- Email: [email protected]
K electron capture ratios in 59Ni decay
4.C
[ I
Nuclear Physics A218 (1974) 372--380; ~ ) North-Holland Publishing Co., Amsterdam N o t to be reproduced b y p h o t o p r l n t or microfilm without written permission f r o m the publisher
NUCLEAR MATRIX ELEMENTS FROM L/K ELECTRON CAPTURE RATIOS
IN S9Ni D E C A Y t w. M. CHEW, A. C. XENOULIS and R. W. FINK School of Chemistry, Georgia Institute of Technology, Atlanta, Georgia 30332 and J. J. PINAJIAN Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830 t* Received 3 October 1973
Abstract: Using a
recent theoretical method, the ratio of nuclear matrix elements R-0 vFzll)was o determl'ned tobe eih +°'aSor25.22_o:xTmthesecond+028--( VF°220-- ~/3A ~ Fz21/ t er 205 • 0_0.55 forbidden nonunique decay of 8 × 104 y S9Ni. These values of R were obtained from a value of L3/K = 0.0084-0.002 found by subtracting the theoretical ratio (Llq-Lz)/K ~ 0.113 (based on QEc = 1070±8 keV) from the total ratio L/K = 0.121-4-0.002, which was measured with a reactor-produced, doubly-mass-separated 59Ni source introduced as gaseous nickelocene, (CsHs)2Ni, into a wall-less, anticoincidence, multiwire proportional counter. The 854-1008 eV L and the 8.33 keV K peaks were measured simultaneously.
I E
RADIOACTIVITY 59Ni [from SSNi (n,~)]; measured L/K EC ratio; calculated (Lx-I-L2)/K ratio; deduced La/K ratio, nuclear matrix element ratio; multiwire proportional counter; isotope separated sources. Enriched 58Ni target.
]
I
1. Introduction A m e t h o d has recently been developed i) to determine a ratio of n u c l e a r matrix elements from the L / K electron capture ratios of n o n u n i q u e transitions o f second- or higher-order forbiddenness. I n the present work, the L / K electron capture ratio o f 5 9Ni is determined, a n d the result is used to o b t a i n a ratio of nuclear matrix elements. The decay o f 8 x 10 4 y s 9Ni is a particularly good case to study. It is a second-forbidden n o n u n i q u e electron capture t r a n s i t i o n only to the g r o u n d state of 5 9C0" It also forms a v a p o r o u s c o m p o u n d , nickelocene, and, therefore, can be studied by m e a n s o f the multiwire p r o p o r t i o n a l c o u n t e r technique that has recently been i m p r o v e d in this laboratory. There have been n o previous electron capture studies of 59Ni.
2. Experimental 2.1. SOURCE PREPARATION The radionuclide 59Ni was prepared by t h e r m a l n e u t r o n irradiation of 99.89 % enriched 5SNi in the S a v a n n a h River Reactor. After the irradiation, the sample was mass t Supported in part by the US Atomic Energy Commission. tt Research supported by the US Atomic Energy Commission under contract with the Union Carbide Corporation. 372
NUCLEAR MATRIX ELEMENTS
373
separated twice and converted to 59NiCI2. The 59Ni activity was introduced into the proportional counter in the form of gaseous nickelocene, (CsHs)2Ni. This is a rather reactive compound and decomposes in air, and also in some organic solvents such as acetone, ethyl alcohol, and ethyl ether. The sample was converted to nickelocene in the following manner. Finely crushed potassium hydroxide was placed in a beaker and 1,2 methoxyethane was added with a magnetic stirring bar. Freshly cracked cyclopentadiene was added, with stirring, followed by the nickel sample dissolved in dimethylsulfoxide. The nickelocene was precipitated by the addition of hydrochloric acid and ice. After filtration, the nickelocene was dissolved in hexane and transferred to a sublimation unit which was then placed in a hot oil bath. After sublimation, the nickelocene was transferred into glass sample containers. The entire synthesis and subsequent sublimation was performed just prior to each measurement using a glove bag in an inert atmosphere and required about 2 h. Nickelocene, which forms dark green crystals, has a slight tendency to sublimate (2 m m vapor pressure at 100 ° C), and this physical property was utilized to introduce the gaseous nickelocene into the proportional counter under vacuum. 2.2. THE PROPORTIONAL COUNTER SYSTEM AND METHOD OF MEASUREMENT The proportional counter measures the energy of both the X-rays and Auger electrons emitted after an electron capture event in the gas. In the wall-less multiwire proportional counter used in this work, wall effects and background were effectively reduced by a surrounding anticoincidence ring counter. A diagram of the counter is
I I 50Fro
L_m
,oo Tub~og~ - -
"
Iolof$
L_ TO "Preomp
Total Volume 15 Liters t"
102em
Fig. 1. The detailed arrangement of the multiwire proportional counter used in the determination of the L/K electron capture ratio of 59Ni. The insert represents the geometrical placement of the anode, or counting, and the cathode, or high voltage, stainless steel wires, depicted as small and large dots respectively.
