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2. Transition probabilities

To calculate the (3d5+3d44s) tex2html_wrap_inline1384 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.

2.1. E1 results

In Table 2 (click here) the log(gf) values for the (3d5+3d44s) tex2html_wrap_inline1384 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.

2.2. Forbidden lines

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 tex2html_wrap_inline1438 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 tex2html_wrap_inline1456. 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.


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