Alfaz Uddin - Academia.edu (original) (raw)
Papers by Alfaz Uddin
Atoms, 2022
This article presents a theoretical investigation of the differential, integrated, elastic, inela... more This article presents a theoretical investigation of the differential, integrated, elastic, inelastic, total, momentum-transfer, and viscosity cross-sections, along with the total ionization cross-section, for elastically scattered electrons and positrons from a carbon dioxide (CO2) molecule in the incident energy range of 1 eV ≤Ei≤ 1 MeV. In addition, for the first time, we report the spin polarization of e±−CO2 scattering systems. The independent atom model (IAM) with screening correction (IAMS) using a complex optical potential was employed to solve the Dirac relativistic equation in partial-wave analysis. The comparison of our results with the available experimental data and other theoretical predictions shows a reasonable agreement in the intermediate- and high-energy regions.
Journal of Physics G: Nuclear and Particle Physics, 2021
The European Physical Journal D, 2020
Abstract A complex optical potential (OP) is employed to study the critical minima (CM) and spin ... more Abstract A complex optical potential (OP) is employed to study the critical minima (CM) and spin polarization in the elastic e − –Ba and e + –Ba scattering for collision energies in the range E i = 1–1500 eV and E i = 1–100 eV respectively in terms of the Dirac partial wave method (OPMD) and the Schrödinger partial wave method (OPMS). The energy dependence of the integral elastic cross sections (IECSs), momentum transfer cross sections (MTCSs), viscosity cross sections (VCSs), inelastic cross sections (INCSs) and total cross sections (TCSs) is also calculated and discussed for both the projectiles in the same energy range. The OPMD optical potential is composed of the static, exchange, polarization and absorption components. On the other hand, the OPMS comprises the static, local exchange, polarization, spin–orbit, and absorption potentials. The number of CM in the DCS distribution of e − –Ba scattering has been found to be 11 using the OPMD method, while the OPMS calculation produces 12 CM points. However, the OPMS calculation with the static and spin–orbit potentials only produces 9 CM. The critical energies and the angular positions of these CM are revealed and discussed. There are 22 and 24 maximum spin polarization points found in the e − –Ba scattering using OPMD and OPMS respectively. For the case of e + –Ba scattering, we have found 2 CM with OPMD calculations of which the angular positions along with the critical energies are discussed. There are 4 maximum polarization points noted with OPMD calculations which fail to attain the condition for sharpness of S ( θ ) distribution. To the best of our knowledge, the present is the first work to determine the CM in the DCS distribution of e ± –Ba scattering. The Sherman function and the DCSs for some energy points are also calculated for the first time. Graphical abstract
Results in Physics, 2021
Abstract Differential, integral, momentum-transfer, viscosity, inelastic and total cross sections... more Abstract Differential, integral, momentum-transfer, viscosity, inelastic and total cross sections as well as spin asymmetries are calculated for electron and positron scattering from the gold atom with nuclear spin 3 2 . The impact energies of the projectiles range from low-energy atomic physics regime to high-energy nuclear physics. This is accomplished by employing two different theoretical approaches, applicable for the aforesaid two domains of energies, and are based on the partial-wave analysis. In one approach, the phase shifts analysis is done at E i 1 MeV using the Dirac relativistic equations. In another approach, at E i ≥ 100 keV, the same analysis is carried out with the distorted wave Born approximation to account for the projectile scattering including the magnetic effect as well. Predictions are reported for 1 eV ≤ E i ≤ 0.5 GeV electrons and positrons colliding with 197 Au target. In addition, we report here systematically the details of the critical minima in the elastic differential cross sections. To date, neither any experimental nor any theoretical study on the critical minima of electron/positron–Au scattering system is available in the literature. Our results of other observables are compared with the available experimental data and other calculations and are found to produce quite reasonable agreements with two forms of data.
Physica Scripta, 2020
This work presents the calculations of differential, integrated elastic and momentum transfer cro... more This work presents the calculations of differential, integrated elastic and momentum transfer cross sections for the elastic scattering of electrons from the ions of xenon isonuclear series over the incident energy range 1 eV–1000 eV. Coulomb glory, the amplification of elastic backscattering of electrons from positive ions owing to the electrostatic screening of nuclear potential by atomic electrons, is investigated throughout the ionic series of xenon, argon and neon. Cross sections for the angular distribution of elastically scattered positron from selected xenon ions are also calculated. Energy dependency of differential cross sections and Sherman functions are predicted for both the projectiles and a comparison is presented to exhibit the dissimilarity arising out of the difference of the interactions of the projectiles with ions. The theoretical methodology of this work employs the Dirac relativistic partial wave analysis using a complex optical potential, comprising static, e...