374
w.M. CHEW et al.
shown in fig. 1. There are four internal effects which further necessitate an anticoincidence gate: (i) Injection (pulses in the central counter caused by free electrons being released into it through the weak field regions between the cathode wires defining the boundary between the central and ring counters following ring counter avalanches); (ii) Induction (electrostatically induced pulses between the ring counter and the central counter); (iii) Pulse degradation (due to recombination of ion pairs in the weak-field regions and the end effects); and (iv) After-pulsing (pulses occurring after an avalanche due primarily to negative ion formation and the emission of secondary electrons by the cathode wires when hit by the positive ion sheath). The central counter pulses are blocked for 180 ps following a ring counter event. This reduces the background and removes the effects of induction and injection. In order to remove the effect of afterpulsing, a paralysis, consisting of an anticoincidence gate, of 6 msec is introduced following each central counter event. Pulse degradation results in a tail of constant intensity below each peak that extends to zero energy. Corrections for these degraded events are applied to the spectra during the data analysis. All these effects have been taken into consideration in previous studies 2, a). In all the previous electron capture ratio investigations, the K, L, and M spectra were measured sequentially. The peak counts, however, had to be normalized to the same amount of activity and to the same real counting time. That is, if the activity changed significantly from one measurement to another, for instance if the activity adsorbed on the counter walls, or the activity had a short half-life, or if a new filling was made, it was necessary to normalize the spectra to correspond to the amount of activity present in the counter. This was done by monitoring the K peak activity of the central counter. In the same manner, the three spectra had to be corrected for the different deadtimes of the electronics in the K, L, and M regions. It was necessary to assume that experimental conditions did not change from one measurement to another. By measuring the K and L spectra simultaneously, the errors associated with these normalization and deadtime corrections are eliminated. In order to eliminate these corrections, as well as insure homogeneity of the conditions during the measurements, the electronic system was revised so as to permit simultaneous measurement of the K and L energy regions. The revised block diagram for the L/K electron capture ratio measurement is shown in fig. 2. Two separate Tennelec TC-200 amplifiers for the K and L regions, respectively, were used to obtain the K and L energy regions of the central counter spectrum. These two amplifiers with different electronic gains were necessary, in order to store simultaneously the K and L peaks with their large separations (8.33 keV and 854-1008 eV, respectively) in two separate 128-channel analyzers. It should be emphasized that since two different amplifiers were used, the output of each had to be controlled by the same logic signals, in order to assure identical electronic deadtime and homogeneity o f measuring conditions. The controlling logic
NUCLEAR MATRIX ELEMENTS • -t~,ng,, Ch. . . . ,Ana,yzer Al i
RingCounter
I~
~
~
~ I SingleChannelAnalyzer SI
~--~LDiscrimi ~-- Logic
i~/I
375
I Discrimi..... A ]
Generator I
I ParalysisG.....
tor
j
r m ~ D m ' ~ ]
DelaY AmPlifier~ I D " I
LLi ....
~
Del ay Ampinh e r ~......m,..~K L.....
Gatej
PulseHeightAnalyzer ND-~lO
I'c" KcAr~0P/itier~
Gate
Fig. 2. The electronic block diagram for the simultaneous measurement of the L and K peaks in 59Ni decay. The path of the analog signals from the central counter to the pulse height analyzers is shown by the heavy lines. signal from the logic generator *, is initiated by pulses from either the central counter or the ring counter. The output of the L amplifier was also used to trigger discriminator A and the paralysis generator (see fig. 2). Since K capture events produce saturated pulses in the L amplifier, they, as well as L events, trigger the lower level discriminator A and the paralysis generator, the output pulses of which are necessary for proper operation of the logic generator. The level of discriminator B was set just above the L peak from ring counter amplifier 2, in order to provide the necessary anticoincidence ring counter pulse to the logic generator. The L and K linear gates will transmit the L and K signals, respectively, unless a pulse from the logic generator is present. The L and K peaks were stored in individual 128-channel ND-110 pulseheight analyzers. The path of the analog signals from the central center to the multichannel analyzers is shown by the heavy lines in fig. 2. Initial attempts to record both spectra in two halves of a 512-channel analyzer by multirouting were not fruitful, because of difficulties associated with the multirouting logic signals coming from the overlapping energy region between the two spectra. Since the K and L spectra were recorded simultaneously, and therefore with the same electronic deadtime, no time normalization was necessary. The deadtime of these measurements, however, was determined, in order to permit subtraction of background spectra with a measurement time equal to that of the K and L spectra. The deadtime of the system was measured by comparing the readings of scalers 1 and 2 which recorded the gated and ungated output of the pulser. The pulser gate, t This logic generator consists of the following units in fig. 2 of ref. a): gating signal gen. B, gating signal hold-off control, coin. gate, gating signal gen., and the OR gate. The paralysis generator consists of lower level disc. and gating signal gen. A in the same figure.
