Elastic Electron Scattering Form Factors Research Articles

Theoretical Study of Density Distributions and Size Radii of 8B and 17Ne

The proton, neutron and matter density distributions, the corresponding size radii and elastic electron scattering form factors of one-proton 8 B and two-proton 17 Ne halo nuclei are calculated. The theoretical technique used to fulfill calculations is by assuming that both nuclei under study are composed of two main parts; the first is the compact core and the second is the unstable halo part. The single-particle radial wavefunctions of harmonic-oscillator (HO) and Woods-Saxon (WS) potentials are used to study core and halo parts, respectively. And other approach is studied by using HO potential for both core and halo parts, but using two HO size parameters for both supposed parts. The long tail behavior which is the main characteristic of halo nuclei are well produced for both 8 B and 17 Ne. The calculated size radii are in general in good agreement with the available experimental data. The electron scattering form factors of the C0+C2 and C0 components are also calculated for 8 B and 17 Ne, respectively and compared with corresponding stable 10 B and 20 Ne nuclei. For 8 B calculations, the core-polarization (CP) effects are taken into account by using Tassie and Bohr-Mottelson models. The contribution from model-space (MS) part C2 component is taken through pwt interaction. The results of the calculated charge form factors are left for the planned electron-radioactive ion beam colliders where the study of skin or halo on the charge form factors are going to be studied.

Theoretical Study of Nuclear Density Distributions and Elastic Electron Scattering Form Factors of Some Proton Halo Nuclei (17Ne and 8B)

Theoretical investigation of proton halo-nucleus (8B and 17Ne) has revealed that the valence protons are to be in pure (1p1/2)1 orbit for 8B and (1d3/2)2 orbit for 17Ne. The nuclear matter density distributions, the elastic electron scattering form factors and (proton, charge, neutron and matter) root-mean square (rms) are studied for our tested nuclei, through an effective two-body density operator for point nucleon system folded with two-body full correlation operator's functions. The full correlation (FC's ) takes account of the effect for the strong short range repulsion (SRC's) and the strong tensor force (TC's) in the nucleon-nucleon forces. The effective two-body density operator is produced and used to derive an explicit form for ground state two-body nucleon density distributions (2BNDD's) applicable for proton – rich halo nuclei and Fortran 95 programs are utilized to obtain theoretical values of our calculation. The effect of the TC's and SRC's on the ground state also calculated. 2BNDD's obtained within the two- frequency shell model (TFSM) approach, the elastic charge scattering form factors F(q)'s of proton halo nuclei are studied through Plane Wave Born Approximation (PWBA) .

Theoretical Study of Nuclear Density Distributions and Elastic Electron Scattering form Factors for Some Halo Nuclei

The nuclear matter density distributions, elastic electron scattering charge formfactors and root-mean square (rms) proton, charge, neutron and matter radii arestudied for neutron-rich 6,8He and 19C nuclei and proton-rich 8B and 17Ne nuclei. Thelocal scale transformation (LST) are used to improve the performance radial wavefunction of harmonic-oscillator wave function in order to generate the long tailbehavior appeared in matter density distribution at high . A good agreement resultsare obtained for aforementioned quantities in the used model.

Proton Momentum Distributions and Elastic Electron Scattering form Factors for Some Even-A 1f-2p Shell Nucle

Proton Momentum Distributions and Elastic Electron Scattering form Factors for Some Even-A 1f-2p Shell Nucle

Shell model and Hartree–Fock calculations for some exotic nuclei

Mass density distributions, the associated nuclear radii and elastic electron scattering form factors of light exotic nuclei, [Formula: see text]Li, [Formula: see text]Be, [Formula: see text]Be and 8B have been calculated using shell model (SM) and Hartree–Fock (HF) methods. We consider truncated spsdpf no core SM and WBP two-body effective interaction to give the SM wave functions. The single-particle matrix elements have been calculated with Skyrme-Hartree–Fock (SHF) potential with different parametrizations. It is shown that the calculated densities and form factors are in fine agreement with experimental data. This agreement can be interpreted as the adequacy of the HF mean-field approximation for exotic nuclei.

