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Total neutron cross section of B10 in the thermal neutron energy range
Nuclear Physics 17 (1960) 109-- 115; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission trom the publisher
T O T A L N E U T R O N C R O S S S E C T I O N OF B t° IN T H E T H E R M A L NEUTRON ENERGY RANGE H. "vV. S C H M I T T , R. C. B L O C K a n d R. L. B A I L E Y
Oak Ridge National Laboratory, Oak Ridge, Tennessee R e c e i v e d 2 N o v e m b e r 1959 A b s t r a c t : A precise d e t e r m i n a t i o n of t h e t o t a l n e u t r o n cross s e c t i on of B 1° h a s be e n m a d e b v m e a n s of t r a n s m i s s i o n m e a s u r e m e n t s of boron s a m p l e s h i g h l y e n r i c h e d in B 1°. The O R N L f ast c h o p p e r t i m e - o f - f l i g h t s p e c t r o m e t e r was used to o b t a i n r e s u l t s in t h e n e u t r o n e n e r g y r a n g e 0.018 _< E _< 0.4 eV. I t is found t h a t the t o t a l cross s e c t i o n of B 1° in t h i s e n e r g y r a n g e follows t h e r e l a t i o n at(b ) = ( 6 1 2 ± 6 ) ] x / E ~ . The t o t a l cross s e c t i o n of B 1° for n e u t r o n s of e n e r g y 0.0253 eV ( v e l o c i t y = 2200 m/sec) is found to be 3 8 4 8 ~ 3 8 b.
1. I n t r o d u c t i o n The total neutron cross section of B 1° in the thermal and low-eV energy range has in general been derived from measurements 1-7) of the total cross section of natural boron together with measurements s-13) of the isotopic abundances of B 1° and B n in the samples. There have been discrepancies of the order of five per cent in the reported values 14) of at for B 1° in recent years, arising primarily from discrepancies in measurements of isotopic abundance. Because of a specific need 15) for more precise knowledge of the B 1° cross section, and for clarification of the above situation, the present direct total cross section measurement using boron samples highly enriched in B 1° has been made.
2. E x p e r i m e n t a l Method Experimentally, a straightforward neutron transmission measurement was made using the ORN L fast chopper time-of-flight spectrometer 16) installed at the Oak Ridge Research Reactor. The M-I rotor, a 45.7-cm diameter stainless steel rotor with 0.076-cm wide parallel slits, was used in conjunction with a 44.6-m flight path. A bank of six B F 3 proportional counters was used to detect the neutrons. The data were collected in a 2048-channel time-of-flight analyzer, used here in two sections of 1.024 channels each to store sample-in and sample-out counts. The rotor was spun at 130 or 220 r.p. rain to allow low energy neutrons to pass through; the resultant resolution was about 2 #sec/m. The energy range covered in a single run was 0.018 ~ E ~ 0 . 0 4 eV, 0.03 ~ E ~ 0 . 1 eV, or 0.1 ~ E =< 0.4 eV. A sample of B203 dissolved in D20 and a compensating sample of pure D20 were alternately placed in the neutron beam at intervals of 109
110
H . W . SCHMITT, R. C. BLOCK AND R. L. BAILEY
5 to l0 minutes to average out the effects of slowly varying pile power and long-term electronic drifts. The B203 was prepared as follows: The original boron metal powder was dissolved in nitric acid, and boric acid was then crystalized out of solution. The boric acid was thoroughly dehydrated to B 20~ which in turn was fused in a platinum dish. The amount of fused B,. 03 was carefully determined by weight. The B203 was immediately dissolved in D20. One of more aliquots were taken and diluted volumetrically with D20 to known concentrations of B.)O3 in solution. After all cross section measurements were completed, titrations of some of the samples were carried out to determine the B 203 concentrations. Titration results agreed with the original weight determinations within 0.7 per cent for these samples. Spectrochemical analysis of the solutions indicated less than 0.1 per cent metallic and rare earth impurities in the samples. Pertinent sample data are given in table 1. TABLE 1 Sample d a t a for total cross section m e a s u r e m e n t of B 1° Sample No.
Isotopic Composition (per cent B 1°)
B~O s Concentration (mg/cnV)
Sample Thicknes:~ (B 1° atoms/cm2 < 1!)-2°)
IA--1 IA--2 IA--3 IIA IIB IIIA
96.644-0.05 96.64-4-0.05 96.64-t-0.05 99.894-0.05 99.89±0.05 96.394-0.05
8.01 25.03 5.43 8.41 8.09 8.48
2.787-t-0.014 8.705-t-0.061 1.891±0.010 3,30810.02~ 3.1834-0.027 3.215±0.026
I n Column 1, the R o m a n n u m e r a l s indicate initial boron samples obtained from the O R N L I s o t o p e s Division; the letters and Arabic n u m e r a l s indicate chemical preparation. F o r example, a single c o n c e n t r a t e d solution of Sample I was used in p r e p a r i n g t r a n s m i s s i o n samples of three different concentrations; in the case of Sample I I , two complete and i n d e p e n d e n t chemical p r e p a r a t i o n s were made. E s t i m a t e d uncertainties in sample thickness are included in Column 4.
