Table of contents

The approximately analytical scattering state solutions of the l-wave Schrödinger equation for the Eckart potential are carried out by a proper approximation to the centrifugal term. The normalized radial wavefunctions of l-wave scattering states on the 'k/2π scale' are presented and the calculation formula of phase shifts is derived. It is interesting to find that the energy levels of the continuum states reduce to those of the bound states at the poles of the scattering amplitude. We consider and verify two special cases: the l=0 and the s-wave Hulthén potential.

The dynamics of the weak nonlinear matter solitary waves in two-component Bose–Einstein condensates (BEC) with cigar-shaped external potential are investigated analytically by a perturbation method. In the small amplitude limit, the two-components can be decoupled and the dynamics of solitary waves are governed by a variable-coefficient Korteweg–de Vries (KdV) equation. The reduction to the KdV equation may be useful to understand the dynamics of nonlinear matter waves in two-component BEC. The analytical expressions for the evolution of soliton, emitted radiation profiles and soliton oscillation frequency are also obtained.

We consider the bifurcation control for the forced Burgers–KdV equation by means of delay feedback linear terms. We use a perturbation method in order to find amplitude and phase modulation equations as well as external force-response and frequency-response curves. We observe in the resonance response a saddle-node bifurcation that leads to jump and hysteresis phenomena. We compare the uncontrolled and controlled systems and demonstrate that control terms can delay or remove the occurrence of the saddle-node bifurcation and reduce the amplitude peak of the resonant response.

We study the quantum teleportation through the three-qubit Heisenberg XX model with a magnetic impurity. The main result is the systematic analysis of the average fidelity's evolution as a function of magnetic impurity B and temperature T. What deserves mentioning here is that the effects of magnetic impurity on the average fidelity obviously behave differently whether the impurity is located on the receiver's site or not.

A model for the localized quantum vacuum is proposed in which the zero-point energy (ZPE) of the quantum electromagnetic field originates in energy- and momentum-conserving transitions of material systems from their ground state to an unstable state with negative energy. These transitions are accompanied by emissions and re-absorptions of real photons, which generate a localized quantum vacuum in the neighborhood of material systems. The model could help resolve the cosmological paradox associated with the ZPE of electromagnetic fields, while reclaiming quantum effects associated with quantum vacuum such as the Casimir effect and the Lamb shift. It also offers a new insight into the Zitterbewegung of material particles.

The multiconfiguration Dirac–Fock (MCDF) method is used to systematically calculate the wavelengths and oscillator strengths for transitions among the levels belong to the 3s²3p, 3s²3d, 3s²4s, 3s²4p, 3s3p², 3s3d², 3s3p3d, 3s3p4d, 3s3d4s, 3s3d4p, 3s3d4d, 3p³, 3p²3d, 3p²4s, 3p²4p, 3p²4d and 3p3d4d configurations of Al-like Fe¹³⁺, Co¹⁴⁺ and Ni¹⁵⁺ ions. Good agreement is found between our calculation and the available experimental wavelengths. Then wavelengths and oscillator strengths of the Cu¹⁶⁺, Zn¹⁷⁺ and Ga¹⁸⁺ from n=3–4 transitions involved in these configurations are extensively reported for the first time. The configuration interactions in the Al-like ions are discussed. In particular, the mixing coefficients and level crossing between the 3s3p3d ⁴P_3/2 and 3s3p3d ⁴D_3/2 states in Al-like Co and Ni are investigated.

In this paper, we re-analyze the ingenious experiment by Kündig (measurement of the transverse Doppler shift by means of the Mössbauer effect) and show that a correct processing of experimental data gives a relative energy shift ΔE/E of the absorption line different from the value of classically assumed relativistic time dilation for a rotating resonant absorber. Namely, instead of the relative energy shift reported by Kündig (v being the linear velocity of absorber and c being the light velocity in vacuum), we derive from his results . We are inclined to think that the revealed deviation of ΔE/E from relativistic prediction cannot be explained by any instrumental error and thus represents a physical effect. In particular, we assume that the energy shift of the absorption resonant line is induced not only by the standard time dilation effect, but also by some additional effect missed at the moment, and related perhaps to the fact that resonant nuclei in the rotating absorber represent a macroscopic quantum system and cannot be considered as freely moving particles.

