A two parameter centroid shift method for measuring nuclear lifetimes

NUCLEAR

A TWO

INSTRUMENTS

PARAMETER

AND METHODS 83 ( I 9 7 0 ) 2 9 - - 3 4 ;

CENTROID

SHIFT

METHOD

©

FOR

NORTH-HOLLAND

MEASURING

PUBLISHING CO.

NUCLEAR

LIFETIMES

J. F. BOULTER, W.V. PRESTWICH and B. ARAD*

Department of Physics, McMaster University,Hamilton, Ontario, Canada Received 9 February 1970 A delayed coincidence technique for measuring nuclear lifetimes in the range of 100 ps is described. The start-stop time interval is recorded along with the stop energy in a two parameter array S(E, t) and the shape of the centroid-energy function < S(E, t)> in the prompt region of the spectrum is determined and extrapolated to the delayed region in order to obtain the centroid

shift. The lifetime of the 31.2 keV level in 2SAI-T~ = 2.15 i 0.06 ns and of the 279 keV level in 2°aT1 -- T~ = 282±15 ps have been measured using this method. As a more direct verification of the technique, a source was displaced through measured distances relative to a second fixed source and the observed centroid shifts compared to the values predicted using the speed of light.

1. Introduction

with time d i s t r i b u t i o n s

The effects which limit the accuracy o f the c e n t r o i d shift m e t h o d o f m e a s u r i n g nuclear lifetimes have been extensively discusseda'2). W h e n the p r o m p t a n d delayed sources are exchanged, spurious shifts can be caused by:

Sp(E, t) = Fp(E) d {t- to(E)}, Sd(E, t) = Fd(E) z - ' exp - [{t- to(E)}/x], where z is the mean life of the delayed component. Thus the CEF is given by

1. c o u n t i n g rate effects; 2. different pulse height d i s t r i b u t i o n s in the energy windows; 3. electronic drift a n d instability; 4. scattering o f r a d i a t i o n between detectors; 5. different effective i n t e r a c t i o n location in the scintillator for the p r o m p t a n d d e l a y e d radiation.

Fd(E) (t(E)> = to(E) + Fp(E)+Fd(E) z. Statistical analysis by Post and Schiff3) and by Sigfridsson4) have shown that for a NaI detector at a triggering level o f 1 p h o t o e l e c t r o n , a n d for the n u m b e r o f p h o t o e l e c t r o n s released from the p h o t o c a t h o d e R > 1, it is expected t h a t

By the use o f small scintillators a n d a p p r o p r i a t e g e o m e t r y the effects (4) a n d (5) cart be minimized while (1), (2) a n d (3) are m o r e difficult to reduce. The c e n t r o i d shift p r o c e d u r e described here consists o f recording the time s p e c t r a in a two d i m e n s i o n a l a r r a y S(E, t) where E is the stop energy a n d t is the s t a r t - s t o p time interval. T h e s h a p e o f the centroid-energy function ( C E F ) , (i.e. walk curve) in the p r o m p t region o f the energy scale is t h e n d e t e r m i n e d a n d e x t r a p o l a t e d to t h e d e l a y e d region in o r d e r to o b t a i n the c e n t r o i d shift. The shifts due to (1), (2) a n d (3) are hence largely e l i m i n a t e d since the p r o m p t a n d d e l a y e d i n f o r m a t i o n is s i m u l t a n e o u s l y a c q u i r e d using the same source. T h e C E F is given by

to(E) ~- (ALE) + tD , where tD is a fixed electronic delay. A s a qualitative example, consider the situation in which the p r o m p t d i s t r i b u t i o n is described as a c o n s t a n t Fp(E) = K, while the delayed d i s t r i b u t i o n exhibits the G a u s s i a n behaviour:

F,I(E) = (2n) -½ a -1 exp [ - (E-Eo)2/2a2]. A l s o consider the case in which the p r o m p t d i s t r i b u t i o n is d o m i n a n t (K>> 1). T h e n Fp(E)+Fd(E ) ~- K a n d

(t (E)) = (A/E) + to + (z/K) exp [-- ( E - Eo)2/2 a2].

