Reply to K. Amos et al nucl-th/0401055.

An expression for the spin–orbit interaction coupling between different levels, which was shown to be aberrant more than thirty years ago persists in the literature without clear indication of what is used. It leads to expressions quite simpler than they should be. After an attempt to warn the community of the nuclear physicists on this strange situation (nucl-th/0312038), the authors of the publication in which the “aberrant” interaction is described and used, try to justify their work (nucl-th/0401055), by a very strange “symmetrization” of something already symmetric. They claim also that their method allows to solve some problem related to the Pauli principle and give some references, among which a book which reports the solution of such problem almost forty years ago, with a very small effect. An examination of their own results shows that their optimism is not completely justified. Nevertheless, any user of ECIS, sensitive to their arguments, is requested to ask their opinion to these five coauthors before publishing. PACS numbers 24.10.-i,25.40.Dn,25.40.Ny,28.20.Cz After the publication of some article [1] in Nuclear Physic A, I wanted to publish a comment [2] warning the nuclear physicist community that two different deformed spin–orbit are used in the literature for nucleon–nucleus inelastic scattering without notifying which one is employed. Because everybody uses the same expression in nuclear structure studies (for this reason, I qualified it as “normal”), for inelastic scattering, I called “normal” the one which has the same behavior between partial waves and “aberrant” the other one. As I am not of native of English language, I was thinking to be allowed to use this word, because I found on page 3 of [3] : ab–er–rant (. . .),adj. [. . .], deviating from what is true, correct, normal, or typical. and on page 3 of the first volume of [4] : ab–er–rant \ . . .\ adj [. . .], 1 : straying from the right or normal way : deviating from truth, rectitude, propriety 2 : deviating from the usual or natural type : EXCEPTIONAL, ABNORMAL. (. . . denoting pronunciation and etymology). My problem to publish such an advertisement is that I have only [1] to cite. On the 14th of June, I was visiting the office of the Nuclear Energy Agency, at Issy–les–Moulineaux, which send nuclear codes to who wants them all over the world (except in USA). We found on the web the answer [5] of which the title is quite terrifying for some body who sent almost 300 ECIS to more than 50 countries. I find this answer largely out of the subject. I have to answer to the spin–orbit question, but also on the antisymmetrization with occupied states, another subject on which I have comments to do but which I did not want to publish. In [2], Eq. (1) is not the spin–orbit interaction but its coefficient; the spin– orbit interaction involves the two following lines. The six–parameter spin– orbit interaction of ECIS can be used to compare results with the two different deformed spin–orbit interactions and many other expressions by who wants it; anyway, the parameters are read only if a special logical is set true. This is like that since ECIS67. Instead of laughing at, why the authors of [1] do not do the same? As the authors of [1] say that the “normal” is derived in some extremely hard–to–find publications”, let us resume it. First of all, the two-body spin– orbit interaction as described in [6, 7, 8, 9] 1 is “normal”; therefore, the intermediate step of its use as a one-body interaction, described by the sums of two terms of Eq. (84) of [6], the Eqs. (21-22) of [7], the Eqs. (51-52) of [8], and Eqs. (4,49-50) of [9] are also “normal”. With a finite range, these expressions are a kind of folding potential for the direct term, to which must be added similar expressions for the exchange term. At the zero–range limit (not δ(r − r) but δ(r − r)), direct and exchange terms for the two–body interaction are identical : they are given by Eq. (30) of [7] and Eq. (55) of [8]. Assuming zero for the eigenvalues of (l . σ) of one particle (which means complete shells for l = j+1/2 and j = l− 1/2 with same radial function), one get the same expression as with the “full Thomas term”. The result must be made hermitian, but not in the sense used by the authors of [1, 5] by dropping the derivative term acting on the right side but by replacing it by a derivation on the left side with opposite sign (that is : acting also on the form–factor). As the “normal” coupled–channel spin–orbit potential is derived in some extremely hard–to–find publications [5] but cannot been published anywhere because it is not new, let us give it here in details. First of all, the spin–orbit obtained when the Dirac equation is changed into its Schrödinger equivalent (“full Thomas form”) can be written as :