New Experimental Test of the Pauli Exclusion Principle Using

VOLUME 85, NUMBER 13

PHYSICAL REVIEW LETTERS

25 SEPTEMBER 2000

New Experimental Test of the Pauli Exclusion Principle Using Accelerator Mass Spectrometry D. Javorsek II,1 M. Bourgeois,2 D. Elmore,1 E. Fischbach,1 D. Hillegonds,2 J. Marder,3,4 T. Miller,1 H. Rohrs,5,2 M. Stohler,1 and S. Vogt6,2 1 Department of Physics, Purdue University, West Lafayette, Indiana 47907 Department of Chemistry, Purdue University, West Lafayette, Indiana 47907 3 Isotech LLC, Euclid, Ohio 44132 4 Brush Wellman Inc., Cleveland, Ohio 44110 5 Department of Chemistry, Washington University, St. Louis, Missouri 63130 6 International Atomic Energy Agency, Vienna, 1400 Austria (Received 7 April 2000)

2

We report the results of a new experimental search for the Pauli-forbidden 1s4 state of Be, denoted by Be0 . Using the Accelerator Mass Spectrometer facility at Purdue University, we set limits on the abundance of Be0 in metallic Be, Be ore, natural gas, and air. Our results improve on those obtained in a previous search for Be0 by a factor of approximately 300. PACS numbers: 31.10. + z, 13.90. + i, 32.10. – f

The Pauli exclusion principle (PEP) has played a central role in quantum mechanics since its formulation in 1925 [1]. Notwithstanding its many successful predictions, the PEP remains somewhat enigmatic, particularly with respect to the question of whether small deviations from it are possible. Recently this question has become the subject of renewed investigation both theoretically [2–9] and experimentally [10–19]. One of the most interesting conclusions to emerge from the theoretical efforts is what Greenberg and Mohapatra (GM) [6] term the “surprising rigidity” of the PEP. By this GM refer to the apparent impossibility of formulating a consistent local field theory of small PEP violations within the framework of a positivemetric Hilbert space. Nonetheless, since the PEP makes clear predictions which have direct experimental implications, tests of the PEP are possible even without a fully consistent theoretical framework. However, in the absence of such a framework comparisons among different experiments are not straightforward, even though the interpretation of individual experiments may be clear, as has been emphasized recently by Baron, Mohapatra, and Teplitz [9]. We return to this point below when we discuss our experimental results. Generally speaking, tests of the PEP fall into one of four classes: searches for PEP-forbidden electronic [11,14,18,19] or nuclear [15] states, or for PEP-forbidden electronic [10,12,16] or nuclear [13,17] transitions. Evidently, a search for a PEP-forbidden electronic configuration can also be viewed as a test of the shell structure of atoms which underlies the periodic table. In an early experiment of this genre Fischbach, Kirsten, and Schaeffer [11] set limits on the abundance of Be0 in air, where Be0 is beryllium in which the PEP-forbidden electronic configuration 1s4 replaces the usual configuration 1s2 2s2 . Although originally conceived as a test for electrons with an additional quantum number, this experiment can also be viewed as a test for PEP violation [5,7,9,14]. We note that the underlying assumption in both Ref. [11] and the 0031-9007兾00兾85(13)兾2701(4)$15.00

present paper is that the chemistry of Be0 is similar to that of He. Specifically, we are assuming that Be0 would behave as an inert gas, whereas Be would be reactive and bound up as a molecular solid. In contrast to previous experiments in which the PEP is violated by a single additional fermion in a forbidden state, a search for Be0 probes for a PEP violation by two electrons. Although such a violation may appear at first sight to be suppressed relative to that for a single fermion, in the absence of a consistent fundamental theory of PEP violation one cannot exclude the possibility that the reverse may be true. The object of the present paper is to improve the limits obtained in Ref. [11] by modifying that experiment in two significant ways: (1) Rather than using conventional mass spectrometry techniques as in Ref. [11], the present experiment utilizes PRIME Lab—the Purdue Accelerator Mass Spectrometer (AMS)—which has far greater sensitivity. (2) In addition, we have started from samples where the probability of Be0 retention is highest. In contrast to Ref. [11], which set a limit on Be0 in air, the present search utilizes pure Be metal, Be ore, and a sample of natural gas containing He, in addition to a sample of laboratory air. The assumption behind the use of the gas sample is that a geological region capable of trapping He might also trap Be0 , which may arise from outgassing of the Earth’s crust or through direct cosmic ray production. To test for the presence of Be0 in a pure metal sample we began with a 3.9 g Be cube that was produced in 1967. Since it was necessary to decompose the metal in such a way as to liberate and collect any Be0 gas trapped inside, a number of methods for decomposing the metal were considered. These included melting the sample, dissolving it in acid, and mechanically breaking it apart. However, each of these methods presented difficulties given the expectation that Be0 would be present in at most trace amounts. For example, dissolving the metal sample in acid had the drawback that it would have produced large volumes of H2 gas which would have swept away any Be0 . In © 2000 The American Physical Society

