arXiv subjects

Vladimir B. Kopeliovich

Publications and source records attributed to Vladimir B. Kopeliovich.

12 recordsLinked to original sources

arXiv2019

Mathematical aspects of the nuclear glory phenomenon; backward focusing and Chebyshev polynomials

The angular dependence of the cumulative particles production off nuclei near the kinematical boundary for multistep process is defined by characteristic polynomials in angular variables, describing spatial momenta of the particles in intermediate and final states. Physical argumentation, exploring the small phase space method, leads to the appearance of equations for these polynomials in $cos (θ/N)$, where $θ$ is the polar angle of the momentum of final (cumulative) particle, the integer $N$ being the multiplicity of the process (the number of interactions). It is shown explicitly how these equations appear, and the recurrent relations between polynomials with different $N$ are obtained. Factorization properties of characteristic polynomials found previously, are extended, and their connection with known in mathematics Chebyshev polynomials of 2-d kind is established. As a result, differential cross section of the cumulative particle production has characteristic behaviour $dσ\sim 1/ \sqrt {π- θ}$ near the strictly backward direction ($θ= π$, the backward focusing effect). Such behaviour takes place for any multiplicity of the interaction, beginning with $n=3$, elastic or inelastic (with resonance excitations in intermediate states), and can be called the nuclear glory phenomenon, or 'Buddha's light' of cumulative particles.

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arXiv2017

Rescaling of quantized skyrmions: from nucleon to baryons with heavy flavor

The role of rescaling (expansion or squeezing) of quantized skyrmions is studied for the spectrum of baryons beginning with nucleon and $Δ(1232)$, and with flavors strangeness, charm or beauty. The expansion of skyrmions due to the centrifugal forces has influence on the masses of baryons without flavor ($N$ and especially $Δ$). The rescaling of skyrmions has smaller influence on the spectrum of strange baryons, it is more important for the case of charm, and is crucial for baryons with beauty quantum number, where strong squeezing takes place. Two competing tendencies are clearly observed: expansion of skyrmions when isospin (or spin) increases, and squeezing with increasing mass of the flavor. For the case of beauty baryon $Λ_b$ satisfactory agreement with data can be reached for the value $r_b= F_B/F_π\simeq 2.6 $, for the case of $Σ_b$ there should be $r_b\sim 2$, so for the beauty flavor the method seems to be not quite satisfactory because of certain intrinsic discrepances. Some pentaquark states with hidden strangeness, charm or beauty are considered as well.

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arXiv2016

Mathematical aspects of the nuclear glory phenomenon: from backward focusing to Chebyshev polynomials

The angular dependence of the cumulative particles production off nuclei near the kinematical boundary for multistep process is defined by characteristic polynomials in angular variables $J_N^2(z_N^θ)$, where $θ$ is the polar angle defining the momentum of the final (cumulative) particle, $z_N^θ= cos (θ/N)$, the integer $N$ being the multiplicity of the process (the number of interactions). Physical argumentation, exploring the small phase space method, leads to the appearance of equations for these polynomials $J_N^2[cos(π/N)]=0$. The recurrent relations between polynomials with different $N$ are obtained, and their connection with known in mathematics Chebyshev polynomials of 2-d kind is established. As a result of this equality, differential cross section of the cumulative particle production has characteristic behaviour $dσ\sim 1/ \sqrt {π- θ}$ at $θ\sim π$ (the backward focusing effect). Such behaviour takes place for any multiplicity of the interaction, beginning with $n=3$, elastic or inelastic (with resonances excitations in intermediate states), and can be called the nuclear glory phenomenon, or 'Buddha's light' of cumulative particles.

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arXiv2014

"Buddha's Light" of Cumulative Particles

We show analytically that in the cumulative particles production off nuclei multiple interactions lead to a glory-like backward focusing effect. Employing the small phase space method we arrived at a characteristic angular dependence of the production cross section $dσ\sim 1/ \sqrt {π- θ}$ near the strictly backward direction. This effect takes place for any number $n\geq 3 $ of interactions of rescattered particle, either elastic or inelastic (with resonance excitations in intermediate states), when the final particle is produced near corresponding kinematical boundary. Such a behaviour of the cross section near the backward direction is in qualitative agreement with some of available data. Explanation of this effect and the angular dependence of the cross section near $θ\sim π$ are presented for the first time.

