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A. S. Rinat

Publications and source records attributed to A. S. Rinat.

At least 19 recordsLinked to original sources
arXiv2010

Tortuous ways to the extraction of neutron observables from inclusive lepton scattering

We analyze new JLAB data for inclusive electron scattering on various targets. Computed and measured total inclusive cross sections in the range $0.3\lesssim x\lesssim 0.95$ show on a logarithmic scale reasonable agreement for all targets. However, closer inspection of the Quasi-Elastic components bares serious discrepancies. EMC ratios which may contain less systematic errors fare the same. The above observations for the new data do not enable the extraction of the magnetic form factor (FF) $G_M^n$ and the Structure Function (SFs) $F_2^n$ of the neutron, although the application of exactly the same analysis to older data had been successful. We add to the above analysis older CLAS collaboration on $F_2^D$. Removing some scattered points, it appears possible to obtain the above mentioned neutron information. We compare our results with others from alternative sources. Particular attention is paid to the A=3 iso-doublet. Present data exist only for $^3$He, but the available input and charge symmetry also enable computations for $^3$H. Their average is the computed iso-scalar part and is compared with the empirical modification of $^3$He towards a fictitious A=3 iso-singlet.

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arXiv2006

Inclusive scattering data on light nuclei as a precision tool for the extraction of G_M^n

We demonstrate that refinements in the analysis of inclusive scattering data on light nuclei enable the extraction of, generally accurate, values of the neutron magnetic form factor G_M^n(Q^2). In particular, a recent parametrization of ep inclusive resonance excitation enables a reliable calculation of the inelastic background, and as a consequence a separation of quasi-elastic and inelastic contributions. A far larger number of data points than previously considered is now available for analysis and enables a more reliable extraction of G_M^n from cross section and R_T data on D and He. The achieved accuracy appears mainly limited by the present uncertainties in the knowledge of proton form factors and by the accuracy of the data.

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arXiv2005

On the relation between nuclear and nucleon Structure Functions and their moments

Calculations of nuclear Structure Functions (SF) F_k^A(x,Q^2) routinely exploit a generalized convolution, involving the SF for nucleons F_k^N and the linking SF f^{PN,A} of a fictitious nucleus, composed of point-particles, with the latter usually expressed in terms of hadronic degrees of freedom. For finite Q^2 the approach seemed to be lacking a solid justification and the same is the case for recently proposed, effective nuclear parton distribution functions (pdf), which exactly reproduce the above-mentioned hadronically computed F_k^A. Many years ago Jaffe and West proved the above convolution in the Plane Wave Impulse Approximation (PWIA) for the nuclear components in the convolution. In the present note we extend the above proof to include classes of nuclear Final State Interactions (FSI). One and the same function appears to relate parton distribution functions (pdf) in nuclei and nucleons, and SF for nuclear targets and for nucleons. That relation is the previously conjectured one,with an entirely different interpretation of f^{PN,A}. We conclude with an extensive analysis of moments of nuclear SF based on the generalized convolution. Characteristics of those moments are shown to be quite similar to the same for a nucleon. We conclude that the above evidences asymptotic freedom of a nucleon in a medium and not of a composite nucleus.

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arXiv2005

On Distribution Functions for Partons in Nuclei

We suggest that a previously conjectured relation between Structure Functions (SF) for nuclei and nucleons also links distribution functions (df) for partons in a nucleus and in nucleons. The above suggestion ensures in principle identical results for SF $F_2^A$, whether computed with hadronic or partonic degrees of freedom. In practice there are differences, due to different $F_2^n$ input. We show that the thus defined nuclear parton distribution functions (pdf) respect standard sumrules. In addition we numerically compare some moments of nuclear SF, and find agreement between results, using hadronic and partonic descriptions. We present computations of EMC ratios for both, and compare those with hadronic predictions and data. In spite of substantial differences in the participating SF, the two representations produce approximately the same EMC ratios. The apparent correlation between the above deviations is ascribed to a sumrule for $F_2^A$. We conclude with a discussion of alternative approaches to nuclear pdf.

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arXiv2004

A simple qualitative description of EMC ratios μ^A for 0.2 <~ x <~ 1.5 and some sample calculations

We study EMC ratios on the basis of a relation between Structure Functions (SF) for a nucleus and for a nucleon, which is governed by a SF f^{PN,A}(x,Q^2) of an unphysical nucleus, composed of point-nucleons. We demonstrate that the characteristic features of EMC ratios μ^A are determined by the above f^{PN,A} and the SF of free nucleons. We account for the positions of the points x_{1,2} in the interval 0.2 <~ x <~ 0.9, where μ^A(x,Q^2)=1 and also for the minimum x_m in that interval. We similarly describe the oscillations in μ^A for Q^2 <~ (3.5-4.0) GeV^2 in the Quasi-Elastic peak region 0.95 <~ x <~ 1.05 and for its subsequent continuous increase up to x\approx 1.4. Finally we compute μ^A over the entire range above for A=^4He, C, Fe and Au and several Q^2 values. The results are in reasonable agreement with both directly measured and indirectly extracted data.

