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SAI_RECLS

This library contains 20 routines for calculation of recoupling matrices


\begin{displaymath}
R\left( \lambda _i,\lambda _j,\lambda
_i^{\prime },\lambda _...
...t(
s,s,s,s,\Lambda _s^{bra},\Lambda _s^{ket},\Gamma _s\right).
\end{displaymath} (21)

For more details see P2 [4] (Section 4). Most of the subroutines from this module use common blocks CONSTS and MEDEFN from MCHF atomic structure package [1,11].

DLSA1 Evaluates the coefficients $C_{1}$ (see (15) P2 [4]).

DLSA2 Evaluates the coefficients $C_{5}$ (see (16) P2 [4]).

DLSA3 Evaluates the coefficients $C_{2}$ (see (23) P2 [4]).

DLSA4 Evaluates the coefficients $C_{4}$ (see (21) P2 [4]).

DLSA5 Evaluates the coefficients $C_{3}$ (see (17) P2 [4]).

DLSA6 Evaluates the coefficients $C^{\prime}_{6}$ (see (25) P2 [4]).

RECOUP0 Checks the angular momentu selection rules for the recoupling coefficients. For example it uses the expression (18) in one interacting shell case (see P2 [4]).

RECOUP2 Checks or calculates the recoupling coefficients for the scalar operator which has the tensorial structure

$\displaystyle \left[ A^{(k)} \left( n_{1}l_{1} \right) \times B^{(k)} \left(
n_{2}l_{2} \right) \right] ^{(0)},$     (22)

where $A^{(k)}$ and $B^{(k)}$ are simple or composite tensor operators of rank k. $A^{(k)}$ acts only on the first active shell and $B^{(k)}$ on the second active shell in the order in which they are coupled in the configuration. It uses (22) from P2 [4].

RECOUP3 Checks or calculates the recoupling coefficients for the scalar operator:

$\displaystyle \left[ \left[ A^{(k_1)} \left( n_{i}l_{i} \right) \times B^{(k_2)...
...\right) \right] ^{(k)} \times C^{(k)} \left( n_{m}l_{m} \right)
\right] ^{(0)}.$     (23)

As in (22), $A^{(k_1}$, $B^{(k_2)}$ and $C^{(k)}$ are simple or composite tensor operators which act, on subshells $i$, $j$ and $m$ respectively. It uses (26) from P2 [4].

RECOUP31 Aids RECOUP3 in calculating the recoupling matrix in the case of three interacting shells.

RECOUP4 Checks or calculates the recoupling coefficients for the the operator:

$\displaystyle \left[ \left[ A^{(k_1)} \left( n_{1}l_{1} \right) \times B^{(k_2)...
...ight) \times D^{(k_4)} \left( n_{4}l_{4}
\right) \right] ^{(k)} \right] ^{(0)},$     (24)

where $A^{(k)}$, $B^{(k_2)}$, $C^{(k_3)}$ and $D^{(k_4)}$ may be simple or composite tensor operators of the orders indicated, corresponding to the structure of (24). The subshells must be ordered so that $A^{(k_1)}$ operates on the first and $D^{(k_4)}$ on the last in order. It uses (33) from P2 [4].

RLSP0 Checks for delta-functions $\delta \left ( L_i, L^{\prime}_i \right)$ for one and two interacting shell (see (14) and (19) in P2 [4]).

RLSP00 Checks for delta-functions $\delta \left ( L_{i},L^{\prime}_i \right)$ for three and four interacting shell (see (24) and (27) in P2 [4]).

RLSP1 Checks or calculates the recoupling coefficients for the operator which has the tensorial structure

$\displaystyle A^{(k)} \left( n_{1}l_{1} \right).$     (25)

It uses (14) from P2 [4].

RLSP2 Checks or calculates the recoupling coefficients for the operator which has the tensorial structure

$\displaystyle \left[ A^{(k_1)} \left( n_{1}l_{1} \right) \times B^{(k_2)} \left(
n_{2}l_{2} \right) \right] ^{(k)}.$     (26)

It uses (19) from P2 [4].

RLSP3 Checks or calculates the recoupling coefficients for the operator:

$\displaystyle \left[ \left[ A^{(k_1)} \left( n_{i}l_{i} \right) \times B^{(k_2)...
...ht) \right] ^{(k_3)} \times C^{(k_4)} \left( n_{m}l_{m} \right)
\right] ^{(k)}.$     (27)

It uses (24) from P2 [4].

RLSP31 is needed by RLSP2.

RLSP32 is needed by RLSP2.

RLSP4a Checks or calculates one part of the recoupling coefficients for the operator:

$\displaystyle \left[ \left[ A^{(k_1)} \left( n_{1}l_{1} \right) \times B^{(k_2)...
...ht) \times D^{(k_5)} \left( n_{4}l_{4}
\right) \right] ^{(k_3)} \right] ^{(k)}.$     (28)

RLSP4b Checks or calculates other parts of the recoupling coefficients for the operator (28).


next up previous
Next: SAI_SQLS1 Up: Description of the Libraries Previous: Description of the Libraries
2001-12-07