The name is absent



Substituting for Xg in the Euler-Lagrange equation for the second segment leads to
an expression for p2(r)X⅜(r), from which an expression for similar to eqn. 7.14
can be obtained. Repeating this procedure through the ∖th backbone segment in the
chain gives

3 — ɪ                                         3 — ɪ           3 — ɪ

/   = cxp(,6f / - [ ⅛ι⅛2..⅛j-ιexp[J2A(ri)]∩Δ^+1∖ri,ri+ι)

⅞(rJ         i=ι   j J                 i=ι       i=ι

J-I

= exp(∕352∕√)∕u(rj∙),                        (7.15)

i=l

where I1j is a recursive function, ʃi,ɪ(r) = 1 and ʃij(r) = ʃ dr'ʃij-ɪ(r') exp[∙Dj-ι(r')]Δ^~lj)(r, r').

For brevity, this procedure is labeled as proc. A, since it is used numerous times in
the derivation.

Similarly, applying proc. A for the linear branch ζbj, from the branch segment 1bj

Γ till the backbone segment ‘j’ gives

bj mj                                              bj m,j           bj τ∏j 1

- =exp(β ∑ μi) .. / drb.ι⅛b.2..dr6j.mj exp[J2 A(r*)] ɪɪ ∆<v+υ(ri, ri+ι)
ʌθlɪ`j`            
i=bjl ''    ∙'                            i=bjl          i=bjl

X1,bjmj (rj,rbjτnj) = exp (/3 J2 Mi)5rj(rj),                (716)

j=63l

where Brj denotes the branch factor for the branch ibj, at (backbone) segment ‘j’.
Clearly, Brj∙(r) = ʃ⅛71*Jm3(r')exp[Dbjmj(r')]Δ^m>(r,r'), where
I^.a is the I1
function for the segment 1bj- a' in the branch ςbj,. The branch factors for all the

189



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