<p>We discuss radiative transitions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo stretchy="false">→</mo><msub><mi>D</mi><mi>s</mi></msub><mi>γ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo stretchy="false">→</mo><msubsup><mi>D</mi><mi>s</mi><mo>*</mo></msubsup><mi>γ</mi></math> of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi></math>-wave mesons. Since <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub></math> mesons have no certain <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi></math>-parity, and the masses of quarks in these mesons differ significantly, then due to the spin-orbit interaction, each of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi></math>-wave mesons with the total angular momentum <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>=</mo><mn>1</mn></math> is a superposition of states with the total spin of quarks <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>S</mi><mi>tot</mi></msub><mo>=</mo><mn>0</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>S</mi><mi>tot</mi></msub><mo>=</mo><mn>1</mn></math>. We explain why the partial width of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>2460</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msub><mi>D</mi><mi>s</mi></msub><mi>γ</mi></math> radiative transition is significantly larger than the corresponding value for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>2536</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msub><mi>D</mi><mi>s</mi></msub><mi>γ</mi></math>. We also predict the corresponding partial widths of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub></math>.</p>

Russia

A.E. Bondar

A.I. Milstein

Phenomenology of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>D</mi></mrow><mrow><mi>s</mi><mn>1</mn></mrow></msub></mrow></math> mesons radiative transitions

It is shown that an account for the final-state interaction of real or virtual nucleon and antinucleon produced in the processes <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><mi>p</mi><mover><mrow><mi>p</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>γ</mi></math>, <math><mi>ψ</mi><mo>(</mo><mn>2</mn><mi>S</mi><mo>)</mo><mo>→</mo><mi>p</mi><mover><mrow><mi>p</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>γ</mi></math>, <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><mi>p</mi><mover><mrow><mi>p</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>ω</mi></math>, and <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><mn>3</mn><mrow><mo>(</mo><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>)</mo></mrow><mi>γ</mi></math> near the threshold of <math><mi>N</mi><mover><mrow><mi>N</mi></mrow><mrow><mo>¯</mo></mrow></mover></math> pair production allows one to obtain self-consistent description of these processes. Predictions of our model are in good agreement with experimental data available. The proposed potential model also reproduces the corresponding partial cross sections of <math><mi>p</mi><mover><mrow><mi>p</mi></mrow><mrow><mo>¯</mo></mrow></mover></math> scattering.

S.G. Salnikov

Meson production in / Decays and Process

The effect of screening by atomic electrons on the behavior of electron and positron wave functions in the continuous spectrum at small distances is studied. It is shown that these asymptotics are affected not only by the static potential of atomic electrons, but also by the polarization potential, as well as by the exchange interaction, which is essential for nonrelativistic electrons. A simple analytical expression is obtained for the photoproduction cross section of <math><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></math> pair in an atomic field near the threshold. The spectrum and angular distribution of the produced particles are considered. It is shown that screening significantly affects the cross section in the near-threshold region.

P.A. Krachkov

Atomic screening and Pair Photoproduction at low Energies

It is shown that the influence of the undulator field on the motion of a relativistic electron leads to a significant increase of the bremsstrahlung cross section on an atom near the end of the spectrum of undulator radiation. Observation of this effect is quite a realistic task.

N.Yu. Muchnoi

Resonant amplification of a relativistic electron bremsstrahlung on an atom in the undulator field

We consider the electron-positron pair production by a photon in Coulomb field near threshold. We obtain the analytical results for the particle energy spectrum and angular distribution exactly in the parameter <math><mi>Z</mi><msup><mrow><mi>e</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>/</mo><mi>ħ</mi><mi>v</mi></math>. We show that Furry-Sommerfeld-Maue approximation for the wave functions used by Nishina, Tomonaga and Sakata in Ref. [1] is not sufficient and leads to wrong results.

R.N. Lee

Photoproduction of pair in a Coulomb field near the threshold

We analyze the one-photon mechanism of <math><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></math> pair production in the collision of nonrelativistic nuclei. The contribution of electric quadrupole radiation of virtual photon to the corresponding cross section is found. The effect of the finite nuclear size is considered in detail. A comparison is made with the contribution of electric dipole radiation of virtual photon and with the contribution of the two-photon pair production mechanism. It is shown that the contribution of electric quadrupole radiation is dominant in a wide range of relative velocities. The cross section for the production of <math><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></math> pair with the capture of an electron by one of the nuclei is also analyzed.

I.V. Obraztsov

Quadrupole radiation and Pair Production in the Collision of Nonrelativistic Nuclei

Parameterization of the form factors of <math><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mn>1285</mn><mo>)</mo></math> meson is proposed. This parameterization is consistent with the available experimental data on the cross sections of <math><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mn>1285</mn><mo>)</mo></math> meson production in the processes <math><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>→</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mn>1285</mn><mo>)</mo></math> and <math><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>→</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mn>1285</mn><mo>)</mo></math>, as well as on the widths of the decays <math><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mn>1285</mn><mo>)</mo><mo>→</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></math>, <math><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mn>1285</mn><mo>)</mo><mo>→</mo><msup><mrow><mi>ρ</mi></mrow><mrow><mn>0</mn></mrow></msup><mi>γ</mi></math>, <math><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mn>1285</mn><mo>)</mo><mo>→</mo><msup><mrow><mi>ρ</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup></math>, and <math><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mn>1285</mn><mo>)</mo><mo>→</mo><mn>2</mn><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><mn>2</mn><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup></math>. Our parameterization is also consistent with the predictions for the asymptotic behavior of these form factors.

A.S. Rudenko

Consistent analysis of (1285) Meson Form Factors

The impact of a laser field on the process of photon radiation by an ultra-relativistic electron in an atomic field is investigated. The angular distribution and the spectrum of the radiated photon are derived. By means of the quasiclassical approximation, the obtained results are exact in the parameters of the laser field and the atomic field. It is shown that the impact of the laser field is significant even for fairly average values of the laser field parameters routinely achievable nowadays. Therefore, an experimental observation of the influence of the laser field on bremsstrahlung in the atomic field is a very feasible task.

Germany

A. Di Piazza

High-energy bremsstrahlung on atoms in a laser field

The cross section of high-energy <math><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></math> pair production by a heavy charged particle in the atomic field is investigated in detail. We take into account the interaction with the atomic field of <math><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></math> pair and a heavy particle as well. The calculation is performed exactly in the parameters of the atomic field. It is shown that, in contrast to the commonly accepted point of view, the cross section differential with respect to the final momentum of a heavy particle is strongly affected by the interaction of a heavy particle with the atomic field. However, the cross section integrated over the final momentum of a heavy particle is independent of this interaction.

Coulomb effects in high-energy Electroproduction by a Heavy Charged Particles in an Atomic Field

We derive the spectrum and the total cross section of electromagnetic e+e− pair production in the collisions of two nuclei at low relative velocity β . Both free–free and bound-free e+e− pair production is considered. The parameters ηA,B=ZA,Bα are assumed to be small compared to unity but arbitrary compared to β ( ZA,B are the charge numbers of the nuclei and α is the fine structure constant). Due to a suppression of the Born term by high power of β , the first Coulomb correction to the amplitude appears to be important at ηA,B≳β . The effect of a finite nuclear mass is discussed. In contrast to the result obtained in the infinite nuclear mass limit, the terms ∝M−2 are not suppressed by the high power of β and may easily dominate at sufficiently small velocities.