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Centroid-shift measurement of the mean lifetimes of the 316 and 612 keV states of 192Pt
1 .E.4:3.A~
Nuclear Physics A202 (1973) 409--420; ~ ) North-HollandPublishino Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher
C E N T R O I D - S H I F T M E A S U R E M E N T OF THE M E A N LIFETIMES OF THE 316 A N D 612 keV STATES OF 19Zpt G. J. S M I T H and P. C. S I M M S Tandem Accelerator Laboratory, Purdue UniversiO', Lafayette, Indiana 47907 t Received 29 September 1972 (Revised 21 November 1972) Abstract: The mean lifetimes o f the 316 and 612 keV levels in 192pt were measured by means o f a new variation o f the centroid-shift method. The technique uses a triple coincidence among a fl-particle and two ~,-rays. Values obtained for the lifetimes are z ( 3 1 6 ) : 61.7±2.1 and z(612) = 38.2 ± 2 . 2 psec. The effect o f these results on the analysis o f the o-factors for these two states is discussed.
El
R A D i O A C T i V I T Y t 921r; measured flTY'c°in" t 92pt levels deduced T~"
I
1. Introduction A modified version of the centroid-shift technique has been used to measure the mean lifetimes of the first two excited states in 192pt" The method employs a triple coincidence between a fl-particle and two ~,-rays. An excited state of the nucleus is populated via fl-decay and is subsequently depopulated via emission of successive 7-rays. An idealized decay scheme is shown in fig. 1. The state B with mean lifetime
\
A
Fig. 1. An idealized decay scheme. State B is populated by f12 and decays by emitting a ~'-ray, 72, thus forming state A, which emits 71. Although fli also populates state A, such events are rejected by requiring a fl-7-~' triple coincidence. + Work supported by National Science Foundation. 409
410
G . J . S M I T H A N D P. C. S I M M S
z(B), is populated via/3-decay and decays by emitting y-ray 72. The state A with mean lifetime T(A), then decays by emitting Yl. The arrangement of the detectors is shown in fig. 2. A thin plastic scintillator detects/3-particles and starts a time-to-amplitude converter (TAC). The other plastic scintillation detector stops the TAC a fixed delay time t o after a y-ray is detected. The energy of the y-ray which stopped the TAC is determined by the detection of a second y-ray by a Ge(Li) detector operated in coincidence with the y-ray timing detector. For example, if 72 is recorded in the Ge(Li) detector at the same time as a fl-y coincidence occurs at the TAC, then 7t must have stopped the TAC. Similarly, if 71 is recorded by the Ge(Li) detector in coincidence with a TAC signal, then it must have been 72 which stopped the TAC.
GE(LI) SOURCE'
[---- T%
I PM TUBE BETADETECTOR' BETAABSORBER-
Fig. 2. Positions of the three detectors. The/~- and y-detectors are made o f plastic scintillator. A n aluminum disk is placed between the source and the),-detector to absorb fl-particles.
For the situation in which 71 stops the TAC, the time interval measured is
t(y 1)
=
to -
tt~ 2 - - tf82 + trr ~ +
z(B)+ z(A),
(1)
where t o is the inherent delay in the electronics, tp2 is the time of flight for the /3particle travelling to the detector, trp2 and trr I are determined by the rise times of the /~ and y detector pulses, and t(B) and T(A) are the mean lifetimes of the two states. Similarly, for the situation in which 72 is detected in the timing detector, the measured time interval is
t(y2) ==-to--tp2-tra~ +t,,2 +'c(B ).
(2)
Notice that/3x cannot interfere with the experiment because it cannot produce a triple coincidence. Thus there is no systematic difference between the /3-particles which start the TAC when either ?1 or 72 stop the TAC. All factors which relate to the fl-particle cancel, so the difference between the two time intervals is t ( ? l ) - t(y2) = z(A) + (trr, - trr~), or
T(A) =
(t(?,)--t(72)) - - ( t r w - tr72).
(3)
CENTROID-SHIFT MEASUREMENTS
411
The term (tr~~-tr~2) is produced by the difference in amplitude walk for the two v-rays in the y-timing device. There are many ways to minimize and correct for this effect 1.2). There are two other corrections which are independent of the decay scheme of the nucleus being studied. The peaks in the ",,-ray spectrum of the Ge(Li) identification detector sit on a background which is produced by Compton scattering and electronic pulse pile-up. A correction for the background can be obtained by using singlechannel analyzers (SCA) to set windows of equal width on the peaks and on the background near the peaks. Separate centroids (or average time intervals) can be recorded for the peak-plus-background (T) and the pure background (tB). It is also necessary to correct for the misidentification which occurs when there is an accidental coincidence between the Ge(Li) identification detector and the v-timing detector. Conventional techniques 2) can be used to recognize chance coincidences and record the corresponding average time interval t c from the TAC. The last correction depends on the decay scheme of the nucleus being investigated. If the decay scheme is complicated there may be several cascades which go through different states and produce the same identification y-ray. Thus, part of the time, the observed time interval ( t + A ) will be different from the correct time interval t. The time-interval difference A and the amount of mixing must be determined in a separate measurement. Several examples of this correction will be given in sects. 2 and 3. When all of these corrections are combined, the observed centroid T can be expressed as a combination of the desired time interval t and the three correction intervals: 7" = ~t + flta + ytc +(5(t + A)
~+fl+7+6 where ~, fl, 7 and 6 are the number of correct, background, chance and decay scheme related events included in the observed centroid T. This equation can be rearranged to yield an expression for the corrected centroid: (4)
t = T + B ( T - t13)+ C ( T - t c ) - D A
where B
]~
C-
y
D-
~
Eqs. (3) and (4) can be combined to yield a final expression for the mean lifetime z(A).
