Transverse Electron Scattering Form Factors Research Articles

STUDYING INELASTIC TRANSVERSE ELECTRON SCATTERING FORM FACTORS OF THE ISOSCALAR TRANSITIONS IN 10B NUCLEUS

The inelastic transverse electron scattering form factors are studied for the fourisoscalar transitions for the states of 10B nucleus. These states are specifiedby J T  =1+0 (0.718 MeV), 1 0 2 (2.154 MeV), 2+0 (3.587 MeV) and 3 0 2 (4.774MeV). These form factors are analyzed in the framework of the harmonic oscillatorshell model.The transverse form factors have been calculated in the framework of the multinucleonconfiguration mixing shell model using the two-body interaction of Cohenand Kurath (C-K) to generate the 1p-shell wave function. The core polarization (CP)effects are included in the calculations through effective g-factors. A higherconfiguration effect outside the 1p-shell model space enhances the form factors forq-values and reasonably reproduces the data. The value of the size parameter (b) ischosen to reproduce the root mean square charge radius. The present results arecompared with available experimental data and with that of other models.PACS:21.60-n,21.60 Cs, 25.30Dh,27.20 th

Calculation of the electromagnetic moments and electroexcitation form factors for some boron isotopes using shell model with skyrme interaction

The magnetic dipole and electric quadrupole moments for some Boron isotopes were calculated using the shell model taking into account the effect of the two-body effective interactions and the single-particle potentials. These isotopes are; (8 5)B(2 +), (1 50)B(3 +), (1 51)B((3/2)−), ( 1 52)B(1 +) and (1 53)B((3/2)−). Also, the elastic and inelastic longitudinal and transverse electron scattering form factors are calculated for 10B and 11B, for which there are available experimental data. The one-body transition density matrix elements (OBDM) were calculated using the two-body effective interactions; PWT, PEWT, PKUO and CKIHE, which are carried out in the p-shell model space. Skyrme interaction was implemented to generate the single-particle matrix elements with Hartree-Fock approximation and compared with those of harmonic-oscillator and Wood-Saxon potentials. All the evaluated results were compared with available experimental data. The present work has led us to conclude that the shell model calculations with Skyrme type interaction give a good tool for nuclear structure studies. All signs for the experimental electromagnetic moments data are reproduced correctly. The longitudinal and transverse form factors for positive and negative parity states are fairly well reproduced when using a suitable model space.

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.

Elastic transverse electron scattering form factors of 11Li exotic nucleus

The elastic transverse electron scattering form factors have been studied for the 11Li nucleus using the Two- Frequency Shell Model (TFSM) approach. The single-particle wave functions of harmonic-oscillator (HO) potential are used with two different oscillator parameters bcore and bhalo. According to this model, the core nucleons of 9Li nucleus are assumed to move in the model space of spsdpf. The outer halo (2-neutron) in 11Li is assumed to move in the pure 1p1/2, 1d5/2, 2s1/2 orbit. The shell model calculations are carried out for core nucleons using the spsdpf-interaction. The elastic magnetic electron scattering of the stable 7Li and exotic 11Li nuclei are also investigated through Plane Wave Born Approximation (PWBA). It is found that the difference between the total form factors of unstable isotope (11Li halo) and stable isotope 7Li is in magnitude. The measured value of the magnetic moment is also reproduced.

Cluster shell model: I. Structure of 9Be, 9B

We calculate energy spectra, electromagnetic transition rates, longitudinal and transverse electron scattering form factors and log ft values for beta decay in 9Be, 9B, within the framework of a cluster shell model. By comparing with experimental data, we find strong evidence for the structure of these nuclei to be two α-particles in a dumbbell configuration with Z2 symmetry, plus an additional nucleon.

Transverse Magnetic Electron Scattering Form Factors for Some Odd-A Nuclei Using Shell Model and Hartree–Fock Calculations

Shell model and Hartree–Fock (HF) calculations have been adopted to study the nuclear structure for some odd-A nuclei; 17O, 27Al, 39K, and 51V. The single-particle nuclear density distributions, the associated nuclear radii, and the transverse magnetic form factors were investigated. The wave functions have been utilized from the shell model using USDA and SAS two-body effective interactions for these nuclei with the sd and d3f7 shell model spaces. On the other hand, different Skyrme parameterizations have been used within the HF method to get the single-particle potential which is used to calculate the single-particle matrix elements. The calculated form factors have been compared with available experimental data.

