This review reports on the scattering of electrons (e(-)) and positrons (e(+)) with few precious metal atoms, namely Al, Ni, Cu, Ag, Pt, and Au over the impact energies 1 eV <= E-i <= 1 MeV. Elastic scattering cross sections-differential, integral, momentum-transfer, and viscosityare presented, and Ionization, inelastic, and total (sum of elastic and inelastic) scattering cross sections are also included. In addition, a systematic analysis of the critical minima in the elastic differential cross sections along with the positions of the corresponding total polarization points in the Sherman function, a phase-sensitive quantity, is furnished. We employ the relativistic Dirac partial wave phase-shift analysis embodying a well-established complex optical-potential model (OPM). The interactions of the incident leptons with both the nucleus and the bound electrons of the target are included in the present OPM approach. The comparison with both the theoretical and the experimental data demonstrates the merit of our proposed method in explaining the details of calculations except in the very low energy region.

The experimental angular distributions of differential cross-section (CS), vector analyzing power (iT11) and tensor analyzing powers (T20, T21 and T22 ) for the 12C(6Li, 6Li)12C elastic scattering at laboratory energy of 30 MeV are simultaneously analyzed in the structure of simple optical model (OM) using shallow Non-Monotonic (NM) and deep Monotonic Woods-Saxon (MWS) potentials. The Pauli-laden energy density functional (EDF) theory which results in NM potentials is also discussed. Equally good fits to the CS, T20, T21, and T22 data are obtained using both NM and MWS potentials. But iT11data is only reproduced well using NM potentials in OM. The conclusion is that the shallow NM potentials seem better than the deep MWS for simultaneous description of the CS, iT11, T20, T21 and T22 data. J. Bangladesh Acad. Sci. 48(1); 99-109: June 2024

A review on the research contributions from the nuclear and particle physics laboratory of Rajshahi University is presented. Special emphasis has been given to the nuclear physics research using the molecular nucleus-nucleus (NN) potentials derived from the Pauli-laden energy density functional (EDF) theory. The successes of EDF-derived non-monotonic (NM) NN potentials, compared to other familiar optical model potentials such as Woods-Saxon (WS), Squared Woods-Saxon (SWS), double folding (DF) for NN interactions, have been discussed. The phenomenal successes of NM potentials with a repulsive core have been found to suggest that the true nature of NN potential is NM with the Pauli-compliant EDF as its root.

The experimental angular distributions of differential cross-section (CS), vector analyzing power (iT11) and tensor analyzing powers (T20, T21 and T22 ) for the 12C(6Li, 6Li)12C elastic scattering at laboratory energy of 30 MeV are simultaneously analyzed in the structure of simple optical model (OM) using shallow Non-Monotonic (NM) and deep Monotonic Woods-Saxon (MWS) potentials. The Pauli-laden energy density functional (EDF) theory which results in NM potentials is also discussed. Equally good fits to the CS, T20, T21, and T22 data are obtained using both NM and MWS potentials. But iT11data is only reproduced well using NM potentials in OM. The conclusion is that the shallow NM potentials seem better than the deep MWS for simultaneous description of the CS, iT11, T20, T21 and T22 data. J. Bangladesh Acad. Sci. 48(1); 99-109: June 2024

The present work reports the analyses of the experimental angular distributions of α+209Bi elastic scattering at Eα=19−104 MeV using the non-monotonic (NM) potential in the framework of optical model (OM). The NM potential is a complex shallow potential with a soft repulsive core in its real part which has its root in the energy-density functional theory of Brueckner et al. (1968) [28]. The data are analyzed using the real NM potentials of unshifted Gaussian repulsive core with D1=0 (Set-1) and shifted repulsive core with D1≠0 (Set-2) in conjunction with the empirically adjusted imaginary potentials. For both sets, the volume integral per nucleon pair, JR/(4A) for the real potential decreases in magnitude with the incident energy for the energy range considered in this study. The χ2 values and almost similar quality of fits to the experimental data using both the potential sets show that the scattering of α-particles from the 209Bi target is dominated by the potential in the surface region, and the scattering is insensitive to the potential in the central region of the 209Bi nucleus.

