Alpha-particle emission probabilities for 239Pu and 240Pu

0883-2889/92 $5.00 + 0.00 Copyright © 1992 Pergamon Press Ltd

Appl. Radiat. Isot. Vol. 43, No. 10, pp. 1241 1245, 1992 Int. J. Radiat. Appl. h2strum. Part A

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Alpha-Particle Emission Probabilities for 239ptl and 24°pH C. J O H N

BLAND ~ and JEAN

TRUFFY

2

~Department of Physics and Astronomy, The University of Calgary, Calgary, Alberta, T2N 1N4, Canada and 2CEA/LPRI, Saclay, 91192 Gif-sur-Yvette, France (Received 17 February 1992)

Tabulated emission probabilities [e.g. IAEA (1986)] for the s-particle decay of the nuclide 239pu appear to require revision in the light of measurements reported here. Although the sum of the probabilities of the two most intense lines, s 0 and st3, has been listed as ca 88% since the work of Baranov et al. (1963). However, the individual probabilities measured for these lines were 70.73 and 17.56%, and these values differ significantly from those appearing in reference tables [e.g. IAEA (1986)]. In earlier measurements, the incomplete resolution of two peaks only ~ 13 keV apart, or the effects of conversion electrons in producting energy-summing effects may have given rise to systematic errors depending on the type of apparatus used. Measurements have been carried out under low geometry with a very thin source of purified 239pu and, for comparison, another of 24°pu. Emission probabilities were obtained from the energy spectra using a computer programme to find a best-fit to the peaks with analytical expressions. The programme is based on an iterative Simplex procedure to find a minimum of Chi-squared. A careful evaluation of the variances provides estimates of the relative uncertainty (at the 2a level) of each emission probability which are, in all cases, < 2 % of the measured values.

Introduction M e a s u r e m e n t s of p l u t o n i u m isotopes are i m p o r t a n t in reactor fuel technology and safeguards. In a n o t h e r paper, the m e a s u r e m e n t s o f the ratio of the activities of 239pu a n d 24°pu have been described (Bland e t al., 1991). In t h a t p a p e r it was n o t e d t h a t m e a s u r e m e n t s from a source of mixed isotopes gave values for the emission probabilities o f the two m a i n lines of 239pu at 5.157 a n d 5.170 M e V (designated c~0 a n d ~13) which were lower a n d higher respectively t h a n the values of 73.1 a n d 15% given in tables ( I A E A , 1986). Measurem e n t s have therefore been completed on isotopically pure p l u t o n i u m sources in order to find accurate values for these emission probabilities.

Preparation of Alpha-particle Sources and Spectrometry Pure solutions of 239pu a n d 24°pu were o b t a i n e d from the C E A L a b o r a t o r i e s at F o n t e n a y - a u x - R o s e s . The 24°pu solution was o b t a i n e d by purification of a n aged solution of 244Cm. Isotopic c o m p o s i t i o n s were m e a s u r e d by mass spectrometry. The values o b t a i n e d are given in Table 1 a l o n g with the c o r r e s p o n d i n g percentage s-particle activities. T h e ~-particle source o f 239pu activity was prepared by electrolytic plating on a stainless steel disc from an

acid SO4 + S O 4 H m e d i u m using a revolving c a t h o d e (A. Becerril, Private c o m m u n i c a t i o n ) . The 24°pu source was plated from p l u t o n i u m nitrate solution containing dimethylsulfoxide a n d nitric acid (J. Truffy, Private c o m m u n i c a t i o n ) . M e a s u r e m e n t s were carried out in vaccum using a 20 m m 2 passivated i o n - i m p l a n t e d silicon j u n c t i o n detector m a d e by Societ~ Intertechnique. The contributions to the F W H M of the peaks are a b o u t 9 keV for the source/detector c o m b i n a t i o n s a n d a b o u t 4 keV for the electronics, m e a s u r e d using a signal generator. These two p a r a m e t e r s add together quadratically to give a total F W H M of 10.8 keV. The geometrical factor used in these m e a s u r e m e n t s was 0.51% of 47z.

