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Electron capture in Tl204
Nuclear Physics 55 (1964) 577--592; ( ~ North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or m i c r o f i l m without written permission from the publisher
E L E C T R O N C A P T U R E I N T!204 P. CHRISTMAS National Physical Laboratory, Teddington, Middlesex
Received 12 February 1964 Abstract: Electron capture in TIis4 was studied by observing X-rays emitted by the daughter nucleus Hgso*.Two similar NaI scintillation detectors were used, each of geometrical efficiencyclose to 50 %. From measurements of coincidences between K and L X-rays, the L/K capture ratio was determined to be 0.604-0.055, substantially higher than previously reported values. The K capture///- ratio was deduced from absolute counting of K X-rays and fl-particles; the value obtained was 0.01594-0.00036. From this value, and that obtained for the L/K ratio, the electron capture branching ratio was determined to be 0.02544-0.0012, again significantly higher than previous values. E
RADIOACTIVITY TIS°*;measured XK, XL, XKXL-Coin. Deduced
~K/~-,eL/SK, Q~-
[
I
1. Introduction ThaUium-204 decays by fl- emission (end-point energy 765 keV) to the ground state o f Pb 2°4 and by electron capture to the ground state of H g 2°4. Both transitions are first-forbidden unique and the electron capture events are some 2 % of the whole. The half-life 1) is 3.76 y. A precise value of the electron capture branching ratio is required for purposes of absolute standardization. This ratio m a y be deduced from measurements o f the K-eapture/fl- ratio and the ratio of L capture to K capture. Electron capture from shells with principal quantum number n > 2 will be neglected; it is a small effect compared to K or L capture 2) and did not contribute to the results o f the experiment to be described. The L / K ratio is o f particular interest because the experimental value can be compared with the predictions o f theory. Two measurements have been reported recently 3, 4) which are in good agreement with each other; the methods used were almost identical, each depending upon the incorporation o f T12°4 into a T1 activated N a I crystal. In the present work a different method has been used; the measurements and results are described in the next section.
2. L/K Capture Ratio 2.1. PRINCIPLE It will be supposed in the following that electron capture is the only decay mode. The K X-ray or K Auger transitions which follow K capture are predominantly transitions in which the vacancy in the K shell is transferred to the L shell; such events are accompanied by L X-rays or L Auger electrons. I f a sample of the nuclear species of interest is viewed simultaneously by two detectors, one sensitive to L X-rays only 577
578
P. CHRISTMAS
and the other sensitive only to K X-rays, then coincidences between the detectors may be observed. The single detector and coincidence count rates may be written as follows: N L = N O¢DLeL(0~-t-nKL),
NK = N o ~ e ~ ,
(1)
N C = NofO~KO~LeKeL,
where No is the K capture disintegration rate of the source, is the L/K capture ratio, C0K,L are the fluorescence yields of the K and L shells, eK, L are the detection efficiencies for the K and L X-rays, ~KL is the number of L shell vacancies produced by the filling of a K shell vacancy, and f is the probability of an L shell vacancy following the emission of a K X-ray. For high Z nuclei, NaI crystals may be used to detect both the K and L X-rays, suitable absorbers being used to prevent the dete~ion of those Auger electrons which emerge from the source. From eqs. (I), NL
(2)
The above equations are only approximate; nevertheless eq. (2) illustrates the principle of the present determination of ~, in which NL/Nc and e~ were measured and values off, coK and nKL were obtained from published data. Eqs. (1) and (2) require modification by reason of the subshell structure of the electron shells for n > 1. The differences between the L l, Ln and L m subshells require that a different fluorescence yield coL, be ascribed to each. Further, because absorbers must be used to stop the Auger electrons, and in the case of TI2°4 the/Irays also, and because the X-ray absorption coefficients are strongly energy dependent, L X-rays from the three subshells will be detected with different efficiencies. These efficiencies will be denoted eL, ; they do not include any effect of gating. Each L~ X-ray is complex. From the data of Compton and Allison s) the mean energies of the L i X-rays may be calculated for Z ~ 82; for Hg, Z --- 80, these energies are respectively 11.8, 12.2 and 10.3 keV for i = I, II and HI. With NaI a single broad L peak is observed. The K X-ray spectrum is also complex, but differential absorption is much less owing to the greater energy; in the present experiment there was no effect provided the gates were set wide enough to include the whole of the observed photopeak and escape peak. It is convenient to distinguish three processes which may depopulate the L shell. These are (i) capture of L electrons, (ii) capture of K electrons and (iii) capture of K electrons with the creation of vacancies in the Lax,
ELECTRON CAPTURE IN 1"1~'1
579
Inn subshells; process (iii) includes all events in which a K X-ray and an L X-ray are emitted simultaneously. For each of these processes, identified by x = 1, 2 or 3, respectively, there is a probability P~(L~) of creating a vacancy in the L~ subshell, and the observed yield of L X-rays is Sx = ~I Px(Lt)OgL,el.,, with
(3)
~ P ~ (L~) = I. I
Eq. (3) must be modified to allow for Coster-Kronig transitions ~), in which a vacancy in the L~ subshell is transferred to the Lj subshell, j > i, with the simultaneous emission of a low-energy Auger electron. Introducing the Coster-Kronig yields fLtL 1 defined by Wapstra et al. 7), eq. (3) becomes Sx = ~, Px (L~)q(Ll),
(4)
where q(~)
---- ('0LxeLi "~fLxLn O)LxxeLxxat- (fLiLm q-fLx LxlfLxxLm)f'OLHx,
q(LII)
= (])LII eLll "I-fLIILII I e L m ,
q(Lm) = (.OLzileLlxl, The evaluation of the S~ for T1~°4 is summarized in the appendix. One other, purely geometrical, effect must be considered, namely the probability p that a photon entering one counter may give rise to an iodine X-ray which is observed in the other counter. With the experimental arrangement described below, p ~ 6 Yo for the Hg K X-ray and a prominent iodine X-ray peak was found in the spectrum of each detector, see fig. 1. In the present experiment the K X-ray detector was gated to include the K photopeak and escape peak and the iodine peak also, and for the other detector a narrow window was set on the centre of the L X-ray peak. Under these conditions the observed count rates may be written NL = Nog[eSx +ngLS2--foJxex(1 +p)S3I,
Nx = NocoKeK(l +p),
(5)
Nc = N o g f w K e x ( 1 - P ) S 3 ,
where 9 is the fraction of the L peak accepted by the window. It is assumed that the etiiciencies of the two detectors are the same apart from gating. The negative terms in eqs. (5) represent the loss of L X-ray counts when the coincident K X-ray is also detected in the L counter, either directly or as in iodine X-ray from the other detector.
580
P, crmm'na~
F r o m eqs. (5),
= = fwKeK A~ {~CC(I--p)+ I +p} --nKLA2,
(6)
where
Ax = $2lS1 a n d ,4 2
$3/$1.
=
I n this instance b o t h A~ a n d A 2 c o u l d be written in t h e f o r m A = 1+6, where 6 was small c o m p a r e d with unity. I f Coster-K.ronJg transitions are neglected I
t
04 ~
w
iO a
I0=
~.
=
..
3:
_
~
o
~'
[
.
I0'* "
~o
i0 3
tO 2
0
I
.5O
I00 Cha Itnll
ISO
NwllbGr
Fig. 1. (a) Typical ungated spectrum from TI 2°4, showing X-ray peaks superimposed on the br©ms-
strahlung continuum, (b) bremsstrahlung spectrum obtained from Cls6 as described in the text, (c) Ti =°4 spectrum with bremsstrahlung subtracted.
