We report the initial results from a systematic study of the hyperfine (HF) structure of antiprotonic helium (n,l) = (37,~35) carried out at the Antiproton Decelerator (AD) at CERN. We performed a laser-microwave-laser resonance spectroscopy using a continuous wave (cw) pulse-amplified laser system and microwave cavity to measure the HF transition frequencies. Improvements in the spectral linewidth and stability of our laser system have increased the precision of these measurements by a factor of five and reduced the line width by a factor of three compared to our previous results. A comparison of the experimentally measured transition frequencies with three body QED calculations can be used to determine the antiproton spin magnetic moment, leading towards a test of CPT invariance.
A full quantum mechanical calculation of partial cross-sections leading to different final states of antiprotonic helium atom was performed. Calculations were carried out for a wide range of antiprotonic helium states and incident (lab) energies of the antiproton.
Recent progress in the spectroscopy of antiprotonic helium has allowed for measuring the separation between components of the hyperfine structure (HFS) of the (37,35) metastable states with an accuracy of 300 MHz, equivalent to a relative accuracy of 3x10^{-5}. The analysis of the uncertainties of the available theoretical results on the antiprotonic helium HFS shows that the accuracy of the value of the dipole magnetic moment of the antiproton (currently known to only 0.3 %) may be improved by up to 2 orders of magnitude by measuring the splitting of appropriately selected components of the H…
Using a newly developed laser-microwave-laser resonance method, we observed a pair of microwave transitions between hyperfine levels of the $(n,L)=(37,35)$ state of antiprotonic helium. This experiment confirms the quadruplet hyperfine structure due to the interaction of the antiproton orbital angular momentum, the electron spin and the antiproton spin as predicted by Bakalov and Korobov. The measured frequencies of $ν_{\text HF}^+ =12.89596 \pm 0.00034$ GHz and $ν_{\text HF}^- =12.92467 \pm 0.00029$ GHz agree with recent theoretical calculations on a level of $ 6 \times10^{-5}$.
We report on the first experimental results for microwave spectroscopy of the hyperfine structure of antiprotonic He-3. Due to the helium nuclear spin, antiprotonic He-3 has a more complex hyperfine structure than antiprotonic He-4 which has already been studied before. Thus a comparison between theoretical calculations and the experimental results will provide a more stringent test of the three-body quantum electrodynamics (QED) theory. Two out of four super-super-hyperfine (SSHF) transition lines of the (n,L)=(36,34) state were observed. The measured frequencies of the individual transitions…
We report on preliminary results from a systematic study of the hyperfine (HF) structure of antiprotonic helium. This precise measurement which was commenced in 2006, has now been completed. Our initial analysis shows no apparent density or power dependence and therefore the results can be averaged. The statistical error of the observable M1 transitions is a factor of 60 smaller than that of three body quantum electrodynamic (QED) calculations, while their difference has been resolved to a precision comparable to theory (a factor of 10 better than our first measurement). This difference is sen…
We report the first measurements of the inelastic spin exchange collision rate between the Hyperfine (HF) levels of antiprotonic helium. We measure the time dependent evolution of the (37, 35) substates to obtain an inelastic collision rate which qualitatively agrees with recent theoretical calculations. We evaluate these results by using the obtained rate as a parameter in a rigorous simulation which we then compare to to previously measured data. We find that our measurement slightly underestimates the collision rate and therefore conclude that the actual value most probably falls within the…
In this work we describe the latest results for the measurements of the hyperfine structure of antiprotonic helium-3. Two out of four measurable super-super-hyperfine SSHF transition lines of the (n,L)=(36,34) state of antiprotonic helium-3 were observed. The measured frequencies of the individual transitions are 11.12548(08) GHz and 11.15793(13) GHz, with an increased precision of about 43% and 25% respectively compared to our first measurements with antiprotonic helium-3 [S. Friedreich et al., Phys. Lett. B 700 (2011) 1--6]. They are less than 0.5 MHz higher with respect to the most recent t…
The state dependent quenching mechanism of metastable antiprotonic He atoms by contaminants is suggested to explain existing experimental data. The effect of antiproton transfer from the antiprotonic He to noble gas contaminants is shown to play a significant role. Preliminary estimations have been done in the framework of the coupled channels model. The obtained results support the idea of strong dependence of quenching cross-sections on the antiprotonic states quantum numbers and enable to explain qualitatively existing discrepancies between experimental results, obtained for different conta…
Heretofore undiscovered spin-0 or spin-1 bosons can mediate exotic spin-dependent interactions between standard-model particles. Here we carry out the first search for semileptonic spin-dependent interactions between matter and antimatter. We compare theoretical calculations and spectroscopic measurements of the hyperfine structure of antiprotonic helium to constrain exotic spin- and velocity-dependent interactions between electrons and antiprotons.
