Inelastic Form Factors Research Articles

Indications for the Substantial Predominance of Short-Range Effects on Inelastic Coulomb Form Factors for Various States in the 26Mg Nucleus

Short-range effects on C2, C3, as well as C4 form factors in the 26Mg nucleus, were examined. The charge density distribution in this nucleus was also tested by means of one and two body fragments of cluster enlargement in cooperation with single-particle wave functions of harmonic potential. The correlation of Jastrow form was employed to inset the influence of short-range into the two body fragment of cluster enlargement. The nucleus of 26Mg was assumed to own a 16O-core with (A-16) nucleons dispersed over the sd-model space. The form factors in 26Mg nucleus ascend from the core-polarization and model space involvements. The form of Tassie model, subject to the charge density, was used to determine the transition density of core polarization. The one body density matrix elements required for determining the transition density of model space for various transitions in 26Mg were found via carrying out shell model computations using the OXBASH program with the universal-sd interaction of Wildenthal. The present calculations were subjected to the oscillator and correlation parameters symbolized by and respectively. These parameters are self-sufficiently generated for every specific nucleus by fitting between the calculated and observed elastic form factors. For determining the charge density, elastic form factors and inelastic Coulomb form factors for dissimilar excited states in 26Mg, one value is needed for and This study shows indications for the substantial predominance of short-range influences on current computations, where considering these influences look to be requisite for carrying out a distinguished adjustment in calculated results which ultimately leads to a remarkable explication of the data throughout all the considered momentum transfers.

Electroexcitation Form Factors and Deformation of 20,22Ne Isotopes Based on the Shell Model and Hartree-Fock plus BCS Calculations

Nuclear structure of 20,22Ne isotopes has been studied via the shell model with Skyrme-Hartree-Fock calculations. In particular, the transitions to the low-lying positive and negative parity excited states have been investigated within three shell model spaces; sd for positive parity states, spsdpf large-basis (no-core), and zbme model spaces for negative parity states. Excitation energies, reduced transition probabilities, and elastic and inelastic form factors were estimated and compared to the available experimental data. Skyrme interaction was used to generate a one-body potential in the Hartree-Fock calculations for each selected excited states, which is then used to calculate the single-particle matrix elements. Skyrme interaction was used to calculate the radial wave functions of the single-particle matrix elements, from which a one-body potential in Hartree-Fock theory with SLy4 parametrization can be generated. Furthermore, we have explored the interplays among neutron and proton density profiles in two dimensions, along with the deformations of 20,22Ne using Hartree-Fock plus BCS calculations.

Inelastic squared form factors of the vibronic states of B1Σu+, C1Πu , and EF1Σg+ for molecular D2 studied by high-energy electron scattering

The inelastic squared form factors of the valence-shell excitations of ${\mathrm{D}}_{2}$ were measured by high-energy electron scattering and calculated by the multireference single- and double-excitation configuration interaction method in the present work. It is found that for the ${B}^{1}{\mathrm{\ensuremath{\Sigma}}}_{u}{}^{+}$ state of ${\mathrm{D}}_{2}$, the theoretical calculation cannot satisfactorily reproduce the inelastic squared form factors with a higher vibrational quantum number. For the vibronic states of ${C}^{1}{\mathrm{\ensuremath{\Pi}}}_{u}$ and $E{F}^{1}{\mathrm{\ensuremath{\Sigma}}}_{g}{}^{+}$ of ${\mathrm{D}}_{2}$, obvious discrepancies between our electron-scattering results and theoretical calculations are found. Similar phenomena observed for ${\mathrm{H}}_{2}$, HD, and ${\mathrm{D}}_{2}$ may be attributed to electronic-vibrational coupling and the failure of the first Born approximation at an incident electron energy of 1500 eV. Furthermore, the present inelastic squared form factors of ${\mathrm{D}}_{2}$ are in good agreement with the ones of ${\mathrm{H}}_{2}$ and HD, which indicates that there is no isotope effect for the electronic matrix elements of ${\mathrm{H}}_{2}$, HD, and ${\mathrm{D}}_{2}$ in the momentum space.