< / ( E ) ) = StS(E, t)dt/S S(E, t ) d t . The s p e c t r u m at arty energy can be d e c o m p o s e d into a prompt and delayed component:

S(E, t) = Sp(E, t) + Sa(E, t ) , * Present address: Department of Physics, Soreq Nuclear Research Centre, Yavne, Israel and Department of Physics, Bar Ilan University, Ramut Gan, Israel. 29

In this idealized situation, the C E F can be described as a G a u s s i a n p e a k o f m a g n i t u d e x/K, centered at Eo, s u p e r i m p o s e d u p o n a h y p e r b o l i c b a c k g r o u n d . A s is well knownS), c o n v o l u t i o n o f the i n s t r u m e n t a l resolution in the time d o m a i n does n o t affect the validity o f these results. It was o b s e r v e d t h a t the C E F for a triggering level o f 1 p h o t o e l e c t r o n d i d n o t display the expected 1/E dependance. C o n s e q u e n t l y in the c e n t r o i d shift analysis an a d d i t i o n a l term, linear in E, was used to

30

J.F.

B O U L T E R et al.

obtain a satisfactory fit to the prompt region of the CEF. Three experiments are described here as a demonstration of the two parameter centroid shift technique. The halflife of the 31 keV level in 28A1 was measured as a relatively simple case which is free from the ambiguities present in the second experiment. The halflife measurement of the 279 keV level irt ~°3T1 illustrates the results obtained under adverse conditions. The displaced source experiment gives a more direct verification of the method.

photomultiplier tube. The stop detector was a 1 2 m m x 2 5 m m d i a m . Na[ mounted on an 8575. The start single channel analyser (SCA) selected 7 rays in the range 0.5 to I MeV while the stop SCA accepted all energies between 2 and 60 keV. The energy selected T A C events were recorded along with the corresponding stop energy in a 256 (time) by 64 (energy) channel array using art N D 3300 multiparameter analyser. Each run was dumped onto magnetic tape and analyzed using an IBM 7040 computer.

2. 28A1 halflife 2.1. EXPERIMENTAL

2.2. RESULTS

The halflife of the 31 keV level in 28A1 populated by thermal neutron capture in natural aluminum was measured. The arrangement (fig. 1) is similar to a conventional delayed coincidence experiment except that in place of setting an analogue window to select the delayed radiation, the energy of the stop event was recorded two dimensionally along with the time. The start signal for the time-to-amplitude converter (TAC) was provided by the detection of high energy capture ? rays in a 3 8 m m × 4 6 m m d i a m . Naton 136 plastic scintillator mounted on an R C A 8 5 7 5

Fig. 2 shows the analysis of a typical ZSAI run. In

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Fig. 2. A n illustration o f the fitted function centroid shift analysis procedure applied to a typical 28A1 run. In (a), the line is the function A + B / E + C . E fitted to the centroid position (points) over the regions indicated by the arrows. (b) is t h e centroid shift, i.e. the difference between the fitted function a n d the centroid position. (c) gives the half life estimate for the 31 keV level obtained by correcting the centroid shift for the relative a m o u n t s o f p r o m p t a n d delayed c o m p o n e n t as determined from the coincidence energy s p e c t r u m (d).

TWO

PARAMETER

CENTROID

(a), the points are the experimental centroid position plotted versus the stop energy while the line is the function A + B / E + C . E (where A , B and C are arbitrary constants), fitted to this CEF. The fit was made over the two regions on either side of the 31 keV photopeak, 10-19keV and 38-62keV where the radiation is essentially prompt, and the resulting centroid shift:

(t(E))-A-B/E-C-

E

is shown in fig. 2(b). The relative amounts of p r o m p t and delayed components, So(E) and Sd(E), were obtained from the coincidence energy spectrum S(E,t) [fig. 2(d)], and a correction applied to the centroid shift in order to calculate the halflife:

T½(E) = 0.693

S d(g) --t-Sp (E) Sd(E )

[(t(E))-A-B/E-C.E].

A weighted mean of the T½(E) [fig. 2(c)] then yielded the halflife. Later experiments using different targets, have shown that scattered neutrons were not completely excluded from the N a I detector by the 6LiF shielding6). Consequently to minimize possible interference from a 30 keV transition in 12sI [T~ = 8.8 nsV)] and from the iodine K X-ray at 28 keV, excited by thermal capture in the N a I detector, the 2SA! half life was determined from the region above 30keV. The straightness of the halflife estimate plot [fig. 2(c)] indicates that the 2SAl measurement was not influenced by the 1281. Table l shows the results of 6 independant measurements of the 2SA1 halflife, changing the target thickness and start energy window in order to minimize any systematic effects. The centroid shift experiments yielded a mean T~ = 2.14_+0.01 ns which is in agreeTABLE 1 Measured values for the halflife o f the 31 keV level in 28A1.

