Distorted Wave Born Approximation Method Research Articles

Study of the timelike electromagnetic form factors of the Λc

In this paper, the reaction of electron-positron annihilation into Λc+Λ¯c− is investigated. The Λc+Λ¯c− scattering amplitudes are obtained by solving the Lippmann-Schwinger equation. The contact, annihilation, and two pseudoscalar-exchange potentials are taken into account in the spirit of the chiral effective field theory. The amplitudes of e+e−→Λc+Λ¯c− are constructed by the distorted wave Born approximation method, with the final state interactions of the Λc+Λ¯c− rescattering implemented. By fitting to the experimental data, the unknown couplings are fixed, and high-quality solutions are obtained. With these amplitudes, the individual electromagnetic form factors in the timelike region, GEΛc, GMΛc, and their ratio, GEΛc/GMΛc, are extracted. Both modulus and phases are predicted. These individual electromagnetic form factors reveal new insights into the properties of the Λc. The separated contributions of the Born term, contact, annihilation, as well as the two pseudoscalar-exchange potentials to the electromagnetic form factors are isolated. It is found that the Born term dominates the whole energy region. The contact term plays a crucial role in the enhancement near the threshold, and the annihilation term is essential in generating the fluctuation of the electromagnetic form factors. Published by the American Physical Society 2024

Electron impact elastic scattering by a calcium atom using the first order distorted wave method with a complex potential

Electron-atom scattering data is required in diverse fields of physics. In particular, inelastic collision cross sections data are needed in photonics and radiation physics. Elastic collision data, on the other hand, are useful in material science for surface analysis. There is a lack of accuracy and completeness of atomic data obtained using theoretical methods relative to experimental techniques. Furthermore, the distorted wave Born approximation method with a complex potential is yet to be applied in calculating cross sections. Differential and total cross sections have been calculated for electron-calcium scattering in the impact energy range 10 – 100 eV. There is good shape resonance between the present results with a complex potential and experimental values as well as other theoretical results

Exploring the sensitivity of charge-exchange(p,n)reactions to the neutron density distribution

$Background:$ The determination of the nuclear neutron properties suffers from uncontrolled uncertainties, which attracted considerable attention recently, such as in the context of the PREX experiment. $Purpose:$ Our aim is to analyze the sensitivity of charge-exchange ($p, n$) reactions to the neutron density distribution $\rho_{n}$ and constrain the neutron characteristics in the nuclear structure models. $Method:$ By combing the folding and the mean-field models, the nucleon-nucleus ($NA$) potential can be obtained from the nuclear density distribution. Further, the ($p, p$) and ($p, n$) cross sections for $^{48}$Ca and $^{208}$Pb are calculated following the distorted-wave Born approximation (DWBA) method. $Results:$ Compared with the ($p, p$) cross section, the effects of $\rho_{n}$ variation on the ($p, n$) cross section are significant, which is due to the impact of isovector properties. Based on the global folding model analyses of data, it is found that $^{48}$Ca and $^{208}$Pb have relatively large neutron skin thickness $\Delta R_{n p}$. $Conclusions:$ Results illustrate that the charge-exchange ($p, n$) reaction is a sensitive probe of $\rho_{n}$. The results in this paper can offer useful guides for future experiments of neutron characteristics.

Analyses of α–nucleus interaction on the 28Si(α, d)30P reaction at 40 and 50 MeV

The angular distributions of the 28Si(α, d)30P reaction at 40 and 50 MeV incident energies have been analyzed using the full finite-range (FFR) distorted-wave Born approximation (DWBA) method. Three forms of the optical model potentials namely, Woods-Saxon, Michel, and molecular potentials are used to analyze the bound states of the 30P nucleus for 8 and 21 transitions at 40 and 50 MeV, respectively. The two-nucleon spectroscopic factors that have been obtained for the three optical model potentials are compared with the previous experimental and theoretical calculations. The χN2 values have been calculated for the optical model potentials to estimate the quality of fits for the α+28Si elastic scattering and the 28Si(α, d)30P reaction at two different incident energies. These analyses show that the Michel and the molecular potentials describe the elastic scattering data more satisfactorily than the Woods-Saxon potential at 40 and 50 MeV incident energies, but for the reaction analyses at 40 MeV the Woods-Saxon potential takes over the other two forms of potential. These investigations also show that the direct two nucleons transfer reaction mechanism with the angular distributions of the admixture of L transfers in most of the states of 30P is seemingly sufficient for all forms of the optical model potential at these incident energies.

