Z. Physik A

Zeitschrift ffir Physik A

Atoms and Nuclei 297, 35-39 (19801

~t-t%r'~c'~ r'XL~,#I I I ~

and Nuclei ~ by Springer-Verlag 1980

A Direct Determination of the Proton Electron Mass Ratio G. Grfiff, H. Kalinowsky, and J. Traut* Institut ffir Physik der Johannes Gutenberg-Universitfit, Mainz, Federal Republic of G e r m a n y Received June 10, 1980 The cyclotron frequencies of free protons and electrons in a magnetic field of 5.81 Tesla with superimposed electrostatic quadrupole field have been measured. The increase of energy connected with a transition at cyclotron frequency is detected by the measurement of the time of flight through an inhomogeneous magnetic field. From the ratio of the measured cyclotron frequencies of both particles the proton electron mass ratio is deduced. The result rap~me= 1,836.1527(11) agrees within the limits of error (0.6 ppm) with the value of the indirect determination.

1. Introduction The precise determination of the numerical values of fundamental constants is necessary for the test of physical theories of elementary particles and atomic systems. For example, to calculate the hydrogen energy levels the knowledge of the proton electron mass ratio is necessary besides the fine structure constant and the Rydberg constant [1]. At present the precision of the computation of the hydrogen 1 S - 2 S isotopic shift is limited by the uncertainty of the proton electron mass ratio mp/me[2]. Therefore, a precise knowledge of this constant permits testing the theories which describe the energy levels of the hydrogen atom. The determination of the proton electron mass ratio is possible by both a direct and an indirect method. The indirect method requires two different types of measurements: the determination of the magnetic moment of the proton in units of the Bohr magneton lL~,/ll8 and the determination of the magnetic moment of the proton in units of the nuclear moment tx'r/tZl~. The ratio l~'p/FlRhas been measured by Phillips et al. Their results is tz~,/tlB= 0.001520992983 (17) [3]. The magnetic moment of the proton in units of the nuclear moment ~f~/llK has been measured by two groups [4, 5]. The weighted mean value is lfp/ll~ * This work comprises part of the thesis of J. Traut

=2.7927741 (10) [6]. The combination of both results leads to a proton electron mass ratio rap~m,, = 1,836.1518(7). The direct determination is based on the measurements of the cyclotron frequencies of proton and electron in the same magnetic field. The first precise direct determination was performed by G/irtner et al. [7]. Their result is mp/m~,= 1,836.1502(531 for the proton electron mass ratio. The error is mainly due to space charge effects within the ion trap.

2. Apparatus

2.1. Ion Trap To determine the electron proton mass ratio the cyclotron frequencies of both particles are measured in the same magnetic field. Protons as well as electrons are trapped alternatively in a homogeneous magnetic field with a superimposed electrostatic quadrupole field, the potential of which is V(.V, y, z) = U / R 2 (.v 2 + 1 '2 - - 2 z 2 ) .

In this configuration within the nonrelativistic limit the ions behave like a three-dimensional harmonic oscillator with the following frequencies

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G. Gr/iff et al. : Direct Determination of the Proton Electron Mass Ratio

J~ = (2 e U/m Roz) 1"2/2

.& =f,/2 +fo ,/E, =./;,/2 -.lo with jo=(J~/4+Jy/2) 1/2 and the cyclotron frequency Je=eB/Tm 2m 7 = ( 1 - v 2 / c 2) 1/2 Under the condition chosen in our experiment ( B = 5 . 8 T, U = I Volt)f~ is about 16 M H z (367 kHz), ./B = 163 G H z (89 MHz) andJ}B =760 Hz (760 Hz) for electrons (protons). The trap is made of O H F L copper. It is carefully machined and polished. Additional correcting electrodes are introduced to guarantee a well-shaped quadrupole field. Rubin spheres serving as insulator keep the electrodes in the correct position. The central ring is splitted parallel to the z-axis to allow the application of the rf-field perpendicular to the magnetic field. At one side of the quadrupole trap, 40 cm far from it but near the magnetic field axis, a heated tungsten wire serves as electron source. These primary electrons impinge partly the interior trap surface through the entrance hole of the end cap (1 m m diameter) producing secondary electrons or protons respectively. A few of them are trapped. Due to synchroton radiation in the strong magnetic field the electrons lose their initial energy of a few eV and cool down to thermal energies of about 30 meV within a second.