376
w.M. CHEW et aL
together with the K and L linear gates, blocked any signals occurring during the output signals of the logic generator. Nickelocene has a tendency to be deposited on the counter walls. K X-rays from decaying atoms on the wall have a small probability to be recorded in the central counter without triggering an anticoincidence gate in the ring counter, while L X-rays are completely absorbed on the ring counter. An increase of the activity absorbed on the walls, therefore, could give a slightly low L/K ratio. In order to correct for this effect, it is necessary to determine the number of K X-rays that originate from the walls during the course of each measurement. Scalers following single-channel analyzers A and B to monitor the singles ringcounter K peak activity and the gated central counter K activity, respectively, were set up so that this correction could be estimated. A decrease in the amount of gaseous activity because of absorption on the walls would result in a larger decrease in the counting rate of the central counter than in the ring counter, since the ring counter has a much greater efficiency of detecting decays from the wall. The contribution to the central counter K spectrum of the activity on the walls was determined as a function of the readings of the monitors. The readings of the monitors were recorded every ten minutes and the L/K measurement was discontinued before the correction for the wall contribution became substantial. The overall correction for this effect to the final L/K capture ratio is very small and typically amounted to no more than 1 ~ (see below). 2.3. SPECTRAL MEASUREMENTS AND EVALUATION OF THE INTENSITY RATIO NL/NK Owing to the high deadtime ( g 80~) caused primarily by the long paralysis time following each central counter event, several independent measurements of the K and L peak intensities were carried out for about 6 h each, and in order to minimize the amount of the activity absorbed on the walls of the counter, the measurements were carried out at 72 ° C. Typical L and K spectra are shown in fig. 3. These L and K spectra were taken simultaneously at 4 atm pressure with the same gas gain ( ~ 104), but with different relative electronic gains of 8.45 and 1.0, respectively. Background was determined by filling the counter before and after each measurement with the same gas mixture and pressure of argon plus 15~ propane. An external 57Co source of 14.4 keV v-rays was used to recalibrate to identical gas gains. After the background spectra were corrected for deadtime, normalized to unit clocktime, and subtracted from the K and L energy spectra, the K and L peak intensities were corrected for degraded events, and the intensity ratio N L / N K was calculated to be 0.125_+0.002, a weighted average of ten independent measurements, where the error limit represents the probable error. 3. Corrections and final results
In order to find the L/K electron capture ratio, i.e. the ratio of the probabilities for electron capture from the L and K shells, the ratio of the intensities, N L / N ~ , must be
N U C L E A R M A T R I X ELEMENTS I
377 |
.~
L PEAK
K PEAK
c
.7 o/
c..)
\
../
"x •\
m
J
e_
!
¢
I
100
60
120
20
40
60
80
ioo
12o
CHANNEL NUMBER
Fig. 3. Typical L and K spectra of S9Ni after subtraction of background. The K peak is at 8.33 keV and has resolution typically of 18% F W H M . The L peak consists of three lines ranging from 853-1008 eV and has a typical total resolution spread of 52%.
corrected for the following effects: (i) the probability, P1, that a photon strikes a central-counter cathode wire; (ii) the probability, P2, that an X-ray passes from the center counter through the ring counter undetected; and (iii) the probability, P3, that an X-ray escapes through the ends of the counter. These probabilities are dependent on photon energy, gas pressure and mixture, and counter dimensions. For the L/K ratio, the following equation is applicable 4): L - NL { l _ ¢ o K ( k ~ p ~ o ) + k # p (- oa ) v tj j - ~ , K, , ~L. - ~ P(1) , K
(1)
NK
where co,: is the K shell fluorescence yield of the daughter (Z = 27), k~ is the fraction of K~ X-rays in the K series of the daughter, and k~ is the corresponding quantity for the Kp X-rays. The quantity P~ is equal to 101 +1°2 +103, where g refers to the evaluation of the probabilities for either the K~ or the K~ (g = a, fl) X-rays. The values of all the quantities used in determining the L/K ratio are presented in table I with references. The superscript (0) indicates the correction for the decrease of the TABLE 1 Values used to determine the L/K orbital electron capture ratio Quantity
p
p(1)
p8¢o)
co,<
k~
k~
Value Reference
0.0048 4)
0.0084 4)
0.0080 4)
O.381 s)
O.881 5)
O.I 19 s)
378
w.M. CHEW et aL
pulses in the K peak due to the escape of K X-rays originating in the central counter that do not trigger an anticoincidence pulse. The superscript (1) indicates the increase of the L peak due to the escape of a K, X-ray originating in the central counter without triggering an anticoincidence pulse. The final result for the L/K capture ratio is: L/K = 0.121___0.002, where the error limit represents the probable error. In the present work the total contribution due to the degradation tails was 8.5~o for the K region and 3.4~o for the L region. The probable error due to counting statistics was less than IX, and the error due to the wall adsorption was also less than 1~, not only due to the care taken during the measurements, but also due to the fact that the gas filling stopped more than 98~o of the K X-rays from the walls which might have entered the central counter.
