XJ0000183
СООБЩЕНИЯ ОБЪЕДИНЕННОГО ИНСТИТУТА ЯДЕРНЫХ ИССЛЕДОВАНИЙ • • • • ЧК I • I • i Дубна
Е14-2000-158
T.N.Mamedov, V.N.Duginov, K.I.Gritsaj, D.Herlach1, O.Kormann2, J.Major2'3, A.V.Stoikov, U.Zimmermann1
MEASUREMENT OF THE MAGNETIC MOMENT OF THE NEGATIVE MUON IN THE 1S-STATE OF DIFFERENT ATOMS
'Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland 2Max-Planck-Institut fur Metallforschung, D-70569 Stuttgart, Germany 'Universitat Stuttgart, Institut fur Theoretische und Angewandte Physik, D-70569 Stuttgart, Germany 3 1/45 2000 © 06teAHHeHHbiti HHCTMTI/T ^AepHbix nccneAOBaHMti. Ay6Ha, 2000 It was shown by Breit in 1928 [1] that the electron in the ls-state should possess a magnetic moment different from the free-electron value due to its relativistic motion. This effect was considered in more detail later in [2]. Unfortunately, measurement of the magnetic moment of a deeply bound electron is practically impossible. In 1958 Hughes and Telegdi [3] paid attention to the fact that the muon in the ls-state should also possess a magnetic moment different from the free-muon one and the relativistic effect on the magnetic moment of a Dirac particle in a bound state can be examined in an experiment with negative muons. The corrections to the magnetic moment of the negative muon bound to a zero spin nucleus and surrounded by a zero spin electronic shell were considered in [4,5], where correctibns to the muon g-factor were given for different atoms:
(9-9o) = Yl9i (1) where (j.^ and //B are the magnetic moment of the bound negative muon and the Bohr magneton for the muon, respectively; g0 = 2; g\...gn are the corrections to the g-factor value: gx is the radiative correction, g% is the relativistic correction to the radiative one,
93/90 = ~lfF2dr (2) where F is the small component of the radial wave function of the muon. Since the magnitude of F is proportional to v/c, the relativistic correction is proportional to the kinetic energy of the muon in the ls-state (v2/(? = T/mc1) and increases with the nuclear charge increasing. The results of the numerical calculations show [4,5] that the relativistic correction to the magnetic moment of a bound muon is about 0.1%, 1.1%, and 3.2% in the case of oxygen, zinc, and lead, respectively. Thus, the relativistic correction is comparable with the radiative one in the case of oxygen and exceeds the latter by one order of magnitude for zinc. Up to now there have only been three experimental investigations per- formed [7-9] where the magnetic moment of the negative muon in the 1 s-state of light (C, O, Mg, Si, S) [7,9] and heavy (Zn, Cd, Pb) [8] atoms was mea- sured. The accuracy of the measurement of the corrections to the negative muon g-factor in Mg, Si, and S atoms is ~ 3%, close to the accuracy of the- oretical calculations. In [7] satisfactory agreement between the experimental and calculated data was obtained for C, O, Mg, Si, and S. But the values of (g+ — gJ)/g+ (#_ is the negative muon g-factor in the ls-state of the atom) measured in [9] for negative muons in Mg, Si, and S appeared to be smaller than in [7] by 17 • 10~4 of absolute value. According to [7], (g+ - g-)/g+ is (29.6 ± 0.7) • 10~\ (36.3 ± 1.1) • 10~4, and (48.2 ± 1.6) • 10~4 for Mg, Si, and S, respectively. In the case of heavy atoms the accuracy of measure- 4 ments is about 50% [8]: the ratio {g+-gj)/g+ is equal to (120 ±62) • 10~ , (201 ± 140) • 10~4, and (468 ± 220) • 10"4 for Zn, Cd, and Pb, respectively. Despite the fact that the experimental data for heavy atoms do not contradict the calculated ones, they cannot be considered as a proof for the effect of a decrease in the magnetic moment of a Dirac particle at its relativistic motion in the Coulomb field of the nucleus. In the present work preliminary results of the measurements of the mag- netic moment of the negative muon in the ls-state of carbon, oxygen, mag- nesium, and silicon atoms are presented. Analogous measurements are now being carried out by J.H.Brewer at TRIUMF (Canada). When the negative muon is implanted in a medium, it slows down and is captured by a medium atom. In condensed matter the muon reaches the ls-state within the time less than 10"l0 s. Because of its large mass, the Bohr radius of the muon is 200 times smaller than that of the K-electron. The negative muon is an unstable particle and decays mainly through the mode /J,~ —> e~ + v^ + i>e. As a consequence of the parity nonconservation in this process, the spatial distribution of the decay electrons is asymmetric. This phenomenon serves as the basis for measuring the magnetic moment of the muon. In the transverse magnetic field its magnetic moment (and spin) precesses with the frequency v = ifi^H/h = g^H/h, where fi^ is the Bohr magneton for the muon. For polarized muons the exponential curve of the time distribution (with respect to muon stops in the sample) of decay electrons is modulated by a cosine with the frequency v. The cosine amplitude is proportional to the muon polarization in the ls-state. Therefore, by measuring the muon spin precession frequency one can determine the magnetic moment of the bound muon. Experimentally the correction to the magnetic moment (g-factor) of a bound negative muon is determined by comparing the spin precession frequencies of the positive and negative muons in the external magnetic field:
9+-9- _ u+ -o>_ . ._
