Determination of nuclear parameters by inelastic electron scattering at low-momentum transfer

The second-order Born-approximation treatment of Cutler and Schucan was applied to inelastic electron scattering data on ⁶Li, ⁶⁰Ni, and ¹¹⁴Cd acquired at low momentum transfers. The form factors as a function of momentum transfer q in the range of 0.25–0.57 fm^?1 were obtained by angular distribution measurements performed at incident energies of 30 to 60 MeV. The correlation between two parameters deduced from the measurements, the reduced transition probability B(E2↑) and the transition radius R⁽²⁾_tr, is discussed. It is suggested that inelastic electron scattering data at low-q is best used either in conjunction with an accurate value of B(EL↑) (available from the model-independent analysis of “photon” experiments at zero momentum transfer) to allow accurate determination of R⁽²⁾_tr, or in conjunction with high-q inelastic electron scattering data to allow accurate determination of B(EL↑) as well as R⁽²⁾_tr.     

On the scale dependence of the dimension of hadronic matter

We advance the notion of a dynamical, scale-dependent Hausdorff dimension for hadronic matter. The physical motivations behind such a concept are explained. For very small scales, we relate this dimension to the anomalous dimension of the product of two momentum densities. For hadrons, we rely on the precocious onset of Bjorken scaling in e-p inelastic scattering and a heuristic parton model to obtain the Hausdorff dimensional profile for the proton d(q²) as a function of the probing photon momentum q². We find that d reaches a maximum around d = 1 for a range of low q² values. This feature is indicative of a string-like structure of the hadrons at low momentum transfers.     

Shadowing effect in inelastic electron scattering on12C and27Al nuclei at small four momentum transfer

The cross section for inelastic electron scattering on¹²C and²⁷Al has been measured for energy transfers of the virtual photon ν<6.2 GeV and four momentum transfers 0.075<Q ²<1 GeV². The influence of different sources of the radiative corrections is studied in detail. Shadowing effects are observed for both nuclei, which decrease with increasing values of the scaling variablex.     

Comparison of inelastic electron and positron scattering cross sections on 12C and 27Al

The ratio R = σ⁺/σ^? of the cross sections for inelastic and electron scattering on ¹²C and ²⁷Al has been measured for four momentum transfers 0.08 (GeV/c)² ?q² ?0.45 (GeV/c)² of the virtual photon and invariant masses 0.95 GeV ? W ? 3.3GeV of the hadronic system. The mean value of the ratio is R = (1.005 ± 0.027). No q², respectively, W dependence of the ratio is observed.     

The tensor force in heavy nuclei: High momentum collectivity of unnatural parity excitations

The possibility of collectivity at high momentum transfer in unnatural parity states in finite nuclei, is outlined. This phenomenon is produced by the strong tensor force in the one pion exchange interaction operating coherently in a large oscillator space. The collectivity is observed at momentaq～(2-3)m _π corresponding to the critical momentum of pion condensation. If existent, such collective behaviour is expected to be seen in differential cross sections, e.g. for proton inelastic scattering, leading to unnatural parity states.     

Investigation of the narrow structure K(1630) decaying into the K S 0 π+π− system

The narrow structure K(1630) is singled out in the effective-mass spectrum of the K _S ⁰ π⁺π^? system originating from π^? p collisions at 16 GeV/c. This structure is predominantly formed in inelastic collisions accompanied by high momentum transfers. For events from the K(1630) region, kinematical distributions show special features that may be associated with spin manifestations and with correlations between the products arising from the decays of the hypothesized exotic resonance state. Experimental observations of narrow hadronic structures formed at high momentum transfers are reviewed.     

Importance of longitudinal contributions to backward inelastic electron scattering

Coulomb contributions of multipolarity 2 are calculated for backward (θ = 180°) inelastic electron scattering by our improved DWBA code. General features are studied such as nuclear charge (Z) dependence, energy transfer dependence, momentum transfer dependence as well as the angle dependence near θ = 180°, with the help of a simple model for the transition charge density. We compare these features with PWBA and other simple approximations. We show, as a specific example, that the C2 contribution is comparable to the M1 and E2 multipole form factors for inelastic scattering to the rotational excited states of ¹⁸¹Ta.     