Inelastic electric and magnetic electron scattering form factors of 24Mg nucleus: Role of g factors

The electric and magnetic transitions in the [Formula: see text]Mg nucleus are studied based on the calculations of the longitudinal and the transverse electron scattering form factors. The universal sd-shell model Hamiltonian (USDA) is used for calculations. The wave functions of radial single-particle matrix elements are calculated using the Skyrme potential. For the longitudinal form factors, a good agreement is obtained between the calculations and the experimental data. For the transverse form factors, the effective [Formula: see text] factors are made as adjustable parameters in order to describe the experimental data.

Microscopic Large Scale psd Shell Model with M3Y Residual Interaction to Calculate Electron Scattering Form Factors

The longitudinal and the transverse electron scattering form factors for 6Li, 9Be, 11B and 12C nuclei have been studied with and without core polarization effects using shell model calculations. The psdmwk is used as effective interaction for psd-shells. The core-polarization effects are calculated in the first-order perturbation theory including excitations up to 4ħω using the Michigan three-range Yakawa M3Y as a realistic interaction. The wave functions of radial single particle matrix elements have been calculated with harmonic oscillator potential. For all nuclei under studying, Comparison between experimental and theoretical calculations show that the form factors with core-polarization effect calculations give good consistency with experiment data. So we concluded that the large scale model space enhanced the results to become closed to the experimental data.

Electron scattering of 14N based on two-hole excitations

The nuclear structure of 14N is studied in the framework of the hole-hole Tamm-Dancoff Approximation (hhTDA) and hole-hole Random Phase Approximation (hh RPA). The Hamiltonian is diagonalized within a model space with particle orbits {1d5/2, 1d3/2, 2s1/2 and 1f7/2}and the hole orbits {1s1/2, 1p3/2 and 1p1/2} using Warburton and Brown interaction WBP. The TDA and RPA amplitudes are used to calculate the longitudinal and transverse electron scattering form factors. The results for JfπTfExMeV= 1+0(0.0), 0+1(2.313), 1+(3.945), 2−0(5.106) and 3−0(5.834) states are interpreted in terms of the harmonic-oscillator (HO) wave functions of size parameter b and compared with the available experimental data. Configurations outside the model space are included approximately, in terms of polarization effective charges and g-factors.

Shell model calculations of inelastic electron scattering for positive and negative parity states in 19F

Shell model and Hartree–Fock calculations have been used to study the nuclear structure of 19F nucleus. In particular, inelastic electron scattering form factors, energy levels and transition probabilities for positive and negative low-lying states. Two different model spaces have been used for this purpose. The first is the full sd-model space for positive parity states with USDA interaction. The second one is the truncated large-basis spsdpf no-core-shell model space for negative parity states with WBP interaction except that in the extreme state 3/21− we used sdpf model space with SDPFK interaction. For all excited states, the radial wave functions for the single-particle matrix elements were calculated using the Skyrme–Hartree–Fock method with SkXcsb parameterization. The calculated form factors, energy level schemes and transition probabilities were compared with the available experimental data. It has been confirmed that the Hartree–Fock mean field method with Skyrme interaction is appropriate with shell model for studying the nuclear structure and essential in obtaining a reasonable description of the longitudinal and transverse electron scattering form factors.

Contribution of high energy configurations to longitudinal and transverse form factors in p- and sd-shell nuclei

Longitudinal and transverse electron scattering form factors for some selected positive and negative parity states of stable odd-A nuclei ( 7 Li, 13 C and 17 O) in the p- and sd-shells are investigated by considering the higher energy configurations outside the p- and sd-shells. The higher energy configurations, referred to as core polarization effects, are considered by means of a microscopic theory that includes excitations from the core 1s-1p ,2 s-1d orbits to the higher allowed orbits with 4�x excitations. The calculations are performed in the p- and sd-shell model spaces by employing Cohen-Kurath, Reehal and Wildenthal interactions respectively, while the core polarization effects are calculated with the modified surface delta interaction as residual interaction. The predicted form factors are compared with the available experimental data and it is shown that the inclusion of the higher excited configurations is very essential in the calculations of the form factors and the reduced transition probabilities to obtain reasonable description of the data with no adjustable parameters.

