Elastic Magnetic Form Factors Research Articles

Comparative studies on nuclear elastic magnetic form factors between the relativistic and non-relativistic mean-field approaches * *Supported by the National Natural Science Foundation of China (11505292, 11605105, 11822503, 11975167, 12035011), the Shandong Provincial Natural Science Foundation, China (ZR2020MA096), the Fundamental Research Funds for the Central Universities (20CX05013A, 22120210138), and the Graduate Innovative Research Funds of China University of Petroleum (East

It is known that elastic magnetic electron scattering can be used to study the magnetic properties of nuclei and determine the outermost-shell single-particle orbitals. In this study, the magnetic form factors of odd-A nuclei calculated with relativistic and non-relativistic models are systematically compared. We use the relativistic mean-field (RMF) and Skyrme Hartree-Fock (SHF) models to generate single-particle wave functions and calculate the values of selected nuclei under relativistic and non-relativistic frameworks, respectively. Geometric factors are introduced through the spherical limit method to consider the influences of deformation, which improves the agreement between the theoretical results and experimental data. It is shown that both the models have the capability to describe the magnetic form factors in the spherical and deformed cases, and the discrepancies in reflect the differences in the descriptions of the single-particle orbital between the two models.

Investigation of nonlinear isoscalar–isovector coupling in a relativistic mean-field model by elastic magnetic electron scattering

In this paper, we study the sensitivity of single valence neutron properties and elastic magnetic form factors to three different relativistic mean-field (RMF) parameter sets: NL3, FSUGold, and IU-FSU. To perform our calculation, seven odd-A nuclei having single valence neutron on top of a magic neutron core: Be7, O17, Ca41, Ni57, Zr91, Ba139, and Pb209 are considered as model nuclei. The wave-function of the outer most neutron orbit, matter density, valence neutron density, and magnetic form factors are numerically calculated. It is shown that there are significant differences between the magnetic form factors in the mediate- and high-momentum transfer regions when calculate with different parameter sets. Such separation is more evident with larger nuclear mass and isospin asymmetry. By fitting to the experimental data, the spectroscopic factors for O17 and Ca41 are obtained. From the fitting, we infer that including the isoscalar–isovector meson self-coupling can give a better performance of the RMF calculation.

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.

Precise Measurement of the Neutron Magnetic Form FactorGMnin the Few-GeV2Region

The neutron elastic magnetic form factor GMn has been extracted from quasielastic electron scattering data on deuterium with the CEBAF Large Acceptance Spectrometer (CLAS) at Jefferson Lab. The kinematic coverage of the measurement is continuous from Q2=1 GeV2 to 4.8 GeV2. High precision was achieved by employing a ratio technique in which many uncertainties cancel, and by a simultaneous in-situ calibration of the neutron detection efficiency, the largest correction to the data. Neutrons were detected using the CLAS electromagnetic calorimeters and the time-of-flight scintillators. Data were taken at two different electron beam energies, allowing up to four semi-independent measurements of GMn to be made at each value of Q2. The dipole parameterization is found to provide a good description of the data over the measured Q2 range.

Elastic magnetic form factors of exotic nuclei

How to identify the orbital of the valence nucleon(s) of exotic nuclei is an important problem. The elastic magnetic electron scattering is an excellent probe to determine the valence structure of odd-$A$ nuclei. The relativistic mean-field theory has been successfully applied to systematic studies of the elastic charge electron scattering from even-even exotic nuclei. The extension of this method to investigate the elastic magnetic electron scattering from odd-$A$ exotic nuclei is a natural generalization. The experimental form factors of $^{17}\mathrm{O}$ and $^{41}\mathrm{Ca}$ are reproduced very well with the help of the spectroscopic factors which are introduced into the relativistic treatment of the magnetic electron scattering for the first time. The emphases are put on the magnetic form factors of $^{15,17,19}\mathrm{C}$, $^{23}\mathrm{O}$, $^{17}\mathrm{F}$, and $^{49,59}\mathrm{Ca}$ calculated in the relativistic impulse approximation. Great differences have been found in the form factors of the same nucleus with different configurations. Therefore, the elastic magnetic electron scattering can be used to determine the orbital of the last nucleon of odd-$A$ exotic nuclei. Our results can provide references for the electron scattering from exotic nuclei in the near future.