Spectral Analysis Pulse-height spectra were recorded o n 4096 channels over an energy region extending from a b o u t 3.9 MeV to a b o u t 6.3 MeV, which provides a n energy scale of 0.58 keV per channel. F o r the purpose of o b t a i n i n g emission probabilities, regions of interest of 230 a n d 330 channels were used for 239pu a n d 24°Pu respectively. D a t a analysis was carried out o n a m i c r o - c o m p u t e r using a peak-fitting p r o g r a m m e based on the Simplex m e t h o d (Nelder a n d M e a d , 1965). P a r a m e t e r s in the 1241

1242

C . JOHN BLAND a n d JEAN TRUFFY Table I. Composition of the two plutonium sources 239pU Source

Isotope 238 239 240 241 242

24°pu Source

% Atoms

% :<-Activity

% Atoms

% ~-Activity

99.10 0.888 0.005 0.007

-96.79 3.18 1.9 x 10 ~ 4.4 x 10 6

0.023 0.090 99.848 0.010 0.029

-0.0245 99.975 0.0001 0.0005

fitting functions are adjusted in successive iterations until a minimum is found in Chi-squared. The programme has been described elsewhere (Martin Sanchez et al., 1991). If a group of peaks are not too widely separated in energy (within about 150 keV), then the same form of the fitting function is used for all the peaks and only the amplitudes and positions change (a~ and a2 in the equation below). Thus for a group of n peaks, there are 5 peak-shape parameters plus 2n parameters for the positions and amplitudes of each peak, to be determined in addition to the estimate of the constant background. The fitting function used to describe the peaks in the spectrum consists of the convolution of two truncated exponential functions with a Gaussian function. In addition a step function convoluted with a Gaussian is used to describe detector response. Usually a small constant background term is needed to fit stray counts. We can write the fitting function for each of the peaks as: y (E) =

f)

a (E -- E ' ) . F(E') dE"

where: G(E) = a," e x p [ - (E - a2)2/(2" a~)], F ( E ) = H ( E ) . [a4" exp( - as" E) + (1 - a4 ) • exp(--a6"E) + av], H(E)=lforE<~a

2 and

0forE>a,

Table 2. Values obtained for the fitting parameters for the :~-particle spectra of the two sources by the Simplex method

Sigma Gaussian, a~ (keV) First exponent, a s (keV) Second exponent, a~ (keV) Ratio 1st. exponent, a a Reduced chi 2 Degrees of freedom, v

2>Pu Source

24°pu Source

3.60 3.61 13,80 0.883 I. 178 213

3.80 5.2 I 32.25 0.969 1.816 313

The ~-particle lines analyzed were for 239Pu, the emission to the j = 1/2 state of 235U designated :~0 with an energy of 5.1 57 MeV, and those to the excited states ( j = 3/2, 5/2 and 7/2). These are identified by the energy differences rounded to the nearest keV as, ~3, ~st and :ql. Three ~-particle lines were analyzed for ~'4°Pu. The ~0 emission going to the ground state of e3~'U with an energy of 5.168 MeV, as well as the ~45 and ~J49 emissions.

Results Table 2 gives some of the fitting parameters obtained in the data analyses carried out for the two sources. Figures l and 2 show the fits to each of the measured spectra, as well as plots of the residuals divided by the Poisson variance, i.e. the parameters (Y~ - Y0:/Y~, where y~ denotes the contents of the ith channel and yf is the fitted value. As may be seen from Fig. 2, the 2~°pu spectrum contains a small peak to the left of the two principle peaks and the counts in the intervening channels are not high ( < 100 per channel). Presumably that is why the overall fit as measured by Chi-square is not as good as in the 239pu spectrum. The relative intensities of the ~-particle lines in each spectrum were obtained by dividing the fitted amplitude of a given line by the sum of the fitted amplitudes of the other lines of that isotope. A small correction, obtained from tablcs ( L A R A , 1987), was

cts.lch. 10000 1000 ! 10010"

sig~ai

Fig. I. The best-fit curve shown superimposed on the data from the 23~Pu source. Underneath are plotted the residuals in terms of the Poisson variance.

Alpha-particle emission probabilities for

239pu

and 24°Pu

1243

cts./ch. |0000 Pu240

1000 100 10 stg~a _ 1 -3 -5

w,

l 5'.03

4.99

" Tp

V

I

5'.07

!