The electron scattering form factor of 10B, 32S and 48Ca nuclei

Longitudinal and transverse electron scattering form factors and transition probabilities have been calculated for different states in 10B, 32Sc and 48Ca nuclei, where a microscopic theory is employed to include the effect of high configuration outside the model space, which is called the core-polarization (CP) effect. The Cohen–Kurath interaction for p-shell, the universal sd of Wildenthal interaction for sd-shell and the GXFP1 interaction for fp-shell are used with the Michigan three-range Yakawa (M3Y) effective NN interaction and modified surface delta interaction as a residual interaction for the CP calculations. The calculation is performed using the shell model codes CPM3Y and NuShell. The radial wave function for the single-particle matrix elements have been calculated with the Skyrme–Hartree Fock, harmonic oscillator potential and Wood Saxson potential to calculate the single-particle wave function. The inclusion of CP effects modifies the form factors markedly and describes the experimental data very well in the momentum transfer dependence.

The Electro-Excitation Form Factors for Low-Lying States of 7Li Nucleus

The transverse electron scattering form factors have been studied for low –lying excited states of 7Li nucleus. These states are specified by J? T= (0.478MeV), (4.63MeV) and (6.68MeV). The transitions to these states are taking place by both isoscalar and isovector components. These form factors have been analyzed in the framework of the multi-nucleon configuration mixing of harmonic oscillator shell model with size parameter brms=1.74fm. The universal two-body of Cohen-Kurath is used to generate the 1p-shell wave functions. The core polarization effects are included in the calculations through effective g-factors and resolved many discrepancies with experiments. A higher configuration effect outside the 1p-shell model space, such as the 2p-shell, enhances the form factors for q-values and reproduces the data. The present results are compared with other theoretical models. PACS: 25.30.Bf Elastic electron scattering - 25.30.Dh Inelastic electron scattering to specific states – 21.60.Cs Shell model – 27.20. +n 5? A ?19

The Electro-Excitation Form Factors for Low-Lying States of 7Li Nucleus

The transverse electron scattering form factors have been studied for low –lying excited states of 7Li nucleus. These states are specified by J? T= (0.478MeV), (4.63MeV) and (6.68MeV). The transitions to these states are taking place by both isoscalar and isovector components. These form factors have been analyzed in the framework of the multi-nucleon configuration mixing of harmonic oscillator shell model with size parameter brms=1.74fm. The universal two-body of Cohen-Kurath is used to generate the 1p-shell wave functions. The core polarization effects are included in the calculations through effective g-factors and resolved many discrepancies with experiments. A higher configuration effect outside the 1p-shell model space, such as the 2p-shell, enhances the form factors for q-values and reproduces the data. The present results are compared with other theoretical models. PACS: 25.30.Bf Elastic electron scattering - 25.30.Dh Inelastic electron scattering to specific states – 21.60.Cs Shell model – 27.20. +n 5? A ?19

Calculations of elastic and inelastic electron scattering on 19F using large-basis no core-shell model wave functions

Large basis no core shell model calculations are performed to study the elastic and inelastic electron scattering on 19F. All major shells s, p, sd and pf are considered with ( 0 + 2 ) ℏ ω truncations. Excitations out of major shell space are taken into account through a microscopic theory which allows particle–hole excitations from the sd and pf shell orbits to all higher orbits with 2 ℏ ω excitations. Calculations are presented for the transitions from J π T = 1 / 2 + 1 / 2 to J π T = 1 / 2 + 1 / 2 , 3 / 2 + 1 / 2 , 5 / 2 + 1 / 2 , 7 / 2 + 1 / 2 and 9 / 2 + 1 / 2 in 19F. Excitations out the no core shell model space are essential in obtaining a reasonable description of the longitudinal and transverse electron scattering form factors.

Transverse electron scattering form factors at low momentum transfer: Sensitivity to in-medium modifications of vector mesons?

