The candelas-weinberg model for spaces M4 × S2N

A method for calculating the one-loop effective potential for matter fields in Kaluza-Klein theories with the structure M⁴ × S^N for both even and odd N is presented. The cases M⁴ × S^N (N = 1, 2, 3, 4, 5, 6, and 8) have been examined. The method leads to finite results when N = odd and divergent results when N = even as expected.     

A Few-Body Approach to Bose–Einstein Condensation

A simple method to calculate ground state energies for a typical condensates containing up to A ~ 10⁷ atoms is presented. The method, based on the expansion of the wave function in terms of the Faddeev components, which in turn are expanded in terms of potential harmonics is numerically efficient. We obtain ground state results for condensates of ⁸⁷Rb containing up to A → 10⁸ atoms. The results agree very well with other methods in regions where the other methods are valid.     

π-π andK-¯K channel coupling and scalar mesons

Total nuclear reaction cross-sections are determined by means of a 4π-γ method. The results cover a wide span of targets for various stable beams. The validity of the method is shown in a combined systematics including also the results of transmission-type experiments. The data are very well described by the formula developed by Kox et al. The same method is applied to secondary fragment beams produced from a 44 MeV/u²²Ne beam on a 332mg/cm^{2 181}Ta target. Using the LISE spectrometer the fragments^{4, 6}He,^{6–9, 11}Li,^{7, 9–12, 14}Be,^{10–15, 17}B^11–19C,^13–19N,^15–21O,^{18– 21}F and^20,21 Ne are analyzed and transported to interact with a 199.4 mg/cm² Cu target surrounded by a 4π-γ counter. The measured total reaction cross-sectionsσ _R are discussed in terms of the reduced strong absorption radiusr ₀ and compared with other experimental results.     

The 181Ta(γ, π+)181Hf reaction

Yields for the reaction ¹⁸¹Ta(γ, π⁺)¹⁸¹Hf have been measured by an activation method using bremsstrahlung radiation with end-point energies in the range 150–360 MeV. The data have been unfolded to give cross section results corresponding to bombarding with monoenergetic photons. A comparison is made with respect to previous results and a semiclassical cascade-model calculation.     

Infrared plasma reflectivity minimum in heavily doped n-Si

This paper presents a numerical analysis of infrared (IR) plasma reflectivity minimum in ultra heavily doped (UHD) n-Si (impurity concentration N up to 6 × 10²¹cm⁻³) by using a self-consistent method (SCM) and a complex physical model. The necessity of taking into account the dependence of effective mass on impurity concentration is shown. The scattering on defects (N_def = 5 × 10¹⁷ cm⁻³) and dislocation (N_dis = 5 × 10¹¹ cm⁻²) is included. The approximate relation for the wavelength λ_m(N) of the reflectivity minimum is given. The results obtained are compared with the experimental results for n-Si and satisfactory agreement is found.     

Results and techniques of multi-loop calculations

In this review some recent multi-loop results obtained in the framework of perturbative quantum chromodynamics (QCD) and quantum electrodynamics (QED) are discussed. After reviewing the most advanced techniques used for the computation of renormalization group functions, we consider the decoupling of heavy quarks. In particular, an effective method for the evaluation of the decoupling constants is presented and explicit results are given. Furthermore, the connection to observables involving a scalar Higgs boson is worked out in detail. An all-order low-energy theorem is derived which establishes a relation between the coefficient functions in the hadronic Higgs decay and the decoupling constants. We review the radiative corrections of a Higgs boson into gluons and quarks and present explicit results up to order α_s⁴ and α_s³, respectively. In this review special emphasis is put on the applications of asymptotic expansions. A method is described which combines expansion terms of different kinematical regions with the help of conformal mapping and Padé approximation. This method allows us to proceed beyond the present scope of exact multi-loop calculations. As far as physical processes are concerned, we review the computation of three-loop current correlators in QCD taking into account the full mass dependence. In particular, we concentrate on the evaluation of the total cross section for the production of hadrons in e⁺e⁻ annihilation. The knowledge of the complete mass dependence at order α_s² has triggered a bunch of theory-driven analyses of the hadronic contribution to the electromagnetic coupling evaluated at high energy scales. The status is summarized in this review. In a further application four-loop diagrams are considered which contribute to the order α² QED corrections to the μ decay. Its relevance for the determination of the Fermi constant G_F is discussed. Finally, the calculation of the three-loop relation between the $\text{MS}$ and on-shell quark mass definitions is presented and physical applications are given. To complete the presentation, some technical details are presented in the appendix, where also explicit analytical results are listed.     