Atoms, 2021
Calculations are presented for differential, integrated elastic, momentum transfer, viscosity, in... more Calculations are presented for differential, integrated elastic, momentum transfer, viscosity, inelastic, total cross sections and spin polarization parameters S, T and U for electrons and positrons scattering from atoms and ions of radon isonuclear series in the energy range from 1 eV–1 MeV. In addition, we analyze systematically the details of the critical minima in the elastic differential cross sections along with the positions of the corresponding maximum polarization points in the Sherman function for the aforesaid scattering systems. Coulomb glory is investigated across the ionic series. A short range complex optical potential, comprising static, polarization and exchange (for electron projectile) potentials, is used to describe the scattering from neutral atom. This potential is supplemented by the Coulomb potential for the same purpose for a charged atom. The Dirac partial wave analysis, employing the aforesaid potential, is carried out to calculate the aforesaid scattering...
Dirac relativistic partial wave analysis has been employed to analyze the angular distributions a... more Dirac relativistic partial wave analysis has been employed to analyze the angular distributions and critical minima along with maximum spin polarization for the elastic scattering of electrons from copper atoms over the energy range 1-2000 eV. Integrated elastic, inelastic, total and momentum transfer cross sections have also been calculated. This work uses a complex electronatom optical potential that includes static, exchange, correlation-polarization and absorption potentials. Comparison of our calculations with the available experimental data and other theoretical calculations show a satisfactory agreement. As far as we are concern, critical minima and corresponding maximum spin polarization points have not yet been reported in literature.
Journal of Physics: Conference Series, 2020
Synopsis Vaisburd and Evdokimov proposed an empirical VE model to calculate the electron impact s... more Synopsis Vaisburd and Evdokimov proposed an empirical VE model to calculate the electron impact single ionization cross-sections of atoms and molecules. The extension of the modified VE model (MVE) has been proposed incorporating the relativistic effects. This model is applied to investigate the total L-shell as well as L1-, L2- and L3-subshells ionization cross-sections of various atomic targets with atomic numbers Z =1892 for incident energies up to 1 GeV. The results from the MVE model are compared with the available experimental data and theoretical findings.
A simple method is proposed and tested by evaluating the electron impact inner-shell ionization c... more A simple method is proposed and tested by evaluating the electron impact inner-shell ionization cross sections of various targets up to ultra high energy region. In this energy region there are not many calculations due to lack of reliable method. In this work we extend the validity of the siBED model [1] in terms of targets and incident energies. The extension of our earlier RQIBED model [2] is also reported here and we examined its findings for the description of the experimental EIICS data of various targets up to E=1000 MeV. Details will be presented at the meeting. [1] W. M. Huo, Phys. Rev A 64, 042719 (2001). [2] M. A. Uddin, A. K. F. Haque, M. S. Mahbub, K. R. Karim, A. K. Basak and B. C. Saha, Phys. Rev. A 71, 032715 (2005).
A recently proposed parameter-free relativistic model is applied to evaluate the total cross sect... more A recently proposed parameter-free relativistic model is applied to evaluate the total cross sections for electron impact ionization of neutral and ionic targets. This model has been applied with great success to obtain ionization cross sections of hydrogen-like systems[1]. We report here the extention of this model to two-electron targets, both simple and heavy, like He, Li+, B3+, Fe24+, Ag45+ and U90+ at intermediate and high energies. The present results are compared with those of more sophisticated theories and of other models as well as experimental values. [1] M. A. Uddin, M. N. A. Abdullah, M. S. Mahbub, A. K. Basak, Phys. Scr. 68, 192 (2003).
Advances in Quantum Chemistry, 2016
Calculations of electron impact ionization cross sections (EIICS) for H to Sc (with atomic number... more Calculations of electron impact ionization cross sections (EIICS) for H to Sc (with atomic number Z =1–21) and their corresponding isoelectronic series over incident energies up to 106 keV have been reviewed. This work reports the results of calculations using our various easy-to-use models reproducing closely the experimental EIICS data. We also report how these models can easily be implemented to generate accurate data as demanded by various model calculations. The selection of the range of atomic number Z for different isoelectronic series was made possible by the wealth of the EIICS data either from experiments or from rigorous quantum calculations. We have furnished the detailed description of our various models with comparison of the outcomes of these models with experimental and other theoretical results. Our models describe the experimental results with reasonable success for various atomic and ionic targets belonging to the H to Sc isoelectronic series over a wide range of atomic number in each series.