~(A) = ET(~,) - T(y2)] + S(y I)[T(y,) - t.(y,)] - B(~2)E r(~2) - t.(y2)] + c(y,)[ r(y,)-
to] - C ( ~ 2 ) [ T ( ~ 2 ) - t o ] - D ( ~ , ) A ( y , ) + O(y2)A(~2)--(t,,,- t,,2). (S)
Most experiments will not require all of these correction terms as will be shown in the examples given in sects. 2 and 3. Notice in eq, (5) that all of the correction centroids can be different for event 1 and 2 except for t c. When a chance coincidence
412
G . J . SMITH AND P. C. SIMMS
occurs the average time interval t c produced by the TAC will be the same as that observed with no identification. There are several advantages to this modified version of the centroid-shift technique. (i) The fast timing characteristics of the plastic detectors give good time resolution. (ii) The fl-detector has high efficiency due to the geometry of the experimental set-up. The source is placed flat against the face of the fl-dector so that the solid angle, and hence, the efficiency of the detector is high. (iii) The Ge(Li) detector has good energy resolution so that complicated decay schemes can be studied. 2. Measurement of lifetimes 2.1. THE 316 keV LEVEL OF 192pt
The major features of the decay scheme 3) for 192pt are shown in fig. 3. The two types of events which were used to measure the mean lifetime of the 316 keV level are E ( k e V ) J "rr
1200 (4)+
,c49
13o86o," 296
920
3+
785
4+
612
2'+
316
2+
612
:516
0
O+
Fig. 3. The major features of the decay scheme of ~92pt. To measure ~(316) f12-F(308) and f12-y(316) events are recorded in coincidence with detection of a 7 ( 6 1 2 ) a n d ~,(604), respectively, in the Ge(Li) detector. To measure z(612), f12-y(308) and fl2-7'(296) events are recorded in coincidence with detection ofv(296) andy(308), respectively, in the Ge(Li) detector.
f12-y(308) and f12-y(316) coincidences. The 612 and 604 k e y y-rays were recorded in the Ge(Li) detector to identify the energy of the y-ray which stopped the TAC. The fll transition does not cause any difficulty because it does not lead to a state which produces either of the identifying y-rays (604 or 612). For the moment we neglect all corrections, including the low intensity f13 transition.
CENTROID-SHIFT MEASUREMENTS
413
The difference between the two centroids produced by /32-7(308) and fl2-7(316) coincidences is the mean lifetime of the 316 keV state t ( 3 1 6 ) - t ( 3 0 8 ) = [ t o + r ( 9 2 0 ) + z ( 3 1 6 ) ] - t t o + r ( 9 2 o ) ] = z(316).
(6)
Several of the corrections contained in eq. (5) were not necessary in this case. The energies (308 and 316 keV) of the y-rays used for timing are so similar that the amplitude walk correction was negligible. The chance-to-true ratios for the Ge(Li) plastic coincidences were small and approximately equal for the two types of events. Thus a single chance-to-true ratio C was used. The two identification y-rays are so close in energy (604 and 612 keV) that the same background window can be used for both peaks, so tB(316 ) = tB(308 ) = tB. When 7(604) is recorded in the Ge(Li) detector, the fl-particle and y-ray are uniquely identified as f12 and 7(316); so there is no A(316) correction term. When 7(612) is recorded in the Ge(Li) detector, y(308) will usually stop the TAC; but for a few percent of the time, y(589) will stop the TAC. The procedure for measuring this correction A will be discussed below. When all of the necessary factors for this case are included, the expression for the mean lifetime of the 316 keV level is r(316) = (T6o4 - 7612)(1 + C) + B 604(Tb04. --/B) -- B612(T612 --/B) N612(589)
+
A.
(7)
U612(589) + X612 (308) A new notation has been used for clarity in writing this expression. The energy of the y-ray which stopped the TAC is shown in parenthesis as before. In addition the energy of the ),-ray identified by the Ge(Li) detector is shown as a subscript. Thus, 7"6o4 and T612 are the observed centroids when the 604 or 612 keV 7-rays are identified by the Ge(Li) detector regardless of the particle that stopped the TAC; B604and B612 are the ratio of background to peak counting rates for the 604 and 612 keV y-rays recorded in the Ge(Li) detector. When the 612 keV y-ray is identified in the Ge(Li ) detector, the two components of the co unting rate are N61 z (308) and N612 (589) for 308 and 589 keV y-rays in the timing detector. In fig. 3 we see that the correction term A can be determined by the difference in flight time between /32 and/33 and the difference in mean lifetime between the 1200 and 920 keV states: A = (z(1200)-tp3 ) - ( r ( 9 2 0 ) - t p 2 ). This combined time correction was determined by measuring the difference between the centroids which were produced when the 308 and 589 keV 7-rays were recorded in the Ge(Li) detector. The TAC was stopped by y(296), y(316), or y(612). No matter which y-ray stopped the TAC, the 589 centroid depends on/33 and z(1200), and the 308 centroid depends on f12 and r(920).
414
G . J . S M I T H A N D P. C. S I M M S
2.2. T H E 612 keV L E V E L O F t9zpt
The mean lifetime of the 612 keV level can be determined by comparing the centroids recorded for f12-y(308) and fie-y(296) coincidences. If there were no correction factors due to chance coincidences, background or decay scheme peculiarities, the two average time intervals would be T296 =
N(308)to + N(316)[/o + z(612) + z(316)], bi(308)+ N(316)
T3os = N(296)[t 0 + z(612)-I + N(316)[to + z(612) + z(316)] N(296) + N(316)
(9) (10)
Now t o is the combination of the fixed delay in the system, the flight time of/32 , and the mean lifetime of the 920 keV level; N(296), N(308) and N(316) are the number of 296, 308 and 316 keV y-rays recorded by the timing detector, respectively. If there were no branching of the 612 keV level or other decay complications, N(296), N(308), and N(316) would be equal and eqs. (9) and (10) would reduce to T296
=
7"308 =
"4-½Z(612) + ½Z(316),
(11)
tO+Z(612)+1Z(316)"
(12)
t0
Subtraction of eq. (11) from eq. (12) gives ½z(612) = T308 - -
T296 .
(13)
Eq. (13) is only an approximation, but it is interesting to note that the 316 keV y-ray causes the observed centroid shift to be only half of the mean lifetime of the state being studied. When the lower intensity transitions in the decay scheme are included, the expressions for the observed centroids become more complicated. If the 296 keV y-ray is recorded in the Ge(Li) detector, f13 transitions must be included when either the 589 keV or 316 keV y-rays stop the TAC: T296
=
{N(308)to + N(316)[to + z(612) + z(316)] + N(589)[to + h i
+ N'(316)[to + A + z(612) + z(316)]] × {N(308) + N(316) + N(589) + N'(316)]- ~, (14) where N(589) and N'(316) are the number of 589 and 316 keV y-rays recorded following /33 transition. The difference in flight time between/33 and/32 and the difference between the mean lifetimes of the 1200 and 920 keV levels are included in A. This is the same correction that was discussed in subsect. 2.1. The probability of detection is essentially the same for the 308 and 316 keV y-rays, so by setting N(308) = N(316), eq. (14) may be written T296 =
N(316) + N'(316) [z(612)+z(316)] 2N(316) + N(589) + N'(316) N(589)+ N'(316) + A. (15) 2 N(316) + N(589) + N'(316)
t 0 q- ..
