Characteristics of double-pomeron exchange

A detailed kinematic study is made of the cross section for double-pomeron exchange. We consider reactions of the type a + b → c + d + (h₁ + h₂ + …) where a → c and b → d are quasi-elastic transitions with limited momentum transfer and (h₁ + h₂ + …) is a centrally produced hadron cluster. The dependence of the cross section on the relative azimuthal angle φ between the final hadrons c and d provides an important test for double-pomeron exchange. We calculate this φ-dependence for all cases of interest, using a model in which pomeron exchange is represented by an effective current-current interaction. For limited momentum transfer, where the pomeron spin is nearly equal to one, this model is equivalent to Reggeized pomeron exchange. We give a complete formalism for the partial-wave analysis of the double-pomeron reaction ab → cd + h₁₂ which differs from the one given by Rushbrooke and Webber. Furthermore, we discuss the two-pomeron vertex, and the construction of detailed and realistic models for double-pomeron reactions.     

Particle production in the double dual pomeron region

By an indirect method we calculate the missing mass discontiniuty of the dual two-loop graph in the double-pomeron region. We confirm the central region scaling and determine the P_⊥ dependence.     

Measurements ofK-shell ionization with132Xe and208Pb projectiles in the energy range of 1.4–5.9 MeV/u

Projectile and targetK-shell ionization cross sections induced by 3.6-, 4.7-, and 5.9 MeV/u¹³²Xe ions and 1.4-, 3.6-, 4.7-, and 5.9 MeV/u²⁰⁸Pb ions from the UNILAC in thin solid targets between C and U are measured. The cross sections are discussed in terms of the molecular model of innershell vacancy production in heavy ion-atom collisions. The sharing of 2p _1/2σ vacancies between theK shells of the two collision partners in these very heavy ion-atom collisions is found to deviate from the Meyerhof-Demkov formula forR≦10^?2. The measured ionization cross sections are compared with theoretical calculations for 1sσ and 2p _1/2σ excitation cross sections. AZ _UA=Z₁+Z ₂ dependence is found independent ofZ ₁/Z ₂. Outer-shell vacancy configurations measured in these close encounters are reported.     

Predictions for cross sections of light proton-rich isotopes in the ~(40)Ca + ~9Be reaction

The cross sections for Z=10–19 with isotopes T_z=-3/2 to-5 in the 140A Me V~(40)Ca+~9Be projectile fragmentation reaction have been predicted.An empirical formula based on the correlation between the cross section and average binding energy of an isotope has been adopted to predict the cross section.The binding energies in the AME16,WS4,and the theoretical prediction by the spherical relativistic continuum Hartree-Bogoliubov theory have been used.Meanwhile,the fracs parametrization and the modified statistical abrasion-ablation model are also used to predict the cross sections for the proton-rich isotopes.The predicted cross sections for the T_z=-3 isotopes are close to 10~(-10)mb,which hopefully can be studied experimentally.In addition,based on the predicted cross sections,Z=14 is suggested to be a new magic number in the light proton-rich nuclei with T_z-3/2,for which the phenomenon is much more evident than it is from the average binding energy per nucleon.     

Calculations of inelastic cross sections for rotational excitation

Cross sections for scattering of N₂ (j=0) molecules on He atoms have been calculated for relative energies below 5 · 10^?3 eV (58 °K). The time independent scattering formalism ofArthurs andDalgarno was used together with an assumed Lennard-Jones type potential with anisotropicP ₂(cos?) terms in the attractive and repulsive parts. The resulting system of coupled differential equations was solved in the distorted wave and close coupling approximations for the differential and integral cross sections for elastic and inelastic (j=0→j=2) scattering. In the integral inelastic cross section several sharp resonances were found to contribute 40% to the cross section at energies below 40 °K. The resonance peaks are attributed to orbiting or short-lived compound states since they are also observed in the elastic cross section at energies which are lower by the excitation energy of 1.5 · 10^?3 eV. Finally, the effect of varying the potential parameters on the integral inelastic cross section was studied at 50 °K and a rough formula for the cross section as a function of the parameters is obtained. The formula shows that a certain ratio of repulsive and attractive anisotropies leads to a small inelastic cross section indicating a mutual cancellation.     

The Coulomb correction to electron pair production by intermediate-energy photons

The Coulomb correction to the total cross section for intermediate-energy pair production is evaluated in terms of a high-energy-expansion formula, with the Davies-Bethe-Maximon correction as the leading term, followed by terms proportional to k^?1ln²k, k^?1lnk, k^?1 etc., the coefficients of which are determined by fitting to the Øverb?-Mork-Olsen exact low-energy results. The formula is estimated to be accurate within a few tenths of a per cent for photon energies between 3.5 m_ec² and infinity.     