Antiprotonic helium, a neutral exotic three-body system consisting of a helium nucleus, an electron and an antiproton, is being studied at the Antiproton Decelerator of CERN by the ASAUCSA collaboration. Using laser spectroscopy of the energy levels of the antiproton in this system and comparison to theory, a value of the antiproton-to-electron mass ratio with an error of 3 ppb could be obtained. This result agrees with the most precise measurement of the value of the proton and allows us to extract a limit of the equality of the proton and antiproton charge and mass of 2 ppb. Using microwave …
We have estimated the shift and broadening of the resonance lines in the spectrum of antiprotonic helium atoms $\bar{p}\mathrm{He}^{+}$ implanted in solid helium $^4$He. The application of the response function for crystalline helium has enabled determination of the contributions from the collective degrees of freedom to the shift and broadening. It occurs that the broadening due to the collective motion is negligible compared to the natural line width. The available pair-correlation functions for crystalline $^4$He have been applied for estimating the resonance-line shift due to collisions of…
We consider a neutralization of excited antiprotonic helium ion accompanied by antiproton transitions to lower states in collisions with helium atoms $(\bar{p}\mathrm{He}^{2+})_{nl} + \mathrm{He} \rightarrow \left[ (\bar{p}\mathrm{He}^{2+})_{n_f l_f} e\right]_{1s} + \mathrm{He}^+$ in low-temperature medium. Interactions in the input and output channels are taken similar to the potentials of $\mathrm{H}^+ - \mathrm{He}$ ($X^1Σ$) and $\mathrm{H} - \mathrm{He}^+$ ($A^1Σ$) systems, respectively. The final term is shifted down by the antiproton transition energy. Therefore initial and final terms c…
We report a determination of the antiproton magnetic moment, measured in a three-body system, independent of previous experiments. We present results from a systematic study of the hyperfine (HF) structure of antiprotonic helium where we have achieved a precision more than a factor of 10 better than our first measurement. A comparison between the experimental results and three-body quantum electrodynamic (QED) calculations leads to a new value for the antiproton magnetic moment is -2.7862 (83) nuclear magnetons, which agrees with the magnetic moment of the proton within 2.9 x 10e-3.
The shift and broadening of the resonance lines in spectrum of the antiprotonic helium atoms $\bar{p}\mathrm{He}^{+}$ located in fluid and superfluid $^4$He have been calculated. The contributions to the shift and broadening from collective degrees of freedom in liquid $^4$He have been estimated using the phenomenological response function. Effects due to the interaction of $\bar{p}\mathrm{He}^{+}$ with a single $^4$He atom have been calculated in the quasistatic approximation using the experimental pair correlation function. It has been shown that an implanted $\bar{p}\mathrm{He}^{+}$ atom es…
This paper describes measurements of the hyperfine structure of two antiprotonic atoms that are planned at the Antiproton Decelerator (AD) at CERN. The first part deals with antiprotonic helium, a three-body system of alpha-particle, antiproton and electron that was previously studied at LEAR. A measurement will test existing three-body calculations and may - through comparison with these theories - determine the magnetic moment of the antiproton more precisely than currently available, thus providing a test of CPT invariance. The second system, antihydrogen, consisting of an antiproton and a …
A systematic study of the decay rates of antiprotonic helium (\pbhef and \pbhet) at CERN AD (Antiproton Decelerator) has been made by a laser spectroscopic method. The decay rates of some of its short-lived states, namely those for which the Auger rates $γ_{\mathrm{A}}$ are much larger than their radiative decay rates ($γ_{\mathrm{rad}} \sim 1$ $μ$s$^{-1}$), were determined from the time distributions of the antiproton annihilation signals induced by laser beams, and the widths of the atomic resonance lines. The magnitude of the decay rates, especially their relation with the transition multip…
Collisions of metastable antiprotonic helium atoms with atoms of the medium induce, among other processes, transitions between hyperfine structure (HFS) states, as well as shifts and broadening of microwave M1 spectral lines. In order to obtain matrix potential of interaction between $(\mathrm{\bar{p} He} ^+)$ and $\mathrm{He}$, we have calculated the potential energy surface (PES) in the framework of unrestricted Hartree-Fock method taking into account electron correlations in the second-order perturbation theory (MP2). With this potential, the system of close-coupling equations for HFS chann…
The long range interaction between an antiprotonic helium atom $\bar{p}$He$^+$ and helium atom in its ground state is studied. We calculate the dispersion coefficients $C_6$ using the Complex Coordinate Rotation (CCR) formalism in order to comply with the resonant nature of metastable states of the antiprotonic helium. We present as well numerical data on static dipole polarizabilities of antiprotonic helium states. The obtained coefficients $C_6$ may be used to estimate the collisional shift and broadening of transition lines in a low density precision spectroscopy of the antiprotonic helium.