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arXiv2013

Effective Strange Quark/Antiquark Masses from the Chiral Soliton Models for Baryons

The effective strange quark and antiquark masses are estimated from the chiral soliton approach (CSA) results for the spectrum of exotic and nonexotic baryons. There are problems when one tries to project results of the CSA on the simple quark models (QM): the parameter in $1/N_c$ expansion is so large for the case of the baryon spectrum that extrapolation to the real $N_c=3$ world is not possible; rigid (as well soft) rotator model and the bound state model coincide in the first two orders in $1/N_c$, but differ in the next orders. There is correspondence of the CSA and simple QM predictions for pentaquarks (PQ) spectra in negative $S$ sector of the $\{27\}$ and $\{35\}$-plets: the effective mass of strange quark is about $135 -130\,MeV$, slightly smaller for $\{35\}$. For positive strangeness components the link between CSA and QM requires strong dependence of the effective $\bar{s}$ mass on particular SU(3) multiplet. The SU(3) configuration mixing is important, it pushes the spectrum towards the simplistic model (with equal masses of the strange quark and antiquark), and explanation of this nice property is lacking still. The success of the CSA in describing many properties of baryons and light nuclei (hypernuclei) means that predictions of pentaquark states should be considered seriously. Existence of PQ by itself is without any doubt, although very narrow PQ may not exist. Wide, even very wide PQ should exist, therefore, searches for PQ remain to be an actual task.

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arXiv2012

Neutron Rich Hypernuclei in Chiral Soliton Model

The binding energies of neutron rich strangeness $S=-1$ hypernuclei are estimated in the chiral soliton approach using the bound state rigid oscillator version of the SU(3) quantization model. Additional binding of strange hypernuclei in comparison with nonstrange neutron rich nuclei takes place at not large values of atomic (baryon) numbers, $A=B\leq\sim 10$. This effect becomes stronger with increasing isospin of nuclides, and for "nuclear variant" of the model with rescaled Skyrme constant $e$. Total binding energies of (Lambda)He-8 and recently discovered (Lambda)H-6 satisfactorily agree with experimental data. Hypernuclei (Lambda)H-7, (Lambda)He-9 are predicted to be bound stronger in comparison with their nonstrange analogues H-7, He-9; hypernuclei (Lambda)Li-10, (Lambda)Li-11, (Lambda)Be-12, (Lambda)Be-13, etc. are bound stronger in the nuclear variant of the model.

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arXiv2008

Selected problems of baryons spectroscopy: chiral soliton versus quark models

Inconsistency between rigid rotator and bound state models at arbitrary number of colors, rigid rotator -- soft rotator dilemma and some other problems of baryon spectroscopy are discussed in the framework of the chiral soliton approach (CSA). Consequences of the comparison of CSA results with simple quark models are considered and the $1/N_c$ expansion for the effective strange antiquark mass is presented, as it follows from the CSA. Strong dependence of the effective strange antiquark mass on the SU(3) multiplet is required to fit the CSA predictions. The difference of `good' and `bad' diquark masses, which is about 100 Mev, is in reasonable agreement with other estimates. Multibaryons (hypernuclei) with strangeness are described and some states of interest are predicted within CSA as well.

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arXiv2007

Strange and Heavy Flavoured Hypernuclei in Chiral Soliton Models

The extention of the chiral soliton approach to hypernuclei - strange or heavy flavoured - becomes more reliable due to success in describing of other properties of nuclei, e.g. the symmetry energy of nuclei with atomic numbers up to ~30. The binding energies of the ground states of light hypernuclei with strangeness S=-1 have been described in qualitative agreement with data. The existence of charmed or beautiful hypernuclei and Theta-hypernuclei (strange, charmed or beautiful) with large binding energy is expected within same approach.

