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Measurements of the total internal conversion coefficient and PKωK probability in the decay of 139Ce
International Journal of Applied Radiation and Imtopet, 1975, Vol. 26, pp. 579-.587. Pergamon Press. Printed in Northern Ireland
Measurements of the Total Internal Conversion Coefficient and Probability in the Decay of'""Ce JIP..1 P L C H and J. Z D E R A D I ~ K A Institute for Research, Production and Application of Radioisotopes (I~VVVR), Prague, Czechoslovakia and O. D R A G O U N Nuclear Physics Institute of the Czechoslovakian Academy of Science l~e~ near Prague, Czechoslovakia (Received23 October 1974; in revisedform 4 February 1975)
The total conversion coefficient of the 165.853 keV transition in XSgLahas been determined to be 0.251 4- 0.002 from measurements of the electron and gamma-ray intensities and the source activity. From the X-ray and F-photon spectra the probability PKoJK has been determined to be 0.639 4- 0.006. Using ~i, = 0.251 4- 0.002, =K = 0.214 4- 0-002, oJK = 0.906 4- 0.026 and PKoJK ----0.639 4- 0.006 the number of K - X rays and 166 keV photons per disintegration has been calculated to be 0.794 4- 0.009 and 0.799 4- 0.001 respectively, giving a K - X ray to F-photon ratio of 0.99 4- 0.01. The discrepancy between the experimental and theoretical conversion coefficients is explained by taking the nuclear structure effect into account.
1. I N T R O D U C T I O N T H E RADIONUCLIDE l a 9 C e decays by electron capture to the first excited state of XagLa which proceeds via a 165.853 keV partly converted g a m m a transition, cl) This radlonuclidc is widely used as a source of conversion electrons, g a m m a - and X-photons. An accurate calculation of electron and photon emissions from sources of known disintegration rate presumes the accurate knowledge of the conversion coefficlents a n d the probability PwoJK. T h e total conversion coefficient ~ , equal to 0-2446 40.0012 has been measured by LEOm~.,CDet al. ~2) 0.2508 4- 0.0014 b y TAYLOR and MERmTT (s'4) and 0.254 4- 0.006 by ARISTOVand BAZI~OV, ~6~ the coefficient 0~K has been measured b y several authors. ~e-s) G~.mP.R e t a l . c°) determined the conversion intensity ratios. T h e difference between L E O ~ D ' S result and the others is considerably higher than the stated errors and none of the values are consistent with the theoretical ~ , = 0.268 for an M1 transition.C~) New measurements of the coefficient 0~,
have been performed b y several methods and the discrepancy between theory a n d experiment is explained b y taking into account the nuclear structure effect. T h e K-capture probability P x has been measured by several authors. ~ea'x°-x6~ Most results are independent of assuming values for the fluorescence yield t ~ x ( L a ) - - ( s e e T a b l e 2). T h e weighted m e a n exhibits a relatively small error of about 1 ~ but the results differ considerably from one another. W h e n the probability PKtoK is calculated from the experimental P K the uncertainties in the experimental ~s'~) or semiempirical as) values of toK(La ) introduce errors of several percent. I n order to reduce this error the probability PKcoK was measured. 2. S O U R C E P R E P A R A T I O N I n total 11 different sources have been used for the ~,r-measurement. T h e carrier-free solution (about 0.5 mCi/ml) was supplied by T h e Radiochemical Centre Amersham. T h e sources were prepared by depositing the
579
580
J. Pith, d. Zderadi~kaand O. Drago.n
decay scheme correction significant. Therefore the measuring conditions must give a linear relation between NpN~[N o and the ( N 7 -- No) / N o when the extrapolation method is performed. (s'4"zT'xs) It is obvious that the linearity is achieved if the efficiency of the conversion 3. D E T E R M I N A T I O N O F T H E T O T A L electron detection does not vary when N d N ~ is CONVERSION COEFFICIENT changed. In order to get reasonable value of Knowing the source activity No, the gamma NdNy the L-events must be detected in the ray and electron intensities N 7 and NE, the proportional counter. When the pressurized total conversion coefficient and its fractional proportional counter as~ working as an electron error can be determined by the three following spectrometer is used, the L-peak is very well separated from the K- and the conversion methods: electron peaks. Consequently the efficiency of 2V E 0t T - - N7 A== = AE = + A7 =. (1) the conversion electron detection does not vary considerably when the NdN~-efficiency is changed by shifting the discrimination level. WE T h e situation is further simplified if the 0t T - ~V0 -- 2rE registration of X-rays is excluded in the gammaA J = [AE= + A0=](1 + =r) s. (2) channel when the analyzer window is set around the gamma-peak. T h e relative slope of the extrapolation line, i.e. the slope divided by the intercept, is expressed by activity on VYNS-foil gold-coated on both sides to about 40 pg/cm s total thickness. For the gamma-ray intensity determinations these VYNS-mounted sources were sandwiched between polyethylene foils of 30 mg/cm 2.