The knowledge of inner-shell ionization cross sections has not only fundamental importance for un... more The knowledge of inner-shell ionization cross sections has not only fundamental importance for understanding collision dynamics of electron-atom interactions, etc, but also is used extensively in many applied fields such as radiation science, astrophysics, plasma physics, etc. The enormous demands of ionization cross sections can only be met by suitable analytical formula that are easy to use and can produce reliable result. We report here an extension of the CVTS [1] model incorporating both the relativistic and ionic factors and tested on 23 atomic targets ranging from He to U [2] with excellent account of the experimental cross sections. [4pt] [1] C. S. Campos, M. A. Z. Vasconcellos, J. C. Trincavelli, and S. Segui, J. Phys. B. 40, 3835 (2007).[0pt] [2] A K F Haque, M R Talukder, M. Shahjahan, M A Uddin, A K Basak and B C Saha, J. Phys. B.; At. Mol. Opt. Phys (under consideration), (2010).
International Journal of Modern Physics B, 2007
The real parts of the alpha-alpha and alpha-nucleus potential, particularly for40,44,48Ca and58Ni... more The real parts of the alpha-alpha and alpha-nucleus potential, particularly for40,44,48Ca and58Ni targets are determined from a realistic two-nucleon potential using an energy-density functional approach and are found to be non-monotonic with a short range repulsion in their functional forms that are similar to those needed in accounting for elastic scattering data. The deduced alpha-alpha potential has no bound states and the calculated decay width of8Be of about 6.4 eV at about 200 keV energy is in agreement with the measurement.
We are the first to report the frequency response and corresponding current density of a wurtzite... more We are the first to report the frequency response and corresponding current density of a wurtzite phase Indium Nitride (InN)-based vertical configuration Gunn diode at 1 \mu m active length. Domain growths dynamics with respect to space and time, variation of domain velocity and the field outside the vicinity of the domain with respect to domain field have also been
Physical Review C, 1999
Angular distributions of the differential cross section of ␣ elastic scattering by 24 Mg, 28 Si, ... more Angular distributions of the differential cross section of ␣ elastic scattering by 24 Mg, 28 Si, and 30 Si nuclei have been studied for various incident energies. The observed enhancement of differential cross sections at back angles, usually known as anomalous large angle scattering ͑ALAS͒, cannot be explained in terms of the normal optical model potential. A molecular type or squared Woods-Saxon optical potential can account for the ALAS and produce satisfactory fits to the angular distributions. A mass dependence of the potential parameters in the range Aϭ24-30 and energy variation in the region E ␣ ϭ15-45 MeV for the 28 Si target and 22-120 MeV for the 24 Mg target have been investigated. ͓S0556-2813͑99͒03104-0͔
Nuclear Physics A, 2006
Experimental differential cross sections for elastic scattering of two α particles have been fitt... more Experimental differential cross sections for elastic scattering of two α particles have been fitted with an l-independent non-monotonic real potential up to 34.2 MeV (lab) and a complex potential with non-monotonic real part from 35.1 to 47.3 MeV (lab). The calculated phase shifts, in general, agree with those derived from the phase shift analyses of the experimental cross sections. In
Nuclear Physics A, 2005
The differential cross sections for the elastic scattering of α particles by 40,44,48 Ca, over a ... more The differential cross sections for the elastic scattering of α particles by 40,44,48 Ca, over a wide range of incident energies, have been analyzed using a deep as well as shallow non-monotonic optical potential and compared with those using a squared Woods-Saxon (SWS) potential. The shallow non-monotonic potential exhibits a volume integral for the real part, characteristic of a molecular potential. The parameters of the SWS potential have also been obtained for α-48 Ca scattering. The parameters of the shallow non-monotonic potential calculated from the energy-density-formalism provide a satisfactory description of the elastic scattering data. The non-monotonic potentials, both deep and shallow, are found to yield consistently a lower value of the radius parameter of the real potential for 48 Ca than that for 40 Ca, in conformity with the observed magnitudes of the rootmean-square radii for the two nuclei. Both the potentials indicate that the semi-magic 44 Ca behaves differently from the doubly-magic 40,48 Ca, in agreement with the findings from the folding potentials. The dispersion effect arising from the causality principle has been investigated for the shallow non-monotonic α-40 Ca potential and is found to play a rather minor role in describing the elastic scattering data.
