Kaonic Hydrogen atom X-rays

The X-ray spectrum obtained with kaons stopping in liquid hydrogen has been measured. Possible candidates for X-ray lines from kaonic hydrogen atoms have been identified and the results compared with previous experiments and with theoretical predictions. X-ray lines from σ^?p atoms may also have been observed.     

Experimental study of pionic Ca and Ti and examination of the pion-nuclear potential for low-Z nuclei

We report the measurement of the strong interaction shifts and widths of the 3d → 2p transitions in pionic ^{40,42,43,44,48}Ca and ^46,48,50Ti. Using these new data in combination with earlier low-Z pionic data (6 ≦ Z ≦ 16), we have studied, in a purely phenomenological way, the pion-nuclear optical potential. Employing nuclear-structure information from Hartree-Fock calculations and measured charge densities, we have fitted the pion-nuclear potential parameters to the pionic atom data. The effect of adding an isovector dependence to the s- and p-wave two-nucleon terms has been investigated. We have also explored the sensitivity of these data to the value of the Lorentz-Lorenz parameter ξ. A small but definite sensitivity to the latter parameter has been observed with the best fit value of ξ being significantly greater than 1. We have used the phenomenological potentials to determine the neutron radii of the Ca and Ti isotopes and, in fact, find reasonable agreement with Hartree-Fock predictions and with the results of other hadronic probes.     

Pionic K X-rays in liquid He

Energies and lorentzian widths of pionic K X-ray transitions have been measured in liquid ³He with improved accuracy. The strong interaction on the π³He 1s level is found to be attractive and to produce an increase in the K transition energies of 34 ± 4 eV; the measured lorentzian width is 36 ±7 eV. Measured values are also presented for K X-ray energies in liquid π⁴He and μ⁴He, the lorentzian width of the 1s level in π⁴He, and relative intensities of K X-ray transitions in π³He, π⁴He and μ⁴He. The measurements are compared with those of others and with recent theoretical calculations.     

X-rays from antiprotonic helium in helium gas

X-ray transitions to the 4F, 3D, and 2P atomic levels of p?He have been observed with antiprotons stopped in He gas at 4 and 1.1 atm NT. The population by radiative transitions of the 3D level in gas Y_M(4atm) = (28±14)% and Y_M(1.1 atm) = (43±22)% exceeds by more than one order of magnitude that measured in liquid He. The annihilation width of the 3D level Γ^a_3D = 2.8±1.0 × 10^?3eV is determined from the ratio between the numbers of X-rays feeding and depopulating the 3D level. The strong-interaction shift of the 2P level ε(2P) = ?14±6 eV is obtained by inputting the $\text{p}\text{He}$ experimental X-ray yields into a cascade calculation, the results of which are in good agreement with well-established data from muonic, pionic, and kaonic helium.     

Precision measurement of the 2p-1s transition wavelength in muonic 13C

With the bent-crystal spectrometer at the SIN muon channel we have measured the wavelength of the 2p-1s transition in muonic ¹³C with a precision of 13 ppm. The result for the $\text{2}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{-1}\text{S}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ transition is $\text{λ(2}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{-1}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{) = 16.46055 ± 0.00021}\text{pm}$; it is interpreted in terms of a short-range muon-nucleon interaction not included in standard QED calculations.     

Pionic X-rays from 12, 13C

The energies and widths of pionic 2p-1s and 3d-2p X-rays have been measured in ^12,13C. Values obtained are

${}^{12}\text{C: 2p-1s E=93.221(55)}\text{keV}\text{, τ=2077(14)}\text{keV}$

$\text{3d-2p E=18.400(6)}\text{keV}\text{, τ=1.17(11)}\text{eV}$

${}^{13}\text{C: 2p-1s E=92.227(27)}\text{keV}\text{, τ=2.59(11)}\text{keV}$

$\text{3d-2p E=18.427(5)}\text{keV}\text{, τ=0.97(10)}\text{eV}$

The muonic 2p-1s X-ray energies in ^12,13C have also been measured. The strong interaction effects are discussed in relation to recent low-energy pion scattering measurements.     