CENTROID-SHIFT MEASUREMENTS
415
When the 308 keV 3)-ray is detected by the Ge(Li) detector, there is no contribution by the f13 transition to the average time interval. However, there are still flz-y(612) coincidences present, so that the average time interval is Tao8 = [N(296)[to + r(612)] + N(316)[to + z(612) + z(316)] + N(612)[t o + z(612)]} x{N(Z96)+N(316)+N(612)} -1,
(16)
where N(612) is the number of 612 keV ),-rays recorded by the timing detector. Again, the detection probabilities for the 296 and 316 keV y-rays are essentially the same so that N(296) = N(316) and T3o 8 = t o + r ( 6 t 2 ) +
N~(3!6) z(316). 2N(316)+ N(612)
(17)
An expression for the mean lifetime r(612) of the 612 keV state can be obtained by subtracting T296 [eq. (15)] from T3o 8 [eq. (17)] and solving for z(612). Background and chance coincidence corrections must be included as shown in eq. (5) and eq. (7): ½D, r(612) = (1 + ~)[(1 -I-C)(T308 - T296) + B30s(T308 - t , ) - B296(T296 --/B)] +(02-D3)z(316)+D4A.
(18)
There are four correction factors which depend on the decay scheme. D 1 -
Nz96(316)+Nz96(589)
N296(316) + ½[N296(589) + N-~96(316)] D 2 --
N296(316) + N296(316) 2N296(316) + Nz96(589) + N~96(316) D3
D4 =
N3°8(316) 2N3o8(316)+ N3o8(612)
,
Nzge(589)+N296(316) • 1, 2N296(316) + N296(589) + N~96(316)
where N~96(316 ) and N296(589 ) are the number of 316 and 589 keV 7-rays which follow f13 transitions and stop the TAC when the 296 keV "~-ray is identified in the Ge(Li) detector (remember that N296 (316) is the counting rate produced by 316 keV ~,-rays following f12 transitions); N3os(612 ) is the number of 612 keV 7-rays which stop the TAC when the 308 keV ~,-ray is identified in the Ge(Li) detector. There is one additional correction factor (1 + ~) in eq. (18) which has not been discussed previously. It is possible for conversion electrons from the 296, 308 and 316 keV transitions to be recorded in the fl-detector. For example, a conversion electron from the 308 keV transition could start the TAC, the 316 keV y-ray could stop the
4t6
G.J. SMITH AND P. C. SIMMS
TAC, and the 296 keV ~,-ray could be recorded in the Ge(Li) detector. Since the conversion coefficients for all three transitions are approximately the same ( ~ 6~o), the conversion electrons will cause the same shift in both centroids (T30s and 7"296) so the magnitude of the shift is not important. However the conversion electron events do effect the results through the weighting factors. That is, since both of the centroids contain contributions from the conversion-electron events, the separation of the centroids is reduced. Therefore a small correction (1 + e ) is necessary in the final formula; 0~ is the ratio of the probability of detecting a conversion electron to the probability of detecting a fl-particle.
3. Apparatus and procedure The electronic system used in this experiment will be described in detail in a subsequent publication 2). A summary of the instrument and all of the operating parameters will be given here. The ~92[r source was made by thermal neutron bombardment of chemically pure It, which had been evaporated onto thin A1 foil. The plastic detectors were made from 2.5 cm diameter NE111 scintillator; the fl-detector was 4 mm thick, and the y-detector was 2.5 cm thick; RCA 8575 photomultiplier tubes were used for both detectors. A 30 c m 3 coaxial Ge(Li) detector with an energy resolution of 2.0 keV at 1.33 MeV was used. Constant-fraction timing discriminators were used to provide good time resolution (550 psec F W H M for 300 keV 7-rays). The fl-~ true to chance ratio was approximately 100, and the ~/-Ge(Li) true-to-chance ratio was 65 or larger. In order to obtain adequate triple coincidence counting rates, the single counting rates were high. The fl-rate was approximately 106 counts/see, the v-timing rate was approximately 105 counts/see and the Ge(Li) rate was approximately 3 x 104 counts/see. The flq, double coincidence rate was approximately 3 × 104 counts/see, yet the fl-~-~ triple coincidence rate for the events of interest was only a few counts per second. The measurement of the mean lifetime of the 316 keV level required 6d and the 612 keV level required 2d. Pulse-height analysis was provided in the fl-channel by connecting a gated pulsestretcher directly to the anode of the photomultiplier. Whenever a coincidence occurred between the timing detectors, the gate was opened, the anode pulse was integrated and stretched, and an output pulse was produced which could be processed by conventional single-channel or multichannel analyzers. Good resolution was maintained for the Ge(Li) detector by being careful to obtain proper pole-zero compensation and by using active DC restoration in front of the pulse-height analyzers. The spectrum in fig. 4, which shows how clearly the 604 and 612 keV ~,-rays were resolved, was taken with a counting rate of 3 x 104 counts/see in the Ge(Li) detector. An analog-to-digital converter ADC, a routing circuit, and a set of sealers were used to record average time intervals. Each TAC pulse was converted to a pulse train
CENTROID-SHIFT MEASUREMENTS
417
by the ADC. Each pulse train was routed to a pair of scalers according to the energy of the 7-ray identified in the Ge(Li) detector. One scaler counted the total number N of pulses from the A D C while the other counted the number of pulse trains, n. The average time interval is (N/n)x (time calibration). The average time intervals and all of the counting rates were printed out at 80 min intervals so that statistical tests could be made for systematic errors. Time calibrations were performed several times during the experiment with an air-core adjustable-length delay line. Single-channel analyzers (SCA) were used for all three detectors. A discrimination level of 180 keV was set for the/J-detector. It is impossible for a 7-ray to enter the 7COUNTS 604
3000-
2000i89
I000-
,
~ -
2'o go 6'o do ,;o CHANNEL NUMBER Fig. 4. Ge(Li) detector spectrum showing the 7-rays of 192pt near to 600 keV. The shaded boxes indicate the SCA windows set on the 604 and 612 keV peaks and on the backgreund.
detector, backscatter into the fl-detector and lose 180 keV or more. Thus, coincidences between the two detectors caused by back-scattered 7-rays were avoided. A SCA window was set for the plastic detector to include approximately 50~ of the C o m p t o n distribution below the C o m p t o n edge of the 316 keV y-ray. This window reduced the probability of detecting the higher-energy 7-rays. The Ge(Li) detector spectrum was expanded by means of a biased amplifier, and windows were set on the peaks of interest, as shown in fig. 4. A third window was set on the background, so that an appropriate correction could be made for background y-rays which occur under the peaks.
