The generalized Levinson theorem for composite particle scattering in the framework of the Saito model

Levinson’s Theorem and the Nonlocal Saito Potential

“…Rather, they point out that their conclusions might need to be modified if a bound state at zero energy were to be included. Glockle and Le Tourneux (1976) analyze the Saito potential by the more conventional method of contour integration in k space. The function which they select for forming a logarithmic derivative for the application of the argument principle yields the extra π at k = 0 in the phase shift due to the Saito potential.…”

“…Qadri). However, attempts to discuss Levinson's theorem in the context of the Saito model (N.J. Englefield, 1974;W. Glockle, 1976) have failed to explain the mechanism by which the extra nodes are produced.…”

“…In particular, both Refs. (N.J. Englefield, 1974) and (W. Glockle, 1976) explicitly exclude the effects on Levinson's theorem resulting from a zero-energy continuum bound state. As has been discussed in detail by Newton ¢ www.ccsenet.org/jmr ISSN: 1916-9795 (R.G.…”

Local Inter-Nucleus Potential and Pauli-Forbidden States

“…We rewrite Eq. (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17), by using Eq. (3.7), into the inequality relation for…”

“…This orthogonality condition can be satisfied if the local potential is constructed to be so deep that all the FS become (in good accuracy) the bound states of this potential. Deep local potential as to support all the FS is quite satisfactory also with respect to the requirement of the generalized Levinson theorem.7).8), 14), 15) , This theorem demands that the phaseshifts Ot(E) (E denoting energy) satisfy Ot(O)-OI(=)=(nBo+nF)7r where nBo is the number of physical bound states and nF is that of the FS. The deep local potential which binds all the FS in addition to the physical bound states can satisfy the condition OI(O)-OI(=)=(nBo+nF)7r by the ordinary Levinson theorem.…”