Measurement of prompt neutron fission yield (v̄p) in thermal neutron fission of 232U, 238Pu, 241Pu, 241Am, 242mAm, 243Cm, 245Cm and in spontaneous fission of 244Cm

I

2.J

] I

Nuclear Physics A145 (1970) 1--27; ( ~ North-Holland Publishiny Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

M E A S U R E M E N T OF P R O M P T N E U T R O N FISSION YIELD (~p) IN T H E R M A L N E U T R O N FISSION OF 232U, 2aSPu, "~IPu, ~ l A m , ~2mAm,

24aCm,24SCmA N D

IN S P O N T A N E O U S FISSION OF 7"4~Cm

A. H. JAFFEY '~ and J. L. LERNER *t

Aryonne National Laboratory, Argonne, lllinois 60439 Received 9 May 1969 (Revised 24 November 1969) Abstract: The prompt neutron fission yield (~,p) has been measured in thermal neutron fission of 232U, 23apu, 24tpu, 2'*~Am, 2'*2roAm, 24acre, 24SCm and in the spontaneous fission of 2'~'*Cm. A coincidence method yielded ratios to the ~p values of the standards 233U, 23sU, 2agpu and 252Cf, with fission fragments detected in an ionization chamber at close to 100 % efficiency, and with fission neutrons detected using four ZnS(Ag) methyl methacrylate discs (Hornyak buttons). The small variation of neutron detection efficiency with fission neutron spectrum differences was calibrated with the four standard nucleides.

E

NUCLEAR FISSION 232U, 23a. 2,,tpu ' 2,,1.2,~2mAm' 2,*3.245Cm(n ' f), E = t h e r m a l ; measured relative prompt neutron fission yields (vp). 24'*Cm(SF); measured (vp).

I I

I. Introduction Measurements of average neutron yields (~) from thermal neutron fission were originally motivated by the need for accurate values in chain-reaction design. Indeed, the most accurate measurements have been made with those nucleides of use in nuclear reactors (233U, 235U, 2 3 9 p u , 2 4 1 p u ) . However, f values are also of interest in that they are a measure of the average excitation energy left in fission fragments immediately after fission. Any systematic consideration of the variation of fission properties over the (A, Z) range of the heavy elements must account for the i~ variation. We have attempted to expand the number of nucleides whose ~ values have been measured, and to check published values for some others. For most of these nucleides, the amounts of material usable in a measurement were limited either by the unavailability of larger amounts or by the fact that too much associated ~t-activity created a disturbing background in the ionization chamber. Hence, a comparative ~ measurement method was chosen, since absolute measurement was not feasible with samples which might be < 1 /~g in size. The results reported are ratios of the ~p value of a measured nucleide with ~p values from standard substances whose neutron yields have been measured absolutely. Our method of measurement gives only ratios Ofgp values, * Work performed under the auspices of the US Atomic Energy Commission. tt A more detailed description of this work may be found in Argonne National Laboratory Report-7625 ref. 29). 1 April 1970

2

A. H . J A F F E Y A N D J. L. L E R N E R

where i~p is the average yield o f p r o m p t fission neutrons, and does not measure i~, the average total yield (which includes delayed neutrons).

2.

Vp Measurement

method

2.1. GENERAL For each u n k n o w n nucleide, ~p was measured by comparison with three nucleides whose i~p values have been determined absolutely with good accuracy, i.e., 233U, 23SU and 23'~pu. In some cases, 252Cf was an added standard. The tissionable material was mounted on a platinum plate, inserted into a gas-filled ionization chamber, and exposed to a collimated thermal neutron beam from the A r g o n n e CP-5 reactor. The chamber had essentially 100 % efficiency for detecting fission fragments. The neutron detector, so placed as to subtend as large a solid angle as possible, contained several H o r n y a k buttons 2"~), each one a mixture o f the scintillator Z n S ( A g ) and methyl methacrylate polymer (Lucite). The output pulse height from a fast neutron and from a ?-ray differed greatly, so that even a high intensity ?-ray flux was easily discriminated against. The measured coincidences between fission fragment and neutron counts corresponded only to neutrons detected within a few microseconds after fission, so delayed neutrons were not included, the experiment measured only i~p. 2.2. CALCULATION OF i~t, FROM COINCIDENCE MEASUREMENTS In the simplest possible case, (i) the sample is uniformly spread, (ii) thermal neutron flux is spatially uniform, (iii) neutron detection efficiency is the same for a neutron originating anywhere in the sample, and (iv) there is no accidental coincidence. Let Av = fission counting rate, A s = neutron counting rate from sample, A,~ = backg r o u n d neutron counting rate, A, = total neutron counting rate = AS+A~, C = coincidence counting rate, 0 = thermal neutron flux, av = fission cross section, M = n u m b e r of a t o m s o f tissionable nucleide, Cv = tission fi'agment counts per fission (efficiency), ~,~ = neutron counts per fission neutron emitted (efficiency). Then, if ~;. is small enough AF = [ M a . ~ ] ~ F ,

A~ = [ M , ~ v 4 d [ ~ o ] ,

c = [Mo~4q[~,,~:.]~.~.

(1)

(2)

c -

-

~,, ~:..

(3)

AF If ~' is measured for nucleides A and B, ?p(A) _ (6~A z,(B) i~p(B)

(4)

%'n ~:,(A)"

T h r o u g h caliblation o f the efficiency ratio, i~p can be calculated from the i~p o f a known nucleide.

NEU rRON FISSION

3

Consider the case when the sample spread, neutron flux or neutron detection efficiency are not uniform. With (p, 0) the spatial coordinates over sample area S, let m = n u m b e r of atoms per unit area = m(p, 0), t,b = ~b(p, 0), en = e,(p, 0), er = ev(P, 0). Then eqs. (1)-(3) become

Av=~f~me~dS, AF

(5) -I evmc~dS

(6)

If e, is constant over the sample, r~ reduces to eq. (3) for any eV, 4' or m distribution. The e,n was theoretically and experimentally verified to be sufficiently constant over the sample dimensions (subsect. 3.2). Since the samples were thin, eF was very close to unity in all cases. 2.3. THE RELATION OF en MAGNITUDE TO ~'p CALCULATION In subsect. 2.2, the probability of counting a fission neutron is written in the simple form ~peo, where ~p is the mean n u m b e r of fission neutrons emitted and e, is the probability that a fission neutron creates a photomultiplier pulse large enough to count if the channel is open. With a fast neutron detector, the simple addition of probabilities used is not valid unlessg2t, the probability that several neutrons from the same fission create countable pulses, is much less than "~t, the probability that only one neutron does so, i.e., ~ t < < ' ~ 1 ° This is true only when e. is small. The g~t m a y be evaluated from some simple probability considerations. Let k = n u m b e r of neutrons emitted in one fission event, ,~, = Prob {at least one neutron creates a countable pulse}, Pi = Prob {j neutrons simultaneously create countable pulses}, Qj(k) = Prob {j neutrons simultaneously create countable pulses, if k are emitted}, P(k) = Prob {k neutrons are emitted}. Since :~n = ~ l + ~ t , the product Ype n is appropriate when ?~. ~ 5~1, i.e., ,~t << ~ 1 . With K = m a x i m u m n u m b e r of neutrons emitted in one fission event, K

Pi

= 2 k=j

Qj(k)P(k).

(7)

The probability P(k) is well represented as a binomial distribution 4v) P(k) = (kr)pk(1 _p)r-k, where p is characteristic of the fissioning nucleide, and with mean value ~ ( k ) = f:p = Kp; Qj(k) is the binomial Qj(k) = (k)~(1--en) k-j. The convolution (7) is then the binomial

pj = (K) (pe.)J(l--pe.)r-J Then,-~. = 1-Prob

(8)

{no neutrons are counted} = 1 - P o , or

'~n = 1 - [ l - P e n ]

K -~ "~ve,[1-½~pe.+½pen].

(9)

4

F o r two nucleides with

A.H.

(K', e',,,p')

J A F F E Y A N D J. L. L E R N E R

a n d ( K " , e',', p " ) , -p

v F~'r!