ELECTRON CAPTURE IN T1204
581
and the further approximation made, that the q (L~) are the same for all values o f i, then both t51 and t~2 vanish and eq. (6) reduces to eq. (2), apart from the terms inp. 2.2. APPLICATION TO T1204 Measurement o f electron capture in T12°4 by the above method is complicated by the intense fl-decay branch. In the present work absorbers were used to prevent the fl-particles themselves from entering the detectors. However, the fl-decay process was still observed, as a photon continuum underlying the X-ray peaks. The continuum was due partly to internal bremsstrahlung and partly to external bremsstratdung produced in the absorbers. Even when a low Z material, beryllium, was used for the absorbers in order to minimize the external bremsstrahlung, the continuum was still significant, as shown in fig. 1, and a correction was necessary. The method of applying this correction is discussed in detail below. In outline, the TI 2°4 count rates were corrected by subtracting from them the suitably normalized count rates from a purely fl-emitting source whose bremsstrahhing spectrum was the same shape as that of TI 2°4. 2.3 APPARATUS The detectors comprised a pair of similar 7.6 can diameter, 1.3 cm thick NaI crystals, each sealed into a dural can with a 0.025 ~ n beryllium radiation window and a quartz optical window. The latter was coupled with silicone oil to a 7.6 cm photomultiplier tube. Crystal, photomultiplier and output cathode follower formed an integral unit. The counters were arranged face-to-face with their common axis horizontal and with a gap between them into which the sources could be inserted. At minimum separation the combined geometrical efficiency of the counters was about 94 ~o; larger separations allowed an absorber to be inserted between the source and each detector. Each absorber comprised a stack of six beryllium foils, total thickness 0.61 g/cm 2, sufficient to stop all the fl-partieles from TI 2°4. The counters were surrounded by 5 cm of lead lined on the inside with copper and aluminium. The phototubes were operated at about 1.3 kV. The detector output pulses were suitably amplified, the amplifier having a maximum gain of about 100 and employing R-C shaping to give output pulses of 3 #s duration and 0.5 #s rise time. Each amplifier fed a single-channel pulse-height analyser and the outputs from these fed a coincidence unit. The single-channel and coincidence outputs were counted on 1 MHz transistorized scalers. The deadtimes were about 5 #s for the single channels and 20 #s for coincidences. The coincidence resolving time was 0.36 #s. Spectra were measured on an R I D L 200-channel kicksorter. The latter could be gated in the coincidence mode with channel output pulses from the single-channel analysers or in the coinc~dcnce/anticoincidence modes with output pulses from the coincidence unit. Sources were prepared on 0.00064 cm Melinex film mounted on aluminium rings of internal diameter 7.0 cm, by evaporation to dryness of a weighed quantity of active solution followed by covering with a second Melinex film. For
582
P. CnPJSTMAS
counting, the sources were mounted in a recessed aluminium plate which located precisely between the counters with the centre of the source on the axis of the counters and the plane of the source at right angles to the axis. 2.4. C O R R E C T I O N F O R T H E B R E M S S T R A . H L U N G C O N T I N U U M
The manner of correcting for the bremsstrahlung contribution to the T12°4 X-ray spectra has already been outlined. The pure fl-cmitter used was commercially available Cl a6, whose decay is second-forbidden with half-life 3 • 105 y and end-point energy 714 keV. Despite the differences in fl-spectral shape, the fl-decay bremsstrahlung spectra of TI2°4 and Cla6 were expected to be similar by reason of the closeness of the end-point energies. Justification for the assumption made here that the two spectra are identical in shape was obtained from calculations based on the theory of Chang and Falkoff s) for internal bremsstrahlung and on the data of Rczanka et al. 9) for external bremsstrahlung. These calculations indicated that the internal effect would predominate for a low Z absorber, and this was confirmed experimentally, with a measured value of about 8 tel for the ratio of internal to external bremsstrahlung for beryllium. The correction of the counts rates from a given TIT M source using those from a given C136 source required a measurement of the ratio r of the bremsstrahiung intensities of the two sources. For a given TIT M source r was measured by storing the TI 2o4 spectrum in the first 100 channels of the kicksorter for a given time and then storing the C136 spectrum in the second 100 channels for such a time that the two bremsstrahlung spectra coincided when superimposed; r was equal to the ratio of the storage times. For greater accuracy the spectra were matched in the more intense region between the K and L X-ray peaks, rather than in the high energy tail; the iodine X-ray peak and some of the K, L X-rays were removed by gating the kicksorter in the anticoincidence mode with the output from the coincidence unit with the single channels accepting all pulses above noise. A correction for resolution was applied by using the difference in resolution of the two detectors. The observed T12°4 count rates NL, NK and Nc were corrected with the observed CIa6 rates N~, N~ and N~ according to Ncorrecte d
=
N--rN'.
The ratio r was measured for each TI2°4 source both before and after the determination of N L / N c. The chief error was due to difficulty in deciding precisely when a match had been obtained. From the scatter of the measured values the error in r was typically about 5 %, giving an error of 2 % in NL/Nc. 2.5. M E A S U R E M E N T O F NI./Nc
Thallium-204 was available as a standard solution of T12SO4 in 0.I N HNO3. The fl-activity was about 4.106 dps per g of solution and the solid content about 100 #g T12SO4 per g of solution. Sources were prepared from this solution as described above.
583
ELECTRON C A P T U R E I N TI le4 5.0
I
I
4.0
3~
0
25
50
75
IOO
Source Solid Contefl[
( ~g
TI2S04)
Fig. 2. Observed variation o f NL/NC with source solid content.
I
I
I
NL .2
N¢
! i
2S"" --T 23
--
21
--
T
N~
1
I
2S
SO
SOUrce Solid
I 7S
I00
Content
Fig. 3. Observed variation o f N c, Arc and N K with source solid content.
584
P. CHRISTMAS
From estimates o f the fl-efficiencies o f sources similar to those used here it was expected that source self-absorption of L X-rays would be small, of the order of 1%. To check this, and to correct for any effect, measurements were made on a series of sources with different amounts of carrier added to give solid contents between 4 and 80 #g T12SO4. Gating on the L X-ray peak was determined by the need to avoid counting noise on the low-energy side and iodine X-rays on the highenergy side, having regard to possible drifts in gain and/or gate settings, and by the desirability of minimizing the bremsstrahlung correction. To meet these requirements a rather narrow window, of efficiency g ~ 30 %, was set on the centre of the L peak. For the K X-ray detector the top level discriminator was set well above the K peak and the bottom level was set just above the L peak. To avoid possible systematic errors all sources were counted successively at several different settings of the K bottom level discriminator. For each source a plateau was obtained within the statistics and a mean value taken for NL/Nc. As an additional check against systematic errors the measurements were repeated with the amplifier inputs reversed, the remainder of the apparatus being unchanged. The results for NL/Nc were indistinguishable from those obtained previously. The L, K and coincidence count rates were typically 50, 1000 and 10 counts c/s respectively for a T1z°4 source and 6, 140 and 0.4 counts/s for the C136 source, with background rates of 0.1, 8.0 and 0.01 cotmts/s. Some 3 or 4 h counting were required to obtain a statistical error of 0.7 ~ on the mean value of NL/Nc for a given source. The results of the measurements of NL/Nc are shown in fig. 2, where NL/Nc increased uniformly with solid content, by about 12.5~ between the lightest and heaviest sources. This increase is attributed to a rise in the L X-ray intensity due to fluorescence excitation of thallium atoms by bremsstrahlung on the one hand, and to a drop in the coincidence rate due to increased self-absorption of electron capture L X-rays on the other. This interpretation accords with the observed variations with solid content of the individual count rates (fig. 3). It will be noted that NK was independent of solid content, as expected. A least-squares fit to the data of fig. 2 gave, for zero solid content NL __ 3.949+0.078.