Precise Determination of the Neutron Magnetic Form Factor to Higher [formula omitted

The neutron elastic magnetic form factor G M n has been extracted from quasielastic scattering from deuterium in the CEBAF Large Acceptance Spectrometer, CLAS [B. Mecking et al., Nucl. Inst. and Meth. A 503 (2003) 513]. The kinematic coverage of the measurement is continuous over a broad range, extending from below 1 GeV 2 to nearly 5 GeV 2 in four-momentum transfer squared. High precision is achieved by employing a ratio technique in which most uncertainties cancel, and by a simultaneous in-situ calibration of the neutron detection efficiency, the largest correction to the data. Preliminary results are shown with statistical errors only.

New empirical fits to the proton electromagnetic form factors

Recent measurements of the ratio of the elastic electromagnetic form factors of the proton, ${G}_{\mathrm{Ep}}{/G}_{\mathrm{Mp}},$ using the polarization transfer technique at Jefferson Lab, show that this ratio decreases dramatically with increasing ${Q}^{2},$ in contradiction to previous measurements using the Rosenbluth separation technique. Using these new high quality data as a constraint, we have reanalyzed most of the world $\mathrm{ep}$ elastic cross section data. In this paper, we present a new empirical fit to the reanalyzed data for the proton elastic magnetic form factor in the region $0<{Q}^{2}<30 {\mathrm{GeV}}^{2}.$ As well, we present an empirical fit to the proton electromagnetic form factor ratio, ${G}_{\mathrm{Ep}}{/G}_{\mathrm{Mp}},$ which is valid in the region $0.1<{Q}^{2}<6 {\mathrm{GeV}}^{2}.$

Measurement of the elastic magnetic form factor of (3)He at high momentum transfer.

New electron scattering measurements have been made that extend data on the (3)He elastic magnetic form factor up to Q(2) = 42.6 fm(-2). These new data test theoretical conjectures regarding non-nucleonic effects in the three-body system. The very small cross sections, as low as 10(-40) cm(2)/sr, required the use of a high-pressure cryogenic gas target and a detector system with excellent background rejection capability. No existing theoretical calculation satisfactorily accounts for all the available data.

Neutron detection efficiency for the measurement of the 2H(e,′en) 1H cross section

We report a measurement of the neutron detection efficiency for an array of neutron detectors behind a lead-steel wall consisting of 10.16 cm thick lead bricks sandwiched between 3.18 cm steel plates. The neutron detection efficiency ε was obtained from the ratio of coincidence to single-arm proton cross sections using the γ + 2 1H → p + n reaction. Knowledge of the neutron detection efficiency was necessary to extract the cross section for the exclusive 2H(e,′e n) 1H reaction, which we used to obtain the elastic magnetic form factor G M n of the neutron. The measurements for three different neutron energies were carried out at the MIT-Bates Linear Accelerator Center with an incident electron beam energy of 254 MeV.

Neutron scattering studies of mixed-valence semiconductors

Neutron scattering experiments on the mixed-valence (MV) compounds SmB 6 and TmSe are reported. The inelastic magnetic response of SmB 6 at T = 2 K, measured on a double-isotope single crystal, displays a strongly damped peak at 35 meV corresponding to the intermultiplet transition of Sm 2+. At lower energies ( h ̵ ω ≈ 14 meV ), a narrow magnetic excitation is observed, with remarkable scattering-vector and temperature dependences of its intensity. This novel feature is discussed in terms of recent theoretical works describing the formation of an anisotropic local bound state in semiconducting MV materials. If the average samarium valence is decreased by substituting La for Sm, a peak is found to appear at higher energies. The elastic magnetic form factor of SmB 6 was determined using polarised neutrons and no significant difference is observed in its Q-dependence with respect to that of pure divalent samarium. This surprising behaviour is consistent with previous measurements on the gold (high-pressure) phase of SmS. The above results are compared with those already reported for other MV materials. In particular existing information for TmSe is supplemented by recent inelastic scattering measurements carried out on a large single crystal.

