Effective  -  t-Matrix Interaction at Medium Energies

Abstract

The α-α transition operator-effective interaction, t αα (E, r) has been evaluated using phenomenological α-α optical potentials at several bombarding energies, E α from 77 to 200 MeV. The results are obtained by solving the Schrödinger equation with appropriate optical potentials for various partial waves and then clubbing these with their respective optical potentials and initial state plane waves. The change of the α-α optical potential with or without hard core has been shown to influence the effective α-α t-matrix interactions drastically. The behaviour of the calculated t αα (E, r) effective interaction indicates towards a solution of the large anomalies found in the (α, 2α) reaction analyses.

Heavy Cluster Knockout ReactionO16(C12,2CJoshi1, Jain2, Gupta3 et al. 2011Phys. Rev. Lett.Self Cite90003View full textAdd to dashboardCite

“…Herer r 12 ,R R 2B and the t 12 ðrÞ, the 12 C-12 C t matrix (evaluated at the final state relative energy-E f ), is given by [21,22]: where É ðþÞ 12 ðrÞ as expanded in terms of partial waves is,…”

Finite Range Effects in (α,2α) Reactions

“…We have examined the nature of theknockout vertex transition operator t ðrÞ at various energies and found it to be of fairly long range [15]. The -t-matrix effective interaction was also found to be strongly dependent on the nature of therealistic optical potentials.…”

“…The factorization can arise either from the zero range nature of the knockout vertex transition operator or from the optical distortion free scattering states. While the ZR-DWIA calculations exhibit large optical distortion characteristics [5,6] the cluster knockout data indicate little influence from it [6].We have examined the nature of theknockout vertex transition operator t ðrÞ at various energies and found it to be of fairly long range [15]. The -t-matrix effective interaction was also found to be strongly dependent on the nature of therealistic optical potentials.…”

“…The -t-matrix effective interaction was also found to be strongly dependent on the nature of therealistic optical potentials. These optical potentials are not unique and equally good fits to the elastic scattering data can be obtained by very different optical potentials [15]. Two drastically different types ofnuclear optical potentials in common use are (i) with short range repulsive core [16] and (ii) a potential which is purely attractive [17,18].…”

“…These two types ofoptical potentials, with their phase shifts matched, fit the elastic scattering data. In a detailed study [15] it has been demonstrated that differentoptical potentials yield different -t-matrix effective interactions, t ðrÞ's. For example with a repulsive core [16] the t-matrix effective interaction peak is shifted away from r ¼ 0 by about 1.5 fm, Fig.…”