Nc The fit is consistent with the errors, shown in the figure, which are a combination of counting statistics and the uncertainty in r. All other errors were negligible by comparison. 2.6. MEASUREMENT OF p The probability p was determined by coincidence counting with each detector gated to accept everything above the L X-ray peak. Under this condition it may be
ELECTRON CAPTURE IN T1z°t
585
shown that F2Ns - 1 PfLNc
1 -'
,
where Ns is the mean single channel count rate. Measurements were made on both the lightest and heaviest thallium sources, with several different settings o f the bottom level discriminators. The result was p = 0.060+0.0005. 2.7. EFFICIENCY TO Hg K X-RAYS The K X-ray efficiency of the detector configuration used for the thallium measurements was obtained from the efficiency calculated for the counters close together with the beryllium foils removed, these two efficiencies being related by measuring for each configuration the apparent 59.6 keV ~-ray activity o f an Am 241 source. 30000
I
I
30 ~,v I
I 60 k,v 1
Np L X-R, ~ 2OOOO
IOO00
: ,,," kJ /
I
SO
k. I
IOO Chonn¢I Number
ISO
200
Fig. 4. Typical spectrum from A m ~4xwith noise biassed out but otherwise u n i t e d . The dashed curve
shows the spectrum after subtraction of the L X-ray peak; it was obtained by using the coincidence spectrum (fig. 5), to determine the shape of the 30 keV peak. With the counters at minimum separation the simple geometry and symmetry of the detectors with respect to the source made possible a reliable estimate of the mean efficiency. The only absorbers present were the Melinex source films and the beryllium windows. The efficiency was calculated at a number of energies between 0 and 100 keV, using the absorption coefficients tabulated by Grodstein lo). Coherent scattering was excluded. Allowance was made for Compton scattering in both the absorbers and the NaI crystals; loss of efficiency from this effect was much reduced by the geometry, since scattered photons which failed to be detected by one counter
586
P. c H r J s r ~
stood a good chance of being detected by the other one. With a crystal separation of 0.45 cm the solid angle for each detector was 47.1 ~ and the mean efficiency at 50 keV was (46.9-t-0.4)~. The quoted error includes uncertainties in the absorption coefficients and in estimating the geometrical efficiency and the amount of absorber present. The Am T M was counted with both detectors gated to include everything above noise. Fig. 4 shows the spectrum obtained from either detector. The peak near 30 keV is due mainly to the 59.6 keV escape peak together with iodine X-rays from the other detector. The shape of this peak was established from the spectrum, shown in fig. 5, obtained with the kicksorter gated coincidence - wise with the output from 20 0 0 0
I
ao k ~ I
i
J~ U
i Ioooo
§
SO
iO0
Chonne! Number
Fig. 5. Spectrum obtained from Am=41with the kicksorter gated in the coincidence mode with the output from the coincidence unit and with each channel accepting all pulses above noise. The peak at 60 keV is not shown. the coincidence unit, the single-channel gating remaining unchanged; the 17 keV neptunium L X-ray peak could then be subtracted. F r o m the areas of the corrected spectra a mean count rate N~ was established for each detector. If the observed coincidence rate was Nc, and the 59.6 keV line only is considered, then 2 N ~ - N c = N~9 6es9 6,
where N59.6 was the true 59.6 keV activity of the source. Thus, in terms of the measurements for the two configurations, es9.6(with absorbers) esg.6(without absorbers)
--
( 2 N r - Nc)with absorbers
(7)
(2Ny-Nc)without absorbers"
A decay scheme correction of order I ~o was applied to eq. (7), using calculated efficiencies and the decay scheme data of Magnusson 11). The correction included contributions to the 30 keV peak from the 26.4 keV T-ray and from simultaneous arrivals of two L X-rays. The resolving time was sufficient to ensure that no coincidences were lost owing to the 60 ns lifetime of the 59.6 keV level.
ELECTRON CAPTURE IN Tl ~
587
The final value for the efficiency ratio, eq. (7), was 0.830±0.010. The efficiency at 60 keV for the "with absorbers" configuration was thus (38.9 ± 0.6)~o. Corrected to 72.5 keV this gave eK = (39.0±0.6)~o. 2.8. I M P U R I T I E S I N T H E B E R Y L L I U M A B S O R B E R S
Analysis of one of the beryllium foils showed the presence of several impurities, the most important being nickel (1 ~ ) and iron (0.3 ~). These impurities were sufficient to cause large changes in the efficiencies eL, and hence in the Sx; the resulting changes in Ax and A2 were of the order of a few per cent. Since the impurities were probably introduced during the manufacture of the foils, by rolling, it seemed reasonable to assume that they were present in all the foils in the same relative proportions, although the total quantity of impurity might vary from foil to foil. Using the relative proportions given by the analysis, values of Sx were calculated for various absolute amounts of impurity. A 1 and A2 were plotted against $3 and the values chosen which corresponded to the measured value of $3. This last was given by the ratio Nc/NK, with the gates set as for the determination of NL/Nc $3-
l ÷ p 1 1 Nc.
1 - p f g Ng' g was measured as the ratio of the areas of the gated and ungated spectra. The value obtained was $3 = 0.039±0.001. The values obtained for//1 and A2 were somewhat dependent upon the value used for the electron capture transition energy Q. The manner in which the final value for ce was arrived at is discussed in the next paragraph. 2.9. R E S U L T S
It has been assumed that electron capture is correctly described by the theory of Brysk and Rose 2). Applied to Tl 2°4, the theory gives the PI(LI) as functions of the transition energy Q, and from these $1 was calculated for various Q. From these values of $1 and the calculated values of $2 and $3, AI and//2 were obtained. These last, taken in eq. (6) with the measured values of NJNc, p and ex and the values of o~g, f and ngL given in the appendix, gave the experimental L/K ratio cc as a slowly varying function of Q. According to Brysk and Rose, the L/K capture ratio for a first-forbidden unique decay is strongly dependent upon Q. The theory gives cz-- q~' gL~ I - F - -
q~ g~
-- + -q~ g~i 9q~R2 ~gL~xJ ,
(8)
588
P. CHRISTMAS
where qK is the m o m e n t u m of the neutrino which accompanies capture from the K shell, similarly for the qL~. (In terms of the notation of Brysk and Rose q~ = W o + W~:, where Wo is the nuclear energy difference and WK is the total energy of the captured electron. With the more usual notation qK = Q - e K where Q is the transition energy and 8~ is the K shell binding energy). The quantity R is the nuclear radius and gK, L, fL are radial wave functions obtained from the graphs of Brysk and Rose. The second and third terms on the right-hand side of eq. (8) are the ones from which the PI (L~) were calculated. ~.
2.0
I
I
hO
I;xp¢rimentol
u 0.5
--
.J ThGoreticol
0.~200
3010
400
~
.
SO0
Fig. 6. L/K capture ratio for TI~4 as a function of the electron capture transition energy Q. The experimental and theoretical predictions for ~ as a function of Q are shown in fig. 6. The values obtained from the intersection of the two curves are = 0.60-t-0.055,
Q = (313_+iT 14)keV.