A,, = (:,o s + AV,)(l- + \
o~T
(s) l
~z " "
8$~, - -
8e
0t T
( , ~ + (I - *~)*x)
- - 1 + ~ , + 1 +0¢ T where A 0 is the total fractional error of the activity and A E, A~ are the errors of the (4) respective intensities. T h e first method was used by I~ORAND et al.t=~ who employed a where 8p~ is the 4w proportional counter 4rr high-pressure proportional counter for elec- sensitivity to the gamma-photons; , z is the tron intensity measurements and a well-type efficiency of the conversion electron registration; scintillation counter for gamma-ray intensity 8x is the total efficiency of the X-ray or Augermeasurements. I f the activity is measured in electron registration, and s o is the probability of addition to the N ~ and N 7 intensities, then the a coincidence event registration when the ECuncertainty of the first method can be reduced event is not registered in the proportional using the second and the third method. Due counter. T w o types of the ¢rr pressurized proportional to the influence of the term 1 + ~ , and counters were used for the coincidence measure(1 + 0tT)/0tT the accuracy of the second and ment: a 4w counter with solid cathode and a 4,r third method is decreased. T h e 0t~,-coefficient can be also determined counter with wire mesh cathode. T h e solidfrom the results of the activity measurement by cathode counter ¢19) has a diameter of 9.6 cm means of the 4,r(X, e) -- 7 coincidence method. and a length of 14 cm; the cathode is made This method (denoted further as the slope one), of stainless steel sheet. Due to the large was used by TAYLOR and M~.RmTa"tS~ and dimensions the working pressure of the 9 0 ~ Ar + 10~o CH4 mixture was only 0.5 M P a A R I S T O V and BAZHENOVCbL (5 atm), which is enough to absorb the electrons 3.1. ActiviOpmeasurement and determination of the in the gas (see later). In order to reduce o~T-coe~ent by means of the slope method electron backscattering inside the counter a T h e source activity was determined by the part of the source holder which splits the counter 4,r(X, e) - - 7 coincidence method. T h e high into two half-cylinders was made of wire mesh. value of the conversion coefficient makes the The mesh-cathode counter has the same
Measurements of the total internal conversion coefficientand P KoJE probability in the decay of x3°Ce
dimensions but the solid cathode was replaced by wire mesh as well as all the source holder. Two scintillation counters with 51 X 76 m m NaI(TI) crystals were used as 7-ray detectors. In order to keep the total error of the instrumental correction for dead-times and accidental coinddences below 0.I ~o the sources with activity less than 104see -I were used. T h e dead-time error is equal to 4-40 nsec, the coincidence resolving time error is -4-10 nsec and the error of the delay between coincidence pulses is 4-50 nsec. With the solid-cathode counter the relative slope k, = 0.1998 4- 0.0004 was found from linear regression. T h e slope slightly decreases to k, -- 0.I 990 4- 0.0004 when the mesh-cathode counter was used. As the typical value of the variable s = (Ny -- N , ) / N , was about 0.75 the error of the decay scheme correction, expressed as s. ~,, was about 4-0.03 ~o. Using non-linear regression function in the following form
(NxN, - ~ ],
= No(1 + k# + a.sS),
(5)
I
I
the km= 0.2019 4- @004 and a = --0.0003 was found for the results from the solid cathode counter. T h e statistical test has shown that neither of the two functions can be preferred. But as there is a small decrease of the efficiency * z when the discrimination level is increased reaching 0.5 ~o for s equalling 6, the non-linear regression is preferred. T h e coefficient =l, equal to 0-249-4-0.006 was calculated from k~ = 0.2019 4-0.0004 using a calculated value for ep7 equalling 0.7 4- 0.2 ~o and estimating e 0 = (0.5 ± 0.5)8p. T h e total error of the a Tcoefficient (given at the 68 ~o confidence level) was calculated by adding the error Asps, Aeo and As, in quadrature. T h e error A~ results from the uncertainty in using either linear or non-linear regression. 3.2. Electron intensity measurements T h e electron intensities have been measured by means of the 4w proportional solid-cathode counter. A typical spectrum is given in Fig. I. In order to exclude the registration of Auger electrons and K-X-rays the discrimination level was shifted to 66 keV. Measured counting rates I
I
l
I
vents
ger e l e c t r o n s
%
26 keV
x .2
K-conversion 127 keV
line
o m L-conversion line- 1 6 0 keV
8 Discrimination I I I I
ZO
40
60 Chonnel
581
80
I00
120
140
16o
number
Fro. I. ISgCe--lagLaconversion electron spectrum taken with the 4~r pr~surized proportional counter.
582
J. Plch, J. Zderadigka and O. Dragoun
were corrected for the background, the dead time, the gamma-sensitivity of the counter and for the lost part of the conversion electron spectrum below the K-peak (discrimination correction). As can be seen from Fig. 2 the discrimination correction depends on the working pressure, but for pressures higher than 0.6 M P a (6 atm) the correction decreases slowly. As there is decrease of the resolution and considerable increase of the gamma-ray sensitivity for high pressures, most results were obtained with a pressure of 0.6 MPa. T h e discrimination correction was calculated for each source as "~40-80
KD = ~
(1
--~0)
(6)
where N4H0 is the area of the spectrum between the channeIs 40 and 80; N>, 0 is the a r e a o f t h e spectrum above channel 40; ~0is the probability of an electron-pulse being raised above the discrimination level due to internal summation with the radiations from the tilling of K-shell vacancies. T h e probability ~0 was determined from the efficiency of K-shell vacancy detection, calculated as ~ = w ~ x + (1 - - o K ) e A E = 0"28, (~°) and from the probability of the K-shell vacancy creation. T h e mean value of the discrimination correction was 3"62~o with a standard deviation for a single source of 10 4
I I - 2 6 keV
I
[
{
I
4-0.05 ~o and an estimated systematic error of
4-0.8%. T h e correction for the gamma-ray sensitivity of the proportional counter was calculated as 1
8p~
O~T
8E
Kg . . . .
,
where e E is the efficiency of the conversion electron registration, and 8pz is the gamma-ray sensitivity of the counter. T h e gas-part of the gamma-ray sensitivity was calculated equal to 0.7-4-0"2~o and the wall-part of the gamma-ray sensitivity was estimated to 0-08-b 0"04~o from U~QuH~a~T's results. (*x) T h e n the correction Kg reached the comparatively high value of 2.9 q- 0.8 Yo. 3.3. Gamma-ray intensity measurement The gamma-ray intensity was measured by means of a windowless 4-x scintillation counter with NaI(TI) crystals. (=~ A typical spectrum measured in this counter is given in Fig. 3. T h e counting rates in the peaks A, B, G a n d D can be expressed as N ~ = No[P,~x(l -- P x e x -- p,e~) + p K r x ( 1 - - p , s x ) ];
(8) (9)
N B = N O. p~. p ~ s x ~ N c = N o . pg. e~(1 -- p , s x ) ;
(10)
ND
(11)
[
- 1 2 7 keV
(7)
=
N O. p , . 8~ . p , s x ;
where O~.K
P, = PKc°~r;
•= ,o'
PK--
- =~ . o~K; I- +
1
[o ¢~ I0 2
i0
l 20
I 40
I 60
1 80
I ioo
l 120
I 140
Chonnel number
F x o . 2. a 8 9 C c - ~ S g L a c o n v e r s i o n electron spect r u m t a k e n w i t h t h e 4 ~r p r o p o r t i o n a l counter
at several pressures of 90% Ar + 10% CH~ mixture (1 at ---0-1 MPa).