A consistent quantum mechanical calculation of partial cross-sections leading to different final states of antiprotonic helium atom was performed. For the four-body scattering wave function, corresponding to the initial state, as well as for the antiprotonic helium wave function, appearing in the final tate, adiabatic approximations was used. Calculations were carried out for a wide range of antiprotonic helium states and incident energies of the antiproton. Obtained energy dependances of some cross sections show a rich low energy structure.
We present improved theoretical calculations of transition frequencies for the fundamental transitions $(L\!=\!0,v\!=\!1)\to(L'\!=\!0,v'\!=\!0)$ in the hydrogen molecular ions H$_2^+$ and HD$^+$ with a relative uncertainty $4\cdot10^{-11}$ and for the two-photon transitions in the antiprotonic helium atom with a relative uncertainty $10^{-10}$. To do that, the one-loop self-energy correction of order $α(Zα)^6$ is derived in the two Coulomb center approximation, and numerically evaluated in the case of the aforementioned transitions. The final results also include a complete set of other spin-i…
We develop a numerical method to calculate the Bethe logarithm for resonant states. We use the Complex Coordinate Rotation (CCR) formalism to describe resonances as time-independent Schrödinger solutions. To get a proper expression for the Bethe logarithm we apply the generalization of the second order perturbation theory to an isolated CCR eigenstate. Using the developed method we perform a systematic calculation of the Bethe logarithm for metastable states in the antiprotonic helium He$^+\bar{p}\,$ atoms with precision of 7--8 significant digits. We also recalculate the nonrelativistic energ…
Numerical ab initio variational calculations of the transition probabilities and ac Stark shifts in two-photon transitions of antiprotonic helium atoms driven by two counter-propagating laser beams are presented. We found that sub-Doppler spectroscopy is in principle possible by exciting transitions of the type (n,L)->(n-2,L-2) between antiprotonic states of principal and angular momentum quantum numbers n~L-1~35, first by using highly monochromatic, nanosecond laser beams of intensities 10^4-10^5 W/cm^2, and then by tuning the virtual intermediate state close (e.g., within 10-20 GHz) to the r…
Quantum calculation of the collision-induced line-shape effects in antiprotonic helium and the new accurate ab initio $\bar{p}$He$^{+}$-He potential energy surface
We extend the results of Bakalov D., B.Jeziorski, T.Korona, K.Szalewicz, E.Tchoukova, Phys. Rev. Lett. {\bf 84} (2000) 2350, on one-photon electric dipole transition line shift and broadening to the case of two-photon transitions. As an example we consider the laser induced transition in antiprotonic helium produced in helium gas target. The transition is between antiprotonic helium states $(n,l)=(33,32)$ and $(31,30)$. PACS 32.70.Jz, 34.20.Gj, 36.10.-k
Physical laws are believed to be invariant under the combined transformations of charge, parity and time reversal (CPT symmetry). This implies that an antimatter particle has exactly the same mass and absolute value of charge as its particle counterpart. Metastable antiprotonic helium ($\bar{p}{\rm He}^+$) is a three-body atom consisting of a normal helium nucleus, an electron in its ground state and an antiproton ($\bar{p}$) occupying a Rydberg state with high principal and angular momentum quantum numbers, respectively $n$ and $\ell$, such that $n\sim\ell\sim 38$. These atoms are amenable to…
An angle-resolved x-ray spectroscopic scheme is presented for determining the hyperfine splitting of highly charged ions. For helium-like ions, in particular, we propose to measure either the angular distribution or polarization of the $1s2p~^{3}P_{1}, F \rightarrow 1s^{2}~^{1}S_{0}, F_{f}$ emission following the stimulated decay of the initial $1s2s~^{1}S_{0}, F_{i}$ level. It is found that both the angular and polarization characteristics of the emitted x-ray photons strongly depends on the (relative) \textit{splitting} of the partially overlapping hyperfine $1s2p~^{3}P_{1}, F$ resonances an…
The usefulness of study of hyperfine splitting in the hydrogen atom is limited on a level of 10 ppm by our knowledge of the proton structure. One way to go beyond 10 ppm is to study a specific difference of the hyperfine structure intervals 8 Delta nu_2 - Delta nu_1. Nuclear effects for are not important this difference and it is of use to study higher-order QED corrections.