418
G.J. SMITH AND P. C. SIMMS
4. Results and discussion T a b l e 1 gives the m e a s u r e d c e n t r o i d shifts a n d the values o f the various c o r r e c t i o n factors. T h e time difference A i n t r o d u c e d by the/~3 transitions is - 8 6 + 18 psec. T h e m e a n lifetimes are 61.7_+2.1 psec for the 316 keV level a n d 38.2_+2.2 psec for the 612 keV level. T a b l e 2 c o m p a r e s these results with previous lifetime m e a s u r e m e n t s using d e l a y e d coincidence techniques a n d lifetimes calculated f r o m B (E2) m e a s u r e ments via C o u l o m b excitation. The present value for ~(316) is n o t in a g r e e m e n t with TABLE 1 Experimental results and corrections for mean lifetimes of 192pt 316 keV level centroid-shift x (1 + C ) correction for background in Ge(Li) detector correction for/~3 and ~(589) mean lifetime
psec 60.0~ 1.8 3.4±0.5 --1.7±0.9 61.7±2.1
612 keV level centroid-shift × (1 + C ) × (1 +~) ×2/Dx correction for background in Ge(Li) detector × 2/D~ (Dz--D3) xT(316) x2/D~ correction for f13 and y(589) (D4A × 2/D1 ) mean lifetime
38.3±1.1 3.5±0.4 3.4±0.9 --7.04-1.9 38.2±2.2
TABLE2 Comparison of measured lifetimes for 19zpt Method delayed coincidence delayed coincidence delayed coincidence delayed coincidence Coulomb excitation Coulomb excitation ~)
Ref.
T(316 keV) (psec)
T(612keV) (psec)
this work 4) 5) 6) v) s)
61.7 ~z2.1
38.2 4-2.2 38.0 ___5.0 29.0 ± 3.0
48.5 i 6 . 5 51.0 ±4.0 56.4 ± 3.2 53.0dz6.0 62.0i3.0
33.0±6.0 39.0±6.0
a) Two results are given in ref. s) for two normalizations. t h e weighted average o f 50.3___ 3.4 psec o b t a i n e d f r o m the two d e l a y e d coincidence results, b u t it is in g o o d a g r e e m e n t with the weighted average o f 58.6___4.2 psec for the B ( E 2 ) m e a s u r e m e n t s . The m e a s u r e d value for the lifetime o f the 612 level is in a g r e e m e n t with all the previously m e a s u r e d values except t h a t o f B e r a u d et al. 5). H o w e v e r , it s h o u l d be n o t e d t h a t the lifetimes r e p o r t e d in ref. 5) are smaller t h a n all o t h e r m e a s u r e d lifetimes for b o t h levels. N u c l e a r g - f a c t o r m e a s u r e m e n t s are directly d e p e n d e n t u p o n accurate values o f t h e m a g n e t i c field at the nucleus a n d the lifetime o f the excited state o f interest. K i n g et al. 9) have d e t e r m i n e d that p e r t u r b e d a n g u l a r correlation m e a s u r e m e n t s o f n u c l e a r
CENTRO[D-SHIFT M E A S U R E M E N T S
419
magnetic moments in Pt are more accurate if the sources are embedded in a nickel host rather than an iron host, because it is very difficult to determine the magnetic field at the nucleus in the iron host. Table 3 shows a comparison of values for the g-factors of the first two excited states in 1 92pt" Measured values are expected to be less than the predicted value Z/A = 0.406 of the hydrodynamical model, and to be in fairly good agreement with the predictions of the pairing-plus-quadrupole model (PPQ) of K u m a r and Baranger l o). However, this is not the case. King et al. 9) obtained a g-factor of 0.45___0.05 for the 316 keV level, using a lifetime of 51.8+2.0 psec for this level. Not only is this value not in agreement with the predicted value of 0.212 of K u m a r and Baranger, but it is greater than Z/A. If the g-factor is recalculated using the same experimental data, but with a lifetime of 61.7+2.1 psec, then a TABLE 3 Comparison of g-factors for 192pt r(psec) Z / A (hydrodynamical model)
g 0.406
316 ke V level
PPQ predicted value King et al. King et al.
51.8~2.0 61.7~2.1
0.212 a) 0.45 ±0.05b) 0.38 -t-0.05
29.0~z3.0 38.2~1.5
0.221 ~) 0.293 ±0.035 0.222±0.03
612 k e V level
PPQ predicted value refs. s.lx,12) refs. s. 11. lz) ") Ref. 10).
b) Ref. 9).
.q-factor of 0.38_+0.05 is obtained. This value is not in agreement with the PPQ prediction, but it is less than Z/A. The weighted average of three measurements 5. tl, ~2) of the g-factor of the 612 keV level is 0.293_+0.035, which is slightly greater than the PPQ prediction of 0.221. Each of the measurements used a lifetime of 29.0+3.0, as measured by Beraud et al. 5). If the same experimental data and a lifetime of 38.2__+ 1.5 psec are used, the g-factor is reduced to 0.222 +0.030. However, these experiments used a source embedded in an iron host, so that on the basis of the work of King et al. 9), these values should be expected to be slightly larger than those obtained if the experiments are done with a nickel-alloy host. As a final example of the versatility of this method of measuring lifetimes it may be noted that v(612) can be measured by comparing fl2-7(604) and //1-7(612) coincidence events with identification provided by detecting the 316 and 308 keV 7-rays in the Ge(Li) detector. The counting rates would be appreciably lower than in the present experiment, but the only decay scheme related correction would be due to//1-7(469) coincidence events. The size of the correction can be limited by the energy
420
G . J . SMITH A N D P. C. SIMMS
s e l e c t i o n i m p o s e d o n t h e 7 - t i m i n g d e t e c t o r . T h e shift in t i m e c a u s e d by the 469 k e V 7-ray c a n be easily m e a s u r e d by c o m p a r i n g fll-7(316) to fl2-~(316) c o i n c i d e n t e v e n t s w h i l e u s i n g the 469 a n d 604 k e V 7-rays for identification. T h e a u t h o r s wish to t h a n k J. H o l m f o r t h e use o f a n 192|r source.
