Inelastic Form Factors Research Articles

Vector and axial nucleon form factors: A duality constrained parameterization

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.

QUARTETTING IN ATTRACTIVE FERMI-SYSTEMS AND ALPHA PARTICLE CONDENSATION IN NUCLEAR SYSTEMS

The famous Hoyle state (02+ at 7.654 MeV in 12 C ) is identified as being an almost ideal condensate of three α-particles, hold together only by the Coulomb barrier. It, therefore, has a 8 Be -α structure of low density. Transition probability and inelastic form factor together with position and other physical quantities are correctly reproduced without any adjustable parameter from our two parameter wave function of α-particle condensate type. The possibility of the existence of α-particle condensed states in heavier nα nuclei is also discussed.

α-Particle Condensation in Nuclear Systems

The fameous Hoyle state ( 0 2 + at 7.654 MeV in 12C) is identified as being an almost ideal condensate of three α-particles, hold together only by the Coulomb barrier. It, therefore, has a 8Be-α structure of low density. Transition probability and inelastic form factor together with position and other physical quantities are correctly reproduced without any adjustable parameter from our two parameter wave function of α-particle condensate type. The possibility of the existence of α-particle condensed states in heavier nα nuclei is also discussed.

Alpha Condensed State in 16O

It is discussed that the recently observed 0+ state at 13.5 MeV in 16 O can be a good candidate of the 4α condensate. The 4α condensed state which is theoretically obtained in the vicinity of the 4α threshold is shown to have a relatively large α decay width, which is in well agreement with the value measured for the 0+ state at 13.5 MeV. The analysis of inelastic form factor of electron scattering to the 4α condensed state is made by artificially varying the size of the 4α condensate. Similarly to the case of Hoyle state, only the magnitude of the form factor is found to depend on its size, while the position of maximum and minimum are not changed.

Alpha-particle condensation in nuclei: Experimental problems

Recently, it was supposed the nα light nuclei may have structures resembling the diluted gas of α particles which could be considered as Bose-Einstein condensate (αBEC) in nuclear systems. At the present time, the only more or less definite candidate for an αBEC state predicted by theory is the second 0+ state of 12C (E = 7.65 MeV) located near the threshold 12C → 3α. We discuss several possible experimental approaches to study the properties of interest of the 7.65-MeV level of 12C. Among them are shift of the positions of the rainbow minima in the inelastic scattering to this level, extraction of the empirical inelastic form factor from the α and 3He scattering and its comparison with theoretical predictions, and getting information on the 8Be transfer reaction form factor. The conclusion was drawn that new measurements of 12C(α, α′) 12C(7.65) inelastic scattering at ∼120 MeV in the full angular range would be most adequate to solving the problem. The possibility of observation of αBEC effects in heavier nα nuclei is also discussed. In particular, 112Ba is of great interest owing to possible existence of an α-particle “halo” outside the Z = N = 50 core.

Folding model analysis of proton scattering from [formula omitted] nuclei

The elastic and inelastic proton scattering on O 18 , 20 , 22 nuclei are studied in a folding model formalism of nucleon–nucleus optical potential and inelastic form factor. The DDM3Y effective interaction is used and the ground state densities are obtained in continuum Skyrme-HFB approach. A semi-microscopic approach of collective form factors is done to extract the deformation parameters from inelastic scattering analysis while the microscopic approach uses the continuum QRPA form factors. Implications of the values of the deformation parameters, neutron and proton transition moments for the nuclei are discussed. The p-analyzing powers on O 18 , 20 , 22 nuclei are also predicted in the same framework.

Inelastic form factors to alpha-particle condensate states in 12C and 16O: What can we learn?

In order to discuss the spatial extention of the 02 +-state of 12C (Hoyle state), we analyze the inelastic form factor of electron scattering to the Hoyle state, which our 3α-condensate wave function reproduces very well like previous 3α RGM/GCM models. The analysis is made by varying the size of the Hoyle state artificially. As a result, we find that only the maximum value of the form factor sensitively depends on its size, while the positions of maximum and minimum are almost unchanged. This size dependence is found to come from a characteristic feature of the transition density from the ground state to the Hoyle state. We further show the theoretical predictions of the inelastic form factor to the 22 +-state of 12C, which was recently observed above the Hoyle state, and of the inelastic form factor to the calculated 03 +-state of 16O, which was conjectured to correspond to the 4α condensed state in previous theoretical work by the present authors.

