Potential inversion for p- and α-scattering at fixed energy

Equivalent local potential for the fish bone optical potential by inversion of its phase shifts

“…and t60 the common harmonic oscillator width parameter a=0.32fm -z is assumed, which means that the norm kernel eigenstates are harmonic oscillator functions of width parameter 0.512 fm -2.. For comparison with previous results we also neglect the imaginary part of the potential [23], which is of lesser importance for our purpose, namely the investigation of the consequences of the Pauli principle in the context of the fish bone optical model. The inversion method would of course be equally suitable for complex potentials, as demonstrated previously [18]. In Fig.…”

“…The 6FBOM are inverted at the stated energies using the mixed inversion scheme described in [18] and in the previous Section. The parameters {a,,fl,} of the mixed scattering function fitted to the bFBOM are given in Table 1 (where r/ is the Sommerfeld parameter), which takes the long-range part of the Coulomb potential into account [18]. The smoothing parameter 2 c and the parameters {%,ft,} completely determine our fits to the (~FBOM.…”

“…We briefly outline the quantal inversion method (mixed scheme) and refer to [16,17,18] for a full description. The potential V(r) is determined iterately, V(r)=Vx(r), The LS~)-+(r) are the logarithmic derivatives* of the Jost solutions f;}")-+(r) to the potential V~(r) in the rational scheme (Im 2 % > 0, Im fi2 < 0), and of the regular functions ~b(~")(r), in the nonrational scheme (Ima2<0, Im/?2>0).…”

“…The potential V(r) is determined iterately, V(r)=Vx(r), The LS~)-+(r) are the logarithmic derivatives* of the Jost solutions f;}")-+(r) to the potential V~(r) in the rational scheme (Im 2 % > 0, Im fi2 < 0), and of the regular functions ~b(~")(r), in the nonrational scheme (Ima2<0, Im/?2>0). The corresponding rational scattering function is given by The two schemes can be combined by writing S(2) as a product of a rational and a nonrational scattering function (mixed scattering function) [18]. The functions (2.6) or (2.7) (i.e., the sets of parameters {%,fin}) are fitted to the scattering function for which the potential is sought.…”

Strong absorption model and its associated potential

“…Usually the mixed procedure works rather well for higher energies. More details about this mixed method have been given in previous applications [18,19]. For many cases, especially at high energies, the inversion procedure can be facilitated by employing the WKBapproximation to the inverse scattering problem at Axed energy [12,20].…”