On duality in e+e- annihilation

With the help of a relativistic generalization of a formula for the leptonic width of quarkonium in the quasiclassical approximation it is shown that the sum of a sufficiently large number of total cross sections for the production of the quarkonium state (Q$\text{Q}$)_n in e⁺e^- annihilation is equal to the total cross section for production of a quasi-free quark- antiquark pair Q$\text{Q}$.     

Direct pair production by positive and negative electrons in a hydrogen bubble chamber

The production of electron pairs by negative and positive electrons in the energy region 0.65 – 5.8 GeV has been investigated in the DESY 81-cm hydrogen bubble chamber. The effective cross section σ = 0.62 ± 0.04 mb averaged over the energy spectrum of incident electrons is found to be in good agreement with the predictions of quantum electrodynamics. The energy distribution of created pairs as well as the dependence of the total cross section on energy are best represented by the expression of Murota, Ueda and Tanaka with the constant c = 0.66 ± _0.17^0.24 and by Bhabhá's formula with the constants c₁ = 1 and c₂ = 2.8 ± _0.7^0.9. The contribution of the interference term between space-like and time-like Feynman diagrams to the cross section is estimated to be less than about 10% and to fall off with an increase of the incident energy.     

Large-PT jet production in QCD

The contribution from qq → qq + X scattering to the large-P_T jet cross section in hadronic collisions is calculated in quantum chromodynamics to order O(g⁶). The result finds a suggestive interpretation in the Parisi-Altarelli parton model, which yields also the general formula, including all quark-gluon subprocesses.     

The shape of the giant dipole resonance for light nuclei

A complete spectrum of the giant dipole resonance is calculated taking into account the finite depth of the single particle potential. The mixing of the one particle-one hole excitations because of residual interactions is treated in the time-dependent Hartree-Fock approximation. If the interaction is approximated by a separable potential a general formula can be derived, which gives the total dipole excitation cross section σ(E) in terms of the simple shell-model cross section σ₀(E). Numerical results are given for O¹⁶ and C¹² by evaluating σ₀(E) in a square well potential.     

New definition for the hadronic contribution to the muon anomalous magnetic moment

A new definition is proposed for the hadronic contribution to the muon anomalous magnetic moment that is based on the inclusion of the effects of vacuum polarization by leptons into the cross section for one-photon annihilation of a lepton pair into hadrons. The formula for the hadronic contribution includes the convolution of the measured cross section for annihilation into hadrons with a certain standard function. This remark concerns radiative correction to this function. A particular form has been proposed for this correction. It has been shown that the use of the new function makes it possible to reduce the uncertainty in such contributions due to radiative correctioins to δa _h/a _h ～ 10^?4.     

Theoretical studies of energy-energy correlation ine + e− annihilation

We calculate theO(α _s ² ) correction to the energy-energy corelation cross section ine ⁺ e^? annihilation using different resolution criteria in the limit of vanishing resolution cuts. We compare this in the back-to-back angular region with results of the logarithm approximation (LA) and deduce higher order corrections (beyondO(α _s ² )) from the LA formula. The final results are compared with recent TASSO data.     

Scattering of charged particles by atoms

A closed variant of the Born approximation for calculating differential scattering cross sections in ion-atom collisions is developed. An expression in terms of the matrix elements J _ij with respect to the single-electron states of the atom is found for the matrix element describing the target atom in the formula for the differential cross section. The matrix elements J _ij are averaged over the relative orientation of the momentum transferred in the collision and the symmetry axis of the electronic orbitals of the target atom, using the single-electron Rutaan-Hartree-Fock wave functions. The algebraic representation of the matrix elements J _ij makes it possible to perform calculations for atoms with any value of Z. The model developed is used to calculate the cross sections σ_Σ and characteristic scattering angles θ_c for the process of electron loss by H^? ions with energy E = 0.1–100 MeV in targets consisting of atoms with Z = 2–54. It is shown that σ_Σ ∝ E ^?1 and θ_c ∝ E ^?1/2 for all Z, and for fixed E the behavior of σ_Σ(Z) and θ_c(Z) is determined by the order of filling of the electronic shells of the target atoms (the ionization potential). The computational results are analyzed and compared with the experimental data and the results of other calculations.     

