On the construction of wavefunctions in the six quark system

Obukhovsky, I. T.; Smirnov, Yu.F.; Tchuvil’sky, Yu. M.

doi:10.1088/0305-4470/15/1/013

Cited by 22 publications

(4 citation statements)

References 30 publications

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“…The quantum numbers for the hypercharge, isospin and spin of the particle pair 12 and the single particle 3 are indicated by subscripts. Finally the fractional parentage coefficient Γ can be presented as a product of two factors [41]. The first is the scalar factor of the Clebsch-Gordan coefficient for the group SU(6) F S in the reduction SU(6) F S ⊃ SU(3) F × SU(2) S , which is determined only by invariants of the groups SU(6) F S , SU(3) F and SU(2) S and does not depend on isospin, hypercharge nor on the third components of isospin and spin:…”

Section: Algebraic Structure Of the Oscillator Wavefunctionsmentioning

confidence: 99%

The spectrum of the nucleons and the strange hyperons and chiral dynamics

1996

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The spectra of the nucleons, ∆ resonances and the strange hyperons are well described by the constituent quark model if in addition to the harmonic confinement potential the quarks are assumed to interact by exchange of the SU(3) F octet of pseudoscalar mesons, which are the Goldstone bosons associated with the hidden approximate chiral symmetry of QCD. In its SU(3) F invariant approximation the pseudoscalar exchange interaction splits the multiplets of SU(6) F S ×U(6) conf in the spectrum to multiplets of SU(3) F ×SU(2) S ×U(6) conf . The position of these multiplets differ in the baryon sectors with different strangeness because of the mass splitting of the pseudoscalar octet and the different constituent masses of the u,d and s quarks that breaks SU(3) F flavor symmetry. A description of the whole spectrum, to an accuracy of ≃ 4% or better, is achieved if one matrix element of the boson interaction for each oscillator shell is extracted from the empirical mass splittings. The ordering of the positive and negative parity states moreover agrees with the empirical one in all sectors of the spectrum. A discussion of the conceptual basis of the model and its various phenomenological ramifications is presented. Preprint DOE/ER/40561-187-INT95-16-01 hep-ph 9505422 Submitted to Physics Reports 7.05.1995 0

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Section: Algebraic Structure Of the Oscillator Wavefunctionsmentioning

confidence: 99%

The spectrum of the nucleons and the strange hyperons and chiral dynamics

1996

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“…The mass difference M(S6p6)-4M(S 3) indicated above is estimated by using the MIT bag formula (3) [19] with fractional parentage coefficients [11,12] while the orbital symmetry may now be characterized by the quasispin s [3,31]. We see that…”

Section: Appendixmentioning

confidence: 94%

“…Such complicated systems, as 9q and 12q, can at present be realistically treated not on the basis of the fractional parentage coefficient (fpc) technique [3,11,12], as was done for the 6q-system [3,13], but in the Casimir operator approximation [14] when in the expression (1) a certain average V is used. Such a simplification seems expedient also because the undertaken extension of the MIT bag model structure, which gives rather far in the number of quarks in the system, is not obvious and qualitative conclusions seem to be enough to check the scheme being developed by its experimental implications.…”

Section: Quark Configurations and Symmetry Typesmentioning

confidence: 99%

On the quark structure of the lightest nuclei

et al. 1983

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It is shown that in the 9q-and 12q-systems, i.e., 3He-3He and 4He nuclei, the most energetically favourable colour magnetic types of symmetry are [flcs = [621] [623]x . The colour magnetic nucleon attraction associated with these configurations increases as the square of the nucleon number in the sequence 2H, 3He, 4He, becoming quite strong in 4He. This may provide a basis for explaining the "mysterious properties" of 3He-3He and 4He. However, with the further increase in A, the above effect drastically decreases. A qualitative calculation on the quark excitation spectrum for the 3H-3He and 4He nuclei is presented. The 4He nucleus seems to possess some properties of a "quark magic nucleus". The experimental situation is discussed.In recent years the opinion has more and more firmly been established in the literature that from the viewpoint of both quark structure of nucleons and the character of quark-gluon interaction the concept of repulsive core in the NN-interaction is far too simplified. Of course, there are channels in which, for example, the spin-colour symmetry is characterized by the Young scheme [f] [2,4]. This configuration leads to CM nucleon attraction [3], because of the rearrangement of the Young spin-colour scheme [23]cs to the more energetically favourable scheme [42]c s in which symmetric quark pairs are prevalent (for estimates, see below). In reality we do not know how quarks are confined in a NN-system. Therefore, at this stage, it appears reasonable to adopt the phenomenological approach to the NN-interaction, following the microscopic description of quarks in choosing the types of interaction, and not their quantitative characteristics. The point is that the colour-magnetic qq-interaction, which plays the most significant role in quark configuration splitting Hint = --~ (~i.~j)(~Tiffj)Vij [42]x configuration in the MIT bag model turn out to be approximately degenerate with the states of the S 6 configuration, so that there is an interesting attraction-repulsion instability, which may be found important for the analysis of weak interactions (free nucleon interpenetration) [5]. It is quite possible that the CM attraction of nucleons is in fact dominant in a NN-system at small distances [3,6] which may be expressed in the NNchannel by a deep attractive potential with the forbidden O S-state [7] (to the quark configuration S4P 2, there corresponds in nonrelativistic model a wave function with a node in the NN channel for the S-wave). There are indirect indications that the

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“…Smirnov was an active participant of the team who developed methods of calculation relative to the dynamics of the six-quark system [34]. (The paper [34] contains a proof of the connection between the isoscalar factors of the Clebsch-Gordan coefficients of the unitary group SU(n) and the Clebsch-Gordan coefficients of the companion permutation group S n .) This team also emphasized the role of color-magnetic attraction and as a consequence of quark configuration mixing in this system [35].…”

Section: B Theory Of Nuclear Reactionsmentioning

confidence: 99%

In memoriam Yurii Fedorovich Smirnov: Some personal reminiscences on a great physicist

Kibler

2012

Phys. Atom. Nuclei

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Yurii Fedorovich Smirnov (1935-2008 was a famous theoretical physicist. He achieved his career mainly at the Institute of Nuclear Physics of Moscow. These notes describe some particular facets of the contributions of the late Professor Smirnov in theoretical physics and mathematical physics. They also relate some personal reminiscences on Yurii Smirnov in connection with some of his numerous works.

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On the construction of wavefunctions in the six quark system

Cited by 22 publications

References 30 publications

The spectrum of the nucleons and the strange hyperons and chiral dynamics

The spectrum of the nucleons and the strange hyperons and chiral dynamics

On the quark structure of the lightest nuclei

In memoriam Yurii Fedorovich Smirnov: Some personal reminiscences on a great physicist

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