Longitudinal and transverse form factors from 65Cu and 71Ga nuclei

In the present work, the inelastic electron scattering for longitudinal and transverse form factors of 65Cu and 71Ga nuclei lies in the fp-shell region are studied in the framework of the shell model. The calculation is performed in the (1f5/2, 2p3/2, 2p1/2, 1g9/2) model space using jun45 effective interaction. The wavefunctions employed to conduct the shell model calculations are extracted from the jun45 effective interaction for these nuclei with the jj44 shell model space and (Sk35−Skzs ∗) residual interaction to evaluate the interactions matrix element between initial and final states. The effective charges used to account for the core-polarization (CP) effect are created using calculations of microscopic perturbations that include intermediate one-particle, one-hole excitation from the core and the model space (MS) orbits into all upper orbits with \(n\hslash \omega\) excitations following the same approach done in [Radhi et al. in Euro. Phys. J. A 50:1–9, 2014]. To account for the (CP) effects contribution, the inelastic form factor is obtained by employing the shape of Tassie and Bohr–Mottelson models with appropriate proton and neutron effective charges. The calculated form factors were compared with available experimental data.

Proof for strong ascendancy of short range effects on inelastic form factors in some open fp-shell nuclei

Short range effects on inelastic C2 form factors in some open fp nuclei ([Formula: see text]Ti, [Formula: see text]Cr, [Formula: see text]Fe and [Formula: see text]Zn) have been researched. The charge densities in these isotopes have been also researched by the one and two particle components of cluster series using single-particle wavefunctions of the harmonic oscillator potential. The short range effects have been inserted into the two particle components of cluster series employing the Jastrow form correlation. The total form factors of isotopes under consideration arise from the model space and core-polarization participations. The one-body density matrix elements (which are needed for computing the model space transition charge density) of valence nucleons for the transition [Formula: see text] have been computed by accomplishment of shell model calculations using the OXBASH code with various interactions. The shape of Tassie model has been adopted for computing the core-polarization transition charge density. The present computations are reliant on b (oscillator parameter) and [Formula: see text] (correlation parameter), where these parameters have been created independently for each individual nucleus by fitting the computed elastic form factors to those of experimental ones. This study provides a proof for strong ascendancy of short range effects on the present calculations, where inclusion of short range correlations on computations seems to be required for performing a notable modification in the computed outcomes which sequentially causes to elucidate the experimental data astoundingly in the momentum transfer under consideration.

Investigation of the Nuclear Structure of Some Ni and Zn Isotopes with Skyrme-Hartree-Fock Interaction

The inelastic C2 form factors and the charge density distribution (CDD) for 58,60,62Ni and 64,66,68Zn nuclei has been investigated by employing the Skyrme-Hartree-Fock method with (Sk35-Skzs*) parametrization. The inelastic C2 form factor is calculated by using the shape of Tassie and Bohr-Mottelson models with appropriate proton and neutron effective charges to account for the core-polarization effects contribution. The comparison of the predicted theoretical values was conducted with the available measured data for C2 and CDD form factors and showed very good agreement.

Elastic and inelastic form factors of the 10B nuclei with the large-basis shell model

In this study, inelastic and elastic form factors for the low-lying excited states of 10B nucleus were calculated utilizing the nuclear shell model theory. We employed a large-basis psd model space with psdmwk interaction and the harmonic oscillator potential in the form factors calculation. The calculated results with the effective charge are in acceptable agreement with experimental results.

Inelastic Electron Scattering Form Factor of Isoscalar (T = 0) and Isovector (T = 1) Particle-hole States in 12C and 16O

Inelastic longitudinal and transverse electron scattering form factors of low-lying T = 0, T = 1 particle-hole states of 12C and 16O are studied in the framework of the Tamm–Dancoff approximation (TDA). The Hamiltonian with the Michigan-three-Yukawa (M3Y) potential is diagonalized. To obtain a good agreement with the experimental data, the ground state is corrected by including the admixture from higher orbits with regard for the core polarization effects.

Study the Nuclear Structure of Some Even-Even Ca Isotopes Using the Microscopic Theory

The root-mean square-radius of proton, neutron, matter and charge radii, energy level, inelastic longitudinal form factors, reduced transition probability from the ground state to first-excited 2+ state of even-even isotopes, quadrupole moments, quadrupole deformation parameter, and the occupation numbers for some calcium isotopes for A=42,44,46,48,50 are computed using fp-model space and FPBM interaction. 40Ca nucleus is regarded as the inert core for all isotopes under this model space with valence nucleons are moving throughout the fp-shell model space involving 1f7/2, 2p3/2, 1f5/2, and 2p1/2 orbits. Model space is used to present calculations using FPBM interaction, and with the effects of core-polarization are obtained by the first order core polarization through a microscopic theory is called modified surface delta interaction which allows all higher orbits are excited by particle-hole excitation from the core and model space orbits. Also, each isotope's effective charge is determined by using the collective model by Bohr and Mottelson formula. The current result corresponds to the experimental data by taking into account core polarization effects.