{))°n

_

t

(]o)

2-,,., Vp~;n

where ~ = ½ [ ~ , e ' - ~ ' p ' e ' . ' ] + ½ [ p " e " - p ' e ' . ] ~ ½eo{[v~,-~,']+ [ p " - p " ] } , since ~,; = e~,'. T a k i n g m a x i m u m differences, a n d with ~, ~ 5 × 10 - 4 , ~m,~ < ~(5× 1 0 - 4 ) [ 1 . 5 + 0.17] = 4 × 10 - 4 , ¢ is much smaller than the experimental error, hence m a y be neglected. This would not be true, however, if c, exceeded 1 % .

3. Measuring apparatus 3.1. GENERAL The i o n i z a t i o n c h a m b e r a n d s a m p l e were placed in a collimated n e u t r o n b e a m f r o m the A r g o n n e CP-5 r e a c t o r t h e r m a l c o l u m n (fig. 1). T h o u g h flux uniformity was n o t necessary, e x p l o r a t i o n with a small source showed the flux to vary by < 4 ~o within an a r e a o f 10 m m radius. { " ~

Sample

.... ;iil

Thermal

~!i: : il

Neutron Beam

u '

u

~~'---Col!ectin~ .

:

~

~

J

Electrode

~i~i-i "~.~"-~-Photomultiplier ~£-.Y Tubes

L_ Coverplote 0.020" AI

I0 89

i 23~HES O~'IN ~"

Gamma Roy Absorbers

Fig. 1. Neutron beam collimator and detector assembly. The bismuth block strongly attenuated the 7-ray flux at only a moderate cost in neutron flux. The ionization chamber structure also served as the scintillator-photomultiplier supports. The sensitivity o f the H o r n y a k b u t t o n a n d p h o t o m u l t i p l i e r to the 7-rays a n d neut r o n s in the b e a m required the neutron d e t e c t o r to be placed outside the beam. T h e detection efficiency was i m p r o v e d t h r o u g h the use o f four identical n e u t r o n d e t e c t o r s a n d their s y m m e t r i c a l p l a c e m e n t a r o u n d the s a m p l e helped in keeping e. quite constant over the s a m p l e area.

NEUTRON F I ~ I O N

5

3.2. CONSTANCY OF e. OVER THE SAMPLE

Fig. 2 illustrates the (calculated) variation in solid angle subtended at the combination of four detectors. Though the sample cups (fig. 3) placed every sample plane at the same position, curve C shows that this positioning was not critical. Curves A and 1.05 1.04 1.03 1.02 j -

#4

>,

t.__

i

E 1.01 -

o eJ tD

N

A

#3

I.OOF

#1

O

E o Z

0.99 f 0.98

t

0.97

0.95

i

#2 (C perpendicular to plane of figure)

0 0.2. 0.4 0.6 0.8 1.0 1.2 L4 CM Displacement of point source from center

Fig. 2. Calculated variation in solid angle subtended by all four Hornyak buttons when a point source was moved. Curves A and B represent points in the plane of the sample. Curve C shows the effect of moving the source perpendicular to the usual sample plane. From C, it is evident that the neutron detection efficiency was insensitive to the exact positioning of the sample plane.

Cover P l Teflon ~ Insul°t ° r - -

o

t

e

~

/ - A I Sample /Cup

I t.~-----'--~J

I Thermol___l_W___L_~L_~_____ --Sample Neutron - - - [ - - - - - I - - ----1 . . . . Beam . . . . . . . . . . . . . . - - P t Sample Moo°,

Counting G O ~ ~ Inlet "

~

z

/

,

FISSION CHAMBER CROSS SECTION Fig. 3. Ionization chamber.

6

A. It. JAFFEY A N D J. L. LI-RNER

B show that the solid angle varied less than 1 0'o over a sample whose radius was < 5.5 mm. Measurements made with a small ZSZCf source placed at a number of positions in the sample plane experimentally demonstrated the constancy of c., since ~6 remained constant within statistical counting error (_+ 1 ~ ) out to a radius of 10 mm in all directions. All the samples used in the fp measurements lay well within this region. The areas covered ranged from 1.5 mm to 5 mm in radius. 3.3. NEUTRON DETECTOR AND IONIZATION CHAMBER The l lornyak button was made by thoroughly mixing very fine powders (about 300 mesil) of RCA scintillator-grade ZnS(Ag) and dried uhra-fine acrylic (Lucite), in the respective wcight ratio 3 to 20. The mixture was die-molded at raised temperature and pressure and then machined to the tinal thickness. Buttons of 3 mm thickness were used, since tests indicated these gave optimum results (minimum net coincidence crror). This scintillator gave very good discrimination against the intense beam of reactor 7-rays. Output pulses fl'om the Hornyak button varied over a wide range of pulse height, because of the inherent energy variation of fission neutrons, the variation of proton energies with recoil angle and because of the variable path length in ZnS crystallites. Over the useful range (i.e., beyond the small pulse heights t¥om )'-ray pile-up), the counting rate versus pulse-height curve dropped exponentially. Because of this sensitivity to gain or pulse-selection level, c. varied during a long series of measurements lasting sevcral weeks; e, variation was an important source of error in this experiment. Frequent measurement of standard samples yielded a running c, calibration, which was used to correct measurements on the unknowns. Even with this correction, data scatter exceeded that expected from counting statistics alone; errors were then calculated entirely from the scatter of measured values (external error). In all cases, enough coincidence counts were accumulated so that counting error was less (and often, rnuch less) than the scatter due to r. variation. The main body of the aluminium ionization chamber was also the supporting structure for the four scmtillator-photomultiplier assemblies (figs. I and 3). A Teflonsupported, perforated thin aluminium plate allowed gas flow and served as collecting and high potential electrode. The aluminium sample-holding cup closed the chamber and served as the ground potential electrode. A mixture of argon and I0 ,~, methane flowed slowly through the chamber after an initial rapid flush. 3.4. SENSITIVITY OF METHOD Measurement sensitivity was limited by the sample size available (or usable), by the fission cross section av, and by the thermal neutron flux, which was typically 3 x 10 v neutrons/cm 2 sec. At this flux, 5 pg o f a nucleide with av = I00 b would give about 2200 fissions/rain and about 3.4 coinc/min. For such a sample, considerable counting time was needed to accumulate enough events for reasonable statistical error.

NEUTRONFI~ION

7

3.5. EFFECT OF g PILE-UP One factor limiting the sensitivity was the amount of material usable if the nucleide was intensely :e-active. To keep ~v very close to unity, measurements were not made unless the fission counter had a good plateau. This was not possible with very high c(-activity, because of pulse pile-up from :(-particles. The tolerable :(-activity was considerably increased through a decrease in the effective dimensions of the chamber. A thin-walled plastic cylinder was placed around the sample between sample and collector plates, reducing the effective chamber to a cylinder 28 mm in diameter and I0 mm high. This reduction considerably decreased the longest c(-particle track-lengths (parallel to the sample plate) with only a moderate loss in the fission fragment track-lengths. The small dimensions further improved the fission-to-:( ionization ratio, since an :(-track's heaviest ionization lies near its end, while a fission track is heaviest near its beginning. The plastic shield did not affect the measured cg, = C / A F ' but did increase the fission rate and neutron background count rate, because of the shield's in-scattering of thermal neutrons and out-scattering of fast reactor neutrons.