Measurements of the polarization of the 2p and 1s states in muonic atoms and the helicity of the muon in pion decay

We have measured the polarization of the 2p and 1s states in muonic selenium (amorphous and metallic modifications), cadmium, palladium and iodine, in order to study the depolarization of muons in the cascading process and to measure the helicity of the μ^?. In the cases of cadmium, palladium and amorphous selenium good agreement between the measurements and cascade calculations is found. There is an unexpected depolarization of the 2p_{$\text{1}\text{2}$} state in metallic selenium. The helicity of the muon after the pion decay was measured to h_μ^? = + 0.99 ± 0.16.     

Systematics of nuclear charge radii of the stable molybdenum isotopes from muonic atoms

The results of precise measurements of the energies of the $\text{2}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{?1}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{and}\text{2}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{?1}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ muonic X-ray transitions of ⁹²Mo, ⁹⁴Mo, ⁹⁵Mo, ⁹⁶Mo, ⁹⁷Mo, ⁹⁸Mo and ¹⁰⁰Mo are reported. The data were analyzed in terms of the Barrett moments 〈r^ke^?αr〉 of the nuclear charge distributions from which the equivalent nuclear radii R_k and the differences ΔR_k between neighboring isotopes were computed. Systematic shell effects have been observed at the neutron numbers N = 50 and N = 56.     

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

We have measured the wavelengths of the $\text{3}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{?2}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and the $\text{3}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{-2}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ X-ray transitions in μ-²⁴Mg, -²⁸Si and -³¹P 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 ¹⁷⁰Tm and ¹⁶⁹Yb 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

$\text{λ}{}_{\mathrm{<mtext>exp</mtext>}}\text{?λ}{}_{\mathrm{<mtext>th</mtext>}}\text{λ}{}_{\mathrm{<mtext>th</mtext>}}\text{= (2 ± 8) × 10}{}^{\mathrm{?6}}$

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

$\text{g}{}_{\mathrm{<mtext>N</mtext>}}\text{g}{}_{\mathrm{\mu }}\text{4π}\text{= (?4 ± 17) × 10}{}^{\mathrm{?9}}$

Alternatively, we can deduce from our experiments the most accurate direct value to date for the negative muon mass,

$\text{m}{}_{\mathrm{\mu }}\text{- = 105.65906(91)}\text{MeV}$

.     

A muonic X-ray study of the charge distribution of 144, 148, 150, 152, 154Sm

We report the measurement of the energies of the 4f → 3d, 3d → 2p and 2p → Is muonic atomic transitions in separated isotopes of ^{144, 148, 150, 152, 154}Sm, and that of the 2s → 2p transitions of ¹⁵²Sm as well. Using these transition energies as well as the hyperfine splittings of the 2p levels, we have interpreted our data in terms of a deformed Fermi distribution for the charge density and obtained good fits. A model independent analysis of the isotope shifts in terms of generalized R_h moments has been made and is in good agreement with electronic X-ray and optical isotope shifts. The static quadrupole moments and the isomer shifts of the first excited state of ^{152, 154}Sm have been determined from the 2p hyperfine structure.     

Measurement of strong interaction effects in kaonic atoms

X-rays produced by kaons stopping in targets of O, Mg, Al, Si, S, Co, Ni, Cu, Ag, Cd, In and Sn have been observed. The shifts, widths and yields of the last observed mesic X-ray due to the effects of the strong interaction have been measured. The results are compared with optical-model predictions.     

Resonant enhancement of the formation of hydrogen-helium muonic molecules

Formation of muonic molecules and , where J is rotational quantum number, in electron conversion process is investigated at collision energies between 0.004 eV and 50 eV. Corresponding reaction rates are calculated in adiabatic approximation for the three-body Coulomb problem. Significant enhancement of the rates for and is found near 7 eV and 30 eV, respectively. It is shown that the enhancement is due to resonances present in elastic and scattering at these energies. Acceleration of dμ atoms up to the resonant energy could be realized in triple H-D-³He mixture due to the muon transfer from protium to deuterium. Experimental investigation of nuclear synthesis from molecular state directly formed in the mixture is suggested.     