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the end, a simple method was devised which consisted of dissolving the Be sample in a saturated solution of iodine in methyl alcohol (MeOH). The exothermic reaction of the metal with the I-MeOH solution produced only a small quantity of MeOH vapor, which was easily condensed out using a conventional cold water condenser and a liquid nitrogen 共LN2 兲 trap. Any gas passing through the condenser and trap (including Be0 if present) was collected in a sample tube where it was mixed with He to produce a gas sample at 528.5 Torr. The search for the presence of Be0 in Be ore presented a number of problems similar to those encountered with the metal sample, and again a number of alternatives were considered for decomposing the ore. Be is extracted from the mineral beryl which has a nominal chemical formula 3BeO?Al2 O3 ?6SiO2 . Beryl dissolves in hydrofluoric acid (HF), albeit slowly. Two separate samples of beryl, weighing 362.0 and 329.5 g, were each placed in Teflon containers along with an excess quantity of 48% HF. The Teflon containers were then inserted into sealed glass dessicators that had previously been coated with silicone grease to retard etching by the HF. The dessicators were connected to a manometer, which monitored the pressure inside, and were left undisturbed at room temperature for a period of 3.5 and 4 months, respectively. Any gas produced in the dessicator was collected in an evacuated vessel after being passed through an LN2 trap which condensed out H2 O vapor and HF, but presumably not Be0 . The gas field sample containing He (and possibly Be0 ) was obtained from the Bush Dome Bivins A-11 site in the Cliffside natural gas field near Amarillo, Texas. It was extracted on 3 April 1996 and analysis of the sample gave the following composition: .93% CH4 , 2.9% He, ,4% C2 H6 , ,1% C3 H8 , ,0.4% C4 H10 , ,0.7% CO2 , ,0.6% N2 , and 共2 6 1兲 ppm O2 . The fact that the sample contained a significant amount of He was critical since, as noted above, this justified the assumption that Be0 could also be trapped at the same site. The unprocessed gas field sample passed through two LN2 traps which condensed the CO2 , O2 , and the hydrocarbons. The remaining gas was collected in a 468 ml glass sample flask which had been evacuated to 1025 Torr and which was maintained at 19 ±C. When the cylinder containing the original gas field sample was shut off, the pressure in the gas sample flask stabilized at 495 Torr. In addition to the gas field sample, we also ran a sample of laboratory air which was obtained by simply opening an intake port of the gas manifold to the atmosphere. The air sample was then run under the same conditions of pressure and temperature as were the other samples. Since the Purdue AMS facility normally deals with solid samples, it was necessary to modify the usual experimental procedure to deal with a sample such as Be0 which is presumed to be a gas. In the first stage of the AMS the sample is given a negative charge by a Cs1 ion beam (which has been accelerated through a potential difference 2702

25 SEPTEMBER 2000

of 5 keV) sputtering on a cathode containing a (usually) solid sample. The three samples described above, each containing a known partial pressure of He (and possibly Be0 ), were admitted to the region containing the Cs1 ion beam through a tube which opened onto a cathode containing either Sm2 O3 or Yb2 O3 . Since the potential which produces the 5 keV Cs1 beam is much greater than the typical binding energies of atomic electrons, it can be presumed that any Be0 atoms initially present in the sample were first converted to Be through highly energetic collisions with Cs1 . Because of the lack of a consistent theory of PEP violation the details of the mechanism for the conversion of Be0 to Be (e.g., as an exchange of electrons between Be0 and Cs1 ) are not known. Thus although we are assuming that the probability P for the Cs1 beam to convert Be0 to Be is 艐1, it could be possible that P , 1. Hence the limits quoted in Table II should be understood as corresponding to P 苷 1. The resulting Be atoms then combined with oxygen supplied by the Sm2 O3 or Yb2 O3 which replaced the usual solid samples in the cathode. This produced the BeO2 ions which eventually entered the accelerator. After passing through the accelerator, BeO2 breaks up into Be and O, and magnets downstream from the accelerator are tuned to detect Be. Any Be atoms detected above background (see below) can then be identified as having come from the gas samples, and hence are candidates for Be0 . To set a limit on the presence of Be0 in each of our samples, it was necessary to determine the efficiency of the AMS in detecting Be in a known gaseous sample. The needed calibrations were carried out by preparing gaseous samples of a volatile Be compound containing a known concentration of Be. The compound was beryllium bis-1,1,1,6,6,6-hexafluoroacetylacetonate, Be共C5 HF6 O2 兲2 , with a molecular weight of 423. A 艐150 mg sample of this compound was obtained and analyzed via a conventional mass spectrometer to verify its composition. The vapor pressure of Be共C5 HF6 O2 兲2 was determined to be 共0.583 6 0.003兲 Torr at 298.15 K which was sufficient to produce an easily detectable gaseous Be signal in the AMS at concentrations that were appropriate for this experiment. Seven standard samples were prepared by mixing Be共C5 HF6 O2 兲2 with He to produce mixtures with known Be兾He concentrations, as shown in Table I. (In this paper all concentrations are quoted as ratios of the number of Be or Be0 atoms to the number of He atoms in the sample.) In addition a blank sample was prepared with pure He. The Be counting rate in the detector varied linearly with the concentration, as expected (see Fig. 1). Since the samples obtained from the Be metal, the ore, and the gas field sample were prepared in the same way as the standards, with similar He partial pressures, a comparison of the Be counting rates in the samples and the standards determined the Be兾He ratio in each sample. The standard samples were then used to calibrate the sensitivity of the AMS to Be by carrying out a least-squares fit to the data in Table I (see Fig. 1). The intersection of the resulting