3.6. CIRCUITRY RESOLUTION LOSSES Fig. 4 shows a block diagram of the circuitry. Since the fixed deadtimes of the multivibrators exceeded those of the sealers (01 > 02, 03 > 0,,), the singles scalar dead-

FISSION H

FRAGMENT DETECTOR

L~'

AMPLIFIER

PULSE FIMONOSTABLE~I MULTIFISSION [ VIBRATOR SCALER i 01 e2

HEIGHT SELECTOR

i r

COINMICIXDER. ENCE r

COINCIDENCE SCALER e~

FAST ~ NEUTRON DETECTOR

[__[ PULSE AMPLIFIER HEIGHT l SELECTOR

J MULTI| VIBRATOR

NEUTRON SCALER e4

Fig. 4. Block diagram of circuit. times were irrelevant. Deadtime losses due to 0s were negligible, because of low coincidence rates. Including deadtimes changes eqs. (1)-(3) to AF = [MaF4~]¢F(1--A¢O,), C = [MaF(b]eF(1--AFO,)[~ve.][I--AB03],

_ C _ ~pe.(l-A~03). Av

(11) (12) (13)

8

A. II. JAFFEY AND J. L. LERNER

Since A.O 3 was always < 8 × 10 -4, the correction term (I -Aa. O3) was neglected, and measured ~-values were related to 9p and e.n as in eq. (4). 3.7. C O I N C I D E N C E

TIME

The coincidence time z was set at the minimum value allowing counting o f all true coincidences. Since the z-value, approximately 1.8 psec, was used in correcting for accidental coincidences, it was empirically calibrated to good precision as follows: A 23~U sample, counted in the usual way, yielded values o f C, Av, A.. A larger 235U sample was fastened to the back o f the same sample cup, hence was very close to the first sample, but outside the ion chamber. The neutron counting efficiencies o f both samples were the same, but the larger sample provided no fission fragment counts. Both samples together yielded values C', A'v, A'. with A'n > An. Then

C = AFenVp+2zABAv,

C' = AFenVp+ZZAB'AF,

(14)

where 2rAdAr represents the accidental coincidences arising from uncorrelated fission and neutron counts. Then C' C 2z = A~: AF B' B" An - A . N o w A ~ ' ~ A s' and A s ~ A s' , so that. vely closely, A n - A : C'

= AnB'_A.,B and

C

2z = A'F

AF A'n- A n

3.8. S T A N D A R D

(15)

SAMPLES

Standard samples and unknowns were prepared in the same way (sect. 5). Isotopic compositions o f the standards are shown in table l. "Ihree to four samples were used o f each standard.

4. Calculations, corrections and systematic effects 4.1. C O R R E C T I O N

FOR ACCIDENTALS

F r o m eqs. (1) and (2), with A ° = Maven, then AF = A°vev, A. = A vo -V p e n + A nB, and Ctot = Ctr.c+Ca¢¢id = A°e.ve.f'.+2rAvAa.. Solving for A~,

Ctr.¢ = C , o t - 2 z a v A ~ = C,o, -

2zAv [tFAn-Cto,]. sF-2zA v

(16)

Or, ifev ~ l, as was the case in this experiment, C...e = Ctot

2zAv [ A . - C t o t ] . 1 - 2tA F

(17)

NEUTRONFISSION

9

The accuracy needed in this correction was modest, since [C,~,,IC~¢¢~d]was never < 6 and was usually larger. The C-values referred to hereafter are C,,,, values, as calculated from eq. (17). 4.2. CORRECTION FOR NEUTRON-DETECTOR DRIFT All C/F = ~-values were corrected for time-dependent e. variation with a calibration curve based on X-values from the standards. During one experiment or series o f measurements, samples o f each o f the standard nucleides 233U, 235U, 239pu were counted 20 to 30 times over a period of one to two weeks, each o f the standard nucleides suffering approximately the same distribution o f e . variation. All X-values for, say 239pu, were averaged to give ~9, and similarly for 235U ((0¢~"5) and 233U (~¢'3)" The ratios ~ 9 / ~ 5 , W9/W 3 and W3/~ 5 werc very closely the same over the many experiments, thus justifying the assumption that e. variation swept over the same distribution o f values for each of the standard nucleides. For each 239pu X-value, the efficiency ratio y~ = W J ~ 9 was evaluated, and similarly for 235U and 233U X-values. For most o f the experiments, ?i varied less than +_3 ~/o a r o u n d 1.00, although the variation in some series was as large as _+6 o//<,.The calibration curve was a best-fitting plot o f all the y-values against time. Every measured Wvalue, standard and unknown, was then corrected to c-6"* = Wj/FJ, where Fj was the calibration factor taken from the smoothed curve. In general, for a ~ j value flora a standard, F~ ¢: 7j. Hereafter, when the term r( x is used, it refers to the drift-corrected average value Wx = ( l / n ) ~ i = t ~i for the nucleide X [for the error calculation, see refs. 29,3o)]. 4.3. CORRECTION FOR OTHER FISSIONING ISOTOPES For most o f the measurements, the " u n k n o w n " nucleide was mixed with other fissionable isotop2s. Their effects could be corrected for, since their ~p values, their relative concentrations, and their relative numbers of fissions were known. Thus, for isotopes X, v, w with Avx = fission rate of X, Cxvw = e,x Vpx A Fx + e,v VpvA Fv+ e,w Vp~,A Vw"

(18)

Ifi;pX is the unknown and measurements are made relative to a standard S, then, with

fx

= AFx/AF

and A F =

AFx+AFv+AFw, t_

ix

ix

,<.s,

SxJ

The ratios (.fx, fv,fw) were calculated from the known mass ratios and thermal neutron fission cross sections. Eq. (19) is used to calculate the ratio Of~px to ~;p of one of the standards. For evaluating a ~px estimate from these ratios and the standard 9p values, the most appropriate averaging procedure uses the measurements on the standards to evaluate ~:,x.

[0

A.H. JAFFEY AND J. L. LERNER

The three standards 235U, 233U and 239pu are numbered (1, 2, 3), and all three *6~-values are used to calculate C,s. Thus, F,~ = c6:t/'vpl, e.2 = W2/i~p2, e3 = c'6"~a/f'p3derive from the known i~p values and the measured C6-values of the standards. These provide independent estimates of e,,x through use of c-ratios taken from tig. 6: (SnX)l = 151 (~nXt , \81 1

(SnX)2 = 82 (L-'nXI , \82/

(SnX)3 = 83 (SnXl , \83/

(20)

where e,x is the average of (e,,x)l, (e,x)2, (e..x)3. Then -

'

"°"<= ; - ' x

L

7x

(21)

with 8-ratios taken from lig. 6. 4.4. CORRECTION FOR A SPONTANEOUSLY FISSIONING ISOTOPE When the interfering isotope spontaneously fissioned, it was corrected for by measuring ~6; with the thermal neutron beam absent (beam shutter closed). To calibrate the difference in e, for the spontaneous fission isotope with and without the thermal neutron beam present, ~6: was evaluated with a 2 S E c f sample, for which the spontaneous fission rate greatly exceeded the neutron tission rate (table l). Twenty-six such comparisons, made during the experiments in sect. 6, averaged to 252Cf:

R - ~ [ b e a m on] _ 1.038+_0.005. ~ [ b e a m off]

(22)

An explanation of the increase in counting efficiency for fission neutrons when the thermal neutron beam is turned on in is: A high flux of),-rays from the reactor beam is scattered from the sample into the neutron detector, creating m a n y very small pulses whose pile-up is well below the selection level. This pile-up creates an increased "noise level" or baseline, with larger positive and negative excursions than occur in the b e a m ' s absence. A pulse generated by a fission neutron has as much chance of hitting a " n o i s e " peak as a valley. Some neutron pulses [Type A], intrinsically just below the selection level, m a y superimpose upon a " n o i s e " peak and be counted; other neutron pulses [Type B], intrinsically just above the selection level, may superimpose upon a " n o i s e " valley and be not-counted. The pulse-height distribution drops off exponentially, so there are more Type A than Type B events, hence the net counting rate is increased. When a mixture of isotopes is measured, fol the spontaneous fission alone (beam off) of, say, the v-isotope, we measure ~ " = e.',,i~r,, where e',v is the efficiency for isotope v with the neutron beam off. Taking e.o,, = Re.',,, with R in eq. (22), c6, = R ~ " = = e.n,.i~p, iS the value ~(,~ would have had if measured by itself in the neutron beam. Then the i~o ratio is

,,,s-

ix

ix,

NEUTRON

FISSION

1l

F o r the averaging relation equivalent to eq. (20), _

1 FC~X,,w-fv c6',,

V°X= nX L

(e._~_)fw

Jx

Jx

]

(24) "

