Calculation of a narrow resonance with the LIT method
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 3P1 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.