TABLE I. Summary of Be counting rates in counts per minute (cpm) for standards and blanks. For the blank and each of the seven standards S1 S7, we exhibit the concentration in parts per million (ppm) and the corresponding 1s errors. Type Blank Standard, Standard, Standard, Standard, Standard, Standard, Standard,

0.00 0.24 0.54 0.97 2.49 4.84 8.47 16.94

S1 S2 S3 S4 S5 S6 S7

6 6 6 6 6 6 6 6

Counting rate [cpm]

0.05 0.05 0.05 0.10 0.10 0.10 0.20 0.20

0.18 1.77 14.56 26.14 65.02 124.91 212.81 426.84

6 6 6 6 6 6 6 6

0.08 0.14 0.47 0.32 0.47 0.82 0.56 0.56

straight line and the horizontal band corresponding to the Be counting rate in the unknown sample then determined the minimum detectable Be concentration, as illustrated in Fig. 2. The extreme sensitivity of the AMS led to a minor problem in determining the background and calibration. The effect of running a Be standard was to produce a small but detectable increase in the subsequent Be background counting rate. This produced a slow upward drift in the background from 0.18 counts per minute (cpm) to 4.8 cpm. To minimize the effects of this drift, the unknown samples (presumably containing no Be) were run first, followed by the standards in order of increasing concentration. These samples were interspersed with blanks which continually monitored the drift of the background. A special gas manifold was designed which allowed the AMS to cycle on a 5 min time scale among the standards, the unknown samples, and the blank, and this helped to further reduce the effects of the drift in the background. The measured drift was then used to correct the counting 500

Counting Rate [cpm]

450 400

y = ax + b

350

a = 24.70 ± 0.71

300

b = 0.12 ± 0.08

0.4 0.35 0.3 Counting Rate [cpm]

Be concentration [ppm]

0.25 0.2 0.15 0.1

200 150

0 0

50 0 4

6 8 10 12 Be Concentration [ppm]

2

4 6 Be Concentration [ppb]

8

10

FIG. 2. Determination of the Be0 concentrations in the beryl and gas field samples. The shaded region is an enlarged version of the lower end of Fig. 1 with the 1s errors included. The horizontal dashed line is the measured counting rate for Be, which is presumed to arise from the presence of Be0 in the samples. The limits on 关Be0 兴兾关He兴 for the beryl and gas field samples are identical, as can be seen from Table II, and are obtained from the intersection of the horizontal line and the 1s band as shown. The limits from the other samples are obtained in a similar manner.

rates for the Be standards. Adhering to the protocol of starting with the most dilute samples minimized the Be background to the extent that no signal for Be above background was detected in any of the unknown samples (Be metal, ore, gas field, and laboratory air). Our results are shown in Table II. We see from Fig. 2 that since no signal for Be0 was detected above background, this translates into a 1s limit on the concentration of Be0 relative to He in each of the samples, as shown in Table II. For air this gives a limit on the Be0 concentration, r 0 , in air of r 0 , 3 3 10214 , which improves on the limit in Ref. [11] by a factor of almost 300. However, the more significant results are those from the Be metal, beryl, and gas field sample, since these were obtained from sources where Be0 was more likely to be found than in air. In the absence of a rigorous fundamental theory of PEP

100

2

Intercept at 5.8 ppb

0.05

TABLE II. Summary of unknown sample concentrations. The first column gives the Be0 concentration, and the second column expresses the Be0 concentration relative to Be or air. All results are at the 1s level. As discussed in the text, these results assume that the probability of converting Be0 to Be in the ion source is unity.