Nucleon Momentum Distributions and Elastic Electron Scattering from 59Co, 61Ni, 63Cu and 65Cu Nuclei

The nucleon momentum distributions (NMD) and the elastic electron scattering form factors F(q) of the ground state for some 1f-2p shell nuclei for 59Co, 61Ni, 63Cu and 65Cu are calculated using the Coherent Density Fluctuation Model (CDFM) and expressed in terms of the fluctuation function (weight function) . The fluctuation function has been related to the nucleon density distribution (NDD) of the nuclei and determined from the theory and experiment. The property of the long-tail behavior at high momentum region of the NMD has been obtained by both the theoretical and experimental fluctuation functions. The calculated form factors of all nuclei under study are in good agreement with those of experimental data throughout all values of momentum transfer

Nucleon momentum distributions and elastic electron scattering from 19F, 25Mg, 27Al, and 29Si nuclei

The nucleon momentum distributions and elastic electron scattering form factors of the ground state for some odd 2s–1d shell nuclei, such as 19F, 25Mg, 27Al, and 29Si, have been investigated using the coherent density fluctuation model and expressed in terms of the fluctuation function (weight function) |f(x)|2. The fluctuation function has been related to the nucleon density distribution of the nuclei and determined from the theory. The property of the long-tail manner at high-momentum region of the nucleon momentum distribution has been obtained by theoretical fluctuation function. The calculated form factors F(q) of all nuclei under study are in very good agreement with those of experimental data throughout all values of momentum transfer q. It is concluded that the contributions of the quadrupole form factor F C2(q) in 25Mg and 27Al nuclei, which are characterized by the undeformed 2s–1d shell model, are necessary for getting a remarkable agreement between the theoretical and experimental form factors.

M3Y-P0 as a Residual Interaction to Study Elastic Magnetic Electron Scattering Form Factors for Ca-41

The studying of elastic magnetic electron scattering form factors has been done for Ca-41with the consideration of 1f7/2 orbit as a model space and F7MBZ as a model space effective interaction to construct the model space wave functions. Core and higher configurations orbits have been included to the calculations as a first order corrections through the so called core polarization effect with the use of M3Y-P0 as a residual interaction to join the particle hole pair across the model space with 2 ħω excitation energy, with the available experimental data, theoretical results have been compared with it.

Nucleon Momentum Distributions and Elastic Electron Scattering form Factors for 22Ne, 26Mg and 30Si Nuclei

Nucleon Momentum Distributions and Elastic Electron Scattering form Factors for 22Ne, 26Mg and 30Si Nuclei

Nucleon momentum distributions and elastic electron scattering form factors for some 1p-shell nuclei

The nucleon momentum distributions (NMD) and elastic electron scattering form factors of the ground state for 1p-shell nuclei with Z = N (such as 6Li, 10B, 12C and 14N nuclei) have been calculated in the framework of the coherent density fluctuation model (CDFM) and expressed in terms of the weight function \(\left| {f( x )} \right|^2\). The weight function has been expressed in terms of nucleon density distribution (NDD) of the nuclei and determined from the theory and the experiment. The feature of the long-tail behaviour at high-momentum region of the NMDs has been obtained by both the theoretical and experimental weight functions. The experimental form factors F(q) of all the considered nuclei are very well reproduced by the present calculations for all values of momentum transfer q. It is found that the contributions of the quadrupole form factors FC2(q) in 10B and 14N nuclei, which are described by the undeformed p-shell model, are essential for obtaining a remarkable agreement between the theoretical and experimental form factors.

Electron scattering form factors from exotic nuclei

The elastic electron scattering form factors, longitudinal and transverse, from the He and Li isotopes and from 8B have been studied. Large space shell model functions have been assumed. The precise distribution of the neutron excess has little effect on the form factors of the isotopes though there is a mass dependence in the charge densities. However, the form factors of the proton-rich nucleus, 8B, are significantly changed by the presence of the proton halo.

The 15N ground state studied with elastic electron scattering

The C0 elastic electron scattering form factor of 15N has been measured over a momentum transfer range q=0.4−3.2 fm −1. From these form factor data the ground state charge density and its RMS radius (2.612±0.009 fm) were determined. This charge density as well as its difference with that of 16O were compared to recent large-basis shell-model calculations. Although these calculations describe the individual charge densities reasonably, the difference between 16O and 15N cannot be reproduced satisfactorily.

Inelastic electron scattering charge form factor of 4He.

In this work we calculate the inelastic electron scattering charge form factor of /sup 4/He using several N-N interactions. We employ the hyperspherical harmonics expansion method and include the contribution of harmonics above the minimal subset (L/sub min/). We find that the inelastic electron scattering form factor obtained by us is in excellent agreement with the experimental observations of Walcher. However, the inelastic form factor is insensitive to the N-N interaction. Further, we find that the minimal subset approximation is inadequate for form factor calculations when the momentum transfer is large. We also calculate the elastic electron scattering form factor and find the usual disagreement between theory and experiment. A possible explanation for this discrepancy is given.

Study of form factors of elastic and inelastic electron scattering by 20Ne

The elastic electron scattering form factor and also the form factor of inelastic scattering accompanied by nuclear transitions to excited states of the ground rotational band are calculated within the Sp z (2, R) model reproducing the dynamics of quadrupole nonsphericity of 20Ne. The Sp z (2, R) model is shown to describe correctly the experimental dependence of the elastic and inelastic (for the 0 + to 2 + state transition) form factors of the momentum transferred and, consequently, to remove some difficulties experienced by other dynamic models.