Matched aluminium sample holders were used for the compensating D20 sample and the B 20~--D20 sample; thus the liquid thicknesses were identical. All of the D20 used in a given solution and compensator was taken from the same original D20 sample. Since the total cross section of the D20 enters into the B 1° total cross section determination, as discussed below, this cross section was directly measured with the chopper. A comparison of this measurement with previously reported results for H~O_17) and D~O is) total cross sections indicates an H20 content of less than 0.9 per cent in each case, as expected for these D20 samples. An additional measurement was made of the relative transmissions of the two empty aluminium sample containers used respectively for the boron solutions and the D20 compensator. These two transmissions agreed within 0.1 per cent, indicating no detectable deposition of boron on the aluminum walls.
TOTAL
NEUTRON
CROSS
SECTION
OF
B 10
Ill
3. Analysis of Data In the determination of B 1° total cross section values as a function of energy, it was necessary to apply only three corrections to the transmission data. These will be discussed in turn. 1) Correction due to background in the BF 3 counters. The neutron backgrounds which inherently affect this type of measurement arise from (a) ambient room background, (b) high energy neutrons which leak through the chopper rotor, (c) neutrons which are scattered by the rotor only to be rescattered into the direction of the counters, and (d) neutrons scattered near the detector which arrive at the detector with an incorrect time of flight. The last of these backgrounds, (d), called the "spurious" background, was negligible in this experiment as the detector was almost completely surrounded by a 1.5-mm thickness of cadmium backed by a 5-cm thickness of boron carbide. Backgrounds from the other three sources were determined by two separate measurements as follows: (1) the background counting rate was measured with the rotor displaced to cut off the neutron beam, and (2) with the rotor in its normal aligned position, the background counting rate was measured with a 1.5-mm thick cadmium absorber in the beam. Results of these two measurements agreed within 10 per cent, indicating that the third source of background, (c) mentioned above, was negligible. Thus the background may be attributed to (a) and (b) and was accurately determined by routine transmission measurements with a 1.5-mm thickness of cadmium in the neutron beam. The total effect of background was quite small; the correction in the determination of at for 13l° amounted to no more than one per cent in any of the measurements. 2) Correction due to displacement of D20. Although the D20 thickness in the sample-out measurement was identical to the solution thickness in the sample-in measurement, a small correction has been included for the fact that the D20 content in molecules per cm 2 was not identical for the two cases. The correction was applied using the known B 203 concentration together with the measured solution density, the measured density of the D20, and the measured total cross section of the D20 sample. The magnitude of the correction is less than 0.4 per cent. 3) Correction due to the presence of oxygen and B n. This correction is straightforward and simply corrects the measured cross section for the presence of oxygen and B 1~ to obtain the B ~° total cross section. Total cross sections of oxygen and B 11 for this purpose were taken from the literature 17,14&); the magnitude of the correction is less than 0.5 per cent. The background correction was applied directly to the transmission data, and from these background-corrected transmission data the "effective total cross section" vs. energy for a given sample in a given run was obtained. The effective total cross section, %r~, is defined according to the equation
112
H.
xv.
SCHMITT,
NB,oaef r = - - l n T =
R.
C. B L O C K
AND
R. L.
BAILEY
NBloamo+NB,laBl,+Noxyaoxy--(AN)aD, o
(1)
where T is the b a c k g r o u n d - c o r r e c t e d transmission, N x is the thickness of m a t e r i a l x in a t o m s per cm 2, A N is the difference in D~O c o n t e n t in a t o m s per cm 2 b e t w e e n the s a m p l e solution a n d the c o m p e n s a t i n g D 2 0 sample, a n d a x is the t o t a l cross section of element x (except aDz O which is the m e a s u r e d t o t a l cross section of the D 2 0 s a m p l e of this e x p e r i m e n t ) . I n solving for the B 1° t o t a l cross section f r o m eq. (1), it is seen t h a t the corrections for o x y g e n a n d B n a n d for the difference in D 2 0 c o n t e n t b e t w e e n the s a m p l e solution a n d c o m p e n s a t o r s a m p l e t e n d to cancel; the net correction is less t h a n a b o u t 0.2 per cent of aet f, a n d the u n c e r t a i n t y is of the order of 0.1 per cent. (As p o i n t e d out b y E g e l s t a f f 2), the effect of chemical binding on the s c a t t e r i n g cross sections introduces an error in at for B ~° of less t h a n 2 b a r n s per b o r o n a t o m , or less t h a n 0.1 per cent in this e x p e r i m e n t . ) T a b l e 2, which contains a s u m m a r y TABLE
2
S u m m a r y of Results
1
Sample [ E n e r g y Range No. (eV) (Table 1)
i ]
Mean aet r ~ / E (b • eV½)
Corrections (b • eV½) I)20
Oxygen +B n
Mean at ~ / E for B 10 (b • eV½)
Mean a t v / E for B l° for each sample ( b . eVl)
IA-- 1 IA--1 IA--2 IA--2 IA--3
0.03 --0.1 0.018--0.04 0.03 --0.1 0.1 --0.4 0.018--0.04
641 640 635 630 644
+0.8 +0.6 +1.5 +2.5 +0.4
1.7 1.3 -- 1.7 --2.9 -- 1.3
641 639 635 630 643
IIA IIA
0.018-- 0.04 0.03 - 0 . 1
611 610
+0.6 +0.8
1.2 -- 1.7
611 609
6104-6
--1,2
610 610
610±6
---
I
639-t-5
l
lib lib
0.018--0.04 0.03 --0.1
610 611
+0.6 +0.8
--1.7
IIIA IIIA
0.03 --0.1 0.018--0.04
617 618
+0.8 +0.6
--1.7
616
--1.3
617
616-t-6
U n c e r t a i n t y in the m e a n value of o't%/E for each sample includes u n c e r t a i n t y in sample thickness and B 1° concentration. (See t e x t for f u r t h e r details.)