9+ w+ where g+, g-, OJ+, and cj_ are the g-factors and the precession frequencies for the positive and negative muons. The present measurements were carried out with the "Stuttgart LFQ- spectrometer" [11] at the //E4 beamline of the Paul Sherrer Institute accelera- tor (Switzerland). The momentum of the muon beam was ~ 68 MeV/c. The external magnetic field of 0.1 T transverse to the direction of the muon spin was produced on the sample by the Helmholtz coils. The middle diameter of the coils was 510 mm, the distance between the coil centers was 240 mm. These dimensions are close to the optimal ones for obtaining the magnetic field with homogeneity not worse than 10~5 in the volume of 3x3x3 cm3 in the center of the coils. The components of the terrestrial magnetic field and stray fields from the magnetic elements nearest to the spectrometer were com- pensated by three pairs of additional coils with an accuracy of 10~2 oersted. The residual magnetic field was measured by three reciprocally perpendicu- lar permalloy sensors. The positioning of the Helmholtz coils relative to the beam axis (collimator) was done with a laser. The samples investigated were shaped as cylinders of 30 mm in diameter and 12, 18, 11, and 10 mm thick in case of carbon (reactor grade graphite), oxygen (water), magnesium, and silicon, respectively. Water was packed in a cylindrical container made of phenoplast with 2 mm thick walls. The weight of the water container was 1.7 gram. The silicon sample was an intrinsic silicon crystal (p ~104 Ohm-cm). The samples were positioned so that the cylinder axis coincided with the axis of the beam. The beam spot size on the sample was about 16 mm. The position of the sample relative to the beam axis was fixed with an accuracy better than 1 mm. To find out the muon distribution in the sample volume, the dependence of the muon stopping rate on the thickness of a copper degrader (muon range curve) was measured for a 1 g/cm2 thick graphite sample. The muon range curve has a maximum at ~ 4 g/cm2 and the full witdth at the half-maximum (at the 5% level of the maximum) 0.8 g/cm2 (1.4 g/cm2). Thus, the volume of the muon stop region in the samples investigated was not larger than 6 cm3. The free muon spin precession frequency was determined by the preces- sion frequency of the fj,+ spin in graphite. Thus the measurements in graphite were carried out alternatively with the positive and negative muon beams ob- tained with the same momentum in the fjE4 channel. The measurements with the negative muon beam and the O(H20), Mg, and Si samples alternated with the graphite measurements. The following values were obtained for the asym- metry coefficient in the space distribution of electrons (positrons) from the + H~(fM ) decay in C, O(H2O), Mg, and Si: 0.0486±0.0003 (0.167±0.0007), 0.0177±0.0004, 0.0324±0.0004 H 0.0304±0.0004.
Table: The measured muon spin precession frequency u>_(w+) and the deduced correction to the g-factor of the bound negative muon (g+—g-)/g+ = (UJ+ — Lj_)/uj+ for carbon, oxygen (water), magnesium and silicon samples. The positive muon precession frequency u>+ is corrected for the paramagnetic shift in carbon (3.8 • 10~4 [7])
target w_(w+), gt-g- g+-g- a±-t io-i 9+ ' 9+ ' 4 9+ rad/fis io- 10-" present exp. present exp. exp. [7] theor. [5] total relativistic C(graphite, fi+) (85.109±0.003) C(graphite) 85.044±0.006 85.060±0.008 85.031 ±0.009 85.047±0.009
(mean value) 85.045±0.004 7.5±0.7 7.6±0.3 8.2±0.1 6.29
0, in H2O 85.053±0.014 6.5±1.6 9.4±1.0 14.3±0.2 11.04±0.01 Mg, in metal 84.931±0.014 21.0±1.6 26.4±0.7 29.8±0.6 23.79±0.06
Mg, in MgH2 29.6±0.7 Si, crystal 84.811 ±0.024 35.1±2.8 36.3±1.1 39.1±1.0 31.70±0.10 Table shows measured spin precession frequencies of positive and neg- ative muons for the samples investigated. The precession frequency for the 4 positive muon is corrected for the paramagnetic shift in carbon (3.8 • 10~ u;+ [7]). The corrections to the g-factor of the negative muon in the Is-state of carbon, oxygen, magnesium, and silicon atoms are compared in the table with the analogous data of [7] and theoretical calculations [5]. In the last column of the table the calculated value [5] of the relativistic correction to the muon magnetic moment is shown. As is seen from the table, the preces- sion frequencies of the negative muon spin in graphite measured at different time (the time interval between the measurements was about 5 hours) coin- cide within statistical errors thus characterizing the long-term stability of the external magnetic field on the sample is not worse than 10~4. The corrections to the g-factor (magnetic moment) of the negative muon in the ls-state of carbon, oxygen, and silicon agree with the data [7] and do not confirm the results [9], where measured (g+ — g~)/g+ for negative muons in Mg, Si, and S were smaller by 17 • 10~4. Thus, the results of the present investigation are close to the experimental data [7] and indicate that the magnetic moment of the negative muon bound in the Coulomb field of the nucleus differs from the one of the free muon. But the experimental correc- tions to the negative muon g-factor (present work and [7]) are systematically smaller than the calculated ones by (10 — 30) %. To find out the causes of the systematic discrepancy between the theoretical and experimental data additional theoretical calculations are to be carried out. The authors are grateful to the Directorate of the Paul Sherrer Institute for the possibility of carrying out the experiment and to Dr. I.A.Yutlandov for providing the magnesium sample.