If fp, is known, eqs. (19) or (21) m a y be used instead o f eqs. (23) a n d (24). A s before, fw is calculated from the k n o w n fission cross sections and mass ratios; fv, on the other hand, is the measured ratio: [fission rate, b e a m off]/[fission rate, b e a m on]. 4.5. EFFECT OF DIRECTIONAL CORRELATION BETWEEN FISSION-FRAGMENT AND FISSION NEUTRONS A potential systematic e r r o r arises from the k n o w n c o r r e l a t i o n between directions o f fission fragments a n d emitted fission neutrons. Because o f this correlation, detected neutrons derive largely from those fragments having large velocity c o m p o n e n t s p a r a l lel to the sample plate; hence, these form the fission f r a g m e n t pulses involved in m o s t o f the true coincidences measured t. W i t h " t h i c k " samples, such fragments tend to be s t o p p e d in the sample m o r e frequently than fragments emitted p e r p e n d i c u l a r to the sample plate. Hence, sample self-absorption cuts the coincidence rate m o r e than the fission rate, with a consequent decrease in ~ = C/,4 F. I

I

I

I

I

I

I

I

1.04 bd

' I--Z

1.02

O

t .00 Z 0

-~ 0 . 9 8 LL

~-

0.96

.J IJJ

0.94

i.o 2.0 3.0 4.0 RELATIVE PULSE SELECTION LEVEL Fig. 5. Counting rate plateau in fission fragment detector. Because o f this p o t e n t i a l error, sample p r e p a r a t i o n m e t h o d s were designed to minimize sample self-absorption. S a m p l e mass was small, frequently < 10 itg, pre* In an experimental demonstration of the effect, a 235U sample was placed in the chamber without a surrounding cylinder (subsect. 3.5). Fission tracks (A) with a large velocity component in the sample plane then yielded full ionization, whereas tracks (B) close to perpendicular to the sample yielded only ionization from about 1 cm of track. When the fission pulse-height selection level was increased to cut the fission rate to 60 ~ of the plateau value, Type (B) tracks were preferentially cut out. This decreased Ar morc than it did C. The observed incrcase in ~ = C/Ar was about 10 °r,',.

12

A. H. JAFFEY AND J. L. LERNER

purified (by solvent extraction a n d ion exchange) to remove non-active solids. Spreading agents were used to i m p r o v e the uniformity o f s a m p l e spread. T h a t s a m p l e abs o r p t i o n was as small as was indicated by the very small fission p l a t e a u slope (fig. 5). T o minimize the s e l l - a b s o r p t i o n effect, the pulse selection level used was as low as was feasible while allowing a d e q u a t e p r o t e c t i o n against ~ pile-up. Finally, for a n u m b e r o f the nucleides measured (including s t a n d a r d s ) , several samples c o n t a i n i n g different a m o u n t s o f the same material gave the same wflues o f ~ = C/AF. 4.6. i,p VALUES FOR THE STANDARDS There is now some uncertainty as to the a b s o l u t e scale for the s t a n d a r d f:p values. E x p e r i m e n t a l ~p ratios agree better than the a b s o l u t e values. Unresolved differences in measured values ot" i:p (2sZCf) is the basic p r o b l e m . W e use a m i d w a y value, ~p(252Cf) = 3.764 [refs. ~0..~)], with c o r r e s p o n d i n g i~p values in table 1. TABLE 1

The .~p values and isotopic composition of the standard samples of 239pu, 235U, 2 3 3 U and 252Cf 235U 2.407:½0.005

239pu

2.884 : 0.007

Vp

composition

isotope

atom

239pu

100.00

24°pu

"~ 0 . 0 0 8

isotope

2.~3U 2.478 ~0.007

atom

isotope

o, /~1

252Cf, ) 3.764 !.0.015

atom

isotope

o, o

-'3'*U 23sU

1.095 i_0.004 93.44 ::0.02

236U 238U

0.0054+0.0003

235U

5.46

238U

~-0.02

233U 23'*U

98.22 4_:0.01 0.1377:-0.001 0.019-: 0.001 1.62 -" 0.01

atom o, o

2'~°Cf 2~°Cf 25~Cf 252C|"

"l In this sample, [spontaneous fissions/thermal neutron fissions] :> 104. O u r results are presented as ratios to the s t a n d a r d values. A n overall averaged i~p value for the u n k n o w n is also calculated t h r o u g h use o f the s t a n d a r d values (table 1 ). F u t u r e definitive results on ~v(252Cf) will shift our r e p o r t e d i~p values by the relative shift from the 3.764 value. 4.7. CALIBRATION OF RELATIVE NEUTRON COUNTING EFFICIENCY VARIATION WITH NEUTRON ENERGY SPECTRUM Since the relative c o u n t i n g efficiency for fission neutrons enters into calculating 9, ratios [eq. (4)], o u r ~p m e a s u r e m e n t s were feasible only because the fission neutron spectra from various nucleides are very similar, so that the ratio e,(A)/~:n(B) is close to unity. W e c a l i b r a t e d this ratio over a wide range o f spectra and f o u n d it not to exceed 1.03; in most cases, it was less. Nevertheless, to a v o i d a systematic error, a c o r r e c t i o n for the spectral differences was necessary, and for this some i n t e r p o l a t i o n m e t h o d was needed. A l t h o u g h neither m e a s u r e m e n t s nor theory o f neutron spectra are well-established, it was sufficient to use the a p p r o x i m a t e relations k n o w n to provide an i n t e r p o l a t i o n device to tie o u r c a l i b r a t i o n d a t a together.

8.8 20.7 7.6 62.9

13

NEUTRON F I ~ I O N

Over a large part of the energy-range, the neutron distribution is fitted fairly closely by the gamma distribution

N(E)dE -

1 1 e~e_~/~dE. Y(!}) V t

(25)

Since the N(E) distributions for various nucleides almost completely overlap, the corresponding values of the mean energy, E = -}T, do not differ much and the e. values are almost the same. The relative ~-values for the standard nucleides 233U, 235U, 239pu, 252Cf were used to calibrate an e, curve. From eq. (3), I~n(233U) .......... -- (~(233U)/~(~(235U)

(26)

The numerator on the right side is derived from ratios averaged over all the experiments. The denominator comes from the known ~p values (table 1). The ratios ~ n ( 2 3 9 p u ) / s n ( 2 3 5 U ) and e,,( 252Cf)/Cn( 235 U) were similarly evaluated. Experimental c6~-ratios, standard Op ratios and values of en(X)/e,(235U) are listed in table 2. TABLE 2 Data entering neutron efficiency calibration Nucleide ratios

"6-ratios ")

~p ratios b)

. .eo(X) ......

~:n(235U)

)

.E,(X) ....

~(235U)

f)

233 U 235 U

1.039 :=0.002

1.030 :-=0.004 c)

1.009 _-_0.005

1.006

1.229 ::t:0.003

1.199 -:-0.004 c)

1.025 -1.-0.004

1.041

1.591 -0.008

1.560±0.002 a)

1.020±0.005

1.112

aSgpu 235 U

2s2Cf 235 U

a) b) ¢) e)

Averaged from all experiments in sect. 6. These are not ratios taken from table 1, but are the direct ratios evaluated in the cited references. F r o m ref. ~9), a survey with least squares averaging. A least squares average o f results ranging from 1.553-.2_0.019 to 1.568 4-0.008. See refs. 5. ~o. ~ . ~2. 16.26.35, 36.37.40, 51).

") Calculated from c o l u m n s 2 a n d 3, as in eq. (26). t) Calculated from semi-theoretical eq. (27). These values are used, since the experimental values scatter widely. T h u s , experimental values o f J~(233U)//~(235U) vary from 0 . 9 5 8 + 0 . 0 2 0 to 1.031 ~ 0 . 0 0 8 [see refs. s, 22.32.a6,49)]; values o f ~(239pu)/.I~(235U) vary from 1.03810.008 to 1.085 ± 0 . 0 3 0 [see refs. 2. a. ~3, 22.32.49)]; values o f J ~ ( z s z c f ) / ~ ( 2 3 s U ) vary from 1.026 + 0 . 0 3 2 to 1.200±0.041 [see refs. a. 9.13.3s. 4,*. as. ,tg)].