Core polarization effects on the magnetic form factors of15N and17O

The effects of the first- and the second-order core polarization on the elastic magnetic form factors of15N and17O are investigated using the perturbation theory based on the harmonic-oscillator shell model, in which for the matrix elements of the two-nucleon interaction the Sussex matrix elements are employed. The core polarization reduces the single-particle value ofM3 part of the form factor of17O, however the reduction of the form factor of15N does not lead to an improved agreement with experiment.

The magnetic moments and form factors of 17O and 41Ca

The elastic magnetic form factors of 17O and 41Ca are calculated by including both the 2ℏω particle-hole excitations and the Zuker-type multi-particle-multi-hole configuration mixing. For both nuclei, a substantial suppression of the magnetic form factors in the momentum-transfer range 0.5–1.5 fm −1 is obtained. It is noted that for 17O, although the Zuker-type calculation does help to explain the M3 suppression, it also results in a magnetic moment that has too small a magnitude compared to the experimental value. For 41Ca, however, both the calculated magnetic moment and the form factor are in reasonable agreement with experiment.

Wave function effects and the elastic magnetic form factor of 17O.

We determine the parameters of an algebraic radial wave function (a solution of the Ginocchio potential) corresponding to the ${\mathit{d}}_{5/2}$ valence neutron orbital of $^{17}\mathrm{O}$ by making a fit to the high ${\mathit{q}}^{2}$ magnetic electron scattering data. The wave function so determined is similar to other finite well wave functions also fitted to these data. It has, however, an rms radius about 6--10 % larger than the corresponding Woods-Saxon wave functions. We suggest from this result that (i) the determination of rms radii of valence nucleon radial wave functions from magnetic electron scattering is more model dependent than previously realized, and (ii) the Okamoto-Nolen-Schiffer anomaly in A=17 may be underestimated by previous calculations with finite wells.

Quark exchange currents in nuclei: Effective operator description

In this paper we introduce for the first time effective quark exchange current operators which can be used in nuclear structure calculations. To this end we first solve the equation of motion for a microscopic quark hamiltonian using the quark cluster model. We then construct the electromagnetic current operator on the quark level, i.e. the photon is coupled directly to the quarks. By eliminating the quark (internal) degrees of freedom, we derive an effective electromagnetic current operator on the nucleon level. A part of this effective current corresponds to the conventional impulse and meson exchange currents with vertex factors predicted by the quark model. In addition, this effective current contains new non-local and isospin-dependent terms which are generated by the Pauli principle on the quark level (quark exchange between nucleons). When we evaluate these quark exchange currents, we use harmonic-oscillator wave functions as nuclear wave functions including short-range correlations. We introduce these short-range correlations by solving the Bethe-Goldstone equation with our effective NN potential, which is derived from a microscopic quark hamiltonian. We investigate the role of these additional quark exchange currents in the magnetic moments and the elastic magnetic form factors of several closed-shell ± 1 nuclei, such as 15N, 17O, and 39K.

Elastic magnetic electron scattering from 41Ca.

The elastic magnetic form factor of $^{41}\mathrm{Ca}$ has been determined by 180\ifmmode^\circ\else\textdegree\fi{} electron scattering in the momentum-transfer range 0.9--2.0 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$. An analysis of the data indicates that the amplitudes of the M3 and M5 multipoles are quenched by factors of 0.57\ifmmode\pm\else\textpm\fi{}0.16 and 0.68\ifmmode\pm\else\textpm\fi{}0.07 relative to the simple shell model. In contrast, the magnitude of the M7 form factor is in good accord with this model. Calculations that include multiparticle-multihole configurations in the 1${\mathit{f}}_{7/2}$ and 1${\mathit{d}}_{3/2}$ subshells, first-order core polarization to higher excited orbitals, and meson exchange currents give reasonable agreement with the data for all multipoles. The rms radius of the 1${\mathit{f}}_{7/2}$ neutron orbit was determined by means of a combined analysis of our results and previous data obtained at higher momentum transfers. After correcting for core polarization and meson exchange currents, the radius was found to be 3.96\ifmmode\pm\else\textpm\fi{}0.05 fm, in agreement with the predictions of mean-field calculations.

