A new approach to physics of nuclei

Abstract

We employ the QCD sum rules method for description of nucleons in nuclear matter. We show that this approach provides a consistent formalism for solving various problems of nuclear physics. Such nucleon characteristics as the Dirac effective mass m * and the vector self-energy Σ V are expressed in terms of the in-medium values of QCD condensates. The values of these parameters at saturation density and the dependence on the baryon density and on the neutron-to-proton density ratio is in agreement with the results, obtained by conventional nuclear physics methods. The contributions to m * and Σ V are related to observables and do not require phenomenological parameters. The scalar interaction is shown to be determined by the pion-nucleon σ term. The nonlinear behavior of the scalar condensate may appear to provide a possible mechanism of the saturation. The approach provided reasonable results for renormalization of the axial coupling constant, for the contribution of the strong interactions to the neutron-proton mass difference and for the behavior of the structure functions of the in-medium nucleon. The approach enables to solve the problems which are difficult or unaccessible for conventional nuclear physics methods. The method provides guidelines for building the nuclear forces. The three-body interactions emerge within the method in a natural way. Their rigorous calculation will be possible in the framework of self-consistent calculation in nuclear matter of the scalar condensate and of the nucleon effective mass m * .

Three nucleon forces in nuclear matter in QCD sum rules

“…It is known [7], [8] that the function S(ρ) is dominated by the pion cloud created by interacting nucleons. Thus it is determined by the expectation value π|qq|π = 2m 2 π /(m u + m d ).…”

“…The details of the finite density QCD sum rules approach are described in [8]. Here we just recall the main points.…”

“…The function E 1 (x) = 1 − (1 + x)e −x with x = W 2 m /M 2 includes the contribution of continuum, the factor r Xn = 1 + α s π c Xn , accounts for the QCD coupling α s correction with the coefficients c Xn presented in [8] includes the logarithmic corrections. Following [14] we present…”

“…The pairs of quarks can carry various combinations of the quantum numbers. These can be the scalar-scalar (SS), vector-vector (V V ), pseudovector-pseudovector (P P ), axial-axial (AA), tensor-tensor (T T ),vector-scalar (V S) and axial-tensor (AT ) combinations [8], [20]. The probe nucleon exchanges by the mesons with the corresponding quantum numbers with one of the nucleons of the matter-see Fig.…”

“…Calculation of the fourquark expectation values N|q a αq b β q c γq d δ |N required model assumptions on the quark structure of nucleon. We employed the relativistic model suggested in [10] in the version described in [8]. The Feynman diagrams providing the main contribution to the nucleon parameters in the gas approximation are shown in Fig.…”