The e, ratios differ slightly from unity because of moderate differences in the N(E) distributions. For interpolation purposes, it is convenient to plot these ratios against ratios of the parameter characterizing N(E), i.e., E = ~T. Because experimental E

14

A.H.

JAFFEY A N D J. L. LERNER

values scatter widely (table 2), we preferred to use a semi-theoretical relation 48, 49.5 o) E = 0 . 7 5 + 0 . 6 5 ( ~ + 1) ~,

(27)

which approximately averages the discordant E results. Values are shown in table 2. Since the variation in the e, ratio is so small, the general validity o f e q . (27) or even o f eq. (25) is not important; only the monotonicity of E with 9p determines the usefulness o f the relation in forming the calibration curve (fig. 6). In using fig. 6, errors in the e. ratio due to uncertainty in the E ratios were less than the experimental error in drawing the curve. I

1.03

!

I

-

:3

1.02 --

,~

1.01

--

1.0o

0.99

0.9,5

1

I

I

I.oo

I.o,5

I.Io

1.15

E (x)/i~ (u zzS)

Fig. 6. Calibration curve for relative neutron detection efficiency. A preliminary i,p value ~,x yields the mean neutron energy ,~x through eq. (27). The relative detection efficiency e°(X)/eo(z35U) is then read from the curve.

For calculating ~p ratios, e, ratios were read from this curve. An error allowance o f 0.7 ~o in the e, ratio was made whenever fig. 6 was used for a nucleide whose ~ (hence E) was not close to that o f a standard. Otherwise, the errors in table 2 were used.

5. Measurements Samples were all m o u n t e d in much the same way. A small volume o f a solution containing the fissionable nucleide was evaporated on a 25 m m diameter platinum disc 0.05 m m thick. In most cases, the material had previously been separated from other elements with an ion-exchange column. Extraneous solids were minimal. Some o f the standard samples were electroplated, rather than evaporated; both kinds gave the same values o f ~ = C/Av. The areas o f spread were kept < 5 mm radius and the average sample thickness varied from 5 to 40 pg/cm 2. Spreading agents were used to prevent clumping and to improve sample thickness uniformity; measurement showed fission counter plateaus to be quite flat, indicating that e,v was close to unity. A sample yielding a p o o r plateau was dissolved, purified, and redeposited; it was not considered acceptable unless it yielded a flat plateau. Each sample was centered and cemented to an aluminium cup, which also served as the second ionization c h a m b e r electrode (fig. 3).

NEUTRON FISSION

15

Samples were counted in sequence, unknown samples and 239pu, 233U, 235U standards (in some experiments, 252Cf as well). Counting the standards allowed comparison of fp values and also calibrated the neutron detector drift. Calibrating the e. variation required that more time be devoted to counting standards than to unknowns. Several samples of each standard nucleide were used and each such nucleide was measured 15 to 30 times in an experiment. 6. Measurements and results 6.1. THE NUCLEIDE 2'*tPu

Two samples were used. (I), formed by a high burn-up irradiation of 239pu, and (II), isotopically separated at Oak Ridge, had the isotopic compositions in table 3. TABLE 3

Isotopic composition 2'*lPu samples Atom percent sample (I)

sample (If)

23Spu 239pu 2'*°Pu 2*Ipu 242pu

0.0166-L0.0008 5.33 39.0 19.8 34.1

2**pu

~0.05 4-0.4 :'-0.3 +0.3

26.2 13.7 59.4 0.671

J=0.3 ±0.2 :!:0.4 --0.006

0.00184-0.0001

Since ~p(2*lpu) is very close to ~p(239pu) we take 8n(239pu) = e,(2*lpu). The relative fission rate AF(239pu)/AF(241PD) is derived from the effective cross-section ratio and the atomic percent. For (I), f(239pu)/f(241pu) = 0.218+0.004, and for (II), 0.357_+0.005. Errors in the f-ratios are unimportant, s i n c e ~;p(241pu) is so closc to '~p(239pu). The tip ratios calculated from eq. (19) are given in table 4. Using cq. (20), ~n(24tpu) = (6.220+0.021)10 -4, which, from eq. (21), yields ~p(24~pu) = 2.874+ 0.015. The quoted error includes only the statistical error. TABLE 4 ~p ratios for 2*tpu ~p(241pu)

~,(S)

239pL1 235U

2aaU

sample(l)

sample (11)

1.000 + 0.005 1.1944-0.008 1.146-2=0.011

0.999 ± 0.005 1.1957k0.008 1.142 ~0.011

average 1.000 __"0.004 1.195_.--'0.006 1.1444-0.008

7,

TABLE 5

Measurements of ~,p(2*tPu) Reference

~p(239Pl-l)

~p(2.1 PU) ~p(235U)

Kalashnikova (1956) ~1)

1.04 -_~:0.01

1.24 .k0.01

2.986~ 0.030

Comparison of coincidence rates. Ion chamber and BFa counters in paraffin

Sanders (1956) '*~)

1.055.+_0.050

1.232 k0.052

3.015 i 0.125

Comparison of coi~lcidence rates. Ion chamber and BFa counters in paraffin

Jaffey (1959) 2s), ,)

1.006"_0.024

1.208-10.028

2.911 .k0.067

Compar,son standards

dc Saussure (1959) ~5)

1.053_--'0.018

1.295-10.019

3.096-10.051

Comparison of coincidence rates. Ion chamber and Hornyak buttons

Z t~

Colvin (1965, 1967) io. l l)

1.021 -t0.012

1.212_t_0.011

2.931 :I_0.027

Comparison of coincidence rates. Ion chamber and BF3 counters in graphite (*)

.r,

Boldeman (1965, 1967) , * . 5 )

1.015--0.004

1.220t-0.005

2.931 --0.010

Compar,son of coincidence rates. Ion chamber and organic scintillator (*)

Westcott (1965) 5~)

1.031 +0.010

1.224-10.010

2.954-2:0.023

Review

Fillmore (1968) 19)

1.017--0.003

1.219--0.004

2.933~0.007

Review

Jaffey (1969)

1.000/0.004

1.195_I_0.006

2.874___0.015

Present work (*)

~p(24"1 ptl)

Method b)

~p(zat pu ) a)

of neutron yields of unknown and

~) Recalculated using new a v values 5~) and g-factors s2.53). The experiment yielded a i, value; it has been corrected for delayed neutrons to give i~p" b) Experiments in which variation of neutron detection efficiency with neutron spectrum was checked or allowed for are indicated with (*).

,<

z

NEUTRON FISSION

17

Results of other measurements o n fp(241pu) are listed in table 5. Values of/;p(241pu) have been corrected to the standard values of table I. The source of the deviation between our result and the more recent measurements i;p(241pu) has not been determined. Aside from this discrepancy we have not found a basis for suspecting a systematic error in the method. Indeed, in the other case where comparison with a recent accurate measurement is possible (i.e. 244Cm), the check with our results is excellent (table 13). 6.2. THE N U C L E I D E 23apu

The 238pu sample was formed in a reactor through the reaction 237Np -~ 238Np ~-~, 238pu. A small total flux-time was used to keep the concentration of the secondorder product 2 3 9 p u very low. The isotopic composition is shown in table 6. "[he ratio f(EagPu),~(238pu) was calculated to be 0.1332_+0.0038, but the error in this ratio was unimportant, because the difference b e t w e e n ~;p(238pu) a n d ~;p(23'~Ptl) is SO small; e,(238pu) was taken to be the same as e,(239pu). Calculated fo ratios are given in table 7. After correcting for the 2 3 9 p u fission, the averaged value is vp(238pu) = 2.895+0.027. TABLE 7 /,p ratios for 23Spu

TABLE 6

Isotopic composition of 238pu sample

~;p(23Spu)

Atom percent z'~aPu 2agPu 24°Pu 2'*tPu 242pu

99.663 ± 0.003 0.310 q-0.003 0.012-1-0.002 <0.0013 0.014___0.003

TABLE 8 Isotopic composition of Am samples Atom percent 241Am samples 24'Am 2'*2Am 2'*3Am

100.0 -<0.003 a) <0.001 a)

24ZAm samples 97.54t0.01 1.32 z_:0.01 1.14 ~.0.01

/,p(S) 239pu 235U 233 U 252Cf

1.008 ±0.011 1.204"-.0.012 1.165;-0.012 0.765 ! 0.008

TABLE 9 The ~p ratios for 241Am and 242mAre i,~,(2,*lAm) S 239pu 235U 233U 252Cf

~,,(S)

bp(2"~2mAm) /,p(S)

1.112:L-0.013 .... 1 ]-27:!_O.()O8-1.332~0.017 1.351 _-' 0.012 1.310_--'0.017 1.329 ~20.011 0.854:2:0.013 0.866220.010

") Limit of detection. 6.3. T H E NUCLEIDES 24tAm A N D 242mAm

Pure 241Am was extracted from a plutonium sample containing 241Pu. Since the plutonium had been previously purified of americium several times, the 241 Am was considered isotopically pure and this was borne out by the analysis (table 8).