Elastic and inelastic C2 form factors of nickel isotopes and two-body correlations

The inelastic form factors for C2 transition have been studied for even nickel isotopes ([Formula: see text]Ni) using the form of Tassie shape for ground state charge density distribution. The charge density distribution is investigated using the one- and two-body terms in the cluster expansion. The effect of short-range correlations is included using Jastrow-type correlation function into the two-body density term of the cluster expansion. This concludes that the inserting of the influence of short-range correlations is required for reaching an important adjustment in the calculated elastic and inelastic form factors which explain the data very well at the high momentum transfers ([Formula: see text][Formula: see text]fm[Formula: see text].

Elastic and inelastic form factors including 2-body short-range correlation effect

The charge distributions and elastic electron form factors for 18O, 42,44Ca, 58Ni, and 118Sn nuclei were considered using the cluster expansion of the 1- and 2-body terms. Inelastic electron form factors to 2+ states with core-polarization effects were studied, where the nuclear collective modes were considered alongside the shell model transition density. The influence of short-range correlations (SRCs) was calculated by the parameter β, which was introduced into the ground-state charge distribution and concluded the Jastrow-type function. It is found that the inclusion of 2-body correlations is necessary to describe the observed data of elastic and inelastic form factors at high momentum transfer q > 3 fm–1.

Inelastic Form Factor Calculations for 46,48,50Ti Isotopes Using Tassie Model

Inelastic form factors of electrical transition have been calculated for 46,48,50Ti isotopes using the Tassie model. The form factors have been calculated for different exciting energies. The harmonic oscillator (HO) wave function has been used as a single-particle wave function. The model space has been considered as 1f7/2, 2p3/2, 2p1/2, and 2f5/2. Gx1 has been used as effective interaction in all calculations. In all calculations, the effective charge has been considered as 1.5e for proton and 0.5e for neutron. All obtained results have been compared with data from an experiment. The calculations show the Tassie model gives a good description of longitudinal form factors of 46,48,50Ti isotopes in E(2+) transitions as compared with experimental data, especially in the region below 2 fm−1 of momentum transfer, but in the E(4+), the theoretical results deviated slightly from experimental data especially in the region greater than 1.5 fm−1 of momentum transfer.

Alpha-induced inelastic scattering and alpha-transfer reactions in $$^{12}$$C and $$^{16}$$O within the Algebraic Cluster Model

The molecular algebraic model based on three and four alpha clusters is used to describe the inelastic scattering of alpha particles populating low-lying states in $^{12}$C and $^{16}$O. Optical potentials and inelastic formfactors are obtained by folding densities and transition densities obtained within the molecular model. One-step and multi-step processes can be included in the reaction mechanism calculation. In spite of the simplicity of the approach the molecular model with rotations and vibrations provides a reliable description of reactions where $\alpha$-cluster degrees of freedom are involved and good results are obtained for the excitation of several low-lying states. Within the same model we briefly discuss the expected selection rules for the $\alpha$-transfer reactions from $^{12}$C and $^{16}$O.

Inelastic Scattering form Factors for Carbon and Oxygen Halo Isotopes

Inelastic Scattering form Factors for Carbon and Oxygen Halo Isotopes

Elastic and Inelastic Electron-Nucleus Scattering Form Factors for Be9 Nucleus

The computations of the elastic and inelastic Coulomb form factors for the electron-nucleus scattering of Beryllium nucleus Be9 have performed with Core Polarization (CP) effects including the realistic Michigan sum of Three Range Yukawa (M3Y) Interaction, and the other residual interaction which is Modified Surface Delta Interaction (MSDI). In addition to mean square root charge density and charge radii for the ground state. The perturbation theory was adopted to compute the Core Polarization by using the Harmonic Oscillators (HO) potential to calculate single-particle radial wave functions.
 In the comparison between the theoretical calculations of Coulomb form factors by (MSDI) interaction, realistic (M3Y) interaction, and the experimental results that measured before, it noticed that the Coulomb form factors for the (M3Y) interaction gave a reasonable depiction of the measured data.

Non-resonant inelastic X-ray scattering spectroscopy: A momentum probe to detect the electronic structures of atoms and molecules

Non-resonant inelastic X-ray scattering (NRIXS) is a new technique for atomic and molecular physics that allows one to measure the electronic structures and dynamic parameters of the ground and excited states of atoms and molecules in momentum space. There is a clearly understood physical picture of NRIXS, which reveals its remarkable advantages of satisfying the first Born approximation and being able to excite dipole-forbidden transitions. Various physical properties of atoms and molecules, such as their elastic and inelastic squared form factors, optical oscillator strengths, and Compton profiles, can be explored using NRIXS under different experimental conditions. In this paper, we review newly developed experimental methods for NRIXS, together with its characteristics and various applications, with emphasis on the new insights into excitation mechanism and other new information revealed by this technique. The intrinsic connections and differences between NRIXS and fast electron impact spectroscopy are elucidated. Future applications of this method to atomic and molecular physics are also described.