The recoil, vacuum polarization and electron vertex corrections of first and second orders in the fine structure constant $α$ and the ratio of electron to muon and electron to α-particle masses are calculated in the hyperfine splitting of the $1s^{(e)}_{1/2}2s^{(μ)}_{1/2}$ state of muonic helium atom (μe ^4_2He) on the basis of a perturbation theory. We obtain total result for the muonically excited state hyperfine splitting $Δν^{hfs}=4295.66$ MHz which improves previous calculations due to the account of new corrections and more accurate treatment of the electron vertex contribution.
The hyperfine structures of the ground states in the ${}^{3}$He$^{2+} μ^{-} e^{-}$ and ${}^{4}$He$^{2+} μ^{-} e^{-}$ helium-muonic atoms are investigated with the use of highly accurate variational wave functions. The differences between corresponding levels of hyperfine structure (i.e. hyperfine splittings) are determined to very high numerical accuracy. In particular, we have found that the hyperfine structure splitting in the ground state of the ${}^{4}$He$^{2+} μ^{-} e^{-}$ atom is $Δν\approx 4464.55454(3)$ $MHz$, while analogous splitting for the ${}^{3}$He$^{2+}μ^{-}e^{-}$ atom is $Δν\ap…
The hyperfine structure splittings are determined for the lowest bound state in the positron-helium ion $e^{+}[^3$He$(2^3S)]$ and $e^{+}[^4$He$(2^3S)]$. In particular, we have fond that for the $e^{+}[{}^3$He$(2^3S)]$ ion one can observe the three following hyperfine structure splittinings: 5824.3986 $MHz$, 76466.5308 $MHz$ and 5824.4019 $MHz$. In the $e^{+}[{}^4$He$(2^3S)]$ ion only one hyperfine structure splitting 82963.0427 $MHz$ can be observed. All these values can be measured in modern experiments.
Precise numerical calculation of radiofrequency intervals between hyperfine sublevels of the $(37,35)$ state of the antiprotonic helium-4 atom is presented. Theoretical consideration includes the QED corrections of order $mα^6$ to the electron spin-orbit interaction. The effective Hamiltonian is derived using the formalism of the nonrelativistic quantum electrodynamics (NRQED).
