INVERSION OF THE LEVEL MATRIX IN R-MATRIX THEORY BY THE METHOD OF RANK ANNIHILATION [report]

T Watanabe
1967 unpublished
A. M.La any warranty or mpmmentntki, ex-or implied, with t e s~t to thc M , -p-, a urdvlaas d fbc iaf-tioo canthad in tht report, or 1h.t the wa of w i d -, appwatpx. matbo8, or ca proocaducloled = Uw repat =Y not pnortab 0rmCdriphtt;or B. Armmar any KabiPtisr with rsspect ta the use d, or f a danwa d & fmm the llrc of m y inf-th, -=cur, method, or process B h c W in tbL repert. & d i n t b e a t r o w , " p e -~o l l b e h . l l d t b a~" i n d u e a m y~~l l p l e m~ coatractor of tbe
more » ... n, or a n p b w d ~u c h omtnetar, to tht atcnt that mch rmpbyee a etractor d thc Comdsaian, or employee d such contractor m n , diPlmLutu, or provides aceen co, any ialomwian putwant to bis anpbymat a contract with the C e n d m h , ar his employment with arch mimctor. ABSTRACT . . . . The level matrix approach to the problem of matrix inversion in R-matrix theory still requires inverting the level matrix if the collision matrix is to be used for ca.lculating cross sections. It is shown that the method of rank annihilatiori inverts the level matrix in analytical form for.the genera'l case. The general results a r e then specialized to the cases of two and three channels, and the expressions for the scattering and fission cross sections are obtained. Although the results of the specialized treatment a r e applied to the two level situation, the relevant expressions a r e in a form that al1ows.a genera.liiation to any number of levels (channels a r e still restricted to 2 and 3 in number). The approximations, which can be made to.simplify the reduced widths and which can eliminate off-diagonal channels a s well a s the application of these modifications, will be discussed.
doi:10.2172/4185418 fatcat:bjc7svmb2vauxog63wsje4vmk4