Elastic and Inelastic Coulomb Transitions in <sup>50,52</sup>Cr

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].

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.

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.

The form factors in (HI, HI') direct reactions

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.

Longitudinal form factors for inelastic electron scattering are studied using the nuclear practical potential to calculate the nucleon-nucleon interaction (NN). Inelastic longitudinal electron scattering form factors including angular momentum and momentum transfer. Longitudinal inelastic shell model and core polarization (CP) effects, electron-scattering form factors, they were examined for 6Li, 7Li ,10B and 13C nuclei have used NuShellX with the potential harmonic-oscillator (HO), the single-particle matrix elements were measured, and inelastic electron-scattering form factors were measured. And then compared with the available experimental data. The results show that the model space is well describe the form factors in NushellX rather than the core-polarization. The comparison shows the NuShellX results of core polarization for longitudinal forms factors have good agreement with available experimental data.

Certain theoretical predictions are presented for the preferential population of final states with angular momentum l' in collisions involving an initially excited atom. Varying l', the authors find that the maxima of both the inelastic form factors and cross sections for the nl to n'l' transitions in hydrogen, induced by collision with electrons and heavy particles, in general oscillate on a background which rises as l' is increased, until they both attain a pronounced peak at a unique value l'max which is strongly dependent on only the initial principal quantum number n and which is fairly insensitive to changes in l and n'. An expression for l'max is derived. For l'>l'max, the form factors and associated cross sections exhibit a dramatic decline, resulting in negligible population of those states. The predictions differ from those suggested by the Bethe high-energy asymptotic limit which favours dipole transitions, and assume significance in situations where excited states are important.

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.

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.

The longitudinal electron scattering form factors in large scale SDPF-shell for 25Mg with SDPF now as effective interaction have been discussed using Bohr-Mottelson model to computation core polarization (CP). The calculation are done with the help of NuShell code. To determine the single-particle wave function, the SKyrme-Hartree Fock potential was used to compute the matrix elements' radial wave function containing a single particle. Bohr-Mottelson model is used in these calculation. The result show good agreement with experimental data for 25Mg nucleus.

Hsieh-Wildenthal (HW) and G-matrix PF1, (GXPF1) interactions for 40Ca and 48Ca, respectively. The 40Ca was considered to be consisted of 32S as a core and 1d3/21f7/2 subshells as a model space. The 48Ca was considered to be consisted of 40Ca as a core and 1f7/22p3/21f5/2 2p1/2 subshells as a model space. The obtained one body-density matrix elements (OBDME) for both interactions for the studied Coulomb transitions: For 40Ca, the three non-normal parity transitions (C3): , and and one C5 transitions, . For 48Ca, the two C2 transitions: and and one C4 transitions were used in parallel with the transformed harmonic-oscillator basis to compute charge density, elastic electron scattering differential cross-section and elastic and inelastic Coulomb form factors. Finally, the Bohr-Mottelson (B-M), Tassie (T), and valence (V) models were included in the theoretical calculations for the computed inelastic coulomb form factors.

We present new parameterizations of vector and axial nucleon form factors. We maintain an excellent descriptions of the form factors at low momentum transfers (Q2), where the spatial structure of the nucleon is important, and use the Nachtman scaling variable ξ to relate elastic and inelastic form factors and impose quark-hadron duality constraints at high Q2 where the quark structure dominates. We use the new vector form factors to re-extract updated values of the axial form factor from νμ experiments on deuterium. We obtain an updated world average value from νμ d, v̄μH and pion electroproduction experiments of MA = 1.014 ± 0.014 GeV/c2. Our parameterizations are useful in modeling v interactions at low energies (e.g. for vμ oscillations experiments). The predictions for high Q2 can be tested in the next generation electron and vμ scattering experiments. (Presented by A. Bodek at the European Physical Society Meeting, EPS2007, Manchester, UK, July 2007).

We present new parameterizations of vector and axial nucleon form factors. We maintain an excellent descriptions of the form factors at low momentum transfers, where the spatial structure of the nucleon is important, and use the Nachtman scaling variable xi to relate elastic and inelastic form factors and impose quark-hadron duality constraints at high momentum transfers where the quark structure dominates. We use the new vector form factors to re-extract updated values of the axial form factor from neutrino experiments on deuterium. We obtain an updated world average value from neutrino-d and pion electroproduction experiments of M_A = 1.014 +- 0.014 GeV/c2. Our parameterizations are useful in modeling neutrino interactions at low energies (e.g. for neutrino oscillations experiments). The predictions for high momentum transfers can be tested in the next generation electron and neutrino scattering experiments.

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.

In this study, the charge density distribution was calculated using the folding model, which has been applied to study the roles upon the center of mass and Pauli pair association affecting the density relying on the efficient two-body interactions, as a formula for the two-body density applicable to limit nuclei may be derived in terms of the pair correlation function for 20Ne and 24Mg nuclei. The elastic electron scattering form factors F(q) and the root of the mean square charge radii were determined. The inelastic longitudinal electron scattering form factors associated with the isosceles transitioning T = 0 of the ( ) and ( ) for the 20Ne and 24Mg nuclei were determined. A wave function within the model space, which is defined by the orbits , and , is unable to produce an acceptable form factor. Using the folding model to estimate the lower state form for the distribution of charge density and adopting the shape of the Tassie model, the core polarization transition density is calculated. An astounding understanding of the computed inelastic longitudinal F(q)'s and those of observational data is seen for all investigated nuclei, and it is noted that the core polarization effects, which reflect the group modes, are crucial to this outcome.