QCD prediction of transverse momentum distribution of partons

A general method to compute the development of the transverse momentum distributions of the partons as Q² increases is presented. As an example, the average 〈p_⊥²〉 is computed for the valence, charmed, sea and gluonic partons in the Q² range from 1 GeV² to 120 GeV². The results show a fast increase of the gluonic contribution, a slow increase of the valence contribution and an almost flat sea contribution.     

Transport cross sections for charged particle scattering in (dense-) cesium plasma; electrical conductivity

Transport cross sections for the electron-ion and electron-electron scattering in (dense) cesium plasmas is determined with the partial wave method. The scattering phase shifts δ_l(k) are calculated numerically by means of the usual Numerov method and the advantageous amplitude — phase method for energies E = 10^-4··· 5 ryd and for Debye screening lengths R_D = (10···10³)a₀. Besides the usual Debye potential, also a Thomas-Fermi potential is applied for the cesium electron-ion interaction. The resulting transport cross sections are compared with the Born and quasi-classical approximations. Furthermore, the electrical conductivity of fully ionized cesium plasmas is determined and compared with respective Spitzer results.     

Some peculiarities of spin-lattice relaxation of impurity rare-earth ions in crystals caused by the structure defects

The spin-lattice relaxation times for Nd³⁺ ions in yttrium-aluminum garnets (YAG) and for Yb³⁺ ions in CaF₂ in the low-temperature range have been measured. For the first system the temperature dependence of the relaxation rate is determined to a great extent by the method of sample preparation. For samples grow by the method of the horizontally oriented crystallization the dependence is described asT ₁ ^?1 =AT ⁿ ,n ? 4.7, which is an evidence of an influence of local structure disordering on the relaxation. The temperature dependence of the relaxation rate in CaF₂:Yb is also “anomalous”:T ₁ ^?1 =AT ^3.3. The results are compared with the previous data on the relaxation in similar systems, and with other cases of observation of “anomalous” temperature dependences. Different manifestations of the local crystal defects in spin-lattice relaxation are discussed.     

Configuration mixing and crystal-field splitting of Cr2+ in CdS

The effect of interaction of excited configurations 3d³4s, 3d³4p and 3d³4d with the ground 3d⁴ configuration on the crystal field splitting (E- T₂) of the tetrahedral Cr²⁺ ion in CdS has been studied by a rigorous method in which the energy matrix constructed in a basis of states belonging to both the ground and excited configurations has been directly diagonalised. Such a fairly rigorous treatment yield surprising results and interesting conclusions. Even though the calculation is based on an ionic model of the crystal field, it is found that inclusion of excited configurations accounts for the entire crystal field splitting observed experimentally in this particular case of Cr²⁺ in CdS. The configuration mixing in our treatment yields for the crystal field splitting a result few times greater than that found when the calculation is confined within the ground configuration only. Furthermore, the present investigation indicates that the second order perturbation method used in the earlier treatment was quite inadequate in the case of Cr²⁺ in CdS.     

QCD predictions for the Q2 dependence of quark and gluon fragmentation functions using Altarelli-Parisi type equations

In the leading logarithmic approximation, the fragmentation functions of quarks and gluons are investigated using Altarelli-Parisi type equations. Using a new method to make the Mellin transformation, the equation is solved. Analytic expressions for the fragmentation functions near z = 0 and z = 1 are also given. Finally, numerical results for the fragmentation functions D_q^π, D_q^K are presented for different Q².     

Partial-wave analysis of the π+π+π− system through the region of the A3 meson

A recent spin-parity analysis of the π⁺π⁺π^? system formed opposite a proton and a coherent deuteron by incident 13 GeV/c²π⁺ mesons, is extended to a three-pion mass of 1.9 GeV/c. Relative proportions of the contributing partial waves are presented, from threshold, and the A₃ region is discussed in detail. Contrary to results with the (3π)^? system, a change in phase is noted for the 2^? amplitude decaying to f⁰π⁺via am S-wave.The method employs the University of Illinois three-body partial-wave-analysis program.     