Experimental study of the low-lying negative-parity states in Be11 using the B12(d,He3)Be11 reaction

Low-lying negative-parity states in $^{11}\mathrm{Be}$ having dominant $p$-wave neutron configurations were studied using the $^{12}\mathrm{B}(d,^{3}\mathrm{He})\phantom{\rule{0.16em}{0ex}}^{11}\mathrm{Be}$ proton-removal reaction in inverse kinematics. The $1/{2}_{1}^{\ensuremath{-}}$ state at 0.32 MeV, the $3/{2}_{1}^{\ensuremath{-}}$ state at 2.56 MeV, and one or both of the states including the $5/{2}_{1}^{\ensuremath{-}}$ level at 3.89 MeV and the $3/{2}_{2}^{\ensuremath{-}}$ level at 3.96 MeV were populated in the present reaction. Spectroscopic factors were determined from the differential cross sections using a distorted wave Born approximation method. The $p$-wave proton removal strengths were well described by the shell model calculations while the Nilsson model calculation underestimates the spectroscopic factors for the higher excited states. Results from both variational Monte Carlo and no-core shell-model calculations were also compared with the experimental observations.

Elastic electron scattering off nuclei with shape coexistence

In this paper, the effects of shape coexistence on the resulting mixed configuration of the ground state are investigated by elastic electron scattering. The shape configurations of ground states are searched by the constraint relativistic mean-field (RMF) model. For nuclei with shape coexistence, the density distributions of the coexistence states are obtained from the mixing of different configurations. With the charge distributions, the Coulomb form factors of the coexistence states are calculated by the distorted wave Born approximation method. By comparing the of coexistence states with the of certain shape configurations, the phenomena of the shape coexistence can be analyzed by electron scattering.

Experimental evidence for x-ray standing wave modulated surface scattering effect

X-ray standing waves generated above flat surfaces will modulate local electric field intensity distributions and in turn alter surface scattering patterns. Such an effect is uncovered in the grazing-incidence small-angle x-ray scattering study of the two-dimensional (2D) colloidal superlattices deposited on Si substrates. There are appreciable differences between the scattering patterns of a single particle simulated by the conventional and multislice distorted-wave Born approximation methods. The single-particle scattering effect is much amplified by the periodic arrangement of the 2D hexagonal superlattice, rendering it experimentally detectable. Numerical simulations incorporating the x-ray standing wave modulated surface scattering effect show remarkable agreement with the experimental data.

Measurement and analysis of 10B +12C elastic scattering at energy of 41.3MeV

Angular distribution of the [Formula: see text] elastic scattering was measured at [Formula: see text][Formula: see text]MeV. Experimental data showed a significant increase in differential cross-sections at backward angles. The optical model with phenomenological potentials reproduces well the experimental cross-sections in the region of the angles of the forward hemisphere, but is not able to explain the increase in cross-sections at large angles. The distorted wave Born approximation method was used to reproduce the experimental data at large angles [Formula: see text] by taking into consideration a deuteron transfer. Spectroscopic amplitude has been extracted for the configuration [Formula: see text]C[Formula: see text]B + [Formula: see text] from the analysis.

Experimental study of the effective nucleon-nucleon interaction using the F21(d,p)F22 reaction

