1. Introduction

Chemically peculiar stars are known to display a high Mn abundance: manganese lines are strong in Bp stars, especially in the HgMn subgroup (Jaschek & Jaschek 1995). Examples are Cancri, HR 7245 and Lupi. Higher ionization will be found in Ap stars. While the 4s-4p transitions of Mn III are certainly expected to appear e.g. in stellar Hubble (HST) spectra, most identification work up to now is restricted to Mn I and Mn II (Adelman et al. 1993; Wahlgren et al. 1994; Lopez-Garcia & Adelman 1994; Wahlgren et al. 1995; Pintado & Adelman 1996). It seems that a lack of knowledge of the Mn III spectrum frustrates the identification possibilities at the moment and therefore, the calculation of Mn III intensities appears a logical project to undertake. The 3d-4p transitions of Mn III, however, fall below the HST 1200 Å\ limit, but may in the near future be observed at high resolution by FUSE-LYMAN down to the onset of the Lyman continuum at 912 Å.

The present work is the second to calculate transition probabilities in the framework of orthogonal operators. It has been shown (Raassen & Uylings 1996) to give reliable results for complex atoms, i.e. atoms with Z> 20 and more than one electron outside closed shells. Characteristics of the method can be found in our recent publication on Ti III and V IV (Raassen & Uylings 1997). In Sect. 2, a short introduction of the method is given. In Sect. 3, details of the calculation as well as the numerical results are presented.

1.1. Orthogonal operators

Theoretical transition probabilities can be obtained either from pure ab initio calculations or from an admixture of first principles theory and input of experimental energies. Examples of the first method are Multi-Configuration Hartree-Fock (MCHF, Froese Fischer 1978) or Dirac-Fock (MCDF, Parpia et al. 1996), and the Configuration Interaction Version 3 code (CIV3, Hibbert 1975). The second, semi-empirical approach is more apt for the study of complex atoms, in view of the required eigenvector accuracy. The semi-empirical method consists of the following steps:

• Fitting eigenvalues of a model Hamiltonian containing adjustable parameters to the experimental energies.
• Obtaining eigenvectors from a diagonalization of this Hamiltonian at the end of the fitting procedure.
• Using theoretical (Hartree-Fock) values for the radial transition integrals to obtain line strengths in pure LS coupling.
• Transforming these LS values by means of the semi-empirical eigenvectors to the final log(gf) or A-values.

In its original form this approach already has considerable success (Cowan 1981; Kurucz 1993), especially in the field of the heavier and more complex atoms where it is particularly powerful compared to other methods.

Subsequently, the introduction of orthogonal operators in the model Hamiltonian (Hansen et al. 1988), as a consequence of which the parameters become more stable and relatively independent of one another, turns out to raise the accuracy of the approach by up to an order of magnitude. The parameter independency offers the possibility to include additional operators that account for smaller effects like higher order or pure relativistic interactions.

   

3d⁴4p 3d³4s4p 3d²4s²4p 3d⁴5p 3d⁴4f

3d⁵ .729 - - .192 .349

3d⁴4s -2.480 .607 - .143 -

3d³4s² - -2.280 .515 - -

3d⁴4d -2.910 - - 3.220 -4.300

3d⁴5s 1.570 - - -5.360 -

   

log(gf) even odd

2433.471 -.741 1.5 71564.21* .5 112645.31*

2423.720 -.390 2.5 71831.98* 1.5 113078.34*

2423.504 -.705 .5 71395.27* .5 112645.31*

2409.301 -.241 3.5 72183.33* 2.5 113676.53*

2408.086 -.616 1.5 71564.21* 1.5 113078.34*

2389.069 -.757 2.5 71831.98* 2.5 113676.53*

2374.314 -.205 3.5 72183.33* 2.5 114287.91*

2365.414 -.679 2.5 71831.98* 1.5 114094.97*

2354.663 -.865 2.5 71831.98* 2.5 114287.91*

2350.520 -.972 1.5 71564.21* 1.5 114094.97*

2238.026 -.604 3.5 72183.33* 3.5 116851.69*

2228.457 -.448 2.5 71831.98* 2.5 116692.14*

2227.451 .428 3.5 72183.33* 4.5 117063.74*

2220.743 -.537 1.5 71564.21* 1.5 116580.17*

   

3d⁵ 3d⁴4s 3d³4s² 3d⁴4d 3d⁴5s

3d⁵ 1.58 -2.25 - -1.49 0.062

3d⁴4s -2.25 1.34 1.24 8.57 -

3d³4s² - 1.24 1.64 - -

3d⁴4d -1.49 8.57 - 1.30 -24.3

- - - 22.3 -

3d⁴5s 0.062 - - -24.3 1.30

   

name name

5588.382 3.61(-2) 4.24(- 2) 2.5 51002.70* 3.5 68892.00*

5586.134 - 2.85(-3) 2.5 51002.70* 4.5 68899.20*

5583.326 - 2.24(-3) 1.5 43674.70* 1.5 61580.20*

5581.487 1.34(-3) 1.30(-3) 1.5 61580.20* 2.5 43668.80*

5574.142 - 3.38(-3) 2.5 43668.80* 2.5 61603.80*

5544.587 - 1.93(-3) 2.5 61603.80* 4.5 43573.20*

5411.274 2.10(-3) 1.95(-3) 1.5 61580.20* 2.5 43105.40*

5404.370 1.58(-3) 1.98(-2) 2.5 43105.40* 2.5 61603.80*

5347.422 1.87(-3) - 2.5 51002.70* 3.5 32307.30*

5268.987 - 2.47(-3) 1.5 61580.20* 3.5 42606.50*

5262.441 3.61(-3) - 2.5 61603.80* 3.5 42606.50*

5086.087 6.82(-2) - 3.5 26859.90* 4.5 46515.90*

While the method is semi-empirical, ab initio calculations are important in the procedure, both in obtaining initial estimates of the parameters (especially the parameters for the relativistic effects are sometimes left fixed at their ab initio value) and in finding the required radial transition integrals.

For more details on the method and for information on the parameter values and their behaviour, we refer to our recently published overview article on d^N-1p configurations (Uylings & Raassen 1996). Everybody interested in orthogonal operators is invited to contact the authors or to visit our Internet address ftp://nucleus.phys.uva.nl in the directory pub/orth.