Experimental Scaling Function Research Articles

Nucleon momentum distribution extracted from the experimental scaling function

The connection between the scaling function, directly extracted from the analysis of electron scattering data, and the nuclear spectral function or nuclear momentum density is investigated at depth. The dependence of the scaling function on the two independent variables in the scattering process, the transfer momentum (q) and the scaling variable (y), is taken into account, and the analysis is extended to both, positive and negative y-values, i.e., below and above the center of the quasielastic peak, respectively. Analytical expressions for the derivatives of the scaling function, evaluated at the finite limits of integration dealing with the kinematically allowed region, are connected with the spectral function. Here, contributions corresponding to zero and finite excitation energies are included. The scaling function is described by the Gumbel density distribution, whereas short-range correlations are incorporated in the spectral function by using some simple models. Also different parameterizations for the nucleon momentum distribution, that are compatible with the general properties of the scaling function, have been considered.

Scaling ideas in neutrino scattering reactions: application to the MiniBooNE experiment

An exhaustive analysis of the world data on electron scattering has shown that scaling and superscaling properties are fulfilled with great accuracy. The relativistic impulse approximation (RIA) yields a satisfactory description of experimental data. Not only scaling and superscaling behavior emerge, but also the specific asymmetric shape of the experimental scaling function is reproduced. In this work two relativistic approaches are considered to evaluate the neutrino-nucleus cross sections. One, based on the relativistic impulse approximation, relies on the microscopic description of nuclear dynamics using relativistic mean field theory, and incorporates a description of final state interactions. The second is based on the superscaling behavior exhibited by electron scttering data and its applicability, due to the universal character of the scaling function, to the analysis of neutrino scattering reactions. The role played by the vector meson-exchange currents in the two-particle two-hole sector is also incorporated and the results obtained are compared with the recent data for neutrinos measured by the MiniBooNE Collaboration.

Scaling function, spectral function, and nucleon momentum distribution in nuclei

The link between the scaling function extracted from the analysis of $(e,{e}^{'})$ cross sections and the spectral function/momentum distribution in nuclei is revisited. Several descriptions of the spectral function based on the independent particle model are employed, together with the inclusion of nucleon correlations, and effects of the energy dependence arising from the width of the hole states are investigated. Although some of these approaches provide rough overall agreement with data, they are not found to be capable of reproducing one of the distinctive features of the experimental scaling function, namely its asymmetry. However, the addition of final-state interactions, incorporated in the present study using either relativistic mean-field theory or via a complex optical potential, does lead to asymmetric scaling functions in accordance with data. The present analysis seems to indicate that final-state interactions constitute an essential ingredient and are required to provide a proper description of the experimental scaling function.

Critical dynamics at the col point of the ternary system methanol- n-hexane-cyclohexane

The ternary system methanol- n-hexane-cyclohexane (MeOH-Hex-CH) has been investigated at the col point in order to look for indications of critical exponent renormalization. Ultrasonic spectroscopy, quasielastic light scattering, and shear viscosity measurement have been performed as a function of temperature and have been evaluated in terms of existing theories for binary critical systems. When compared to the results for the limiting binary mixtures MeOH-Hex and MeOH-CH it is found that, as a function of reduced temperature, both the fluctuation correlation length and the relaxation rate of fluctuations of the ternary mixture display power law behaviour with critical exponents as applying to binary systems near their consolute point. Also the experimental scaling function of the ultrasonic attenuation spectrum agrees well with the Bhattacharjee–Ferrell theory for binary mixtures. Hence with respect to power laws and scaling the MeOH-Hex-CH mixture at col point composition behaves like a quasibinary system. The individual parameters of the ternary system fit to the data for the systems MeOH-Hex and MeOH-CH.

Model for BCS-type correlations in superscaling

Using ideas from BCS descriptions of systems of fermions, a covariant extension of the relativistic Fermi gas model is presented as a way to incorporate correlation effects in nuclei. The model is developed for the BCS nuclear ground state and for final states consisting of a single plane-wave nucleon plus a BCS recoiling daughter nucleus. The nuclear spectral function is obtained, and from it the superscaling function for use in treating high-energy quasielastic electroweak processes. Interestingly, this model has the capability of yielding the asymmetric tail seen in the experimental scaling function.

