Elastic Electron Scattering Form Factors Research Articles

Study of Nuclear Structure and Elastic Electron Scattering Form Factors for Neutron Halo Nuclei (22N ,23O and 24F) Using Full Correlation Functions with Two Size Parameters

The study of neutron-rich nuclei's form factors, root-mean-square radius (rms), and nuclear density distributions is the focus of this work for the nuclei (22N,23 O and 24F). With the use of a strong short-range effect and a strong tensor force, the nucleons distribution function of the two oscillating harmonic particles in a two-frequency shell model operates with two different parameters: the first (bcore), for the inner (core) orbits, and the second (bvalence) for the outer (halo) orbits. This work demonstrated the existence of neutron halo nuclei for the nuclei (22N, 23O and 24F) in the (2s1/2) shell. The computed density distribution of neutron, proton and matter for these nuclei displayed the long tail performance. Using the Borne approximation of the plane wave, the elastic form factor of the electron scattering from the alien nucleus was calculated, this form factor is independent of the neutrons that make up the halo, but rather it results from a difference in the proton density distribution of the last proton in the nuclei. Fortran 95 power station program was used to the neutron, proton and matter density, elastic electron scattering form factor, and rms radii. The calculated outcomes for these exotic nuclei were in good agreement with the experimental data.

Theoretical Study of Matter Density Distributions, and Elastic Electron Scattering Form Factors of Exotic Nuclei (26F and 9C)

Abstract: The distributions of nuclear density, root mean square radii, and elastic electron scattering form factor are calculated for nuclei (9C) (core +2p) and (26F) (core +2n) with the two different nuclear potential parameters for (bc) and (bv), were correlations for both the (effects tensor force and short-range) are used, and the appearance of the long extension is observed in Nuclear density distributions for these nuclei. Fortran 95 power station was used to program nuclear properties such as nucleon density (matter, neutron, and proton), elastic electron scattering form factor, and rms radii. The computed results for these exotic nuclei are determined to correspond pretty well with the experimental data.

Theoretical Study of Proton Halo Structure and Elastic Electron Scattering Form Factor for 23Al and 27P Nuclei by Using Full Correlation Functions (Tensor Force and Short Range)

The study of proton-rich nuclei's form factors, root-mean-square radius (rms), and nuclear density distributions is the focus of this work for nuclei (23Al and 27P), use two body charge density distributions (2BCDD's). With the effects of the strong tensor force and short range, the nucleon distribution function of the two oscillating harmonic particles in a two-frequency shell model operates with two different parameters: bc for the inner (core) orbits and bv for the outer (halo) orbitals. This work demonstrated the existence of proton halo nuclei for the nuclei (23Al and 27P) in the shell (2s1/2), and the computed proton, neutron, and matter density distributions for these nuclei both displayed the long tail of the performance. Using the Borne approximation of the plane wave, the elastic form factor of the electron scattering from the alien nucleus was calculated, this form factor is dependent on the difference in the proton density distribution of the last proton in the nucleus. The Fortran 95 power station program was used to calculate the neutrons, protons, matter density, elastic electron scattering form factor, and rms radii. The calculated outcomes for these exotic nuclei agree well with the experimental data.

Study of Matter Density Distributions, Elastic Electron Scattering Form factors and Root Mean Square Radii of 9C, 12N, 23Al, 11Be and 15C Exotic Nuclei

The ground state densities of neutron-rich (11Be,15C) and proton-rich (9C,12N,23Al) exotic nuclei are investigated using a two-body nucleon density distribution (2BNDD) with two frequency shells model (TFSM). The structure of the valence one-neutron of 11Be is in pure (1p1/2) and of 15C in pure (1d5/2) configuration, while the structure of valence one-proton configuration is in 9C,12N are to be in a pure (1p1/2) and 23Al in a pure (2s1/2) . For our studied nuclei, an efficient (2BNDD) operator for point nucleon system folded with two-body correlation operator's functions is used to investigate nuclear matter density distributions, elastic electron scattering form factors, and root-mean square (rms) radii. The effect of the strong tensor force (TC) in nucleon-nucleon forces is taken into account in the correlation. The wave functions of a single particle harmonic oscillator are used with two different oscillator size parameters, βc and βv, the former for core (inner) orbits and the latter for valence (halo) orbits. The measured matter density distributions of these nuclei clearly show the long tail results. The plane wave born approximation (PWBA) is used to investigate the elastic electron scattering form factors for these exotic nuclei.

