MODIFIED EFFECTIVE RANGE FUNCTION
Jan, 198115 pages
Published in:
- Phys.Rev.A 26 (1982) 1218-1225
Report number:
- Print-81-0065 (GRONINGEN)
View in:
Citations per year
Abstract: (APS)
We derive a general formula for a modified effective-range function (MERF), KlM(k2), for all partial waves, l=0,1,…. This is a generalization of the effective-range function associated with a short-range potential, Kl(k2)=k2l+1cotδl(k). Here k2 is the energy variable and δl(k) the phase shift. The MERF KlM(k2) can be associated with a potential V(r) that allows a decomposition into a long-range and a short-range component. It is a complex real-meromorphic function of k2 in the complex k plane in a domain containing the origin. This (large) domain is determined by the short-range part of the potential. We give a simple formula for KlM(k2), valid for all l=0,1,…. It can be used if the long-range part of the potential is analytic at r=0. For l=0 we have the simple expression K0M(k2)=|f0(k)|−2k[cotδ0M(k)−i]+f0′(k,0)f0(k). Here f0(k) and f0(k,r) are the Jost function and Jost solution, respectively, associated with the long-range part of the potential, and δ0M(k) is the difference between the s-wave phase shift associated with the total potential and that of the long-range potential. The prime in f0′(k,0) denotes differentiation with respect to r. The extension to the case of the Coulomb potential which violates the condition of analyticity at r=0 is briefly discussed.- QUANTUM MECHANICS: SCATTERING
- SCATTERING: QUANTUM MECHANICS
- MODEL: POTENTIAL
- APPROXIMATION: EFFECTIVE RANGE
References(42)
Figures(0)