References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12)
H. Kuhlman, thesis, Purdue University, 1969 H. Kuhlman, G. J. Smith and P. C. Simms, to be published C. M. Lederer, J. M. Hollander and 1. Perlman, Table of isotopes (Wiley, New York, 1967) p. 372 L. Keszthelyi, private communication via Z. W. Grabowski R. Beraud, 1. Berkes, R. Chery, R. Haroutunian, M. Levy, G. Marguier, G. Marest and R. Roughny, Phys. Rev. C1 (1970) 303 A. Schwarzschild, Phys. Rev. 141 (1966) 1206 W. Milner, F. McGowan, R. Robinson, P. Stelson and R. Sayer, Nucl. Phys. A177 (1971) 1 E. Bruton, J. Cameron, A. Gibb, D. Kenyon and L. Keszthelyi, Nucl. Phys. A152 (1970) 495 W. C. King, Z. W. Grabowski and R. P. Scharenberg, Phys. Rev. C4 (1971) 1382 K. Kumar and M. Baranger, Nucl. Phys. A122 (1968) 273 M. Levanoni, F. Zawislak and D. Cook, Nucl. Phys. A144 (1970) 369 D. Kenyon, L. Keszthelyi and J. Cameron, Can. J. Phys. 47 (1969) 2395
Nuclear Physics A202 (1973) 409--420; ~ ) North-HollandPublishino Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher
C E N T R O I D - S H I F T M E A S U R E M E N T OF THE M E A N LIFETIMES OF THE 316 A N D 612 keV STATES OF 19Zpt G. J. S M I T H and P. C. S I M M S Tandem Accelerator Laboratory, Purdue UniversiO', Lafayette, Indiana 47907 t Received 29 September 1972 (Revised 21 November 1972) Abstract: The mean lifetimes o f the 316 and 612 keV levels in 192pt were measured by means o f a new variation o f the centroid-shift method. The technique uses a triple coincidence among a fl-particle and two ~,-rays. Values obtained for the lifetimes are z ( 3 1 6 ) : 61.7±2.1 and z(612) = 38.2 ± 2 . 2 psec. The effect o f these results on the analysis o f the o-factors for these two states is discussed.
El
R A D i O A C T i V I T Y t 921r; measured flTY'c°in" t 92pt levels deduced T~"
I
1. Introduction A modified version of the centroid-shift technique has been used to measure the mean lifetimes of the first two excited states in 192pt" The method employs a triple coincidence between a fl-particle and two ~,-rays. An excited state of the nucleus is populated via fl-decay and is subsequently depopulated via emission of successive 7-rays. An idealized decay scheme is shown in fig. 1. The state B with mean lifetime
\
A
Fig. 1. An idealized decay scheme. State B is populated by f12 and decays by emitting a ~'-ray, 72, thus forming state A, which emits 71. Although fli also populates state A, such events are rejected by requiring a fl-7-~' triple coincidence. + Work supported by National Science Foundation. 409
410
G . J . S M I T H A N D P. C. S I M M S
z(B), is populated via/3-decay and decays by emitting y-ray 72. The state A with mean lifetime T(A), then decays by emitting Yl. The arrangement of the detectors is shown in fig. 2. A thin plastic scintillator detects/3-particles and starts a time-to-amplitude converter (TAC). The other plastic scintillation detector stops the TAC a fixed delay time t o after a y-ray is detected. The energy of the y-ray which stopped the TAC is determined by the detection of a second y-ray by a Ge(Li) detector operated in coincidence with the y-ray timing detector. For example, if 72 is recorded in the Ge(Li) detector at the same time as a fl-y coincidence occurs at the TAC, then 7t must have stopped the TAC. Similarly, if 71 is recorded by the Ge(Li) detector in coincidence with a TAC signal, then it must have been 72 which stopped the TAC.
GE(LI) SOURCE'
[---- T%
I PM TUBE BETADETECTOR' BETAABSORBER-
Fig. 2. Positions of the three detectors. The/~- and y-detectors are made o f plastic scintillator. A n aluminum disk is placed between the source and the),-detector to absorb fl-particles.
For the situation in which 71 stops the TAC, the time interval measured is
t(y 1)
=
to -
tt~ 2 - - tf82 + trr ~ +
z(B)+ z(A),
(1)
where t o is the inherent delay in the electronics, tp2 is the time of flight for the /3particle travelling to the detector, trp2 and trr I are determined by the rise times of the /~ and y detector pulses, and t(B) and T(A) are the mean lifetimes of the two states. Similarly, for the situation in which 72 is detected in the timing detector, the measured time interval is
t(y2) ==-to--tp2-tra~ +t,,2 +'c(B ).
(2)
Notice that/3x cannot interfere with the experiment because it cannot produce a triple coincidence. Thus there is no systematic difference between the /3-particles which start the TAC when either ?1 or 72 stop the TAC. All factors which relate to the fl-particle cancel, so the difference between the two time intervals is t ( ? l ) - t(y2) = z(A) + (trr, - trr~), or
T(A) =
(t(?,)--t(72)) - - ( t r w - tr72).
(3)
CENTROID-SHIFT MEASUREMENTS
411
The term (tr~~-tr~2) is produced by the difference in amplitude walk for the two v-rays in the y-timing device. There are many ways to minimize and correct for this effect 1.2). There are two other corrections which are independent of the decay scheme of the nucleus being studied. The peaks in the ",,-ray spectrum of the Ge(Li) identification detector sit on a background which is produced by Compton scattering and electronic pulse pile-up. A correction for the background can be obtained by using singlechannel analyzers (SCA) to set windows of equal width on the peaks and on the background near the peaks. Separate centroids (or average time intervals) can be recorded for the peak-plus-background (T) and the pure background (tB). It is also necessary to correct for the misidentification which occurs when there is an accidental coincidence between the Ge(Li) identification detector and the v-timing detector. Conventional techniques 2) can be used to recognize chance coincidences and record the corresponding average time interval t c from the TAC. The last correction depends on the decay scheme of the nucleus being investigated. If the decay scheme is complicated there may be several cascades which go through different states and produce the same identification y-ray. Thus, part of the time, the observed time interval ( t + A ) will be different from the correct time interval t. The time-interval difference A and the amount of mixing must be determined in a separate measurement. Several examples of this correction will be given in sects. 2 and 3. When all of these corrections are combined, the observed centroid T can be expressed as a combination of the desired time interval t and the three correction intervals: 7" = ~t + flta + ytc +(5(t + A)
~+fl+7+6 where ~, fl, 7 and 6 are the number of correct, background, chance and decay scheme related events included in the observed centroid T. This equation can be rearranged to yield an expression for the corrected centroid: (4)
t = T + B ( T - t13)+ C ( T - t c ) - D A
where B
]~
C-
y
D-
~
Eqs. (3) and (4) can be combined to yield a final expression for the mean lifetime z(A).