Theoretical Study of Elastic Electron Scattering from 8B, 17Ne, 11Be and 11Li Halo Nuclei

The nuclear density distributions and size radii are calculated for one-proton 8B, two-proton 17Ne, one-neutron 11Be and two-neutron 11Li halo nuclei. The theoretical outlines of calculations assume that the nuclei understudy are composed of two parts: the stable core and the unstable halo. The core part is studied using the radial wave functions of harmonic-oscillator (HO) potentials, while the halo is studied through Woods-Saxon (WS) potential. The long tail behaviour which is the main characteristic of the halo nuclei are well generated in comparison with experimental data. The calculated size radii are in good agreement with experimental values. The elastic electron scattering form factors of the C0 component are also calculated for the aforementioned nuclei. The calculated form factor results give predictions for the results of future experiments on electron-radioactive ion beam colliders.

Matter Density Distributions, Root-mean Square Radii and Elastic Electron Scattering Form Factors of Some Exotic Nuclei (17B, 11Li, 8He)

The two-neutron halo-nuclei (17B, 11Li, 8He) was investigated using a two-body nucleon density distribution (2BNDD) with two frequency shell model (TFSM). The structure of valence two-neutron of 17B nucleus in a pure (1d5/2) state and in a pure (1p1/2) state for 11L and 8He nuclei. For our tested nucleus, an efficient (2BNDD's) operator for point nucleon system folded with two-body correlation operator's functions was used to investigate nuclear matter density distributions, root-mean square (rms) radii, and elastic electron scattering form factors. In the nucleon-nucleon forces the correlation took account of the effect for the strong tensor force (TC's). The wave functions of single particle harmonic oscillator are used with two different oscillator size parameters βc and βv, where the former is for the core (inner) orbits and the latter is for the valence (halo) orbits. The measured matter density distributions of these nuclei clearly showed long tail results. To investigate elastic electron scattering form factors the plane wave born approximation (PWBA) with two body nucleon density distribution (2BNDD's) was use.

Stable15N and Neutron Halo 16N Nuclei Structure Study by Elastic Electron Scattering Form Factors and Nucleon Momentum Distributions

In this manuscript, the elastic electron scattering form factors and the nucleon momentum distributions (NMD) for stable 15N and neutron halo 16N at the ground state were reported. This was accomplished by utilizing the well-known Coherent Density Fluctuation Model (CDFM) via the employment of fluctuation function (|F(q)|2) which is coupled with the density distributions nuclei. The long-tail performance in the NMD at high momentum region was further determined via experimental and theoretical fluctuation functions. The evaluated elastic electron scattering form factors were evaluated on the bases of the density distributions as well as the root mean square (RMS) radii for each measured nucleon. The proposed study provides a robust correlation between the theoretical formation factors and the practical results of 15N and 16N nuclei.

Study of the Halo Structure for Some Light Neutron-Rich Nuclei Using the Cosh Potential

The radial wave functions of the cosh potential within the three-body model of $$\left({\textrm{Core}+2n}\right)$$ have been employed to investigate the ground state properties such as the proton, neutron and matter densities and the associated rms radii of neutron-rich $${}^{{6}}$$ He, $${}^{{11}}$$ Li, $${}^{{14}}$$ Be, and $${}^{{17}}$$ B exotic nuclei. The density distributions of the core and two valence (halo) neutrons are described by the radial wave functions of the cosh potential. The obtained results provide the halo structure of the above exotic nuclei. Elastic electron scattering form factors of these halo nuclei are studied by the plane-wave Born approximation.

The neutron halo structure of $$^{14}\hbox {B}$$, $$^{22}\hbox {N}$$, $$^{23}\hbox {O}$$ and $$^{24}\hbox {F}$$ nuclei studied via the generalised Woods–Saxon potential

The radial wave functions of the generalised Woods–Saxon (GWS) potential within the two-body model of $$\left( \mathrm {Core}+n \right) $$ have been used to study the ground-state density distributions of protons, neutrons and matter and the associated root mean square (rms) radii of neutron-rich $$^{\mathrm {14}}\hbox {B}$$ , $$^{\mathrm {22}}\hbox {N}$$ , $$^{\mathrm {23}}\hbox {O}$$ and $$^{\mathrm {24}}\hbox {F}$$ halo nuclei. The calculated results show that the radial wave functions of the generalised Woods–Saxon potential within the two-body model succeed in reproducing neutron halo in these exotic nuclei. Elastic electron scattering form factors for these nuclei are studied by combining the charge density distributions with the plane-wave Born approximation (PWBA).

Density Distributions and Elastic Electron Scattering Form Factors of Proton-rich 8B, 17F, 17Ne, 23Al and 27P Nuclei

In this work, the nuclear density distributions, size radii and elastic electron scattering form factors are calculated for proton-rich 8B, 17F, 17Ne, 23Al and 27P nuclei using the radial wave functions of Woods-Saxon potential. The parameters of such potential for nuclei under study are generated so as to reproduce the experimentally available size radii and binding energies of the last nucleons on the Fermi surface.