Studies of the crystal field energy levels and g factors for Ce in LiYF4 crystal

The five observed crystal field energy levels and EPR g factors g_//and g_⊥ for Ce³⁺-doped LiYF₄ crystal are calculated together from a complete diagonalization (of energy matrix) method. In the method, the contributions to g factors of ground Kramers doublet from all the rest doublets within the ground and excited manifolds ²F_5/2 and ²F_7/2 are included. The calculated results show reasonable agreement with the experimental values. The calculations suggest that the crystal field parameter B₂₀ > 0 in LiYF₄: Ce³⁺ crystal. The opinion of the parameter B₂₀ < 0 in the previous paper is not correct. Since this opinion is based on the calculation of g factors using a very simple method where only the contributions to g factors from the doublets within the ground manifold ²F_5/2 are considered, it is suggested that this simple method is not effective in the calculation of g factors for 4f¹ ions in crystals.     

Dispersion analysis of the K±p forward scattering amplitudes

The currently available experimental data on the K^±p forward scattering amplitudes are analyzed by three different methods: a discrepancy-function method, the Haber-Schaim linear extrapolation method, and a method based on a once-subtracted dispersion relation. Substantially more data are used than in previous analyses. The results of the three methods are found to be in good qualitative agreement. Predictions are obtained for the value of the effective KNY coupling constant and for the real parts of the K^±p forward scattering amplitudes over a wide range of energies.     

Collision induced transitions between Zeeman substates of laser excited sodium atoms in very high magnetic fields

This is a report on a new method of measuring cross sections for the collision induced population transfer between single Na — 3p ² P fine structure Zeeman states. The experiments are done for the five inert gases at the magnetic field strengths of 6, 17, 24, and 51 kOe. From the optically excited² P _3/2,±3/2 and² P _1/2,±1/2 states, respectively, the transfer to the other Zeeman states is studied. The method allows the determination of cross sections for which the influence of the magnetic field is cancelled and which render possible the calculation of cross sections for the transfer and the relaxation of all² P density tensor components of the degreek=1, 2, and 3. The comparison with previous theoretical and experimental results gives satisfactory agreement. As an application the six Grawert parameters are deduced for the inert gases.     

Heterodiffusion of chromium and cobalt in liquid iron

The heterodiffusion has been studied by the method of stationary diffusion source. In that method the saturated radioactive vapour of the diffusing element comes into contact with the liquid in which diffusion is being studied. Two variants of that method were applied and the diffusion coefficients of chromium and cobalt in liquid iron were determined, i.e.D _{(Cr→Fe, 1860K)}= =4·9×10^?5cm²/s andD _{(Co→Fe, 1820K)}=5×10^?5cm²/s, respectively. The values of maximum concentration of chromium in Fe-samples after diffusion were of the order of 10^?1 to 10^?2 wt-%, those of cobalt of 10^?4 wt-%. This experimental method is rather simple and the results obtained are in good conformity with other measurements.     

Calculation of the energy dependence of the fusion cross section and total cross sections for peripheral reactions on the basis of an analysis of data on elastic heavy-ion scattering: Strongly bound ions

A method is proposed for calculating the energy dependence of the fusion cross section (in general, the sum of the cross sections for complete and incomplete fusion, quasifission, and reactions of deep-inelastic scattering) σ _F (E) and the total cross section for peripheral (or quasielastic) reactions, σ _D (E). The method is based on an analysis of a limited set of angular distributions for the elastic scattering in a given pair of nuclei. The predictive power of the method is illustrated by considering the ¹⁶O + ²⁰⁸Pb, ¹⁶O + ⁴⁰Ca, and ¹⁶O + ²⁸Si systems. For each of these systems, the calculations were performed at energies in the range extending from subbarrier values to those exceeding the barrier height substantially. The results of the calculations are found to be in good agreement with relevant experimental data, whereby the reliability of the method is confirmed. By virtue of this, it is proposed to employ the method to study the energy dependences σ _F (E) and σ _D (E) in collisions involving unstable nuclei, for which it is difficult to determine experimentally the above dependences because of a low intensity of secondary beams.     

Eigenvalues of theµx 2 +λx 2m interaction

The even and odd parity eigenvalues for the bounded potentialμx ² +λx ^2m with both positive and negative values ofμ andm=2, 3, 4, 5, 6 are obtained by the method of series solution for any positive value of the coupling constantλ. Whenμ is negative the lower order eigenvalues are closely bunched in pairs in the low-λ regime (λ≪1). The results agree well with existing results.     

Effective threshold energy for pair production in nonpolar semiconductors

A streaming model (high field) analysis is given for the average energy for and the probability of electron-hole pair production in a semiconductor when a quadratically energy dependent impact ionization cross-section exists above a threshold energy and competes with a nonpolar optical phonon scattering mechanism. A power series expansion method and tabulated results are provided to treat the resulting probability integrals of the form ∫₀^∞xⁿ exp {?(βx + x³)}dx.