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Spectroscopy of muonic hydrogen : measurement of the proton charge radius (presentation of the experiment - 2007)

F. Biraben, P. Indelicato, L. Julien, E.O Le Bigot, F. Nez, C. Schwob

At the present time, the poor knowledge of the proton charge radius limits the comparison of theory with experiment in atomic hydrogen. In a first approximation, the proton is considered as a sphere uniformly charged in volume, whose radius is known with an uncertainty of 2% ! With the accuracy one reaches today on experiments, the calculated frequency of transitions in atomic hydrogen strongly depends on the proton charge radius.

The present knowledge of the proton radius ( $r_{p}$ ) comes from electron scattering experiments or from high resolution measurements in hydrogen. Electron scattering experiments dated from the years 1960 and 1980. Subsequently, many analysis of the available data have been performed. The most recent one (I. Sick, 2003) leads to $r_{p}=$ 0,895(18) fm. The value of $r_{p}$ deduced from atomic hydrogen spectroscopy is strongly dependent on QED corrections. The corresponding value is $r_{p}$ =0,8750(68) fm.

The goal of the international collaboration developed at the Paul Scherrer Institut (PSI, Switzerland) is to measure the proton charge radius at 0,1 %.

Principle of the experiment

The key point of this experiment is the measurement of the 2S-2P Lamb shift in muonic hydrogen (an hydrogen atom in which a muon takes the place of the electron). As the muon is 207 times heavier than the electron, muonic hydrogen has a correspondingly smaller size than a hydrogen atom. The relative contribution of the proton charge to the Lamb shift is as much as 2%, that is two orders of magnitude more than for normal hydrogen. For the same reason, the effect of vacuum polarization is more important than the self-energy. Consequently the 2S level is below the 2P one and the 2S-2P transition is in the infrared region, around 6 µm. The transition probability is smaller by a factor $(m_{e}/m_{\mu})^{3}$ (about $10^{7}$ ) compares to normal hydrogen. This very weak transition probability, added to the small number of muonic hydrogen atoms one can product, makes this experiment very difficult. We expect a signal of a few events per hour...

The initial scheme has been suggested in 1999. It uses a low density hydrogen target in which an ultra low energy muon beam is stopped, whereby highly excited $\mu p$ atoms are formed (n=14). Most of them deexcite quickly to the ground state, but about 1% form long-lived $\mu p_{2S}$ atoms. As the corresponding lifetime is on the order of 1,3 $\mu s$ , the laser pulse should be triggered on the muon entry to the apparatus in a stochastic way, with a short delay of about 1 $\mu s$ . For this, we use an excimer laser. A multistage laser system converts the 308 nm excimer laser pulse to a 6 $\mu m$ pulse. The excitation is observed from the 2 keV-Lyman $\alpha$ fluorescence. All the data are recorded on a computer, the analysis is performed a posteriori. The goal is to measure the 2S-2P Lamb shift with an uncertainty better than 30 ppm (accuracy of the calculated frequency of the transition), which represents 10% of the natural linewidth (20 GHz).

The experimental set-up is made of two parts : the production of muonic hydrogen and the 6 $\mu m$ -laser source. Our group is involved in the laser development part : it is in charge of the seeded oscillator-amplifier titanium sapphire laser system and of the frequency measurement of the full laser system.

Production of muonic hydrogen

The laser source

Two high power XeCl excimer lasers provide the pump energy for the whole system. Their pulses have a 1 $\mu s$ delay relative to the trigger signal. Each excimer pumps a multimode dye laser which converts the 308 nm excimer pulse to a 540 nm pulse. The green light pumps an injection-seeded oscillator-amplifier Ti:Sa laser system which delivers a 708 nm pulse. The 6 $\mu m$ radiation needed to excite the 2S-2P transition is obtained from the conversion of the 708 nm pulse by a third-Stockes Raman shifter operated with 14 bar H $_{2}$ gas. Our group has developed the oscillator-amplifier system, the oscillator being seeded by a tunable cw-Ti:Sa laser.