4. Discussion and comparison with theory The electron capture decay of 59Ni to the ground state of 5 9Co requires a spin change of two units and no parity change. In such a second-forbidden nonunique electron capture process, capture of electrons from atomic orbits other than the s~ and p½ becomes significant. Specifically an L 3 (pk) contribution to the L / K ratio is expected. As has been shown recently 1), such a contribution can be utilized to determine certain of the matrix elements involved in the electron capture process. Using the theory of Behrens and Btihring 6) and certain approximations applied by Vatai :), the electron capture decay constant can be written as follows for capture of an electron from the X-shell: =
2rc2 nx C x f x ,
(2)
where X = K, L 1 , L2, . . . , f x = ~i n q x2f l x2 B x , n x is the occupation number, and C x = r 2 ( p x R ) 2(kx- 1)(qx R ) 2(kv-1)
x
VF°,n-l,1
t
aZ / V F O - - x / i n + l ) / n A F ° n 1) 2 k x + l ~ .... o . , •
(3)
Within Vatai's approximations ~), it is obvious that for electron capture ratios in which atomic shells withequal values of the quantum number k x are involved, the terms that include the form factors (AF°rz and VF°rz ) cancel, and, therefore, such electron capture ratios are independent of the nuclear matrix elements. Specifically, the ( L ~ + L 2 ) / K ratio is independent of the nuclear matrix elements, because all three orbits have k x = 1. The ratio (L~ + L 2 ) / K can be determined from the following expression: (L, + L 2 ) / K ---- (q~lfl2 B L l + qL2 4. ill.2 2 BLE)/qK4-f12 BK ' (4) where fix are Coulomb amplitudes, B x are exchange corrections, and q x is the neutrino
N U C L E A R MATRIX ELEMENTS
379
emission energy for capture to the X-shell. Using eq. (4) and values of fix and B x from refs. 7, a), and QEC = 1070+8 keV [ref. 9)], the (L 1 + L 2 ) / K ratio for the decay of 59Ni was calculated to be 0.113. Since the K and L Coulomb amplitudes and exchange corrections appear in eq. (4) as ratios, and the errors associated with these individual terms are correlated, the final error associated with the calculated ( L x + L 2 ) / K ratio is negligible. The difference (L/K)~xp-[(Ll + L2)/K]eale = 0.1210.113 = 0.008___0.002 represents the L3/K contribution, i.e. the ratio of capture from the 2p+ and the Is+ orbits, where the error is contributed exclusively by the uncertainty in the experimental measurement. In contrast to the (L 1 + L2)/K ratio, the La/K ratio is dependent on the nuclear matrix elements involved in the electron capture process. Using eqs. (2) and (3), I0
V'
I
1
I
I
I
16
[8
20
22
24
i0 -r
P'3
._I
i0 -2
jo-3 14
R
26
28
:( VF;~o- 3-v'3-7-~"F~,2, )/VF;,,
Fig. 4. The theoretical La/K ratio plotted as a function o f the nuclear matrix ratio R for the limited range of R pertinent to a comparison with the experimental measurement. The measured La/K ratio is represented by the horizontal line and its associated error, by the height of the shaded area. Two values of R, 20.50_+0"~. and 25.22+°'2a_o.t7,are deduced from this comparison.
380
W.M. CHEW et al.
and n = 2 = A J, we can derive for L3/K: L3/K = (p23 q23 fl2jq~ f l 2 ) { ( x / ~ _ l ~ Z R ) / ( ~ / ~ _ ½aZR)}2,
(5)
where I-VF0
/ R = /
4 ~ A F 0 -I 220--'__2_ 2211 VF°11
_l,
is the fine structure constant (1/137) and Px is the m o m e n t u m o f the b o u n d state electron in the X-subshell. It should be pointed out that such a dependence of the L a / K ratio on the form factor coefficients is possible because the K and L a orbits are characterized by different k x values, 1 and 2, respectively. Using eq. (5) the variation o f the L a / K ratio was calculated as a function of R, and the result is plotted in fig. 4 for a certain range o f R. The ratio of the shape factors becomes infinite at R = 23.21 and there the L a / K ratio can be very large. The quadrupole dependence o f the L a / K ratio on the ratio o f the matrix elements permits two possible values o f R for a given L a / K ratio. The physical significance of this feature, if any, is not clear; it is obvious, however, that only one o f the values is relevant. By comparing the experimental L a / K ratio and its associated error, which is represented in fig. 4 by the shaded area, with the theoretical calculation, the value o f the nuclear matrix element ratio, R, is determined to be either -~a . . . . ~n . . +0.350.55 or o~ . . . . ,')0 . . +0.280.17. It should be mentioned that since the theoretical treatment utilized in this study does not permit any further qualification o f this double value o f the ratio of the matrix elements, both of these values should be considered. These experimental ratios o f nuclear matrix elements can be c o m p a r e d with the results o f theoretical calculations using different nuclear models. A realistic nuclear model should be able to reproduce either the one or the other o f the ratios.
We are indebted to E. Vatai for m a n y helpful discussions and suggestions during his exchange visit to our laboratory. We thank J. G. Pengra and J. P. Renier for helpful consulations on certain experimental aspects of this work.