of results, gives for each run the weighted m e a n value of aer r vIE, the corrections applied, a n d the m e a n value of a t ~ / E for B 1°. Fig. 1 shows a plot of %rf ~ / E vs. v ' E for a t y p i c a l run. In order to check the 1/v (v = n e u t r o n velocity) dependence of the s a m p l e cross section, a second analysis was done as follows: the curves of ae~~ x / E vs. %/E were fitted b y the m e t h o d of least squares to the e q u a t i o n
aVE = a+bVE
(2)
where b ~ 0 indicates non-1/v b e h a v i o u r of the cross section. F o r e v e r y r u n
TOTAL NEUTRON CROSS SECTION OF B1°
113
the values of a and b together with the associated statistical uncertainties were obtained. In all cases except one, the value of b was within two standard deviations of zero. A weighted mean value of the constant a for all runs of a given sample (IA, IIA, IIB or IIIA) was obtained; this value agreed within 0.8 per cent with the mean value of aett~/E obtained from the corresponding runs. Thus it is indicated that any non-1/v term in the measured total cross E (eV) 0.018
>~ 6 4 0
.
0.020
.
.
.
0.025
.
.
.
.
t
.
.
.
0.030
.
.
.
0.03.5
.
¢_...
{,. .
[
i
.".
. . . . .". . . . .. :--',
.i
50o. . . . . . . . . . . . . . . . . . . . ~-
ua
0.t3
0.t4
0.t5
0.16
0040
0.t?'
0.t8
0.19
0.20
Fig. 1. a e t t ~ / E vs. ~v/E for a typical run. Points plotted are averages of eleven channels; the entire n e u t r o n energy range is covered b y 1024 channels. Flags indicate typical statistical uncertainties only.
section is negligible, and that indeed the total cross section for B z° follows the 1/v law to quite good accuracy in the energy range of the present experiment. This particular result is not surprising inasmuch as, for example, the scattering cross section of B l° is of the order of 4 barns 1,a), compared with measured total cross sections greater than 2000 barns for this experiment.
4. Results and D i s c u s s i o n A summary of results is given in table 2. Fifteen runs were made using four independent chemical preparations of samples and various combinations of boron concentration and energy range. Results are reported according to sample and energy range; see table 1 caption for explanation of sample designation. Weighted mean values of aett~/E are tabulated, and the corrections are indicated. Finally, the weighted mean values of at~/E for B 1° for all cases are tabulated in column 6, and the weighted mean value of atx/E for B 1° for each independently prepared sample is given in column 7. A sufficient number of counts was accumulated in each transmission measurement so that the effect of counting statistics on the mean value of aettA/E , and hence atv'E for B 1°, for each run was of the order of 2 0 . 3 per cent or less. The fluctuations which occurred for runs on the same sample were not inconsistent with such a variation; thus, the effect of small pile power changes, small changes in electronic circuit characteristics, etc., appears to be negligible. It is evident that the dominant uncertainty in the mean value of atx,/E for B 1° obtained from a single sample is the uncertainty in the sample content itself.
114
H.
W.
SCHMITT,
R.
C. B L O C K
AND
R.
L.
BAILEY
All uncertainties are taken into account in the combined uncertainties given in column 7, table 2. It is seen in table 2 that the result obtained for sample IA 19) differs markedly from the results obtained for samples IIA, IIB, and IIIA. Since the discrepancy is more than four standard deviations, it is concluded that a systematic error, whose source is unknown, occurred. All calibrations and other tests in all transmission measurements indicated valid measurements were made; titration of the samples after completion of the measurements yielded results which agreed within 0.7 per cent with the original quantitative preparations based on weights. Also the q u a n t i t y a t x / E for B 1° appeared to be constant over the entire energy range of the experiment. While it is difficult to designate the source of such a systematic error, two possibilities may be suggested: (1) high cross section impurities whose presence was not detected in spectrochemical tests, (2) errors at some point in the determination of boron content in the sample in question. In view of the considerations of the preceding paragraph, the result obtained with Sample IA is disregarded in arriving at a final mean value of a t v ' E for B 1°. The total cross section of B 1° in the neutron energy range 0.018 ~ E --< 0.4 eV, obtained from the present experiment, is then 612~6 .... b. at -- VE(eV)
(3)
The total cross section for neutrons of energy 0.0253 eV (velocity = 2200 m/sec) is at(0.0253 eV) = 3848±38 b.