R u n no.

1 2 3 4 5 6 Mean

Halflife (ns) (from slope)

2.14d 0.04 2.24±0.04 2.22±0.06 2.08~z0.03 2.09-/-0.04 2.18±0.03 2.162_0.02 ns

Halflife (ns) (centroid shift)

1.95j 0.02 2.26±0.02 2.14±0.03 2.08i0.02 2.174-0.02 2.265-0.02 2.14±0.01 ns

SHIFT

METHOD

31

ment with a value T~ = 2.16_+0.02 ns obtained from a slope analysis of the same data. No correction for chance background was made in determining the centroid of each time distribution, but this was calculated to introduce less than a I % error in the halflife. The timescale was calibrated with a 1% precision using a 100 Mhz oscillator procedureS). A possible error arises because a fraction of the 31keV y rays which escape the photopeak cause a centroid shift in the prompt region below the peak. The lineshape of the N a I detector at this energy was determined by observing the 32 keV X-rays from 137Cs in coincidence with the conversion electrons. The correction thus applied to the centroid position below the 31 keV peak increased the halflife by 1%. Including these systematic effects and using the 66% confidence interval based on the Student t-distribution, a 3% error has been assigned. The final result, T, = 2.15_+ 0.06 ns, is in agreement with a previous measurement, T½ = 2.3_+0.2 nsT). 3. 2 ° 3 H g halflife 3.1. EXPERIMENTAL The halflife of the 279 keV level in Z°3Tl populated in the fl- decay of 2°3Hg was measured as an illustration of the results that can be obtained under adverse conditions. Low energy fl-rays give the only indication of when the 279 keV level is populated, so in order to provide good detection efficiency, the 2°3Hg source was located directly on the surface of the start detector. It was therefore impossible to use anti-Compton shielding to prevent scattering from one detector into the other. Secondly the 50% solid angle subtended by the source at the start detector caused a large probability for coincidence summing envolving fl-rays conversion electrons and Compton scattered ~,-rays as discussed in detail below. In order to provide a prompt background on either side of the 279 keV photopeak, 6°Co was mixed with the 2°3Hg. fl-rays between 100 and 120 keV from the decays of 2°SHg and 6°Co detected in a 2 m m x 25 m m diam. Naton 136 plastic scintilator mounted on an 8575 provided the start signals. A 12 m m ×25 m m diam. N a I mounted on an RCA C31000D was used as the stop detector. A differential discriminator was used to restrict the start events according to anode pulse height in the arrangement shown in fig. 3. The use of the anode pulse height from the plastic detector rather than the integrated dynode signals greatly reduced pile-up

32

J.F.

B O U L T E R et at.

at high counting rates with a negligible loss of energy resolution. A fast coincidence between the differential discriminator (stretched to 200 ns width) and the timing discriminator (delayed by 56 ns), was used to start the TAC. The signal from the timing discriminator was sufficiently delayed that the timing information was always obtained from this pulse while the TAC start was inhibited unless the energy condition imposed by the differential discriminator was satisfied. Because of the complexity of the resulting CEF [fig. 4(a)], a run containing substantially only prompt events was obtained by raising the s t a r t window to accept electrons between 210 and 250 keV. Since the /~ endpoints are 214 keV for decay to the 279 keV level in 2°3T19) and 314 keV for decay to the 2.5 MeV level in 6°Ni9), with the exception of coincidence summing is the plastic detector, only prompt 6°Co events were accepted using the higher window. To compensate for walk in the plastic detector as the s t a r t window was raised, the prompt curve was displaced in time so as to line up with the delayed curve over the prompt regions of both CEF's. The difference between the prompt and delayed CEF's in the energy range 262-296 keV was then used to obtain the halflife.

