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The method
Energy is divided in g=1,..,
G groups
of width ΔE
g
so that energy decreases as group
order decreases
)1(
)
(
1 4
,
,
)ˆ,(
,
)ˆ,(
ˆ
pr r
P
p
gpq
g scat q
rg gt
rg
)2(
0
) ,(
1'
)( ' , ,
)(
' ,,
)ˆ,( ,
l
l
l m
m
lY
G
g
r gml
rg gls
rg scat
q
O
i
)3(
1
'
)' ,( )
,(,
1 1'
'
)(
' ,,
gE
dE dE Er E Erls
gE
gE
gE
gE
rg gls
ur equat ons
become:
1
1
) ,(
gE
gE
dEEr
gE
1
)4(
4
'
)ˆ(
)ˆ, ,(
) ,( ,
)( , ,
gE
dE d m
lY Er
gE
gE
dEErml
rgml
)5(
) ,(
1
)' ,( ) ,(
)( ,
dEEr
gE
dE Er Ert
gE
rgt
gE