5.11

5.15

Fig. 2. The best-fit curve shown superimposed on the data from the 24°pu source. Underneath are plotted the residuals in terms of the Poisson variance.

needed for lines not included in the analysis. The results are given in Table 3. The uncertainties in the derived values arise mainly from deviations in the fitted function. These deviations arise from the combined effects of less-thanperfect fitting function as well as Poissonian fluctuations in the contents of each channel. In the absence of any trend of the deviations to remain predominantly negative or positive over a region of several channels (Figs 1 and 2) which would point to a failure of the chosen fitting function, we may assume that the majority of fluctuations arise as a result of the counting statistics. In order to assess uncertainties in the derived emission probabilities, a computer programme was written which generates replicate spectra from the recorded spectrum by generating random deviates from a Poisson probability distribution. A suitable sub-routine is described in the well-known text, Numerical Recipes (Press et al., 1986). After having determined the linearly-independent fitting functions gi(x) for the recorded spectrum, we can determine the best (in the least-squared sense) solution vector A of amplitudes for each of the replicated spectra. This involves solving the matrix equation [for a fuller explanation refer to, e.g. Debertin and Helmer (1988)]: A=M

IV

Discussion

Before comparing the results obtained with those by other workers, we need to consider possible causes of error in the measurement of s-emission probabilities. When measurements are carried out with larger geometrical factors, there exists the possibility of alpha-electron coincidence summing. Conversion electrons of 7.4 and 11.5 keV energies are often ejected from the M and N shells of 235U in the

Table 3. Measured emission probabilities for 239Pu and 24°Pu and, for comparison, earlier tabulated values

where

M/k=~ Vt'igj(xi)gk(xi) Vj= ~ wiYigj(xi) i=l

There is some correlation between the emission probabilities derived for the s 0 and ~3 lines emitted b y 239pu and, to a lesser extent, between the ~0 and ~44 lines of 24°pu. It is interesting to compute the confidence-limit ellipses for the former cases (see again in Numerical Recipes). Figure 3 shows these ellipses plotted for various confidence limits. To derive the uncertainties from such ellipses one can use the intercepts with the axes. Alternatively if one would impose the constraint that the sum of both emission probabilities equals a constant (a value of about 0.88) then one can estimate the uncertainties from the intersection of the ellipses with the line at - 4 5 ° as shown in the figure (i.e. A x / x = - A y / y ) .

Line

239pa

~0 a~3 ~5~ ~1

0.7073 0.1756 0.1180 0.0003

24°pu

:% • 44 • 147

0.7255 [40] 0.2735 [20] 0.0010 [3]

i=l

in which the wi are the weights. This procedure not only furnishes a new set of emission probabilities for each replicate spectrum, but the elements of the inverse matrix M - ~provide the internal variances and covariances. Alternatively these variances and covariances can be computed from the ensemble of values for each emission probability obtained from several replicate spectra.

Emission probability (This work)*

Nuclide

[46] [28] [19] [1]

Emission probability (IAEA, 1986) 0.7315 0.1505 0.1185 0.00036

[75]]. [25]]. [25]]" [4l

0.7295 [55]t 0.2705 [55]]. 0.00089 [2]

*Numbers in brackets in this column are the 2a uncertainties in the least-significant digits of the measured values. tMid-interval digit (5) appended to original 3 significant digits and single digit uncertainty to facilitate comparison with our measurements.

1244

C. JOHN BLAND and JEAN TRUFFY

Ay(%)

Fig. 3. Confidence region ellipses corresponding to 68.3, 90 and 99% limits. Parameters Ay, Ax (where A)' refers to the % lines, and Ax to the 213 line) of 239pu are expressed as percentages of the means of the emission probabilities. When the total emission from two lines is constrained to a certain value, uncertainties may be read off from the intersections of the ellipses with the line at 45 C (see text). de-excitation of the 13.04 keV nuclear level following ~3 decays. In coincidence with the ~-particles emitted they would simulate emissions from the % level, thus lowering the measured emission probabilities for the ~3 level and increasing that of the ~0 level. This effect is not present in magnetic spectrometer measurements since the magnetic rigidity of electrons of the order of keV energy is about a thousand times less than that of a-particles of a few MeV energy. In the case of measurements made with silicon diodes however, the effect must be prevented by either applying a magnetic field at the radioactive source to sweep away conversion electrons, or by counting particles within a small solid angle. As noted above, we used an effective solid angle of only 0.51% of 4n in these experiments. U n d e r these conditions, we would not expect the relative systematic error to exceed a few parts per thousand in the measured emission probabilities for the ~0 and ~13 lines of 239pu. We also note that the lack of summing events above the higher energy peaks confirms that chance coincidences with /3-particles such as those arising from relatively short-lived impurities such as 242Pu, were negligible in these measurements. The emission probabilities agree with those tabulated (IAEA, 1986) within the quoted uncertainties for all the measured lines with the exception of the two principle lines of 239pu, i.e. ~0 and cq3 (leaving aside the results for the weak ~47 line of -'4°pu). We note that tabulated values for these lines are based on

