The Lamb-shift experiment in Muonic helium

We propose to measure several transition frequencies between the 2S and the 2P states (Lamb shift) in muonic helium ions (μ ⁴He^?+? and μ ³He^?+?) by means of laser spectroscopy, in order to determine the alpha-particle and helion root-mean-square (rms) charge radius. In addition, the fine and hyperfine structure components will be revealed, and the magnetic moment distribution radius will be determined. The contribution of the finite size effect to the Lamb shift (2S???2P energy difference) in μHe^?+? is as high as 20 %. Therefore a measurement of the transition frequencies with a moderate (for laser spectroscopy) precision of 50 ppm (corresponding to 1/20 of the linewidth) will lead to a determination of the nuclear rms charge radii with a relative accuracy of 3 ×10^???4 (equivalent to 0.0005 fm). The limiting factor for the extraction of the radii from the Lamb shift measurements is given by the uncertainty of the nuclear polarizability contribution. Combined with an ongoing experiment at MPQ aiming to measure the 1S???2S transition frequency in the helium ion, the Lamb shift measurement in μHe^?+? will lead to a sensitive test of problematic and challenging bound-state QED terms. This measurement will also help to clarify the discrepancy found in our previous μ _p experiment. Additionally, a precise knowledge of the absolute nuclear radii of the He isotopes and the hyperfine splitting of μ ³He^?+? provide a relevant test of few-nucleon theories.     

Precision spectroscopy of metastable hydrogen and antihydrogen with a Lamb-shift polarimeter

A spinfilter, the most important component of a Lamb-shift polarimeter, can be used to produce a beam of metastable hydrogen (deuterium) atoms in one hyperfine state (α1, α2 and together with the Sona transition β3). As function of a magnetic field separated transitions between the 2S _1/2 metastable hyperfine states seem to be observable as well as single transitions into the short-lived 2P _1/2 and 2P _3/2 states. The Breit-Rabi diagrams for these states can be measured with good precision. Furthermore, the hyperfine splittings and the Lamb shift can be observed as well. Application of this method to anti-hydrogen atoms are suggested.     

Emergence and space–time structure of lump solution to the (2$$$$1)-dimensional generalized KP equation

We derive the relativistic Hamiltonian of hydrogen atom in dynamical non-commutative spaces (DNCS or τ-space). Using this Hamiltonian we calculate the energy shift of the ground state as well the 2P _1/2, 2S _1/2 levels. In all the cases, the energy shift depends on the dynamical non-commutative parameter τ. Using the accuracy of the energy measurement, we obtain an upper bound for τ. We also study the Lamb shift in DNCS. Both 2P _1/2 and 2S _1/2 levels receive corrections due to dynamical non-commutativity of space which is in contrast with the non-dynamical non-commutative spaces (NDNCS or ??-space) in which the 2S _1/2 level receives no correction.     

Lamb shifts for hydrogen,using the sachs elementary interaction theory

The Lamb shifts of theS _1/2 andP _1/2 states of hydrogen atoms are calculated using the Sachs elementary interaction theory. BothS _1/2 andP _1/2 levels are shifted with respect to the Dirac levels by energies of the same order of magnitude. Agreement with experiment is obtained for the² S _1/2 –² P _1/2 and³ S _1/2 –³ P _1/2 Lamb shifts, but the predicted¹ S _1/2 –² P _1/2 Lamb shift term of 12,164 MHz is in disagreement with the experimental value of 7860 ± 1140 MHz.     

Nuclear-structure corrections to the energy spectra of ordinary and muonic deuterium

One-loop nuclear-structure-induced corrections of order (Zα)⁵ to the Lamb shift and to the hyperfine structure of deuterium are calculated. The contribution of deuteron-structure effects to the (ep)-(ed) and (μp)-(μd) isotopic shifts for the 1S–2S splitting is obtained with the aid of modern experimental data on the electromagnetic form factors for the deuteron. A comparison with the analogous contributions to the Lamb shift for ordinary and muonic hydrogen shows that the relative contribution of corrections associated with the nuclear structure increases as we go over from the hydrogen to the deuterium atom owing to the growth of the nuclear size.     