A theoretical investigation of differential, integrated elastic, inelastic, transport (momentum transfer & viscosity), grand total (elastic+inelastic) and total ionisation cross-sections along with the Sherman functions for the scattering of electron and positron by hydrogen cyanide (HCN) in the energy range 1 eV - 1MeV are presented in this report. We perform calculations using the single scattering independent atom model (IAM) and IAM with screening correction (IAMS). The scattering observables are calculated using a complex optical model potential in the framework of the Dirac partial wave analysis (DPWA). The inclusion of screening correction to the IAM appreciably improves the cross-sections, especially at low-impact energies. Our calculated results are compared with the available experimental and theoretical works found in the literature. Our present computational data agree well with prior results. [GRAPHICS] .

The differential, integrated elastic, total and momentum transfer cross sections along with Sherman function for the elastic scattering of electrons and positrons by cadmium atoms have been evaluated from the partial wave solution of the Dirac relativistic scattering equations for a projectile-atom complex potential at the energy range 6.4 eV < E < 1.0 keV. For various scattering quantities, a comparison of our results exhibits better agreement with the experimental data than the other available theoretical values.

This article reports on the scattering of unpolarized and spin polarized electrons and positrons from 28Ni58,29Cu63,46Pd108, and 78Pt196, covering light to heavy precious metal targets. To cover the wide energy domain of 1 eV ≤Ei≤300 MeV, Dirac partial-wave phase-shift analysis is employed, using a complex optical potential for Ei≤1 MeV and a potential derived from the nuclear charge distribution for Ei>1 MeV. Results are presented for the differential and integral cross-sections, including elastic, momentum transfer, and viscosity cross-sections. In addition, the inelastic, ionization, and total (elastic + inelastic) cross-section results are provided, together with mean free path estimates. Moreover, the polarization correlations S,T, and U, which are sensitive to phase-dependent interference effects, are considered. Scaling laws with respect to collision energy, scattering angle, and nuclear charge number at ultrahigh energies are derived using the equivalence between elastic scattering and tip bremsstrahlung emission. In addition, a systematic analysis of the critical minima in the differential cross-section and the corresponding total polarization points in the Sherman function S is carried out. A comparison with existing experimental data and other theoretical findings is made in order to test the merit of the present approach in explaining details of the measurements.

Non-monotonic (NM) nucleus-nucleus potential families rooted in the Pauli-compliant Energy Density Functional (EDF) theory and especially their behavior at higher energies have been investigated using experimental data for O-16 + O-16 elastic scattering in the range 25 <= E-lab <= 1120 MeV. At E-lab = 75 MeV, the O-16 + O-16 NM potentials in a simple optical model (OM) are found to support five rotational bands of O-16 + O-16 bound and quasi-molecular states in S-32 with the cluster global quantum numbers G = 24, 26, 28, 30 and 32. The lowest band in the experimental spectrum starting at E-x = 7.5357 MeV, and having I-pi = 0(+), 2(+), 4(+), 6(+) and 8(+), has been located for the first time. In the simple OM, the NM potentials are found to reproduce the experimental O-16 + O-16 fusion cross-sections in the energy range 12-31 MeV. The present work shows that both the O-16 + O-16 cluster bands and fusion cross-sections in the Coulomb barrier region can be reproduced using NM potentials. Copyright (C) 2022 EPLA

‘Goldberg criterion’ [Goldberg and Smith, Phys. Rev. Lett. 29 (1972) 500] tells that at sufficiently high energies, where pronounced refractive scattering with nuclear rainbow oscillations are followed by an ‘exponential-type falloff’ in the angular distribution, discrete ambiguities are eliminated for the deep monotonic potential. The criterion is also confirmed in the work of Bartnitzky et al. [Phys. Lett. B 365 (1996) 23] on the 16 O+ 16 O elastic scattering in the energy range of 250 - 704 MeV. However, their finding ‘using model-independent potentials’ suggests that heavy-ion elastic scattering data unambiguously favour deep potentials. The Goldberg criterion is examined in our work for non-monotonic shallow potentials using the 16 O+ 16 O elastic scattering at energy region up to 350 MeV.