1 + ~------~;
8x, 8~ are the absolute efficiency of the K - X - r a y and y-photon detection respectively. T h e gamma-ray intensity N e + N D = N o . Po • 8~ was measured by setting the discrimination level above the X + X-peak. T h e corrections for background, dead time and discrimination were applied. As the efficiency used, % = 0.96 4- 0"005 (m) is the total one, the correction for the discrimination is the correction for the cutting off the Compton spectrum below the X and X q- X peaks. T h e Compton to peak ratio
Measurements of the total internal aonversioncoeffg@ntand PKmK probabili@ in the decay of lseCe IOs
g
Ix I 3 4 k e y X-I-X j~ - 6 8 keV
I
I
583
I I~ I ?'-166 key , ¢ ~ - - T + X keV
I0 ~
'-'
~_. j+
,'t
,
,o,
_;
~!
l ,I " . t
,
'r-""~
', 60 ',
: 20i /I 40r
~t
,'s.+.,oo,
oo o,o.
spectrum
h
"
i
80
t
I00
120
i~t
i!t
140
160
Chonnel number
Fzo. 3. A a~9Ce X-ray and gamma-photon spectrum taken with the 4vr windowless schatillation counter. was determined cxperlmentally; X-rays were absorbed in the filter consisting of Cd and Cu sheets of several thicknesses. T h e spectra with different filters are given in Fig. 4. T h e results of the Compton to peak ratio measurements are summarized in T a b l e 1. A considerable decrease of the Compton to peak ratio in the 4-tr geometry with respect to 2rr geometry is caused by the fact that most scattered photons escaping
i°F 'o'LE
f
/
FI\
//
Cd 210/J.m+Cu 50 ~*'~p~ filter fO#v-
j~q/zm
,~
14
r'o+f
m-filter i
o
20
= ~ 40 60 80 Channel number
I00
Filter 210 pm 210 pm 120 pm 120 pm
Cd Cd Cd Cd
+ 200 pm Cu + 50 pm Cu + 50 pm Cu + 50 pm Cu
Detection Compton/ solid angle peak 4nr 4¢r 4~r 2¢r
0"025 0.024 0.024 0.041
from the front area are redetectcd in the opposite crystal and comcqucntly this compensation effectreduces the area of the Compton spectrum. W h e n this compensation effect was taken into account for the case when no filter was placed between the crystals,a Compton to peak ratio of (2 -4-0.4) % was deduced. This rcsuh was verifiedby reconstructing the Compton spectrum below the X and X + X peaks. W h e n the internal coincidences between X-rays and y-photons were taken into account, a spectrum given in Fig. 3 was obtained which successfully explained the dcvlations of the measured spectrum from the Gaussian shape of the peaks.
A
cdx
TAaLg 1. Results of the Compton to peak measurelent.
120
FIG. 4. A 1seCt g a m m a - p h o t o n s p e c t r u m t a k e n
with the ~ windowless scintillation counter; X-rays were absorbed in the Cu and Cd f~Iters.
3.4. Results of the ~T-coe~ent measurement I n total the activity, and the g a m m a and electron intensities of 11 sources were measured. T h e reproducibility of each method was good
584
J. Plch, J. Zderadi~ka and O. Dragoun
and the statistical errors did not contribute significantly to the total error; when aT was determined as Ng/~v the standard deviation of the mean was + 0"07%. Therefore the total error consists mainly of systematic errors of the applied corrections. Using the following systematic error A N o = -4-0.2%, AN~ = 1.13%, A N y = 4-0-64% and AN 0 = - 4 - 0 . 1 5 % the total errors given at the 68 % confidence level were calculated from equations (1-3). T h e final results obtained by the different methods are:
~ - - 0 . 2 5 1 -4-0.003 (4-1.3%); =T-- g/~,
au
"r
L2/L , L3/L = K/L
K/(M+_..)
I'IC
~
1"05
~
M,
_
1"0•
0"9~ 0 "90
E
M I ÷ 0 . 2 % E2
t.~c
~.
1"05
%.
I'00 0.9~
F-
Ng
=0.2504-0.004
(4-1.4%);
I.Jo-
-- I = 0.255 4- 0.008
(4-3.2 %) ;
~.oo- - - - ~
0tT (slope method) = 0.249 4- 0.006
(4-2.5 %).
I.o5
=T
= ~
.
MI .X=3.1
_
--
0"95 --
T h e weighed mean is equal to =T = 0.251 40.002 (4-0"8~'o). T h e present results support Taylor and Merritt's and Aristov and Bazhenov's values. 3.5. Comparison with theory T h e 165.853 keV transition in laSLa take place between the 5/2 + and 7/2 + levels. G~mEg et al. (9) measured precisely relative intensities of the L-subshell conversion electrons and determined the transition multipolarity to be M I + 0"2 -o.~+°'ao//o E2. In a recent compilation Om~zNwooDm adopted a pure M1 character for this transition. The relevant theoretical coefficients, 0~T = 0.264, ate: = 0.226, were obtained by polynomial interpolations (~a) from the tables. (~4.z5) There is a 5 % discrepancy between the experimental result of this work 0tT = 0.251 -40.002 and the total conversion coefficient for the M I multipolarity which cannot be explained by any E2 admixture. For an 165.853 keV E2 transition oc~,= 0.340 and 0cK = 0"251; these results were obtained from the tables (=4'=5) by interpolation.C=~) Taking our value of the ~ . and the intensity ratios ¢K/L a n d / K / ( M + . . . ) of G~m~g et al. c~) we derive the conversion coefficient g~- = 0.214 4- 0.002. Thus the above
0"90
--
FIo. 5. Comparison of theoretical and experimental conversion coefficients. discrepancy is due principally to the discrepancy in = x (see Fig. 5). In order to explain the discrepancy it was taken into account that the 166 keV transition is hindered and therefore its internal conversion can be influenced by the nuclear structure effect. In fact the experimental half-life Tz/z = 1.50 nsec (x) is 380 times longer than WEISSKOI'F'S theoretical estimation for M1 radiation. If it is assumed that the two lowest levels in Z39La are essentially pure shell model levels d5/2 and gT/z we see that this transition is 1-forbidden. For such cases, anomalies in the internal conversion process have been already observed. (~) The effect arises from the penetration of the atomic electrons within the converting nucleus. For magnetic multipoles and the particular subshell i the resulting conversion coefficient can be expressed in the following form
The static conversion coefficient ~0) and the dynamic correction coefficients bn, b~z depend on the electron wave functions only. For the subshells K through M5 the quantities a[0l and
Measureraents ~f th~ t~ta~ intsrna~ ~nversi~n ~el~knt ~nd P 1 ~ E pr~babi~i~y in ths ds~ay ~ f 1 a ~
b,1, b,, are tabulated in 0 a ' ~ respectively. Calculation of the nuclear parameter 2 requires knowledge of the nuclear wave functions. It can also be derived from the experiment (see e.g. m~ where the nuclear parameters were determined for a more complicated case of electric dipole conversion). T h e case g-----0 corresponds to the normal internal conversion process for unhindered transitions when the conversion coefficients are to a good approximarion independent of the nuclear structure. T h e b~l, b~s-coefficients were obtained by a double interpolation in Z and energy from the tables. ~ T h e value of the nuclear parameter g was derived from (12) using the experimental 0cx -- 0.214 q- 0.002 and the theoretical = ~ = 0.226. Assuming rather optimistically 1 ~o error in the theoretical coefficient 0 ~ ~ the two roots of (12) 2 = 3.1 -4- 0.7 and 2 -4- 226 -4- 3 were found. T h e smaller value is more justified from the physical point of view.
