Orthogonal intersection adapted coordinates

The lowest order contributions to the energy are described by the conical parameters g, h, and s, k = x,y,z, or by d, A = 1,2 and s, k = x,y,z-Here and below the superscript ij is suppressed when no confusion will result. We also will use the nonrelativistic convention g - x,fi" y and h J z, where is real is parallel to. These parameters [9] are reported in Figure 4a and b. Their continuity is attributable to the use of orthogonal intersection adapted coordinates. For comparison, Figure 4a and b reports the nonrelativistic quantities g , and s, respectively. While noting that there is no unique correspondence... 

These results can be simplified by introducing scaled orthogonal intersection adapted coordinates x =, y = and z = In these coordinates,... 

Examples of orthogonal intersection adapted coordinates are provided in Sec. 4. 

Figures 6(a) and 6(b) report the conical parameters Sy and g, h, respectively, obtained from orthogonal intersection adapted coordinates. If orthogonal g and h had not been used g and h would vary erratically along the path, making interpolation and extrapolation impossible. Significantly, from Figs. 6(a) and 6(b), it can be seen that although these conical parameters are by no means constant, the inequalities > g > h, discussed above for Tl trans,p, 2.95), are, in a qualitative sense, typical.

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