00

Tam.t-: 10 Measurements of );p(2"~lAm) and i,p(2'*2"Am) Reference

vp(Am) ~(2asU)

vp(Am) ~p(2saU)

Method b) > .-e

24~am Lebedev (1959) 3a) Jaffey (1969)

1.27 =0.01 1.332 !O.017

3.057 !0.026 1.310 -0.017

0.854

0.013

3.219 t 0.038

Comparison of coincidence rates. Ion chamber and BFs counters in paraffin Present work (*)

,< Z

2 * 2 m A Ill

Fultz (1966) 2o) Jaffey (1969)

1.333:: 0.066 1.351 -_:0.012

1.276 ! 0.051 1.329.-__0.011

0.857

0.032

0.866-_._0.010

3.23

! 0.12

3.264.-_0.024

Comparison of coincidence rates. Spark chamber and BF3 counters in paraffin (*) Present ,~ork (*)

a) Recalculated, using ,5~,values in table I. i,) Experiments in which variation of neutron detection efficiency ~ith neutron spectrum was checked or allowed for are indicated with (*).

;I. m

NEUTRON FI~ION

19

N e u t r o n i r r a d i a t i o n o f 2'*1Am leads to a m e t a s t a b l e excited state (242mAre)which has a relatively long lifetime. Its high fission cross section leads to a low e q u i l i b r i u m c o n c e n t r a t i o n (table 8). A l t h o u g h s p o n t a n e o u s fission activity from A m isotopes was negligible, 242mAm decays to the g r o u n d state, thence to 242Cm, which has considerable s p o n t a n e o u s fission activity. M e a s u r e m e n t s with the closed shutter indicated that < 0.2 % o f the tission from the 242mAm sample was spontaneous. This was considered negligible. T a k i n g ~p(Z4ZAm) ~ ~;p(242mAm) "~ 3.2, from eq. (27), E ( A m ) / E ( 2 3 5 U ) -~ 1.07. F r o m fig. 6, eo(Am)/en(235U)= 1.026+0.007. The i~p ratios are in table 9. T h e q u a n t i t y e, was taken as the same for both A m isotopes and was m e a s u r e d to be (6.095+0.035)10 -4. Then, i~p(24~Am)= 3.219__+0.038 and, correcting for 24~Am fission,* i~p(242mAm) = 3.264+0.024. Results o f other m e a s u r e m e n t s on these two nucleides are listed in table 10. 6.4. THE NUCLEIDE 2aaCm The nucleide 244Cm was present in the samples used for measuring vp(243Cm) a n d ~p(245Cm). To correct for 244Cm s p o n t a n e o u s fission, these samples were m e a s u r e d with b e a m shutter closed. These measurements, c o m b i n e d with eq. (22), yield ~;p(24aCm). TABLE 11 The vv ratios for 244Cm ~p(2"*4Cm)

,Sp(S) "''7 . '\,,,S// \f'

. 239p u

.

.

. 235U

.

. 233U

252Cf

243Cm

samples

0.931 :::0.026

1.109 -t-0.032

1.076-: 0.031

0.720 ±0.020

0.938 ~=0.009 0.937 ± 0.008

1.121 - 0.011 I. 120 2.0.010

1.086 !_0.007 1.086 _-'0.007

0.720 =_0.020

24SCm

samples average

TABLE I 2 The i,. averages for 2a4Cm Sample

i;o(244Cm)

2a'3Cm (l)

2.706 i 0.109 2.661 _:_0.1124 2.684 :-0.076 2.693 ! 0.025

samples (11) average 2,t5Cm samples overall average * f(241Am),~f(2"~2mAm) ~ 0.031 +0.002.

2.692 .{.0.024

TABLE 13

Measurements of '3p(2*aCm) Reference

~.(2aaCm) "i;~,(233U) -

vp(2*'*Cm) ~0(235U)

~o(2-4Cm) ~,p(zS9pu)

Hicks (1955) 23) a)

~;t~(244Cnl) ~,p---('5i i~t~3-

O

~;V(2a-~Cm) i,,(2401,u)

0.741 q 0.006

1.087¢-0.035 [2.694±0.087]

1.138=0.028 [2.739~ 0.068]

0.922-~:0.031 [2.659:!.0 090]

Hicks (1956) z4) a)

0.726-!~0.021 [2.732±0.079]

0.743 '0.033 [2.797 : (}.124] 0.741 .-0.016 [2.789 ! 0.062]

Crane (1956) ,4)

Bol'shov (1964) ~) a)

Jaffey (1969) =) b) ~) a)

1.245-._::0.036 [2.679:t--0.078]

1.258 A:0.047 [2.707:2:0.102] 1.246!0.046 [2.681 ! 0.098]

1•250 !.0.018 [2.690 ! 0.040]

1.086:F0.007

1.1202:0.010

0.937 ! 0.008

0.720:!-0.020

Method b)

2.788 :L0.021

Higgins (1955) 2s)

Diven (1956) iT) a)

~r,(24-lCm) ~)

Comparison of coincidence rates. Ion chamber and cadmium-loaded scintillator 2.60 0.1 I ~) Comparison of activation of Mn in MnSO, bath. Relative to calibrated Po Be sources 2.700~:0.057 Comparison of coincidence rates. Fragment counter and cadmium-loaded scintillator 2.752~_:0.102 As in rcf. 2.t) 2.753 ~0.055

2.690 :h0.040

2.692 ! 0.024

Comparison of coincidence rates. Ion chamber and LiI(Eu) neutron dctector Comparison of coincidcnce rates• Ion chamber and BF3 counters in paraffin Present work (*)

Recalculated, using i,~ values in table 1 or relative to ~p(2*°Pu). Experiments in which variation of neutron dctcction efficiency with neutron spectrum was checked or allowed for are indicated with (*). Total neutron yield measured 1~]. The quantities in [ ] are values of i,(zt4Cm) calculated using standard values of table I, ~,p(2"t°Pu) is taken as 2.152 k0.007, averaged from results in refs. ~.L6. to, 18.39).