Zur formelmäßigen Darstellung des Ionisierungsquerschnitts für den Atom-Atomstoß und über die Ionen-Elektronen-Rekombination im dichten Neutralgas

Thomson's classical theory for the calculation of ionisation cross sections in electron-atom encounters is applied for calculating the ionisation cross section for atom-atom collisions. A very simple formula is obtained permitting a rapid calculation of the total ionisation cross sections as a function of the kinetic energyE _a and the massm _A of the ionizing atom, and of the binding energyE _i and the number ξ_i of equivalent electrons in the electronic shell to be ionized. The formula is in good agreement with quantum mechanical calculations and with experimental results. It can be applied to ionization from ground and from excited states. From this formula one obtains an expression for the rate coefficient for ionization in the center-of-mass system of the colliding particles. Then, the method of detailed balancing is applied to calculate the rate coefficient for ion-electron three-body collisional recombination with a neutral atom acting as the third body. This latter formula is applicable to recombination into the ground and into excited states.     

Fusion cross section at sub-Coulomb energies

The effective barrier at low energies is approximated by a Coulomb and parabolic barriers. A simple closed formula is obtained for the total reaction cross section which is the natural extension of Wong's results into the low energy domain. Theoretical predictions of averaged energy behaviour agree fairly well with various experimental results. The relation?ω ₀≧π(2kh ²Z₁Z₂ e ²/μ)^1/2 R ₀ ^?3/2 between the curvature and the extremum point of the nucleus-nucleus potential is suggested, based on low energy fusion experiments. By assuming equality sign, it is possible to extract the parameters of the barrier directly from experiment. Incidentally it is found that?ω ₀ remains persistently arround 4.5 MeV for all the reactions which have been investigated.     

Autoionization cross section of potassium atom excited by electron impact

The autoionization cross section of potassium atoms excited by electron impact is measured in the energy range from the first autoionization threshold at 18.72 eV to 202 eV. The data are obtained by deter-mining the total intensity of electron spectra resulting from the decay of the 3p ⁵ n ₁ l ₁ n ₂ l ₂ autoionizing states. The cross section has two maxima, 1.8 × 10^?16 and 2.2 × 10^?16 cm², at 21 and 32 eV, respectively. The excitation dynamics of autoionization states suggests that the first maximum is associated with the resonance character of the near-threshold excitation. The second maximum, as well as the behavior of the cross section at energies above 50 eV, reflects the dynamics of electron excitation of quartet and doublet autoionizing states. The measured autoionization cross section is compared with known data for the total single ionization cross section of potassium atom by electron impact. The relative contribution of the autoionization cross section to the total single ionization cross section is found to reach 30% at 32 eV.     

The ratio of the charm structure functions F k c (k = 2, L) at low x in deep inelastic scattering with respect to the expansion method

We study the expansion method for the gluon distribution function at low x values and calculate the charm structure functions in the LO and NLO analysis. Our results provide a compact formula for the ratio R ^c = F _L ^c /F ₂ ^c , which is approximately independent of x and the details of the parton distribution function at low x values. This ratio could be a good probe of the charm structure function F ₂ ^c in the proton deduced from the reduced charm cross sections at DESY HERA. These results show that the charm structure functions obtained are in agreement with HERA experimental data and other theoretical models.     

Operator equivalents in general

We show that recent criticism of a formula for diagonal operator equivalents (OE's) is unfounded. We generalise this formula to derive off-diagonal OE's ^jT_l^m, as a finite polynomial in J_Z, and claim that this is a definitive formula for the ^jT_l^m.     

Saturation Approach in Top Production

The reduced cross section for the top production, in deep inelastic scattering, determined when we use the Kharzeev–Levin–Nardi (KLN) model of the low x gluon distributions. With respect to this model, a compact formula for the ratio R^t(τ) provided that it is approximately independent of τ behavior at low- τ values. For the top production where Q_sr_⊥ ? 1, the model reduced to color transparency.     

Cross section of the reaction 6Li(p, γ)7Be

The cross section of the reaction ⁶Li(p, γ)⁷Be has been measured using Ge(Li) γ-ray spectrometers for proton bombarding energies E_p from 200 keV to 1200 keV. At E_p = 800 keV, the total (p, γ) integrated cross section is found to be 3.1 ± 0.4 μb. The cross section adopted from consideration of this and previous measurements is in good agreement with that predicted from the known thermal neutron cross section for ⁶Li(n, γ)⁷Li on the assumption that properties of mirror direct capture reactions can be well described by optical potentials that use the same parmeter values for the two reactions.