Electron scattering studies of magnetic isovector transitions in 12C at high momentum transfer

The inelastic electron scattering cross sections for the M1 transition to the 15.11 MeV (1⁺, T = 1) level and for the M2 transition to the 16.58 MeV (2^?, T = 1) level in ¹²C have been measured in the momentum transfer region q = 0.4–3.0 fm^?1, with emphasis on precise data at high momentum transfers. Additionally, a broad state near 15.4 MeV excitation has been observed and its excitation energy and natural width have been established as 15.44 ± 0.04 MeV and 1.5 ± 0.2 MeV, respectively. The Fourier-Bessel technique for determining the Mλ transition current density has been applied to the M1 and M2 transitions. Particular attention has been paid to the Coulomb corrections required to deduce the PWBA form factors. The M1 radiative width is Γ_γ0 = 38.5 ± 0.8 eV.     

Nuclear and Coulomb deformation parameters of 142Nd

Nuclear and Coulomb deformation parameters have been deduced from DWBA analyses of angular distributions of 67.5 MeV ¹³C ions inelastically scattered from ¹⁴²Nd. Optical model parameters from fits of measured elastic scattering data were used with previously measured B(EL) values to determine initial deformation parameters. Comparison With the experimental data indicates that DWBA calculations can be used to understand the inelastic scattering from the nearly spherical nucleus ¹⁴²Nd.     

Ionization of Rydberg atoms by the kicks of half-cycle pulses

We present a quantum mechanical model to study the ionization of quasione-dimensional Rydberg atoms interacting with half-cycle pulses (HCPs) and use it to demonstrate the inadequacy of semiclassical approaches to calculate ionization probabilities of such atoms subject to the impact of more than one HCP. For a single-kicked atom both models correctly reproduce the experimentally observed ‘s-curve’ as can be seen by plotting the ionization probability P as a function of momentum transfer q₁. We demonstrate that for a twice-kicked atom, the semiclassical model yields numbers for P which are not physically realizable. For fixed values of momentum transfers q₁ and q₂, in a twice-kicked atom, the ionization probability as a function of time delay between the kicks exhibits periodic decay and revival. The results of the semiclassical approach appear to agree with the quantum mechanical values at the times of revival of P, else these show considerable deviation. We attempt to provide a physical explanation for the limitation of the semiclassical approach.     

Analytic proton-nucleus scattering amplitudes

Analytic expressions for the elastic nucleon-nucleus amplitudes F(q) and G(q) are derived. They are based on analytic approximations of the nuclear profile functions in the Glauber formulation. Our amplitudes are sums of terms with a familiar structure, black-sphere Bessel functions multiplied by form factors accounting for the diffuseness of the nuclear surface. Their accuracy is tested with the Woods-Saxon density and found to be excellent for momentum transfers q? 5fm^?1.     

The 4He condensate: Experiment and theory reconciled

The extremely small values of the condensate fraction in superfluid ⁴He II (of order 1% or less), obtained from inelastic neutron scattering experiments involving large momentum transfers are shown to be consistent with the calculated zero temperature values (of order 10%).     

Higher-q Quasi-elastic 3He Transverse (e,e��) Response in a Two-Fragment Model

Recently (Efros et?al. in Phys Rev C81:034001, 2010) we have computed the ³He transverse response in the quasielastic region for momentum transfers up to 700?MeV/c using the AV18 potential with the UrbanaIX three body potential. These calculations were carried out in the active nucleon Breit (ANB) frame. Owing to the use of the ANB frame the disagreement of the conventional non-relativistic calculations with experiment has been removed for q values up to 500?MeV/c. However, for higher q values some disagreement still persists. In order to further study the issue we present here results for R _T (q, ??) computed in the Breit and Lab frames with the use of the two-fragment model.     

The dependence of proton correlations on integral characteristics of eA interactions

We report the results of analysis of correlations of the product protons from inelastic eA collisions at smallQ ². The experimental data were measured by the ARGUS detector. The correlation effect at small relative momentaq (interference and final state interaction) is closely associated with the angular correlations due to momentum conservation. The examined correlations in eA collisions also show features similar to correlations in hA collisions.     

