Quantum electrodynamic corrections to the 23S1 → 11S0 + one photon transition rate in helium and helium-like lons

The order (Zα)⁵, α(Zα)⁴, and α(Zα)⁴ log(Zα) energy denominator and recoil corrections to the leading order (Zα)⁴ decay amplitude for the 2³S₁ → 1¹S₀ + one photon transition are considered. It is found that order α(Zα)⁴ terms arise in the individual diagrams but exactly cancel upon summation. In view of the results of this and other recent theoretical work it is concluded that the rates predicted by pure quantum electrodynamics are known to considerable precision. The recent discrepancy between theory and experiment in the decay rate for several helium-like ions appears to have been resolved by placing the detector farther downstream from the foil where the metastable states are produced. At present, all the experimental values are in good agreement with the theory.     

Nuclear finite-size effects in light muonic atoms

The finite nuclear size corrections to the s-state energy levels of light muonic (or hydrogenic) atoms are calculated analytically through order (Zα)⁶. In addition to the usual expression of order (Zα)⁴, the (Zα)⁵, (Zα)⁶ and (Zα)⁶ log(Zα) contributions have been determined. These corrections have been separated into terms of nonrelativistic and relativistic orders. The results have been checked by solving perturbatively the exact eigenvalue equations of the Schroedinger and Dirac problems of a particle orbiting in the Coulomb field of a uniform charge distribution of fixed radius. Application is made to the case of the μ-⁴He atom. Finite-size contributions to the hydrogen Lamb shift and the relativistic recoil effect are briefly discussed.     

Approximate normalized wave functions for the finite-size Coulomb problem

Using perturbation methods developed previously for the finite-size energy shift, thes-state wave functions for a bound lepton in the Coulomb field of a nucleus with an arbitrary charge distribution are developed through order (Zα)². This technique allows a determination of the finite-size contribution to the normalization of the wave function up to order (Zα)², both for small separations of the lepton and nucleus and for the lepton outside the nucleus. General features of the wave function are discussea, including the transition of the Dirac problem to the (singular) point charge limit. A practical application is developed using these results.     

Low-energy gluon to the vacuum polarization of heavy quarks

We calculate a correction to the effective electromagnetic current at low energies, induced by a heavy-quark loop, and determine the analytic structure of the vacuum polarization function at small q ², for which an explicit expression is given to the O(α _s ³ ) order of perturbation theory. Implications to the high-precision analysis of experimental data on heavy-quark production in e ⁺ e ^? annihilation are discussed.     

The Breit equation as a zeroth-order approximation for calculation of the bound-state energy

An equation whose kernel is determined by the one-photon exchange between interacting particles is analyzed in the framework of the Bethe-Salpeter formalism. This equation is considered as a zeroth-order approximation in the calculation of the corrections to the energy levels. This is the Breit equation that takes into account additional small terms (with respect to the parameter (Zα)²). A procedure that employs the Brillouin-Wigner perturbation theory and makes it possible to sequentially take into account the corrections to the energy levels is considered.     

Coulomb correction to Delbrück scattering investigated atZ=94

Differential cross sections for the elastic scattering of 2.754 MeV photons by Pu were measured for angles ranging from 45 to 120° and interpreted in terms of Delbrück, nuclear Thomson, Rayleigh and nuclear resonance scattering. It is shown that the largest part of the discrepancy between experiment and the lowest-order Delbrück theory can be removed by introducing a (Zα)⁴-dependent Coulomb correction term. Evidence is obtained for additional Coulomb correction terms of higher order in (Z α).     

Delbrück scattering of 2754 keV photons by Nd,Ce, I,Sn, Mo and Zn

The elastic scattering of 2754 keV photons has been investigated for charge numbers Z between 30 and 92. The lowest-order Delbrück theory was found valid for small Z. A Coulomb correction term proportional to (Zα)⁴ fits the experimental data with few exceptions.     

