpolation in terms of the target mass could lead to errors as large as 0.5 MeV, even for isotopes of uranium and plutonium; larger uncertainties could be expected for other elements such as thorium and neptunium for which interpolation or extrapolation must be made in atomic number also. We must therefore be careful to choose a reliable method. It is useful to recall the main features of the quantities yi and mi. For nuclides in the range in which we are interested, and for relatively low energy (< 14 MeV) incident neutrons, the yields yi form two well-separated peaks with maxima at mass-numbers ~90-100 for the light fraction, and ~138-140 for the heavy fraction. Plotted against mass number Ai, the yi give fairly smooth curves with some fine structure which is especially noticeable near the peaks. Typical widths of the mass distribution peaks are ~14-16 mass units at half maxima, and ~22-24 mass units at one tenth of the maxima. The mass defects -m, (for m, < 0 for all stable fission products) are nearly constant (~89 MeV) in the mass range 90 < A < 140, but outside this range they fall off approximately linearly with A (with a gradient of about f 1 MeV/mass

516

M. F.

JAMES

number). On top of this general behaviour, as might be expected, there are fluctuations of about f 1 or 2 MeV between neighbouring mass numbers. In searching for a reliable interpolation scheme, there are two important questions to answer. First, are the fluctuations or fine structure in yi and (-m,) important in the calculation of sL and gi,? Secondly, is it possible to relate C, and fiH to a few parameters (preferably one or at most two) defining the position and shape of the yield peaks? To attempt to answer these questions, we have used the accuratelyknown yields for 233U, 235U, 23*U, 23gPu and 241Pu, and have calculated sL and fii, from the light and heavy peaks for those nuclides, shifting them & 1, &2 . . . mass numbers. That is, we have calculated: (H)

fidk) = 2

i

corresponding

yimi+k

to a heavy mass peak with average mass number A-,(k): A-,(k) =

2

yi(Ai i

k) = k +

A;

(5)

2

fork=O,fl,f2 ,.... Similarly, we have calculated fiL(k) corresponding to a light mass peak centred at AZ(k). For the 5 nuclides for which accurate yields are available, this procedure shows how fiL and fi, depend on the positions of the mass peaks. For each nuclide, the calculated 5zH(k) and fiL(k) are smooth functions of AH(k) and AL(k), indicating that the effects of fluctuations in yi and -mi cancel out. The results of the calculations are shown in Fig. 1 for the heavy mass peak, and in Fig. 2 for the light mass peak. It will be seen that, to a good approximation, two sets of curves are obtained: one for 233Uand 236U, and one for 238U, 23gPu and 241Pu. Presumably the difference between these curves arises from differences in the shapes of the yield curves for the two sets of nuclides. The evaluation of VON GUNTEN (1969) has been examined to see if there is any single parameter of the shape that can be correlated with this difference. It appears that the relevant parameter may possibly be the full width at tenth maximum (FWTM): this is about 22 mass units for 233Uand 235U, and about 24 mass units for 238U,23gPuand 241Pu. No other parameter is easily identified which appears to have one value for the former set and a different one for the latter. Thus we have established a smooth variation of rE, with AH and of fiL with IL, and have suggested a possible correlation of fi, and CL with the FWTM of the peaks. By extending the curves of fiH and fi, to a wide range of values of A;i and AL we are also able to obtain values by interpolation, without having to indulge in the riskier business of extrapolation. Because of the observed dependence of fiH and CL on the shapes of the yield curves, we obtain from the present method a better estimate of the uncertainties involved in interpolation than we would from a more straightforward plot of fii, or fiH against the mass of the fissioning nucleus : the estimated uncertainties are probably larger, but more realistic. For 232Th and 237Np, values of AL, AE and FWTM are tabulated in the paper of VON GUNTEN (1969), and additional data for the latter nuclide may be found in NAMBOODIRI eral.(1968). The curves of %&AH) and fii,(AL) may therefore be used directly for these two nuclides. Similar data are not available for the other nuclides being considered here (viz. %U, 236U, 23sPu, 240Pu, and 242Pu), and the procedure

The useful energy released in LXTh, 233U, S4U, SSU, 237Np, ZSSPu,ZaoPu and ZdzPu

Curve”A”obtained

from

Curve”B”obtoined

yields

o

of “?J and =U

.