250

0

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14

16

18

FIG. 1. Calibration of the AMS for gaseous Be. The open circles represent the experimental data for the blank and the seven Be standards exhibited in Table I. The solid line is the result of the least-squares fit shown in the figure, where the central value is represented by the solid line, and the 1s errors by the dashed lines.

Sample

Be0 concentration

Be metal

,2 3 1028

Beryl

,6 3 1029

Gas field

,6 3 1029

Air

,5 3 1029

Corresponding ratio 关Be0 兴 , 9 3 10212 Be 关Be0 兴 , 1 3 10211 Be ··· r0 苷

关Be0 兴 , 3 3 10214 关air兴

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violation, it is unclear how to convert the results from Ref. [11] or from the present samples into meaningful limits on the PEP-violating parameter b 2 often quoted in the literature [6], or in terms of the more recent quon parametrization introduced by Greenberg and Hilborn [20]. For this reason we list in Tables I and II only the quantities directly measured by our experiment and defer the interpretation of these results to a future complete theory. That theory could, of course, indicate that PEP violation would not be expected to arise in some or all of the systems studied to date, in which case a new class of experiments may be required. The authors are deeply indebted to Professor Graham Cooks for his help in the initial stages of this experiment and for many useful suggestions. We also thank Professor Don Gaines and Dr. Dovas Saulys of the Chemistry Department, University of Wisconsin, for discussions on the chemistry of Be共C5 HF6 O2 兲2 and for providing us with a sample. We express our appreciation to the Brush Wellman Corporation for the samples of Be metal and Be ore. We thank Bill Moore of the U.S. Bureau of Mines for providing us with the Bush Dome gas field sample and for determining its chemical composition. We appreciate Adam Carr, Otto Furuta, and James Klaunig for their helpful discussions. This work was supported in part by the U.S. Department of Energy under Contract No. DE-AC0276ER01428 and by National Science Foundation Grant No. 9809983-EAR.

[1] W. Pauli, Z. Phys. 31, 765 (1925). [2] H. S. Green, Phys. Rev. 90, 270 (1953); D. V. Volkov, Sov. Phys. JETP 38, 375 (1960).

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[3] A. M. Messiah and O. W. Greenberg, Phys. Rev. 136, B248 (1964); O. W. Greenberg and A. M. Messiah, Phys. Rev. 138, B1155 (1965). [4] A. Yu. Ignat’ev and V. A. Kuz’min, Sov. J. Nucl. Phys. 46, 444 (1987). [5] O. W. Greenberg and R. N. Mohapatra, Phys. Rev. Lett. 59, 2507 (1987); Phys. Rev. D 39, 2032 (1989). [6] O. W. Greenberg and R. N. Mohapatra, Phys. Rev. Lett. 62, 712 (1989). [7] R. N. Mohapatra, Phys. Lett. B 242, 407 (1990). [8] O. W. Greenberg, Phys. Rev. D 43, 4111 (1991). [9] E. Baron, R. N. Mohapatra, and V. L. Teplitz, Phys. Rev. D 59, 036003 (1999). [10] M. Goldhaber and G. S. Goldhaber, Phys. Rev. 73, 1472 (1948). [11] E. Fischbach, T. Kirsten, and O. A. Schaeffer, Phys. Rev. Lett. 20, 1012 (1968). [12] F. Reines and H. W. Sobel, Phys. Rev. Lett. 32, 954 (1974). This paper searched for a transition that is forbidden by the superselection rule that absolutely prohibits transitions between states in which the identical particles are in inequivalent representations of the permutation group. See also R. D. Amado and H. Primakoff, Phys. Rev. C 22, 1338 (1980). [13] B. A. Logan and A. Ljubi˘cic´, Phys. Rev. C 20, 1957 (1979). [14] V. M. Novikov et al., Phys. Lett. B 240, 227 (1990). [15] E. Nolte et al., Nucl. Instrum. Methods Phys. Res., Sect. B 52, 563 (1990). [16] E. Ramberg and G. A. Snow, Phys. Lett. B 238, 438 (1990). [17] T. Kishimoto, T. Shibata, M. Imamura, S. Shibata, and Y. Uwamino, J. Phys. G 18, 443 (1992). [18] K. Deilamian, J. D. Gillaspy, and D. E. Kelleher, Phys. Rev. Lett. 74, 4787 (1995). [19] A. S. Barabash, V. N. Kornoukhov, Yu. M. Tsipenyuk, and B. A. Chapyzhnikov, JETP Lett. 68, 112 (1998). [20] O. W. Greenberg and R. C. Hilborn, Phys. Rev. Lett. 83, 4460 (1999).