2.2. Dri[i Tube and Detector System The trap is installed in a 37cm long copper drift tube of 30 m m diameter. The surface of the tube was cleaned by a glow-discharge in an atmosphere of hydrogen. To obtain a vacuum of 10 9 Torr the complete apparatus was baked out at a temperature of 600 ~ for two days. The trap and the tube can be cooled down to liquid helium temperature by a flow cryostat.

At the open end of the tube a channelplate detector is mounted to count alternatively electrons or protons after their ejection out of the trap (Fig. 1). The pulses from the channelplate detector are registered in 24 C A M A C counters. These counters are read by a PDP 11/20 data acquisition computer, which also serves via C A M A C as controller of the timing cycle during the measurement. A commercial electromagnetic shielding cabin contains the complete apparatus to avoid any disturbances of the measurement by unwanted electromagnetic fields. For this reason the data transfer between the apparatus inside the cabin and the data acquisition computer is made by fiber optic transmission lines.

2.3. Magnetic Field In this experiment a superconducting magnet is used. Its m a x i m u m field strength is 6.4 Tesla. R o o m temperature access is provided along a horizontal bore with 52 m m diameter. To ensure a sufficient homogeneity over the trap volume a series of coils is mounted on the vacuum enclosure. They allow a systematic correction of linear field gradients in three directions and of the quadratic term along the axis of symmetry. These coils are run at room temperature. The drift of the magnetic field was less than 0.02 ppm per day when the magnet was run at 5.28 T and about 1.0 p p m per day when run at 5.81 Tesla (Fig. 2).

3. Method

There are three possibilities to get the cyclotron frequency : a) A measurement ofJB at different trapping potentials U and an extrapolation to zero electrostatic field strength.

magnetic field [T] &O 4s

2D 0

5

It ap

10

15

drift t u b e J

20

25

30

[CM] channel plate detector

'U

1

Fig. 1. The experimental arrangement for the time of flight measurement

G. Gfiiff et al. : Direct Determination of the Proton Electron Mass Ratio

720

the ejected particles. With the same pulses a series of consecutive gates is generated, which open 24 fast counters one after the other. By this method one gets the time of flight spectrum. The time of flight is determined by the initial energy of the particles along the magnetic field axis (about 10 meV for electrons and some 100 meV for protons) and by their transverse energy incorporated in the cyclotron motion. Corresponding to this energy the particles are accelerated by the inhomogeneous magnetic field. When the cyclotron frequency is induced, the trapped particles gain energy in their transverse degree of freedom. The cyclotron orbit of the particle increases and consequently its magnetic moment as well. When these particles are expelled out of the trap they get an additional acceleration in tile inhomogeneous part of the magnetic field. Their axial energy increases leading to a corresponding decrease of their time of flight which is measured. By these means thc cyclotron frequency is detected. This idea was proposed originally by Bloch and used in different experiments [81.

vcp [Hz] frequency N

640600

1~{\{~

] 210-7

{\{t\ 88754440 i

i

,

J

,

L

L

0 20 40 60 time [hf Fig. 2. Proton cyclotron frequency shift as a function of time caused by the magnetic field drift (error bars correspond to FWHM)

b) A measurement o f / B and J):B, the sum of which amounts to the cyclotron frequency f.. c) A direct induction of a transition at frequency (I~+./).B), which can be enforced at low electric field strengths. Of these different methods we selected the latter one since that transition is most insensitive to a misalignment of the trap, to space charge effects and more or less unknown surface potentials. To detect the cyclotron frequency the following procdure is used: After creation of a few electrons the potential is kept constant for one second during which the electrons (protons) cool down (Fig. 3). Then the cyclotron frequency is applied for about 500 ms. Finally the trap is cleared by a linear sweep superimposed by a sequence of pulses which define the starting time of

time

10

[ms]

200 L 300 400 , ~

i

,

4. The Measurement of the Cyclotron Frequencies

4.1. The Proton Ct'clotron Frequency The cyclotron frequency of the proton has been determined as outlined in Sect. 3. Choosing an initial energy of 300 meV the mean time of flight is about 30 ItS. At resonance it decreases by a few percent depending on the rf-amplitude (Fig. 4). At each frequency the whole cycle is repeated 30 times. The resulting time distribution stored in the 24 counters is then read by a PDP 11/20 computer which calculates the mean

1000 I

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-

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1100

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frequency fc frequency

fz

Fig. 3. Trapping potential

38

G. Gr/iff et al. : Direct Determination of the Proton Electron Mass Ratio

Tcyclotronfrequency

31 [time of flight [ps]

3010f vcp [Hz]

I= 1107

oo 29 30 I

~

i

~

i

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9 .