585
In Fig. 5 three theoretical predictions are compared with the experimental conversion coefficients. T h e upper part of the figure corresponds to the pure M l multipolarity without correction for the nuclear structure effect. T h e L-subshell ratios do not exclude a-small E2 admixture. Assuming 0"2 ~o E2 admixture the agreement for the L-subshell intensity ratios is improved (see middle part of Fig. 5), but the anomaly in the total and K-shell conversion coefficients remain unchanged. T h e lower part of the Fig. 5 refers to the pure M l character of the transition including the nuclear structure effect with the parameter 2 = 3.1. T h e agreement between the theory and the experiment is now observed, not only for the 0¢E-coefficient but also for the aT-coefficient and the Lsubshell intensity ratios. In progress are further calculations of the conversion coefficients for the transition energy equalling 165.853 keV without interpolations.
TABLE2. The Pg-probability measurements Author
PK
Pruett and Wgkinson (s)
0.83 ±0.04
Ketdle eta/. (v) (1956)
0.73 4-0.03
Stanford et aL In) (1960)
0.83 4-0.04
Marelius et al. (is) (1967)
0.68 4-0.02
(1954)
Aclamowicz et al. (14) (1968) 0.75 4-0.01
Schmidt-Ott eta/. (iS)
0.78 4-0.03
(1972) Vatai and Hochmuth (1°)
0,69 4-0-02
(1968) Campbell and McNelles (la) (1972)
0.705 +0"02
Weighted mean Mean Present work
0.7344-0.007 (4-0.9%) 0-75 4-0.02 (4-2.8%) 0.705 4-0-02
Method
Remark
Mag./~-spectrometry independent of wE and scintill, coincidence X + 7 + E - - 4 lr scintillation spectrometer with NaI(T1) independent of wE crystal coincident scintillation independent of wK (?) spectrometry Auger-conversion electron independent of oJE coincidence K-cony. electron-KX-ray independent of oJK coincidence L-cony. electron-KX-ray coincidence K-conv. electron-KX-ray independent of o~K coincidence X + 7 + E - - 4 ~rscintillation independent of ~ox spectrometer with CsI(T1) crystal X + y - 4 ~rscintillation pard 7 dependent on spectrometer with CsI(TI) oJE =0.92 4-0.01 crystals X + ? --4 ¢rscintillation spectrometer with NaI(T1) crystal
586
,1". Pl¢h, J. Zderadigka and O. Dragoun
4. P ~ o a ~ - P R O B A B I L I T Y UREMENT
MEAS-
T h e probability P x c o x can be deduced from the area of the peak D (denoted as Nz~) and the areas N~ + N o in the y,X-spectrum (see Fig. 3). From equations (10) and (11) P x c o x can be calculated as P~rc°lr = ( N ~ + N o ) e x "
(13)
T h e ratio N D / ( N D + ~ e ) was determined by fitting the Gaussian peaks by the iterative least-squares method. In the middle part of the spectrum, between the 85th and 140th channel, which is not influenced by secondary effects such as the photon backscatter and pile-up summing, the largest resid-al~ were less than 4-3a. T h e efficiency *x was calculated as *x
= (~=
-
E=). k + (eK# -- E#). (I - - k),
(14)
where *K~ = 0.985 4- 0"003 is the efficiency for the K~-X-ray detection in the 4qr counter; Csl~ 8KB = 0.987 4- 0.003 is similar effide,ncy for theK#-X-rays; czs~ E~ and E~ are the corrections for the iodine X-ray escape; k is the probability of the K~-X-ray emission. As the energy of the La X-rays is very near to the iodine absorption edge, the iodine X-ray escape from the single crystal is very high, reaching 0.40 4- 0.04 and 0.36 4- 0.004 respectively. ¢~'~ Thanks to the compensation effect of the opposite crystalt2a~ the corrections E, and E~ are equal to Ea = 0.40. (1 - - p . ) -- 6.8. l0 ~ , E# = 0.36. (1 - - p . ) = 6 . 1 . 1 0 -3, where p. is the probability of the iodine X-ray passing through the polyethylene foils. Thus ex 0.978.4- 0.005. The measurement of the probability P ~ o ~ : leads to the value PKw~: = 0.639 4- 0.006 (4-0.9 ~o). Using ~oK = 0.906 -4- 0"026, at) P~: = 0.705 4- 0.02 was obtained which is in agreement with CAMPBELLand McN~.LLES' result (ls) --(see Table 2). Using ~K = 0.214 4- 0.002, ~o~: = 0-906 4=
0.026an) and Pxo~ x = 0"639 + 0.006, the number of K-X-rays per disintegration has been calculated to be 0.794 -4- 0.009. T h e number of 166 keV photons per disintegration is 0.799 -40.001 from a~, = 0.251 + 0.002 and then the ratio K - X / g a m m a is 0.993 4- 0.01 which is in agreement with CAMPBELL and MCNELLSS' value 1.01 4- 0-025. aa~ AdmowledgementNThe authors are indebted to Mrs.
M. Vladykovk and Mrs. M. Boukslovk for their assistance in preparing the manuscript. REFERENCES 1. GREENWOOD L. R., Nucl. Data Sheets 12, 139 (1974). 2. I~op~,~o J., BLO~DSX, M. and MAOmSR P. Nud. Imtrum. Meth. 112, l01 (1973). 3. TAYLORJ. O. V. and MSRmTr J. s. Bull. Am. Phys. Soc. 7, 352 (1962). 4. TAYLORJ. G.V. Private communication (1974). 5. Amsrov E. A. and BAZ~SNOVMeas. Techol. 14, 1883 (1971). 6. PRtm'rr C. H. and WizatmSON R. G. Phys. Rev. 96, 1340 (1954). 7. KZTSLLE B. H., THOMAS H. and BRosx A. Phys. Rev. 103, 190 (1956). 8. HANSEN H. H. and DSL~AYS M. Proc. Sym. Standardization of Radionuclides. SM-79124 IAEAVienna (1967). 9. GEmERJ. S., Gaxt-mM R. L., Bm~OSTR6ML and BROWNF. Nud. Phys. 68, 352 (1965). 10. VATAaE. and Hocnmtrm K. Proc. Int. Conf. on Orbital Electron Capture, p. 88. Debrecen (1968). II. STANFORDA. L., Ba.~sN C. H. and WYLYL. D. Bull. Am. Phys. Soc. 5, 448 (1960). 12. M.~ta~as A., SP,~tmoa~ P. and H3kaLm~mS. E. Nud. Phys. A95, 632 (1967). 13. CaAMPBELLJ. L. and MGNELLES L. A. Nud. Instmm. Meth. 98, 433 (1972). 14. AVAMOWmZ B., Mogoz Z., Px~mxsz Z. and ZGLXfiSKIA. Acta Phys. Polen 3 ~ 88 (1968). 15. ScH~mT-O'rr W. D. and FmK R. W. Z. Physik 249, 286 (1972). 16. BAMBYNEKW., CRASEMANNB., FINK R. W., FREUDH. V., MARKH., Swwr G. D., PRICER. E. and VENUOOPALARAO P. Rev. Mod. Phys. 44, 716 (1972). 17. B~RG A. P. Nud. Instrum. Meth. 112, 143 (1973). 18. BAERG A. P., Nud. Instrum. Meth. 112, 95 (1973). 19. BU6INAI., PLCHJ., Z v ~ I ~ Z ~ J. and J. dadernd energie 15, 369 (1969).