Dynamic scaling and background relaxation in the ultrasonic spectra of the ethanol–dodecane critical mixture

Ultrasonic attenuation spectroscopy of a noncritical ethanol–dodecane mixture revealed a low frequency relaxation term. Considering this term in the spectra for the mixture of critical composition the experimental scaling function agrees well with the predictions of the dynamic scaling theory. Dynamic light scattering and shear viscosity measurements yield the amplitudes ξ 0 = (0.37 ± 0.02) nm and Γ 0 = (6.4 ± 0.3) × 10 9 s −1 for the fluctuation correlation length and relaxation rate of concentration fluctuations, respectively. The adiabatic coupling constant results as small as ∣ g∣ = 0.13 ± 0.03 from the ultrasonic spectra and as g = 0.094 ± 0.01 from the pressure dependence of the critical temperature and the thermal expansion coefficient.

General study of superscaling in quasielastic(e,e')and(ν,μ)reactions using the relativistic impulse approximation

The phenomenon of superscaling for quasielastic lepton induced reactions at energies of a few GeV is investigated within the framework of the relativistic impulse approximation. A global analysis of quasielastic inclusive electron and charged-current neutrino scattering reactions on nuclei is presented. Scaling and superscaling properties are shown to emerge from both types of processes. The crucial role played by final state interactions is evaluated by using different approaches. The asymmetric shape presented by the experimental scaling function, with a long tail in the region of positive values of the scaling variable, is reproduced when the interaction in the final state between the knockout nucleon and the residual nucleus is described within the relativistic mean field approach. The impact of gauge ambiguities and off-shell effects in the scaling function is also analyzed.

Critical Dynamics of the Binary System Nitroethane/3-Methylpentane: Relaxation Rate and Scaling Function

Shear viscosity and dynamic light scattering measurements as well as ultrasonic spectrometry studies of the nitroethane/3-methylpentane mixture of critical composition have been performed at various temperatures near the critical temperature, T(c). A combined evaluation of the shear viscosity and mutual diffusion coefficient data yielded the amplitude, xi(0), of the fluctuation correlation length, xi, assumed to follow power law, and the relaxation rate, Gamma, or order parameter fluctuations. The latter was found to follow power law with the theoretical universal exponent. The amplitudes xi(0) = 0.23 +/- 0.02 nm and Gamma(0) = (125 +/- 5) x 10(9) s(-1) nicely agree with literature values. Using the relaxation rates resulting from the viscosity and diffusion coefficient data, the scaling function has been calculated assuming the ultrasonic spectra to be composed of a critical part and a noncritical background contribution. The experimental scaling function fits well to the predictions of the Bhattacharjee-Ferrell dynamic scaling model with scaled half-attenuation frequency, Omega(BF)1/2= 2.1. The amplitude of the sonic spectra yields the amount |g| = 0.26 of the adiabatic coupling constant, g, in fair agreement with -0.29 from another thermodynamic relation.

Superscaling in Charged Current Neutrino Quasielastic Scattering in the Relativistic Impulse Approximation

Superscaling of the quasielastic cross section in charged-current neutrino-nucleus reactions at energies of a few GeV is investigated within the framework of the relativistic impulse approximation. Several approaches are used to describe final-state interactions and comparisons are made with the plane-wave approximation. Superscaling is very successful in all cases. The scaling function obtained using a relativistic mean field for the final states shows an asymmetric shape with a long tail extending towards positive values of the scaling variable, in excellent agreement with the behavior presented by the experimental scaling function.

Scaling function of the critical binary mixture methanol–cyclohexane

Acoustical attenuation spectra of the methanol–cyclohexane mixture of critical composition have been measured at different temperatures near the critical temperature. The noncritical background contribution of the spectra has been determined and subtracted from the total attenuation to yield the critical contribution. The latter enabled an accurate experimental determination of the scaling function. Regression analysis of the experimental scaling function data in terms of theoretical models yielded the relaxation rate of order parameter fluctuations as a function of temperature. Close agreement with relaxation rate data from other experimental methods has been found. The amplitude of the acoustical attenuation at the critical temperature has been discussed in terms of the adiabatic coupling constant. Its amount is likewise as small (|g|=0.14) as that of the alcohol–alkane system ethanol–dodecane (|g|=0.1).