Elastic and inelastic magnetic form factors of deuteron in the model of orthogonal coupled channels

The model of orthogonal coupled channels is carried out for theNN interaction and the description of electromagnetic processes in two-nucleon system. Both the adequate reflection of the six-quark dynamics in the region of nucleon overlap and mesonic physics at middle and long ranges is attained in the given model. The processes of elastic and inelastic magnetic scattering of electrons on deuteron are investigated and compared with traditional description on the basis of the potentials with a repulsive core.

Relativistic effects in the elastic magnetic form factor of 17O

We study the elastic magnetic form factor of 17O in a relativistic direct-interaction-based impulse approximation model. The scheme used emphasizes consistency in the determination of current operators and nuclear wave functions. The results are compared with recent high-q data and with previous non-relativistic and relativistic calculations.

A deformed model approach to elastic magnetic scattering from 29Si

The elastic magnetic form factor of 29Si is calculated using the deformed model. Agreement is found with the experimental data for the M1 form factor and static moment using Nilsson wave functions with a deformation parameter δ ⋍ −0.2. An analysis of the dependence on deformation of the magnetic form factor which applies to many odd-nucleon Nilsson orbitals is presented.

Magnetic structure of 17O at high momentum.

The elastic magnetic form factor of $^{17}\mathrm{O}$ has been measured for effective momentum transfers 2.47\ensuremath{\le}${\mathrm{q}}_{\mathrm{eff}}$\ensuremath{\le}3.65 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$ by electron scattering. The form factor drops by almost three decades in this range. The data follow an extreme single-particle Woods-Saxon shell-model calculation. Many-body effects such as meson-exchange currents or core polarization do not seem to play a significant role in the q range of this experiment.

Deuteron properties of the coupled nucleon and isobar channels model.

The system of NN, N\ensuremath{\Delta}, \ensuremath{\Delta}\ensuremath{\Delta}, and ${\mathrm{NN}}^{\mathrm{*}}$(1440) channels, coupled by long-range meson exchange forces and a short-range boundary condition, has been successfully applied to medium energy NN scattering. The deuteron system includes the NN${(}^{3}$${\mathit{S}}_{1}$, $^{3}$${\mathit{D}}_{1}$), \ensuremath{\Delta}\ensuremath{\Delta}${(}^{3}$${\mathit{S}}_{1}$, $^{3}$${\mathit{D}}_{1}$, $^{7}$${\mathit{D}}_{1}$), and NN*${(}^{3}$${\mathit{S}}_{1}$) channels. The scattering data for nucleon ${T}_{\mathrm{lab}l1}$ GeV put strong restrictions on the short-range parameters of the model, imposing \ensuremath{\sim}2% total isobar content in the deuteron, but do not determine the relative strength of coupling among the isobar channels. In contrast, the deuteron elastic magnetic form factor is sensitive to the mixture of isobars. Adding meson exchange current contributions, a good fit to these data can be achieved, including a nontrivial prediction of a minimum near ${q}^{2}$=50 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}2}$, by a balance between \ensuremath{\Delta}\ensuremath{\Delta}${(\mathrm{}}^{3}$${D}_{1}$,${\mathrm{}}^{7}$${D}_{1}$) components. Balancing \ensuremath{\Delta}\ensuremath{\Delta}${(\mathrm{}}^{3}$${S}_{1}$,${\mathrm{}}^{7}$${D}_{1}$) with ${\mathrm{NN}}^{\mathrm{*}}$${(\mathrm{}}^{3}$${\mathrm{S}}_{1}$), assuming a negative ${\mathrm{N}}^{\mathrm{*}}$ isoscalar magnetic moment, is only adequate for ${q}^{2}$25 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}2}$. The static properties of the deuteron are well fitted, and the electric and tensor polarization form factors are consistent with the data. The inclusion of the lowest six-quark state, with cloudy bag model dynamics, increases the boundary radius, requiring \ensuremath{\sim}7% isobar content proportioned as above to approximately fit the data.