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arXiv2003

The neutron magnetic form factor G_M^n(Q^2) from Quasi-Elastic inclusive scattering data on D and 4He

We analyze cross sections for Quasi-Elastic inclusive scattering of electrons on nuclei and show that the observed isolated peaks for relatively low $Q^2$ are unique for the lightest targets. Focusing in particular on D and $^4$He, we investigate in two ways to what measure the above peaks can be allocated to nucleon-elastic processes. We first compute approximate upper limits for the nucleon-inelastic background in the Quasi-Elastic region due to inclusive $Δ$ excitation, and find those to be small. Far more precise is a semi-phenomenological approach, where the dominance of nucleon-elastic processes is translated into a set of stringent requirements. We show that those are very well fulfilled for recent D data, and to a somewhat lesser extent for older D and $^4$He data. With knowledge of $G_{E,M}^p$ and information on $G_E^n$, we then extract $G_M^n$ and find agreement with values obtained by alternative methods. We discuss the sensitivity of the extraction method and mention future applications.

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arXiv2002

Extraction of the static magnetic form factor and the structrue function of the neutron from inclusive scattering on light nuclei

We show that quasi-elastic inclusive scattering data on light nuclei for medium Q^2 furnish information on $G_M^n$, whereas the deep-inelastic region for large $Q^2$ provides the Structure Function $F_2^n(x,Q^2)$. Common to the two extractions is the possibility to de-convolute medium effects, which is most accurately done for light targets. Results are independent of the target.

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arXiv2002

Extraction of the n structure function $F_2^n$ from inclusive scattering data on composite nuclei

We consider a generalized convolution, linking Structure Functions (SF) $F^N_2$ for nucleons, $F^A_2$ for a physical nucleus and $f^{PN,A}$ for a nucleus, composed of point-nucleons. In order to extract $F_2^n$ we employ data on $F_2^{p,A}$ and the computed $f^{PN,A}$. Only for $Q^2\approx 3.5 {\rm GeV}^2$ do data permit the extraction of $F_2^A(x,3.5)$ over a sufficiently wide $x$-range. Applying Mellin transforms, the above relation between SF turns into an algebraic one, which one solves for the Mellin transform of the unknown $F_2^n$. We present inversion methods leading to the desired $F_2^n$, all using a parametrization for $C(x,Q^2)=F_2^n(x,Q^2)/F_2^p(x,Q^2)$. Imposing motivated constraints, the simplest parametrization leaves one free parameter $C(x=1,Q^2)$. For $Q^2= 3.5 {\rm GeV}^2$ its average over several targets and different methods is $ =0.54\pm0.03$. We argue that for the investigated $Q^2$, $C(x\to 1,3.5)$ is determined by the nucleon-elastic ($NE$) part of SF. The calculated value is near the extracted one and both are close to the SU(6) limit 2/3.

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arXiv2001

Description of inclusive scattering of 4.045 GeV electrons from D

We exploit a relationship between the Structure Functions of nucleons, the physical deuteron and of a deuteron, composed of point-nucleons to compute angular distributions of inclusive cross sections of 4.05 GeV electrons. We report general agreement with data and interpret the remaining discrepancies. We discuss the potential of the data for information on neutron structure functions $F_k^n(x,Q^2)$ and the static form factor $G_M^n(Q^2)$.

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arXiv2001

Relativistic approaches to structure functions of nuclei

We employ a propagator technique to derive a new relativistic $1/\qq$ expansion of the structure function of a nucleus, composed of point-nucleons. We exploit non-relativistic features of low-momentum nucleons in the target and only treat relativistically the nucleon after absorption of a high-momentum virtual photon. The new series permits a 3-dimensional reduction of each term and a formal summation of all Final State Interaction terms. We then show that a relativistic structure function can be obtained from its non-relativistic analog by a mere change of a scaling variable and an addition of an energy shift. We compare the obtained result with an ad hoc generalized Gersch-Rodriguez-Smith theory, previously used in computations of nuclear structure functions.

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arXiv1999

Applications of computed Nuclear Structure Functions to Inclusive Scattering R-ratios and their Moments

We discuss applications of previously computed nuclear structure functions (SF) to inclusive cross sections, compare predictions with recent CEBAF data and perform two scaling tests. We mention that the large $Q^2$ plateau of scaling functions may only in part be due to the asymptotic limit of SF, which prevents the extraction of the nucleon momentum distribution in a model-independent way. We show that there may be sizable discrepancies between computed and semi-heuristic estimates of SF ratios. We compute ratios of moments of nuclear SF and show these to be in reasonable agreement with data. We speculate that an effective theory may underly the model for the nuclear SF, which produces overall agreement with several observables.