708 nm-Ti:Sa oscillator

This set-up has been developed in Paris and then brought to PSI. Using a very short oscillator cavity (the cavity is a few cm long with no Pockels cell) associated with an 8 pass-amplifier, we obtain pulses of 12 mJ, with a length shorter than 7 ns for a pump energy between 90 and 100 mJ. During a run of 3 weeks, performed at the end of 2003, we have shown that the laser system was reliable. The frequency of the 6 $\mu m$ radiation is given by the cw Ti:Sa laser. This one is frequency locked on a stable Fabry Perot cavity whose length is fixed. A lambdameter and an iodine cell are also used to measure the laser frequency. The mesurement of the frequency difference between the cw laser and the oscillator is in very good agreement with the simulations. The calibration of the absolute frequency of the 6 $\mu m$ source is performed by measuring a water absorption line. The Raman shift due to the dihydrogen cell and deduced from the 708 nm and 6 $\mu m$ calibrations is in goog agreement with the previous measurements, demonstrating the coherence of the frequencies measurements of the all system.

During a first run, at the end of 2002, we have demonstrated that the different parts of the system could run together during a long period, showing the validity of our experimental set-up. During the second run (3 weeks at the end of 2003), no resonance has been observed because of the low statistic due in parts to the weakness of the pump laser (excimer and dye lasers). It has now been substituted by an Yb:YAG disk laser, developed in collaboration with the Stuttgart University. A new run will take place in july and august 2007.

Members of the international collaboration

D. Taqqu, Paul Scherrer Institute, Villigen, Suisse.

F. Kottmann, Labor für Hochenergiephysik, ETH-Zürich, Suisse.

O. Huot, P. Knowles, L. Ludhova, F. Mulhauser, L.A. Schaller, Institut de Physique de l’Université, Fribourg, Suisse.

F. Amaro, J.M.R. Cardoso, C.A.N. Conde, L.M.P. Fernandes, C.M.B Monteiro, J.M.F. dos Santos, J.F.C.A. Veloso, Départment de Physique, Université de Coimbra, Portugal.

A. Antognini, T.W. Hänsch, T. Nebel, R. Pohl, Max-Planck-Institut für Quantenoptik, Garching, Allemagne.

P. Rabinowitz, Department of Chemistry, Princeton University, Princeton, USA.

A. Dax, S. Dhawan, V.W. Hughes, Physics department, Yale University, New Heaven, USA.

Y.W. Liu, Physics department, National Tsing Hua University, Hsinchu, Taïwan.

Institut für Strahlwerkzeuge, Universität Stuttgart, Stuttgart, Allemagne

F. Biraben, P. Indelicato, L. Julien, E.O. Le Bigot, F. Nez, C. Schwob, Laboratoire Kastler Brossel, ENS, CNRS, UPMC, Paris, France.

Publications on this experiment

2005
L. Ludhova, A. Antognini, F.D. Amaro, F. Biraben, J.M.R. Cardoso, C.A.N. Conde, A. Dax, S. Dhawan, L.M.P. Fernandes, T.W. Hänsch, F.J. Hartmann, V.-W. Hughes, O. Huot, P. Indelicato, L. Julien, P.E. Knowles, F. Kottmann, Y.-W. Liu, C.M.B. Monteiro, F. Mulhauser, F. Nez, R. Pohl, P. Rabinowitz, J.M.F. dos Santos, L.A. Schaller, D. Taqqu, and J.F.C.A. Veloso, Nucl. Instr. and Meth. A540 (2005) 169 : “Planar LAAPDs : Temperature Dependence, Performance, and Application in Low Energy X-ray Spectroscopy”