~(A) = ET(~,) - T(y2)] + S(y I)[T(y,) - t.(y,)] - B(~2)E r(~2) - t.(y2)] + c(y,)[ r(y,)-
to] - C ( ~ 2 ) [ T ( ~ 2 ) - t o ] - D ( ~ , ) A ( y , ) + O(y2)A(~2)--(t,,,- t,,2). (S)
Most experiments will not require all of these correction terms as will be shown in the examples given in sects. 2 and 3. Notice in eq, (5) that all of the correction centroids can be different for event 1 and 2 except for t c. When a chance coincidence
412
G . J . SMITH AND P. C. SIMMS
occurs the average time interval t c produced by the TAC will be the same as that observed with no identification. There are several advantages to this modified version of the centroid-shift technique. (i) The fast timing characteristics of the plastic detectors give good time resolution. (ii) The fl-detector has high efficiency due to the geometry of the experimental set-up. The source is placed flat against the face of the fl-dector so that the solid angle, and hence, the efficiency of the detector is high. (iii) The Ge(Li) detector has good energy resolution so that complicated decay schemes can be studied. 2. Measurement of lifetimes 2.1. THE 316 keV LEVEL OF 192pt
The major features of the decay scheme 3) for 192pt are shown in fig. 3. The two types of events which were used to measure the mean lifetime of the 316 keV level are E ( k e V ) J "rr
1200 (4)+
,c49
13o86o," 296
920
3+
785
4+
612
2'+
316
2+
612
:516
0
O+
Fig. 3. The major features of the decay scheme of ~92pt. To measure ~(316) f12-F(308) and f12-y(316) events are recorded in coincidence with detection of a 7 ( 6 1 2 ) a n d ~,(604), respectively, in the Ge(Li) detector. To measure z(612), f12-y(308) and fl2-7'(296) events are recorded in coincidence with detection ofv(296) andy(308), respectively, in the Ge(Li) detector.
f12-y(308) and f12-y(316) coincidences. The 612 and 604 k e y y-rays were recorded in the Ge(Li) detector to identify the energy of the y-ray which stopped the TAC. The fll transition does not cause any difficulty because it does not lead to a state which produces either of the identifying y-rays (604 or 612). For the moment we neglect all corrections, including the low intensity f13 transition.
CENTROID-SHIFT MEASUREMENTS
413
The difference between the two centroids produced by /32-7(308) and fl2-7(316) coincidences is the mean lifetime of the 316 keV state t ( 3 1 6 ) - t ( 3 0 8 ) = [ t o + r ( 9 2 0 ) + z ( 3 1 6 ) ] - t t o + r ( 9 2 o ) ] = z(316).
(6)
Several of the corrections contained in eq. (5) were not necessary in this case. The energies (308 and 316 keV) of the y-rays used for timing are so similar that the amplitude walk correction was negligible. The chance-to-true ratios for the Ge(Li) plastic coincidences were small and approximately equal for the two types of events. Thus a single chance-to-true ratio C was used. The two identification y-rays are so close in energy (604 and 612 keV) that the same background window can be used for both peaks, so tB(316 ) = tB(308 ) = tB. When 7(604) is recorded in the Ge(Li) detector, the fl-particle and y-ray are uniquely identified as f12 and 7(316); so there is no A(316) correction term. When 7(612) is recorded in the Ge(Li) detector, y(308) will usually stop the TAC; but for a few percent of the time, y(589) will stop the TAC. The procedure for measuring this correction A will be discussed below. When all of the necessary factors for this case are included, the expression for the mean lifetime of the 316 keV level is r(316) = (T6o4 - 7612)(1 + C) + B 604(Tb04. --/B) -- B612(T612 --/B) N612(589)
+
A.
(7)
U612(589) + X612 (308) A new notation has been used for clarity in writing this expression. The energy of the y-ray which stopped the TAC is shown in parenthesis as before. In addition the energy of the ),-ray identified by the Ge(Li) detector is shown as a subscript. Thus, 7"6o4 and T612 are the observed centroids when the 604 or 612 keV 7-rays are identified by the Ge(Li) detector regardless of the particle that stopped the TAC; B604and B612 are the ratio of background to peak counting rates for the 604 and 612 keV y-rays recorded in the Ge(Li) detector. When the 612 keV y-ray is identified in the Ge(Li ) detector, the two components of the co unting rate are N61 z (308) and N612 (589) for 308 and 589 keV y-rays in the timing detector. In fig. 3 we see that the correction term A can be determined by the difference in flight time between /32 and/33 and the difference in mean lifetime between the 1200 and 920 keV states: A = (z(1200)-tp3 ) - ( r ( 9 2 0 ) - t p 2 ). This combined time correction was determined by measuring the difference between the centroids which were produced when the 308 and 589 keV 7-rays were recorded in the Ge(Li) detector. The TAC was stopped by y(296), y(316), or y(612). No matter which y-ray stopped the TAC, the 589 centroid depends on/33 and z(1200), and the 308 centroid depends on f12 and r(920).
414
G . J . S M I T H A N D P. C. S I M M S
2.2. T H E 612 keV L E V E L O F t9zpt
The mean lifetime of the 612 keV level can be determined by comparing the centroids recorded for f12-y(308) and fie-y(296) coincidences. If there were no correction factors due to chance coincidences, background or decay scheme peculiarities, the two average time intervals would be T296 =
N(308)to + N(316)[/o + z(612) + z(316)], bi(308)+ N(316)
T3os = N(296)[t 0 + z(612)-I + N(316)[to + z(612) + z(316)] N(296) + N(316)
(9) (10)
Now t o is the combination of the fixed delay in the system, the flight time of/32 , and the mean lifetime of the 920 keV level; N(296), N(308) and N(316) are the number of 296, 308 and 316 keV y-rays recorded by the timing detector, respectively. If there were no branching of the 612 keV level or other decay complications, N(296), N(308), and N(316) would be equal and eqs. (9) and (10) would reduce to T296
=
7"308 =
"4-½Z(612) + ½Z(316),
(11)
tO+Z(612)+1Z(316)"
(12)
t0
Subtraction of eq. (11) from eq. (12) gives ½z(612) = T308 - -
T296 .
(13)
Eq. (13) is only an approximation, but it is interesting to note that the 316 keV y-ray causes the observed centroid shift to be only half of the mean lifetime of the state being studied. When the lower intensity transitions in the decay scheme are included, the expressions for the observed centroids become more complicated. If the 296 keV y-ray is recorded in the Ge(Li) detector, f13 transitions must be included when either the 589 keV or 316 keV y-rays stop the TAC: T296
=
{N(308)to + N(316)[to + z(612) + z(316)] + N(589)[to + h i
+ N'(316)[to + A + z(612) + z(316)]] × {N(308) + N(316) + N(589) + N'(316)]- ~, (14) where N(589) and N'(316) are the number of 589 and 316 keV y-rays recorded following /33 transition. The difference in flight time between/33 and/32 and the difference between the mean lifetimes of the 1200 and 920 keV levels are included in A. This is the same correction that was discussed in subsect. 2.1. The probability of detection is essentially the same for the 308 and 316 keV y-rays, so by setting N(308) = N(316), eq. (14) may be written T296 =
N(316) + N'(316) [z(612)+z(316)] 2N(316) + N(589) + N'(316) N(589)+ N'(316) + A. (15) 2 N(316) + N(589) + N'(316)
t 0 q- ..