a set of magnetic spectrometer measurements made some time ago (Baranov et al., 1963). Later measurements using surface-barrier detectors (Ahmad, 1984) gave substantially lower intensities for the % and ~45 of 24°pu than measured earlier using magnetic spectrometers (Kondratev et al., 1956). Unfortunately A h m a d does not provide separate emission probabilities for these two principle lines of z39pu, presumably because of the limits of resolution of his detection system. Later measurements (Bortels and Collaers, 1987) using ion-implanted silicon detectors and sophisticated computer software to separate the peaks, gave emission probabilities of 0.71217] and 0.16715] for ~0 and ~ respectively, which agree with our measurements to within the quoted onestandard-deviation uncertainties. There is also agreement with measurements provided by Westmeier (1986) who obtained values of 0.697[35] and 0.190118] for these lines. These results were obtained with a source of mixed plutonium isotopes and thus the precision was not as high as with measurements made with purified 2~Pu. Martin Sanchez et al. (1991) used the a-particle spectrum from a purified ~39pu source to test various programmes for peak analysis and also found ranges of values (depending on the method of peak-fitting used) close to those reported here, i.e. 0.702 --0,707 and 0,176 0.181. These modern measurements agree very well with one of the first determinations of these emission probabilities (Asaro and Perlman, 1952) who found values of 0.69 and 0.20 using a magnetic spectrometer. They employed a narrow slit for these measurements giving a fullwidth at half-maximum of 8 keV. It was necessary to open the slit wider in order to measure the weaker -particle lines which were more fully investigated in the later work of Baranov et al. (1963).

Conclusions Recent measurements of the a-particle emission probabilities for 239pu and 24°Pu show that values obtained for the former nuclide are not in agreement with those quoted in standard nuclear data tables [e.g. I A E A (1986), L A R A (1987)], in particular the emission probabilities of 0.7073 and 0.1756 found for the % and ~13 lines of 23~Pu. Acknowledgements--This work benefited from the encouragement and valuable advice received from Dr Francois Amoudry. One of us (CJB) received a sabbatical fellowship from the University of Calgary during his visit to Saclay. He is grateful for the hospitality received during his stay there.

References Ahmad I. (1984) Relative alpha intensities of several actinide nuclides. Nucl. &strum. Methods" 224, 319. Asaro F. and Perhnan I. (1952) The alpha-spectrum of Pu 239 and Pu 240. Phys. Rev. 88, 828. Baranov S. A., Kulakov V. M. and Belenky S. N. (1963) Fine structure of ~-radiation of Pu 2~9. Nucl. Phys. 41, 95.

Alpha-particle emission probabilities for 239Pu and 24°pu Bland C. J., Truffy J. and De Bruin T. (1992) Deconvolution of alpha-particle spectra to obtain plutonium isotopic ratios. Appl. Radiat. Isot. (in press). Bortels G. and Collaers P. J. (1987) Analytical functions for fitting peaks in alpha particle spectra. Appl. Radiat. Isot. 38, 831. Debertin K. and Helmer R. G. (1988) Gamma and X-ray Spectrometry with Semiconductor Detectors. NorthHolland, Amsterdam. IAEA (1986) Decay data of the transactinium nuclides. Tech. Report Series No. 261, International Atomic Energy Agency, Vienna. Kondratev L. M., Novikova G. I., Sobolv Y. P. and Gol'din L. L. (1956) ~-decay of Pu 24°. Zh. Eksp. Teor. Fiz. 31,771; Eng. trans. Sot,. Phys. JETP 4, 645.

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LARA (1987) Fichier de rkfkrences L M R I pour la spectrometrie gamma et alpha. Commissariat ft. l'Energie Atomique, Gif-sur-Yvette, France. Martin Sanchez A., Vera Tom6 F. and Bland C. J. (1991) Data analysis of alpha-particle spectra from low level sources. In Low-level Measurements of Man-made Radionuclides in the Environment (Garcia I.~on M. and Madruga G., eds), pp. 119 137. World Sci. Press, Singapore. Nelder J. A. and Mead R. (1965) A simplex method for function minimisation. Computer J. 7, 308. Press W. H., Flannery B. P., Teukolsky S. A. and Vetterling W. T. (1986) Numerical Recipes, the Art of Scientific Computing. Cambridge University Press, Cambridge. Westmeier W. (1986) The fitting of solid state detector spectra. Nucl. Instrum. Methods A242, 437.