2'0 .......... 40 6 0 80

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Fig. 4. Proton time of flight as a function of frequency (fiUed by Gauss function)

time of flight and the statistical error. To study the line shape and possible line shifts several parameters have been varied: the rf-amplitude, the trap position relative to the magnetic field, the magnetic field strength, the trap potential and the space charge. As additional test the cyclotron frequency of molecular ion H I has also been measured.

4.1.1. Electric and Magnetic Field Dependanee. As far as a pure quadrupole field is achieved the transition frequency ([}~+,/EB) should not depend on the electric field strength. Within the statistical error this appeared to be correct. At very low voltages (100 meV), however, when surface potentials become dominant, the center of ion motion was evidently shifted along the z-axis. This lead to observable shifts of the cyclotron frequency depending on the position of the trap and the magnetic field inhomogeneity. As expected the transition probability was inversely proportional to the electric field strength. Measurements were performed at 5.28 T and 5.81 T. The mass ratios m~/m,, resulting from both experiments agree within their statistical errors. 4.1.2. Space Charge Ej]i'cts. Depending on the specific charge distribution in the trap the two frequencies ./}~ and ./"f:R might be influenced in a different way and therefore the cyclotron frequency f. as well. The cyclotron frequency.#, is both shifted and broadened proportional to the number of stored ions. Since the protons are generated by electron bombardement of the residual gas, other ions of heavier masses a s H z O ~ and N + are also produced and stored inside the trap. These ions contribute of course to the space charge. Therefore, the trap was cleared of all other ions before inducing the proton cyclotron frequency in the following way: After the ion creation the trap voltage is decreased linearly down to 1 Volt. Simultaneously, a if-field is applied, the frequency of which is chosen so that all ions heavier than the protons experience their resonant frequency .1~, (Fig. 3). The amplitude of this rf-field is high enough to guarantee the ejection of all unwanted ions. The cyclotron frequency was

i

I

30

50 H§ Ions

Fig. 5. Proton cyclo|ron frequency as a function of the number of trapped protons (error bars correspond to F W H M )

then measured for different numbers of trapped protons. Figure 5 shows the line width and the transition frequency as a function of the number of stored protons.

4.2. The Eh'ctron Crelotron Frequen O, For the electrons the mean value of the time of flight through the magnetic field is 3 las. At resonance the time of flight decreases by about ten percent. The enlargement of the microwave amplitude causes an energy absorption by the trapped electrons, which leads to a relativistic mass increase and therefore to a shift and broadening of the cyclotron frequency (Fig. 6). By a measurement at different microwave amplitudes this dependance was determined and extrapolated to zero energy absorption. The line width is almost entirely determined by the relativistic mass increase. Smaller line widths can be obtained by increasing the sensitivity for the detection of energy changes connected with the induction of cyclotron frequency [9]. This sensitivity is presently limited by surface potentials on the inner side of the drift tube. Experiments with drift tubes of different materials which expect to give a longer time of flight are now under way. Within a second after their generation the trapped electrons are in a thermal state which shifts the elec-

time of flight [l~S]

38

4

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mlcroweve (arbitrary

~

9 450 250 o 77

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10590834

amphtude units)

L

I

I

I

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50

58

66

J

v[Hz] frequency

Fig. 6. Electron time of flight as a function of frequency and microwave amplitude

G. (h'/iff ct al.: Direct Determination of the Proton [ilcctron Mass Ratio

39

Table I. (7orrections for the determination of the cbclotron frequencies of electrons and prolons and error contribution to electron proton mass ratio /,-electron Space charge effects Trapping voltage extrapolation Zero kinetic energy extrapolation Zero microwave amplitude extrapolation l.rror due to line shape (0.5 F W H M )