Dynamics of theO16+O16→S32fusion process

The collective mass and potential, the quantum corrections, and the inertia parameters of the /sup 16/O+ /sup 16/O..-->.. /sup 32/S system are evaluated by means of the quantized adiabatic time dependent Hartree-Fock theory in a three-dimensional coordinate and momentum lattice. The interaction used, consisting of a direct finite range Yukawa force and a density-dependent term, is fitted by static Hartree-Fock calculations (including center-of-mass corrections) to binding energies and elastic electron scattering form factors in the mass region of interest here. The result of the fit is a new interaction, still without exchange terms, which for light nuclei reproduces the binding energies, the diffraction radii, and the surface widths. The sub-barrier fusion cross section for /sup 16/O+ /sup 16/O..-->.. /sup 32/S calculated with this force in quantized adiabatic time dependent Hartree-Fock theory is in excellent agreement with experimental data in contrast to calculations using other interactions. For the evaluation of the fusion cross section above the barrier classical trajectory calculations are performed using a suitable phenomenological friction force. This yields agreement with experimental data up to energies of 40 MeV above the barrier. The quantum corrections and the dependence of the mass parameter on the fragment distance are shown to havemore » an important impact only below the barrier.« less

The salient features of charge density distributions of medium and heavy even-even nuclei determined from a systematic analysis of elastic electron scattering form factors

All available information on charge distributions of even-even nuclei is analysed systematically. For medium and heavy nuclei five general features of ρ( r) are investigated: (i) The extension for which we discuss several different definitions. The measured extension together with experimental binding energies allows a determination of nuclear compressibility within the framework of the droplet model, the resulting value being K = 165 ± 10 MeV. (ii) The surface thickness. Here too, several definitions are discussed. A close relationship between the surface thickness and binding energies is demonstrated. (iii) The average slope in the inner part of the nucleus. A method is formulated to separate this slope from the oscillations observed. All nuclei show a positive slope of comparable size. (iv) The oscillations on ρ( r). They are related to an abrupt breakdown in the form factor around q = 2.25 fm −1.This effect seems to be closely related to the fact that ρ( r) is built up out of single particles, details however being unimportant, (v) The high- q components of the form factor are indicative for a scattering mechanism involving pairs of nucleons.

Vibrational states in108Pd studied by elastic and inelastic electron scattering

The elastic electron-scattering form factor, and inelastic form factors for the 21+ (0.434 MeV), 22+ (0.931 MeV) and 3- (2.046 MeV) states in 108Pd were measured. The ground-state charge distribution parameters were obtained from a phase-shifted analysis of the elastic form factor. Analysis of the 21+ and 22+ form factors in the anharmonic vibrator model yields the reduced transition probabilities and the 21+ quadrupole moment (Qx, x=21+) which is in excellent agreement with recent Coulomb reorientation measurements. The 3- form factor is well described by the assumption that this state is a pure octupole vibration.

Elastic electron scattering as a test of effective interactions in the 1s-0d shell

Wave functions obtained from untruncated shell-model calculations for various effective interactions have been used to calculate the elastic electron scattering form factors for 24Mg and 32S. Chung-Wildenthal matrix elements best reproduce the form factors and the experimental excitation spectra for these nuclei. It is also shown that the use of harmonic oscillator wave functions and/or Born approximation can lead to a misjudgement of the actual situation.

Energy dependence of the zero-range DWBA normalization of the [formula omitted] reaction

Strong transitions in the 58Ni( 3He, α) 57Ni reaction were analyzed using both the zero-range and exact finite-range DWBA. Data considered covered a range of bombarding energies from 15 to 205 MeV. The zero-range DWBA described all data well when finite-range and non-locality corrections were included in the local energy approximation. Comparison of zero-range and exact finite-range calculations showed the local energy approximation correction to be very accurate over the entire energy region. Empirically determined D 0 values showed no energy dependence. A theoretical D 0 value calculated using an α wave function which reproduced the measured α rms charge radius and the elastic electron scattering form factor agreed well with the empirical values. Comparison was made between these values and D 0 values quoted previously in the literature.

Quasielastic electron scattering in a square-well shell model

The process of quasielastic electron scattering from 12C and 40Ca is studied within the framework of a square-well shell model. The nuclear potential well parameters are assigned prior to the electron scattering calculation by fitting separation energies, elastic electron scattering form factors and results obtained from nucleon scattering experiments. The general behaviour of the calculated cross section, is investigated over a wide range of excitation energies and three-momentum transfers and detailed comparisons with recent experimental data are presented.