Form factor measurements of $M2$ and $M4$ transitions to the lowest ${J}^{\ensuremath{\pi}}{=2}^{\ensuremath{-}}$ and ${4}^{\ensuremath{-}}$ states, respectively, in ${}^{48}\mathrm{Ca}$ with inelastic electron scattering at $180\ifmmode^\circ\else\textdegree\fi{}$ are reported for momentum transfers $q\ensuremath{\simeq}0.4\ensuremath{-}0.8{\mathrm{fm}}^{\ensuremath{-}1}.$ These form factors complement previous measurements at higher $q$ which have been treated by Lallena [Phys. Rev. C 48, 344 (1993)], as a test case to derive information on in-medium modifications of the $\ensuremath{\rho}$-meson mass. He deduced within the random-phase approximation (RPA) an effective mass ${m}_{\ensuremath{\rho}}^{*}\ensuremath{\simeq}0.9\ensuremath{-}0.95{m}_{\ensuremath{\rho}}$ assuming simultaneous scaling of the $\ensuremath{\pi}$ coupling constant (Brown-Rho scaling). The validity of the analysis is critically assessed by comparing the measured form factors to second random-phase approximation (SRPA) calculations with a $\ensuremath{\pi}+\ensuremath{\rho}$ exchange interaction. The dependence of the form factors on the choice of the interaction and corrections such as mesonic exchange currents (MEC) are found to be of comparable magnitude to effects from a dropping of ${m}_{\ensuremath{\rho}},$ and in-medium effects hence cannot be clearly inferred from the data. To quantify the latter would require first the construction of an interaction which is capable of describing simultaneously and optimally a large variety of low-energy nuclear properties in ${}^{48}\mathrm{Ca}.$ Remaining discrepancies in such a description could then be studied with the aim to single out in-medium effects of the type advocated by Lallena.

Electron scattering and nuclear structure at the S-DALINAC

Results on ongoing research of elementary electric and magnetic nuclear excitations at the superconducting Darmstadt electron linear accelerator (S-DALINAC) are presented. In the first part of this lecture electric excitation modes in the continuum are discussed by way of two examples employing the coincident detection of inelastically scattered electrons in an (e,e′x) reaction. The first example is the reaction 48Ca(e,e′n) where the excitation and decay of isoscalar electric monopole and quadrupole giant resonances has been studied. The results on the strength distribution and the partial exhaustion of energy weighted sum rules are compared to those from RPA and second-RPA (SRPA) predictions as well as to those from hadronic reactions of the type (p,p′) and (p,p′n). The second example, a discussion of the 90Zr(e,e′p) reaction and its results, can be viewed as a direct proof that in coincidence reactions of the form (e,e′x) one is able to isolate and identify narrow weakly excited levels — here isobaric analog resonances — buried in the continuum and determine their excitation and decay properties and thus subtle nuclear structure properties. The second part of the lecture is concerned with high-resolution inelastic electron scattering under 180° which is selective with respect to magnetic excitations. Of those, first systematic studies on the hitherto scarcely explored magnetic quadrupole giant resonance which is mainly a spin-isospin excitation are presented. As an example, results for 48Ca and 90Zr, in which a strongly fragmented and quenched M2 strength has been detected, are compared to SRPA and sum rules approaches. Evidence is presented for a new excitation mode, the so called nuclear twist mode, and its parameters are determined. In the third part of the lecture, the possible use of transverse electron scattering form factors at low momentum transfer for an advocated test of in-medium modifications of vector mesons is critically examined, and finally an outlook is given on the nuclear physics research program at the S-DALINAC.

Transverse form factors in the collective and symplectic models

Transverse electron scattering form factors are calculated for 0 + → 2 + excitations in 16O, 24Mg and 40Ca. The objective is to learn about the current flows associated with nuclear collective motions. The 2 + states considered in 16O and 40Ca are giant quadrupole vibrational excitations. In 24Mg, the 2 + state is the first excited rotational state. The form factors have been computed microscopically within the framework of the symplectic model and, in order to interpret the dynamical content of collective flows of the model, the results are compared with form factors calculated with collective models, for different collective flows. For the giant resonance state, we calculate the form factor for irrotational-flow vibrational motion and, for the rotational state, we use the rotor model with both rigid and irrotational current flows.

Magnetic electron scattering from p-shell nuclei

In this paper we report on shell-model calculations of transverse electron scattering form factors of states in several selected p-shell nuclei. Results will be presented for calculations in the p-shell model space and in the extended (0 + 2) h ̷ model space. The influence of meson-exchange currents on the calculated form factors will be examined. We find that in the beginning of the p-shell the description of the transverse form factors is improved by extending the model space. However, towards the end of the p-shell the situation deteriorates, indicating deficiencies in the wave functions.

A symplectic model calculation of transverse electron scattering form factors for 24Mg

The electron scattering transverse form factors for the transitions 0 + → 2 1 + and 0 + → 2 2 + for 24Mg are calculated in the symplectic model. Results show that the predictions of the sp(3, R ) model are improved over calculations restricted to the valence shell. Unlike longitudinal form factor calculations the effects of higher shells are not accounted for by simply introducing an effective charge factor.