Maximal acceleration corrections to the Lamb shift of hydrogen,deuterium and He+

The maximal acceleration corrections to the Lamb shift of one-electron atoms are calculated in a nonrelativistic approximation. They are compatible with experimental results, are in particularly good agreement with the 2S2P Lamb shift in hydrogen and reduce by ∼ 50% the experiment-theory discrepancy for the 2S2P shift in He⁺.     

Fine and hyperfine structure of <Emphasis Type="Italic">P</Emphasis>-wave levels in muonic hydrogen

Corrections of order α ⁵ and α ⁶ are calculated for muonic hydrogen in the fine-structure interval ΔE ^fs = E(2P _3/2) − E(2P _1/2) and in the hyperfine structure of the 2P _1/2-and 2P _3/2-wave energy levels. The resulting values of ΔE ^fs = 8352.08 μeV, ΔẼ ^hfs(2P _1/2) = 7819.80 μeV, and ΔẼ ^hfs(2P _3/2) = 3248.03 μeV provide reliable guidelines in performing a comparison with relevant experimental data and in more precisely extracting the experimental value of the (2P–2S) Lamb shift in the muonic-hydrogen atom. Original Russian Text ? A.P. Martynenko, 2008, published in Yadernaya Fizika, 2008, Vol. 71, No. 1, pp. 126–136.     

Theory of the muonic hydrogen-muonic deuterium isotope shift

Corrections of the α³, α⁴, and α⁵ orders are calculated for the Lamb shift of the 1S and 2S energy levels of muonic hydrogen μp and muonic deuterium μd. The nuclear structure effects are taken into account in terms of the charge radii of the proton r _p and deuteron r _d for one-photon interaction, as well as in terms of the electromagnetic form factors of the proton and deuteron for the case of one-loop amplitudes. The μd-μp isotope shift for the 1S-2S splitting is found to be equal to 101003.3495 meV, which can be treated as a reliable estimate when conducting the corresponding experiment with an accuracy of 10^?6. The fine-structure intervals E(1S)-8E(2S) in muonic hydrogen and muonic deuteron are calculated.     

Calculation of QED Effects in Hydrogen

Atomic mass differences are influenced by QED corrections, and a reliable understanding of these corrections is therefore of importance for the current and next generation of high-precision mass determinations based on Penning traps. We present a numerical evaluation of the self-energy correction, which is the dominant contribution to the Lamb shift, in the region of low nuclear charge. Our calculation is nonperturbative in the binding field and has a numerical uncertainty of 0.8Hz in atomic hydrogen for the ground state and of 1.0Hz for L-shell states (2S_1/2, 2P_1/2, and 2P_3/2). This revised version was published online in July 2006 with corrections to the Cover Date.     

Spins,moments and charge radii in the isotopic series181Hg-191Hg

The hyperfine structure splitting and the isotope shift in the (6 s^{2 1}S₀ - 6s 6p³P₁,λ=2,537 Å) line of very neutron deficient Hg isotopes were determined by the β radiation detected optical pumping method (β-RADOP). In addition, nuclear magnetic resonance was observed in the atomic ground state. The results are Mean-square nuclear charge radii are calculated. Interpreting the sudden change of nuclear radius between¹⁸⁷Hg and¹⁸⁵Hg δ〈r²〉^187,185=0.42(5)fm² as oblate-prolate shape transition, one obtains δ〈β²〉 =0.054(5).     

Structure and energy level of native defects in as-grown and electron-irradiated zinc germanium diphosphide studied by EPR and photo-EPR