Measurements of the total internal conversion coe~cient and PK~OK probability in the decay of JnCe 90. BAMBY~CEKW. AVU~[.InsUre. Meth. 112, 103 (1973). 21. U n Q ~ T D. F. Proc.@mp. on tt~ Standardization of Radionudides, SM-79/27 IAEA-Vienna (1967). 22. PLCrI J., ZDEn~DI~rO,J. and KOKTA L. Int. J. ajppl. Radiat. Isotopes 24, 407 (1973). 23. Sp,~aJx A. and DRAoou~ O. Czech. J. Phys. B24, 161 (1974). 24. H.AOBR R. S. and SELTZER E. C. Nud. Data A4, 1 (1968).
587
25. DnAOOUN O., P~jx~mR Z. and SCHMXYrZERF.: Nud. Data Ag, 119 (1971). 26. GEnxIO~ T. R. and PETrEnsso~ B. G. in Siegbahn K., Alpha-, Beta. and Gamma-Ray Spectroscopy, p. 981. North-Holland, Amsterdam (1965). 27. DnAoou~ O., P ~ j ~ R Z. and M~XR~N B. Numl. Phys. 150, 291 (1970). 28. I-IAoER R. S. and SELTZER E. C. Nud. Data A6, I (1969). 29. AXEL P. Rev. Sci. Instrum. 25, 391 (1954).
Measurements of the Total Internal Conversion Coefficient and Probability in the Decay of'""Ce JIP..1 P L C H and J. Z D E R A D I ~ K A Institute for Research, Production and Application of Radioisotopes (I~VVVR), Prague, Czechoslovakia and O. D R A G O U N Nuclear Physics Institute of the Czechoslovakian Academy of Science l~e~ near Prague, Czechoslovakia (Received23 October 1974; in revisedform 4 February 1975)
The total conversion coefficient of the 165.853 keV transition in XSgLahas been determined to be 0.251 4- 0.002 from measurements of the electron and gamma-ray intensities and the source activity. From the X-ray and F-photon spectra the probability PKoJK has been determined to be 0.639 4- 0.006. Using ~i, = 0.251 4- 0.002, =K = 0.214 4- 0-002, oJK = 0.906 4- 0.026 and PKoJK ----0.639 4- 0.006 the number of K - X rays and 166 keV photons per disintegration has been calculated to be 0.794 4- 0.009 and 0.799 4- 0.001 respectively, giving a K - X ray to F-photon ratio of 0.99 4- 0.01. The discrepancy between the experimental and theoretical conversion coefficients is explained by taking the nuclear structure effect into account.
1. I N T R O D U C T I O N T H E RADIONUCLIDE l a 9 C e decays by electron capture to the first excited state of XagLa which proceeds via a 165.853 keV partly converted g a m m a transition, cl) This radlonuclidc is widely used as a source of conversion electrons, g a m m a - and X-photons. An accurate calculation of electron and photon emissions from sources of known disintegration rate presumes the accurate knowledge of the conversion coefficlents a n d the probability PwoJK. T h e total conversion coefficient ~ , equal to 0-2446 40.0012 has been measured by LEOm~.,CDet al. ~2) 0.2508 4- 0.0014 b y TAYLOR and MERmTT (s'4) and 0.254 4- 0.006 by ARISTOVand BAZI~OV, ~6~ the coefficient 0~K has been measured b y several authors. ~e-s) G~.mP.R e t a l . c°) determined the conversion intensity ratios. T h e difference between L E O ~ D ' S result and the others is considerably higher than the stated errors and none of the values are consistent with the theoretical ~ , = 0.268 for an M1 transition.C~) New measurements of the coefficient 0~,
have been performed b y several methods and the discrepancy between theory a n d experiment is explained b y taking into account the nuclear structure effect. T h e K-capture probability P x has been measured by several authors. ~ea'x°-x6~ Most results are independent of assuming values for the fluorescence yield t ~ x ( L a ) - - ( s e e T a b l e 2). T h e weighted m e a n exhibits a relatively small error of about 1 ~ but the results differ considerably from one another. W h e n the probability PKtoK is calculated from the experimental P K the uncertainties in the experimental ~s'~) or semiempirical as) values of toK(La ) introduce errors of several percent. I n order to reduce this error the probability PKcoK was measured. 2. S O U R C E P R E P A R A T I O N I n total 11 different sources have been used for the ~,r-measurement. T h e carrier-free solution (about 0.5 mCi/ml) was supplied by T h e Radiochemical Centre Amersham. T h e sources were prepared by depositing the
579
580
J. Pith, d. Zderadi~kaand O. Drago.n
decay scheme correction significant. Therefore the measuring conditions must give a linear relation between NpN~[N o and the ( N 7 -- No) / N o when the extrapolation method is performed. (s'4"zT'xs) It is obvious that the linearity is achieved if the efficiency of the conversion 3. D E T E R M I N A T I O N O F T H E T O T A L electron detection does not vary when N d N ~ is CONVERSION COEFFICIENT changed. In order to get reasonable value of Knowing the source activity No, the gamma NdNy the L-events must be detected in the ray and electron intensities N 7 and NE, the proportional counter. When the pressurized total conversion coefficient and its fractional proportional counter as~ working as an electron error can be determined by the three following spectrometer is used, the L-peak is very well separated from the K- and the conversion methods: electron peaks. Consequently the efficiency of 2V E 0t T - - N7 A== = AE = + A7 =. (1) the conversion electron detection does not vary considerably when the NdN~-efficiency is changed by shifting the discrimination level. WE T h e situation is further simplified if the 0t T - ~V0 -- 2rE registration of X-rays is excluded in the gammaA J = [AE= + A0=](1 + =r) s. (2) channel when the analyzer window is set around the gamma-peak. T h e relative slope of the extrapolation line, i.e. the slope divided by the intercept, is expressed by activity on VYNS-foil gold-coated on both sides to about 40 pg/cm s total thickness. For the gamma-ray intensity determinations these VYNS-mounted sources were sandwiched between polyethylene foils of 30 mg/cm 2.