Density distributions and form factors of the exotic 8B nucleus

Results of charge, neutron and matter densities and related form factors for one- proton halo nucleus 8B are presented using a two- frequency shell model approach. We choose a model space for the core of 7Be different from that of the extra one valence proton. One configuration is assumed for the outer proton to be in 1p1/2 - shell. The results of the matter density distributions are compared with those fitted to the experimental data. The calculated proton and matter density distributions of this exotic nucleus exhibit a long tail behavior, which is considered as a distinctive feature of halo nuclei. Elastic electron scattering form factors of this exotic nucleus are also studied. The effects of the proton halo on the electron scattering form factors are analyzed. The form factors of the exotic unstable 8B nucleus are compared with those of the stable 10B nucleus. The differences between the results of unstable 8B and stable 10B nuclei come from the long tail in the density distribution of the last proton.

Nucleon momentum distributions and elastic electron scattering form factors for 48Ti and 54Fe nuclei

The nucleon momentum distributions (NMD) for the ground state and elastic electron scattering form factors have been calculated in the framework of the coherent fluctuation model and expressed in terms of the weight function (fluctuation function). The weight function has been related to the nucleon density distributions of nuclei and determined from theory and experiment. The nucleon density distributions (NDD) is derived from a simple method based on the use of the single particle wave functions of the harmonic oscillator potential and the occupation numbers of the states. The feature of long-tail behavior at high momentum region of the NMD has been obtained using both the theoretical and experimental weight functions. The observed electron scattering form factors for 48Ti and 54Fe nuclei are in reasonable agreement with the present calculations throughout all values of momentum transfer q.

Nucleon momentum distributions and elastic electron scattering form factors for 58Ni, 60Ni, 62Ni, and 64Ni isotopes using the framework of coherent fluctuation model

The nucleon momentum distributions (NMD) and elastic electron scattering form factors of the ground state for some 1f-2p-shell nuclei, such as 58Ni, 60Ni, 62Ni, and 64Niisotopes have been calculated in the framework of the coherent fluctuation model (CFM) and expressed in terms of the weight function lf(x)l2 . The weight function (fluctuation function) has been related to the nucleon density distribution (NDD) of the nuclei and determined from the theory and experiment. The NDD is derived from a simple method based on the use of the single particle wave functions of the harmonic oscillator potential and the occupation numbers of the states. The feature of the long-tail behavior at high momentum region of the NMD’s has been obtained by both the theoretical and experimental weight functions. The calculated elastic electron scattering form factors for considered isotopes are in reasonable agreement with those of experimental data throughout all values of momentum transfer q.

Investigation of density and form factor of some F isotopes using Hartree-Fock and shell model calculations

Structure of unstable 21,23,25,26F nuclei have been investigatedusing Hartree – Fock (HF) and shell model calculations. The groundstate proton, neutron and matter density distributions, root meansquare (rms) radii and neutron skin thickness of these isotopes arestudied. Shell model calculations are performed using SDBAinteraction. In HF method the selected effective nuclear interactions,namely the Skyrme parameterizations SLy4, Skeσ, SkBsk9 andSkxs25 are used. Also, the elastic electron scattering form factors ofthese isotopes are studied. The calculated form factors in HFcalculations show many diffraction minima in contrary to shellmodel, which predicts less diffraction minima. The long tailbehaviour in nuclear density is noticeable seen in HF more than shellmodel calculations. The deviation occurs between shell model andHF results are attributed to the sensitivity of charge form factors tothe change of the tail part of the charge density. Calculations donefor the rms radii in shell model showed excellent agreement withexperimental values, while HF results showed an overestimation inthe calculated rms radii for 21,23F and good agreement for 25,26F. Ingeneral, it is found that the shell model and HF results have the samebehaviour when the mass number (A) increase.

Charge density distributions and electron scattering form factors of 25Mg, 27Al and 29Si nuclei

An effective two-body density operator for point nucleon systemfolded with the tenser force correlations( TC's), is produced and usedto derive an explicit form for ground state two-body charge densitydistributions (2BCDD's) applicable for 25Mg, 27Al and 29Si nuclei. It isfound that the inclusion of the two-body TC's has the feature ofincreasing the central part of the 2BCDD's significantly and reducingthe tail part of them slightly, i.e. it tends to increase the probability oftransferring the protons from the surface of the nucleus towards itscenteral region and consequently makes the nucleus to be more rigidthan the case when there is no TC's and also leads to decrease the1/ 2r 2 of the nucleus. It is also found that the effect of the TC's and theeffect of increasing the values of  on the 2BCDD's, elasticelectron scattering form factors and r2 1/ 2 are in the same directionfor all considered nuclei.