References
1) 2) 3) 4) 5) 6) 7) 8) 9)
E. Vatai, Nucl. Phys. A212 (1973) 413 J. G. Pengra, H. Genz, J. P. Renier and R. W. Fink, Phys. Rev. C5 (1972) 2007 H. Genz, J. P. Renier, J. G. Pengra and R. W. Fink, Phys. Rev. C3 (1971) 172 E. Vatai, Acta Phys. Acad. Scient. Hungaricae 28 (1970) 103 W. Bambynek, B. Crasemann, R. W. Fink, H. Freund, H. Mark, C. D. Swift, R. E. Price and P. Rao, Rev. Mod. Phys. 44 (1972) 716 H. Behrens and W. Biihring, Nucl. Phys. A162 (1971) 111 H. Behrens and J. J~inecke, Landolt-Brrnstein, New Series I/4 (Springer Verlag, Berlin, 1968) M. J. Martin and P. H. Blichert-Toft, Nucl. Data Tables A8 (1970) 1 T. Hayashi and J. R. Comerford, Jr., US Atomic Energy Commission report TID-6080, appendix 1 (1960)
[ I
Nuclear Physics A218 (1974) 372--380; ~ ) North-Holland Publishing Co., Amsterdam N o t to be reproduced b y p h o t o p r l n t or microfilm without written permission f r o m the publisher
NUCLEAR MATRIX ELEMENTS FROM L/K ELECTRON CAPTURE RATIOS
IN S9Ni D E C A Y t w. M. CHEW, A. C. XENOULIS and R. W. FINK School of Chemistry, Georgia Institute of Technology, Atlanta, Georgia 30332 and J. J. PINAJIAN Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830 t* Received 3 October 1973
Abstract: Using a
recent theoretical method, the ratio of nuclear matrix elements R-0 vFzll)was o determl'ned tobe eih +°'aSor25.22_o:xTmthesecond+028--( VF°220-- ~/3A ~ Fz21/ t er 205 • 0_0.55 forbidden nonunique decay of 8 × 104 y S9Ni. These values of R were obtained from a value of L3/K = 0.0084-0.002 found by subtracting the theoretical ratio (Llq-Lz)/K ~ 0.113 (based on QEc = 1070±8 keV) from the total ratio L/K = 0.121-4-0.002, which was measured with a reactor-produced, doubly-mass-separated 59Ni source introduced as gaseous nickelocene, (CsHs)2Ni, into a wall-less, anticoincidence, multiwire proportional counter. The 854-1008 eV L and the 8.33 keV K peaks were measured simultaneously.
I E
RADIOACTIVITY 59Ni [from SSNi (n,~)]; measured L/K EC ratio; calculated (Lx-I-L2)/K ratio; deduced La/K ratio, nuclear matrix element ratio; multiwire proportional counter; isotope separated sources. Enriched 58Ni target.
]
I
1. Introduction A m e t h o d has recently been developed i) to determine a ratio of n u c l e a r matrix elements from the L / K electron capture ratios of n o n u n i q u e transitions o f second- or higher-order forbiddenness. I n the present work, the L / K electron capture ratio o f 5 9Ni is determined, a n d the result is used to o b t a i n a ratio of nuclear matrix elements. The decay o f 8 x 10 4 y s 9Ni is a particularly good case to study. It is a second-forbidden n o n u n i q u e electron capture t r a n s i t i o n only to the g r o u n d state of 5 9C0" It also forms a v a p o r o u s c o m p o u n d , nickelocene, and, therefore, can be studied by m e a n s o f the multiwire p r o p o r t i o n a l c o u n t e r technique that has recently been i m p r o v e d in this laboratory. There have been n o previous electron capture studies of 59Ni.
2. Experimental 2.1. SOURCE PREPARATION The radionuclide 59Ni was prepared by t h e r m a l n e u t r o n irradiation of 99.89 % enriched 5SNi in the S a v a n n a h River Reactor. After the irradiation, the sample was mass t Supported in part by the US Atomic Energy Commission. tt Research supported by the US Atomic Energy Commission under contract with the Union Carbide Corporation. 372
NUCLEAR MATRIX ELEMENTS
373
separated twice and converted to 59NiCI2. The 59Ni activity was introduced into the proportional counter in the form of gaseous nickelocene, (CsHs)2Ni. This is a rather reactive compound and decomposes in air, and also in some organic solvents such as acetone, ethyl alcohol, and ethyl ether. The sample was converted to nickelocene in the following manner. Finely crushed potassium hydroxide was placed in a beaker and 1,2 methoxyethane was added with a magnetic stirring bar. Freshly cracked cyclopentadiene was added, with stirring, followed by the nickel sample dissolved in dimethylsulfoxide. The nickelocene was precipitated by the addition of hydrochloric acid and ice. After filtration, the nickelocene was dissolved in hexane and transferred to a sublimation unit which was then placed in a hot oil bath. After sublimation, the nickelocene was transferred into glass sample containers. The entire synthesis and subsequent sublimation was performed just prior to each measurement using a glove bag in an inert atmosphere and required about 2 h. Nickelocene, which forms dark green crystals, has a slight tendency to sublimate (2 m m vapor pressure at 100 ° C), and this physical property was utilized to introduce the gaseous nickelocene into the proportional counter under vacuum. 2.2. THE PROPORTIONAL COUNTER SYSTEM AND METHOD OF MEASUREMENT The proportional counter measures the energy of both the X-rays and Auger electrons emitted after an electron capture event in the gas. In the wall-less multiwire proportional counter used in this work, wall effects and background were effectively reduced by a surrounding anticoincidence ring counter. A diagram of the counter is
I I 50Fro
L_m
,oo Tub~og~ - -
"
Iolof$
L_ TO "Preomp
Total Volume 15 Liters t"
102em
Fig. 1. The detailed arrangement of the multiwire proportional counter used in the determination of the L/K electron capture ratio of 59Ni. The insert represents the geometrical placement of the anode, or counting, and the cathode, or high voltage, stainless steel wires, depicted as small and large dots respectively.