3.2. RESULTS Fig. 4(a) shows a typical delayed CEF (points) and a smoothed prompt CEF (line) shifted in time so as to line up over the two regions 20-60keV and 410-530 keV. The region between the 72keV and 279keV photopeaks was not used in the analysis because of distortion of the prompt CEF as a result of coincidence summing in the start detector (discussed below). The delayed CEF below the 279 keV photopeak can be explained in terms of the relative amounts of prompt and delayed components present. Fig. 4(c) shows the resolution of the coincidence energy spectrum into a delayed and a prompt component in a proportion consistent with the observed centroid shift (using an estimated prompt CEF). The shape of the delayed component represents the coincidence response of the NaI detector to 279 keV y-rays. The prompt component consists of: T

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TWO

PARAMETER

CENTROID

1. Compton from the 1.17 MeV and 1.33 MeV

6°Co y-rays and their backscattering peaks at 210 keV and 215 keV. 2. A strong peak at 167 keV resulting from scattering of a 279 keV y-ray out of the plastic detector into the NaI through an angle 105 ° (here the start pulse arises from the Compton scattered electron whose energy is in the centre of the l l 0 _ 1 0 k e V plastic window). 3. The 72 keV X-ray peak resulting from coincidences with the conversion electron detected in the plastic (a portion of this line resulting from coincidences with a/Y-ray will be delayed). 4. A small peak at approximately 270 keV from scattering of 6°Co y-rays at an angle 116 °. As observed in fig. 4(a) where the prompt CEF lies above the delayed curve, the prompt CEF contains a portion of delayed components. This arises from coincidence summing in the plastic detector of a ]?-ray and an electron from the Compton scattering of the corresponding 279 keV y-ray. Thus the energy condition, (i.e. 230+20 keV) on the start event is satisfied, and the Compton scattered y-ray with an energy between 133 keV and 265 keV will be delayed with respect to the start//-ray.

SHIFT

33

METHOD

the 279 keV photopeak to later times, hence producing an underestimate of the halflife when the prompt CEF is fitted. Secondly, as shown in fig. 1(c), the prompt distribution under the 279 keV photopeak is curved, but this was approximated by a linear background in the analysis. The present result, T½ = 282___15ps, is in good agreement with a number of previous measurements as summarized by Schwarzschildt).

4. Displaced source experiment As a final verification of the procedure, a source was moved through a measured distance relative to a second fixed source, and the observed centroid shift compared to the value predicted using the speed of light. The electronic arrangement was similar to that used for the 2aA1 experiment. An SCA selected start y-rays in the energy range ll00_+50keV as detected in a 38 m m x 5 0 m m diam. NaI. Stop 7-rays between

t"6Sc +60Co DISPLACEO SOURCE 350

300

TABLE 2 Measured values for the half life o f the 279 keV level in 2°3T1.

Separate Prompt AnOlysms

R u n no.

1 2 3 4 5 6 Unweighted mean

Halflife (ps) ( p r o m p t no. 1)

291 ~ 4 285±8 281 ± 3 270±4 284±8 299±25 2 8 5 ± 2 ps

Haiti±re (ps) ( p r o m p t no. 2)

289±4 280±8 277-t-3 263±4 275±8 288~ 25 2 7 9 ! 2 ps

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Table 2 shows the experimental values obtained for the halflife of the 279 keV level from six delayed runs using different geometry and 2°3Hg source strength. The two sets of results were obtained using different prompt CEF's. The error quoted for each measurement represents only the statistical uncertainty, and the total error has been increased to + 5% after inclusion of possible systematic effects. The centroid position was sensitive to shifts introduced by random adding in the NaI amplifier at rates above 5 kHz. This effect caused a distortion of the CEF by shifting the portion above

Intercept O=5±11ps

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I 5.0

S.5

Fig. 5. T h e results o f the displaced source experiment. T h e observed centroid shift expressed as a n effective m e a n life is plotted vs the source displacement (using a n arbitrary zero) for the two analysis procedures. T h e lines have a slope fixed by the speed o f light a n d are adjusted for the i n t e r c e p t - a only.

34

J . F . BOULTER et al.