Study of refractive structure in the inelastic [formula omitted] scattering at the incident energies of 250 to 1120 MeV

The data of inelastic O 16 + O 16 scattering to the lowest 2 + and 3 − excited states of O 16 have been measured at E lab = 250 , 350 , 480 , 704 and 1120 MeV and analyzed consistently in the distorted wave Born approximation (DWBA), using the semi-microscopic optical potentials and inelastic form factors given by the folding model, to reveal possible refractive structure of the nuclear rainbow that was identified earlier in the elastic O 16 + O 16 scattering channel at the same energies. Given the known transition strengths of the 2 1 + and 3 1 − states of O 16 well determined from the ( e , e ′ ) data, the DWBA description of the inelastic data over the whole angular range was possible only if the absorption in the exit channels is significantly increased (especially, for the O 16 + O 2 + ∗ 16 exit channel). Although the refractive pattern of the inelastic O 16 + O 16 scattering was found to be less pronounced compared to that observed in the elastic scattering channel, a clear remnant of the main rainbow maximum could still be seen in the inelastic cross section at E lab = 350 – 704 MeV .

Inelastic processes in the interaction of an atom with an ultrashort electromagnetic pulse

Electron transitions occurring during the interaction of a heavy relativistic atom with a spatially inhomogeneous ultrashort electromagnetic pulse are considered by solving the Dirac equation. The corresponding transition probabilities are expressed in terms of known inelastic atomic form factors, which are widely used in the theory of relativistic collisions between charged particles and atoms. By way of example, the inelastic processes accompanying the interaction of ultrashort pulses with hydrogen-like atoms are considered. The probabilities of ionization and production of a bound-free electron-positron pair on a bare nucleus, which are accompanied by the formation of a hydrogen-like atom in the final state and a positron in the continuum, are calculated. The developed technique makes it possible to take into account exactly not only the spatial inhomogeneity of an ultrashort electromagnetic pulse, but also the magnetic interaction.

Sudden-perturbation approximation for the dirac equation

We solve the Dirac equation describing the behavior of a hydrogen-like atom interacting with a spatially inhomogeneous ultrashort electromagnetic field pulse in the sudden-perturbation approximation. We express the corresponding transition probabilities through the known inelastic atomic form factors widely used in the theory of relativistic collisions of charged particles with atoms.

Double-logarithmic behavior of inelastic fermion form factors in QED and QCD

The effective kinematic diagram technique is applied to study inelastic form factors of electron and quark in QED and QCD. The explicit expressions for these form factors in the double-logarithmic approximation are presented. The self-consistency of the results is shown by demonstrating the fulfillment of the Kinoshita–Lee–Nauenberg theorem.

THE ROLE OF LINEAR ALPHA-CLUSTER CONFIGURATION FOR 12C

In the framework of the Alpha Cluster Model extended calculations of form factors of elastic and inelastic [Formula: see text] and [Formula: see text] (7.66 MeV) electron scattering on 12C were performed. Two possible alpha cluster configurations (linear and triangular) were considered for states assigned to different rotational bands and although the configuration mixture was found to be important for explanation of the inelastic monopole form factor, a fully consistent picture, including all available data, was not obtained.

Folding model analysis of elastic and inelastic proton scattering on sulfur isotopes

The folding formalism for the nucleon–nucleus optical potential and inelastic form factor is applied to study elastic and inelastic proton scattering on 30–40S isotopes. A recently developed realistic density dependent M3Y interaction, well tested in the folding analysis of nucleus–nucleus elastic and inelastic scattering, is used as effective NN interaction. The nuclear ground state and transition densities (for the 2 + excitations in sulfur isotopes) are obtained in the Hartree–Fock-BCS and QRPA approaches, respectively. The best fit ratios of transition moments M n 2 + / M p 2 + for the lowest 2 + states in sulfur isotopes are compared to those obtained earlier in the DWBA analysis of the same data using the same structure model and inelastic form factors obtained with the JLM effective interaction. Our folding + DWBA analysis has shown quite a strong isovector mixing in the elastic and inelastic scattering channels for the neutron rich 38,40S nuclei. In particular, the relative strength of the isovector part of the transition potential required by the inelastic p+ 38 S data is significantly stronger than that obtained with the corresponding QRPA transition density.

Isovector Mixing in Inelastic Scattering Induced by the Radioactive Beams

The folding model for the nucleon-nucleus inelastic form factor is applied to study inelastic scattering of 1 8 , 2 0 O isotopes on proton target. A realistic density dependent M3Y interaction, well tested in the folding analysis of nucleus-nucleus scattering, is used as effective NN interaction. The nuclear ground state and transition densities (for the low-lying 2 + and 3- states in the oxygen isotopes) are obtained in the Hartree-Fock-BCS and generalized Bohr-Mottelson approach, respectively. Strong isovector mixing has been observed in the 2 + inelastic channel of the 2 0 O+p system. The isovector strength of the form factor, implied by the inelastic 2 0 O+p data at 43A MeV, gives a ratio of transition moments M n 2 + /M p 2 + ≃ 4.3 for the lowest 2 + excitation in 2 0 O.

