Investigation of baryon-like bound states of nonrelativistic quarks in the self-consistent field approximation
Teoretičeskaâ i matematičeskaâ fizika, Tome 54 (1983) no. 2, pp. 258-267
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The $1/N$ expansion is used to investigate the nonrelativistic model of baryons proposed by Witten: $N$ quarks ($N\gg1$) of one flavor in the same spin state bound by two-particle attractive forces determined by a potential $V(r)$. The coordinate part of the wave function of the $N$ quarks forming the bound state is represented in the form $\psi(\mathbf{x}_1,\dots,\mathbf{x}_N)= \prod\limits_{i=1}^N\varphi(\mathbf{x}_i)$. The resulting integrodifferential spectral problem is solved by reduction to nonlinear differential equations of higher order. The following potentials are considered: 1) $V(r)=-g^2r^{-1}$, 2) $V(r)=g^2\alpha^2r$, 3) $V(r)=g^2(-r^{-1}+\alpha^2r)$. A computer was used to find the characteristics of the corresponding baryon-like bound states of $N$ quarks.
@article{TMF_1983_54_2_a9,
author = {A. A. Bogolyubskaya and I. L. Bogolyubskii},
title = {Investigation of baryon-like bound states of nonrelativistic quarks in the self-consistent field approximation},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {258--267},
year = {1983},
volume = {54},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1983_54_2_a9/}
}
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%0 Journal Article %A A. A. Bogolyubskaya %A I. L. Bogolyubskii %T Investigation of baryon-like bound states of nonrelativistic quarks in the self-consistent field approximation %J Teoretičeskaâ i matematičeskaâ fizika %D 1983 %P 258-267 %V 54 %N 2 %U http://geodesic.mathdoc.fr/item/TMF_1983_54_2_a9/ %G ru %F TMF_1983_54_2_a9
A. A. Bogolyubskaya; I. L. Bogolyubskii. Investigation of baryon-like bound states of nonrelativistic quarks in the self-consistent field approximation. Teoretičeskaâ i matematičeskaâ fizika, Tome 54 (1983) no. 2, pp. 258-267. http://geodesic.mathdoc.fr/item/TMF_1983_54_2_a9/
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