A. Antognini, F.D. Amaro, F. Biraben, J.M.R. Cardoso, C.A.N. Conde, A. Dax, S. Dhawan, L.M.P. Fernandes, T.W. Hänsch, F.J. Hartmann, V.-W. Hughes, O. Huot, P. Indelicato, L. Julien, P.E. Knowles, F. Kottmann, Y.-W. Liu, L. Ludhova, C.M.B. Monteiro, F. Mulhauser, F. Nez, R. Pohl, P. Rabinowitz, J.M.F. dos Santos, L.A. Schaller, C. Schwob, D. Taqqu, and J.F.C.A. Veloso, Opt. Comm. 253 (2005) 362 : « Powerful fast triggerable 6µm laser for the muonic hydrogen 2S Lamb shift experiment ».

2007
L. Ludhova, F. D. Amaro, A. Antognini, F. Biraben, J. M. R. Cardoso, C. A. N. Conde, A. Dax, S. Dhawan, L. M. P. Fernandes, T. W. Hänsch, V. W. Hughes, P. Indelicato, L. Julien, P. E. Knowles, F. Kottmann, Y.-W. Liu, J. A. M. Lopes, C. M. B. Monteiro, F. Mulhauser, F. Nez, R. Pohl, P. Rabinowitz, J. M. F. dos Santos, L. A. Schaller, C. Schwob, D. Taqqu, and J. F. C. A. Veloso, Phys. Rev. A 75, 040501(R) (2007) : « Muonic hydrogen cascade time and lifetime of the short-lived 2S state ».

Proccedings

2000
R. Pohl, F. Biraben, C.A.N. Conde, C. Donche-Gay, T.W. Hänsch, F.J. Hartmann, P. Hauser, V.W. Hughes, O. Huot, P. Indelicato, P. Knowles, F. Kottmann, Y.W. Liu, F. Mulhauser, F. Nez, C. Petitjean, P. Rabinowitz, J.M.F. dos Santos, L.A. Schaller, Y.H. Schneuwly, W. Schott, L.m. Simons, D. Taqqu, F. Trehin, J.F.C.A. Veloso, Hyperfine-Interactions 127 (2000) p. 161-166. : "Experiment to measure the Lamb shift in muonic hydrogen".

2001
R. Pohl, F. Biraben, C.A.N. Conde, C. Donche-Gay, T.W. Hänsch, F.J. Hartmann, P. Hauser, V.W. Hughes, O. Huot, P. Indelicato, P. Knowles, F. Kottmann, Y.W. Liu, F. Mulhauser, F. Nez, C. Petitjean, P. Rabinowitz, J.M.F. Dos Santos, L.A. Schaller, H. Schneuwly, W. Schott, L. Simons, D. Taqqu et J.F.C.A. Veloso, Lecture Notes in Physics (Springer), The Hydrogen Atom, Precision Physics of Simple Atomic Systems, édité par S.G. Karshenboïm, F.S. Pavone, G.F. Bassani, M. Inguscio and T.W. Hänsch, LNP 570 (2001) sur cdrom : "Towards a measurement of the Lamb shift in muonic hydrogen".

F. Kottmann, F. Biraben, C.A.N. Conde, C. Donche-Gay, T.W. Hänsch, F.J. Hartmann, P. Hauser, V.W. Hughes, O. Huot, P. Indelicato, P. Knowles, Y.W. Liu, F. Mulhauser, F. Nez, C. Petitjean, R. Pohl, P. Rabinowitz, J.M.F. Dos Santos, L.A. Schaller, H. Schneuwly, W. Schott, L. Simons, D. Taqqu et J.F.C.A. Veloso, Proceedings of the Conference QED 2000 (Trieste, 2000), Quantum Electrodynamics and Physics of the Vacuum, édité par G. Cantatore, AIP-Conference proceedings 564 (2001) p.13-20 : "Towards a Lamb shift measurement in muonic hydrogen".