The single-neutron configurations of several low-lying states in $^{22}\mathrm{F}$ have been determined from neutron-adding cross sections of a ($d,p$) reaction using a $^{21}\mathrm{F}$ radioactive beam in inverse kinematics. Final states in $^{22}\mathrm{F}$ consisting of a proton in the $\ensuremath{\pi}0{d}_{5/2}$ orbital coupled to a neutron in either the $\ensuremath{\nu}0{d}_{5/2}$, $\ensuremath{\nu}1{s}_{1/2}$, or $\ensuremath{\nu}0{d}_{3/2}$ orbitals were observed up to an excitation energy of $\ensuremath{\sim}5$ MeV. Spectroscopic factors and strengths were determined from the angular distribution of the cross sections using a distorted wave Born approximation method. The distribution of the $\ensuremath{\nu}0{d}_{5/2}$ and $\ensuremath{\nu}1{s}_{1/2}$ strength was well described by all USD effective shell model interactions, while only the more recent USDA/USDB interactions showed a marked improvement in describing the observed $\ensuremath{\nu}0{d}_{3/2}$ strength. Diagonal two-body matrix elements of the ${(0{d}_{5/2})}_{J=0--5}^{2}$ effective nucleon-nucleon interaction were extracted from the data and compared with previous determinations of the same matrix elements from particle-particle and hole-hole spectra, as well as the calculated results of the USDA interactions. No significant discrepancies were observed. Inspection of the monopole energies showed that an improved agreement between the different empirical matrix elements is found if a mass dependence is included.

Simulation of Neutron Reflection from the Surface of a Nanostructured Object in the Modified Kinematic Approximation

The applicability of the modified kinematic approximation for simulation of the specular reflection and the diffraction of a neutron beam from regularly ordered nanostructured objects on the surface and in the surface material layer is analyzed. The obtained results are compared with those of the real experiment and simulation of the distorted-wave Born approximation (DWBA). The influence of various factors on the obtained results is analyzed. These factors include the effect of neutron-wave refraction at the interfaces between media, the spectrometer-resolution function, and renormalization of the results for a nonspecular scattering signal based on data obtained for a specular channel. It is shown that, in many cases, it is possible to obtain rather good agreement with the experimental data and with the results of calculations using DWBA methods and of calculations using the Parratt algorithm.

Coulomb form factors of odd- A nuclei within an axially deformed relativistic mean-field model

Background: The nuclear Coulomb form factor $|{F}_{C}{(q)|}^{2}$ is a useful tool to study nuclear structure. For spherical nuclei, $|{F}_{C}{(q)|}^{2}$ can be calculated by combining the spherical relativistic mean-field (RMF) model and the distorted wave Born approximation (DWBA) method.Purpose: In a previous paper, the axially deformed RMF model + DWBA method was successfully applied to study the Coulomb form factors of deformed even-even nuclei. In this paper, we further extend this method to study the Coulomb form factors of deformed odd-$A$ nuclei.Method: First, the charge distributions of odd-$A$ nuclei are calculated with the deformed RMF model and expanded into multipole components. Next, with the multipole moment charge distributions, the Coulomb multipoles $C0, C2$, and $C4$ are calculated. Finally, by summing over Coulomb multipoles required, the Coulomb form factors of odd-$A$ nuclei can be obtained.Results: For deformed odd-$A$ nuclei, the theoretical Coulomb form factors calculated from the deformed RMF charge densities are in better agreement with the experimental data. For nuclei with $J\ensuremath{\ge}1$, the diffraction minima of Coulomb form factors are much flatter, which is due to the contributions of quadrupole charge distributions.Conclusions: Results indicate that the axially deformed RMF model can give reasonable descriptions for multipole moment charge distributions of odd-$A$ nuclei. The method in this paper can provide a useful guide for future experiments of electron scattering off exotic odd-$A$ nuclei.

Optical model potentials for He6+Zn64 from Cu63(Li7,He6)Zn64 reactions

Angular distributions of the transfer reaction $^{63}\mathrm{Cu}(^{7}\mathrm{Li},^{6}\mathrm{He})^{64}\mathrm{Zn}$ were measured at ${E}_{\mathrm{lab}}(^{7}\mathrm{Li})=12.67$, 15.21, 16.33, 23.30, 27.30, and 30.96 MeV. With the interaction potentials of the entrance channel $^{7}\mathrm{Li}+^{63}\mathrm{Cu}$ obtained from elastic scattering data as input, the optical potentials of the halo nuclear system $^{6}\mathrm{He}+^{64}\mathrm{Zn}$ in the exit channel were extracted by fitting the experimental data with the distorted-wave Born approximation (DWBA) and coupled reaction channels (CRC) methods, respectively. The results show that the threshold anomaly presents in the weakly bound system of $^{7}\mathrm{Li}+^{63}\mathrm{Cu}$ and the dispersion relation can be adopted to describe the connection between the real and imaginary potentials, while both the real and imaginary potentials nearly keep constant within the researched energy region for the halo system of $^{6}\mathrm{He}+^{64}\mathrm{Zn}$. Moreover, calculations by the potentials extracted from the CRC method can reproduce the experimental elastic scattering of the $^{6}\mathrm{He}+^{64}\mathrm{Zn}$ system rather well, but those by the potentials from the DWBA method cannot, where the couplings between $^{7}\mathrm{Li}$ and $^{6}\mathrm{He}$ are absent. This work verifies the validity of the transfer method in the medium-mass target region and lays a solid foundation for the further study of optical potentials for exotic nuclear systems.