/,-proton 0.1)40(63) p p m / l l ) i o n s I)Y)I 1 (31) ppm/V

+0.022(52) ppm/V § (51) ppm +0.10(14) ppm/100 arb. units

tron cyclotron frequency by 0.05 ppm due to the relativistic mass effect. By applying a stepwise increasing potential at an electrode located at the end of the drift tube the energy distribution of the electrons has been measured. Since the magnetic field strength is negligible at the position of this electrode this method yields the sum of the energies in the longitudinal and transverse degree of freedom. As a result the width of the energy distribution appeared to be less than 50 lneV. The transition frequency is influenced by power broadening, relativistic mass increase and cooling effects due to synchrotron radiation. The resulting line shape could not be explained theoretically. Therefore, half of the F W H M (0.4 ppm) is quoted as the experimental error. Within the statistical error the line shape appeared symmetrical and was fitted by a Gaussian function. Again at very low trapping potentials a shift of the cyclotron frequency was observed. Space charge effects were negligible.

error m,/m v 0.03 ppm 0.116 ppm 0.05 ppm 0.07 ppm (1.4 ppm

Table 2. C'yelotron frequencies of electron and proton and the rcsuhing proton electron mass ratio tk~r two magnetic fields Magnetic field

Electron cycloIron frequency

5.21"ITesla 148,031.88(7)Mltz 0.5 ppm 5.81 Tcsla

162,96(~.95(8)Mttz (1.5 ppm

Proton cyclotron frequency 80,02(),~'~6814)H• 0.05 ppm 88.754,594(4)Hz 0.05 ppm

our final resuh result of the indirect determination (3). (41, (5)

N'lass ratio

/,:/m< 1.836.1530(11) 0.6 ppm 1.836.1523(11) 0.6 ppm 1,836.1527(1 I1 11.6 ppm 1.N36.1518(7) I).4 ppm

[4]. The error o1 our measurement is ahnost entirely due to the line width of the electron cyclotron frequency, which is ahnost an order of magnitude larger than the line width of the proton cyclotron frequency. At present we are improving the sensitivity of our apparatus for the detection of the electron cyclotron transition. As the result we expect the same relative line width as in the case of protons ( 2 . 1 0 ~').

5. Results and Discussions References

The measurements of proton and electron cyclotron frequencies were performed alternatively in two dill ferent magnetic fields of 5.28 Tesla (run duration 120 h) and 5.81 Tesla (run duration 63 h). The drift of the magnetic field during the experiment was determined by the variation in time of both the proton and the electron cyclotron frequencies. The values of the magnetic field drift calculated separately from the proton and the electron cyclotron frequencies agree within their statistical errors. The transition frequencies were corrected accordingly. Table 1 summarizes all corrections and error contributions. The final results are shown in Table 2. The average of the wdues of the proton electron mass ratio is m v / m ,, = 1,836.1527(11).

This result of our direct measurement of the proton electron mass ratio agrees within the error limits with the value derived from the measurements of Phillips et al. [3] and Petley et al. [5], Mamyrin et al.

1. Garcia. J.D.. Mack. J.E.: J. Opt. Soc, Am. 55, 654 (1965} 2. Lcc, S.A., Wallenstcin, R., tliinsch, T.W.: Ph>s. Rex. Lett. 35. 12r (1975) 3. Phillips, W.D., Cooke. W.[:.., Kleppner. D.: Metrologica 13, 179 (1977) 4. Mamyrin, B.A., Art@w, N.N.. Alekseenko, S.A.: Zh. Lksp. Tcor. Fiz 63, 3 (1972) 5. Petlcy. B.W., Morris, K.: J. Phys. A7. 167 (1974) 6. Taylor, B.N., Cohen. I,.R.: Atmnic Masses and Fundamental (~onstanls, Vol. 5, lnd ed. pp. 663 673. New York-I ondon: Plenum Press 1976 7. (iiirtner, G., Klcmpl. [5.: Z. Plays. A287. l (1978) 8. Bloch, F.: Phvsica [9, 821 (1953) 9. Van D xck. R.S., Schwinberg. P.B., Dehmeh. I[.G.: Plays. Rev. l.etL 38. 310 (1977) G. Griiff H. Kalino,a sky J. Trant lnstitut t'fir Physik Johannes-Gutenberg-U niversitfit Jakob-Weldcr-Weg 1 I D-6500 Mainz Federal Republic of G e r m a n y