This library is for calculating the angular parts of matrix elements for a scalar two-particle operator. It contains 18 subroutines. Most of the subroutines from this module use common blocks CONSTS and MEDEFN from MCHF atomic structure package [1,11]. The calculations are performed according to the methodology P2 [4].
COULOMBLS Investigates
the two-electron submatrix elements of electrostatic interaction
The value of the output parameter AA of this subroutine is:
Table 3 lists the expressions used by each of the subroutines NONRELAT1, NONRELAT2, NONRELAT31, NONRELAT32, NONRELAT33, NONRELAT41, NONRELAT51, NONRELAT52, NONRELAT53. The numbering of expressions is the same as in paper P2 [4], where all these expressions are presented. As the structure of all the subroutines mentioned earlier is the same, and only different expressions are used and different subroutines are called, we will discuss in more detail only one of these subroutines.
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NONRELAT1 | |||||||||
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(47) | (5) | (38),(35) | - | - | - | (48),(49) | (18) | (41) |
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(50) | (6) | (35) | (35) | - | - | (51) | (22) | (41) |
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(50) | (6) | (35) | (35) | - | - | (51) | (22) | (41) |
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(54) | (6) | (35) | (35) | - | - | (55) | (22) | (41) |
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(54) | (6) | (35) | (35) | - | - | (55) | (22) | (41) |
NONRELAT2 | |||||||||
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(52) | (6) | (35) | (35) | - | - | (53) | (22) | (41) |
NONRELAT31 | |||||||||
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(56) | (6) | (36) | (34) | - | - | (58) | (22) | (42) |
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(56) | (6) | (36) | (34) | - | - | (59) | (22) | (42) |
NONRELAT32 | |||||||||
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(60) | (6) | (34) | (37) | - | - | (62) | (22) | (42) |
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(60) | (6) | (34) | (37) | - | - | (63) | (22) | (42) |
NONRELAT33 | |||||||||
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(50) | (7) | (34) | (34) | (35) | - | (51) | (26) | (42) |
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(50) | (7) | (34) | (34) | (35) | - | (51) | (26) | (42) |
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(54) | (7) | (34) | (34) | (35) | - | (55) | (26) | (42) |
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(54) | (7) | (34) | (34) | (35) | - | (55) | (26) | (42) |
NONRELAT41 | |||||||||
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(52) | (7) | (34) | (34) | (35) | - | (53) | (26) | (42) |
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(52) | (7) | (34) | (34) | (35) | - | (53) | (26) | (42) |
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(52) | (7) | (34) | (34) | (35) | - | (53) | (26) | (42) |
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(52) | (7) | (34) | (34) | (35) | - | (53) | (26) | (42) |
NONRELAT51 | |||||||||
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(52) | (8) | (34) | (34) | (34) | (34) | (53) | (33) | (43) |
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(52) | (8) | (34) | (34) | (34) | (34) | (53) | (33) | (43) |
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(52) | (8) | (34) | (34) | (34) | (34) | (53) | (33) | (43) |
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(52) | (8) | (34) | (34) | (34) | (34) | (53) | (33) | (43) |
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(52) | (8) | (34) | (34) | (34) | (34) | (53) | (33) | (43) |
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(52) | (8) | (34) | (34) | (34) | (34) | (53) | (33) | (43) |
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(52) | (8) | (34) | (34) | (34) | (34) | (53) | (33) | (43) |
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(52) | (8) | (34) | (34) | (34) | (34) | (53) | (33) | (43) |
NONRELAT52 | |||||||||
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(50) | (8) | (34) | (34) | (34) | (34) | (51) | (33) | (43) |
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(54) | (8) | (34) | (34) | (34) | (34) | (55) | (33) | (43) |
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(50) | (8) | (34) | (34) | (34) | (34) | (51) | (33) | (43) |
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(54) | (8) | (34) | (34) | (34) | (34) | (55) | (33) | (43) |
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(50) | (8) | (34) | (34) | (34) | (34) | (51) | (33) | (43) |
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(50) | (8) | (34) | (34) | (34) | (34) | (51) | (33) | (43) |
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(54) | (8) | (34) | (34) | (34) | (34) | (55) | (33) | (43) |
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(54) | (8) | (34) | (34) | (34) | (34) | (55) | (33) | (43) |
NONRELAT53 | |||||||||
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(50) | (8) | (34) | (34) | (34) | (34) | (51) | (33) | (43) |
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(50) | (8) | (34) | (34) | (34) | (34) | (51) | (33) | (43) |
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(54) | (8) | (34) | (34) | (34) | (34) | (55) | (33) | (43) |
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(54) | (8) | (34) | (34) | (34) | (34) | (55) | (33) | (43) |
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(50) | (8) | (34) | (34) | (34) | (34) | (51) | (33) | (43) |
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(50) | (8) | (34) | (34) | (34) | (34) | (51) | (33) | (43) |
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(54) | (8) | (34) | (34) | (34) | (34) | (55) | (33) | (43) |
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(54) | (8) | (34) | (34) | (34) | (34) | (55) | (33) | (43) |
NONRELAT1 is meant for finding angles for the distributions
,
and
.
In the
case, the program uses expression
(5) from P2 [4]. In this case
where
and
and
The value of the reduced matrix element of operator (43) is
found by subroutine WWLS1, and that of
(44) by W1 (see section SAI_SQLS1).
The value of coefficient
is calculated by COULOMBLS subroutine, because this coefficient, to the
accuracy of a factor and a phase, is equal to that part of the
two-electron submatrix elements of electrostatic interaction,
which this subroutine is calculating. The coefficient
is found by COULOMBLS and SIXJ,
and the recoupling matrix is investigated by
RECOUP0 (see section SAI_RECLS).
For the distributions
and
the subroutine NONRELAT1 uses
(6) of P2 [4], keeping in mind that
is expressed as (51) of P2 [4] and tensorial parts
,
are equal to (35) from
P2 [4]. The coefficients
are investigated by COULOMBLS, the coefficients
and
are found by W1W2LS
from the SAI_SQLS1 library, and the recoupling matrix is
calculated by RECOUP2.
For the distributions
and
the subroutine NONRELAT1 uses
(6) of P2 [4], keeping in mind that
is expressed as (55) of P2 [4] and tensorial parts
,
are equal to (35) from
P2 [4]. The coefficients
are investigated by COULOMBLS and SIXJ, the coefficients
and
are found by W1W2LS
from the SAI_SQLS1 library, and the recoupling matrix is
calculated by RECOUP2.