Constraints on a possible fifth-force interaction between hadrons are derived based on an analysis of results from laser precision frequency measurements of antiprotonic helium atoms, both $\bar{p}\,^{4}$He$^{+}$ and $\bar{p}\,^{3}$He$^{+}$ species, and from experiments on resonant formation rates of $ddμ^{+}$-ions in muon-catalyzed fusion processes. A comparison is made between accurate experimental data and first-principles theoretical descriptions of the exotic systems within a quantum electrodynamical framework. The agreement between theory and experiment sets limits on a possible addition…
The linear polarization of the characteristic photon emission from few-electron ions is studied for its sensitivity with regard to the nuclear spin and magnetic moment of the ions. Special attention is paid, in particular, to the K$α_1$ ($1s 2p_{3/2} ^{1,3}P_{1,2} \to 1s^2 ^1S_0$) decay of selected helium-like ions following the radiative electron capture into initially hydrogen-like species. Based on the density matrix theory, a unified description is developed that includes both, the many-electron and hyperfine interactions as well as the multipole-mixing effects arising from the expansion o…
The present knowledge of Lamb shift, fine-, and hyperfine structure of the 2S and 2P states in muonic helium-3 ions is reviewed in anticipation of the results of a first measurement of several $\mathrm{2S\rightarrow2P}$ transition frequencies in the muonic helium-3 ion, $\mathrm{μ^3He^+}$. This ion is the bound state of a single negative muon $μ^-$ and a bare helium-3 nucleus (helion), $\mathrm{^3He^{++}}$. A term-by-term comparison of all available sources, including new, updated, and so far unpublished calculations, reveals reliable values and uncertainties of the QED and nuclear structure-d…
The ground state hyperfine splitting of light muon-electron ions of lithium, beryllium, boron and helium is calculated on the basis of analytical perturbation theory in terms of small parameters of the fine structure constant and electron-muon mass ratio. The corrections of vacuum polarization, nuclear structure and recoil effects and electron vertex corrections are taken into account. The dependence of the corrections on the nucleus charge Z is studied. The obtained total values of hyperfine splitting intervals can be used for comparison with future experimental data.
We consider the most accurate tests of bound state QED theory of the hyperfine splitting in two-body atoms related to the HFS interval of the 1s state in muonium and positronium and the 2s state in hydrogen, deuterium and the helium-3 ion. We summarize their QED theory and pay special attention to involved effects of strong interactions and to recent optical measurements of the 2s HFS interval in hydrogen and deuterium. We present results for specific ratios of the 1s-2s frequencies in hydrogen and deuterium which happen to be among the most accurately measured and calculated quantities.
The calculation of hadronic polarizability contribution of the nucleus to hyperfine structure of muonic hydrogen and helium is carried out within the unitary isobar model and experimental data on the polarized structure functions of deep inelastic lepton-proton and lepton-deuteron scattering. The calculation of virtual absorption cross sections of transversely and longitudinally polarized photons by nucleons in the resonance region is performed in the framework of the program MAID.
On the basis of the perturbation theory in the fine structure constant $α$ and the ratio of the electron to muon masses we calculate one-loop vacuum polarization and electron vertex corrections and the nuclear structure corrections to the hyperfine splitting of the ground state of muonic helium atom $(μ e \ ^3_2He)$. We obtain total result for the ground state hyperfine splitting $Δν^{hfs}=4166.471$ MHz which improves the previous calculation of Lakdawala and Mohr due to the account of new corrections of orders $α^5$ and $α^6$. The remaining difference between our theoretical result and experi…
Collinear Laser Spectroscopy of the $1s2s\,^3\!S_1\rightarrow 1s2p\,^3\!P_{0,2}$ Transitions in Helium-like $^{11}$B$^{3+}$
Institut für Kernphysik, Universität Münster（明斯特大学核物理研究所）；Institut für Kernphysik, Technische Universität Darmstadt（达姆施塔特工业大学核物理研究所）；Helmholtz Research Academy Hesse for FAIR, GSI Helmholtzzentrum für Schwerionenforschung GmbH（黑森州FAIR亥姆霍兹研究院，GSI重离子研究中心有限公司）；GSI Helmholtzzentrum für Schwerionenforschung GmbH（GSI重离子研究中心有限公司）；Argonne National Laboratory（阿贡国家实验室）