A multi-slice simulation algorithm for grazing-incidence small-angle X-ray scattering

Grazing-incidence small-angle X-ray scattering (GISAXS) is an important technique in the characterization of samples at the nanometre scale. A key aspect of GISAXS data analysis is the accurate simulation of samples to match the measurement. The distorted-wave Born approximation (DWBA) is a widely used model for the simulation of GISAXS patterns. For certain classes of sample such as nanostructures embedded in thin films, where the electric field intensity variation is significant relative to the size of the structures, a multi-slice DWBA theory is more accurate than the conventional DWBA method. However, simulating complex structures in the multi-slice setting is challenging and the algorithms typically used are designed on a case-by-case basis depending on the structure to be simulated. In this paper, an accurate algorithm for GISAXS simulations based on the multi-slice DWBA theory is presented. In particular, fundamental properties of the Fourier transform have been utilized to develop an algorithm that accurately computes the average refractive index profile as a function of depth and the Fourier transform of the portion of the sample within a given slice, which are key quantities required for the multi-slice DWBA simulation. The results from this method are compared with the traditionally used approximations, demonstrating that the proposed algorithm can produce more accurate results. Furthermore, this algorithm is general with respect to the sample structure, and does not require any sample-specific approximations to perform the simulations.

Analysis of the normal optical, Michel and molecular potentials on the 40Ca(6Li, d)44 Ti reaction

Full finite-range (FFR) distorted-wave Born approximation (DWBA) method has been applied to analyse the angular distributions of cross-sections of the 40Ca(6Li, d) 44Ti reaction at 28 MeV incident energy for the 22 transitions involving both the bound and unbound states of 44Ti by using the normal optical, Michel and molecular potentials. The extracted spectroscopic factors for the three optical potentials are compared with those of some previous studies of zero-range (ZR) calculations of the 40Ca(6Li, d) 44Ti reaction using the normal optical potential. The χ 2 values of all the levels are obtained for the three optical potentials to estimate the quality of the fits. Molecular and Michel potentials have been used for the first time to analyse the four-nucleon transfer reaction and it seems that the molecular potential fits the experimental data more satisfactorily for some of the states than the normal optical and Michel potentials.

One-two step transfer observed in 16O+11B nuclear system

The angular distribution measurements for 16O ion beam elastically scattered from 11B target of thickness 32.9μg/cm2 at energy 22.4 MeV had been performed in the cyclotron DC-60 INP NNC RK. The previous measurements for 16O+11B nuclear system at energies 27, 30, 32.5 and 35 MeV showed an increase in the differential cross-section at backward angles due to the contribution of cluster transfer. Such transfer process could not be described in terms of optical model (OM); it could be described within the framework of distorted wave Born approximation method implemented in FRESCO code. Both one (5Li) and two-step transfer (proton transfer followed by Alpha transfer) were taken into considerations. We have extracted the spectroscopic amplitude (SA) for the configuration 16O→11B+5Li.

Transfer induced by core excitation within an extended distorted-wave Born approximation method