(4)
Since, as pointed out in the previous section, the scattering cross section of B 1° is negligible compared to the total cross section, the absorption cross section for B 1° in the present energy range is essentially given by eqs. (3) and (4). This result is thus far the only published measurement of the total cross section of B 1° in which a sample highly enriched in B 1° has been used. Measurements of the total cross section of the Argonne-Brookhaven standard of California natural boron have been made by a number of groups 1, 2, 4, e, 2) ; the average of all results given by Hughes and Schwartz 1~) is 755 b for E = 0.0253 eV (2200 m/sec). Using this cross section together with that obtained for B ~° in this experiment, we compute the isotopic abundance of B 1° in the ArgonneBrookhaven boron sample to be 19.610.2 per cent. This value is in agreement with recent measurements of Sites and Spitzer 2o) and Haas et al. 21), giving 19.84-0.1 per cent, but in disagreement with earlier measurements of Thode et al. 12) and Inghram la).
TOTAL NEUTRON CROSS SECTION OF B1°
l l5
Further discussion added in proo/: An experiment identical with that reported in this paper has been carried out using a sample of the Argonne-Brookhaven standard natural boron, graciously provided by G. R. Ringo of Argonne National Laboratory. The sample solution was prepared exactly as described for the B 1° samples, and used in a sample holder similar to that of the above experiment; the concentration and sample thickness were respectively 8.62+0.04 mg B 2 0 3 per cm ~ and 6.08=t=0.03 × 1020 atoms B per cm 2. Transmission measurements were carried out as above, using the B 2O3--D 20 solution and a D 20 compensator. Two separate runs were made covering the energy range 0.022 to 0.042 eV; data were analyzed and corrections applied as described in text. Results of the two runs agreed within i 0 . 7 per cent. The weighted average of these runs gives the result at(0.0253 eV) = 7574-6 b for the Argonne-Brookhaven standard natural boron. Using the scattering cross sections for B 1° and B n given in ref. 1~), we obtain aabs(0.0253 e V ) = 753=t=6 b, in excellent agreement with other measurements 7, 14, ~ ) in which samples of the same boron were used. The authors wish to thank J. R. Sites of the O R N L Analytical Chemistry Division for the mass spectrometric analyses and Mrs. Jacqueline Blackwood for her assistance in many of the calculations. Helpful discussions with J. A. H a r v e y and G. G. Slaughter are gratefully acknowledged. References 1) W. W. Havens, Jr., E. Melkonian and B. M. Rustad, Columbia University Report CU-160, 1957 (unpublished) 2 P. A. Egelstaff, J. Nucl. Energy 5 (1957) 41 3 Collie, Meads and Lockett, Proc. Phys. Soc. A 69 (1956) 464 4 G. yon Dardel and N. G. Sjostrand, Phys. Rev. 96 (1954) 1566 5 Scott, Thompson and Wright, Phys. Rex,. 95 (1954) 582 6 Green, Littler, Lockett, Small, Spurway and Bowell, J. Nucl. Energy 1 (1954) 144 7 Carter, Palevsky, Myers and Hughes, Phys. Rev. 92 (1953) 716 8 Melton, Gilpatrick, Baldock and Healy ,Anal. Chem. 28 (1956) 1049 9 V. Shiuttse, J. Exp. and Theor. Phys. 2 (1956) 402 10 G.M. Panchenkov and B. D. Moisseev, Zh. Fiz. Khim. 30 (1956) 1118 11 O. Osberghaus, Z. Physik 128 (1950) 366 12 Thode, Macnamara, Lossing and Collins, J. Am. Chem. Soc. 70 (1948) 3008 13 M. G. Inghram, Phys. Rev. 70 (1946) 653 14 See for example values given (a) by D. J. Hughes and R. B. Schwartz, Report BNL-325, 2nd Ed. (Supt. of Documents, U. S. Printing Office, Washington, D. C. 1958), and (b) by Hughes and Harvey in the same report, first edition (1955) 15) H. W. Schmitt, Nuclear Physics, to be published 16) R. C. Block, J. A. Harvey and G. G. Slaughter, Bull. Am. Phys. Soc. 4 (1959) 270 17) E. Melkonian, Phys. Rev. 76 (1949) 1750 18) Rainwater, Havens, Dunning and Wu, Phys. Rev. 73 (1948) 733 19) H. W. Schmitt, R. C. Block and R. L. Bailey, Bull. Am. Phys. Soc. 4 11959) 415 20) J. R. Sites and E. J. Spitzer (1959) (unpublished) 21) Haas, Rourke, Mewherter and McDonald, Knolls Atomic Power Laboratory Report KAP1.2062 (1959) (unpublished)
T O T A L N E U T R O N C R O S S S E C T I O N OF B t° IN T H E T H E R M A L NEUTRON ENERGY RANGE H. "vV. S C H M I T T , R. C. B L O C K a n d R. L. B A I L E Y
Oak Ridge National Laboratory, Oak Ridge, Tennessee R e c e i v e d 2 N o v e m b e r 1959 A b s t r a c t : A precise d e t e r m i n a t i o n of t h e t o t a l n e u t r o n cross s e c t i on of B 1° h a s be e n m a d e b v m e a n s of t r a n s m i s s i o n m e a s u r e m e n t s of boron s a m p l e s h i g h l y e n r i c h e d in B 1°. The O R N L f ast c h o p p e r t i m e - o f - f l i g h t s p e c t r o m e t e r was used to o b t a i n r e s u l t s in t h e n e u t r o n e n e r g y r a n g e 0.018 _< E _< 0.4 eV. I t is found t h a t the t o t a l cross s e c t i o n of B 1° in t h i s e n e r g y r a n g e follows t h e r e l a t i o n at(b ) = ( 6 1 2 ± 6 ) ] x / E ~ . The t o t a l cross s e c t i o n of B 1° for n e u t r o n s of e n e r g y 0.0253 eV ( v e l o c i t y = 2200 m/sec) is found to be 3 8 4 8 ~ 3 8 b.