Critical fluctuations in the domain structure of lipid membranes

Between 100 kHz and 2 GHz ultrasonic attenuation spectra of two aqueous solutions of vesicles from 1,2-dimyristoyl-L-3-phosphatidylcholine have been measured at 13 temperatures around the main phase transition temperature of the membranes. The spectra are analyzed in terms of an asymptotic high frequency background contribution and three relaxation terms. Two of these terms can be represented by a discrete relaxation time, respectively, the other one extends over a significantly broader frequency range than a Debye-type relaxation term. It was found to nicely follow the predictions of the Bhattacharjee–Ferrell model of three-dimensional critical fluctuations. This finding has been additionally verified by measurements of the scaling function and by an analysis of the relaxation rate of order parameter fluctuations following from the fit of the experimental scaling function data to the theoretical form. Theoretical arguments are presented to indicate why the three-dimensional theory applies so well to the quasi-two-dimensional membrane system.

A non-classical Widom form of the equation of state for triglycine sulphate (TGS) ferroelectric

A Widom form of the equation of state taking into account non-Landau invariants for triglycine sulphate (TGS) ferroelectric is proposed. The experimental values of the invariant Q and the exponents and are crucial for the determination of this equation. It is shown to be not derivable from the existing theories based on the renormalization group and -expansion and represents very well the experimental susceptibility data above and below TC. The analytical properties of the proposed theory are compared with Landau and Domb-Hunter expansions. A method of determining the invariant Q from the experimental susceptibility scaling function is demonstrated on TGS and deuterated triglycine selenate ferroelectrics used as examples.

Y-scaling and nucleon momentum distributions in few body systems and light nuclei

The basic elements of y-scaling, which takes properly into account nucleon binding and momentum are reviewed. A new method of analysis which allows one to obtain the experimental asymptotic scaling function from inclusive cross sections even if these data are affected by final state interactions is illustrated and the nucleon momentum distributions obtained by such a method are discussed. For few-body systems these momentum distributions satisfactorily agree with the ones extracted from (e,e'p) reactions and with theoretical calculations performed within Faddeev or variational approaches, whereas for complex nuclei they qualitatively agree with predictions of theoretical many-body approaches which take nucleon-nucleon correlations into account and disagree, at k ⩾ 350 MeV/c, with predictions by mean field approaches.

Y-scaling analysis of quasielastic electron scattering and nucleon momentum distributions in few-body systems, complex nuclei, and nuclear matter.

The approach to y scaling previously adopted to obtain the nucleon momentum distribution in the two- and three-nucleon systems is extended to the case of complex nuclei and nuclear matter. The basic elements of this approach, which takes properly into account nucleon binding and momentum, are reviewed. A new method of analysis, which allows one to obtain the experimental asymptotic scaling function from inclusive cross sections even if these data are affected by final-state interactions, is proposed and illustrated. By such a method, the asymptotic scaling functions of $^{3}\mathrm{He}$, $^{4}\mathrm{He}$, $^{12}\mathrm{C}$, $^{56}\mathrm{Fe}$, and nuclear matter are obtained from recent experimental data and it is demonstrated that, particularly at high negative values of the scaling variable, the available data points at the highest value of the momentum transfer are affected by final-state interaction and cannot therefore be considered to represent the asymptotic scaling function. It is shown that, unlike what is commonly stated, the nucleon momentum distribution is not simply defined in terms of the derivative of the asymptotic scaling function, but as a sum of such a derivative plus the derivative of a quantity, the binding correction, generated by the removal energy distribution of nucleons embedded in the nuclear medium.The binding correction and its derivative are evaluated with various types of spectral functions, and the nucleon momentum distributions in $^{3}\mathrm{He}$, $^{4}\mathrm{He}$, $^{12}\mathrm{C}$, $^{56}\mathrm{Fe}$, and nuclear matter are obtained up to nucleon momenta k\ensuremath{\approxeq}500 MeV/c. For few-body systems the obtained momentum distributions satisfactorily agree with the ones extracted from (e,e'p) reactions and with theoretical calculations performed within Faddeev or variational approaches, whereas for complex nuclei they qualitatively agree with predictions of theoretical many-body approaches which take nucleon-nucleon correlations into account and, at the same time, at k\ensuremath{\ge}350 MeV/c they are larger by orders of magnitude than the ones predicted by mean field approaches. Such a result does represent unambiguous evidence of correlation effects in nuclei.

Precocious y-scaling and nucleon momentum distributions in nuclei

Recent quasi-elastic electron scattering data on 56Fe are compared with an impulse approximation calculation based on a theoretical nuclear matter spectral function. A y-scaling analysis of the data shows that the scaling limit is approached at lower Q 2 than the theoretical calculation. A new y-scaling analysis based on the properties of the theoretical spectral function is introduced which allows direct comparison of the momentum distribution with the experimental scaling function.

