Corrections to the wave function and the hyperfine structure in exotic atoms

We present an analytical evaluation of radiative corrections in exotic atoms induced by the one-loop electronic vacuum polarization. We evaluate corrections to the energy levels, to the wave function (at the origin) and to the hyperfine structure. We treat all corrections analytically within a non-relativistic approximation. Agreement is found with a few available numerical results. The analytical treatment allows to determine the asymptotic forms of the corrections in the limit of a small atomic radius, which for the atomic systems considered corresponds to a large mass of the constituent particle as compared to the electron mass. The asymptotics can be verified using the effective charge approach. Received: 28 January 1998 / Accepted: 13 March 1998     

Nuclear size correction to the hyperfine splitting in low- hydrogen-like atoms

The finite nuclear size effect on the hyperfine splitting of low-Z hydrogen-like atoms is studied in the external field approximation. A simple non-relativistic formula is proposed which expresses the nuclear size correction to the hyperfine splitting in terms of moments of the nuclear charge and magnetization distribution. The numerical results obtained via this formula are compared with corresponding results derived by means of the Zemach formula. A relativistic formula for the nuclear size correction to the hyperfine splitting is also derived. Received 18 March 2002 / Received in final form 14 November 2002 Published online 28 January 2003 RID="a" ID="a"e-mail: plunien@physik.tu-dresden.de     

Radiative and interelectronic-interaction corrections to the hyperfine splitting in highly charged B-like ions

The ground-state hyperfine splitting values of high-Z boronlike ions are calculated. Calculation of the interelectronic-interaction contribution is based on a combination of the 1/Z perturbation theory and the large-scale configuration-interaction Dirac-Fock-Sturm method. The screened QED corrections are evaluated utilizing an effective screening potential approach. Total hyperfine splitting energies are presented for several B-like ions of particular interest: ⁴⁵Sc¹⁶⁺, ⁵⁷Fe²¹⁺, ²⁰⁷Pb⁷⁷⁺, and ²⁰⁹Bi⁷⁸⁺. For lead and bismuth the experimental values of the 1s hyperfine splitting are employed to improve significantly the theoretical results by reducing the uncertainty due to the nuclear effects.     

Radiative recoil corrections to hyperfine splitting: Polarization insertions in the electron factor

We consider three-loop radiative recoil corrections to hyperfine splitting in muonium due to insertions of the one-loop polarization operator in the electron factor. The contribution generated by electron polarization insertions is a cubic polynomial in the large logarithm of the electron—muon mass ratio. The leading logarithm cubed and logarithm squared terms are well known for some time. We calculate all single-logarithmic and nonlogarithmic radiative recoil corrections of the order α³ (m/M)E_F generated by diagrams with the electron and muon polarization insertions.     

Recoil corrections to muonic atom energy levels

The relativistic correction due to nuclear recoil is calculated for a distributed nuclear charge using the effective potential model of Grotch and Yennie. For the lowest states the results differ substantially from the well-known point nucleus values and disagree somewhat with the recent calculation of Fricke.     

O(alpha(3) lnalpha) corrections to muonium and positronium hyperfine splitting

We compute O(alpha(3)lnalpha) relative corrections to the ground-state hyperfine splitting of a QED two-body bound state with different masses of constituents. The general result is then applied to muonium and positronium. In particular, a new value of the muon-to-electron mass ratio is derived from the muonium ground-state hyperfine splitting.     

Anomalies in resonant absorption line profiles of atoms with large hyperfine splitting

We examine a monochromatic absorption line in the velocity-nonselective excitation of atoms when the components of the hyperfine stricture of the electronic ground states are optically pumped. We show that the absorption lines possess unusual substructures for some values of the hyperfine splitting of the ground state (which exceed the Doppler absorption linewidth severalfold). These substructures in the absorption spectrum are most apparent if the hyperfine structure of the excited electronic state is taken into account. We calculate the absorption spectra of monochromatic light near the D ₁ and D ₂ lines of atomic rubidium ^85,87Rb. With real hyperfine splitting taken into account, the D ₁ and D ₂ lines are modeled by 4-and 6-level diagrams, respectively. Finally, we show that atomic rubidium vapor can be successfully used to observe the spectral features experimentally. Zh. éksp. Teor. Fiz. 111, 93–106 (January 1997)     

A non-perturbative approach to hyperfine splitting

A hyperfine energy splitting for atomic hydrogen is calculated in a non-perturbative manner for a finite width contact interaction. A close agreement between this result and first order perturbation theory is obtained.     

