Geodesic
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 
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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     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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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.

[1] Vainshtein A. I. i dr., UFN, 123:2 (1977), 217 | DOI

[2] Witten E., Nucl. Phys., B160:1 (1979), 57–115 | DOI | MR

[3] 't Hooft G., Nucl. Phys., B72:3 (1974), 461–473 ; Nucl. Phys., B75:3 (1974), 461–470 ; Coleman S., 1/N, Preprint SLAC-PUB-2484, SLAC, Stanford, 1980 | DOI

[4] Bogolyubskii I. L., Bogolyubskaya A. A., Sfericheski-simmetrichnye svyazannye sostoyaniya v sisteme bolshogo chisla nerelyativistskikh kvarkov s lineinym potentsialom poparnogo prityazheniya, Soobschenie R2-80-803, OIYaI, Dubna, 1980

[5] Bogolyubskii I. L., Bogolyubskaya A. A., Modelirovanie barionopodobnykh svyazannykh sostoyanii kvarkov s mezhkvarkovym potentsialom $V(r)=-g^2r^{-1}(1-\alpha^2r^2)$, Soobschenie R2-81-553, OIYaI, Dubna, 1981