1. I n t r o d u c t i o n The total neutron cross section of B 1° in the thermal and low-eV energy range has in general been derived from measurements 1-7) of the total cross section of natural boron together with measurements s-13) of the isotopic abundances of B 1° and B n in the samples. There have been discrepancies of the order of five per cent in the reported values 14) of at for B 1° in recent years, arising primarily from discrepancies in measurements of isotopic abundance. Because of a specific need 15) for more precise knowledge of the B 1° cross section, and for clarification of the above situation, the present direct total cross section measurement using boron samples highly enriched in B 1° has been made.
2. E x p e r i m e n t a l Method Experimentally, a straightforward neutron transmission measurement was made using the ORN L fast chopper time-of-flight spectrometer 16) installed at the Oak Ridge Research Reactor. The M-I rotor, a 45.7-cm diameter stainless steel rotor with 0.076-cm wide parallel slits, was used in conjunction with a 44.6-m flight path. A bank of six B F 3 proportional counters was used to detect the neutrons. The data were collected in a 2048-channel time-of-flight analyzer, used here in two sections of 1.024 channels each to store sample-in and sample-out counts. The rotor was spun at 130 or 220 r.p. rain to allow low energy neutrons to pass through; the resultant resolution was about 2 #sec/m. The energy range covered in a single run was 0.018 ~ E ~ 0 . 0 4 eV, 0.03 ~ E ~ 0 . 1 eV, or 0.1 ~ E =< 0.4 eV. A sample of B203 dissolved in D20 and a compensating sample of pure D20 were alternately placed in the neutron beam at intervals of 109
110
H . W . SCHMITT, R. C. BLOCK AND R. L. BAILEY
5 to l0 minutes to average out the effects of slowly varying pile power and long-term electronic drifts. The B203 was prepared as follows: The original boron metal powder was dissolved in nitric acid, and boric acid was then crystalized out of solution. The boric acid was thoroughly dehydrated to B 20~ which in turn was fused in a platinum dish. The amount of fused B,. 03 was carefully determined by weight. The B203 was immediately dissolved in D20. One of more aliquots were taken and diluted volumetrically with D20 to known concentrations of B.)O3 in solution. After all cross section measurements were completed, titrations of some of the samples were carried out to determine the B 203 concentrations. Titration results agreed with the original weight determinations within 0.7 per cent for these samples. Spectrochemical analysis of the solutions indicated less than 0.1 per cent metallic and rare earth impurities in the samples. Pertinent sample data are given in table 1. TABLE 1 Sample d a t a for total cross section m e a s u r e m e n t of B 1° Sample No.
Isotopic Composition (per cent B 1°)
B~O s Concentration (mg/cnV)
Sample Thicknes:~ (B 1° atoms/cm2 < 1!)-2°)
IA--1 IA--2 IA--3 IIA IIB IIIA
96.644-0.05 96.64-4-0.05 96.64-t-0.05 99.894-0.05 99.89±0.05 96.394-0.05
8.01 25.03 5.43 8.41 8.09 8.48
2.787-t-0.014 8.705-t-0.061 1.891±0.010 3,30810.02~ 3.1834-0.027 3.215±0.026
I n Column 1, the R o m a n n u m e r a l s indicate initial boron samples obtained from the O R N L I s o t o p e s Division; the letters and Arabic n u m e r a l s indicate chemical preparation. F o r example, a single c o n c e n t r a t e d solution of Sample I was used in p r e p a r i n g t r a n s m i s s i o n samples of three different concentrations; in the case of Sample I I , two complete and i n d e p e n d e n t chemical p r e p a r a t i o n s were made. E s t i m a t e d uncertainties in sample thickness are included in Column 4.