Atoms, 2022
This article presents a theoretical investigation of the differential, integrated, elastic, inela... more This article presents a theoretical investigation of the differential, integrated, elastic, inelastic, total, momentum-transfer, and viscosity cross-sections, along with the total ionization cross-section, for elastically scattered electrons and positrons from a carbon dioxide (CO2) molecule in the incident energy range of 1 eV ≤Ei≤ 1 MeV. In addition, for the first time, we report the spin polarization of e±−CO2 scattering systems. The independent atom model (IAM) with screening correction (IAMS) using a complex optical potential was employed to solve the Dirac relativistic equation in partial-wave analysis. The comparison of our results with the available experimental data and other theoretical predictions shows a reasonable agreement in the intermediate- and high-energy regions.
Journal of Physics G: Nuclear and Particle Physics, 2021
The European Physical Journal D, 2020
Abstract A complex optical potential (OP) is employed to study the critical minima (CM) and spin ... more Abstract A complex optical potential (OP) is employed to study the critical minima (CM) and spin polarization in the elastic e − –Ba and e + –Ba scattering for collision energies in the range E i = 1–1500 eV and E i = 1–100 eV respectively in terms of the Dirac partial wave method (OPMD) and the Schrödinger partial wave method (OPMS). The energy dependence of the integral elastic cross sections (IECSs), momentum transfer cross sections (MTCSs), viscosity cross sections (VCSs), inelastic cross sections (INCSs) and total cross sections (TCSs) is also calculated and discussed for both the projectiles in the same energy range. The OPMD optical potential is composed of the static, exchange, polarization and absorption components. On the other hand, the OPMS comprises the static, local exchange, polarization, spin–orbit, and absorption potentials. The number of CM in the DCS distribution of e − –Ba scattering has been found to be 11 using the OPMD method, while the OPMS calculation produces 12 CM points. However, the OPMS calculation with the static and spin–orbit potentials only produces 9 CM. The critical energies and the angular positions of these CM are revealed and discussed. There are 22 and 24 maximum spin polarization points found in the e − –Ba scattering using OPMD and OPMS respectively. For the case of e + –Ba scattering, we have found 2 CM with OPMD calculations of which the angular positions along with the critical energies are discussed. There are 4 maximum polarization points noted with OPMD calculations which fail to attain the condition for sharpness of S ( θ ) distribution. To the best of our knowledge, the present is the first work to determine the CM in the DCS distribution of e ± –Ba scattering. The Sherman function and the DCSs for some energy points are also calculated for the first time. Graphical abstract
Results in Physics, 2021
Abstract Differential, integral, momentum-transfer, viscosity, inelastic and total cross sections... more Abstract Differential, integral, momentum-transfer, viscosity, inelastic and total cross sections as well as spin asymmetries are calculated for electron and positron scattering from the gold atom with nuclear spin 3 2 . The impact energies of the projectiles range from low-energy atomic physics regime to high-energy nuclear physics. This is accomplished by employing two different theoretical approaches, applicable for the aforesaid two domains of energies, and are based on the partial-wave analysis. In one approach, the phase shifts analysis is done at E i 1 MeV using the Dirac relativistic equations. In another approach, at E i ≥ 100 keV, the same analysis is carried out with the distorted wave Born approximation to account for the projectile scattering including the magnetic effect as well. Predictions are reported for 1 eV ≤ E i ≤ 0.5 GeV electrons and positrons colliding with 197 Au target. In addition, we report here systematically the details of the critical minima in the elastic differential cross sections. To date, neither any experimental nor any theoretical study on the critical minima of electron/positron–Au scattering system is available in the literature. Our results of other observables are compared with the available experimental data and other calculations and are found to produce quite reasonable agreements with two forms of data.
Physica Scripta, 2020
This work presents the calculations of differential, integrated elastic and momentum transfer cro... more This work presents the calculations of differential, integrated elastic and momentum transfer cross sections for the elastic scattering of electrons from the ions of xenon isonuclear series over the incident energy range 1 eV–1000 eV. Coulomb glory, the amplification of elastic backscattering of electrons from positive ions owing to the electrostatic screening of nuclear potential by atomic electrons, is investigated throughout the ionic series of xenon, argon and neon. Cross sections for the angular distribution of elastically scattered positron from selected xenon ions are also calculated. Energy dependency of differential cross sections and Sherman functions are predicted for both the projectiles and a comparison is presented to exhibit the dissimilarity arising out of the difference of the interactions of the projectiles with ions. The theoretical methodology of this work employs the Dirac relativistic partial wave analysis using a complex optical potential, comprising static, e...
