An absolute measurement of the 6He decay energy

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NuclearPhysics 41 (1963) 167--172; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or mierotilrn without written permission from the publisher

AN ABSOLUTE M E A S U R E M E N T OF T H E 6He DECAY ENERGY C. H. J O H N S O N , F R A N C E S P L E A S O N T O N and T. A. C A R L S O N

Oak Ridge National Laboratory, Oak Ridge, Tennessee Received 6 September 1962 Abstract: The end-point of the energy spectrum of recoil ions from the fl-decay of 6He was observed with a spectrometer which is calibrated in terms of a standard voltage cell. The average o f two independent measurements gives a maximum/~-energy of 35084-4 keV. This result is weighted with other measurements to give a maximum/~-energy of 3508.4+3.8 keV. Addition of the 1.4 keV m a x i m u m recoil energy yields the decay energy 3509.84-3.8 keV.

1. Introduction

Measurements related to the electron-antineutrino correlation 1) in the fl-decay of erie have yielded, as a bonus, the 6He decay energy. The measurement is unusual in that it observes the end-point energy for the recoil ions rather than for the/~particles. Both particles achieve their maximum or end-point energy when their momenta are equal and opposite; hence their energies have the relationship 2 M E o = m o ( W g - 1),

(1)

where M and m 0 are the rest masses of the ion and the electron and Eo and (W o - 1) are their kinetic energies in mo c2 units. The total decay energy is E o + W o - 1. Usually it is impractical to observe the low energy recoil ions from ]~-decay; however, 6He is a special case because it is a light rare gas undergoing energetic decay. Thus the ions recoil with relatively high energy, maximum near 1400 eV, undisturbed by molecular or solid state effects. In fact, measurements on the ions have inherent advantages over the usual measurements on the/~-particles; the recoil spectrum drops abruptly rather than asymptotically to the end-point which can be measured absolutely in terms of a standard cell, and according to eq. (1) the uncertainty in the decay energy is about half the uncertainty in the observed end-point. We have made two independent measurements with a recoil spectrometer having about 3 ~ energy resolution. In the first measurement the spectrometer is calibrated in a conventional manner with a (*He) + ion source whose potential is measured in terms of a standard cell. In the second method two spectra are observed, one with the 6He source volume at the same potential as the spectrometer and the other with the source raised to a potential sufficient to shift the end point to twice its original energy. Measurement of this potential gives an energy calibration for assigning the end point. 167

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The resulting maximum fl-particle energy Ep(max) = 3508 + 4 keV is in agreement with previous results from the fl-particle energy spectrum or from nuclear reaction energies. The small uncertainty associated with this result makes it the controlling entry for assigning the 6He-6Li mass difference.

2. Recoil Spectrometer The recoil spectrometer is the one that Snell and Pleasonton 2) used for a study of aTAr. Some modifications will be discussed in our reports of the recoil charge spectrum a) and of the electron-antineutrino correlation. Briefly, 6He created by the 9Be(n, ct)rHe reaction in the fast flux of the Oak Ridge Research Reactor is swept to our laboratory and admitted, after purification, into a large, field-free conical source volume. Ions recoiling from the decay of 6He in this volume are observed with the spectrometer, which subtends a small solid angle at the tip of the cone. The spectrometer uses 96 ° magnetic analysis followed, in tandem, by 90 ° electrostatic analysis. This arrangement accepts ions with given ratios of mass/charge and energy/charge and, thus, provides almost unique identification of the (6Li)+ recoil ions. The analysed ions are detected with an electron multiplier which is in vacuum communication with the spectrometer. Background counts are minimized by three stages of differential pumping between the source and detector. The energies of the analysed ions are defined primarily by the electrostatic analyser. It has a theoretical energy resolution of 2.4~o, full width af half maximum, whereas the magnet has about a 4 ~o resolution width. The spectrometer's energy setting is proportional to the electrostatic deflector voltages which are measured with a resistance divider, a potentiometer, and a standard cell. Correct alignment for the magnetic analyser is found by first tuning for maximum transmission of ions whose energies are selected from the fiat portion of the recoil spectrum. The setting for the magnetic analyser at other energies is then made with the aid of a proton magnetic resonance fluxmeter, taking due caution to avoid errors from non-uniform hysteresis in various parts of the magnetic field. Energy calibrations for both of our results are based on measurements of the source potential. This potential is set relative to the spectrometer by means of a stabilized voltage supply and is measured by a Leeds and Northrup type-K potentiometer and a standard cell in conjunction with a calibrated resistance divider. This divider, as well as those used with the electrostatic deflector, was made from wire-wound resistors which had been intercompared by measuring their voltage drops while connected in series. The divider ratio was established to within +__0.01~o before work began in 1958; when work was completed in 1961 an intercomparison of the three dividers showed that the ratio for the source divider had not changed. During this same period the standard cell showed negligible drift, 0.004~. The measurement of the source potential has, therefore, a negligible uncertainty of about +0.01 ~ .

