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 TMF, 1972, Volume 10, Number 2, Pages 215–222 (Mi tmf2657)

Conditions for the existence of solutions of the equations of the type of the differential method equations

G. N. Chermalykh

Abstract: Equations of the type of the differential method equations are regarded as singular linear integral equations for the inelasticity coefficients under the assumption that the real parts of the phase shifts are known. For any finite system the existence of a unique solution (except for the CDD polynomial ambiguity) is proved under fairly weak restrictions on the dependence of the elements of the crossing matrix, $\beta_{ll'}(\omega,\omega')$ on $\omega$ and $\omega'$ ($l$, and $l'$ are the angular momenta and $\omega$ and $\omega'$ are the cms energies of the direct and crossed channels, respectively). Iris also shown that the condition that there exist a solution (in the class of continuous bounded functions) of the linear integral equation equivalent to an infinite system leads to the restriction $\beta_{ll'}(\omega,\omega')\to0$, $ll'\to\infty$, $\omega$, $\omega'\in[\omega_i,\infty)$, where $\omega_i$ is the inelastic threshold and to a behavior of the partial amplitude $T_l(\omega)\xrightarrow[l\to\infty] 0$ $(\omega\in[\omega_i,\infty))$, characlteristic for strong interactions and which is usually deduced from the axiomatic $s\bigotimes t$ analyticity. Models with a short-range repulsion are discussed and allowance is made for inelasticity in the models of the differential method.

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English version:
Theoretical and Mathematical Physics, 1972, 10:2, 140–145

Citation: G. N. Chermalykh, “Conditions for the existence of solutions of the equations of the type of the differential method equations”, TMF, 10:2 (1972), 215–222; Theoret. and Math. Phys., 10:2 (1972), 140–145

Citation in format AMSBIB
\Bibitem{Che72} \by G.~N.~Chermalykh \paper Conditions for the existence of solutions of the equations of the type of the differential method equations \jour TMF \yr 1972 \vol 10 \issue 2 \pages 215--222 \mathnet{http://mi.mathnet.ru/tmf2657} \transl \jour Theoret. and Math. Phys. \yr 1972 \vol 10 \issue 2 \pages 140--145 \crossref{https://doi.org/10.1007/BF01090725}