References
[1] G.Breit, Nature 122, 649 (1928). [2] H.Margenau, Phys.Rev. 57, 383 (1940). [3] V.W.Hughes, V.L.Telegdi, Bull.Am.Phys.Soc. 3, 229 (1958).
[4] K.W.Ford, J.G.Wills, NucLPhys. 35, 295 (1962). [5] K.W.Ford, V.W.Hughes, J.G.Wills, Phys.Rev., 129, 194 (1963). [6] Particle Data Group, Review of Particle Properties, Euro Phys. J C 3, 1 (1998). [7] D.P.Hutchinson, J.Menes, G.Shapiro, A.M.Patlach, Phys. Rev., 131, 1362 (1963). [8] T.Yamazaki, S.Nagamiya, O.Hashimoto et.al., Phys.Lett., 53B, 117 (1974). [9] J.H.Brewer, Hyp. Interact. 17-19, 873 (1984). [10] D.P.Hutchinson, J.Menes, G.Shapiro, A.M.Patlach, Phys. Rev., 131, 1351 (1963). [11] R.Scheuermann, J.Schmidl, A.Seeger et.al., Hyp. Interact. 106, 295 (1997).
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Publishing Department Joint Institute for Nuclear Research Dubna, Moscow Region 141980 Russia E-mail: [email protected]. Мамедов Т.Н. и др. Е14-2000-158 Измерение магнитного момента отрицательного мюона в 1 S-состоянии в различных атомах
В 1958 году Хьюз и Телегди (V.W.Hughes and V.L.Telegdi, Bull. Am. Phys. Soc, 3, 229, 1958) обратили внимание на тот факт, что релятивистское движение отрицатель- ного мюона, находящегося на lS-орбите атома, должно приводить к отличию его маг- нитного момента от магнитного момента свободного мюона. Как следует из расчетов Форда и др. (К.W.Ford et al., Phys. Rev., 129, 194, 1963), разность между величинами g-фактора связанного и свободного мюона сильно зависит от заряда ядра. До настоящего времени было выполнено всего три эксперимента по измерению магнитного момента отрицательного мюона в 1 S-состоянии в различных атомах. В слу- чае тяжелых элементов относительная ошибка измерения поправок к величине магнит- ного момента мюона в связанном состоянии превышает 50 %, вследствие чего сравне- ние экспериментальных данных с теоретическими расчетами не имеет смысла. В случае легких атомов имеется расхождение в результатах двух работ для Mg, Si и S. В настоящей работе представлены результаты предварительных измерений магнит- ного момента отрицательного мюона в углероде, кислороде, магнии и кремнии.
Работа выполнена в Лаборатории ядерных проблем им. В.П.Джелепова ОИЯИ.
Сообщение Объединенного института ядерных исследований. Дубна, 2000
Mamedov T.N. et al. E14-2000-158 Measurement of the Magnetic Moment of the Negative Muon in the IS-State of Different Atoms
In 1958 Hughes and Telegdi (Bull. Am. Phys. Soc., 3, 229, 1958) paid attention to the fact that the negative muon in the 1 S-state should possess a magnetic moment different from the free muon one due to its relativistic motion. As follows from the calculations of Ford et al. (Phys. Rev., 129, 194, 1963), the difference of the g-factor for the bound and free muon strongly depends on the nuclear charge Z. Up to now there have only been three measurements of the magnetic moment of the negative muon in the ls-s(ate of different atoms. The relative error of the measure- ments of the corrections to the magnetic moment of a bound muon is larger than 50 % in the case of heavy atoms and therefore a comparison of the experimental data with the the- oretical calculations makes little sense. For light atoms there is a discrepancy in the results of two works for Mg, Si, and S atoms. In this work preliminary results of the measurements of the magnetic moment of the negative muon in carbon, oxygen, magnesium and silicon are presented.
The investigation has been performed at the Dzhelepov Laboratory of Nuclear Prob- lems, J1NR.
Communication of the Joint Institute for Nuclear Research. Dubna, 20(X) MaxeT T.E.IloneKo
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