>

¢-,

z

NEUTRON FISSION

21

The fission rate of 244Cm was quite low in the 243Cm samples, so the statistical accuracy of this measurement was limited. For using fig. 6, 9p(244Cm) was taken as ~ 2.7, whence E(244Cm)/E(235U) 1.026. Fig. 6 then gave en(244Cm)/en(23sU) = 1.021 +0.007. A small correction was made for the spontaneous fission of the 2 4 2 C m present (tables 14 and 16). The relative fission rates, calculated from the known spontaneous fission half-lives and composition, were f(2'*2Cm),/f(24*Cm)= 0.027+0.003 for 243Cm(I), 0.0053+0.0007 for 243Cm(II)and 0.0153 +0.0006 for the 2¢5Cm samples. Since the correction was small, vp(242Cm)did not have 1o be known accurately. From the ratio fp(2*2Cm)/~p(244Cm) = 0.933 +0.043 [ref. 28)] and ~:p(244Cm) = 2.69, we have ~p(2't2Cm) ~ 2.51. The ~p ratios relative to the standards are shown in table I 1. The averaged ~v value from the two samples is given in table 12, yielding i;o(24'tCm) --- 2.692+0.024. The results of other measurements are listed in table 13. 6.5. THE NUCLEIDE 2*aCm The nucleide 243Cm was formed by successive neutron captures through the reactions 2*lAin L.~ 242Am a_~ 242Cm ~ 243Cm" The curium fraction from an irradiation contains a mixture of 242Cm and 243Cm together with 24"Cm, 24SCm and 246Cm. The last three isotopes are formed through successive neutron captures by 243Cm. Interference from the 244Cm is not serious; its spontaneous fission effect can be corrected. However, pulse pile-up from the very intense 242Cm co-activity (subsect. 3.5) made it difficult to use a freshly-irradiated sample. We were fortunate to borrow a sample* which had decayed 3½ years after irradiation, attenuating the 242Cm 230fold. The isotopic composition is shown in table 14. Two 9 measurements were made about a year apart and the mass analysis (II) was actually made at the time of the second measurement; decay corrections gave composition (I). TAm2 14 Isotopic composition of 24SCm samples Atom percent (I) 242Cm z*aCm 24~Cm 24SCm 24~Cm

0.81 +0.09 40.2 ±0.4 58.4 +0.6 0.66 +0.08 0.0052 ±0.0007

(II) 0.161 -t-0.028 40.9 +0.4 58.3 +0.6 0.69 -/-0.08 0.0054±0.0007

t We are indebted for the source of this sample to E. K. Hulet, Lawrence Radiation Laboratory, University of California, Livermore.

22

A. H. JAFFEY AND J. L. I-ERNER

Corrections were made for the other isotopes using the ratiosf(245Cm)/f(243Cm) = 0 . 0 4 9 + 0 . 0 0 6 for (I) and 0 . 0 5 0 + 0 . 0 0 6 for (It); f(2'~4Cm) = 0.1804+0.0023 for (I) and 0.1648+0.0065 for (lI);f(Z¢2Cm)/f(244Cm) = 0.00265+0.0029 for (I) and 0.00534-0.0007 for (II). In the corrections, we use ~p(244Cm) = 2.692+0.024 (subsect. 6.4), ~p(245Cm) = 3.832_+0.034 (subsect. 6.6), vp(242Cm) --- 2.51; the last two corrections are quite small. For fig. 6, i~p(243Cm) was taken as ~ 3.4, whence E(243Cm)/E(235U) ~ 1.074. The curve gives F,n(243Cm)/gn(235U) = 1.025+_0.007. Similar calculations give e,(2¢2Crn)/~:.(235U)= 1.011, ~;,(244Cm)/e,,(235U) = 1.021, e,(245Cm)/e,(235U)= 1.020. Ratios ofi~0(243Cm) to the standard values are shown in table 15. The ~p value, averaged over the standards, was 3.460+0.078 for (I) and 3.412+0.059 for (II); the average was ~p(243Cm) = 3.430+0.047. TABLE 15 The *-,pratios for 2"3Cm vp(:43Cm) ~.pis)-\\ S / \k /

239pu

23su

2.~3U

1.418 +0.032

1.376 --0.031

252Cf

(1)

I. 199 "-0.027

0.943 --0.021

(ll)

1.182--0.023

1.420 ! - 0 . 0 2 7

1.377,0.026

0.905--0.018

Av.

1.189 ~0.0I 8

1.419 + 0.021

1.377 ,0.020

0.921 -:-0.014

6.6. THE NUCLEIDE 245Cm A long irradiation (high nvt) of 239pu gave the reactions 239pu --*n240pu ---~n24ipu n 242pu ._5, 243pu aS, 243Am --* . 24¢An1 aS, 24.4Cm --* n 245Cm" The 245Cm/24'l'Cm --~ ratio was an equilibrium value and small, because o f the very large difference in total cross sections. 2 4 t A m (from 24ipu fl-decay) also yielded some lower curium isotopes (subsect. 6.5). Higher curium isotopes were formed through further neutron capture by 245Cm. The isotopic composition is shown in table 16. Corrections were made for the effects of 242Cm, 243Cm and 244Cm; f(247Cm)/ f ( 2 4 5 C m ) was about 0 . 1 % , hence negligible. Sincef(243Cm)/f(245Cm)=0.0172+ 0.0017 and f ( 2 ¢ 2 C m ) / f ( 2 4 ¢ C m ) = 0.0153+0.0006, these corrections were small; however, the 244Cm correction was much larger and was more important than in the measurement o f subsect. 6.5. The value o f f ( 2 4 4 C m ) d e p e n d e d upon the neutron flux at the time o f the run; in cight experiments, it varied from 0.433 to 0.705. Using the e, values evaluated in subscct. 6.5, the ratios ofi~p(24~Cm) to the standard values were calculated, as in table 17. Averaged over the three standards, %(245Cm) = 3.832__+0.034. 6.7 THE NUCLEIDE 232U Neutron irradiation o f 23~pa gave the reactions 231pa ~" 232pa ~ Z3zU. A second order neutron capture yields the highly fissionable 233U, so the total irradiation (nvt)

23

NEUFRON FISSION

was limited to keep such capture low. The 2 3 2 U yield per milligram of 231pa w a s correspondingly low, and this may explain the 235U and 23SU, probably present in low concentration in the difficult to totally purify 231pa source material. The isotopic composition is shown in table 18. TABLE 16 Isotopic composition of the 2'*-*Cm samples Atom percent

TABLE I 7 The ?,p ratios for 2'*5Cm S

i;p(24~Cm)

242Cm

0.76 --0.03

243Cm

0.053 :!~0.005

239pu

1.328 .!_0.013

~,p(S)

2't'~Cm 24~Cm 246Cm 247Cm 24SCm

96.0 --0.1 1.04 :.-0.02 2.10 :i.0.1 0.024 ± 0.008 0.008+0.003

235U

1.591:i 0.016

233U

1.553--0.016

TABLE 18 Isotopic composition of 232U sample

TABLE 19 The i.p ratios for 232U

Atom percent

S

~;p(232U)

232U

99.213 ±0.009

233U

0.195 - 0 . 0 0 4

235U

1.308 2:0.026

v°(S)

23sU 23sU

0.078.!.0.004 0.514±0.007

233U

1.260±0.026

The measurements on this nucleide were less satisfactory than the previous measurements, because the neutron detector showed greater tendency to drift. We used only the data gathered during periods of modest drift, and there was no external evidence of difficulty during these periods. We have made no allowance in the error calculation for the possibility of detector drifts not accounted for. Unfortunately, the 232U measurement could not be repeated, because of termination of the experiment. Corrections were small, since f ( 2 3 5 U ) / f ( 2 3 2 U ) = 0.00584-0.0003 and f(233U)/ f ( 2 3 2 U ) = 0.0132+0.0003. With a preliminary estimate ~p(z32U) ~ 3.1, E(232U)/ E(235U) = 1.060; then from fig. 6, gn(232U)//~n(235U) = 1.026+0.007. Relative ~p ratios are given in table 19. Correcting for 235U and 233U fission in the 232U sample, ~p(232U) = 3.130+0.060.