We have calculated ac polarizabilities of the $2 \ ^3S$ and $2 \ ^1S$ states of both $^4$He and $^3$He in the range 318 nm to 2.5 $μ$m and determined the magic wavelengths at which these polarizabilities are equal for either isotope. The calculations, only based on available ab initio tables of level energies and Einstein A coefficients, do not require advanced theoretical techniques. The polarizability contribution of the continuum is calculated using a simple extrapolation beyond the ionization limit, yet the results agree to better than 1% with such advanced techniques. Several promising ma…
Quantum interference between energetically close states is theoretically investigated, with the state structure being observed via laser spectroscopy. In this work, we focus on hyperfine states of selected hydrogenic muonic isotopes, and on how quantum interference affects the measured Lamb shift. The process of photon excitation and subsequent photon decay is implemented within the framework of nonrelativistic second-order perturbation theory. Due to its experimental interest, calculations are performed for muonic hydrogen, deuterium, and helium-3. We restrict our analysis to the case of phot…
A large-scale full-configuration-interaction calculation based on Dirac-Coulomb-Breit (DCB) Hamiltonian is performed for the $2\,^1S_0$ and $2\,^3S_1$ states of helium. The operators of the normal and specific mass shifts are directly included in the DCB framework to take the finite nuclear mass correction into account. High-accuracy energies and matrix elements involved n (the main quantum number) up to 13 are obtained from one diagonalization of Hamiltonian. The dynamic dipole polarizabilities are calculated by using the sum rule of intermediate states. And a series of magic wavelengths with…
The structure of the excited $2^{3}$S and $2^{3}$P triplet states of $^{3}$He and $^{4}$He in an applied magnetic field B is studied using different approximations of the atomic Hamiltonian. All optical transitions (line positions and intensities) of the 1083 nm $2^{3}$S-$2^{3}$P transition are computed as a function of B. The effect of metastability exchange collisions between atoms in the ground state and in the $2^{3}$S metastable state is studied, and rate equations are derived, for the populations these states in the general case of an isotopic mixture in an arbitrary field B. It is shown…
We measure the absolute frequency of seven out of the nine allowed transitions between the 2$^3${\it S} and 2$^3${\it P} hyperfine manifolds in a metastable $^3$He beam by using an optical frequency comb synthesizer-assisted spectrometer. The relative uncertainty of our measurements ranges from $1\times 10^{-11}$ to $5\times 10^{-12}$, which is, to our knowledge, the most precise result for any optical $^3$He transition to date. The resulting $2^3${\it P}-2$^3${\it S} centroid frequency is $276\,702\,827\,204.8\,(2.4)$kHz. Comparing this value with the known result for the $^4$He centroid and …
We demonstrate coherent microwave control of the rotational, hyperfine and Zeeman states of ultracold CaF molecules, and the magnetic trapping of these molecules in a single, selectable quantum state. We trap about $5\times 10^{3}$ molecules for 2 s at a temperature of 65(11) $μ$K and a density of $1.2 \times 10^{5}$ cm$^{-3}$. We measure the state-specific loss rate due to collisions with background helium.
The Antiproton Decelerator of CERN began operation in 1999 to serve experiments for studies of CPT invariance by precision laser and microwave spectroscopy of antihydrogen ($\bar{\rm H}$) and antiprotonic helium ($\bar{p}{\rm He}^+$). The first 12 years of operation saw cold $\bar{\rm H}$ synthesized by overlapping clouds of positrons ($e^+$) and antiprotons ($\bar{p}$) confined in magnetic Penning traps. Cold $\bar{\rm H}$ was also produced in collisions between Rydberg positronium atoms and $\bar{p}$. Ground-state $\bar{\rm H}$ was later trapped for up to $\sim 1000$ s in a magnetic bottle t…
Helium-3 has nowadays become one of the most important candidates for studies in fundamental physics [1, 2, 3], nuclear and atomic structure [4, 5], magnetometry and metrology [6] as well as chemistry and medicine [7, 8]. In particular, $^3$He nuclear magnetic resonance (NMR) probes have been proposed as a new standard for absolute magnetometry [6, 9]. This requires a high-accuracy value for the $^3$He nuclear magnetic moment, which, however, has so far been determined only indirectly and with a relative precision of $12$ parts per billon (p.p.b.) [10,11]. Here we investigate the $^3$He$^+$ gr…
Splitting Isotope Shift in the $1s2p\,^3\!P_{0,1,2}$ Fine-Structure Triplet in $^{12,13,14}$C$^{4+}$: Experiment and Theory
Institut für Kernphysik, Technische Universität Darmstadt（达姆施塔特工业大学核物理研究所）；Helmholtz Research Academy Hesse for FAIR, GSI Helmholtzzentrum für Schwerionenforschung（黑森FAIR亥姆霍兹研究院，GSI重离子研究中心）；Department of Physics, University of Windsor（温莎大学物理系）；Physics Division, Argonne National Laboratory（阿贡国家实验室物理部）