of ‘%

x

from yields

239P”

and 24’Pu

84.00

138.0

Mean

138 5

139.5

139.0

moss number

&of

r?

m

heavy

fission

140.0

140.5

products

FIG. I.-The variation of the mean mass defect (-7ira MeV) with the mean mass number (A,> of heavy stable fission products. Curve A was obtained using the method described in the text, from the yields from thermal fission of zsaU(0) and z”5U(0). Curve B was similarly obtained from the yields from thermal fission of 23BP~(0) and ar1Pu(~), and from the fission of Z38U(x ) by fission spectrum neutrons. Error bars represent uncertainties of 1 standard deviation. When they are not shown, the uncertainties are smaller than the size of the symbol.

Curve”A”

obloined

from

I

I

of 233~

o

and % from yields of ‘%lJ

Curve”B”obfoined

85.090 91

yields

??

x

I

I

I

I

1

I

1

I

[

92

93

94

95

96

97

98

99

100

al

of light

Meon

moss number

fission

1 lOI

1

1

102

103

products

FIG. 2.-The variation of the mean mass defect (--Z, MeV) with the mean mass number (K,) of light stable fission products. For explanation of the symbols, see caption to Fig. 1.

517

M. F. JAMES

518

that has been adopted for these has been to obtain KH and XL by linear interpolation or extrapolation in the effective fissioning mass A,, = A + 1 - F?, between isotopes of the same element for which the mean mass numbers are known, with the additional requirement that AL + KN = A,,. Some justification for this comes from the data for 233U, 236U and 238U, for which AL and A; are, within the experimental uncertainties, linear functions of A,,. Having estimated AL and A-,, Cii, and CiiHmay be read off the appropriate curves. For 232Th and 237Np, we assume a correlation of curve with FWTM (but give an appropriate uncertainty in case this guess is wrong), while for 2a’W, 236U, 238Pu, 240Pu and 242Pu points are chosen mid-way between the curves, again with appropriate uncertainties. Table 2 gives values of m(A, Z), fi,, Gii,,?ii=Fii=$fii,, and the derived values of Qi,,. 4. THE

FISSION

PRODUCT

DECAY

ENERGY

To complete the calculation of the useful energy from the fission, it is necessary to subtract from the total effective energy Qk,, given in Table 2 the kinetic energy of the antineutrinos from fission product beta-decay, and also the small amount of decay energy that is only emitted after very long times. So far as this latter quantity is concerned, we assume that it is the same for all the nuclides, and take a value of (O-15 & 0.15) MeV, which is the mean of the values for the energy emitted from 2W and 23QPuafter 3 yr. The antineutrino kinetic energy is estimated by assuming that the fractions of the total decay energy carried by gamma rays, electrons, and antineutrinos are the same for all fissile nuclides, so that we take these fractions to be equal to those estimated for 235U thermal fission in I, namely 0*303,0.294 and 0403 respectively. In I, the total effective chain length, z, was defined, and estimated from the formula : z = 4.28 + 0*214(A - i, - 23257) + 46 - (Z/2). (7) The total decay energy was assumed in I to be proportional to z2, but it can be shown that it should be more nearly proportional to z2/(A + 1 - it); the difference is at most about 3 per cent in the decay energy. Table 3 gives our estimates for z, for R = (Decay energy)/(Decay energy of 235U thermal fission products), for the antineutrino kinetic energy, and for the useful energy Q,, from fission. It also gives an estimate of the mean number ng of beta decays per fission, from the formula (I, Section 4.3): nfi = ?z8(23W)+ 2[z - z(2W)]. 5. OTHER CONTRIBUTIONS To complete this note, we estimate the remaining contributions to the total energy released from fission. Referring to equations (2) and (3) of I,

Ei+ Q;,,= J% + -% + &, + J%,

(8)

whereEi is the mean incident neutron energy (given in Table l), & is the mean kinetic energy of thefi ssion fragments after prompt neutron emission, l?,, is the mean kinetic energy of the prompt and delayed neutrons, L?,,yz) is the prompt gamma-ray . energy, and Ed is the fission product decay energy: Ed = Eyd -I- El + &

(9)