A review on recent calculations of the differential, integrated, and total cross sections along with the spin-polarization parameters for the elastic collisions of electrons and positrons with various atomic targets, ranging from medium heavy Cd with the atomic number Z = 54 to heavier Hg and Pb with Z ≥ 80, is presented for the projectile energy (Ei) range 1 eV ≤ Ei ≤ 1 GeV. Also are analyzed the critical minima (CMs) in differential cross sections, and the positions of maximum polarization points in the CM's proximity. For such a wider energy domain, these scattering observables are computed using the partial-wave decompositions of Dirac relativistic equation with two different complex optical potentials (OPs). The first model OPM incorporates interactions of the incident lepton with both the nucleus and the bound electrons of the target atom. The second approach, the nuclear structure approach (NSA), retains only the lepton–nucleus interaction and thus neglects the shielding effect of the target bound electrons. Detailed results for the cross sections and spin polarizations are presented for Cd, Hg, and Pb atoms. The comparison with the experimental and other theoretical results reveals reasonable agreements for the above mentioned range of projectile energies.

This paper reports on the differential, integral, momentum transfer and viscosity cross sections along with spin polarisation for elastically scattered electrons and positrons from iron atoms in the incident energy (E-i) range 1 <= E-i <= 10(4) eV. In addition, we report here systematically the details of the critical minima in the elastic differential cross sections, and the absorption and total cross sections. An optical model using a complex optical potential, composed of static, exchange, polarisation and imaginary terms, is used to solve the Dirac relativistic equation in partial-wave analysis. A comparison of our evaluated cross sections with the available experimental data and other theoretical findings shows a reasonable agreement over the studied energy range. [GRAPHICS]

A review on recent calculations of the differential, integrated, and total cross sections along with the spin-polarization parameters for the elastic collisions of electrons and positrons with various atomic targets, ranging from medium heavy Cd with the atomic number Z = 54 to heavier Hg and Pb with Z >= 80, is presented for the projectile energy (E-i) range 1 eV <= E-i <= 1 GeV. Also are analyzed the critical minima (CMs) in differential cross sections, and the positions of maximum polarization points in the CM's proximity. For such a wider energy domain, these scattering observables are computed using the partial-wave decompositions of Dirac relativistic equation with two different complex optical potentials (OPs). The first model OPM incorporates interactions of the incident lepton with both the nucleus and the bound electrons of the target atom. The second approach, the nuclear structure approach (NSA), retains only the lepton-nucleus interaction and thus neglects the shielding effect of the target bound electrons. Detailed results for the cross sections and spin polarizations are presented for Cd, Hg, and Pb atoms. The comparison with the experimental and other theoretical results reveals reasonable agreements for the above mentioned range of projectile energies.

A novel method for the determination of the yet not well-known quantity of nuclear incompressibility, K is presented. Non-monotonic (NM) nucleus-nucleus potentials from the energy-density functional (EDF) theory including the Pauli principle have been considered for K in the range 188-266 MeV. The experimental cross sections of 16O+16O elastic scattering over the 31-350 MeV incident energies have been analyzed in the optical model using the NM potentials. Sensitivity of K on the elastic scattering data is studied and its value for infinite cold nuclear matter deduced to be 222 ± 5 MeV