Atoms, 2021
Calculations are presented for differential, integrated elastic, momentum transfer, viscosity, in... more Calculations are presented for differential, integrated elastic, momentum transfer, viscosity, inelastic, total cross sections and spin polarization parameters S, T and U for electrons and positrons scattering from atoms and ions of radon isonuclear series in the energy range from 1 eV–1 MeV. In addition, we analyze systematically the details of the critical minima in the elastic differential cross sections along with the positions of the corresponding maximum polarization points in the Sherman function for the aforesaid scattering systems. Coulomb glory is investigated across the ionic series. A short range complex optical potential, comprising static, polarization and exchange (for electron projectile) potentials, is used to describe the scattering from neutral atom. This potential is supplemented by the Coulomb potential for the same purpose for a charged atom. The Dirac partial wave analysis, employing the aforesaid potential, is carried out to calculate the aforesaid scattering...
Dirac relativistic partial wave analysis has been employed to analyze the angular distributions a... more Dirac relativistic partial wave analysis has been employed to analyze the angular distributions and critical minima along with maximum spin polarization for the elastic scattering of electrons from copper atoms over the energy range 1-2000 eV. Integrated elastic, inelastic, total and momentum transfer cross sections have also been calculated. This work uses a complex electronatom optical potential that includes static, exchange, correlation-polarization and absorption potentials. Comparison of our calculations with the available experimental data and other theoretical calculations show a satisfactory agreement. As far as we are concern, critical minima and corresponding maximum spin polarization points have not yet been reported in literature.
Journal of Physics: Conference Series, 2020
Synopsis Vaisburd and Evdokimov proposed an empirical VE model to calculate the electron impact s... more Synopsis Vaisburd and Evdokimov proposed an empirical VE model to calculate the electron impact single ionization cross-sections of atoms and molecules. The extension of the modified VE model (MVE) has been proposed incorporating the relativistic effects. This model is applied to investigate the total L-shell as well as L1-, L2- and L3-subshells ionization cross-sections of various atomic targets with atomic numbers Z =1892 for incident energies up to 1 GeV. The results from the MVE model are compared with the available experimental data and theoretical findings.
A simple method is proposed and tested by evaluating the electron impact inner-shell ionization c... more A simple method is proposed and tested by evaluating the electron impact inner-shell ionization cross sections of various targets up to ultra high energy region. In this energy region there are not many calculations due to lack of reliable method. In this work we extend the validity of the siBED model [1] in terms of targets and incident energies. The extension of our earlier RQIBED model [2] is also reported here and we examined its findings for the description of the experimental EIICS data of various targets up to E=1000 MeV. Details will be presented at the meeting. [1] W. M. Huo, Phys. Rev A 64, 042719 (2001). [2] M. A. Uddin, A. K. F. Haque, M. S. Mahbub, K. R. Karim, A. K. Basak and B. C. Saha, Phys. Rev. A 71, 032715 (2005).
A recently proposed parameter-free relativistic model is applied to evaluate the total cross sect... more A recently proposed parameter-free relativistic model is applied to evaluate the total cross sections for electron impact ionization of neutral and ionic targets. This model has been applied with great success to obtain ionization cross sections of hydrogen-like systems[1]. We report here the extention of this model to two-electron targets, both simple and heavy, like He, Li+, B3+, Fe24+, Ag45+ and U90+ at intermediate and high energies. The present results are compared with those of more sophisticated theories and of other models as well as experimental values. [1] M. A. Uddin, M. N. A. Abdullah, M. S. Mahbub, A. K. Basak, Phys. Scr. 68, 192 (2003).
Advances in Quantum Chemistry, 2016
Calculations of electron impact ionization cross sections (EIICS) for H to Sc (with atomic number... more Calculations of electron impact ionization cross sections (EIICS) for H to Sc (with atomic number Z =1–21) and their corresponding isoelectronic series over incident energies up to 106 keV have been reviewed. This work reports the results of calculations using our various easy-to-use models reproducing closely the experimental EIICS data. We also report how these models can easily be implemented to generate accurate data as demanded by various model calculations. The selection of the range of atomic number Z for different isoelectronic series was made possible by the wealth of the EIICS data either from experiments or from rigorous quantum calculations. We have furnished the detailed description of our various models with comparison of the outcomes of these models with experimental and other theoretical results. Our models describe the experimental results with reasonable success for various atomic and ionic targets belonging to the H to Sc isoelectronic series over a wide range of atomic number in each series.