The useful energy released in 232Th,ZSSU,284U,238u, 287Np,238pu,24Opuand B4apu

519

520

M. F. JAMBS TABLE 3.-CHAIN

LENGTHS, NUMBER OF BETA DECAYS, AND THE USEFUL ENERGY RELEASED FROM FISSION Antineutrino

Nuclide Mean effective chain length, Z

(Decay energy) (Decay en. for 2S5U) = R

kinetic_energy

Meanno.of

LsSi!Zr (MeVzsion)

=Th *s*U

464 3.84

1.19 0.81

11.4 + 0.7 7.8 + 0.5

931U %%U “a7NP SaSPu **opu eazPu

4.01 4.43 4.11 3.82 4.18 4.63

0.88 l-07 0.92 0.79 0.94 1.14

8.5 10.3 8.8 7.6 9.0 10.9

"B

Useful energy from fission i&if

(MeV/fission)

6.8 YO-07).

184.2 * 0.9 190.0 * 0.5

5.5 6.3 5.7 5.1 5.8 6.7

188.9 191.4 193.6 196.9 196.9 200.0

(5.21 f * f + f &

0.5 0.6 0.6 0.5 0.6 0.7

f f + * i f

1.0 0.9 1.0 0.8 1.0 1.9

* Value in brackets calculated directly from yields for ‘WJ; these also give a value of B, = 2.474 f 0.031, to be compared with the recommended value (HANNA et al.1969) of 2.487 & 0.007.

where Eyd is the delayed gamma ray energy, $ is the mean electron kinetic energy; and & is the mean antineutrino kinetic energy. Using arguments discussed in I, we make the following assumptions. (i) &, is the same for all the nuclides discussed here, and equal to (8.0 f l-5) MeV, which is the value recommended in I for 235U, with an increased uncertainty. (ii) ,!?, = ?9 x

(mean prompt neutron kinetic energy) = ~,(a + bdF,

+ I),

(lOa) where

a = (0.74 i O-02) MeV b = (0.653 i O-02) MeV; I

(lob)

(TERRELL, 1962); we neglect the very small contribution from delayed neutrons ( ~0.04 MeV). (iii) As already explained in the previous section, we assume that Ed cc z2/ (A + 1 - FJ, and that ,$,,,/E,, &/$, and &,,I,?$ are the same as for 235U thermal fission. It is now possible to use equation (8) to calculate the average kinetic energies in MeV of the fission fragments after neutron emission (J!&). Table 4 gives estimated values of the various contributions. As has been stressed throughout this paper, measured values of any of the contributions for these nuclides are sparse. However, some measurements of &, the mean fragment kinetic energy before neutron emission, have been made for 233Uand 237Np. This quantity (see I) is related to J?$ by:

Ek % &(l

- &/A).

(11)

The last column of Table 4 gives the estimates of J!$~and in Table 5 some of these are compared with measured values. It will be remembered from I that &.. may be measured either by time-of-flight (TOF) methods, or by means of solid state surface barrier detectors (SD), and that there is a discrepancy between the results of these two methods, the former giving values -4 MeV less than the latter. As in I, the theoretical values agree better with the time-of-flight measurements.

Z.E 7 I.PLI 9.Z i S.&L1 z.z F I.PLI 9.z i P.ILI 8.2 =F 9.L9I P*Z i S.L91 E.Z F S.L91 0.E T 8.6S[

Z.E i 9.z f Z.Z F 9.Z f 8.Z T P.Z F E.Z ? 0.E f

6.ILI S.ILI O.ZLI E.691 L.S91 9491 8.597 Z.SSt

z.z T O.LZ 6.1 f E.ZZ s.1 'f 8.81 6.1 F 8.12 1.z 3= s.sz L.1 7= O.IZ L.1 F E.6T S.Z F E.SZ 9.0 =F 5.0 T P.0 F 5.0 i s.0 F 5.0 ‘f 9.0 F 9.0 F

96.L 9s.9 zs.s IP.9 0S.L 81.9 89.5 ES.8

L.‘[ F 61.8 P.1 3= SL.9 z.1 T L9.S P.1 i 09.9 L.1 i 0L.L E.1 T 9E.9 E.I 'F S8.S 0.5 T LS.8

5.1 i 0.8 S.I ? 0.8 S.1 ? O-8 S.1 'f 0.8 S.1 F O-8 5.1 F 0.8 S.1 -f 0.8 S.1 F 0.8 sr.0 ?= s1.0 T st.0 T VT.0 i PI.0 F CI.0 i ZI.0 ?= zr.0 i