The experimental differential cross section of the C-12 + C-12 elastic scattering over a wide laboratory energy scale 25 <= E (lab) <= 360 MeV are analyzed within the framework of the optical model (OM) using non-monotonic (NM) nucleus-nucleus potential. The real parts of the NM potentials are derived from the energy density functional (EDF) formalism with the sudden approximation embodying the Pauli exclusion principle and the imaginary parts are taken as phenomenology. The diffractive and the refractive scattering with Airy structures in the whole angular region of the C-12 + C-12 elastic scattering in the above mentioned energy range are found profoundly successful in OM with the NM nucleus-nucleus potentials in five of different potential families. All the families at lower energies converge at 240 MeV to the unique potential family starting with the EDF potential. This, in conjunction with our recent findings for the O-16 + O-16 system in Islam et al (2021 J. Phys. G 48 075109), not only verifies the Goldberg criterion for elimination of discrete potential ambiguities for NM potentials, but also establishes that this leads uniquely to the EDF family. The 90 degrees excitation function is also successfully reproduced with extension using NM potentials. The near- and far-side (N/F) decomposition of total elastic scattering amplitude has also been studied using our NM potentials.

The experimental differential cross-sections of O-16 + O-16 elastic scattering in the energy range 75 MeV <= E (lab) <= 1120 MeV are analysed using families of non-monotonic (NM) shallow nucleus-nucleus potential in the framework of the optical model. The experimental data is reproduced successfully using six families of NM potentials. It is found that all families converge at 350 MeV. The clear indication of the convergence of the potential families at 350 MeV conforms to the Goldberg criterion concerning the removal of discrete ambiguities even for the shallow NM potential. The study further suggests that the energy of convergence heralds the occurrence of the primary rainbow at that incident energy.

Experimental differential cross sections of elastic scattering by 40Ca, over a wide range of incident energies, have been analyzed in terms of non-monotonic (NM) potentials, generated from the energy density functional (EDF) theory using a realistic two-nucleon potential coupled with an appropriate consideration of the Pauli principle. The Airy structure of the nuclear rainbow scattering data in the energy range of 36.1–42.6 MeV is well accounted for the first time by the shallow NM potential.

This work illustrates, for the first time, the analysis of tensor analyzing powers ( T 20 , T 21 , T 22 ) along with the differential cross-section (CS) and the vector analyzing power iT 11 for the 6 Li+ 12 C elastic scattering at 30 and 50 MeVwithin the framework of an optical model (OM) using microscopic shallow non-monotonic (NM) potentials. The NM potential is generated from the energy density functional formalism (EDF) [Brueckner et al., Phys. Rev. , 168 (1968) 1184] using a realistic two-nucleon interaction incorporating Pauli Exclusion principle. The shallow NM potential can describe the experimental angular distributions of CS and analyzing powers of the elastic scattering data. The OM analysis of the data at this energy does not indicate their sensitivity on the nuclear matter incompressibility K .

A theoretical investigation on differential, integral, momentum transfer, viscosity cross sections and spin polarization for elastically scattered electrons and positrons from Ar atoms in the energy range 1 eV <= E-i <= 0.5 GeV is presented. In addition, we have studied the critical minima in the elastic differential cross sections, and the absorption, total and ionization cross sections. Two different theoretical approaches, depending upon the incident energy, are employed for solving the relativistic Dirac equation with the partial-wave decomposition. The solution of the relativistic equation involves the use of either complex optical-model potentials or only nuclear potentials at higher energies. A comparison of the present results with the available experimental data and other theoretical findings produces a reasonable agreement throughout the investigated energy range.

Calculations of electron-impact ionization cross sections (EIICS) for L-subshell of neutral atoms with atomic number Z = 14-92 and also for M-subshell targets, having atomic number Z 1/4 35-92 for incident energies Ethreshold <= E <= 10(6) keV, have been reported. This review comprises the results of our two easy-to-use models, capable of reproducing very closely the experimental EIICS data. We also show systematically how these models can be implemented easily to generate accurate data as demanded by various model applications. The choice of the range of atomic number Z for both L-and M-subshell targets was made possible by the wealth of the EIICS data in literature either from experiments or from rigorous quantal calculations. The detailed findings due to our XMCN and XMUIBED models are compared with the experimental and other theoretical results. Present results describe the experimental data quite well for the L-and M-subshell for various atomic targets over a wider range of projectile energy.