Study the Nuclear Form Factors of Low-Lying Excited States in $${}^{7}\hbox {Li}$$ Nucleus Using the Shell Model with Skyrme Effective Interaction

In the present work, the Skyrme interaction with the core polarization calculations has been used and implemented to study the inelastic electroexcitation form factor for low-lying excited states in \({}^{7}\hbox {Li}\). In particular, the \(1/2^{-}\) (0.478 MeV) and \(7/2^{-}\) (4.630 MeV) states have been analyzed within the \(0\hbar \omega \) shell model including core-polarization effect. The present results reveal that the core-polarization calculation incorporating Skyrme type interaction for the single-particle states reproduces the longitudinal electron scattering data and predicts the diffraction minimum correctly and describes the high momentum data that has not been reported before. The measured \(B(C2{\uparrow })\) value for the \(1/2^{-}\) transition is very well described. The result of the \(7/2^{-}\) transition is close to the measured value. Transverse form factors are better described by the single-particle wave functions obtained from Hartree–Fock with Skyrme type interaction, rather than by the harmonic-oscillator wave functions.

The effect of short range correlation on the inelastic C4 form factors of 18O nucleus

The effect of short range correlations on the inelastic longitudinalCoulomb form factors for different states of J   4 , T  1withexcitation energies 3.553,7.114, 8.960 and 10.310 MeV in 18O isanalyzed. This effect (which depends on the correlation parameter )is inserted into the ground state charge density distribution throughthe Jastrow type correlation function. The single particle harmonicoscillator wave function is used with an oscillator size parameter b.The parameters  and b are considered as free parameters, adjustedfor each excited state separately so as to reproduce the experimentalroot mean square charge radius of 18O. The model space of 18O doesnot contribute to the transition charge density. As a result, theinelastic Coulomb form factors of 18O comes absolutely from thecore polarization transition charge density. According to thecollective modes of nuclei, the core polarization transition chargedensity is assumed to have the form of Tassie shape. It is found thatthe introduction of the effect of short range correlations is necessaryfor obtaining a remarkable modification in the calculated inelasticlongitudinal Coulomb form factors and considered as an essential forexplanation the data amazingly throughout the whole range ofconsidered momentum transfer.

Inelastic electron scattering form factors involving the second excited 2+ level in the isotopes 50,54,52Cr

An expression for the transition charge density is investigated where the deformation in nuclear collective modes is taken into consideration besides the shell model transition density. The inelastic longitudinal form factors C2 calculated using this transition charge density with excitation of the levels for Cr54,52,50 nuclei. In this work, the core polarization transition density is evaluated by adopting the shape of Tassie model together with the derived form of the ground state two-body charge density distributions (2BCDD's). It is noticed that the core polarization effects which represent the collective modes are essential in obtaining a remarkable agreement between the calculated inelastic longitudinal F(q)'s and those of experimental data.

The effects of core polarisation on some even–even sd-shell nuclei using Michigan three-range Yukawa and modified surface delta interactions

Elastic and inelastic electron scattering from even–even \(Z=N\) sd-shell (\(^{28}\hbox {Si}, {}^{32}\hbox {S}\) and \(^{36}\hbox {Ar}\)) nuclei has been studied using the nuclear shell-model configurations. The transition rates \(B\left( {C2\uparrow } \right) \) from the ground 0\(^{+}\) state to the first excited \(2_{1}^{+}\) state, the electric quadrupole moments Q, the elastic longitudinal C0 and inelastic longitudinal C2 form factors are calculated. SDBA and USDA model spaces have been used. The radial wave functions of the single-particle matrix elements have been calculated in terms of the harmonic oscillator (HO) and Skyrme–Hartree–Fock (SHF) potentials. The configurations higher than the core and the model space are taken into account within a microscopic theory that includes one particle–one hole excitations from the core and model space orbits to higher allowed orbits with 2\(\hbar \omega \) excitations. These effects are defined as core polarisation (CP) effects. Two-body Michigan three-range Yukawa (M3Y) effective nucleon–nucleon interaction and the modified surface delta interaction (MSDI) have been used as residual interactions for the CP matrix elements. The calculations are performed using the shell-model code Nushell@MSU, where the deduced results, including CP, are more compatible with the available experimental and theoretical results.