Recoil corrections to elastic electron scattering in the Breit approximation

Recoil corrections to the cross sections for elastic electron scattering from spin-0 nuclei are investigated in the Breit approximation. The form of the scattering amplitude in first- and second-Born approximation is investigated in detail using time-dependent perturbation theory, and it is found that the center-of-mass (CM) frame is particularly convenient to work in. Transformation equations relating the lab and CM frames are developed. Those parts of the second-Born amplitude which correspond to the Breit amplitude are isolated, and the Breit equation with the electromagnetic Breit interaction is investigated in detail. Corrections to the scattering cross sections which are inversely proportional to the nucleus mass (recoil corrections) are calculated. Numerical results are presented for the particular case of ¹⁶O.     

Proton-polarizability contribution to the hyperfine splitting in hydrogen

The contribution of the proton polarizability to the hyperfine splitting in hydrogen is evaluated on the basis of modern experimental and theoretical results on the proton polarized structure functions. The value of this correction is 1.4 ppm.     

Recoil corrections for single-nucleon transfer reactions

A formalism is developed for approximately treating the recoil of the projectile in single-nucleon transfer reactions. The “no-recoil” term is evaluated exactly by rotating the nuclear matrix element to a coordinate system where the lighter projectile lies along the z-axis relative to the target nucleus. Recoil terms are constructed by expanding the “recoil phase factor” in terms of spherical harmonic and Bessel functions, and they are again evaluated exactly. Numerical results are then obtained for some representative light-ion reactions of high incident energies. For these reactions, we find that although the first-order recoil term may be very large, higher order terms are correspondingly less important, and convergence is always easily obtained. However, absolute magnitudes of cross sections at forward angles predicted by the present theory and by the local energy approximation differ by up to 50% for the reactions we consider.     

Proton polarizability contribution to hydrogen hyperfine splitting

The contribution of proton polarizability to hydrogen hyperfine splitting is evaluated on the basis of modern experimental and theoretical results on the proton polarized structure functions. The value of this correction is equal to 1.4 ppm. Received: 10 July 2000 / Published online: 12 April 2002     

多电子原子能量的相对论修正

以Breit-Pauli哈密顿的球张量形式为基础,借助不可约张量理论,建立了计算多电子原子能量的相对论修正的一种解析理论形式,导出了多电子原子相对论修正项(包括相对论质量修正项、单体和双体达尔文修正项、自旋-自旋接触相互作用项和轨道-轨道相互作用项)在斯莱特表象中的矩阵元的解析表达式,完成了所有角向积分和自旋求和计算.利用所建立的理论,对类锂体系(1s)2(2p)2P态能量的相对论修正进行了具体计算.     

Ground-state hyperfine splitting of antihydrogen

ASACUSA collaboration at CERN’s antiproton decelerator (CERN AD) plans to measure the ground-state hyperfine splitting (GS-HFS) of antihydrogen () to test the CPT symmetry to high precision. Our scheme is to produce an (anti-) atomic beam with a novel two-frequency superconducting Paul trap, and to use sextupole magnets and a 1.4-GHz cavity to analyze the HFS resonance frequency.      

Experimental constraints on polarizability corrections to hydrogen hyperfine structure

We present a state-of-the-art evaluation of the polarizability corrections--the inelastic nucleon corrections--to the hydrogen ground-state hyperfine splitting using analytic fits to the most recent data. We find a value Delta(pol)=1.3+/-0.3 ppm. This is 1-2 ppm smaller than the value of Delta(pol) deduced using hyperfine splitting data and elastic nucleon corrections obtained from modern form factor fits.     

On the formation of exotic atoms

A general disagreement exists between theory and experiment in the field of formation and decay of muonic and pionic atoms. Allowing for collisional processes in the deexcitation of heavy exotic atoms can substantially change the interpretation of experimental Coulomb-capture ratios, particularly of those measured by the muonic X-ray method.Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.The author is grateful to Prof. F. Measday (Univ. of British Columbia, Vancouver, Canada) and Dr. J. Révai (C. R. I. P., Budapest) for illuminating discussions.     

Recoil corrections to magnetic moments of octet baryons in the MIT bag model

The presence of certain recoil corrections in the determination of baryon magnetic moments is described and taken into account for the octet members. Inclusion of these recoil corrections makes the MIT bag model, even in its zeroth-order version, very appealing, if the sum of many other corrections is not important by comparison.