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arXiv1999

Extraction of nucleon momentum distributions from inclusive electron scattering on nuclei

We address the problem of extracting single-nucleon momentum distributions $n(p)$ from inclusice scattering data. A model for these relates nuclear and nucleon structure functions (SF) through an intermediate SF $f^{PN}$ for a nucleus of point-particles. In addition to the asymptotic limit (AL) which depends on $n(p), f^{PN}$ contains, generally $q$-dependent Final State Interactions (FSI) parts. In the inverse problem one wishes to separate $q$-dependent FSI from the AL. In general it suffices to know the structure of the theory, but not numerical results. It appears, that in the $q$-range of the analyzed electron scattering data, FSI are only weakly $q$-dependent, making it virtually impossible to obtain parameters in a free fit of the parametrized components of $f$. Imposing a restriction, we obtain $n(p)$ for Fe and $^4$Fe.

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arXiv1999

Theoretical aspects of the CEBAF 89-009 experiment on inclusive scattering of 4.05 GeV electrons from nuclei

We compare recent CEBAF data on inclusive electron scattering on nuclei with predictions, based on a relation between structure functions (SF) of a nucleus, a nucleon and a nucleus of point-nucleons. The latter contains nuclear dynamics, e.g. binary collision contributions in addition to the asymptotic limit. The agreement with the data is good, except in low-intensity regions. Computed ternary collsion contributions appear too small for an explanation. We perform scaling analyses in Gurvitz's scaling variable and found that for $y_G\gtrless 0$, ratios of scaling functions for pairs of nuclei differ by less than 15-20% from 1. Scaling functions for $ 0$ are, for increasing $Q^2$, shown to approach a plateau from above. We observe only weak $Q^2$-dependence in FSI, which in the relevant kinematic region is ascribed to the diffractive nature of the NN amplitudes appearing in FSI. This renders it difficult to separate asymptotic from FSI parts and seriously hampers the extraction of $n(p)$ from scaling analyses in a model-independnent fashion.

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arXiv1999

R-ratios and moments of nuclear structure functions

We study implications of a model, which links nuclear and nucleon structure functions. Computed Callen-Gross functions $κ^A(x,Q^2)= 2xF_1^A(x,Q^2)/F_2^A(x,Q^2)$ appear for finite $Q^2$ to be close to their asymptotic value 1. Using those $κ$, we compure $R$ ratios for $Q^2\ge 5 GeV^2$. We review approximate methods in use for the extraction of $R$ from inclusive scattering and ENC data. Further we calcuate ratios of the moments of $F_k$ and find these to describe the data, in particular their $Q^2$ dependence. The above observables, as well as inclusive cross sections, are sensitive tests for the underlying relation between nucleonic and nuclear structure functions. In view of the overall agreement, we speculate that the above relation effectively circumvents a QCD calculation.

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arXiv1998

On the equivalence of the Impulse Approximation and the Gersch-Rodriguez-Smith theory for structure functions

We derive for a non-relativistic system an approximation for Final State Interactions in a form, resembling a DWIA which corrects the structure function computed in the PWIA. We then compare the Gersch-Rodriguez-Smith and the IA series for structure functions and prove that to order ${\cal O}(1/q^2)$ the above DWIA representation is contained in the GRS series to the same order. There is an additional term in the GRS series that is missing in the DWIA due to the eikonal approximations in the latter. This strongly suggests that the two approaches, when treated exactly, produce identical structure function to arbitrary order in $1/q$.

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arXiv1998

Beyond the binary collision approximation for the large-$q$ response of liquid $^4$He

We discuss corrections to the linear response of a many-body system beyond the binary collision approximation. We first derive for smooth pair interactions an exact expression of the response $\propto 1/q^2$, considerably simplifying existing forms and present also the generalization for interactions with a strong, short-range repulsion. We then apply the latter to the case of liquid $^4$He. We display the numerical influence of the $1/q^2$ correction around the quasi-elastic peak and in the low-intensity wings of the response, far from that peak. Finally we resolve an apparent contradiction in previous discussions around the fourth order cumulant expansion coefficient. Our results prove that the large-$q$ response of liquid $^4$He can be accurately understood on the basis of a dynamical theory.

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arXiv1997

Description of recent large-$q$ neutron inclusive scattering data from liquid $^4$He

We report dynamical calculations for large-$q$ structure functions of liquid $^4$He at $T$=1.6 and 2.3 K and compare those with recent MARI data. We extend those calculations far beyond the experimental range $q\le 29\Ain$ in order to study the approach of the response to its asymptotic limit for a system with interactions having a strong short-range repulsion. We find only small deviations from theoretical $1/q$ behavior, valid for smooth $V$. We repeat an extraction by Glyde et al of cumulant coefficients from data. We argue that fits determine the single atom momentum distribution, but express doubt as to the extraction of meaningful Final State Interaction parameters.

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