Matched aluminium sample holders were used for the compensating D20 sample and the B 20~--D20 sample; thus the liquid thicknesses were identical. All of the D20 used in a given solution and compensator was taken from the same original D20 sample. Since the total cross section of the D20 enters into the B 1° total cross section determination, as discussed below, this cross section was directly measured with the chopper. A comparison of this measurement with previously reported results for H~O_17) and D~O is) total cross sections indicates an H20 content of less than 0.9 per cent in each case, as expected for these D20 samples. An additional measurement was made of the relative transmissions of the two empty aluminium sample containers used respectively for the boron solutions and the D20 compensator. These two transmissions agreed within 0.1 per cent, indicating no detectable deposition of boron on the aluminum walls.
TOTAL
NEUTRON
CROSS
SECTION
OF
B 10
Ill
3. Analysis of Data In the determination of B 1° total cross section values as a function of energy, it was necessary to apply only three corrections to the transmission data. These will be discussed in turn. 1) Correction due to background in the BF 3 counters. The neutron backgrounds which inherently affect this type of measurement arise from (a) ambient room background, (b) high energy neutrons which leak through the chopper rotor, (c) neutrons which are scattered by the rotor only to be rescattered into the direction of the counters, and (d) neutrons scattered near the detector which arrive at the detector with an incorrect time of flight. The last of these backgrounds, (d), called the "spurious" background, was negligible in this experiment as the detector was almost completely surrounded by a 1.5-mm thickness of cadmium backed by a 5-cm thickness of boron carbide. Backgrounds from the other three sources were determined by two separate measurements as follows: (1) the background counting rate was measured with the rotor displaced to cut off the neutron beam, and (2) with the rotor in its normal aligned position, the background counting rate was measured with a 1.5-mm thick cadmium absorber in the beam. Results of these two measurements agreed within 10 per cent, indicating that the third source of background, (c) mentioned above, was negligible. Thus the background may be attributed to (a) and (b) and was accurately determined by routine transmission measurements with a 1.5-mm thickness of cadmium in the neutron beam. The total effect of background was quite small; the correction in the determination of at for 13l° amounted to no more than one per cent in any of the measurements. 2) Correction due to displacement of D20. Although the D20 thickness in the sample-out measurement was identical to the solution thickness in the sample-in measurement, a small correction has been included for the fact that the D20 content in molecules per cm 2 was not identical for the two cases. The correction was applied using the known B 203 concentration together with the measured solution density, the measured density of the D20, and the measured total cross section of the D20 sample. The magnitude of the correction is less than 0.4 per cent. 3) Correction due to the presence of oxygen and B n. This correction is straightforward and simply corrects the measured cross section for the presence of oxygen and B 1~ to obtain the B ~° total cross section. Total cross sections of oxygen and B 11 for this purpose were taken from the literature 17,14&); the magnitude of the correction is less than 0.5 per cent. The background correction was applied directly to the transmission data, and from these background-corrected transmission data the "effective total cross section" vs. energy for a given sample in a given run was obtained. The effective total cross section, %r~, is defined according to the equation
112
H.
xv.
SCHMITT,
NB,oaef r = - - l n T =
R.
C. B L O C K
AND
R. L.
BAILEY
NBloamo+NB,laBl,+Noxyaoxy--(AN)aD, o
(1)
where T is the b a c k g r o u n d - c o r r e c t e d transmission, N x is the thickness of m a t e r i a l x in a t o m s per cm 2, A N is the difference in D~O c o n t e n t in a t o m s per cm 2 b e t w e e n the s a m p l e solution a n d the c o m p e n s a t i n g D 2 0 sample, a n d a x is the t o t a l cross section of element x (except aDz O which is the m e a s u r e d t o t a l cross section of the D 2 0 s a m p l e of this e x p e r i m e n t ) . I n solving for the B 1° t o t a l cross section f r o m eq. (1), it is seen t h a t the corrections for o x y g e n a n d B n a n d for the difference in D 2 0 c o n t e n t b e t w e e n the s a m p l e solution a n d c o m p e n s a t o r s a m p l e t e n d to cancel; the net correction is less t h a n a b o u t 0.2 per cent of aet f, a n d the u n c e r t a i n t y is of the order of 0.1 per cent. (As p o i n t e d out b y E g e l s t a f f 2), the effect of chemical binding on the s c a t t e r i n g cross sections introduces an error in at for B ~° of less t h a n 2 b a r n s per b o r o n a t o m , or less t h a n 0.1 per cent in this e x p e r i m e n t . ) T a b l e 2, which contains a s u m m a r y TABLE
2
S u m m a r y of Results
1
Sample [ E n e r g y Range No. (eV) (Table 1)
i ]
Mean aet r ~ / E (b • eV½)
Corrections (b • eV½) I)20
Oxygen +B n
Mean at ~ / E for B 10 (b • eV½)
Mean a t v / E for B l° for each sample ( b . eVl)
IA-- 1 IA--1 IA--2 IA--2 IA--3
0.03 --0.1 0.018--0.04 0.03 --0.1 0.1 --0.4 0.018--0.04
641 640 635 630 644
+0.8 +0.6 +1.5 +2.5 +0.4
1.7 1.3 -- 1.7 --2.9 -- 1.3
641 639 635 630 643
IIA IIA
0.018-- 0.04 0.03 - 0 . 1
611 610
+0.6 +0.8
1.2 -- 1.7
611 609
6104-6
--1,2
610 610
610±6
---
I
639-t-5
l
lib lib
0.018--0.04 0.03 --0.1
610 611
+0.6 +0.8
--1.7
IIIA IIIA
0.03 --0.1 0.018--0.04
617 618
+0.8 +0.6
--1.7
616
--1.3
617
616-t-6
U n c e r t a i n t y in the m e a n value of o't%/E for each sample includes u n c e r t a i n t y in sample thickness and B 1° concentration. (See t e x t for f u r t h e r details.)