Nuclear charge radii from muonic X-ray transitions in F,Na, Al,Si, P,S and K

Energies of muonic X-rays of the Lyman series of seven light natural elements (F, Na, Al, Si, P, S and K) have been determined with an accuracy of between 15 and 30 eV. Equivalent charge radii have been deduced. For μ^?-K, transitions to the 2s state allowed an additional constraint on the Fermi c-t diagram. The results are in good agreement with, and generally of an order of magnitude higher precision than, comparable electron scattering data.     

Quadrupole interactions in pionic and muonic tantalum and rhenium

The hyperfine splitting of pionic and muonic X-rays in natural Re has been studied using the known ratio (accurate to 1.6 parts in 10⁵) of the quadrupole moments of the two naturally occurring ¹⁸⁵Re and ¹⁸⁷Re isotopes. From the hyperfine splitting of the ⁵g → 4f and 4f → 3d pionic X-rays the effective quadrupole hyperfine constants were determined to be ¹⁸⁷A₂^eff(4f) = 1.163 ± 0.010 keV and ¹⁸⁷A₂^eff(3d) = 5.39 ± 0.63 keV, giving strong interaction quadrupole shifts ₂(4f) = 46 ± 10 eV and ₂(3d) = 1.3 ± 0.6 keV. The strong interaction monopole shifts ₀ and widths Γ₀ of the 5g, 4f and 3d levels have also been measured. For the two higher orbits, standard optical-potential calculations fit the measured shifts and widths quite well. The observed deeper-lying 3d state, however, has shifts and widths that differ by a factor of 2 or more from the predictions. From the measured quadrupole hyperfine constants of the 4f level we calculate the spectroscopic quadrupole moments to be ¹⁸⁷Q^μ(gm) = 2.09 ± 0.04 b, ¹⁸⁷Q^π = 2.07 ± 0.02 b, ¹⁸⁵Q^μ = 2.21 ± 0.04 b, and ¹⁸⁵Q^π = 2.1 addition, muonic X-rays from ¹⁸¹Ta were observed; using the same methods for determining the quadrupole moment as above, a value of ¹⁸¹Q^μ = 3.28 ± 0.06 b was obtained, in good agreement with earlier published data.     

Measurement of average electron densities in Si and Ge using MeV δ-rays produced by channelled high-energy projectiles

For the first time, average electron densities in silicon and germanium were measured using the channeling effect for 5 and 12 GeV/c protons, π⁺ and π^?. In the investigation, the yield of MeV electrons emitted through the back of the target was measured. Such gd-ray yields are proportional to the local electron density averaged along the path of the projectile in the target. For well-aligned, positive particles, the electron yield is reduced to around 15% of normal yield for germanium and 25% for silicon, whereas negatively charged, channeled projectiles give an increase in yield by a a factor of three compared to normal yield. The experimental results have been compared to yield curves calculated using the Lindhard channeling model in connection with special potential models, and very good agreement is obtained for positive particles when the electron density in the middle of the channels is obtained by summing the contributions from many neighbouring strings. For positive projectiles, this channeling method is most sensitive far away from the strings, where other techniques are weak. The results for negative, channeled particles agree fairly well with simplified theoretical calculations, neglecting dechanneling and the lack of equilibrium in angular momenta in the transverse plane.     

Muonic and pionic L- and M-series in carbon and oxygen and the pionic 2p level shift and width of oxygen

Muonic and pionic X-rays of the L- and M-series in C and O have been measured with a Si(Li) detector in the energy range between 7 keV and 60 keV. The target consisted of mylar (C₅H₄O₂). Energies and intensities of 21 transitions have been determined. The strong interaction shift of the pionic 2p level in O was measured and found to be +4.1 ±2.3 eV. The measured width of this level is 11±6 eV. The measured yields have been compared with cascade calculations.