A,, = (:,o s + AV,)(l- + \
o~T
(s) l
~z " "
8$~, - -
8e
0t T
( , ~ + (I - *~)*x)
- - 1 + ~ , + 1 +0¢ T where A 0 is the total fractional error of the activity and A E, A~ are the errors of the (4) respective intensities. T h e first method was used by I~ORAND et al.t=~ who employed a where 8p~ is the 4w proportional counter 4rr high-pressure proportional counter for elec- sensitivity to the gamma-photons; , z is the tron intensity measurements and a well-type efficiency of the conversion electron registration; scintillation counter for gamma-ray intensity 8x is the total efficiency of the X-ray or Augermeasurements. I f the activity is measured in electron registration, and s o is the probability of addition to the N ~ and N 7 intensities, then the a coincidence event registration when the ECuncertainty of the first method can be reduced event is not registered in the proportional using the second and the third method. Due counter. T w o types of the ¢rr pressurized proportional to the influence of the term 1 + ~ , and counters were used for the coincidence measure(1 + 0tT)/0tT the accuracy of the second and ment: a 4w counter with solid cathode and a 4,r third method is decreased. T h e 0t~,-coefficient can be also determined counter with wire mesh cathode. T h e solidfrom the results of the activity measurement by cathode counter ¢19) has a diameter of 9.6 cm means of the 4,r(X, e) -- 7 coincidence method. and a length of 14 cm; the cathode is made This method (denoted further as the slope one), of stainless steel sheet. Due to the large was used by TAYLOR and M~.RmTa"tS~ and dimensions the working pressure of the 9 0 ~ Ar + 10~o CH4 mixture was only 0.5 M P a A R I S T O V and BAZHENOVCbL (5 atm), which is enough to absorb the electrons 3.1. ActiviOpmeasurement and determination of the in the gas (see later). In order to reduce o~T-coe~ent by means of the slope method electron backscattering inside the counter a T h e source activity was determined by the part of the source holder which splits the counter 4,r(X, e) - - 7 coincidence method. T h e high into two half-cylinders was made of wire mesh. value of the conversion coefficient makes the The mesh-cathode counter has the same
Measurements of the total internal conversion coefficientand P KoJE probability in the decay of x3°Ce
dimensions but the solid cathode was replaced by wire mesh as well as all the source holder. Two scintillation counters with 51 X 76 m m NaI(TI) crystals were used as 7-ray detectors. In order to keep the total error of the instrumental correction for dead-times and accidental coinddences below 0.I ~o the sources with activity less than 104see -I were used. T h e dead-time error is equal to 4-40 nsec, the coincidence resolving time error is -4-10 nsec and the error of the delay between coincidence pulses is 4-50 nsec. With the solid-cathode counter the relative slope k, = 0.1998 4- 0.0004 was found from linear regression. T h e slope slightly decreases to k, -- 0.I 990 4- 0.0004 when the mesh-cathode counter was used. As the typical value of the variable s = (Ny -- N , ) / N , was about 0.75 the error of the decay scheme correction, expressed as s. ~,, was about 4-0.03 ~o. Using non-linear regression function in the following form
(NxN, - ~ ],
= No(1 + k# + a.sS),
(5)
I
I
the km= 0.2019 4- @004 and a = --0.0003 was found for the results from the solid cathode counter. T h e statistical test has shown that neither of the two functions can be preferred. But as there is a small decrease of the efficiency * z when the discrimination level is increased reaching 0.5 ~o for s equalling 6, the non-linear regression is preferred. T h e coefficient =l, equal to 0-249-4-0.006 was calculated from k~ = 0.2019 4-0.0004 using a calculated value for ep7 equalling 0.7 4- 0.2 ~o and estimating e 0 = (0.5 ± 0.5)8p. T h e total error of the a Tcoefficient (given at the 68 ~o confidence level) was calculated by adding the error Asps, Aeo and As, in quadrature. T h e error A~ results from the uncertainty in using either linear or non-linear regression. 3.2. Electron intensity measurements T h e electron intensities have been measured by means of the 4w proportional solid-cathode counter. A typical spectrum is given in Fig. I. In order to exclude the registration of Auger electrons and K-X-rays the discrimination level was shifted to 66 keV. Measured counting rates I
I
l
I
vents
ger e l e c t r o n s
%
26 keV
x .2
K-conversion 127 keV
line
o m L-conversion line- 1 6 0 keV
8 Discrimination I I I I
ZO
40
60 Chonnel
581
80
I00
120
140
16o
number
Fro. I. ISgCe--lagLaconversion electron spectrum taken with the 4~r pr~surized proportional counter.
582
J. Plch, J. Zderadigka and O. Dragoun
were corrected for the background, the dead time, the gamma-sensitivity of the counter and for the lost part of the conversion electron spectrum below the K-peak (discrimination correction). As can be seen from Fig. 2 the discrimination correction depends on the working pressure, but for pressures higher than 0.6 M P a (6 atm) the correction decreases slowly. As there is decrease of the resolution and considerable increase of the gamma-ray sensitivity for high pressures, most results were obtained with a pressure of 0.6 MPa. T h e discrimination correction was calculated for each source as "~40-80
KD = ~
(1
--~0)
(6)
where N4H0 is the area of the spectrum between the channeIs 40 and 80; N>, 0 is the a r e a o f t h e spectrum above channel 40; ~0is the probability of an electron-pulse being raised above the discrimination level due to internal summation with the radiations from the tilling of K-shell vacancies. T h e probability ~0 was determined from the efficiency of K-shell vacancy detection, calculated as ~ = w ~ x + (1 - - o K ) e A E = 0"28, (~°) and from the probability of the K-shell vacancy creation. T h e mean value of the discrimination correction was 3"62~o with a standard deviation for a single source of 10 4
I I - 2 6 keV
I
[
{
I
4-0.05 ~o and an estimated systematic error of
4-0.8%. T h e correction for the gamma-ray sensitivity of the proportional counter was calculated as 1
8p~
O~T
8E
Kg . . . .