Perturbative expansions in QCD and analytic properties of α s

It is shown that analytic properties of standard QCD perturbation theory contradict known spectral properties and contain, in particular, infrared-generated Landau ghost poles and cuts. As an outcome, a rigorous background perturbation theory is developed and its analytic properties are shown to be in agreement with general requirements. In the limiting case of large N _c, where QCD amplitudes contain only pole singularities, the strong coupling constant α _s(Q ²) is shown to be a meromorphic function of external momenta as well. Some simple models and examples are given where nonperturbative β function and α _s(Q ²) can be written explicitly. The general form of amplitudes at large N _c is given in the framework of background perturbation theory, and its correspondence with standard perturbation theory at highmomenta is demonstrated in the example of e ⁺ e ^? annihilation. For timelike momenta, the background coupling constant differs drastically from the standard one, but the background series averaged over energy intervals has the same (AF) behavior at high momenta in the Euclidean and in the Minkowskian region.     

Hyperfine structure in hydrogen and helium ion

QED theory of the hyperfine splitting of the 1s and 2s state in hydrogen isotopes and helium-3 ion is considered. We develop an accurate theory of a specific difference 8E_HFS(2s)−E_HFS(1s). We take into account higher-order QED and nuclear structure effects. In particular, we found the vacuum polarization contribution in order α(Zα)³E_F and examined the recoil contribution in order (Zα)³m/M and thus completed a calculation of the fourth order QED corrections. The higher-order nuclear structure contributions were also analysed. The theoretical predictions reported here are now of a higher accuracy than the experiment. The study of the difference provides the most accurate test (at a level of a part in 10⁸) of the QED theory of ns HFS up to date. The theory agrees with most of the experimental data.     

The Callan-Symanzik coefficient β in a massive thirring model in 2 + ϵ dimensions

Using perturbation theory we find that there is no zero of the Callan-Symanzik coefficient β(g, ?) in a massive Thirring model in 2 + ? dimensions at a coupling g ～ ?^α with positive α. This follows from the identically vanishing of β(g, 0) in 2 dimensions.     

40Ca(d, α)38K and isospin

We investigate the ⁴⁰Ca(d, α_{0, 1, 2, 4})³⁸K reactions for E_d = 4.00–4.61 MeV. The α₁ and α₄ transitions are isospin forbidden. The resonant-like structures observed in the α₀, α₁, α₂, and α₄ transitions are consistent with Ericson theory. In addition we can fit a portion of the α₁, data with a few interfering Breit-Wigner resonances. The level parameters for the corresponding ⁴²Sc levels are given.     

Resonance spectroscopy of44Ti in the excitation energy range 9.05 to 10.28 MeV

The absolute differential cross sections for the⁴⁰Ca(α,α)⁴⁰Ca reaction have been measured in the bombarding energy range from 4.33 to 5.68 MeV at the four laboratory angles 85°, 125°, 141° and 165°. An analysis of the data using multilevelR matrix theory has provided the spin-parities and widths of 29 levels in the compound nucleus⁴⁴Ti. A comparison has been made with the levels deduced from the (α,γ) reaction and existing theoretical calculations of⁴⁴Ti levels.     

Isomerenverhältnisse für die Reaktionen107Ag(α,2n)109g,mIn und109Ag(α,2n)111g,mIn

Isomeric cross-section ratios have been measured for the reactions¹⁰⁷Ag(α,2n)^109g,mIn and¹⁰⁹Ag(α, 2n)^111g,mIn for energies of theα-particles between 19 and 40 MeV. The experimental isomeric cross-section ratios are compared with statistical-model calculations. The program ofHafner et al. was extended by including the competition of the (α,n)- and (α, 3n)-reactions and of charged particle emission. Agreement between experiment and theory could be achieved.     

Investigation of the e<Subscript>0</Subscript>-electron yield from the surface of thin films under bombardment by α and β particles from radioactive sources

The yields of near-zero (e₀) electrons from the surface of targets with different Z under their bombardment by α particles from ²²⁶Ra decay were measured by the method of e_α coincidences. The ratios of the e₀-electron yields for α particles with different energies E _α are described well by the dependence Y _e (E _α) ～ υ _α ^?1 , where υ _α is the α-particle velocity. The e₀-electron yield from the surface of thin films under their bombardment by β particles from radioactive sources with ¹⁵²Eu, ¹⁵⁴Eu, and ²²⁶Ra has been investigated by the method of eγ coincidences. It is established that ionization rate of target atoms in this case is inversely proportional to the velocity of incident β particles (υ _β ^?1 ), i.e., is proportional to the time of atomic electron perturbation induced by a β particle passing near an atom.     