We have calculated energy splittings of 53 fine-structure levels as well as oscillator strengths and radiative decay rates for all electric-dipole-allowed and intercombination transitions among the (1s²2s²2p⁶)3s²(¹S), 3s3p(^1,3P^o), 3s3d(^1,3D), 3s4s(^1,3S), 3s4p(^1,3P^o), 3s4d(^1,3D), 3s4f(^1,3F^o), 3p²(¹S,³P,¹D), 3p3d(^1,3P^o,^1,3D^o,^1,3F^o), 3p4s(^1,3P^o) and 3d²(¹S,³P,¹D,³F,¹G) states of Ge XXI, using extensive configuration–interaction (CI) wavefunctions, obtained with the CIV3 computer code of Hibbert. The important relativistic effects in intermediate coupling are incorporated by means of the Breit–Pauli Hamiltonian. In order to keep our calculated energy splittings as close as possible to the experimental values, we have made small adjustments to the diagonal elements of the Hamiltonian matrices. Our excitation energies, including their ordering, are in excellent agreement with the available experimental results. The enormous mixing among several fine-structure levels makes it very difficult to identify them correctly with the result that their positions in the calculation of Ivanova et al are interchanged compared to our results and the experimental values. From our transition probabilities, we have also calculated radiative lifetimes of some fine-structure levels. Our calculated oscillator strengths and the lifetimes are found to be in good agreement with the other available theoretical results. In this calculation, we also predict new data for several fine-structure levels where no other theoretical and/or experimental results are available.

Two-dimensional (2D) magneto-hydrodynamic (MHD) liner-on-plasma computations have been performed to study the growth of instabilities in a magnetized target fusion system involving the cylindrical compression of an inverse Z-pinch target plasma by a metallic liner. The growth of modes in the plasma can be divided into two phases. During the first phase, the plasma continues to be Kadomtsev stable. The dominant mode in the liner instability is imposed upon the plasma in the form of a growing perturbation. This mode further transfers part of its energy to its harmonics. During the second phase, however, non-uniform implosion of the liner leads to axial variations in plasma quantities near the liner–plasma interface, such that certain regions of the plasma locally violate the Kadomtsev criteria. Further growth ofthe plasma modes is then due to plasma instability. The above numerical study has been complemented with a linear stability analysis for the plasma, the boundary conditions for this analysis being obtained from the liner-on-plasma simulation. The stability of axisymmetric modes in the first phase is found to satisfy the Kadomtsev condition Q₀<1. Furthermore, the growth rates of these modes in the second phase are found to agree well with the predictions of the linear stability analysis. A linear stability analysis for m>1 modes, using equilibrium profiles from the 2D MHD study, shows that their growth rates can exceed those for m=0 by as much as an order of magnitude.

Linear and nonlinear dynamics of an electron acoustic wave in an inhomogeneous magnetized plasma are studied in the presence of non-uniform background current. The modified Rayleigh instability condition is found due to shear in the magnetic field and the current. A nonlinear stationary solution is also obtained in the form of tripolar vortices. The relevance of the present study to auroral and magnetotail plasmas is pointed out.

Using kinetic theory, new dispersion relations based on relativistic Maxwellian velocity distribution are obtained for ordinary and extraordinary modes in a strongly magnetized hot plasma. It is observed that, unlike the non-relativistic Maxwellian distribution case where only real dispersion relation appears for the relativistic case both the real dispersion relations and the damping decrements occur. To illustrate the results graphically, we have plotted the phase velocity squared and the growth rate versus frequency for different values of n. For O-mode, the non-propagation region disappears as we increase the values of the harmonic number n while for the X-mode, the propagation region occurs only for the large harmonics. As regards damping, for O-mode the damping rate is small for small n and increases with n. For X-mode, on the contrary, the damping rate decreases as n increases.

Several current theories concerning the nature of ball lightning predict a substantial electrostatic charge in order to account for its observed motion and shape (Turner 1998 Phys. Rep.293 1; Abrahamson and Dinniss 2000 Nature403 519). Using charged soap bubbles as a physical model for ball lightning, we show that the magnitude of charge predicted by some of these theories is too high to allow for the types of motion commonly observed in natural ball lightning, which includes horizontal motion above the ground and movement near grounded conductors. Experiments show that at charge levels of only 10–15 nC, 3-cm-diameter soap bubbles tend to be attracted by induced charges to the nearest grounded conductor and rupture. We conclude with a scaling rule that can be used to extrapolate these results to larger objects and surroundings.

We report a study on the micro-structural changes in GaN due to neon ion implantation using the x-ray diffraction and Raman scattering techniques. An implantation dose of 10¹⁴ cm⁻² was found unable to produce lattice deformation observable by Raman measurements. For higher doses of implantation several disorder activated Raman scattering centers were observed which corroborate the literature. A new dose dependent feature has been recorded at 1595 cm⁻¹ for higher implantation doses which is suggested to be the vibrational mode of microcavities produced in the lattice.

We present compact analytical solutions for the energy spectrum of carriers in Kane-type semiconductors in a certain varying magnetic field. We find an analytical expression for the effective g-factor of electrons in the three-dimensional semiconductors in a certain magnetic field.

We describe the scientific content of the International School of Physics 'Enrico Fermi' on atom optics and space physics, organized by the Italian Physical Society in Varenna at Lake Como, Italy, 2–13 July 2007.