Transition charge densities of low-lying collective states in even Zn isotopes

The inelastic electron scattering cross sections for the quadrupole transitions to the 2₁⁺ and 2₂⁺ states in the even Zn isotopes ⁶⁴Zn, ⁶⁶Zn and ⁶⁸Zn and for the hexadecapole transition to the 4⁺₁ state in ⁶⁴Zn have been measured in a momentum transfer range up to q = 2.2 fm^?1. In the frame-work of the vibrational model these states are considered as one- and two-quadrupole-phonon states. The measurements are characterized by high statistical accuracy and by an overall resolution of δE/E₀ = 10^?3 which permitted separation of almost all members of the two-phonon triplet. The measured cross sections are analyzed with phenomenological models as well as with a Fourier-Bessel expansion of the transition charge density. The latter analysis yields realistic error bands for the transition charge densities and model-independent values for the reduced transition probabilities and transition radii.     

Probing lepton and quark substructure in polarized e∓N scattering

If leptons and quarks are composite objects their non-elementary nature would emerge clearly from deep inelastic scattering at momentum transfers of the order of the compositeness scale Λ_H. On the other hand, residual lepton-quark interactions induced by the new binding force would indicate the existence of a further layer of substructure already at considerably smaller momentum transfers. The effects of such non-standard interactions on various cross sections and asymmetries in polarized e^?N scattering are studied in detail. It is shown that, if Λ_H < 5 TeV, one should encounter rather striking deviations from the standard model expectations in the Q²-range accessible at future ep colliders like HERA.     

Magnetic sub-state population cross sections in inelastic alpha-nucleus scattering

Properties of the sub-state population cross sections σ_M for inelastic α-nucleus scattering are explored within the deformed collective nuclear model. The interference between the nuclear and Coulomb parts of the inelastic transition potential is calculated with the DWBA. The effect on the M = ?2 sub-state cross section is substantially more pronounced than that for the usual inelastic differential cross section Σ_mσ_m. The effect of re-orientation terms is calculated by means of a coupled channel formalism for small values of the quadrupole deformation parameter β₂. It is found to shift the angular position of the minima of the σ_M relative to the DWBA result, in a way which depends on the sign of β₂. A spin orbit potential has only a small effect on the σ_M. The calculations refer to 15 MeV α-particles incident on a nucleus of the size and charge of Ca.     

Unelastische Elektronenstreuung am4He bei kleinem Impulsübertrag

Using a liquid helium target, inelastic electron scattering from⁴He was investigated at momentum transfers below 0.5 fm^?1 with improved resolution. The assignment 0⁺ for the state at (20.10±0.05) MeV (measured excitation energy) has been confirmed, and new values for the monopole matrix element (1.10±0.16) fm² and the total width (270±50) keV were derived. The giant resonance region shows evidence for theM2-resonance at 24 MeV.     

Spin observables for 208Pb(→p, →p) elastic scattering at 290 MeV

A newly constructed focal-plane polarimeter for the medium resolution spectrometer at TRIUMF has been used to measure polarizations and polarization transfer coefficients for protons elastically scattered from ²⁰⁸Pb at 290 MeV. These results combined with existing cross section data at 300 MeV completely determine the elastic scattering amplitudes for momentum transfers q<2.6 fm⁻¹. The data are in quantitative agreement with Dirac calculations which take the effects of Pauli blocking into account, but disagree at small momentum transfer with density-dependent Schrödinger calculations.     

A neutron spin-echo study of the dynamics of star-shaped polymers (with polystyrene arms grafted to C60) in solutions and in the bulk

Methods of small-angle and inelastic neutron scattering were used to study star-shaped polymers obtained by grafting polystyrene to fullerene C₆₀ (six arms with an elementary mass M=5×10³). The behavior of stars in the solution and bulk was compared with the dynamics of free molecules of polystyrene with a mass equal to the mass of an arm. The slow dynamics of arms in the ranges of times t=0.01–20 ns, momentum transfers q=0.2–0.6 nm^?1, and temperatures T=20–60°C does not obey the simple models of Rouse and Zimm. The interaction of the rays with the C₆₀ fullerene under the conditions of the specific geometry of the macromolecule leads to unusual oscillations of time correlations in the arms of stars.