The 56Fe(α, γ)60Ni reaction at excitation energies in the region of the giant dipole resonance

Excitation functions for the ⁵⁶Fe(α, γ₀)⁶⁰Ni and ⁵⁶Fe(α, γ₁)⁶⁰Ni reactions have been measured at 90° to the beam direction over the bombarding energy range 8.0–17.6 MeV. Gamma-ray angular distributions were measured at ten bombarding energies. Excitation functions for the ⁵⁹Co(p, γ₀)⁶⁰Ni and ⁵⁹Co(p, γ₁)⁶⁰Ni reactions were measured over the range E_x = 16.58–16.92 MeV and compared with the (α, γ) data. The angular distribution data indicate that the (α, γ₀) and (α,γ₁) reactions proceed through 1^?, and 1^? and 3^? states, respectively. The (α, γ) excitation functions are discussed with respect to isospin splitting of the ⁶⁰Ni giant dipole resonance. The fine structure observed in the excitation functions is shown to be most probably due to Ericson fluctuations. The gross (α, γ) cross sections are shown to be in reasonable agreement with the results of calculations made using the theory of Hauser and Feshbach assuming excitation of the giant dipole resonance.     

Heavy ion e+e− pairs to all orders in Zα

The heavy ion cross section for continuum e⁺e^? pair production has been calculated to all orders in Zα. Comparison is made with available CERN SPS and RHIC STAR data. Computed cross sections are found to be reduced from perturbation theory with increasing charge of the colliding heavy ions and for all energy and momentum regions investigated. Au or Pb total cross sections are reduced by 28% (SPS), 17% (RHIC) and 11% (LHC). For very high energy (E _e ⁺, E _e ^?>3 GeV) forward pairs at LHC the reduction from perturbation theory is a bit larger (17%). Use of zero degree calorimeter triggering (and thus small impact parameter weighting) makes impact parameter representation of exact pair production useful. Preliminary exact calculations in the zero impact parameter limit show a much larger reduction from perturbation theory (about 40%) at both RHIC and LHC.     

Excitation of promising nuclear fusion reactions in picosecond laser plasmas

The results of experiments devoted to studying the excitation of the promising nuclear fusion reactions ⁶Li(d, α)⁴He, ³He(d, p)⁴He, ¹¹B(p, 3α), and ⁷Li(p, α)⁴He, along with the standard reaction D(d, n)³He, in picosecond laser plasmas are presented. For the first time, it was shown that these reactions may proceed at a moderate laser-radiation intensity of 2 × 10¹⁸ W/cm², the respective yield being 2 × 10³ to 10⁵ per laser pulse. A brief survey of the main processes responsible for the generation of fast electrons and fast ions (protons) at the front surface of the target and for the excitation of nuclear fusion reactions is given. The calculated and experimental results on the yield from nuclear fusion reactions in picosecond laser plasmas are compared. The possibilities for optimizing the yield from the promising fusion reactions excited in femto- and picosecond laser plasmas are discussed.     

Gell-Mann-Low function in the ϕ4 theory

An algorithm is proposed for the determination of the asymptotics of a sum of a perturbation series from the given values of its coefficients in the strong-coupling limit. When applied to the ?⁴ theory, the algorithm yields the β(g)∝g ^α behavior with α≈1 at large g for the Gell-Mann-Low function.     

Classical Hamiltonian perturbation theory without secular terms or small denominators

We consider perturbation theory in ? for the classical Hamiltonian H = H₀ + ?H₁, where H₀ gives rise to a known motion and ? is small. First we demonstrate how the usual secular terms and small denominators arise from a straightforward expansion in ? and argue that they are artifacts of the method. Then we present an alternative perturbation theory based on an analysis of the operator (s ? L)^?1, where s is a complex number and L is the Liouville operator corresponding to H. This perturbation series contains neither secular terms nor small denominators. In the case of almost multiply periodic systems we show, to lowest non-trivial order in ?, how our series reproduces the standard results both in the resonant and nonresonant regions — all in one analytic formula. As a final exercise we demonstrate that energy is conserved at order ?ⁿ⁺¹ when the accuracy of the theory is order ?ⁿ.