of results, gives for each run the weighted m e a n value of aer r vIE, the corrections applied, a n d the m e a n value of a t ~ / E for B 1°. Fig. 1 shows a plot of %rf ~ / E vs. v ' E for a t y p i c a l run. In order to check the 1/v (v = n e u t r o n velocity) dependence of the s a m p l e cross section, a second analysis was done as follows: the curves of ae~~ x / E vs. %/E were fitted b y the m e t h o d of least squares to the e q u a t i o n
aVE = a+bVE
(2)
where b ~ 0 indicates non-1/v b e h a v i o u r of the cross section. F o r e v e r y r u n
TOTAL NEUTRON CROSS SECTION OF B1°
113
the values of a and b together with the associated statistical uncertainties were obtained. In all cases except one, the value of b was within two standard deviations of zero. A weighted mean value of the constant a for all runs of a given sample (IA, IIA, IIB or IIIA) was obtained; this value agreed within 0.8 per cent with the mean value of aett~/E obtained from the corresponding runs. Thus it is indicated that any non-1/v term in the measured total cross E (eV) 0.018
>~ 6 4 0
.
0.020
.
.
.
0.025
.
.
.
.
t
.
.
.
0.030
.
.
.
0.03.5
.
¢_...
{,. .
[
i
.".
. . . . .". . . . .. :--',
.i
50o. . . . . . . . . . . . . . . . . . . . ~-
ua
0.t3
0.t4
0.t5
0.16
0040
0.t?'
0.t8
0.19
0.20
Fig. 1. a e t t ~ / E vs. ~v/E for a typical run. Points plotted are averages of eleven channels; the entire n e u t r o n energy range is covered b y 1024 channels. Flags indicate typical statistical uncertainties only.
section is negligible, and that indeed the total cross section for B z° follows the 1/v law to quite good accuracy in the energy range of the present experiment. This particular result is not surprising inasmuch as, for example, the scattering cross section of B l° is of the order of 4 barns 1,a), compared with measured total cross sections greater than 2000 barns for this experiment.
4. Results and D i s c u s s i o n A summary of results is given in table 2. Fifteen runs were made using four independent chemical preparations of samples and various combinations of boron concentration and energy range. Results are reported according to sample and energy range; see table 1 caption for explanation of sample designation. Weighted mean values of aett~/E are tabulated, and the corrections are indicated. Finally, the weighted mean values of at~/E for B 1° for all cases are tabulated in column 6, and the weighted mean value of atx/E for B 1° for each independently prepared sample is given in column 7. A sufficient number of counts was accumulated in each transmission measurement so that the effect of counting statistics on the mean value of aettA/E , and hence atv'E for B 1°, for each run was of the order of 2 0 . 3 per cent or less. The fluctuations which occurred for runs on the same sample were not inconsistent with such a variation; thus, the effect of small pile power changes, small changes in electronic circuit characteristics, etc., appears to be negligible. It is evident that the dominant uncertainty in the mean value of atx,/E for B 1° obtained from a single sample is the uncertainty in the sample content itself.
114
H.
W.
SCHMITT,
R.
C. B L O C K
AND
R.
L.
BAILEY
All uncertainties are taken into account in the combined uncertainties given in column 7, table 2. It is seen in table 2 that the result obtained for sample IA 19) differs markedly from the results obtained for samples IIA, IIB, and IIIA. Since the discrepancy is more than four standard deviations, it is concluded that a systematic error, whose source is unknown, occurred. All calibrations and other tests in all transmission measurements indicated valid measurements were made; titration of the samples after completion of the measurements yielded results which agreed within 0.7 per cent with the original quantitative preparations based on weights. Also the q u a n t i t y a t x / E for B 1° appeared to be constant over the entire energy range of the experiment. While it is difficult to designate the source of such a systematic error, two possibilities may be suggested: (1) high cross section impurities whose presence was not detected in spectrochemical tests, (2) errors at some point in the determination of boron content in the sample in question. In view of the considerations of the preceding paragraph, the result obtained with Sample IA is disregarded in arriving at a final mean value of a t v ' E for B 1°. The total cross section of B 1° in the neutron energy range 0.018 ~ E --< 0.4 eV, obtained from the present experiment, is then 612~6 .... b. at -- VE(eV)
(3)
The total cross section for neutrons of energy 0.0253 eV (velocity = 2200 m/sec) is at(0.0253 eV) = 3848±38 b.