50 keV and 1400 keV detected in a 25 m m × 25 m m diam. N a I were recorded in the energy dimension. The sources were located on the line joining the two detectors. A 6°Co source was fixed in position close to the start detector and a 46Sc source m o u n t e d on an optical bench was free to move between the 6°Co source and the start detector. Both decays lead to two y cascades in which the intermediate state has a negligible lifetime, T½ ~< 4 p s 9) (1.33 MeV and 1.17 MeV for 6°Co and 0.89 MeV and 1.12 MeV for 46Sc). The energy spectrum in the stop detector in coincidence with the 1.15 MeV start energy region thus consists of the 1.33 MeV and 0.89 MeV lines. The 0.89 MeV line will be delayed by an a m o u n t equal to twice the separation of the two sources with respect to the 1.33 MeV b a c k g r o u n d and a corresponding centroid shift will appear at this energy and below its C o m p t o n edge at 0.69 MeV. The 46Sc source was moved in 1.000cm steps and the spectra S(E,t) acquired for four different positions. After the four runs, the 46Sc source was removed and a 6°Co p r o m p t run obtained. The centroid shift o f the 0.89 MeV line was then determined for each 46Sc position by the two analysis procedures. The function A + B / E + C . E + D . E 2 or the 6°Co p r o m p t C E F was fitted over the two p r o m p t regions on either side of the 0.89 MeV peak and the centroid shift (equal to the effective mean life z) calculated. The results obtained using the two analysis procedures are shown in fig. 5(a) and (b). The centroid shifts corresponding to effective mean lives in the range 150-350ps are plotted vs the 46Sc source position (using art arbitrary zero). A least squares fit of a straight line with a slope fixed by the speed of light was made to the experimental points. The intercept-a and goodness of fit criterion X2/f for the two analysis procedures: fitted function a = - 10_+ 8 p s separate p r o m p t a = 5 + 11 ps

X2/f = 1.76, X2/f = 0.56,

indicate satisfactory agreement within the statistical uncertainty. 5. Conclusion

Later experiments have emphasized the importance of proper shielding o f the two detectors from each other to prevent the introduction of artificial delays which can be caused by scattering or radiation from one detector into the other. While this effect, in addition to those due to r a n d o m adding or coincidence summing, impose a limit on the sensitivity of the delayed coincidenc e measurement, the two parameter analysis

allows such spurious shifts to be more easily identified. In favourable cases such as the complex spectra following thermal neutron capture, where the level to be measured decays by a strong 7-ray which is superimposed on a p r o m p t b a c k g r o u n d of high energy compton scattered y-rays, halflives in the range of 100 ps can be reliably measured. Because of the basic similarity of capture y-ray energy spectra, a corresponding p r o m p t C E F can then be obtained, e.g. using natural mercury or cadmium, in order to check for shifts due to scattering effects. The point by point analysis of the coincidence energy spectrum yields more information regarding the relative contributions o f p r o m p t and delayed components than when analog windows are set and hence allows a better correction to be applied to the observed centroid shift. As a final c o m m e n t it can be noted that this procedure can be extended to include a third m o m e n t analysis 1°) of the time st:ectra S(E, t). The third m o m e n t of the time spectra about their centroid positions is calculated and the third m o m e n t - - e n e r g y function obtained. After correction for the relative intensity of p r o m p t and delayed components, the expression1°): z = [½ {Ma(Delayed ) - Ma(Prompt)}] ¢ can then be used to obtain the mean life using the shift of the delayed third moment: M3(D~layed ) = ( [ t 3 S(E, t ) - (tS(E, t ) ) ] ) from the extrapolated p r o m p t third m o m e n t over the delayed energy region. The authors gratefully acknowledge the financial assistance provided by the National Research Council of C a n a d a and by the Ontario D e p a r t m e n t of University Affairs. References 1) A. Schwarzschild, Nucl. Instr. and Meth. 21 (1963) 1. 2) E. Ye. Berlovich and V.V. Lukashevich, Nucl. Instr. and Meth. 55 (1967) 323. 8) R. F. Post and L. I. Schiff, Phys. Rev. 80 (1950) 1113. 4) B. Sigfridsson, Nucl. Instr. and Meth. 54 (1967) 13. ~) Z. Bay, V. P. Henri and H. Kanner, Phys. Rev. 100 (1955) 1197. 6) j. F. Boulter, W. V. Prestwich and B. Arad, Can. J. Phys. 47 (1969) 591. 7) S. J. Du Toit and L. M. Bollinger, Phys. Rev. 123 (1961) 629. s) j. F. Boulter, W. V. Prestwich and T. J. Kennett, Nucl. Instr. and Meth. 77 0970) 163. 9) C. M. Lederer, J. M. Hollander and I. Perlman. Table of isotopes, 6th ed. (Wiley, New York, 1967).. 10) R.S. Weaver and R.E. Bell, Nucl. Instr. and Meth. 9 (1960) 149.