The properties of defects in as-grown p-type zinc germanium disphosphide (ZnGeP₂) and the influence of electron irradiation and annealing on the defect behavior were studied by means of electron paramagnetic resonance (EPR) and photo-EPR. Besides the well-known three native defects (V_Zn, V_P, Ge_Zn), an S=1/2 EPR spectrum with an isotropic g=2.0123 and resolved hyperfine splitting from four equivalent I=1/2 neighbors is observed in electron-irradiated ZnGeP₂. This spectrum is tentatively assigned to the isolated Ge vacancy. Photo-EPR and annealing treatments show that the high-energy electron irradiation-induced changes in the EPR intensities of the zinc and phosphorus vacancies are caused by the Fermi level shift towards the conduction band. Annealing of the electron-irradiated samples induces a shift of the Fermi level back to its original position, accompanied by an increase of the EPR signal associated with the V_Zn⁻ and a proportional increase of the EPR signal assigned to the V_P⁰ under illumination (λ<1 eV) as well as generation of a new defect. The results indicate that the EPR spectra originally assigned to the isolated V_Zn⁻ and V_P⁰ are in fact associated defects and the new defect is probably the isolated phosphorus vacancy V_Pi.     

Precision Lamb shift measurement in hydrogenic nitrogen by fast beam laser spectroscopy

A measurement of the 2S_1/2–2P_3/2 (fine structure–Lamb shift) transition in N⁶⁺ is under way. The technique involves fast beam spectroscopy with a transverse interaction geometry and uses an isotopic CO₂ laser and a resonant build up cavity. This revised version was published online in August 2006 with corrections to the Cover Date.     

Hyperfine splitting constants in the optical transition \boldsymbol{{4{f}^{7}} {6{s}^{2}} \;{^{8}{\rm S}_{7/2}} \to {4{f}^{7}} {6{s}6{p}}\; {^{6}{\rm P}_{5/2}} \ {\rm of} \ {^{151-155}{\rm Eu}}} isotopes and hyperfine anomaly

Using the method of laser-induced fluorescence in an atomic beam we have measured the hyperfine splitting constants, A and B, of the ground and excited states of the optical transition 4f ⁷6s ^{2 8}S $_{1/2}\to 4f^{7}$ 6s6p ⁶P_5/2 (564.58 nm) for ^151???155Eu isotopes. For all isotopes, the magnetic dipole constants of the ⁶P_5/2 atomic level are determined to a precision better than 0.04%. The A and B constants for the ground state ⁸S_7/2 of the radioactive ^152,154,155Eu were obtained for the first time with a precision better than 0.5%. Our data along with previous ground state hyperfine structure measurements for the stable europium isotopes allow us to determine the hyperfine anomaly for mentioned Eu isotopes.     

On the spin-orbit splitting of the rare gas-monohalide molecular ground state

The spin orbit splitting of the molecular ground state of two atomsA(² P _{1/2, 3/2}) andB(¹ S ₀) is discussed. If the spin orbit matrix elements do not depend on the internuclear distance, it is sufficient to know any two of the three potentials of the ground state manifold. The third can then be calculated analytically. Data are presented for theA II 1/2 state of F+Ne; (F, Br)+(Ar, Kr, Xe); and Cl+Xe, as well as for theA I 3/2 state of HeNe⁺.     

Stark interaction for excited states in alkali atoms,investigated by laser spectroscopy

The scalar polarizability constantα ₀ for excitedS- andD-states in rubidium and cesium was measured utilizing a two-step excitation scheme. An rf lamp and a single-mode dye laser were used to excite the atoms in a collimated atomic beam. Values ofα ₀ were determined for the 9–10² S _1/2 and 7–8² D _3/2 states of rubidium and for the 10–13² S _1/2, 9–10² D _3/2 and 9–11² D _5/2 states of cesium. Further, the isotope shift was evaluated in the 5579 Å rubidium line. A review of experimental polarizability constants for rubidium and cesium is given, and the results are compared with theoretical values.     

Two-color three-photon excitation studies of thallium Rydberg states

We present new data on the even-parity Rydberg states of atomic thallium using two-step three-photon laser excitation technique in conjunction with a thermionic diode ion detector. Atoms are excited from the 6p ²P_1/2 ground state to the 7p ²P_1/2 intermediate state via two-photon excitation and subsequently promoted to the high lying ns ² S_1/2 and nd ²D_3/2 Rydberg states. The first ionization potential of thallium is determined as 49,266.66(1) cm^-1 using data for the ns ² S_1/2 (25 ≤ n ≤ 54) and nd ²D_3/2 (24 ≤ n ≤ 65) Rydberg series. This value is believed to be more accurate because the contribution due to the hyperfine structure splitting of the 7p ²P_1/2 state (0.07185 cm^-1) is much smaller as compared to that of the 6p ²P_1/2 ground state (0.711 cm^-1).     