374
w.M. CHEW et al.
shown in fig. 1. There are four internal effects which further necessitate an anticoincidence gate: (i) Injection (pulses in the central counter caused by free electrons being released into it through the weak field regions between the cathode wires defining the boundary between the central and ring counters following ring counter avalanches); (ii) Induction (electrostatically induced pulses between the ring counter and the central counter); (iii) Pulse degradation (due to recombination of ion pairs in the weak-field regions and the end effects); and (iv) After-pulsing (pulses occurring after an avalanche due primarily to negative ion formation and the emission of secondary electrons by the cathode wires when hit by the positive ion sheath). The central counter pulses are blocked for 180 ps following a ring counter event. This reduces the background and removes the effects of induction and injection. In order to remove the effect of afterpulsing, a paralysis, consisting of an anticoincidence gate, of 6 msec is introduced following each central counter event. Pulse degradation results in a tail of constant intensity below each peak that extends to zero energy. Corrections for these degraded events are applied to the spectra during the data analysis. All these effects have been taken into consideration in previous studies 2, a). In all the previous electron capture ratio investigations, the K, L, and M spectra were measured sequentially. The peak counts, however, had to be normalized to the same amount of activity and to the same real counting time. That is, if the activity changed significantly from one measurement to another, for instance if the activity adsorbed on the counter walls, or the activity had a short half-life, or if a new filling was made, it was necessary to normalize the spectra to correspond to the amount of activity present in the counter. This was done by monitoring the K peak activity of the central counter. In the same manner, the three spectra had to be corrected for the different deadtimes of the electronics in the K, L, and M regions. It was necessary to assume that experimental conditions did not change from one measurement to another. By measuring the K and L spectra simultaneously, the errors associated with these normalization and deadtime corrections are eliminated. In order to eliminate these corrections, as well as insure homogeneity of the conditions during the measurements, the electronic system was revised so as to permit simultaneous measurement of the K and L energy regions. The revised block diagram for the L/K electron capture ratio measurement is shown in fig. 2. Two separate Tennelec TC-200 amplifiers for the K and L regions, respectively, were used to obtain the K and L energy regions of the central counter spectrum. These two amplifiers with different electronic gains were necessary, in order to store simultaneously the K and L peaks with their large separations (8.33 keV and 854-1008 eV, respectively) in two separate 128-channel analyzers. It should be emphasized that since two different amplifiers were used, the output of each had to be controlled by the same logic signals, in order to assure identical electronic deadtime and homogeneity o f measuring conditions. The controlling logic
NUCLEAR MATRIX ELEMENTS • -t~,ng,, Ch. . . . ,Ana,yzer Al i
RingCounter
I~
~
~
~ I SingleChannelAnalyzer SI
~--~LDiscrimi ~-- Logic
i~/I
375
I Discrimi..... A ]
Generator I
I ParalysisG.....
tor
j
r m ~ D m ' ~ ]
DelaY AmPlifier~ I D " I
LLi ....
~
Del ay Ampinh e r ~......m,..~K L.....
Gatej
PulseHeightAnalyzer ND-~lO
I'c" KcAr~0P/itier~
Gate
Fig. 2. The electronic block diagram for the simultaneous measurement of the L and K peaks in 59Ni decay. The path of the analog signals from the central counter to the pulse height analyzers is shown by the heavy lines. signal from the logic generator *, is initiated by pulses from either the central counter or the ring counter. The output of the L amplifier was also used to trigger discriminator A and the paralysis generator (see fig. 2). Since K capture events produce saturated pulses in the L amplifier, they, as well as L events, trigger the lower level discriminator A and the paralysis generator, the output pulses of which are necessary for proper operation of the logic generator. The level of discriminator B was set just above the L peak from ring counter amplifier 2, in order to provide the necessary anticoincidence ring counter pulse to the logic generator. The L and K linear gates will transmit the L and K signals, respectively, unless a pulse from the logic generator is present. The L and K peaks were stored in individual 128-channel ND-110 pulseheight analyzers. The path of the analog signals from the central center to the multichannel analyzers is shown by the heavy lines in fig. 2. Initial attempts to record both spectra in two halves of a 512-channel analyzer by multirouting were not fruitful, because of difficulties associated with the multirouting logic signals coming from the overlapping energy region between the two spectra. Since the K and L spectra were recorded simultaneously, and therefore with the same electronic deadtime, no time normalization was necessary. The deadtime of these measurements, however, was determined, in order to permit subtraction of background spectra with a measurement time equal to that of the K and L spectra. The deadtime of the system was measured by comparing the readings of scalers 1 and 2 which recorded the gated and ungated output of the pulser. The pulser gate, t This logic generator consists of the following units in fig. 2 of ref. a): gating signal gen. B, gating signal hold-off control, coin. gate, gating signal gen., and the OR gate. The paralysis generator consists of lower level disc. and gating signal gen. A in the same figure.