A N A B S O L U T E M E A S U R E M E N T OF T H E

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3. Measurements 3.1. MEASUREMENT BASED ON A CALIBRATING (4He)+ ION SOURCE Helium ions, produced by 45 V electron bombardment and extracted by a 3 V potential, were accelerated to their final energy before entering along the axis of the conical volume which normally contained 6He. After travelling the length of the cone the ions entered the analyser through the 1.3 cm aperture near the cone's apex. The normal alignment of the two analysers was altered for (4He)÷ ions in accord with the known 4) (6Li)+/(4He)+ mass ratio. Curve (a) in fig. I is the observed resolution function, that is, the dependence of counting rate on source potential for a fixed analyser setting. Curves obtained at two settings, 1044 eV and 1789 eV, gave the same calibration constant and the same resolution width. 4

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0 t

t__ t200

t400

~500 RECOIL

ENERGY

(eV}

Fig. 1. Energy spectrum near the end-point for the recoil ions from the decay of 6He. The data are compared to the predicted spectral shape without correction for instrumental resolution and also with the indicated resolution functions folded in. Calibration was made with a ('He) + ion source and the result of the measurement gives E#(max) = 3.509-t-0.005 MeV. The data points in fig. 1 give the relative counting rate of (6Li)+ recoil ions versus energy near the end-point of the recoil energy spectrum. Background corrections were determined by counting while a negative bias prevented ions from entering the analyser. All counts are normalized relative to those of the monitor near the source. The points, whose statistical uncertainties are less than the vertical heights of the symbols, are averaged for two sets of data, one set preceding and one following the calibration. In order to find the end-point these data are compared to the predicted spectral shape. The three theoretical curves in the figure are calculated 5) for the axial-vector interaction using Eo(max) = 3509 keV. The first curve, which has no correction for finite resolution, falls to zero more abruptly than does the observed spectrum. The second curve, which folds in resolution function (a), also falls too abruptly. The third curve achieves a fit with the broader function (b) which is a normal curve

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having about the same width at half maximum as function (a). This demand for a broader function results because the (4He) ÷ source and the recoil ion source present different ion optical objects to the analyser. Both sources use the same object aperture; however, the (4He)÷ ions leave the aperture with almost no divergence, and the recoil ions leave with a divergence defined by the 8 ° source cone. It is not surprising that the resolution function is broadened for the more divergent beam. The largest uncertainty in the end-point arises in the choice of the broadened resolution function. Negligible error would arise if the broadening were known to be symmetric even if the shape of the function were not known; however, an asymmetric broadening produces a shift in calibration which requires the choice o f a different end-point. A standard error of _+4 keV is assigned for this effect on the basis of curve fitting with various asymmetric functions. An additional :1:1.5 keV uncertainty arises from counting statistics and + 1.2 keV from measurement of the source voltage including the correction for extractor voltages. Accurately known values 4, 6) for the ion-to-electron mass ratio and the electron rest energy were used in eq. (1). The combined standard error is -I- 5 keV. Thus the result of this first measurement is E~(max) = 3509-1-5 keV. 3.2. MEASUREMENT BASED ON A SHIFT IN THE END-POINT During the year that intervened between the measurement with the (4He) + source calibration and this one, the various vacuum chambers were disassembled and then reassembled with improved interior wall baffles, the deflector plates were readjusted, and a new electron multiplier installed. This measurement, basically, observes the spectrum first with the 6He source volume at the same potential as the analyser and then at a potential that shifts the end-point to twice its original energy; the voltage producing the shift is equal to the end-point energy. Data are presented in fig. 2 with two symbols representing groups o f data obtained about one month apart. Here, as in fig. 1, background corrections have been made and statistical uncertainties are smaller than the point sizes. The ordinate scale is arbitrary and, at the beginning of the discussion, the abscissa or energy scale is also arbitrary. The data for "non-accelerated" ions in the upper part o f the figure were obtained, in the same manner as those in fig. 1, with the source and analyser both at ground potential; the "pre-accelerated" data in the lower part o f the figure were obtained by applying source voltages which shifted each point to about twice its original analyser setting. The analyser's calibration was then chosen to give mutually consistent end points when the non-accelarated data are plotted at the analyser energy and the pre-accelerated data are plotted at the analyser energy minus the source voltage. This comparison of the end-points is complicated by an effective change in resolution. One might expect the pre-accelerated resolution function to have just double the width of the non-accelerated function; however, since pre-acceleration reduces the beam divergence, the function may be less than doubled in width. Thus, as in