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arXiv2006

Pentaquarks in Chiral Soliton Models; notes and discussion

The spectra of pentaquarks, some of them being observed recently, are discussed within topological soliton model and compared with simplified quark picture. Results obtained within chiral soliton model depend to some extent on the quantization scheme: rigid rotator, soft rotator, or bound state model. The similarity of spectra of baryon resonances obtained within quark model and chiral soliton model is pointed out, although certain differences take place as well, which require careful interpretation. In particular, considerable variation of the strange antiquark mass in different SU(3) multiplets of pentaquarks is required to fit their spectra obtained from chiral solitons. Certain difference of masses of "good" and "bad" diquarks is required as well, in qualitative agreement with previously made estimates. The partners of exotic states with different values of spin which belong to higher SU(3) multiplets, have the energy considerably higher than states with lowest spin, and this could be a point where the difference from simple quark models is striking. The antiflavor excitation energies for multibaryons are estimated as well, and binding energies of $Θ$-hypernuclei and anticharm (antibeauty) hypernuclei are presented for several baryon numbers. Some deficiencies in the argumentation against validity of the chiral soliton approach and/or SU(3) quantization models, existing in the literature, are pointed out.

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arXiv2006

Baryon Spectrum in Large N(C) Chiral Soliton and in Quark Models

Strangeness contents of baryons are calculated within rigid rotator model for arbitrary number of colors $N_c$. The problem of extrapolation to realistic value $N_c=3$ is noted, based on explicit calculations and comparison of rigid rotator and rigid oscillator variants of the model. Some features of exotic baryon spectra ($\{\bar{10}\}, \{27\}$-and $\{35\}$-plets of baryons) obtained in the chiral soliton approach can be understood in terms of simplified quark $(4q\bar{q})$ wave functions. The effective mass of strange antiquark in different SU(3) multiplets of pentaquarks should depend on the particular multiplet, to link the predictions of soliton and quark models. The estimate of the $6_F$ and $\bar{3}_F$ diquarks mass difference can be made from comparison with chiral soliton model results for masses of exotic baryons from different SU(3)-multiplets. The masses of baryons partners with different values of spin $J$ are also estimated.

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arXiv2001

Multiskyrmions and baryonic bags

Analytical treatment of skyrmions given by rational map (RM) ansaetze proposed recently for the Skyrme model is extended to the model including the 6-th order term in chiral fields derivatives in the lagrangian (the SK6 variant of the model) and used for calculation of different properties of multiskyrmions. For special class of profile functions approximating the true profile and the domain wall behaviour at the same time, the masses and other static properties of multiskyrmions are expressed in terms of the Euler-type integrals. An upper bound is obtained for the masses of RM multiskyrmions which is close to the calculated masses, especially at large B. The gap between rigorous upper bound and lower bound, obtained for the SK6 model as well, for large B multiskyrmions is less than 9%, in comparison with about 4% for the SK4 (Skyrme) variant. The basic properties of such bubbles of matter are investigated, some of them, e.g. the thickness of the bubbles envelope, being of universal character, i.e. they do not depend on baryon number of configuration, or reveal a simple and natural dependence. The dependence of these properties on the number of flavours is absent or very weak in both models. Qualitatively, the properties of the baryonic bags are the same for the SK6 and SK4 variants of the model, although differ in some details.

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arXiv1997

Strange Skyrmions: status and observable predictions

The chiral soliton approach (CSA) provides predictions of the rich spectrum of baryonic states with different values of strangeness for any baryon number B. In the sector with B=1 the well known octet and decuplet of baryons are described within CSA, and some exotic states are predicted. In the B=2 sector there are many predictions, but only few of them - e.g. the existence of the virtual $Λ$N-state - have been confirmed till now. Possible reasons for this are discussed. In particular, the B=2 SO(3) hedgehog interpreted usually as H-particle within CSA has dimensions considerably smaller than dimensions of the deuteron. Therefore, the estimates of its production cross section made previously in the assumption that H-particle and deuteron are approximately of the same size, may be too optimistic. Other branches of the CSA predictions corresponding to other local minima of the B=2 configurations of the SU(3) chiral fields: SU(2) torus and skyrmion molecule with strangeness content close to 0.5 are also considered.

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