7. Discussion

Fission theory is not well enough developed to allow prediction of i;p values. The fission energy E F arises from the difference in mass of the fissioning nucleus and fission fragments and also from the energy added by the incoming particle. Most of E r goes

24

A.H. JAFFEY AND .1. L. LERNER

into the kinetic energy EK o f the fission fragments. The residual excitation energy Ex = E F - - E K is a relatively small difference between two large numbers. Hence, even when Ez and EK are predictable, they must be k n o w n very accurately for E x to be k n o w n even m o d e r a t e l y well. A further c o m p l i c a t i o n is that E x is shared between neutron a n d y-ray emission in p r o p o r t i o n s that are not u n d e r s t o o d theoretically, so that Ex = E . + E~, but E , is not p r e d i c t a b l e even when Ex is known. In view o f the difficulty in calculating i~p from first principles, a n o t h e r a p p r o a c h has been to use theory only to p r o v i d e a qualitative guide for developing i n t e r p o l a t i o n relations. I f we assume that the factors g o v e r n i n g the values o f Ev, EK a n d E~./E, vary s m o o t h l y with Z and A, we m a y form an i n t e r p o l a t i o n f o r m u l a for i~o with adj u s t a b l e constants. These c o n s t a n t s m a y be least-squares fitted t h r o u g h the use o f s o m e m e a s u r e d i~p values. T h e o r y enters only qualitatively, by suggesting the most suitable f o r m for such a relation. Since nuclear masses vary s m o o t h l y over the small ranges 90 < Z < 100 a n d 140 < N < 152, ref. 2 t ) considered it r e a s o n a b l e to take ~ for thermal neutron fission as a p p r o x i m a t e l y a linear function o f A a n d Z, with a m i n o r c o r r e c t i o n for odd-even effects t. T h e coefficients were evaluated by fitting the linear relation to the e x p e r i m e n t a l values: 229-['11,2.09; 2 3 3 U , 2.50; 2 3 5 U , 2.43; 239pU, 2.89; 241pu, 2.95; 2"~Am, 3.09. The resulting e q u a t i o n was then ~r = 0 . 1 8 9 4 Z + 0.007,4 - 16.60 + 0.09(,

(28)

where ( = + I for a target nucleus with ( o d d N, o d d Z ) , ( = - 1 for (even N, even Z ) , (= 0foroddA. W i t h the same nucleides but with values corrected to the s t a n d a r d values in table 1 [229Th, 2.08; 233U, 2.478; 235U, 2.407; 239ptt. 2.884; 241pu, 2.933; 2 * t A m , 3.057], a least squares fit gives ~p = 0 . 1 9 0 9 Z + 0 . 0 0 8 8 A - 16.34+0.09(.

(29)

O u r e x p e r i m e n t a l values are c o m p a r e d to values p r e d i c t e d from eq. (29) in table 20. On the whole, the e x p e r i m e n t a l values agree qualitatively with eq. (29), in that i;p changes much m o r e with A Z = I than with AA = 1, a n d usually di~p is positive for A`4 > 0. Q u a n t i t a t i v e a g r e e m e n t is less g o o d , i m p l y i n g that coefficients which fit best in one (Z, `4) range m a y n o t a p p l y as well when the range is e x p a n d e d . t Our measurements suggest a change in an interpretation derived from the result calculated in ref. 2t). With ~p(z'~3Cm) calculated from eq. (28), the difference: i;p(243Cm+n)i;p(z44cm, spont.) -- 0.53 ~0.12 was there estimated. Since the same nucleus was fissioning, the difference was due to the added neutron binding energy B,. However, from the known B, value, di;p would be predicted to be 0.862:0.08; the difference between 0.53 and 0.86 was interpreted as due to an increase in J~¢ in thermal neutron fission relative to spontaneous fission, with zl~ K = 2.5--1.1 MeV. With our measured values (subsects. 6.4. and 6.5), the difference is ~o(243Cm+n)--~p(244Cm, spont.) = 0.74+0.05. The distinction between this value and the calculated value 0.86_+.0.08 is not statistically significant, so the data are consistent with z~/~K = 0.

TABLI-: 20 *) nucleide

~p b) experimental

229Th

232 U

~p, calc. from

i,p, calc. from (Z, A) expansion from eq. (29)

from eq. (30)

from eq. (31)

Z2/A expansion

from ref. 42)

renormalized *)

2.08010.020

2.059 ( 0 . 0 2 1 )

2.604 (--0.015)

1.977 (--0.103)

2.172 (+0.092)

2.156 (+0.076)

2.514 (--0.616)

2.372 (-.0.758)

2.380 ( - 0 . 7 5 0 )

2.345 ( - 0 . 7 8 5 )

3.130 - 0.060'

2.359 (--0.771)

233 U

2.478 -£ 0.007

2.458 ( - 0 . 0 2 0 )

2.568 (-1-0.090)

2.463 ( - 0 . 0 1 4 )

2.394 ( - 0 . 0 8 4 )

2.376 (-.-0.102)

235 U

2.407 :t .0.005

2.476 (+0.069)

2.495 (-t 0.088)

2.465 (-t-0.058)

2.425 (-~ 0.018)

2.407 (0.000)

23Spu

2.895- ~0.027*

2.776 (.-0.119)

2.945 (~. 0.050)

2.860 (--0.035)

2.874 (-.0.021)

2.853 (- 0.042)

239pu

2.884 -0.007

2.875 ( - 0 . 0 0 9 )

2.998 (+0.114)

2.951 (+0.067)

2.896 (-~ 0.012)

2.875 (--0.009)

2.953 (-t 0.079)

2.941 (+0.067)

2.919 (+0.045) 3.157 ( - 0 . 0 6 2 )

241pu

2.874 t-0.015*

2.893 (-} 0.019)

2.926 (-~ 0.052)

24tAm

3.2194-0.038"

3.075 (

0.144)

3.250 (+0.031)

3.194 (--0.024)

3.181 ( - 0 . 0 3 8 )

2,,t2mAm

3.264-t0.024"

3.174 ( - 0 . 0 9 0 )

3.304 (+0.040)

3.285 (+0.021)

3.221 ( - 0 . 0 4 3 )

3.197 (--0.067)

243Cm

3.430 5:0.047*

3.274 ( - 0 , 1 5 6 )

3.502 (+0.072)

3.437 (-I 0.007)

3.501 (1-0.071)

3.475 (+0.045)

245Cm

3.832-t-0.034"

3.292 ( - 0 . 5 4 0 )

3.429 ( - 0 . 4 0 3 )

3.439 (--0.392)

3.524 ( - 0 . 3 0 8 )

3.498 ( - 0.334)

*) Numbers in parentheses are - ~,p(calc.)-i,p(experimental). b) Measurements reported in this paper are indicated with (*). ¢) Renormalized to ~p(2asU) = 2.407.

26

A . H . 3AFFEY AND J. L. LERNER

W e have recalculated eq. (29) including all the values in tables 5 and 10 a n d in subsects. 6.2, 6.5, 6.6 and 6.7, with the result ~p = 0.288 l Z - 0.0363A - 18.80 + 0.09{.

(30)

The negative coefficient o f A is generated by the large i~p value o f 232U. If the 232U result is o m i t t e d , the least squares tit gives i~p = 0 . 2 4 2 2 Z + 0.00089A - 19.95 + 0.09ft.

(31 )

T a b l e 20 also c o m p a r c s the cxperimcntal m e a s u r e m e n t s with eqs. (30) a n d (31). The 232U result does not agree with the very small a n d positive AA effect p r e d i c t e d by eqs. (28), ( 2 9 ) o r (31). Ref. 3 3 ) n o t e s the possibility that shell effects in the fission fragments m a y m a k e Op increase with decreasing ,4, and suggests this to be the case for the light u r a n i u m isotopes. In an alternative empirical s y s t e m a t i z a t i o n 4t), i~r is expressed as a p o l y n o m i a l in the fissility p a r a m e t e r Ze/A, t h r o u g h successive least-squares fitted p o l y n o m i a l exp a n s i o n s : ~p =./'(EK), E K = .q(Et) a n d E, = h(ZZ/A), with Et = fission t h r e s h o l d energy. Some predicted values are listed in table 20. On the whole this is a m o r e successful a p p r o a c h . W e wish to a c k n o w l e d g e o u r a p p r e c i a t i o n a n d indebtedness: to A l b e r t Hirsch, for early e x p e r i m e n t s in d e v e l o p i n g a p p a r a t u s and for p r e l i m i n a r y m e a s u r e m e n t s on 24tpu; to Ruth S j o b l o m , for p r e p a r a t i o n o f most o f the samples; to Lee H a r k n e s s , for mass s p e c t r o m e t r i c analyses o f the samples; to R o b e r t Scott, who aided in the long a n d tedious gathering o f counts; to E. K. Hulet ( L i v e r m o r e ) for the use o f a 2 4 a c m sample; a n d to the CP-5 o p e r a t o r s , who aided in the initial stages o f setting up the e x p e r i m e n t , and who were effective in keeping the neutrons coming.

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