376
w.M. CHEW et aL
together with the K and L linear gates, blocked any signals occurring during the output signals of the logic generator. Nickelocene has a tendency to be deposited on the counter walls. K X-rays from decaying atoms on the wall have a small probability to be recorded in the central counter without triggering an anticoincidence gate in the ring counter, while L X-rays are completely absorbed on the ring counter. An increase of the activity absorbed on the walls, therefore, could give a slightly low L/K ratio. In order to correct for this effect, it is necessary to determine the number of K X-rays that originate from the walls during the course of each measurement. Scalers following single-channel analyzers A and B to monitor the singles ringcounter K peak activity and the gated central counter K activity, respectively, were set up so that this correction could be estimated. A decrease in the amount of gaseous activity because of absorption on the walls would result in a larger decrease in the counting rate of the central counter than in the ring counter, since the ring counter has a much greater efficiency of detecting decays from the wall. The contribution to the central counter K spectrum of the activity on the walls was determined as a function of the readings of the monitors. The readings of the monitors were recorded every ten minutes and the L/K measurement was discontinued before the correction for the wall contribution became substantial. The overall correction for this effect to the final L/K capture ratio is very small and typically amounted to no more than 1 ~ (see below). 2.3. SPECTRAL MEASUREMENTS AND EVALUATION OF THE INTENSITY RATIO NL/NK Owing to the high deadtime ( g 80~) caused primarily by the long paralysis time following each central counter event, several independent measurements of the K and L peak intensities were carried out for about 6 h each, and in order to minimize the amount of the activity absorbed on the walls of the counter, the measurements were carried out at 72 ° C. Typical L and K spectra are shown in fig. 3. These L and K spectra were taken simultaneously at 4 atm pressure with the same gas gain ( ~ 104), but with different relative electronic gains of 8.45 and 1.0, respectively. Background was determined by filling the counter before and after each measurement with the same gas mixture and pressure of argon plus 15~ propane. An external 57Co source of 14.4 keV v-rays was used to recalibrate to identical gas gains. After the background spectra were corrected for deadtime, normalized to unit clocktime, and subtracted from the K and L energy spectra, the K and L peak intensities were corrected for degraded events, and the intensity ratio N L / N K was calculated to be 0.125_+0.002, a weighted average of ten independent measurements, where the error limit represents the probable error. 3. Corrections and final results
In order to find the L/K electron capture ratio, i.e. the ratio of the probabilities for electron capture from the L and K shells, the ratio of the intensities, N L / N ~ , must be
N U C L E A R M A T R I X ELEMENTS I
377 |
.~
L PEAK
K PEAK
c
.7 o/
c..)
\
../
"x •\
m
J
e_
!
¢
I
100
60
120
20
40
60
80
ioo
12o
CHANNEL NUMBER
Fig. 3. Typical L and K spectra of S9Ni after subtraction of background. The K peak is at 8.33 keV and has resolution typically of 18% F W H M . The L peak consists of three lines ranging from 853-1008 eV and has a typical total resolution spread of 52%.
corrected for the following effects: (i) the probability, P1, that a photon strikes a central-counter cathode wire; (ii) the probability, P2, that an X-ray passes from the center counter through the ring counter undetected; and (iii) the probability, P3, that an X-ray escapes through the ends of the counter. These probabilities are dependent on photon energy, gas pressure and mixture, and counter dimensions. For the L/K ratio, the following equation is applicable 4): L - NL { l _ ¢ o K ( k ~ p ~ o ) + k # p (- oa ) v tj j - ~ , K, , ~L. - ~ P(1) , K
(1)
NK
where co,: is the K shell fluorescence yield of the daughter (Z = 27), k~ is the fraction of K~ X-rays in the K series of the daughter, and k~ is the corresponding quantity for the Kp X-rays. The quantity P~ is equal to 101 +1°2 +103, where g refers to the evaluation of the probabilities for either the K~ or the K~ (g = a, fl) X-rays. The values of all the quantities used in determining the L/K ratio are presented in table I with references. The superscript (0) indicates the correction for the decrease of the TABLE 1 Values used to determine the L/K orbital electron capture ratio Quantity
p
p(1)
p8¢o)
co,<
k~
k~
Value Reference
0.0048 4)
0.0084 4)
0.0080 4)
O.381 s)
O.881 5)
O.I 19 s)
378
w.M. CHEW et aL
pulses in the K peak due to the escape of K X-rays originating in the central counter that do not trigger an anticoincidence pulse. The superscript (1) indicates the increase of the L peak due to the escape of a K, X-ray originating in the central counter without triggering an anticoincidence pulse. The final result for the L/K capture ratio is: L/K = 0.121___0.002, where the error limit represents the probable error. In the present work the total contribution due to the degradation tails was 8.5~o for the K region and 3.4~o for the L region. The probable error due to counting statistics was less than IX, and the error due to the wall adsorption was also less than 1~, not only due to the care taken during the measurements, but also due to the fact that the gas filling stopped more than 98~o of the K X-rays from the walls which might have entered the central counter.