,
where e E is the efficiency of the conversion electron registration, and 8pz is the gamma-ray sensitivity of the counter. T h e gas-part of the gamma-ray sensitivity was calculated equal to 0.7-4-0"2~o and the wall-part of the gamma-ray sensitivity was estimated to 0-08-b 0"04~o from U~QuH~a~T's results. (*x) T h e n the correction Kg reached the comparatively high value of 2.9 q- 0.8 Yo. 3.3. Gamma-ray intensity measurement The gamma-ray intensity was measured by means of a windowless 4-x scintillation counter with NaI(TI) crystals. (=~ A typical spectrum measured in this counter is given in Fig. 3. T h e counting rates in the peaks A, B, G a n d D can be expressed as N ~ = No[P,~x(l -- P x e x -- p,e~) + p K r x ( 1 - - p , s x ) ];
(8) (9)
N B = N O. p~. p ~ s x ~ N c = N o . pg. e~(1 -- p , s x ) ;
(10)
ND
(11)
[
- 1 2 7 keV
(7)
=
N O. p , . 8~ . p , s x ;
where O~.K
P, = PKc°~r;
•= ,o'
PK--
- =~ . o~K; I- +
1
[o ¢~ I0 2
i0
l 20
I 40
I 60
1 80
I ioo
l 120
I 140
Chonnel number
F x o . 2. a 8 9 C c - ~ S g L a c o n v e r s i o n electron spect r u m t a k e n w i t h t h e 4 ~r p r o p o r t i o n a l counter
at several pressures of 90% Ar + 10% CH~ mixture (1 at ---0-1 MPa).
1 + ~------~;
8x, 8~ are the absolute efficiency of the K - X - r a y and y-photon detection respectively. T h e gamma-ray intensity N e + N D = N o . Po • 8~ was measured by setting the discrimination level above the X + X-peak. T h e corrections for background, dead time and discrimination were applied. As the efficiency used, % = 0.96 4- 0"005 (m) is the total one, the correction for the discrimination is the correction for the cutting off the Compton spectrum below the X and X q- X peaks. T h e Compton to peak ratio
Measurements of the total internal aonversioncoeffg@ntand PKmK probabili@ in the decay of lseCe IOs
g
Ix I 3 4 k e y X-I-X j~ - 6 8 keV
I
I
583
I I~ I ?'-166 key , ¢ ~ - - T + X keV
I0 ~
'-'
~_. j+
,'t
,
,o,
_;
~!
l ,I " . t
,
'r-""~
', 60 ',
: 20i /I 40r
~t
,'s.+.,oo,
oo o,o.
spectrum
h
"
i
80
t
I00
120
i~t
i!t
140
160
Chonnel number
Fzo. 3. A a~9Ce X-ray and gamma-photon spectrum taken with the 4vr windowless schatillation counter. was determined cxperlmentally; X-rays were absorbed in the filter consisting of Cd and Cu sheets of several thicknesses. T h e spectra with different filters are given in Fig. 4. T h e results of the Compton to peak ratio measurements are summarized in T a b l e 1. A considerable decrease of the Compton to peak ratio in the 4-tr geometry with respect to 2rr geometry is caused by the fact that most scattered photons escaping
i°F 'o'LE
f
/
FI\
//
Cd 210/J.m+Cu 50 ~*'~p~ filter fO#v-
j~q/zm
,~
14
r'o+f
m-filter i
o
20
= ~ 40 60 80 Channel number
I00
Filter 210 pm 210 pm 120 pm 120 pm
Cd Cd Cd Cd
+ 200 pm Cu + 50 pm Cu + 50 pm Cu + 50 pm Cu
Detection Compton/ solid angle peak 4nr 4¢r 4~r 2¢r
0"025 0.024 0.024 0.041
from the front area are redetectcd in the opposite crystal and comcqucntly this compensation effectreduces the area of the Compton spectrum. W h e n this compensation effect was taken into account for the case when no filter was placed between the crystals,a Compton to peak ratio of (2 -4-0.4) % was deduced. This rcsuh was verifiedby reconstructing the Compton spectrum below the X and X + X peaks. W h e n the internal coincidences between X-rays and y-photons were taken into account, a spectrum given in Fig. 3 was obtained which successfully explained the dcvlations of the measured spectrum from the Gaussian shape of the peaks.
A
cdx
TAaLg 1. Results of the Compton to peak measurelent.
120
FIG. 4. A 1seCt g a m m a - p h o t o n s p e c t r u m t a k e n
with the ~ windowless scintillation counter; X-rays were absorbed in the Cu and Cd f~Iters.
3.4. Results of the ~T-coe~ent measurement I n total the activity, and the g a m m a and electron intensities of 11 sources were measured. T h e reproducibility of each method was good
584
J. Plch, J. Zderadi~ka and O. Dragoun
and the statistical errors did not contribute significantly to the total error; when aT was determined as Ng/~v the standard deviation of the mean was + 0"07%. Therefore the total error consists mainly of systematic errors of the applied corrections. Using the following systematic error A N o = -4-0.2%, AN~ = 1.13%, A N y = 4-0-64% and AN 0 = - 4 - 0 . 1 5 % the total errors given at the 68 % confidence level were calculated from equations (1-3). T h e final results obtained by the different methods are:
~ - - 0 . 2 5 1 -4-0.003 (4-1.3%); =T-- g/~,
au
"r
L2/L , L3/L = K/L
K/(M+_..)
I'IC
~
1"05
~
M,
_
1"0•
0"9~ 0 "90
E
M I ÷ 0 . 2 % E2
t.~c
~.
1"05
%.
I'00 0.9~
F-
Ng
=0.2504-0.004
(4-1.4%);
I.Jo-
-- I = 0.255 4- 0.008
(4-3.2 %) ;
~.oo- - - - ~
0tT (slope method) = 0.249 4- 0.006
(4-2.5 %).
I.o5
=T
= ~
.