Background: Dynamic core-excitation effects have been found to be of importance in breakup reactions and may be of relevance when obtaining spectroscopic information from transfer reactions. Purpose: In this paper we extend the distorted-wave Born approximation (DWBA) formalism in order to allow for noncentral components in the core-core term appearing in the transition operator, which allows for dynamic core-excitation effects. Then we study these effects by applying the formalism to different (d,p) reactions. Methods: The expression of the nonlocal kernels required for the evaluation of the DWBA amplitudes has been extended so as to include noncentral parts in the core-core interaction. The DWBA scattering amplitude is then obtained by solving the corresponding inhomogeneous equation, with the new computed kernels, and the usual outgoing boundary conditions. A new DWBA code has been developed for this purpose. Results: For 10 Be(d,p) 11 Be, core-excitation effects are found to be almost negligible (<3%). The importance of this effect has been found to depend to a large extent on the excitation energy of the core. This has been confirmed in the 30 Ne(d,p) 31 Ne case, for which the excitation energy of the first 2 + state is 0.8 MeV, and the effect of core excitation increases to ≈10%. Conclusions: We find dynamic core-excitation effects in transfer reactions to have small contributions to cross sections, in general. However, they should not be neglected, since they may modify the spectroscopic information obtained from these reactions and may become of importance in reactions with nuclei with a core with high deformation and low excitation energy.

One-two step transfer observed in 16O+11B nuclear system

The angular distribution measurements for 16O ion beam elastically scattered from 11 B target of thickness 32.9μg/cm2 at energy 22.4 MeV had been performed in the cyclotron DC-60 INP NNC RK. The previous measurements for 16 O +11 B nuclear system at energies 27, 30, 32.5 and 35 MeV showed an increase in the differential cross-section at backward angles due to the contribution of cluster transfer. Such transfer process could not be described in terms of optical model (OM); it could be described within the framework of distorted wave Born approximation method implemented in FRESCO code. Both one (5 Li ) and two-step transfer (proton transfer followed by Alpha transfer) were taken into considerations. We have extracted the spectroscopic amplitude (SA) for the configuration 16 O →11 B +5 Li .

Interplay Between Valence and Core Excitation Mechanisms in the Breakup of Halo Nuclei

The phenomenon of core excitation in the breakup of a two-body halo nucleus is investigated. We show that this effect plays a significant role in the reaction dynamics and, furthermore, its interference with the valence excitation mechanism has sizable and measurable effects on the breakup angular distributions. These effects have been studied in the resonant breakup of (11)Be on a carbon target, populating the resonances at 1.78 MeV (5/2(+)) and 3.41 MeV (3/2(+)). The calculations have been performed using a recent extension of the distorted-wave Born approximation method, which takes into account the effect of core excitation in both the structure of the halo nucleus and in the reaction mechanism. The calculated angular distributions have been compared with the available data [Fukuda et al., Phys. Rev. C 70, 054606 (2004).]. Although each of these resonances is dominated by one of the two considered mechanisms, the angular patterns of these resonances depend in a very delicate way on the interference between them. This is the first clear evidence of this effect but the phenomenon is likely to occur in other similar reactions.

Post-collision interactions and the polarization effect in (e, 2e) collisions of helium

A modified distorted-wave Born approximation (DWBA) method is used to calculate the triple differential cross sections (TDCSs) in a coplanar asymmetric geometry for the electron impact single ionization of a He (1s2) atom at intermediate and lower energies. The post-collision interaction and the polarization effect in (e, 2e) collisions of helium are considered in the calculations. The polarization potentials from the damping method and density functional theory (DFT) are compared. Theoretical results are compared with the recent experimental data.

Rotational de-excitation of hydrogen–helium muonic molecules in non-ionizing collisions with hydrogen atoms

Rotational J = 1 → J = 0 transitions in muonic molecules (3Heμh)++J, in the process (3Heμh)++1 + H → (3Heμh)++0 + H, where h = p, d, t; H is the respective hydrogen isotope atom (H, D, T) and μ = μ− (the negative muon), are investigated. The corresponding cross sections and reaction rates are calculated for collision energies 0.001–0.5 eV in the frame of the distorted-wave Born approximation method using the Born–Oppenheimer approximation for a two-centre wavefunction of the hydrogen atom electron. The results obtained for transition rates, normalized to the liquid hydrogen density, are relatively small and range between 102 s−1 and 103 s−1 for (3Heμp)++1 − H and (3Heμd)++1 − D, whereas for (3Heμt)++1 − T they range between 103 s−1 and 104 s−1. They are about 6–8 orders of magnitude smaller than reaction rates for the 1 → 0 de-excitation induced by the hydrogen atom ionization considered in our previous paper (Czapliński et al 2008 J. Phys. B: At. Mol. Phys. 41 035101).