The total error quoted on • is __.9.2%; of this 5.1% is due to experimental errors, while the remainder derives from uncertainties in f , coK and nKL and in A1 and A2, as summarized in the appendix. The above value of a is to be compared with the values of 0.42-t-0.05 obtained by Joshi a) and 0.41 -t-0.03 obtained by Leutz and Ziegler 4). These results give higher o and .am+3o values for Q . . .a.~. + s 30 . . . 23 keV, respectively. (Leutz and Ziegler quoted a R 2) in eq. (8) value for Q of ~a~+3o 2 --r-r,u_ 2 4 keV, but their numerical value for (qL,I/qL, was too large by a factor of 2.) There have beert several determinations of Q from measurements on the end-point energy of the internal bremsstrahlung spectrum accompanying electron capture. These measurements are summarized in table 1. The present measurement of ~ favours the value of 335 keV, while the other measurements are in agreement with the higher values. In view of the discrepancy which appears to exist it would seem desirable to repeat the internal bremsstrahlung measurement. This measurement is a difficult one because the process of interest is o f
ELECTRON CAPTta~ IN T1~
589
second order and must be identified in the presence of the fl-decay branch; any contribution from the fl-deeay bremsstrahlung would increase the apparent value o f the end-point energy, and hence the value obtained for Q. TABLE 1 Q measurements
Q (keY)
Ref.
335
a*)
3764-20 3934- I0
xs) I~)
3. The K Capture/#- Ratio and Electron Capture Branch/rig Ratio The ratio of K capture to fl- emission was obtained from separate absolute determinations of the K X-ray activity and the fl- activity of a standard solution of TI 2°4 as TIe SO4 in 0.1 N H N O a . The X-ray measurements were made on the apparatus used for the L/K ratio, with the gates set as for the determination of p. Under these conditions the mean single counter rate Ns and the coincidence rate Arc were given by
Ns = Nocozez(1 +p), whence
Nc = 2No coz eKP, No-
(9)
2Ns-Ne 2¢-ozez
Measurements were made at several different settings o f the bottom level discriminator for each o f several sources. The efficiency e z was determined as already described. The K capture activity No was then calculated from eq. (9), using the value o f coK given in the appendix. Referred to the time o f the fl- measurements, the final mean value was No = 64.19+ 1.35 dps/mg. The quoted error derived about equally from uncertainties in the bremsstrahlung correction and in ez. The fl- activity was determined by the efficiency tracing technique 15). The measurements were made on a 47rfl-~ coincidence apparatus similar to that described by Campion 16). The tracer employed was 36 h Br a2, in the form of a solution of T1Br. A number of sources o f different solid content were prepared, each containing a known amount of the Tl 2°4 solution together with a suitable quantity of Br a2. The number of B r - ions was in every case much greater than the number of SO~ ions. The fl efficiency of each source was measured with respect to the Br a2. The sources were stored for two weeks, after which time the residual Br a2 activity was negligible,
590
P. CHRISTMAS
and were finally 4 ~ counted to obtain their apparent TI T M activities. These activities were plotted against the corresponding etTiciencies and the true activity obtained by extrapolating to 100~ efficiency a least-squares fit to the data, as shown in fig. 7. Tli~ final value on the reference date was
N#
3500
= (4.032+0.021). 103 dps/mg.
--
0
5ooo
IO0
I
90
I
(10
O
-/0
60
¢1'~,for BI'll;e (°/o/)
Fig. 7. Determination of TP °4/~- activity by the tracer method, see text. The experimental errors are too small to be shown.
Corrections were applied for the sensitivity of the // counter to electron capture events and for the Br 8z decay scheme. The quoted error reflects the scatter of the individual measurements (fig. 7); this scatter is attributed to incomplete mixing of the activities on the sources. From the above measurements the K c a p t u r e / p - ratio was determined K capture _ 0.0159 +0.00036. From the measured values of the L/K ratio and the K capture///- ratio the branching ratio was calculated E.C. --- 0.0254+0.0012. Leutz and Ziegler 4) gave a value for E.C.//~- of 0.0215+0.0005, while the results of Joshi 3) yield 0.0220, error unknown. I am indebted to Dr. P. J. Campion both for suggesting the experiment and for his interest and advice at all times, and to Mr. A. Williams for many useful discussions. I am also grateful to DSIR for the award of a Senior Research Fellowship. This work has been carried out as part of the research programme of the National Physical Laboratory and is published by permission of the Director of the Laboratory.
Eta~CTRONCAFYURBIN 31))t
591
Aplmadix Unless otherwise stated, the numerical values and errors given below have been taken from ref. 7). CALCULATION OF .41 AND .41 In evaluating the quantities S. the following values were used for the L fluorescence yields: t0L, = 0.087, t0t~x = 0.42, 0~t~,1 = 0.30. NO errors were given in ref. 7), a possible error of + 10 ~o has been ascribed to each value, giving 4- 4.1 ~o in ~t. The values taken for the Coster-Kronig yields were ft~t~1 = 0.12,
fL,Lm = 0.68,
ft~,Lm = 0.00.
Again, no errors were given; it has been assumed that frzL,~ and fr~L=, are each subject to an error o f 4-10~o, giving an error o f +4.6~/o in ~t. Values o f the PI(Li) were calculated from Brysk and Rose 2) as described in the text. The following values were taken for the P2(Lt) and P3(Li): P2(h)
= 0,
P2(LI~) = 0.355--+0.0042, P2(L..) = 1 - e 2 ( L ~ ) ,
with corresponding error -+ 0.9 Yo in a, Pa(L~) = 0.037_+0.012, P3(Ln) = 0.354-+0.012, Pa(Lm) = 0.6104-0.012, with corresponding error 4-3.5~/o in a. VALUES FOR f, toL AND nKL The following values were used: f=
0.777_+0.014,
tot = 0.954-+0.005;
nKL was calculated from the equation nXL = fOX + (1 -- tox)Ax, where =
A~
,
LL+KLY
\KLL + ~ Y / "
592
1).
The partial A u g e r yields K L L , K L Y a n d K X Y were o b t a i n e d f r o m ref. 7). A t was calculated to be 1.55+_0.037, giving a value of 0.813 for nra.. The latter is consistent with the value o f 0.82 o b t a i n e d f r o m the s u m o f the Pa(L~) before n o r m a l i z a t i o n . The error i n ~ due to the uncertainties i n f , oJx a n d A K was +_2.7%. T h e total error i n ~ was o b t a i n e d b y a d d i n g the i n d i v i d u a l errors i n q u a d r a t u r e .