MI .X=3.1
_
--
0"95 --
T h e weighed mean is equal to =T = 0.251 40.002 (4-0"8~'o). T h e present results support Taylor and Merritt's and Aristov and Bazhenov's values. 3.5. Comparison with theory T h e 165.853 keV transition in laSLa take place between the 5/2 + and 7/2 + levels. G~mEg et al. (9) measured precisely relative intensities of the L-subshell conversion electrons and determined the transition multipolarity to be M I + 0"2 -o.~+°'ao//o E2. In a recent compilation Om~zNwooDm adopted a pure M1 character for this transition. The relevant theoretical coefficients, 0~T = 0.264, ate: = 0.226, were obtained by polynomial interpolations (~a) from the tables. (~4.z5) There is a 5 % discrepancy between the experimental result of this work 0tT = 0.251 -40.002 and the total conversion coefficient for the M I multipolarity which cannot be explained by any E2 admixture. For an 165.853 keV E2 transition oc~,= 0.340 and 0cK = 0"251; these results were obtained from the tables (=4'=5) by interpolation.C=~) Taking our value of the ~ . and the intensity ratios ¢K/L a n d / K / ( M + . . . ) of G~m~g et al. c~) we derive the conversion coefficient g~- = 0.214 4- 0.002. Thus the above
0"90
--
FIo. 5. Comparison of theoretical and experimental conversion coefficients. discrepancy is due principally to the discrepancy in = x (see Fig. 5). In order to explain the discrepancy it was taken into account that the 166 keV transition is hindered and therefore its internal conversion can be influenced by the nuclear structure effect. In fact the experimental half-life Tz/z = 1.50 nsec (x) is 380 times longer than WEISSKOI'F'S theoretical estimation for M1 radiation. If it is assumed that the two lowest levels in Z39La are essentially pure shell model levels d5/2 and gT/z we see that this transition is 1-forbidden. For such cases, anomalies in the internal conversion process have been already observed. (~) The effect arises from the penetration of the atomic electrons within the converting nucleus. For magnetic multipoles and the particular subshell i the resulting conversion coefficient can be expressed in the following form
The static conversion coefficient ~0) and the dynamic correction coefficients bn, b~z depend on the electron wave functions only. For the subshells K through M5 the quantities a[0l and
Measureraents ~f th~ t~ta~ intsrna~ ~nversi~n ~el~knt ~nd P 1 ~ E pr~babi~i~y in ths ds~ay ~ f 1 a ~
b,1, b,, are tabulated in 0 a ' ~ respectively. Calculation of the nuclear parameter 2 requires knowledge of the nuclear wave functions. It can also be derived from the experiment (see e.g. m~ where the nuclear parameters were determined for a more complicated case of electric dipole conversion). T h e case g-----0 corresponds to the normal internal conversion process for unhindered transitions when the conversion coefficients are to a good approximarion independent of the nuclear structure. T h e b~l, b~s-coefficients were obtained by a double interpolation in Z and energy from the tables. ~ T h e value of the nuclear parameter g was derived from (12) using the experimental 0cx -- 0.214 q- 0.002 and the theoretical = ~ = 0.226. Assuming rather optimistically 1 ~o error in the theoretical coefficient 0 ~ ~ the two roots of (12) 2 = 3.1 -4- 0.7 and 2 -4- 226 -4- 3 were found. T h e smaller value is more justified from the physical point of view.
585
In Fig. 5 three theoretical predictions are compared with the experimental conversion coefficients. T h e upper part of the figure corresponds to the pure M l multipolarity without correction for the nuclear structure effect. T h e L-subshell ratios do not exclude a-small E2 admixture. Assuming 0"2 ~o E2 admixture the agreement for the L-subshell intensity ratios is improved (see middle part of Fig. 5), but the anomaly in the total and K-shell conversion coefficients remain unchanged. T h e lower part of the Fig. 5 refers to the pure M l character of the transition including the nuclear structure effect with the parameter 2 = 3.1. T h e agreement between the theory and the experiment is now observed, not only for the 0¢E-coefficient but also for the aT-coefficient and the Lsubshell intensity ratios. In progress are further calculations of the conversion coefficients for the transition energy equalling 165.853 keV without interpolations.
TABLE2. The Pg-probability measurements Author
PK
Pruett and Wgkinson (s)
0.83 ±0.04
Ketdle eta/. (v) (1956)
0.73 4-0.03
Stanford et aL In) (1960)
0.83 4-0.04
Marelius et al. (is) (1967)
0.68 4-0.02
(1954)
Aclamowicz et al. (14) (1968) 0.75 4-0.01
Schmidt-Ott eta/. (iS)
0.78 4-0.03
(1972) Vatai and Hochmuth (1°)
0,69 4-0-02
(1968) Campbell and McNelles (la) (1972)
0.705 +0"02
Weighted mean Mean Present work
0.7344-0.007 (4-0.9%) 0-75 4-0.02 (4-2.8%) 0.705 4-0-02
Method
Remark
Mag./~-spectrometry independent of wE and scintill, coincidence X + 7 + E - - 4 lr scintillation spectrometer with NaI(T1) independent of wE crystal coincident scintillation independent of wK (?) spectrometry Auger-conversion electron independent of oJE coincidence K-cony. electron-KX-ray independent of oJK coincidence L-cony. electron-KX-ray coincidence K-conv. electron-KX-ray independent of o~K coincidence X + 7 + E - - 4 ~rscintillation independent of ~ox spectrometer with CsI(T1) crystal X + y - 4 ~rscintillation pard 7 dependent on spectrometer with CsI(TI) oJE =0.92 4-0.01 crystals X + ? --4 ¢rscintillation spectrometer with NaI(T1) crystal
586
,1". Pl¢h, J. Zderadigka and O. Dragoun
4. P ~ o a ~ - P R O B A B I L I T Y UREMENT
MEAS-
T h e probability P x c o x can be deduced from the area of the peak D (denoted as Nz~) and the areas N~ + N o in the y,X-spectrum (see Fig. 3). From equations (10) and (11) P x c o x can be calculated as P~rc°lr = ( N ~ + N o ) e x "
(13)
T h e ratio N D / ( N D + ~ e ) was determined by fitting the Gaussian peaks by the iterative least-squares method. In the middle part of the spectrum, between the 85th and 140th channel, which is not influenced by secondary effects such as the photon backscatter and pile-up summing, the largest resid-al~ were less than 4-3a. T h e efficiency *x was calculated as *x
= (~=
-
E=). k + (eK# -- E#). (I - - k),
(14)
where *K~ = 0.985 4- 0"003 is the efficiency for the K~-X-ray detection in the 4qr counter; Csl~ 8KB = 0.987 4- 0.003 is similar effide,ncy for theK#-X-rays; czs~ E~ and E~ are the corrections for the iodine X-ray escape; k is the probability of the K~-X-ray emission. As the energy of the La X-rays is very near to the iodine absorption edge, the iodine X-ray escape from the single crystal is very high, reaching 0.40 4- 0.04 and 0.36 4- 0.004 respectively. ¢~'~ Thanks to the compensation effect of the opposite crystalt2a~ the corrections E, and E~ are equal to Ea = 0.40. (1 - - p . ) -- 6.8. l0 ~ , E# = 0.36. (1 - - p . ) = 6 . 1 . 1 0 -3, where p. is the probability of the iodine X-ray passing through the polyethylene foils. Thus ex 0.978.4- 0.005. The measurement of the probability P ~ o ~ : leads to the value PKw~: = 0.639 4- 0.006 (4-0.9 ~o). Using ~oK = 0.906 -4- 0"026, at) P~: = 0.705 4- 0.02 was obtained which is in agreement with CAMPBELLand McN~.LLES' result (ls) --(see Table 2). Using ~K = 0.214 4- 0.002, ~o~: = 0-906 4=
0.026an) and Pxo~ x = 0"639 + 0.006, the number of K-X-rays per disintegration has been calculated to be 0.794 -4- 0.009. T h e number of 166 keV photons per disintegration is 0.799 -40.001 from a~, = 0.251 + 0.002 and then the ratio K - X / g a m m a is 0.993 4- 0.01 which is in agreement with CAMPBELL and MCNELLSS' value 1.01 4- 0-025. aa~ AdmowledgementNThe authors are indebted to Mrs.
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