Proton momentum distributions and elastic electron scattering form factors for some Ge isotopes

The proton momentum distributions (PMD) and the elasticelectron scattering form factors F(q) of the ground state for someeven mass nuclei in the 2p-1f shell for 70Ge, 72Ge, 74Ge and 76Ge arecalculated by using the Coherent Density Fluctuation Model (CDFM)and expressed in terms of the fluctuation function (weight function)|F(x)|2. The fluctuation function has been related to the chargedensity distribution (CDD) of the nuclei and determined from thetheory and experiment. The property of the long-tail behavior at highmomentum region of the proton momentum distribution has beenobtained by both the theoretical and experimental fluctuationfunctions. The calculated form factors F (q) of all nuclei under studyare in good agreement with those of experimental data throughout allvalues of momentum transfer q.

Nuclear structure study of 20Ne, 24Mg, 28Si and 32S nuclei using Skyrme-Hartree-Fock method

The Skyrme–Hartree–Fock (SHF) method with the Skyrmeparameters; SKxtb, SGII, SKO, SKxs15, SKxs20 and SKxs25 havebeen used to investigate the ground state properties of some 2s-1dshell nuclei with Z=N (namely; 20Ne, 24Mg, 28Si and 32S) such as, thecharge, proton and matter densities, the corresponding root meansquare (rms) radii, neutron skin thickness, elastic electron scatteringform factors and the binding energy per nucleon. The calculatedresults have been discussed and compared with the availableexperimental data.

Charge density distributions and electron scattering form factors of 19F, 27Al and 25Mg nuclei

An effective two-body density operator for point nucleon system folded with two-body correlation functions, which take account of the effect of the strong short range repulsion and the strong tensor force in the nucleon-nucleon forces, is produced and used to derive an explicit form for ground state two-body charge density distributions (2BCDD's) and elastic electron scattering form factors F (q) for 19F, 27Al and 25Mg nuclei. It is found that the inclusion of the two-body short range correlations (SRC) has the feature of reducing the central part of the 2BCDD's significantly and increasing the tail part of them slightly, i.e. it tends to increase the probability of transferring the protons from the central region of the nucleus towards its surface and to increase the root mean square charge radius ˂ r 2˃ 1/2 of the nucleus and then makes the nucleus to be less rigid than the case when there is no (SRC). It is also found that the effects of two body tensor correlations (TCs) on 2BCDD's and ˂ r 2˃ 1/2 are in opposite direction to those of (SRC).

Elastic electron scattering form factors of deformed exotic Xe isotopes

Background: The positions of diffraction minima of Coulomb form factors $|{F}_{C}{(q)|}^{2}$ are important landmarks for electron scattering experiments, which are sensitive to the nuclear size. For the isotopic chain, previous studies show the minima of $|{F}_{C}{(q)|}^{2}$ have an outward shift as the target nucleus moves to the proton-rich side.Purpose: Based on previous studies, the Coulomb form factors of Xe isotopes are further investigated by the deformed relativistic mean-field (RMF) model and distorted wave Born approximation (DWBA) method.Method: First, the nuclear charge density distributions are calculated by the constrained calculations of deformed RMF model. Next, the axially deformed density distributions are expanded into multipole components. With the charge density multipoles, the Coulomb form factors of Xe isotopes are calculated by the DWBA method.Results: For the nucleus with deformation, there are differences on the Coulomb form factors calculated from the spherical and deformed RMF models. For the Xe isotopic chain, the changing trend of $|{F}_{C}{(q)|}^{2}$ from the deformed RMF model is different from the results from the spherical RMF model at high momentum transfers.Conclusions: The minima of $|{F}_{C}{(q)|}^{2}$ of isotopes are directly influenced by the nuclear deformation parameter ${\ensuremath{\beta}}_{2}$, not just the charge radius ${R}_{C}$. For the studies of electron scattering, the nuclear deformation should be taken into account, especially in high momentum transfers.

Theoretical Study of The Electromagnetic Structure of Boron Isotopes Using Local Scale Transformation Technique

The radial wavefunctions of transformed harmonic-oscillator in the local scale transformation technique are used to calculate the root-mean square proton, charge, neutron and matter radii, nuclear density distributions and elastic electron scattering charge form factors of stable ( 10,11 B) and (unstable) exotic ( 8,14,17 B) Boron isotopes. For 10 B and 11 B, the transformed harmonic-oscillator wavefunctions are applied to all subshells in no-core shell model approach using wbp interaction. For 8,14,17 B, the radial wavefunctions of harmonic-oscillator and THO are used to calculate the aforementioned quantities for the core and halo parts, respectively. The calculated matter and charge density distributions are found to be in very good agreement with experimental data for 8,14,17 B and 10,11 B, respectively. The calculated elastic electron scattering form factors of the longitudinal C0+C2 components for 10,11 B are in very good agreement with experimental data.