References 1) Nuclear Data Sheets (National Academy of Science, National Research Council, Washington, D.C., 1962) 2) H. Brysk and M. E. Rose, ORNL 1830 (1955) 3) B. R. Joshi, Prec. Phys. Soc 77 (1961) 1205 4) H. Leutz and K. Ziegler, Z. Phys. 166 (1962) 582 5) A. H. Compton and S. K. Allison, X-rays in theory and experiment (D, Van Nostrand Co., New York, 1935) 6) Coster and Kronig, Physica 2 (1935) 13 7) A. H. Wapstra, G. J. Nijgh and R. van Lieshout, Nuclear spectroscopy tables (North-Holland Publ. Co., Amsterdam, 1959) 8) C. S. Wang Chang and D. L. Falkoff, Phys. Rev. 76 (1949) 365 9) I. Rezanka, J. Frana and J. Adam, Czech. J. Phys. 12 (1962) 101 10) G. W. Grodstein, N.B.S. Circular 583 (1957) and supplement 11) L. B. Magnusson, Phys. Rev. 107 (1957) 161 12) E. der Mateosian and A. Smith, Phys. Rev. 88 (1952) 1186 13) R. G. Jung and M. L. Pool, Bull. Am. Phys. Soc. 1 (1956) 172 14) M. H. Biavati, S. J. Nassif and C. S. Wu, Phys. Rev. 125 (1962) 1364 15) P. J. Campion, J. G. V. Taylor and J. S. Merritt, Int. J. Appl. Rad. Isotopes 8 0960) 8 16) P. J. Campion, Int. J. Appl. Rad. Isotopes 4 (1959) 232
E L E C T R O N C A P T U R E I N T!204 P. CHRISTMAS National Physical Laboratory, Teddington, Middlesex
Received 12 February 1964 Abstract: Electron capture in TIis4 was studied by observing X-rays emitted by the daughter nucleus Hgso*.Two similar NaI scintillation detectors were used, each of geometrical efficiencyclose to 50 %. From measurements of coincidences between K and L X-rays, the L/K capture ratio was determined to be 0.604-0.055, substantially higher than previously reported values. The K capture///- ratio was deduced from absolute counting of K X-rays and fl-particles; the value obtained was 0.01594-0.00036. From this value, and that obtained for the L/K ratio, the electron capture branching ratio was determined to be 0.02544-0.0012, again significantly higher than previous values. E
RADIOACTIVITY TIS°*;measured XK, XL, XKXL-Coin. Deduced
~K/~-,eL/SK, Q~-
[
I
1. Introduction ThaUium-204 decays by fl- emission (end-point energy 765 keV) to the ground state o f Pb 2°4 and by electron capture to the ground state of H g 2°4. Both transitions are first-forbidden unique and the electron capture events are some 2 % of the whole. The half-life 1) is 3.76 y. A precise value of the electron capture branching ratio is required for purposes of absolute standardization. This ratio m a y be deduced from measurements o f the K-eapture/fl- ratio and the ratio of L capture to K capture. Electron capture from shells with principal quantum number n > 2 will be neglected; it is a small effect compared to K or L capture 2) and did not contribute to the results o f the experiment to be described. The L / K ratio is o f particular interest because the experimental value can be compared with the predictions o f theory. Two measurements have been reported recently 3, 4) which are in good agreement with each other; the methods used were almost identical, each depending upon the incorporation o f T12°4 into a T1 activated N a I crystal. In the present work a different method has been used; the measurements and results are described in the next section.
2. L/K Capture Ratio 2.1. PRINCIPLE It will be supposed in the following that electron capture is the only decay mode. The K X-ray or K Auger transitions which follow K capture are predominantly transitions in which the vacancy in the K shell is transferred to the L shell; such events are accompanied by L X-rays or L Auger electrons. I f a sample of the nuclear species of interest is viewed simultaneously by two detectors, one sensitive to L X-rays only 577
578
P. CHRISTMAS
and the other sensitive only to K X-rays, then coincidences between the detectors may be observed. The single detector and coincidence count rates may be written as follows: N L = N O¢DLeL(0~-t-nKL),
NK = N o ~ e ~ ,
(1)
N C = NofO~KO~LeKeL,
where No is the K capture disintegration rate of the source, is the L/K capture ratio, C0K,L are the fluorescence yields of the K and L shells, eK, L are the detection efficiencies for the K and L X-rays, ~KL is the number of L shell vacancies produced by the filling of a K shell vacancy, and f is the probability of an L shell vacancy following the emission of a K X-ray. For high Z nuclei, NaI crystals may be used to detect both the K and L X-rays, suitable absorbers being used to prevent the dete~ion of those Auger electrons which emerge from the source. From eqs. (I), NL
(2)
The above equations are only approximate; nevertheless eq. (2) illustrates the principle of the present determination of ~, in which NL/Nc and e~ were measured and values off, coK and nKL were obtained from published data. Eqs. (1) and (2) require modification by reason of the subshell structure of the electron shells for n > 1. The differences between the L l, Ln and L m subshells require that a different fluorescence yield coL, be ascribed to each. Further, because absorbers must be used to stop the Auger electrons, and in the case of TI2°4 the/Irays also, and because the X-ray absorption coefficients are strongly energy dependent, L X-rays from the three subshells will be detected with different efficiencies. These efficiencies will be denoted eL, ; they do not include any effect of gating. Each L~ X-ray is complex. From the data of Compton and Allison s) the mean energies of the L i X-rays may be calculated for Z ~ 82; for Hg, Z --- 80, these energies are respectively 11.8, 12.2 and 10.3 keV for i = I, II and HI. With NaI a single broad L peak is observed. The K X-ray spectrum is also complex, but differential absorption is much less owing to the greater energy; in the present experiment there was no effect provided the gates were set wide enough to include the whole of the observed photopeak and escape peak. It is convenient to distinguish three processes which may depopulate the L shell. These are (i) capture of L electrons, (ii) capture of K electrons and (iii) capture of K electrons with the creation of vacancies in the Lax,
ELECTRON CAPTURE IN 1"1~'1
579
Inn subshells; process (iii) includes all events in which a K X-ray and an L X-ray are emitted simultaneously. For each of these processes, identified by x = 1, 2 or 3, respectively, there is a probability P~(L~) of creating a vacancy in the L~ subshell, and the observed yield of L X-rays is Sx = ~I Px(Lt)OgL,el.,, with
(3)
~ P ~ (L~) = I. I
Eq. (3) must be modified to allow for Coster-Kronig transitions ~), in which a vacancy in the L~ subshell is transferred to the Lj subshell, j > i, with the simultaneous emission of a low-energy Auger electron. Introducing the Coster-Kronig yields fLtL 1 defined by Wapstra et al. 7), eq. (3) becomes Sx = ~, Px (L~)q(Ll),
(4)
where q(~)
---- ('0LxeLi "~fLxLn O)LxxeLxxat- (fLiLm q-fLx LxlfLxxLm)f'OLHx,
q(LII)
= (])LII eLll "I-fLIILII I e L m ,
q(Lm) = (.OLzileLlxl, The evaluation of the S~ for T1~°4 is summarized in the appendix. One other, purely geometrical, effect must be considered, namely the probability p that a photon entering one counter may give rise to an iodine X-ray which is observed in the other counter. With the experimental arrangement described below, p ~ 6 Yo for the Hg K X-ray and a prominent iodine X-ray peak was found in the spectrum of each detector, see fig. 1. In the present experiment the K X-ray detector was gated to include the K photopeak and escape peak and the iodine peak also, and for the other detector a narrow window was set on the centre of the L X-ray peak. Under these conditions the observed count rates may be written NL = Nog[eSx +ngLS2--foJxex(1 +p)S3I,
Nx = NocoKeK(l +p),
(5)
Nc = N o g f w K e x ( 1 - P ) S 3 ,
where 9 is the fraction of the L peak accepted by the window. It is assumed that the etiiciencies of the two detectors are the same apart from gating. The negative terms in eqs. (5) represent the loss of L X-ray counts when the coincident K X-ray is also detected in the L counter, either directly or as in iodine X-ray from the other detector.
580
P, crmm'na~
F r o m eqs. (5),
= = fwKeK A~ {~CC(I--p)+ I +p} --nKLA2,
(6)
where
Ax = $2lS1 a n d ,4 2
$3/$1.
=
I n this instance b o t h A~ a n d A 2 c o u l d be written in t h e f o r m A = 1+6, where 6 was small c o m p a r e d with unity. I f Coster-K.ronJg transitions are neglected I
t
04 ~
w
iO a
I0=
~.
=
..
3:
_
~
o
~'
[
.
I0'* "
~o
i0 3
tO 2
0
I
.5O
I00 Cha Itnll
ISO
NwllbGr
Fig. 1. (a) Typical ungated spectrum from TI 2°4, showing X-ray peaks superimposed on the br©ms-
strahlung continuum, (b) bremsstrahlung spectrum obtained from Cls6 as described in the text, (c) Ti =°4 spectrum with bremsstrahlung subtracted.
