To calculate the (3d5+3d44s) 3d44p transitions in Mn III
properly,
it is necessary to take into account the interaction with neighbouring
configurations.
For that reason the even system was built from
(3d5+3d44s+3d34s2+3d44d+3d45s) and the odd system from
(3d44p+3d34s4p+3d24s24p+3d45p+3d44f).
Interactions with other (far-lying) configurations are taken into account
by means
of so-called effective operators. As outlined in the above, the full
transition matrix is
calculated after completing the fitting procedure.
The angular part of the pure LS transition matrix
is found from straightforward Racah algebra, while the radial transition
integrals are obtained from a relativistic Hartree-Fock program (MCDF from
Parpia et al. 1996).
The values of the transition integrals, corrected for core polarization, are
given in Table 1 (click here). Subsequently, the pure LS transition matrix is
transformed by the eigenvectors of the bra (even) and the ket (odd for E1,
even for M1 or E2) system to obtain the transition probabilities between the
initial and final states that are in reality expansions of pure LSJ states.
In Table 2 (click here) the log(gf) values for the (3d5+3d44s)
3d44p electric dipole (E1) transitions are given.
This system is selected by cutting off the higher energy values of both
the even and the odd system in the final printing procedure;
only log(gf) values larger than -1 are included. In this paper, a sample
of the 14 highest lines is given; as explained in a footnote to the abstract,
the complete table can be obtained at CDS.
The first column of this table shows the wavelength obtained from the energy differences between the experimental level values. Wavelengths below 2000 Å are given as vacuum wavelengths and above 2000 Å\ as air wavelengths. The second column gives the log(gf) values followed by the J-value, energy value and the name of the lower (even) level. The first character of the level name designates the configuration number: for the even levels i"1" refers to 3d5 and i"2" to 3d44s; for the odd levels i"1" refers to 3d44p. An i"*" after the energy value indicates that the level is known, in which case the experimental level value is given. When unknown, the calculated energy value is given and used to approximate the wavelength. Full results including weaker lines and lines involving higher lying levels can be found on Internet.
Transition probabilities of forbidden, i.e. non-E1, transitions are only given for the lower even configurations, in view of their astrophysical relevance.
The radial part of the E2 transitions is, just as in the case of the E1
transitions,
calculated from MCDF wavefunctions. In Table 3 (click here)
the radial integrals for the electric quadrupole transitions are given in
the form
of a symmetric matrix.
For E2-transitions within the 3d44d configuration,
there are two non-zero contributions, one for the and one for the
4d-4d
transition. For this case, there are
two rows in the table, the upper for the 3d-3d
integral and the lower for the 4d-4d transition integral.
The A-values for the forbidden lines given in Table 4 (click here), are restricted
to the magnetic dipole (M1) and electric quadrupole (E2)
transitions within the 3d5+3d44s configurations,
from levels with an energy of less than 75 000 cm-1 above the ground and with
A-values larger than . The level with the lower J-value is
given
first in the designation of the transition. Again, a sample of the table
available
at CDS is included in the paper.