CENTROID-SHIFT MEASUREMENTS
415
When the 308 keV 3)-ray is detected by the Ge(Li) detector, there is no contribution by the f13 transition to the average time interval. However, there are still flz-y(612) coincidences present, so that the average time interval is Tao8 = [N(296)[to + r(612)] + N(316)[to + z(612) + z(316)] + N(612)[t o + z(612)]} x{N(Z96)+N(316)+N(612)} -1,
(16)
where N(612) is the number of 612 keV ),-rays recorded by the timing detector. Again, the detection probabilities for the 296 and 316 keV y-rays are essentially the same so that N(296) = N(316) and T3o 8 = t o + r ( 6 t 2 ) +
N~(3!6) z(316). 2N(316)+ N(612)
(17)
An expression for the mean lifetime r(612) of the 612 keV state can be obtained by subtracting T296 [eq. (15)] from T3o 8 [eq. (17)] and solving for z(612). Background and chance coincidence corrections must be included as shown in eq. (5) and eq. (7): ½D, r(612) = (1 + ~)[(1 -I-C)(T308 - T296) + B30s(T308 - t , ) - B296(T296 --/B)] +(02-D3)z(316)+D4A.
(18)
There are four correction factors which depend on the decay scheme. D 1 -
Nz96(316)+Nz96(589)
N296(316) + ½[N296(589) + N-~96(316)] D 2 --
N296(316) + N296(316) 2N296(316) + Nz96(589) + N~96(316) D3
D4 =
N3°8(316) 2N3o8(316)+ N3o8(612)
,
Nzge(589)+N296(316) • 1, 2N296(316) + N296(589) + N~96(316)
where N~96(316 ) and N296(589 ) are the number of 316 and 589 keV 7-rays which follow f13 transitions and stop the TAC when the 296 keV "~-ray is identified in the Ge(Li) detector (remember that N296 (316) is the counting rate produced by 316 keV ~,-rays following f12 transitions); N3os(612 ) is the number of 612 keV 7-rays which stop the TAC when the 308 keV ~,-ray is identified in the Ge(Li) detector. There is one additional correction factor (1 + ~) in eq. (18) which has not been discussed previously. It is possible for conversion electrons from the 296, 308 and 316 keV transitions to be recorded in the fl-detector. For example, a conversion electron from the 308 keV transition could start the TAC, the 316 keV y-ray could stop the
4t6
G.J. SMITH AND P. C. SIMMS
TAC, and the 296 keV ~,-ray could be recorded in the Ge(Li) detector. Since the conversion coefficients for all three transitions are approximately the same ( ~ 6~o), the conversion electrons will cause the same shift in both centroids (T30s and 7"296) so the magnitude of the shift is not important. However the conversion electron events do effect the results through the weighting factors. That is, since both of the centroids contain contributions from the conversion-electron events, the separation of the centroids is reduced. Therefore a small correction (1 + e ) is necessary in the final formula; 0~ is the ratio of the probability of detecting a conversion electron to the probability of detecting a fl-particle.
3. Apparatus and procedure The electronic system used in this experiment will be described in detail in a subsequent publication 2). A summary of the instrument and all of the operating parameters will be given here. The ~92[r source was made by thermal neutron bombardment of chemically pure It, which had been evaporated onto thin A1 foil. The plastic detectors were made from 2.5 cm diameter NE111 scintillator; the fl-detector was 4 mm thick, and the y-detector was 2.5 cm thick; RCA 8575 photomultiplier tubes were used for both detectors. A 30 c m 3 coaxial Ge(Li) detector with an energy resolution of 2.0 keV at 1.33 MeV was used. Constant-fraction timing discriminators were used to provide good time resolution (550 psec F W H M for 300 keV 7-rays). The fl-~ true to chance ratio was approximately 100, and the ~/-Ge(Li) true-to-chance ratio was 65 or larger. In order to obtain adequate triple coincidence counting rates, the single counting rates were high. The fl-rate was approximately 106 counts/see, the v-timing rate was approximately 105 counts/see and the Ge(Li) rate was approximately 3 x 104 counts/see. The flq, double coincidence rate was approximately 3 × 104 counts/see, yet the fl-~-~ triple coincidence rate for the events of interest was only a few counts per second. The measurement of the mean lifetime of the 316 keV level required 6d and the 612 keV level required 2d. Pulse-height analysis was provided in the fl-channel by connecting a gated pulsestretcher directly to the anode of the photomultiplier. Whenever a coincidence occurred between the timing detectors, the gate was opened, the anode pulse was integrated and stretched, and an output pulse was produced which could be processed by conventional single-channel or multichannel analyzers. Good resolution was maintained for the Ge(Li) detector by being careful to obtain proper pole-zero compensation and by using active DC restoration in front of the pulse-height analyzers. The spectrum in fig. 4, which shows how clearly the 604 and 612 keV ~,-rays were resolved, was taken with a counting rate of 3 x 104 counts/see in the Ge(Li) detector. An analog-to-digital converter ADC, a routing circuit, and a set of sealers were used to record average time intervals. Each TAC pulse was converted to a pulse train
CENTROID-SHIFT MEASUREMENTS
417
by the ADC. Each pulse train was routed to a pair of scalers according to the energy of the 7-ray identified in the Ge(Li) detector. One scaler counted the total number N of pulses from the A D C while the other counted the number of pulse trains, n. The average time interval is (N/n)x (time calibration). The average time intervals and all of the counting rates were printed out at 80 min intervals so that statistical tests could be made for systematic errors. Time calibrations were performed several times during the experiment with an air-core adjustable-length delay line. Single-channel analyzers (SCA) were used for all three detectors. A discrimination level of 180 keV was set for the/J-detector. It is impossible for a 7-ray to enter the 7COUNTS 604
3000-
2000i89
I000-
,
~ -
2'o go 6'o do ,;o CHANNEL NUMBER Fig. 4. Ge(Li) detector spectrum showing the 7-rays of 192pt near to 600 keV. The shaded boxes indicate the SCA windows set on the 604 and 612 keV peaks and on the backgreund.
detector, backscatter into the fl-detector and lose 180 keV or more. Thus, coincidences between the two detectors caused by back-scattered 7-rays were avoided. A SCA window was set for the plastic detector to include approximately 50~ of the C o m p t o n distribution below the C o m p t o n edge of the 316 keV y-ray. This window reduced the probability of detecting the higher-energy 7-rays. The Ge(Li) detector spectrum was expanded by means of a biased amplifier, and windows were set on the peaks of interest, as shown in fig. 4. A third window was set on the background, so that an appropriate correction could be made for background y-rays which occur under the peaks.
