Calculation of a narrow resonance with the LIT method

ISSN： 0177-7963

Source： Few-Body Systems, Vol.42, Iss.1-4, 2008-07, pp. : 139-151

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Abstract

The possibility to resolve narrow structures in reaction cross sections in calculations with the Lorentz integral-transform (LIT) method is studied. To this end we consider a fictitious two-nucleon problem with a low-lying and narrow resonance in the ³ P ₁ nucleon-nucleon partial wave and calculate the corresponding “deuteron photoabsorption cross section”. In the LIT method the use of continuum wave functions is avoided and one works instead with a localized function $widetilde{Psi}$ . In this case study it is investigated how far into the asymptotic region $widetilde{Psi}$ has to be determined in order to obtain a precise resolution of the artificially introduced E1 resonance. Comparing with the results of a conventional calculation with explicit neutron-proton continuum wave functions it is shown that the LIT approach leads to an excellent reproduction of the cross section in the resonance region and of further finer cross-section details at higher energies. To this end, however, for $widetilde{Psi}$ one has to take into account two-nucleon distances up to at least 30 fm.