arXiv subjects

V. A. Sadovnikova

Publications and source records attributed to V. A. Sadovnikova.

At least 19 recordsLinked to original sources

arXiv2020

Zero-sound in nuclear matter with the asymmetry parameter $-1\leq β\leq 1$

Results for the frequencies of zero-sound excitations in the isospin asymmetric nuclear matter are presented for the different parameters of asymmetry -1\leqβ\leq 1. The dispersion equations are constructed within the random phase approximation. We use the effective Landau-Migdal quasiparticle interaction with the special isospin dependence of the phase volume in the normalization factor C_0. In the paper we present zero-sound branches of the dispersion equation solutions in the symmetric, asymmetric and neutron matter. The branches correspond to the different channels of decay of the zero-sound excitation in the nuclear matter or nuclei. In the asymmetric nuclear matter we obtain three branches of solutions on the physical and unphysical sheets of the complex frequency plane, ω_{s\,τ}(k,β), τ=p,n,np. We demonstrate the change of branches with βand conversion of the three branches into two branches in symmetric nuclear matter (β=0) and into one branch in the neutron matter (β=1).

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arXiv2020

Structure functions generated by zero sound excitations

In isospin symmetric and asymmetric nuclear matter we study the structure functions connected with the zero sound excitations. In the simple model with Landau-Migdal quasiparticle interactions the density response $Π^R(ω,k)$ of the nuclear matter to the small isovector external field $V_0(ω,k)$ is considered. In the previous papers the complex branches of solutions $ω_{si}(k)$, $i=n,p,np$ of the dispersion equation corresponding to zero sound excitations in the symmetric and asymmetric nuclear matter are obtained. Now we investigate the structure and response functions of nuclear matter based on these solutions.

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arXiv2018

Equilibrium of nuclear matter in QCD sum rules

We calculate the nucleon parameters in symmetric nuclear matter employing the QCD sum rules approach. We focus on the average energy per nucleon and study the equilibrium states of the matter. We treat the matter as a relativistic system of interacting nucleons. Assuming the dependence of the nucleon mass on the light quark mass $m_q$ to be more important than that of nucleon interactions we find that the contribution of the relativistic nucleons to the scalar quark condensate can be expressed as that caused by free nucleons at rest multiplied by the density dependent factor $F(ρ)$. We demonstrate that there are no equilibrium states while we include only the condensates with dimension $d \leq 3$. There are equilibrium states if we include the lowest order radiative corrections and the condensates with $d \leq 4$. They manifest themselves for the nucleon sigma term $σ_N >60$ MeV. Including the condensates with $ d \leq 6$ we find equilibrium states of nuclear matter for $σ_N> 41$ MeV. In all cases the equilibrium states are due to influence of the relativistic motion of the nucleons composing the matter on the scalar quark condensate.

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arXiv2017

Many body effects in nuclear matter QCD sum rules

We calculate the single-particle nucleon characteristics in symmetric nuclear matter with inclusion of the 3N and 4N interactions. We calculated the contribution of the 3N interactions earlier, now we add that of the 4N ones. The contribution of the 4N forces to nucleon self energies is expressed in terms of the nonlocal scalar condensate (d=3) and of the configurations of the vector-scalar and the scalar-scalar quark condensates (d=6) in which two diquark operators act on two different nucleons of the matter.These four-quark condensates are obtained in the model-independent way. The density dependence of the nucleon effective mass, of the vector self energy and of the single-particle potential energy are obtained. We traced the dependence of the nucleon characteristics on the actual value of the pion-nucleon sigma term. We obtained also the nucleon characteristics in terms of the quasifree nucleons, with the noninteracting nucleons surrounded by their pion clouds as the starting point. This approach leads to strict hierarchy of the many body forces.

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arXiv2016

Three nucleon forces in nuclear matter in the QCD sum rules

We calculate the single-particle nucleon characteristics in symmetric nuclear matter with inclusion of the 3N interactions. The contribution of the 3N forces to the nucleon self energies are expressed in terms of the nonlocal scalar condensate (d=3) and of the configuration of the two four-quark condensates (d=6) in which two diquark operators act on two different nucleons of the matter. The most important part of the contribution of the four-quark condensate is calculated in a model-independent way. We employed a relativistic quark model of nucleon for calculation of the rest part. The density dependence of the vector and scalar nucleon self energies and of the single-particle potential energy are obtained.

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arXiv2015

Nucleon QCD sum rules in instanton medium

We try to find the grounds for the standard nucleon QCD sum rules, based on more detailed description of QCD vacuum. We calculate the polarization operator of the nucleon current in the instanton medium. The medium (QCD vacuum) is assumed to be a composition of the small-size instantons and some long-wave gluon fluctuations. We solve the corresponding QCD sum rules equations and demonstrate that there is a solution with the value of the nucleon mass close to the physical one if the fraction of the small size instantons contribution w_s \approx 2/3.

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arXiv2014

On the loop approximation in nucleon QCD sum rules

There was a general believe that the nucleon QCD sum rules which include only the quark loops and thus contain only the condensates of dimension d=3 and d=4 have only a trivial solution. We demonstrate that there is also a nontrivial solution. We show that it can be treated as the lowest order approximation to the solution which includes the higher terms of the Operator Product Expansion. Inclusion of the radiative corrections improves the convergence of the series.