418
G.J. SMITH AND P. C. SIMMS
4. Results and discussion T a b l e 1 gives the m e a s u r e d c e n t r o i d shifts a n d the values o f the various c o r r e c t i o n factors. T h e time difference A i n t r o d u c e d by the/~3 transitions is - 8 6 + 18 psec. T h e m e a n lifetimes are 61.7_+2.1 psec for the 316 keV level a n d 38.2_+2.2 psec for the 612 keV level. T a b l e 2 c o m p a r e s these results with previous lifetime m e a s u r e m e n t s using d e l a y e d coincidence techniques a n d lifetimes calculated f r o m B (E2) m e a s u r e ments via C o u l o m b excitation. The present value for ~(316) is n o t in a g r e e m e n t with TABLE 1 Experimental results and corrections for mean lifetimes of 192pt 316 keV level centroid-shift x (1 + C ) correction for background in Ge(Li) detector correction for/~3 and ~(589) mean lifetime
psec 60.0~ 1.8 3.4±0.5 --1.7±0.9 61.7±2.1
612 keV level centroid-shift × (1 + C ) × (1 +~) ×2/Dx correction for background in Ge(Li) detector × 2/D~ (Dz--D3) xT(316) x2/D~ correction for f13 and y(589) (D4A × 2/D1 ) mean lifetime
38.3±1.1 3.5±0.4 3.4±0.9 --7.04-1.9 38.2±2.2
TABLE2 Comparison of measured lifetimes for 19zpt Method delayed coincidence delayed coincidence delayed coincidence delayed coincidence Coulomb excitation Coulomb excitation ~)
Ref.
T(316 keV) (psec)
T(612keV) (psec)
this work 4) 5) 6) v) s)
61.7 ~z2.1
38.2 4-2.2 38.0 ___5.0 29.0 ± 3.0
48.5 i 6 . 5 51.0 ±4.0 56.4 ± 3.2 53.0dz6.0 62.0i3.0
33.0±6.0 39.0±6.0
a) Two results are given in ref. s) for two normalizations. t h e weighted average o f 50.3___ 3.4 psec o b t a i n e d f r o m the two d e l a y e d coincidence results, b u t it is in g o o d a g r e e m e n t with the weighted average o f 58.6___4.2 psec for the B ( E 2 ) m e a s u r e m e n t s . The m e a s u r e d value for the lifetime o f the 612 level is in a g r e e m e n t with all the previously m e a s u r e d values except t h a t o f B e r a u d et al. 5). H o w e v e r , it s h o u l d be n o t e d t h a t the lifetimes r e p o r t e d in ref. 5) are smaller t h a n all o t h e r m e a s u r e d lifetimes for b o t h levels. N u c l e a r g - f a c t o r m e a s u r e m e n t s are directly d e p e n d e n t u p o n accurate values o f t h e m a g n e t i c field at the nucleus a n d the lifetime o f the excited state o f interest. K i n g et al. 9) have d e t e r m i n e d that p e r t u r b e d a n g u l a r correlation m e a s u r e m e n t s o f n u c l e a r
CENTRO[D-SHIFT M E A S U R E M E N T S
419
magnetic moments in Pt are more accurate if the sources are embedded in a nickel host rather than an iron host, because it is very difficult to determine the magnetic field at the nucleus in the iron host. Table 3 shows a comparison of values for the g-factors of the first two excited states in 1 92pt" Measured values are expected to be less than the predicted value Z/A = 0.406 of the hydrodynamical model, and to be in fairly good agreement with the predictions of the pairing-plus-quadrupole model (PPQ) of K u m a r and Baranger l o). However, this is not the case. King et al. 9) obtained a g-factor of 0.45___0.05 for the 316 keV level, using a lifetime of 51.8+2.0 psec for this level. Not only is this value not in agreement with the predicted value of 0.212 of K u m a r and Baranger, but it is greater than Z/A. If the g-factor is recalculated using the same experimental data, but with a lifetime of 61.7+2.1 psec, then a TABLE 3 Comparison of g-factors for 192pt r(psec) Z / A (hydrodynamical model)
g 0.406
316 ke V level
PPQ predicted value King et al. King et al.
51.8~2.0 61.7~2.1
0.212 a) 0.45 ±0.05b) 0.38 -t-0.05
29.0~z3.0 38.2~1.5
0.221 ~) 0.293 ±0.035 0.222±0.03
612 k e V level
PPQ predicted value refs. s.lx,12) refs. s. 11. lz) ") Ref. 10).
b) Ref. 9).
.q-factor of 0.38_+0.05 is obtained. This value is not in agreement with the PPQ prediction, but it is less than Z/A. The weighted average of three measurements 5. tl, ~2) of the g-factor of the 612 keV level is 0.293_+0.035, which is slightly greater than the PPQ prediction of 0.221. Each of the measurements used a lifetime of 29.0+3.0, as measured by Beraud et al. 5). If the same experimental data and a lifetime of 38.2__+ 1.5 psec are used, the g-factor is reduced to 0.222 +0.030. However, these experiments used a source embedded in an iron host, so that on the basis of the work of King et al. 9), these values should be expected to be slightly larger than those obtained if the experiments are done with a nickel-alloy host. As a final example of the versatility of this method of measuring lifetimes it may be noted that v(612) can be measured by comparing fl2-7(604) and //1-7(612) coincidence events with identification provided by detecting the 316 and 308 keV 7-rays in the Ge(Li) detector. The counting rates would be appreciably lower than in the present experiment, but the only decay scheme related correction would be due to//1-7(469) coincidence events. The size of the correction can be limited by the energy
420
G . J . SMITH A N D P. C. SIMMS
s e l e c t i o n i m p o s e d o n t h e 7 - t i m i n g d e t e c t o r . T h e shift in t i m e c a u s e d by the 469 k e V 7-ray c a n be easily m e a s u r e d by c o m p a r i n g fll-7(316) to fl2-~(316) c o i n c i d e n t e v e n t s w h i l e u s i n g the 469 a n d 604 k e V 7-rays for identification. T h e a u t h o r s wish to t h a n k J. H o l m f o r t h e use o f a n 192|r source.
References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12)
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