ELECTRON CAPTURE IN T1204
581
and the further approximation made, that the q (L~) are the same for all values o f i, then both t51 and t~2 vanish and eq. (6) reduces to eq. (2), apart from the terms inp. 2.2. APPLICATION TO T1204 Measurement o f electron capture in T12°4 by the above method is complicated by the intense fl-decay branch. In the present work absorbers were used to prevent the fl-particles themselves from entering the detectors. However, the fl-decay process was still observed, as a photon continuum underlying the X-ray peaks. The continuum was due partly to internal bremsstrahlung and partly to external bremsstratdung produced in the absorbers. Even when a low Z material, beryllium, was used for the absorbers in order to minimize the external bremsstrahlung, the continuum was still significant, as shown in fig. 1, and a correction was necessary. The method of applying this correction is discussed in detail below. In outline, the TI 2°4 count rates were corrected by subtracting from them the suitably normalized count rates from a purely fl-emitting source whose bremsstrahhing spectrum was the same shape as that of TI 2°4. 2.3 APPARATUS The detectors comprised a pair of similar 7.6 can diameter, 1.3 cm thick NaI crystals, each sealed into a dural can with a 0.025 ~ n beryllium radiation window and a quartz optical window. The latter was coupled with silicone oil to a 7.6 cm photomultiplier tube. Crystal, photomultiplier and output cathode follower formed an integral unit. The counters were arranged face-to-face with their common axis horizontal and with a gap between them into which the sources could be inserted. At minimum separation the combined geometrical efficiency of the counters was about 94 ~o; larger separations allowed an absorber to be inserted between the source and each detector. Each absorber comprised a stack of six beryllium foils, total thickness 0.61 g/cm 2, sufficient to stop all the fl-partieles from TI 2°4. The counters were surrounded by 5 cm of lead lined on the inside with copper and aluminium. The phototubes were operated at about 1.3 kV. The detector output pulses were suitably amplified, the amplifier having a maximum gain of about 100 and employing R-C shaping to give output pulses of 3 #s duration and 0.5 #s rise time. Each amplifier fed a single-channel pulse-height analyser and the outputs from these fed a coincidence unit. The single-channel and coincidence outputs were counted on 1 MHz transistorized scalers. The deadtimes were about 5 #s for the single channels and 20 #s for coincidences. The coincidence resolving time was 0.36 #s. Spectra were measured on an R I D L 200-channel kicksorter. The latter could be gated in the coincidence mode with channel output pulses from the single-channel analysers or in the coinc~dcnce/anticoincidence modes with output pulses from the coincidence unit. Sources were prepared on 0.00064 cm Melinex film mounted on aluminium rings of internal diameter 7.0 cm, by evaporation to dryness of a weighed quantity of active solution followed by covering with a second Melinex film. For
582
P. CnPJSTMAS
counting, the sources were mounted in a recessed aluminium plate which located precisely between the counters with the centre of the source on the axis of the counters and the plane of the source at right angles to the axis. 2.4. C O R R E C T I O N F O R T H E B R E M S S T R A . H L U N G C O N T I N U U M
The manner of correcting for the bremsstrahlung contribution to the T12°4 X-ray spectra has already been outlined. The pure fl-cmitter used was commercially available Cl a6, whose decay is second-forbidden with half-life 3 • 105 y and end-point energy 714 keV. Despite the differences in fl-spectral shape, the fl-decay bremsstrahlung spectra of TI2°4 and Cla6 were expected to be similar by reason of the closeness of the end-point energies. Justification for the assumption made here that the two spectra are identical in shape was obtained from calculations based on the theory of Chang and Falkoff s) for internal bremsstrahlung and on the data of Rczanka et al. 9) for external bremsstrahlung. These calculations indicated that the internal effect would predominate for a low Z absorber, and this was confirmed experimentally, with a measured value of about 8 tel for the ratio of internal to external bremsstrahlung for beryllium. The correction of the counts rates from a given TIT M source using those from a given C136 source required a measurement of the ratio r of the bremsstrahiung intensities of the two sources. For a given TIT M source r was measured by storing the TI 2o4 spectrum in the first 100 channels of the kicksorter for a given time and then storing the C136 spectrum in the second 100 channels for such a time that the two bremsstrahlung spectra coincided when superimposed; r was equal to the ratio of the storage times. For greater accuracy the spectra were matched in the more intense region between the K and L X-ray peaks, rather than in the high energy tail; the iodine X-ray peak and some of the K, L X-rays were removed by gating the kicksorter in the anticoincidence mode with the output from the coincidence unit with the single channels accepting all pulses above noise. A correction for resolution was applied by using the difference in resolution of the two detectors. The observed T12°4 count rates NL, NK and Nc were corrected with the observed CIa6 rates N~, N~ and N~ according to Ncorrecte d
=
N--rN'.
The ratio r was measured for each TI2°4 source both before and after the determination of N L / N c. The chief error was due to difficulty in deciding precisely when a match had been obtained. From the scatter of the measured values the error in r was typically about 5 %, giving an error of 2 % in NL/Nc. 2.5. M E A S U R E M E N T O F NI./Nc
Thallium-204 was available as a standard solution of T12SO4 in 0.I N HNO3. The fl-activity was about 4.106 dps per g of solution and the solid content about 100 #g T12SO4 per g of solution. Sources were prepared from this solution as described above.
583
ELECTRON C A P T U R E I N TI le4 5.0
I
I
4.0
3~
0
25
50
75
IOO
Source Solid Contefl[
( ~g
TI2S04)
Fig. 2. Observed variation o f NL/NC with source solid content.
I
I
I
NL .2
N¢
! i
2S"" --T 23
--
21
--
T
N~
1
I
2S
SO
SOUrce Solid
I 7S
I00
Content
Fig. 3. Observed variation o f N c, Arc and N K with source solid content.
584
P. CHRISTMAS
From estimates o f the fl-efficiencies o f sources similar to those used here it was expected that source self-absorption of L X-rays would be small, of the order of 1%. To check this, and to correct for any effect, measurements were made on a series of sources with different amounts of carrier added to give solid contents between 4 and 80 #g T12SO4. Gating on the L X-ray peak was determined by the need to avoid counting noise on the low-energy side and iodine X-rays on the highenergy side, having regard to possible drifts in gain and/or gate settings, and by the desirability of minimizing the bremsstrahlung correction. To meet these requirements a rather narrow window, of efficiency g ~ 30 %, was set on the centre of the L peak. For the K X-ray detector the top level discriminator was set well above the K peak and the bottom level was set just above the L peak. To avoid possible systematic errors all sources were counted successively at several different settings of the K bottom level discriminator. For each source a plateau was obtained within the statistics and a mean value taken for NL/Nc. As an additional check against systematic errors the measurements were repeated with the amplifier inputs reversed, the remainder of the apparatus being unchanged. The results for NL/Nc were indistinguishable from those obtained previously. The L, K and coincidence count rates were typically 50, 1000 and 10 counts c/s respectively for a T1z°4 source and 6, 140 and 0.4 counts/s for the C136 source, with background rates of 0.1, 8.0 and 0.01 cotmts/s. Some 3 or 4 h counting were required to obtain a statistical error of 0.7 ~ on the mean value of NL/Nc for a given source. The results of the measurements of NL/Nc are shown in fig. 2, where NL/Nc increased uniformly with solid content, by about 12.5~ between the lightest and heaviest sources. This increase is attributed to a rise in the L X-ray intensity due to fluorescence excitation of thallium atoms by bremsstrahlung on the one hand, and to a drop in the coincidence rate due to increased self-absorption of electron capture L X-rays on the other. This interpretation accords with the observed variations with solid content of the individual count rates (fig. 3). It will be noted that NK was independent of solid content, as expected. A least-squares fit to the data of fig. 2 gave, for zero solid content NL __ 3.949+0.078.
