Browsing by Author "Mezhoud, R."

Now showing 1 - 14 of 14

Complex potentials with real eigenvalues and the inverse problem
(Institute of Atomic Physics, 2017) Lombard, R. J.; Mezhoud, R.; Yekken, Rabia
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
An efficient method to solve the Schrödinger equation with complex PT-symmetric potentials
(World Scienti¯c Publishing Company, 2023) Rouabhi, Fatma Zohra; Ami, I.; Mezhoud, R.; Lombard, R. J.
In this work, we present a simple and efficient method to compute numerically the eigenvalues of complex PT-symmetric Hamiltonian. Numerous works have been devoted to such Hamiltonians since the discovery that they admit totally or partially real spectra. To our knowledge, the method we are advocating has not been used in this context. Besides the determination of real eigenvalues, it allows us to observe the symmetry breaking and to calculate the imaginary parts of the energy.
Finite energy ground states of the −|x|^n potentials
(2021) Lombard, R. J.; Garidi, S.; Mezhoud, R.
Infinitely negative potentials have finite ground state energy if use is made of complex wave function. We study a few analytical examples and give numerical solutions for some −|x| n potentials
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
The inverse problem from discrete states in the d=1 dimensional space
(Institute of Atomic Physics, 2016) Lombard, R. J.; Yekken, R.; Mezhoud, R.
The linear PT-symmetric complex potential
(Institute of Atomic Physics, 2017) Lombard, R. J.; Mezhoud, R.
The spectrum of a PT-symmetric complex-valued linear potential is investigated. Working in the D =1 dimensional space, we consider V(x)= jxj+icx. Semianalytical solutions are given by using the properties of the Airy functions. The numerical integration of the differential equation system is discussed. We show that the number of eigenstates with a real eigenvalue is limited, depending on the ratio c= and on the quantum number n. This is reflecting the spontaneous breaking of PT symmetry. For the ground state, we conjecture the eigenvalue to be real for any value of c
Observables of complex PT-symmetric “Shifted” potentials
(Editura Academiei Romane, 2020) Lombard, R.J.; Mezhoud, R.; Yekken, R.
We study complex PT-symmetric potentials, with real eigenvalues, co responding to a complex coordinate shift (equation found) of a real even potential. In this case, the rules to achieve a coherent quantum mechanics are known. They allow the calculation of observables, which are found to be independent on c. This result is illustrated by few analytical or semi analytical examples. On the other hand, trying to test this property numerically faces problems linked to the difficulty of finding the proper solutions of the Schrödinger equation. In particular, the large distance behaviour of the wave functions generates instabilities. As an example, we have studied the (equation found) potential.
A pseudoCoulombian potential in D=1 dimensional space
(2009) Lombard, R. J.; Mezhoud, R.; Yekken, R.
In the D = 1 dimensional space, we study the bound state solutions of the potential V(x) = −e x + b x2 (e, b > 0). They occur on the right half-plane x 2 [0,1[. In the limit b!0, we recover the spectrum of the D = 1 Coulomb potential. Supersymmetric properties are briefly discussed. The model is extended by considering complex coupling constants. Nonlinear effects are also treated by considering a linear energy dependence of the e coupling constant
Spectral analysis : a consistency criterion. application to the 208 Λ Pb hypernucleus
(2010) Mezhoud, R.; Lombard, R. J.
We present a consistency criterion applicable to spectral data analysis in the case of a particle in a local potential. The method relies on the connection between the yrast energies and the ground state density moments, as well as on the technique used to determine the value of a positive definite function at the origin from its moments. As an illustrative example, the spectrum of the 208 Pb hypernucleus is considered
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
γ -ray emission in α -particle interactions with C, Mg, Si, and Fe at Eα=50-90 MeV
(American Physical Society, 2021) Kiener, J.; Bundesmann, J.; Deloncle I., I.; Denker, A.; Tatischeff, V.; Gostojic, A.; Hamadache, C.; Röhrich, J.; Benhabiles, H.; Bourgaoub, I.; Coc, A.; Hammache, F.; Mezhoud, R.; Peyré, J.
Nuclear deexcitation lines are regularly observed in the γ-ray emission spectra of strong solar flares. The most prominent lines are produced by interactions of protons and α particles, accelerated up to hundreds of MeV, with abundant nuclei of the solar atmosphere. Analysis and interpretation of these lines, which carry valuable information on the solar flare properties, need cross-section data for the γ-ray line emission in these interactions for a wide particle energy range. To this purpose, we measured the γ-ray emission in interactions of α-particle beams of Eα=50-90 MeV with target foils of C, Mg, Si, and Fe at the center for proton therapy of the Helmholtz-Zentrum Berlin. Setups of three high-purity Ge detectors and one LaBr3:Ce detector have been employed to detect the γ rays in two experiment campaigns. Relatively large distances of the detectors from the target and pulsed beams with sub-ns-wide pulses allowed the separation of beam-induced prompt γ-ray emission from the targets from other γ rays and neutron-induced background. γ-ray production cross sections for about 60 deexcitation lines from excited target nuclei or reaction products have been determined. For the strongest deexcitation lines from the major target isotopes, C12, Mg24, Si28, Fe56, there are now measured cross-section data from reaction threshold to Eα=90 MeV that can be directly used for astrophysical applications like solar flares. Comparison of the results with a cross-section compilation for strong γ-ray lines in solar flare emissions and the predictions of the talys nuclear reaction code were done. They underline the importance of cross-section determinations at accelerator laboratories for the establishment of an accurate cross-section data base in a wide projectile energy range