arXiv subjects
Publications and source records attributed to A. I. Milstein.
In the recent paper by Zhang the order $α^4 R_{\infty}$ corrections to the positronium P levels were reconsidered. Those calculations confirm our corresponding results, except for the contribution due to the squared spin-orbit interaction. We present here a new derivation of our previous result for this last correction, this derivation being to our opinion both simple and convincing.
The universal curve $σ/A$ of nuclear photoabsorption is investigated within a Fermi gas model of nuclear matter. An energy range from pion threshold up to 400 MeV is considered. The interactions between nucleon, pion, $Δ$-isobar and photon are considered in the non-relativistic approximation with corrections of the order $1/M$ taken into account with respect to proton mass. Analytical expressions are obtained, in which the influence of nuclear correlations, two-nucleon contributions and relativistic corrections is studied explicitely. An extension of the model calculation to nucleon knock-out reactions is discussed.
We rederive here in a simple and transparent way the master formula for the dominant part of large relativistic corrections to the positronium decay rate.
The contact Darwin term is demonstrated to be of the same origin as the spin-orbit interaction. The $(Zα)^4 m^3/M^2$ correction to the Lamb shift, generated by the Darwin term, is found for an arbitrary nonvanishing spin of the nucleus, both half-integer and integer. There is also a contribution of the same nature to the nuclear quadrupole moment.
Photon splitting in a very strong magnetic field is analyzed for energy $ω< 2m$. The amplitude obtained on the base of operator-diagram technique is used. It is shown that in a magnetic field much higher than critical one the splitting amplitude is independent on the field. Our calculation is in a good agreement with previous results of Adler and in a strong contradiction with recent paper of Mentzel et al.
The contribution of mesonic exchange currents to nuclear Compton scattering is investigated within the framework of a Fermi gas model of nuclear matter in the non-relativistic limit. The additional interaction between the nucleons is accounted for by including two- and three-body diagrams. As a test of this model, the enhancement constant $κ$ is calculated. The full correlators for the central and tensor part of the nucleon-nucleon interaction due to pion exchange are obtained and the energy dependence of the amplitude is investigated. The contribution of the $Δ$-excitation to the mesonic part of the Compton amplitude is calculated explicitely using an effective Hamiltonian in the static limit.
The low-energy theorem for the forward Compton scattering is generalized to the case of an arbitrary target spin. The generalization is used to calculate the corresponding contribution to the deuterium hyperfine structure. The nuclear-structure corrections are quite essential in this case due to the deuteron large size. Corrections of this type calculated here remove the discrepancy between the theoretical and experimental values of the deuterium hyperfine splitting. Explicit analytical result is obtained also for the deuteron polarizability contribution to the Lamb shift.
A simple integral representation is derived for the quasiclassical Green function of the Dirac equation in an arbitrary spherically-symmetric decreasing external field. The consideration is based on the use of the quasiclassical radial wave functions with the main contribution of large angular momenta taken into account. The Green function obtained is applied to the calculation of the Delbruck scattering amplitudes in a screened Coulomb field.
The order $α^4 (m/M) R_{\infty}$ shift of hydrogen P levels is found. The corrections are predominantly of relativistic origin. Our approach is a straightforward extension of that developed and applied by us previously to positronium P levels. The corrections to the Lamb shift in hydrogen constitute numerically δE(2 P_{1/2})=0.55 kHz, δE(2 P_{3/2}) =0.44 kHz.
The physical origin of the $mα^5$ radiative corrections to $P$-levels in the two-body QED problem is elucidated. Then we demonstrate that the next order, $mα^6$, corrections to those levels are due to the anomalous magnetic moment only.
Elastic scattering of photons in a Lorentz-scalar potential via virtual spin-zero particle-antiparticle pairs (`` Delbrück scattering") is considered. An analytic expression for the Delbrück amplitude is found exactly in case of an oscillator potential. General properties of the amplitude and its asymptotics are discussed.
Relativistic corrections to the positronium decay rate are calculated. They are close to $40(α/π)^2$ and $46(α/π)^2$ for singlet and triplet states respectively.
The order $α^4 R_{\infty}$ corrections to positronium $P$ levels are found. The calculation is reduced to the ordinary perturbation theory for the nonrelativistic Schrödinger equation. The perturbation operators have the Breit-type structure and are obtained by calculating on-mass-shell diagrams. Found energy corrections constitute numerically $δE(2 ^1 P_1)=0.06$ MHz, $δE(2 ^3 P_2)=0.08$ MHz, $δE(2 ^3 P_1)=0.025$ MHz, $δE(2 ^3 P_2)=-0.58$ MHz.