Browsing by Author "Lghezou, F. Z."

Now showing 1 - 5 of 5

Connecting the ground state mean square radius to the dipole excitation
(2007) Mezhoud, R.; Lghezou, F. Z.; Lombard, R. J.
We study relationships between the dipole excitation and the ground state ms radius of a two-body system in the case of local potentials. We recall the inequality obtained long ago by Bertlmann and Martin, and discuss correction factors transforming the inequality in an approximate expression. Connecting the correction factor to the contribution of the lowest dipole state to the sum rule, we get a lower bound to the ms radius. Inverting the relationships yields a bound for the square of the dipole transition matrix element, and thus a bound to the lowest dipole state transition rate
Determination of the central density on the basis of its moments
(2005) Ngo, H.; Lombard, R. J.; Lghezou, F. Z.; Mezhoud, R.
The value of the central density is of key importance for annihilation processes. For the ground state we discuss its determination from the moments of the ground state density. We first review the way of reaching the moments from the spectrum. In particular we show how to get the lowest moments in D = 3, namely Ær 2æ and Ær 1æ from the series expansion of the Laplace transform of the density. We then recall a method to obtain the central density based on the Stieltjes moment problem. If the number of known moments is finite, this technique yields a lower bound. We investigate the possibilities to estimate the accuracy of the bound and the corresponding asymptotic value. An application to the muonic 208Pb atom is presented
Generalized Bertlmann–Martin inequalities and power-law potentials
(2003) Mezhoud, R.; Lghezou, F. Z.; Chouchaoui, A.; Kerris, A. T.; Lombard, R. J.
In the three-dimensional Schr€odinger equation, the generalized Bertlmann–Martin inequalities connect the moments of the ground state density to the energy differences between the lowest level of each angular momentum ‘ and the ground state. They are discussed in the case of the power-law potentials, as well as the ln r potential. Use is made of the derived moments to reconstruct the form factor F ðqÞ, i.e., the Fourier transform of the ground state density. Pad e approximants are used to describe the high q behavior of the form factor when only a limited number of low order moments are known. The estimate of the ground state density at the origin is also discussed
Spectral analysis in the case of a complex potential
(2009) Mezhoud, R.; Lghezou, F. Z.; Lombard, R. J.
We extend to complex potentials a method developed to solve the inverse problem from bound states in the case of a local real potential. A first example is presented, which is based on a complex version of the Kratzer potential. In this case, the Schr¨odinger equation admits analytical solutions, providing us with a test of the method. The application to the π−–28Si and K−–208Pb hadronic atoms shows the possibilities and limitations of our approach
Weakly bound systems in the case of complex potentials
(2006) Mezhoud, R.; Lghezou, F. Z.; Lombard, R. J.
We consider weakly bound two-body systems. We study the behavior of the ground state mean square radius as the binding energy tends to zero in the case of complex potentials. We show that the asymptotic law, obtained with real potentials, is modified by the occurrence of a finite width in the case of finite-range potentials. The case of the PT-symmetric potentials is also discussed. We complete our study with few remarks concerning the same problem for three weakly bound particles