W. Beer

Das fokussierende kristallspektrometer der universität fribourg

Abstract The construction of a DuMond type curved crystal spectrometer is described. The apparatus is designed to operate with a fixed source. The crystal and collimator are rotated by independent precision gears driven by stepmotors. One step corresponds to a crystal rotation of 0.3″. A magnetostrictive driving mechanism allows interpolation between steps. The complete spectrometer is enclosed in a thermostatic hut. The reproducibility of a measurement within a two day period is shown to be better than 0.1″. The nonlinearity of the system has been calibrated with a Wild T3 theodolite and a Moore table with a precision better than 0.2″. The measurements of many transitions in the decays of 182 W and 198 Hg in several orders and the application of the energy combination principle allow a very good test of the performances. They have shown that the precision has not been over-estimated. As a practical result a new more precise set of energies for the transitions in 182 W below 264 keV are given with reference to the W K α1 and Hg-411, 794 keV standards.

SPECTROSCOPIC QUADRUPOLE MOMENT OF 23Na FROM MUONIC X-RAYS+

Abstract With the crystal spectrometer at muon channel I at SIN we measured the 3 d 5 2 −2 p 3 2 transition in muonic 23Na. The h.f.s. of the 2 p 3 2 level was resolved and the spectroscopic quadrupole moment of the nuclear ground state determined: Q = 0.1006 ± 0.0020 b. Using a collective particle-rotor model description of 23Na which includes small ΔK = 1 admixtures in the wave functions, we find agreement between our measured spectroscopic quadrupole moment and the one derived from measured B(E2) values. Combining the quadrupole moment Q with the quadrupole coupling constant measured in the electronic atom of 23Na, we derive the electric field gradient at the nucleus for two different electronic states: 〈dE/dz〉 = 0.1185(32)ea−30 for the 3 2 P 3 2 state, 〈dE/dz〉 = 0.0410(27)ea−30 for the 4 2 P 3 2 state. The field gradient for the 3 2 P 3 2 state is compared with recent many-body calculations of the hyperfine interaction in alkali atoms.

New precision measurements of the muonic 3d52−2p32 X-ray transition in 24Mg and 28Si: Vacuum polarisation test and search for muon-hadron interactions beyond QED☆

Abstract Motivated by the importance of scalar particles in the current work on gauge theories of fundamental interactions, we have performed an improved muonic-atom experiment to search for long-range muon-hadron interactions. We remeasured the wavelengths of the 3 d 5 2 −2 p 3 2 X-ray transitions in 24Mg and 28Si with the bent-crystal spectrometer at the SIN muon channel. The relative difference between the X-ray wavelength λexp and the theoretical value as obtained from QED calculations, averaged over the two elements, is λ exp -λ QUED /λ QUED = (-0.2 +-3.1) × 10 6 Assuming the validity of the QED calculations, we can put limits on an additional muon-nucleon interaction: If such an interaction were mediated, for example, by a scalar or vector (isoscalar) boson with a mass smaller than about 1 MeV, the corresponding coupling constant is gμgN ⩽ 0.8 × 10−6 × e2. Alternatively, if additional muon-hadron interactions are negligible, our result corresponds to a 950 ppm test of the vacuum polarisation effect in QED. The result can also be interpreted as a 3 ppm measurement of the negative muon mass.

Precision measurement of the 2p-1s transition in muonic 12C: Search for new muon-nucleon interactions or accurate determination of the rms nuclear charge radius☆

The wavelength of the 2p32-ls12 transition in muonic 12C was measured with a crystal spectrometer as 16.473765 (88) pm. With an improved model-independent analysis we deduce an rms charge radius for 12C of 2.4829 (19) fm. A 2.4 standard deviation difference between our rms charge radius and that deduced from recent elastic electron-scattering experiments is tentatively attributed to a short-range additional interaction between muon and nucleons. A comparison is made with other experiments yielding information on such interactions.