Hyperfeinstrukturuntersuchungen an wasserfreien Eisenhalogeniden mit Hilfe des Mössbauereffektes

Mössbauer effect measurements were performed with the anhydrous iron halides FeCl₂, FeBr₂ and FeI₂ at 78° K and 4 K° and with FeCl₃ at 4 °K. The quadrupole splitting, the isomer shift and the magnetic field at the nucleus were determined. From the quadrupole splitting it follows that in FeCl₂, FeBr₂ and FeI₂ the ground state is a doublet and that the singulet in these compounds is separated from it by (145±35) cm^?1, (175±35) cm^?1 and (135±35) cm^?1 respectively. The isomer shift shows the presence of strong covalence effects in all compounds. The large isomer shift in FeBr₂ cannot be fully explained. From the isomer shift and the magnetic field at the nucleus in FeCl₃ it can be concluded that the Fe⁺⁺⁺ ions has an 3d ^5,6 4s ^0,45 configuration. In FeCl₂, FeBr₂ and FeI₂ the smallness of the magnetic field can be explained by a not fully quenched orbital angular momentum of 0.6<L _z<1.     

Lasing conditions in recombining helium plasmas

Lasing conditions for He have been evaluated numerically. We have used a collisional radiative model to calculate overpopulation densities Δn_ij, which are defined as differences between population densities per unit statistical weight of the upper and lower excited levels i and j, respectively. Laser oscillations for the level pairs 2¹P-3¹S, 2¹P-4¹S, 2¹P-3¹D, 2¹P-4¹D, 3¹D-4¹F, 3¹P-4¹S, 3¹P-4¹D, and 3³P-4³S are possible when the electron densities are within well defined limits at low electron temperature (T_e = 0.1 eV). For level pairs of the singlet state, the inversion mechanism for He is the same as for H. Only collisional processes produce population inversion in the triplet level pair 3³P-4³S.     

Measurement of the fine structure of the n = 4 state of hydrogen

A time-resolved spectroscopy technique has been used to measure the fine structure of the n = 4 state of hydrogen. The excited hydrogen atoms were formed by the use of an electron beam to dissociate molecular hydrogen. The resonance transitions were observed by keeping the radio frequency field fixed and sweeping the magnetic field. Measurements on deuterium were used to study the effects of pressure and motional electric fields. The ²S_1/2 → ²P_1/2 Lamb shift transition , the ²P_3/2 → ²S_1/2 fine structure interval ΔE − L, and the ambient electric field in the measurement volume were determined by using measurements on three separate transitions made at fixed magnetic field. The measurements gave and     

Approximation of the electron excitation cross sections for triplet states excited from the 23 S 1 metastable state in helium

The method of approximated four-parameter representation of the electron-impact cross sections for a helium atom excited from the 2³ S ₁ metastable state into higher triplet states is applied and discussed. The approximation consists in interpolation over the whole set of the cross section values for each helium atomic level measured in our experiments and reported by other researchers. The approximation parameters and the cross sections calculated using these parameters for the maxima of the corresponding excitation functions are presented for 19 triplet levels of the S, P, and D HeI series with n=2–10. The interpolated values are compared to the theoretical cross sections. The serial regularities were investigated for the S, P, and D levels studied and a decrease in the cross sections for excitation from the given metastable state within each series, described by the approximate law Q=Cn ^?5, was revealed. Validity of the similarity relationship and the Bethe approximation for cross sections in the 2³ S?n ³ P series was verified. It is shown that the cross sections for a triplet level excitation from the 2³ S ₁ metastable state exceed the corresponding values for excitation from the ground state of helium by a factor of approximately 10³ for n=2 and 3 and 10 2 for the higher levels. It is concluded that the proposed method of representation of the cross sections for the electron-impact excitation of triplet levels from the metastable state increases accuracy and more importantly, reliability of the final results.