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Contents:
  1. Open Physics
  2. Associate Professor Nicholas Robins - Researchers - ANU
  3. Optimal investment horizons for the main indices of the Warsaw Stock Exchange
  4. Breadcrumb

Note that the close relation between shadowing and di! It suggests signi"cantly larger shadowing for gluons than for quarks.

JVE Conferences

Nuclear e! T Typical results from Ref. Momentum-space ratios from Ref. The kinematic range where enhancement takes place is related to processes which involve typical longitudinal distances of 1 fm in the laboratory. This is the region where components of the nuclear wave function with overlapping parton distributions should be relevant.

In such a picture the enhancement of gluons should increase with the density of the nuclear target. More detailed information on nuclear parton distributions is certainly needed.

Open Physics

A more quantitative separation of nuclear e! However, an extraction of nuclear parton distributions in hadron production processes from nuclei, e. Nuclear structure functions at large Bjorken-x Deep-inelastic scattering from nuclei probes the nuclear parton distributions. On the other hand, conventional nuclear physics works well with the concept that nuclei are composed of interacting hadronic constituents, primarily nucleons and pions. In this kinematic region, incoherent scattering from hadronic constituents of the target nucleus dominates.

Such processes explore the quark distributions of nucleons bound in the nucleus. To gain "rst insights suppose that the nucleus is described by nucleons moving in a mean "eld. The quark substructure of bound nucleons may di!

Associate Professor Nicholas Robins - Researchers - ANU

First, there is a purely kinematical e! This e! To illustrate this recall that for a free nucleon the light-cone momentum fraction of partons cannot exceed x"1. A nucleon bound in a nucleus carries a non-vanishing momentum which adds to the momenta of individual partons in that nucleon. As a consequence light-cone momentum fractions up to x"A are possible in principle, although the extreme situation in which a single parton carries all of the nuclear momentum will of course be very highly improbable.

On the other hand, intrinsic properties of bound nucleons, e. This may lead to additional, dynamical modi"cations of their partonic structure. Impulse approximation Nuclei are, in many respects, dilute systems. Final state interactions of the scattered hadron with the residual nuclear system are neglected at high energy. One should note, however, that the validity of this approximation, illustrated in Fig.

Given the small average momenta of the weakly bound nucleons, their quark sub-structure is described by structure functions similar to those of free nucleons [,]. This becomes immediately obvious from the following simple kinematic consideration. In the laboratory frame deep-inelastic scattering from a nucleon bound in a nucleus involves the removal energy,! The energy of the interacting nucleon is then: p "M e! The squared four momentum of the active nucleon is obviously not restricted by its free invariant mass. It is determined by the nuclear wave function which describes the momentum distributions of bound target nucleons as well as the mass spectrum of the residual nuclear system.

This quark belongs to a nucleon with momentum p which is removed from the target nucleus. It is determined by the momentum-space amplitude W p "1 A! Note that the spectral function is normalized to A, the total number of nucleons in the nucleus. This leads to the proper normalization of the nucleon distribution function in Eq. The nuclear structure functions are then obtained by a convolution over the squared fourmomentum of the interacting nucleons and their light-cone momentum fraction.


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This implies that the nucleon light-cone distribution 6. Expanding the bound nucleon structure function in Eq.


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Then 1e2 coincides with the separation energy. Corrections to 0 Eq. Let us brie y discuss the physical meaning of the di!

Optimal investment horizons for the main indices of the Warsaw Stock Exchange

The second term on the right-hand side of Eq. As such it is determined by nuclear binding. In the range 0. Finally, the fourth term in 6. Note that this contribution enters at the same order as binding and Fermi-motion corrections. Nevertheless, such e! An important and not yet completely solved problem with respect to the binding and Fermimotion corrections in Eq.

In a simple nuclear shell G. This in turn causes an increase of the average separation energy 1e2 [,]. This sum rule is exact if only two-body forces are present in the nuclear Hamiltonian. We refer in this context to a calculation [] of the spectral function of nuclear matter based on a variational method. This calculation shows that there is a signi"cant probability to "nd nucleons with high momentum and large separation energies. An integration of the spectral function of Ref. In order to estimate these quantities for heavy nuclei one usually assumes [] that the high-momentum components of the nucleon momentum distribution are about the same as in nuclear matter.

Together with Eq.

Breadcrumb

We observe that a qualitative understanding of the EMC e! One should note, of course, that the presentation of nuclear e!

The impulse approximation picture of nuclear deep-inelastic scattering can also be maintained in a relativistically covariant way []. Here, however, a simple factorization of nuclear structure functions into nuclear and nucleon parts as in Eq. A relativistic calculation of nuclear structure functions requires relativistic nuclear wave functions as well as Fig. Nevertheless, relativistic e! In the region x'1, where nuclear structure functions are very small however, larger deviations are expected. In this context a word of caution is in order. A description of nuclear structure functions based on nucleons alone is necessarily incomplete since it violates the momentum sum rule [1].

Non-nucleonic degrees of freedom are brie y discussed in Section 6.


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Beyond the impulse approximation The quality of the impulse approximation has frequently been questioned see e. Here we give a brief summary of possible shortcomings in terms of models for nuclear deep-inelastic scattering which go beyond this approximation. Quark exchange in nuclei The impulse approximation includes only incoherent scattering processes from hadronic constituents of the target nucleus.

On the other hand, contributions involving several bound nucleons could also be important, and their role needs to be examined. One such possibility, namely quark exchange between di! The nuclear quark wave function which is probed in deep-inelastic scattering must be antisymmetric with respect to permutations of quarks.

This however is not realized in the impulse approximation 6. Antisymmetrization introduces additional quark exchange terms between di! Under several simplifying assumptions a softening of the nuclear quark momentum distribution due to quark exchange has been found. For small nuclei the e! Only minor modi"cations have been found for heavier nuclei []. While the estimates based on a simple quark exchange model may not be reliable at a quantitative level, they certainly point to the fact that the impulse approximation is incomplete as soon as correlations between quarks in several nucleons come into play.

Final state interactions in a mean xeld approach One of the basic assumptions of the impulse approximation is that interactions of the struck, highly excited nucleon with the residual nuclear system can be ignored.

In general, there is no solid basis for this assumption since the debris of the struck nucleon includes also low momentum fragments as seen from the target rest frame. A proper treatment of their "nal state interaction requires however a description of the nucleus in terms of quark and gluon degrees of freedom. Investigations in this direction have been made starting out from a quark model for nuclear matter, with nucleons modeled as non-overlapping MIT bags [,,].

The nucleons interact via the exchange of scalar and vector mesons which couple directly to quarks. Within the mean "eld approximation for the meson "elds it is possible to describe several basic properties of nuclear matter, such as its compressibility and the binding energy per nucleon at saturation density.