Vacuum polarization test and search for muonhadron interactions from muonic X-rays:: Crystal-spectrometer experiments

Abstract We have measured the wavelengths of the 3 d 5 2 −2 p 3 2 and the 3 d 3 2 -2 p 1 2 X-ray transitions in μ - 24 Mg, - 28 Si and - 31 P with the bent-crystal spectrometer at the SIN muon channel. The X-rays are measured relative to the wavelengths of the 84 keV and the 63 keV γ-rays of 170 Tm and 169 Yb which have recently been calibrated to about 1 ppm. The measured X-ray wavelengths λ exp are compared with theoretical values λ th , as obtained from QED calculations. The relative difference, averaged over all six measured transitions, is λ exp −λ th λ th = (2 ± 8) × 10 −6 This result corresponds to a test of the vacuum polarization effect in QED of (0.6 ± 2.4) × 10 −3 . Assuming the QED calculations to be correct, we can use the result to put limits on additional muon-nucleon interactions (as required by gauge theories). If such an interaction is mediated by a scalar, isoscalar boson with a mass smaller than 1 MeV, the coupling constant is found to be g N g μ 4π = (−4 ± 17) × 10 −9 Alternatively, we can deduce from our experiments the most accurate direct value to date for the negative muon mass, m μ - = 105.65906(91) MeV .

Determination of the strong interaction shift in pionic hydrogen with a high resolution crystal spectrometer system

Abstract The 3P-1S X-ray transition energy was measured in pionic hydrogen with a double focussing silicon crystal spectrometer in combination with a cyclotron trap and CCD detectors: E = 2885.98 ± 0.17 (stat.) ± 0.15 (syst.) eV. The corresponding strong intera ction shift ϵ 1S = 7.12 ± 0.32 eV (attractive) yields the scattering length combination 1 3 (2a 1 + a 3 ) = 0.086 ± 0.004 m π −1 .

Spectroscopic quadrupole moments of 25Mg and 27Al from muonic X-rays

Abstract With the crystal spectrometer at Muon Channel I at SIN we measured the 3d 5 2 -2p 3 2 X-ray transitions in muonic 25Mg and 27Al. The h.f.s. of the 2p 3 2 was resolved and the spectroscopic quadrupole moment of the nuclear ground states determined: Q( 25 Mg ) = +0.201 ± 0.003 b , Q( 27 Al ) = +0.150 ± 0.006 b . We find agreement between the intrinsic quadrupole moment value derived from Q( 25 Mg ) with those calculated from measured B(E2) values. This indicates that for 25Mg the strong-coupling limit of the rotational model with an axially symmetric charge distribution is realized in the lower part of the ground-state rotational band. We combine the quadrupole moments Q with the quadrupole coupling constants measured in electronic atoms of 25Mg and 27Al and derive the electric field gradients at the nucleus (in units of e · a0−3, where a0 is the Bohr radius): 〈 d E d z 〉 = 0.339± 0.005 for the 3P2 state of 25Mg, 〈 d E d z 〉 = 0.54± 0.02 for the 2P 3 2 state of 27Al. From Hartree-Fock calculations of the 2P 3 2 state of Al we derive values for the Sternheimer correction factor R and compare them with calculated values.

Precision measurement of the wavelengths and natural line widths of 3d-2p pionic X-ray transitions in low-Z atoms

Abstract The wavelengths and the natural line widths of the 3d-2p transitions in the pionic atoms of 12 C, 16 O, 18 O, 24 Mg, 26 Mg, 28 Si and 30 Si have been measured at SIN with a bent-crystal spectrometer. The precision reached in the transition wavelengths ranges from 4 to 18 ppm, and in the widths from 2 to 14%.

New precision determination of the π− mass from pionic X-rays

Abstract The wavelength of the pionic 4f-3d transition in 24 Mg has been measured with a curved crystal spectrometer at SIN. The average population of the electronic K-shell during the pionic transition has been determined from the line shape of the pionic X-ray peak which allows a precise calculation of the electron screening correction to the transition energy. The wavelength calibration is based on the 25.7 keV γ-ray standard in the decay of 161 Tb ( λ = 48.334488 (64) pm). From the measured wavelength the new value of the pion-electron mass ratio is deduced to be m π − / m e − = 273.12677 (71). The obtained accuracy of 2.6 ppm is by a factor of 2.5 better compared with the best previous measurement. With this new π − /e − mass ratio the upper limit for the muon neutrino mass is reevaluated.

Energy of a muonic X-ray transition measured with a crystal spectrometer☆

Abstract The wavelength of the 3 d 5 2 −2 p 3 2 muonic X-ray transition in 28 Si has been measured relative to the wavelength of the 84 keV gamma ray from a 170 Tm source. The result is λ Si / λ Tm = 1.099675 (39). Using the reported value for λ Tm we find ( λ exp Si - λ th Si )/ λ th Si = (−9±35) × 10 −6 .