Nc The fit is consistent with the errors, shown in the figure, which are a combination of counting statistics and the uncertainty in r. All other errors were negligible by comparison. 2.6. MEASUREMENT OF p The probability p was determined by coincidence counting with each detector gated to accept everything above the L X-ray peak. Under this condition it may be
ELECTRON CAPTURE IN T1z°t
585
shown that F2Ns - 1 PfLNc
1 -'
,
where Ns is the mean single channel count rate. Measurements were made on both the lightest and heaviest thallium sources, with several different settings o f the bottom level discriminators. The result was p = 0.060+0.0005. 2.7. EFFICIENCY TO Hg K X-RAYS The K X-ray efficiency of the detector configuration used for the thallium measurements was obtained from the efficiency calculated for the counters close together with the beryllium foils removed, these two efficiencies being related by measuring for each configuration the apparent 59.6 keV ~-ray activity o f an Am 241 source. 30000
I
I
30 ~,v I
I 60 k,v 1
Np L X-R, ~ 2OOOO
IOO00
: ,,," kJ /
I
SO
k. I
IOO Chonn¢I Number
ISO
200
Fig. 4. Typical spectrum from A m ~4xwith noise biassed out but otherwise u n i t e d . The dashed curve
shows the spectrum after subtraction of the L X-ray peak; it was obtained by using the coincidence spectrum (fig. 5), to determine the shape of the 30 keV peak. With the counters at minimum separation the simple geometry and symmetry of the detectors with respect to the source made possible a reliable estimate of the mean efficiency. The only absorbers present were the Melinex source films and the beryllium windows. The efficiency was calculated at a number of energies between 0 and 100 keV, using the absorption coefficients tabulated by Grodstein lo). Coherent scattering was excluded. Allowance was made for Compton scattering in both the absorbers and the NaI crystals; loss of efficiency from this effect was much reduced by the geometry, since scattered photons which failed to be detected by one counter
586
P. c H r J s r ~
stood a good chance of being detected by the other one. With a crystal separation of 0.45 cm the solid angle for each detector was 47.1 ~ and the mean efficiency at 50 keV was (46.9-t-0.4)~. The quoted error includes uncertainties in the absorption coefficients and in estimating the geometrical efficiency and the amount of absorber present. The Am T M was counted with both detectors gated to include everything above noise. Fig. 4 shows the spectrum obtained from either detector. The peak near 30 keV is due mainly to the 59.6 keV escape peak together with iodine X-rays from the other detector. The shape of this peak was established from the spectrum, shown in fig. 5, obtained with the kicksorter gated coincidence - wise with the output from 20 0 0 0
I
ao k ~ I
i
J~ U
i Ioooo
§
SO
iO0
Chonne! Number
Fig. 5. Spectrum obtained from Am=41with the kicksorter gated in the coincidence mode with the output from the coincidence unit and with each channel accepting all pulses above noise. The peak at 60 keV is not shown. the coincidence unit, the single-channel gating remaining unchanged; the 17 keV neptunium L X-ray peak could then be subtracted. F r o m the areas of the corrected spectra a mean count rate N~ was established for each detector. If the observed coincidence rate was Nc, and the 59.6 keV line only is considered, then 2 N ~ - N c = N~9 6es9 6,
where N59.6 was the true 59.6 keV activity of the source. Thus, in terms of the measurements for the two configurations, es9.6(with absorbers) esg.6(without absorbers)
--
( 2 N r - Nc)with absorbers
(7)
(2Ny-Nc)without absorbers"
A decay scheme correction of order I ~o was applied to eq. (7), using calculated efficiencies and the decay scheme data of Magnusson 11). The correction included contributions to the 30 keV peak from the 26.4 keV T-ray and from simultaneous arrivals of two L X-rays. The resolving time was sufficient to ensure that no coincidences were lost owing to the 60 ns lifetime of the 59.6 keV level.
ELECTRON CAPTURE IN Tl ~
587
The final value for the efficiency ratio, eq. (7), was 0.830±0.010. The efficiency at 60 keV for the "with absorbers" configuration was thus (38.9 ± 0.6)~o. Corrected to 72.5 keV this gave eK = (39.0±0.6)~o. 2.8. I M P U R I T I E S I N T H E B E R Y L L I U M A B S O R B E R S
Analysis of one of the beryllium foils showed the presence of several impurities, the most important being nickel (1 ~ ) and iron (0.3 ~). These impurities were sufficient to cause large changes in the efficiencies eL, and hence in the Sx; the resulting changes in Ax and A2 were of the order of a few per cent. Since the impurities were probably introduced during the manufacture of the foils, by rolling, it seemed reasonable to assume that they were present in all the foils in the same relative proportions, although the total quantity of impurity might vary from foil to foil. Using the relative proportions given by the analysis, values of Sx were calculated for various absolute amounts of impurity. A 1 and A2 were plotted against $3 and the values chosen which corresponded to the measured value of $3. This last was given by the ratio Nc/NK, with the gates set as for the determination of NL/Nc $3-
l ÷ p 1 1 Nc.
1 - p f g Ng' g was measured as the ratio of the areas of the gated and ungated spectra. The value obtained was $3 = 0.039±0.001. The values obtained for//1 and A2 were somewhat dependent upon the value used for the electron capture transition energy Q. The manner in which the final value for ce was arrived at is discussed in the next paragraph. 2.9. R E S U L T S
It has been assumed that electron capture is correctly described by the theory of Brysk and Rose 2). Applied to Tl 2°4, the theory gives the PI(LI) as functions of the transition energy Q, and from these $1 was calculated for various Q. From these values of $1 and the calculated values of $2 and $3, AI and//2 were obtained. These last, taken in eq. (6) with the measured values of NJNc, p and ex and the values of o~g, f and ngL given in the appendix, gave the experimental L/K ratio cc as a slowly varying function of Q. According to Brysk and Rose, the L/K capture ratio for a first-forbidden unique decay is strongly dependent upon Q. The theory gives cz-- q~' gL~ I - F - -
q~ g~
-- + -q~ g~i 9q~R2 ~gL~xJ ,
(8)
588
P. CHRISTMAS
where qK is the m o m e n t u m of the neutrino which accompanies capture from the K shell, similarly for the qL~. (In terms of the notation of Brysk and Rose q~ = W o + W~:, where Wo is the nuclear energy difference and WK is the total energy of the captured electron. With the more usual notation qK = Q - e K where Q is the transition energy and 8~ is the K shell binding energy). The quantity R is the nuclear radius and gK, L, fL are radial wave functions obtained from the graphs of Brysk and Rose. The second and third terms on the right-hand side of eq. (8) are the ones from which the PI (L~) were calculated. ~.
2.0
I
I
hO
I;xp¢rimentol
u 0.5
--
.J ThGoreticol
0.~200
3010
400
~
.
SO0
Fig. 6. L/K capture ratio for TI~4 as a function of the electron capture transition energy Q. The experimental and theoretical predictions for ~ as a function of Q are shown in fig. 6. The values obtained from the intersection of the two curves are = 0.60-t-0.055,
Q = (313_+iT 14)keV.