OS.9 OL.9 68.5 L8.S SE4 trE.S L8.P 0L.P

1.0 F ZE.Z I.0 F 6E.Z 0 I.0 F LE.Z I.0 F Z8.Z I.0 i 9E.Z 0 I.0 F 6E.E

nsrz f-h necz YLLa&Z

“dew “dsse d&z

“dove

522

JAMES

M. F.

TABLE 5.-COMPARISON OF PRESENT ESTIMATES OF PRE-NEUTRON EMISSION FRAGMENT KINETIC ENERGIES WITH MEASURED VALUES

Nuclide

Present estimate (MeV/f)

zssu

167.5 f 2.3

ZSSU,238U

0.992 f 0.01 171.4 f 2.6

‘B,NP

Measured value Value (MeV/f) 163 167.0 171.2 0.9909 174.0

Method*

Reference

TOF TOF SD

STEIN (9157) MILTON and FRASER (1962) BENNETT et al.(1967) OKOLOVICH et al.(1963) BENNETT et& (1967)

*2 k 1.7 i 2.0 f 0.0014 i 2.0

SD

* TOF = Time-of-flight. SD = Solid state detector.

We can also make some comparison of our theoretical estimates of ,?& for 232Th and 233U with the experimental results of FISHER and ENGLE (1964), who measured the delayed gamma energy released up to 45 set after fission. Making the assumptions described in Section 4.3 of I, extrapolated values for EYd were obtained from the measured data, and these are compared with the present estimates in Table 6; the agreement is reasonable. TABLE 6.-COMPARISON OF PRESENT ESTIMATES OF DELAYED GAMMA-RAY ENERGY (&ydMeV/fission) WITH MEASUREMENTS OF FISHER AND ENCLE (1964)

Nuclide

Measured (0.245 set)

Extrapolated (0-m)

lszTh 233U

5.04 * 0.71 1.97 * 0.28

8.96 & 0.71 5.89 * 0.28

Present estimate 8.57 + 2.0 5.85 & 1.3

CONCLUSIONS

Values of the useful energy released from the fission of 232Th, 233U, 234U, 236U, Py 238Pu, 240Pu and 242Pu have been obtained using mass excesses, and estimates have been made of the contributions to this energy from the kinetic energies of the various particles emitted in fission. Where experimental data are available, the present estimates appear to be confirmed. The methods outlined in this note may readily be extended to any fissile nuclide. The accuracy attainable is probably more than adequate for reactor calculations, remembering that only a relatively small fraction

237N

TABLED.-TOTAL EFFECTIVE ENERGY PER FISSION IN A THERMAL REACTOR, INCLUDING CONTRIBUTIONS FROM CAPTURE (MeV/fission)

Nuclide asPTh HsU 284U WU WN

P 1S8Pu P'OPU a'aPu

Contribution from fission 184.2 190.0 188.9 191.4 193.6 196.9 196.9 200.0

f 0.9 * 0.5 f 1.0 & 0.9 &- 1.0 & 0.8 f 1.0 * 1.9

Contribution from capture 8.6 9.1 10.3 10.4 11.5 11.6 13.5 13.1

f * f & + f & f

0.4 0.4 0.8 0.6 0.6 0.6 0.8 1.4

Total 192.8 199.1 199.2 201.8 205.1 208.5 210.4 213.1

f f & f f f f f

1.0 0.6 1.3 1.1 1.2 1.0 1.3 2.4

The useful energy released in 232Th, 233U, 23aU, 236U, *37Np, z3BPu, ztoPu and z4zP~

523

of the total energy will be obtained from the fission of these nuclides (except for 233U, for which the accuracy of our results is in any case much better). The useful energy released per fission in a nuclear reactor includes contributions from neutron capture and other reactions besides fission. In Appendix A of I it was stated that, for a wide range of thermal neutron reactors, a single value of (6.1 & 0.3) MeV could be used for the mean energy released per neutron captured. Since (F - 1) neutrons are captured (in the core, reflector, or shielding) per fission, this constant value has to be multiplied by (Yt - 1) to give the contribution from capture to the energy per fission. The contributions and the total values are given in Table 7. author is grateful to Dr. Cond& of FOA, for private communications.

Acknowledgements-The A.N.L.

Sweden, and to Dr. Jaffey of

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