F. Kottmann, W. Amir, F. Biraben, C.A.N. Conde, S. Dhawan, T.W. Hänsch, F.J. Hartmann, V.W. Hughes, O. Huot, P. Indelicato, L. Julien, P. Knowles, S. Kazamias, Y.-W. Liu, F. Mulhauser, F. Nez, R. Pohl, P. Rabinowitz, J.M.F.D. Santos, L.A. Schaller, H. Schneuwly, W. Schott, D. Taqqu et J.F.C.A. Veloso, Hyp. Int. 138 (2001), p. 55-60 : “The Muonic Hydrogen Lamb Shift Experiment at PSI”.

2003
F. Kottmann, A. Antognini, F. Biraben, M. Boucher, C.A.N. Conde, A. Dax, S. Dhawan, L.M.P. Fernandes, T.W. Hänsch, F.J. Hartmann, V.-W. Hughes, O. Huot, P. Indelicato, L. Julien, P.E. Knowles, Y.-W. Liu, J.A.M. Lopes, L. Ludhova, C.M.B. Monteiro, F. Mulhauser, F. Nez, R. Pohl, P. Rabinowitz, J.M.F. dos Santos, L.A. Schaller, J-T. Shy, D. Taqqu, and J.F.C.A. Veloso, “the muonic hydrogen Lamb shift experiment at PSI” Proc. Of the International Workshop on Exotic Atoms (EXA02) Nov 28-30, 2002 Vienna, Austria, Eds P.Kienle, J.Marton and J.Zmeskal, Anstrian Academy of Sciences Press, p.159, Vienna (2003).

2004
W. Amir, A. Antognini, F. Biraben, M. Boucher, C.A.N. Conde, A. Dax, S. Dhawan, L.M.P. Fernandes, T.W. Hänsch, F.J. Hartmann, V.-W. Hughes, O. Huot, P. Indelicato, L. Julien, S. Kazamias, P.E. Knowles, F. Kottmann, Y.-W. Liu, J.A.M. Lopes, L. Ludhova, C.M.B. Monteiro, F. Mulhauser, F. Nez, R. Pohl, P. Rabinowitz, J.M.F. dos Santos, L.A. Schaller, J-T. Shy, D. Taqqu, and J.F.C.A. Veloso, “Towards the most precise test of bound state QED” Proc of workshop”HadAtom03”, Trento, Italy arXiv.org:hep-ph/0401204, p.41 (2004).

2005
R. Pohl, A.Antognini, F.D. Amaro, F. Biraben, J.M.R. Cardoso, C.A.N. Conde, A. Dax, S. Dhawan, L.M.P. Fernandes, T.W. Hänsch, F.J. Hartmann, V.-W. Hughes, O. Huot, P. Indelicato, L. Julien, P.E. Knowles, F. Kottmann, Y.-W. Liu, L. Ludhova, C.M.B. Monteiro, F. Mulhauser, F. Nez, P. Rabinowitz, J.M.F. dos Santos, L.A. Schaller, C. Schwob, D. Taqqu, and J.F.C.A. Veloso, Can. J. Phys. 83 (2005) p.339-349 : “The muonic hydrogen Lamb shift experiment”.

T. Nebel, F.D. Amaro, A. Antognini, F. Biraben, J.M.R. Cardoso, C.A.N. Conde, A. Dax, S. Dhawan, L.M.P. Fernandes, A. Giesen, T.W. Hänsch, P. Indelicato, L. Julien, P.E. Knowles, F. Kottmann, E. Le Bigot, Y.-W. Liu, J.A.M. Lopez, L. Ludhova, C.M.B. Monteiro, F. Mulhauser, F. Nez, R. Pohl, P. Rabinowitz, J.M.F. dos Santos, L.A. Schaller, K. Schuhmann, C. Schwob, D. Taqqu, and J.F.C.A. Veloso, soumis à Can. J. Phys. : "Status of the muonic hydrogen Lamb-shift experiment".

Dans la même rubrique :

Mesure de la distribution de charge du proton (présentation de l’expérience - 2007)