In order to see the effects of the renormalization due to the relativistic
structure of the potential (#self2#288>) we solve the Schrödinger
equation with the equivalent nonrelativistic potential
[#jam89##1###,#klein##1###]
#math37#
|
USEP(r) = Σs(r) + #tex2html_wrap_indisplay1345#Σv(r) + #tex2html_wrap_indisplay1346#
|
(12) |
with
#math38#
| UDarwin(r) |
= |
#tex2html_wrap_indisplay1351##tex2html_wrap_indisplay1352##tex2html_wrap_indisplay1353##tex2html_wrap_indisplay1354##tex2html_wrap_indisplay1355# - #tex2html_wrap_indisplay1356##tex2html_wrap_indisplay1357# - #tex2html_wrap_indisplay1358##tex2html_wrap_indisplay1359# , |
|
| D(r) |
= |
E + Σs(r) - Σv(r) . |
(13) |
The single-particle wavefunctions obtained from the solution of the
Schroedinger equation with USEP are used to evaluate the matrix
elements of the #math39##tex2html_wrap_inline1365#(#tex2html_wrap_inline1366# + #tex2html_wrap_inline1367# ')/2M operator and
we find
#math40#
;SPMlt; 0+|#tex2html_wrap_indisplay1369##tex2html_wrap_indisplay1370#| 0- ;SPMgt; =
#math41#
|
i(- 1)j'+l'+1/2#tex2html_wrap_indisplay1372##tex2html_wrap_indisplay1373#F(n'l'j', nlj;λ = 0)
|
(14) |
where the function F is defined in the appendix.