Asymptotic scaling function and nucleon momentum distribution in few nucleon systems

The nucleon momentum distributions in 3He and 4He are extracted from the inclusive (e,e') cross sections analyzed in terms of y-scaling. The method is based upon a model independent extrapolation to q → ∞ of the experimental scaling function and upon a careful consideration of binding effects. The obtained momentum distributions are in good agreement with the ones extracted from exclusive (e,e'p) cross sections.

The phase transition in TGSe at a pressure close to atmospheric pressure

Abstract In the expansion of the expression for free energy density relative to polarization: G = G0 + ½AP 2 + ¼BP 4 + ⅙CP 6 + … in the pressure range 105 Nm−2 < p < 50 × 106 Nm−2 and temperature range 296K < T < 298.2K, a value (independent of p and T) for coefficient B was found i.e. B = 1.1 × 1011 (±0.05 × 1011) Vm5C−3. This fact would appear to contradict the suggestion reported in the literature of the occurrence of a tricritical point close to atmosphere pressure. The experimental scaling function was also determined for paraelectric susceptibility, in this way finding the value of the ratio of exponents δ/γ = 1.45.

Critical scattering function in a binary fluid mixture: A study of sodium-deuteroammonia solution at the critical concentration by small-angle neutron scattering.

Small-angle neutron scattering experiments have been performed on the Na-${\mathrm{ND}}_{3}$ mixture of critical composition. Neutrons are very sensitive to the fluctuations of concentration in this system (high contrast). This allowed good statistics for a reasonable counting time, typically 0.5% at each value of the momentum transfer q for a 40-min run. Momentum transfers q between 0.008 and 0.067 A${\r{}}^{\mathrm{\ensuremath{-}}1}$ were investigated with the chosen experimental setup. Using several approximations of the scattering function at small x=q\ensuremath{\xi}, and after very careful data correction, the correlation length \ensuremath{\xi} has been determined with a good precision (2% for \ensuremath{\xi}300 A\r{}). The experimental scaling function g(q\ensuremath{\xi}) was then fitted in the whole x range using different approximate equations discussed in literature. A value of the critical index \ensuremath{\eta}=0.030\ifmmode\pm\else\textpm\fi{}0.0015 was thus found with a precision not yet obtained from experiments. A lower limit for the validity of the scaling hypothesis is given for the first time: 2-\ensuremath{\eta}-\ensuremath{\gamma}/\ensuremath{\nu}\ensuremath{\le}0.002. These results reconcile neutron scattering results with those obtained with light scattering and are in favor of renormalization-group-theory predictions for the three-dimensional Ising model.

Neutron Scattering Experiments with a Binary Critical Mixture for the Determination of the Critical Exponent ζ

AbstractSmall angle neutron scattering experiments are carried out with an isobutyric acid (COOD)/deuterium oxide mixture of critical composition. The scattering patterns are measured at small temperature differences (T ‐ Tc) ≦ 1.0 K above the critical temperature Tc. In his temperature range and for scattering vectors larger than 0.03 Å−1 the critical scattering was found to be independent of temperaure. From these data the experimental correlation scaling function gexp(x) is constructed for values of the scaling variable x in the range 4 &lt; x &lt; 540. The Fisher‐Langer approximation of the correlation scaling function and its asymptotic form for large values of x are fitted to gexp(x). In this way a value of the critical exponent η of η = 0.039 ± 0.009 is obtained. It is based on the analysis of the experimental correlation scaling function composed of five scattering patterns obtained at five different temperature differences (ΔT ≤ 1.0 K). The analysis of 4 individual scattering patterns (ΔT ≤ 0.08 K) gives η = 0.037 ± 0.006.

Two-parameter scaling function for a two-dimensional system

The authors construct a two-parameter scaling function due to power-law localisation in two dimensions. The scaling function is in good agreement with the experimental beta function of Davies, Pepper and Kaveh (see ibid., vol.16, p.L285, 1983). It is shown that although a diffusive-hopping transition is expected above the mobility edge, this has little effect on the form of the two-parameter scaling function. The authors also show that transport mechanisms associated with exponentially localised states lead to a beta function which contradicts the data. They conclude that the experimental scaling function of DPK strongly supports the existence of a mobility edge with power-law state above it.