(4)
Since, as pointed out in the previous section, the scattering cross section of B 1° is negligible compared to the total cross section, the absorption cross section for B 1° in the present energy range is essentially given by eqs. (3) and (4). This result is thus far the only published measurement of the total cross section of B 1° in which a sample highly enriched in B 1° has been used. Measurements of the total cross section of the Argonne-Brookhaven standard of California natural boron have been made by a number of groups 1, 2, 4, e, 2) ; the average of all results given by Hughes and Schwartz 1~) is 755 b for E = 0.0253 eV (2200 m/sec). Using this cross section together with that obtained for B ~° in this experiment, we compute the isotopic abundance of B 1° in the ArgonneBrookhaven boron sample to be 19.610.2 per cent. This value is in agreement with recent measurements of Sites and Spitzer 2o) and Haas et al. 21), giving 19.84-0.1 per cent, but in disagreement with earlier measurements of Thode et al. 12) and Inghram la).
TOTAL NEUTRON CROSS SECTION OF B1°
l l5
Further discussion added in proo/: An experiment identical with that reported in this paper has been carried out using a sample of the Argonne-Brookhaven standard natural boron, graciously provided by G. R. Ringo of Argonne National Laboratory. The sample solution was prepared exactly as described for the B 1° samples, and used in a sample holder similar to that of the above experiment; the concentration and sample thickness were respectively 8.62+0.04 mg B 2 0 3 per cm ~ and 6.08=t=0.03 × 1020 atoms B per cm 2. Transmission measurements were carried out as above, using the B 2O3--D 20 solution and a D 20 compensator. Two separate runs were made covering the energy range 0.022 to 0.042 eV; data were analyzed and corrections applied as described in text. Results of the two runs agreed within i 0 . 7 per cent. The weighted average of these runs gives the result at(0.0253 eV) = 7574-6 b for the Argonne-Brookhaven standard natural boron. Using the scattering cross sections for B 1° and B n given in ref. 1~), we obtain aabs(0.0253 e V ) = 753=t=6 b, in excellent agreement with other measurements 7, 14, ~ ) in which samples of the same boron were used. The authors wish to thank J. R. Sites of the O R N L Analytical Chemistry Division for the mass spectrometric analyses and Mrs. Jacqueline Blackwood for her assistance in many of the calculations. Helpful discussions with J. A. H a r v e y and G. G. Slaughter are gratefully acknowledged. References 1) W. W. Havens, Jr., E. Melkonian and B. M. Rustad, Columbia University Report CU-160, 1957 (unpublished) 2 P. A. Egelstaff, J. Nucl. Energy 5 (1957) 41 3 Collie, Meads and Lockett, Proc. Phys. Soc. A 69 (1956) 464 4 G. yon Dardel and N. G. Sjostrand, Phys. Rev. 96 (1954) 1566 5 Scott, Thompson and Wright, Phys. Rex,. 95 (1954) 582 6 Green, Littler, Lockett, Small, Spurway and Bowell, J. Nucl. Energy 1 (1954) 144 7 Carter, Palevsky, Myers and Hughes, Phys. Rev. 92 (1953) 716 8 Melton, Gilpatrick, Baldock and Healy ,Anal. Chem. 28 (1956) 1049 9 V. Shiuttse, J. Exp. and Theor. Phys. 2 (1956) 402 10 G.M. Panchenkov and B. D. Moisseev, Zh. Fiz. Khim. 30 (1956) 1118 11 O. Osberghaus, Z. Physik 128 (1950) 366 12 Thode, Macnamara, Lossing and Collins, J. Am. Chem. Soc. 70 (1948) 3008 13 M. G. Inghram, Phys. Rev. 70 (1946) 653 14 See for example values given (a) by D. J. Hughes and R. B. Schwartz, Report BNL-325, 2nd Ed. (Supt. of Documents, U. S. Printing Office, Washington, D. C. 1958), and (b) by Hughes and Harvey in the same report, first edition (1955) 15) H. W. Schmitt, Nuclear Physics, to be published 16) R. C. Block, J. A. Harvey and G. G. Slaughter, Bull. Am. Phys. Soc. 4 (1959) 270 17) E. Melkonian, Phys. Rev. 76 (1949) 1750 18) Rainwater, Havens, Dunning and Wu, Phys. Rev. 73 (1948) 733 19) H. W. Schmitt, R. C. Block and R. L. Bailey, Bull. Am. Phys. Soc. 4 11959) 415 20) J. R. Sites and E. J. Spitzer (1959) (unpublished) 21) Haas, Rourke, Mewherter and McDonald, Knolls Atomic Power Laboratory Report KAP1.2062 (1959) (unpublished)