The knowledge of inner-shell ionization cross sections has not only fundamental importance for un... more The knowledge of inner-shell ionization cross sections has not only fundamental importance for understanding collision dynamics of electron-atom interactions, etc, but also is used extensively in many applied fields such as radiation science, astrophysics, plasma physics, etc. The enormous demands of ionization cross sections can only be met by suitable analytical formula that are easy to use and can produce reliable result. We report here an extension of the CVTS [1] model incorporating both the relativistic and ionic factors and tested on 23 atomic targets ranging from He to U [2] with excellent account of the experimental cross sections. [4pt] [1] C. S. Campos, M. A. Z. Vasconcellos, J. C. Trincavelli, and S. Segui, J. Phys. B. 40, 3835 (2007).[0pt] [2] A K F Haque, M R Talukder, M. Shahjahan, M A Uddin, A K Basak and B C Saha, J. Phys. B.; At. Mol. Opt. Phys (under consideration), (2010).
International Journal of Modern Physics B, 2007
The real parts of the alpha-alpha and alpha-nucleus potential, particularly for40,44,48Ca and58Ni... more The real parts of the alpha-alpha and alpha-nucleus potential, particularly for40,44,48Ca and58Ni targets are determined from a realistic two-nucleon potential using an energy-density functional approach and are found to be non-monotonic with a short range repulsion in their functional forms that are similar to those needed in accounting for elastic scattering data. The deduced alpha-alpha potential has no bound states and the calculated decay width of8Be of about 6.4 eV at about 200 keV energy is in agreement with the measurement.
We are the first to report the frequency response and corresponding current density of a wurtzite... more We are the first to report the frequency response and corresponding current density of a wurtzite phase Indium Nitride (InN)-based vertical configuration Gunn diode at 1 \mu m active length. Domain growths dynamics with respect to space and time, variation of domain velocity and the field outside the vicinity of the domain with respect to domain field have also been
Physical Review C, 1999
Angular distributions of the differential cross section of ␣ elastic scattering by 24 Mg, 28 Si, ... more Angular distributions of the differential cross section of ␣ elastic scattering by 24 Mg, 28 Si, and 30 Si nuclei have been studied for various incident energies. The observed enhancement of differential cross sections at back angles, usually known as anomalous large angle scattering ͑ALAS͒, cannot be explained in terms of the normal optical model potential. A molecular type or squared Woods-Saxon optical potential can account for the ALAS and produce satisfactory fits to the angular distributions. A mass dependence of the potential parameters in the range Aϭ24-30 and energy variation in the region E ␣ ϭ15-45 MeV for the 28 Si target and 22-120 MeV for the 24 Mg target have been investigated. ͓S0556-2813͑99͒03104-0͔
Nuclear Physics A, 2006
Experimental differential cross sections for elastic scattering of two α particles have been fitt... more Experimental differential cross sections for elastic scattering of two α particles have been fitted with an l-independent non-monotonic real potential up to 34.2 MeV (lab) and a complex potential with non-monotonic real part from 35.1 to 47.3 MeV (lab). The calculated phase shifts, in general, agree with those derived from the phase shift analyses of the experimental cross sections. In
Nuclear Physics A, 2005
The differential cross sections for the elastic scattering of α particles by 40,44,48 Ca, over a ... more The differential cross sections for the elastic scattering of α particles by 40,44,48 Ca, over a wide range of incident energies, have been analyzed using a deep as well as shallow non-monotonic optical potential and compared with those using a squared Woods-Saxon (SWS) potential. The shallow non-monotonic potential exhibits a volume integral for the real part, characteristic of a molecular potential. The parameters of the SWS potential have also been obtained for α-48 Ca scattering. The parameters of the shallow non-monotonic potential calculated from the energy-density-formalism provide a satisfactory description of the elastic scattering data. The non-monotonic potentials, both deep and shallow, are found to yield consistently a lower value of the radius parameter of the real potential for 48 Ca than that for 40 Ca, in conformity with the observed magnitudes of the rootmean-square radii for the two nuclei. Both the potentials indicate that the semi-magic 44 Ca behaves differently from the doubly-magic 40,48 Ca, in agreement with the findings from the folding potentials. The dispersion effect arising from the causality principle has been investigated for the shallow non-monotonic α-40 Ca potential and is found to play a rather minor role in describing the elastic scattering data.