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arXiv2014

QCD sum rules for the nucleon and the non-locality of quark condensates

We emphasize the role of the x dependence of the quark condensate <|\bar q(0)q(x)|> originated by the zero fermion modes in the instanton vacuum. The effect is not negligible since the inverse size of the instanton 1/ρ~600MeV is comparable with the value of Borel mass M~1GeV. Using as an example the sum rules for the nucleon we show that this "non-locality" may strongly affected the conventional results obtained under the <|\bar q(0)q(x)|>=<|\bar q(0)q(0)|> approximation.

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arXiv2014

Nucleon QCD sum rules in instanton vacuum

We calculate the polarization operator of the nucleon current in the instanton medium. The medium (QCD vacuum) is assumed to be a composition of the instantons of large and small sizes. The former are described in terms of the local scalar condensate, while the latter can be interpreted as the nonlocal scalar condensate. We solve the corresponding QCD sum rules equations and demonstrate that there is a solution with the value of the nucleon mass close to the physical one if the fraction of the small size instantons w_s \approx 2/3.

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arXiv2014

Non-locality of the scalar quark condensate

We suggest a somewhat indirect method for estimation of the nonlocal scalar quark condensate. The approach is based on analysis of the polarization operator of nucleon current in instanton medium.

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arXiv2013

Dependence of nucleon mass on parameters of instanton medium

We trace the dependence of the nucleon mass and of the effective size of the nucleon on the characteristics of the instanton medium, which are the average instanton size $ρ$ and the distance between the instantons in instanton medium R. We consider several scenario for variation of the values of $ρ$ and R.

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arXiv2013

Evaluation of the escape widths of the giant dipole resonances in the fermi-liquid theory

In the theory of the finite fermi-systems [1], it was shown that giant resonances in nuclei can be consider as the zero-sound excitations which exhaust the large part of the energy-weighted sum rules. In the framework of [1] the solutions of the zero-sound dispersion equation in the symmetric nuclear matter, ω_s(k), are considered. The method of calculation of these solutions is based on the analytical structure of the polarization operators Π(ω,k). The solutions of the dispersion equation, which are real at small k, become complex with k increasing when the overlapping of the collective and 1p1h modes starts. The imaginary part of ω_s(k) is the result of the collective zero-sound excitation decay to the real particle-hole pairs and can be compared with the escape width of resonances. We compare the experimental energy and escape width of the giant dipole resonance (GDR) in the nucleus A with Reω_s(k) and Imω_s(k) taken at a definite wave vector k=k_A.

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arXiv2012

A New Approach to Physics of Nuclei

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 method. 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 guide-lines for building the nuclear forces. The three-body interactions emerge within the method in a natural way. There rigorous calculation will be possible in framework of self-consistent calculation in nuclear matter of the scalar condensate and of the nucleon effective mass $m^*$.

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arXiv2012

The role of the in-medium four-quark condensates revised

We calculate the nucleon self-energies in nuclear matter in the QCD sum rules approach, taking into account the contributions of the four-quark condensates. We analyze the dependence of the results on the model employed for the calculation of the condensates and demonstrate that the relativistic character of the models is important. The condensates are calculated with inclusion of the most important terms beyond the gas approximation. This corresponds to inclusion of the two-body nucleon forces and of the most important three-body forces. The results are consistent with the convergence of the operator product expansion. The density dependence of the nucleon self-energies is obtained. The results are consistent with those obtained by the standard nuclear physics methods, thus inspiring further development of the approach.

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arXiv2012

Solutions of the dispersion equation in the region of overlapping of zero-sound and particle-hole modes

In this paper the solutions of the zero-sound dispersion equation in the random phase approximation (RPA) are considered. The calculation of the damped zero-sound modes ω_s(k) (complex frequency of excitation) in the nuclear matter is presented. The method is based on the analytical structure of the polarization operators Π(ω,k). The solutions of two dispersion equations with Π(ω,k) and with Re(Π(ω,k)) are compared. It is shown that in the first case we obtain one-valued smooth solutions without "thumb-like" forms. Considering the giant resonances in the nuclei as zero-sound excitations we compare the experimental energy and escape width of the giant dipole resonance (GDR) in the nucleus A with ω_s(k) taken at a definite wave vector k=k_A.

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arXiv2009

Role of unphysical solution in nucleon QCD sum rules

We show that at certain values of QCD condensates the nucleon QCD sum rules with "pole+continuum" model for the hadron spectrum obtain an unphysical solution. This provides constrains for the values of condensates to be consistent with existence of a physical solutions. The constrains become much weaker if the radiative corrections are included perturbatively. We demonstrate that the most important dependence of nucleon mass on the quark scalar condensate becomes much weaker under factorization assumption for the four-quark and six-quark condensates.

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arXiv2009

Nucleon QCD sum rules in nuclear matter including radiative corrections

We calculate the nucleon parameters in nuclear matter using the QCD sum rules method. The radiative corrections to the leading operator product expansion terms are included, with the corrections of the order α_s beyond the logarithmic approximation taken into account. The density dependence of the influence of radiative corrections on the nucleon parameters is obtained. At saturation density the radiative corrections increase the values of vector and scalar self-energies by about 40 MeV, and 30 MeV correspondingly. The results appear to be stable with respect to possible variations of the value of Λ_{QCD}.

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arXiv2006

Nucleon sum rules in symmetric and asymmetric nuclear matter

We calculate the nucleon parameters in isospin symmetric and asymmetric nuclear matter using the QCD sum rules. The higher moments of the nucleon structure functions are included. The complete set of the nucleon expectation values of the four-quark operators is employed. We analyze the role of the lowest order radiative corrections beyond the logarithmic approximation.

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