4. Discussion and comparison with theory The electron capture decay of 59Ni to the ground state of 5 9Co requires a spin change of two units and no parity change. In such a second-forbidden nonunique electron capture process, capture of electrons from atomic orbits other than the s~ and p½ becomes significant. Specifically an L 3 (pk) contribution to the L / K ratio is expected. As has been shown recently 1), such a contribution can be utilized to determine certain of the matrix elements involved in the electron capture process. Using the theory of Behrens and Btihring 6) and certain approximations applied by Vatai :), the electron capture decay constant can be written as follows for capture of an electron from the X-shell: =
2rc2 nx C x f x ,
(2)
where X = K, L 1 , L2, . . . , f x = ~i n q x2f l x2 B x , n x is the occupation number, and C x = r 2 ( p x R ) 2(kx- 1)(qx R ) 2(kv-1)
x
VF°,n-l,1
t
aZ / V F O - - x / i n + l ) / n A F ° n 1) 2 k x + l ~ .... o . , •
(3)
Within Vatai's approximations ~), it is obvious that for electron capture ratios in which atomic shells withequal values of the quantum number k x are involved, the terms that include the form factors (AF°rz and VF°rz ) cancel, and, therefore, such electron capture ratios are independent of the nuclear matrix elements. Specifically, the ( L ~ + L 2 ) / K ratio is independent of the nuclear matrix elements, because all three orbits have k x = 1. The ratio (L~ + L 2 ) / K can be determined from the following expression: (L, + L 2 ) / K ---- (q~lfl2 B L l + qL2 4. ill.2 2 BLE)/qK4-f12 BK ' (4) where fix are Coulomb amplitudes, B x are exchange corrections, and q x is the neutrino
N U C L E A R MATRIX ELEMENTS
379
emission energy for capture to the X-shell. Using eq. (4) and values of fix and B x from refs. 7, a), and QEC = 1070+8 keV [ref. 9)], the (L 1 + L 2 ) / K ratio for the decay of 59Ni was calculated to be 0.113. Since the K and L Coulomb amplitudes and exchange corrections appear in eq. (4) as ratios, and the errors associated with these individual terms are correlated, the final error associated with the calculated ( L x + L 2 ) / K ratio is negligible. The difference (L/K)~xp-[(Ll + L2)/K]eale = 0.1210.113 = 0.008___0.002 represents the L3/K contribution, i.e. the ratio of capture from the 2p+ and the Is+ orbits, where the error is contributed exclusively by the uncertainty in the experimental measurement. In contrast to the (L 1 + L2)/K ratio, the La/K ratio is dependent on the nuclear matrix elements involved in the electron capture process. Using eqs. (2) and (3), I0
V'
I
1
I
I
I
16
[8
20
22
24
i0 -r
P'3
._I
i0 -2
jo-3 14
R
26
28
:( VF;~o- 3-v'3-7-~"F~,2, )/VF;,,
Fig. 4. The theoretical La/K ratio plotted as a function o f the nuclear matrix ratio R for the limited range of R pertinent to a comparison with the experimental measurement. The measured La/K ratio is represented by the horizontal line and its associated error, by the height of the shaded area. Two values of R, 20.50_+0"~. and 25.22+°'2a_o.t7,are deduced from this comparison.
380
W.M. CHEW et al.
and n = 2 = A J, we can derive for L3/K: L3/K = (p23 q23 fl2jq~ f l 2 ) { ( x / ~ _ l ~ Z R ) / ( ~ / ~ _ ½aZR)}2,
(5)
where I-VF0
/ R = /
4 ~ A F 0 -I 220--'__2_ 2211 VF°11
_l,
is the fine structure constant (1/137) and Px is the m o m e n t u m o f the b o u n d state electron in the X-subshell. It should be pointed out that such a dependence of the L a / K ratio on the form factor coefficients is possible because the K and L a orbits are characterized by different k x values, 1 and 2, respectively. Using eq. (5) the variation o f the L a / K ratio was calculated as a function of R, and the result is plotted in fig. 4 for a certain range o f R. The ratio of the shape factors becomes infinite at R = 23.21 and there the L a / K ratio can be very large. The quadrupole dependence o f the L a / K ratio on the ratio o f the matrix elements permits two possible values o f R for a given L a / K ratio. The physical significance of this feature, if any, is not clear; it is obvious, however, that only one o f the values is relevant. By comparing the experimental L a / K ratio and its associated error, which is represented in fig. 4 by the shaded area, with the theoretical calculation, the value o f the nuclear matrix element ratio, R, is determined to be either -~a . . . . ~n . . +0.350.55 or o~ . . . . ,')0 . . +0.280.17. It should be mentioned that since the theoretical treatment utilized in this study does not permit any further qualification o f this double value o f the ratio of the matrix elements, both of these values should be considered. These experimental ratios o f nuclear matrix elements can be c o m p a r e d with the results o f theoretical calculations using different nuclear models. A realistic nuclear model should be able to reproduce either the one or the other o f the ratios.
We are indebted to E. Vatai for m a n y helpful discussions and suggestions during his exchange visit to our laboratory. We thank J. G. Pengra and J. P. Renier for helpful consulations on certain experimental aspects of this work.
References
1) 2) 3) 4) 5) 6) 7) 8) 9)
E. Vatai, Nucl. Phys. A212 (1973) 413 J. G. Pengra, H. Genz, J. P. Renier and R. W. Fink, Phys. Rev. C5 (1972) 2007 H. Genz, J. P. Renier, J. G. Pengra and R. W. Fink, Phys. Rev. C3 (1971) 172 E. Vatai, Acta Phys. Acad. Scient. Hungaricae 28 (1970) 103 W. Bambynek, B. Crasemann, R. W. Fink, H. Freund, H. Mark, C. D. Swift, R. E. Price and P. Rao, Rev. Mod. Phys. 44 (1972) 716 H. Behrens and W. Biihring, Nucl. Phys. A162 (1971) 111 H. Behrens and J. J~inecke, Landolt-Brrnstein, New Series I/4 (Springer Verlag, Berlin, 1968) M. J. Martin and P. H. Blichert-Toft, Nucl. Data Tables A8 (1970) 1 T. Hayashi and J. R. Comerford, Jr., US Atomic Energy Commission report TID-6080, appendix 1 (1960)