Inelastic neutron scattering measurements and Ab initio calculations of hydrogen in single-crystal palladium

Using a single-crystal sample of PdH, we have measured the inelastic form factor for exciting the proton from its ground state to various excited states as a function of crystal orientation. Because of the anharmonicity of the potential well which splits otherwise degenerate states, each inelastic form factor could be measured individually. Agreement between theory and experiment is excellent, both with regard to the transition energies and to the modulation of the intensity, giving confidence in the quantum treatment of the proton and hence in the use of the model to predict other properties of the system.

Structure and dynamics of few-nucleon systems

Few-nucleon physics is a field rich with high-quality experimental data and possibilities for accurate calculations of strongly correlated quantum systems. In this article the authors discuss the traditional model of the nucleus as a system of interacting nucleons and outline many recent experimental results and theoretical developments in the field of few-nucleon physics. The authors describe nuclear structure and spectra, clustering and correlations, elastic and inelastic electromagnetic form factors, low-energy electroweak reactions, and nuclear scattering and response in the quasielastic regime. Through a review of the rich body of experimental data and a variety of theoretical developments, a coherent description of the nuclear strong- and electroweak-interaction properties emerges. In this article, the authors attempt to provide some insight into the practice and possibilities in few-nucleon physics today.

Electromagnetic effects in light nuclei and the cluster potential model

Photodisintegration and radiative capture in the N 2 H , N 3 H , N 3 He , 2 H 2 H , 2 H 3 He , 2 H 4 He , 3 He 3 H , 4 He 3 H , and 4 He 3 He channels are studied on the basis of the corresponding two-cluster potential models. The astrophysical S factors at low energies are calculated. It is shown that various electromagneticcharacteristics of light nuclei, including the Coulomb form factors at momenta of up to 4 F −1 , can be studied using a single set of intercluster interactions containing forbidden states and consistent with the phase shifts of the cluster low-energy elastic scattering. The calculated inelastic form factors have a second maximum at 3–4 F −1 , although it is lower than the experimental one. The orbital states are classified for the lightest cluster systems, and the phase shifts and intercluster potentials are separated on the basis of Young orbital schemes.

Ionization in ion-atom collisions: off-shell and three-body effects

The recently developed channel-distorted 2-centre (D2C) approximation remains to be evaluated in exact form but two different approximation schemes that lead to computable forms have been identified. In one of these schemes the ionization amplitude is expressed as a product of three factors with distinct characteristics. The first term is the off-energy-shell amplitude for electron scattering in the field of the approaching ion and represents a pure projectile property. The second term is the inelastic form factor and represents a pure target property. The third term represents a residue of a renormalization factor due to long-range and off-shell aspects of the considered interactions and is manifestly of three-body character. The second scheme is more accurate than the first but less transparent from a physical point of view and restricted by additional conditions on the form of the channel potential. It is shown that final-state interaction and channel distortion are very essential elements of the theory and various characteristic features in the ionization spectrum are discussed. Finally, we identify the popular CDW-EIS theory as a special case of the D2C theory and solve an outstanding question about the applicability of the CDW formulation.

Role of nuclear couplings in the inelastic excitation of weakly bound neutron-rich nuclei

We study the breakup of weakly bound systems close to the neutron drip line in collisions with heavy-ions. The process is described in terms of inelastic excitations leading to states in the continuum. The nuclear and Coulomb multipole fields induced by the reaction partner are both included in the microscopic construction of the inelastic form factors. A fraction of the dissociation cross sections is triggered by the presence of resonances at high excitation energy. The largest probabilities for breakup result, however, from strongly coupled transitions to low-lying states in the continuum. Nuclear couplings associated with inelastic excitation to these states are found to extend to unusually large distances. As a consequence, the interplay of nuclear and Coulomb excitations differs from the ordinary situation encountered in heavy-ion inelastic processes involving systems close to the stability line.

Three-Body Calculations of A = 9 Nuclei with Supersymmetric α-α Potentials

The three-body α-α-N system is considered as a model for the 9Be and 9B nuclei. Two alternative models for the α-α interaction, which are approximate supersymmetric partners of each other, are tested. One model is a shallow agr;-α potential with l-dependent repulsive core, while the other one is a deep attractive potential with Pauli-forbidden states. All static observables have been calculated for the 9Be ground state together with its spectrum, elastic and inelastic (to the $${5^-\over 2}$$ state) longitudinal electromagnetic form factors and the Coulomb displacement for the 9B ground state. The shallow repulsive-core α-α potential turns out to provide an almost quantitative description of all these observables.