The total error quoted on • is __.9.2%; of this 5.1% is due to experimental errors, while the remainder derives from uncertainties in f , coK and nKL and in A1 and A2, as summarized in the appendix. The above value of a is to be compared with the values of 0.42-t-0.05 obtained by Joshi a) and 0.41 -t-0.03 obtained by Leutz and Ziegler 4). These results give higher o and .am+3o values for Q . . .a.~. + s 30 . . . 23 keV, respectively. (Leutz and Ziegler quoted a R 2) in eq. (8) value for Q of ~a~+3o 2 --r-r,u_ 2 4 keV, but their numerical value for (qL,I/qL, was too large by a factor of 2.) There have beert several determinations of Q from measurements on the end-point energy of the internal bremsstrahlung spectrum accompanying electron capture. These measurements are summarized in table 1. The present measurement of ~ favours the value of 335 keV, while the other measurements are in agreement with the higher values. In view of the discrepancy which appears to exist it would seem desirable to repeat the internal bremsstrahlung measurement. This measurement is a difficult one because the process of interest is o f
ELECTRON CAPTta~ IN T1~
589
second order and must be identified in the presence of the fl-decay branch; any contribution from the fl-deeay bremsstrahlung would increase the apparent value o f the end-point energy, and hence the value obtained for Q. TABLE 1 Q measurements
Q (keY)
Ref.
335
a*)
3764-20 3934- I0
xs) I~)
3. The K Capture/#- Ratio and Electron Capture Branch/rig Ratio The ratio of K capture to fl- emission was obtained from separate absolute determinations of the K X-ray activity and the fl- activity of a standard solution of TI 2°4 as TIe SO4 in 0.1 N H N O a . The X-ray measurements were made on the apparatus used for the L/K ratio, with the gates set as for the determination of p. Under these conditions the mean single counter rate Ns and the coincidence rate Arc were given by
Ns = Nocozez(1 +p), whence
Nc = 2No coz eKP, No-
(9)
2Ns-Ne 2¢-ozez
Measurements were made at several different settings o f the bottom level discriminator for each o f several sources. The efficiency e z was determined as already described. The K capture activity No was then calculated from eq. (9), using the value o f coK given in the appendix. Referred to the time o f the fl- measurements, the final mean value was No = 64.19+ 1.35 dps/mg. The quoted error derived about equally from uncertainties in the bremsstrahlung correction and in ez. The fl- activity was determined by the efficiency tracing technique 15). The measurements were made on a 47rfl-~ coincidence apparatus similar to that described by Campion 16). The tracer employed was 36 h Br a2, in the form of a solution of T1Br. A number of sources o f different solid content were prepared, each containing a known amount of the Tl 2°4 solution together with a suitable quantity of Br a2. The number of B r - ions was in every case much greater than the number of SO~ ions. The fl efficiency of each source was measured with respect to the Br a2. The sources were stored for two weeks, after which time the residual Br a2 activity was negligible,
590
P. CHRISTMAS
and were finally 4 ~ counted to obtain their apparent TI T M activities. These activities were plotted against the corresponding etTiciencies and the true activity obtained by extrapolating to 100~ efficiency a least-squares fit to the data, as shown in fig. 7. Tli~ final value on the reference date was
N#
3500
= (4.032+0.021). 103 dps/mg.
--
0
5ooo
IO0
I
90
I
(10
O
-/0
60
¢1'~,for BI'll;e (°/o/)
Fig. 7. Determination of TP °4/~- activity by the tracer method, see text. The experimental errors are too small to be shown.
Corrections were applied for the sensitivity of the // counter to electron capture events and for the Br 8z decay scheme. The quoted error reflects the scatter of the individual measurements (fig. 7); this scatter is attributed to incomplete mixing of the activities on the sources. From the above measurements the K c a p t u r e / p - ratio was determined K capture _ 0.0159 +0.00036. From the measured values of the L/K ratio and the K capture///- ratio the branching ratio was calculated E.C. --- 0.0254+0.0012. Leutz and Ziegler 4) gave a value for E.C.//~- of 0.0215+0.0005, while the results of Joshi 3) yield 0.0220, error unknown. I am indebted to Dr. P. J. Campion both for suggesting the experiment and for his interest and advice at all times, and to Mr. A. Williams for many useful discussions. I am also grateful to DSIR for the award of a Senior Research Fellowship. This work has been carried out as part of the research programme of the National Physical Laboratory and is published by permission of the Director of the Laboratory.
Eta~CTRONCAFYURBIN 31))t
591
Aplmadix Unless otherwise stated, the numerical values and errors given below have been taken from ref. 7). CALCULATION OF .41 AND .41 In evaluating the quantities S. the following values were used for the L fluorescence yields: t0L, = 0.087, t0t~x = 0.42, 0~t~,1 = 0.30. NO errors were given in ref. 7), a possible error of + 10 ~o has been ascribed to each value, giving 4- 4.1 ~o in ~t. The values taken for the Coster-Kronig yields were ft~t~1 = 0.12,
fL,Lm = 0.68,
ft~,Lm = 0.00.
Again, no errors were given; it has been assumed that frzL,~ and fr~L=, are each subject to an error o f 4-10~o, giving an error o f +4.6~/o in ~t. Values o f the PI(Li) were calculated from Brysk and Rose 2) as described in the text. The following values were taken for the P2(Lt) and P3(Li): P2(h)
= 0,
P2(LI~) = 0.355--+0.0042, P2(L..) = 1 - e 2 ( L ~ ) ,
with corresponding error -+ 0.9 Yo in a, Pa(L~) = 0.037_+0.012, P3(Ln) = 0.354-+0.012, Pa(Lm) = 0.6104-0.012, with corresponding error 4-3.5~/o in a. VALUES FOR f, toL AND nKL The following values were used: f=
0.777_+0.014,
tot = 0.954-+0.005;
nKL was calculated from the equation nXL = fOX + (1 -- tox)Ax, where =
A~
,
LL+KLY
\KLL + ~ Y / "
592
1).
The partial A u g e r yields K L L , K L Y a n d K X Y were o b t a i n e d f r o m ref. 7). A t was calculated to be 1.55+_0.037, giving a value of 0.813 for nra.. The latter is consistent with the value o f 0.82 o b t a i n e d f r o m the s u m o f the Pa(L~) before n o r m a l i z a t i o n . The error i n ~ due to the uncertainties i n f , oJx a n d A K was +_2.7%. T h e total error i n ~ was o b t a i n e d b y a d d i n g the i n d i v i d u a l errors i n q u a d r a t u r e .
References 1) Nuclear Data Sheets (National Academy of Science, National Research Council, Washington, D.C., 1962) 2) H. Brysk and M. E. Rose, ORNL 1830 (1955) 3) B. R. Joshi, Prec. Phys. Soc 77 (1961) 1205 4) H. Leutz and K. Ziegler, Z. Phys. 166 (1962) 582 5) A. H. Compton and S. K. Allison, X-rays in theory and experiment (D, Van Nostrand Co., New York, 1935) 6) Coster and Kronig, Physica 2 (1935) 13 7) A. H. Wapstra, G. J. Nijgh and R. van Lieshout, Nuclear spectroscopy tables (North-Holland Publ. Co., Amsterdam, 1959) 8) C. S. Wang Chang and D. L. Falkoff, Phys. Rev. 76 (1949) 365 9) I. Rezanka, J. Frana and J. Adam, Czech. J. Phys. 12 (1962) 101 10) G. W. Grodstein, N.B.S. Circular 583 (1957) and supplement 11) L. B. Magnusson, Phys. Rev. 107 (1957) 161 12) E. der Mateosian and A. Smith, Phys. Rev. 88 (1952) 1186 13) R. G. Jung and M. L. Pool, Bull. Am. Phys. Soc. 1 (1956) 172 14) M. H. Biavati, S. J. Nassif and C. S. Wu, Phys. Rev. 125 (1962) 1364 15) P. J. Campion, J. G. V. Taylor and J. S. Merritt, Int. J. Appl. Rad. Isotopes 8 0960) 8 16) P. J. Campion, Int. J. Appl. Rad. Isotopes 4 (1959) 232