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fig. 1, the data are analysed by folding resolution functions into the theoretical spectrum. The non-accelerated data in fig. 2 are described successfully with a function a b o u t the same as the " 4 H e " function; apparently the new wall b a k e s improved the resolution for this measurement. An attempt is made in the figure to fit the preaccelerated data with the double-width function (c); but, as expected, a slightly narrower function (d) gives a better fit. An energy Ea(max) = 3506 keV is used for all curves. i

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3

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THEO 'Y W,TH

ACCELERATED

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THEORY THEORY WITH (d) FOLDED IN - - ~

1200

1,500

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1400

RECOIL ENERGY (ev)

Fig. 2. Energy spectra near the recoil energy end-point for non-accelerated and for pre-accelerated ions. Open and closed circles indicate measurements obtained one month apart. Theoretical curves are shown with the indicated resolution functions folded in. The two sets of data are brought into mutual agreement with E~(max) = 3.506-t-0.007 MeV. There would be little uncertainty resulting from the unknown shapes of the resolution functions if the pre-accelerated function were known to be broadened symmetrically; however, allowance must be made for possible asymmetric broadening with an associated shift in calibration. Auxiliary measurements were made in order to assign this error; the magnetic analyser was set to select ions from the fiat portion of the spectrum and the counting rate was observed as a function of the electrostatic deflector voltage. The resulting transmission curves for non-accelerated and for pre-accelerated ions are symmetric within the experimental uncertainty and require a single constant to match the two analysers for m a x i m u m transmission. Uncertainties in these observed transmission curves are correlated to uncertainties in the resolution functions by use of transmission and resolution functions calculated from the geometry of the spectrometer. The resulting standard error assigned to Ep(max) for this effect is -t-7 keV.

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The u n c e r t a i n t y from c o u n t i n g statistics is + 2 keV, a n d the u n c e r t a i n t y in the source p o t e n t i a l is less t h a n __.0.5 keV. Thus this m e a s u r e m e n t yields Ep(max) = 35064-7 keV.

4. Summary of Results Since systematic errors c o m m o n to these two m e a s u r e m e n t s are believed to b e negligible, the two results are t r e a t e d as i n d e p e n d e n t m e a s u r e m e n t s which give a weighted average Ea(max) = 3 5 0 8 + 4 keV. T a b l e 1 c o m p a r e s this m e a s u r e m e n t t o results f r o m the fl-particle energy s p e c t r u m (first a n d third entry) a n d from nuclear reactions (second entry) a n d gives the weighted average, 3 5 0 8 . 4 + 3 . 8 keV, for all o f the entries in the table. A d d i t i o n o f the m a x i m u m recoil energy, 1.4 keV, yields a decay energy o f 3509.8__ 3.8 keV. (Strictly speaking, the t a b l e ' s second entry which is f o u n d from reaction d a t a is the decay energy rather t h a n Ep(max); however, its large u n c e r t a i n t y does n o t justify s u b t r a c t i o n o f the recoil energy). TABLE 1

Maximum E-particle energy Et~(max) from the decay of 6He Eg(max) (MeV) 3.50 3.55 3.508 3.508

+0.02 i0.03 ±0.015 ±0.004

3.508410.0038

Ref. Schwarzschild, Rustad and Wu ~) Allen, Almqvist, Dewan and Pepper s) Vise and Rustad 9) Present result Weighted average

The 1961 nucleidic mass o f 6He which was derived 4) f r o m the first t w o entries in table 1 can be a d j u s t e d to the new weighted average w i t h o u t d i s t u r b i n g o t h e r masses. The new 6He mass excess (t2C = 0) is 17599.1 +__4.0 keV o r 18894.4-1-4.2/m. (This choice o f the 12C scale o f nucleidic masses follows the r e c o m m e n d a t i o n o f t h e 10th G e n e r a l A s s e m b l y o f I n t e r n a t i o n a l U n i o n o f Pure a n d A p p l i e d Physics in O t t a w a , C a n a d a , 1960),

References I) 2) 3) 4) 5) 6) 7) 8) 9)

C. H. Johnson, Frances Pleasonton and T. A. Carlson, Bull. Am. Phys. Soc. 6 (1961) 227 A. H. Snell and F. Pleasonton, Phys. Rev. 100 (1955) 1396 T. A. Carlson, Frances Pleasonton and C. H. Johnson, Phys. Rev., to be published L. A. K6nig, J. H. E. Mattauch and A. H. Wapstra, Nuclear Physics 31 (1962) 18 M. E. Rose, ORNL-1593 (Sept. 15, 1953) Cohen, Dumond, Layton and Rollett, Revs. Mod. Phys. 27 (1955) 363 Schwarzschild, Rustad and Wu, Bull. Am. Phys. Soc. 1 (1956) 336 Allen, Almqvist, Dewan and Pepper, Phys. Rev. 96 (1954) 684 J. Vise and B. M. Rustad, private communication (1961)