3. Transition probabilities

The transition probabilities, A_ki, were calculated for magnetic dipole (M1) and electric quadrupole (E2) lines connecting the 47 energetically lowest levels belonging to the 3d⁸, 3d⁷4s and 3d⁶4s² configurations of Co II, i.e. the transitions in which both energy levels are below the lowest level of odd parity.

Table 3 (click here) contains the experimental wavelengths deduced from the observed energy levels (Sugar & Corliss 1985) and the A-values calculated in the present work. All the calculations were carried out using the computed energy intervals but the use of experimental energy differences would only produce a marginal change in the final results. If the two types of radiation (M1 and E2) contribute significantly to the total intensity of a line, the sum of both components is given. The exclusion criterion of one particular type of radiation for a given transition is that the corresponding A-value should be less than 1% of the sum of M1 and E2 contributions. Owing to the extensive nature of the results, only transitions for which A_ki is greater than 0.001 s^-1 are reported in the table. The complete data can be obtained upon request to the author.

As already noticed for other ions, examining the results, it is seen that for most of the strong multiplets either magnetic dipole radiation predominates (electric quadrupole radiation being negligible) or electric quadrupole radiation predominates (magnetic dipole radiation being negligible). In the former case, the transitions are mostly intercombination multiplets (S 0) made possible by spin-orbit interaction. In the latter case, the transitions are mostly allowed by the LS-coupling selection rules for electric quadrupole radiation (i.e. S = 0, L = 0, 1, 2). There are few transitions in which the two types of radiation are of comparable intensities.

 

Multiplet J-J' Type A_ki

a³F-a³F 4-3 105178.00 M1 2.21(-2)

3-2 154562.77 M1 9.88(-3)

a³F-b³F 4-4 10187.81 E2 5.36(-2)

4-3 9335.84 E2 2.30(-2)

4-2 8829.97 E2 1.01(-3)

3-4 11280.47 E2 6.33(-3)

3-3 10245.24 E2 3.47(-2)

3-2 9639.21 M1,E2 3.16(-2)

2-3 10972.56 E2 8.74(-3)

2-2 10280.34 M1,E2 4.06(-2)

a³F-a¹D 4-2 8580.24 E2 9.74(-3)

3-2 9342.38 M1 1.74(-1)

2-2 9943.41 M1,E2 8.16(-2)

a³F-a³P 4-2 7538.96 E2 4.98(-2)

3-2 8121.07 M1,E2 6.70(-2)

3-1 8027.36 E2 4.20(-2)

2-2 8571.44 M1,E2 1.63(-2)

2-1 8467.11 M1,E2 1.68(-2)

2-0 8333.82 E2 5.34(-2)

a³F-a⁵P 4-2 5544.26 E2 3.42(-3)

3-1 5749.40 E2 1.13(-3)

a³F-a¹G 4-4 5209.57 M1 1.36(-1)

3-4 5481.05 M1,E2 7.03(-2)

a³F-a³G 4-5 4623.06 E2 7.73(-1)

4-4 4542.23 E2 1.22(-1)

4-3 4460.13 E2 6.87(-3)

3-5 4835.61 E2 3.33(-2)

3-4 4747.24 E2 5.61(-1)

3-3 4657.64 E2 1.49(-1)

2-4 4897.68 E2 3.76(-2)

2-3 4802.36 E2 5.31(-1)

a³F-b³P 4-2 4152.58 E2 3.12(+0)

3-2 4323.28 E2 5.12(-1)

3-1 4287.50 E2 9.37(-1)

2-2 4447.69 E2 4.72(-2)

2-1 4409.83 E2 5.47(-1)

2-0 4382.03 E2 8.77(-1)

a³F-c³P 4-2 4017.10 E2 2.66(-1)

3-1 4102.73 E2 2.03(+0)

2-2 4292.62 E2 4.32(-3)

2-1 4214.61 E2 3.97(-1)

2-0 4120.12 E2 3.10(+0)

a³F-b¹G 4-4 3975.43 M1,E2 2.07(-2)

3-4 4131.60 M1,E2 4.99(-3)*

2-4 4245.08 E2 1.04(-1)

a³F-a³H 4-6 3688.18 E2 2.66(+0)

4-5 3639.41 E2 1.42(-1)

4-4 3582.90 M1,E2 6.10(-3)

3-5 3769.86 E2 2.23(+0)

3-4 3709.26 E2 1.86(-1)

2-4 3800.47 E2 1.93(+0)

Table 3: Radiative transition probabilities, A_ki in s^-1, as calculated in the present work for forbidden lines of Co II. A(B) stands for A.10^B. Only transitions for which A_ki is greater than 0.001 s^-1 are reported  

 

Multiplet J-J' Type A_ki

a³F-a³D 4-3 3637.36 E2 1.59(+0)

4-2 3556.18 E2 8.62(-2)

3-3 3767.66 E2 4.60(-1)

3-2 3680.63 E2 1.26(+0)

3-1 3530.26 E2 2.88(-2)

2-3 3861.80 E2 4.54(-2)

2-2 3770.42 E2 6.30(-1)

2-1 3612.78 E2 8.77(-1)

a³F-a¹P 3-1 3753.42 E2 2.64(-1)

2-1 3846.84 E2 7.53(-1)

a³F-a¹H 3-5 3375.49 E2 5.52(-2)

a³F-b¹D 3-2 3304.94 M1,E2 1.60(-2)

2-2 3377.16 M1,E2 5.60(-3)*

a³F-a⁵D 4-4 2456.52 M1,E2 2.53(-2)*

4-3 2419.74 M1,E2 1.76(-3)

3-4 2515.28 M1,E2 5.70(-3)

3-3 2476.73 M1,E2 1.83(-3)

a³F-c³F 4-2 2451.97 E2 5.88(-2)

4-3 2445.48 E2 8.87(-1)

4-4 2435.49 E2 2.92(+0)

3-2 2510.51 E2 1.08(+0)

3-3 2503.70 E2 1.80(+0)

3-4 2493.23 E2 6.84(-1)

2-2 2551.96 E2 2.18(+0)

2-3 2544.92 E2 8.00(-1)

2-4 2534.11 E2 3.04(-2)

a³F-a¹F 4-3 2267.34 E2 1.83(-2)

3-3 2317.30 E2 1.59(-2)

2-3 2352.57 E2 2.14(-2)

a⁵F-a⁵F 5-4 147361.14 M1 1.03(-2)

4-3 187985.83 M1 9.27(-3)

3-2 256741.94 M1 5.00(-3)

2-1 392635.09 M1 1.57(-3)

a⁵F-b³F 5-4 15469.95 M1 2.66(-2)

4-4 17284.47 M1 2.98(-3)*

4-3 14967.16 M1 4.17(-3)

3-4 19034.62 M1 4.81(-3)

3-3 16261.91 M1 4.53(-3)*

2-3 17361.59 M1 9.59(-3)

2-2 15689.96 M1 4.34(-3)

1-2 16343.04 M1 1.34(-2)

a⁵F-a⁵P 5-3 6932.36 E2 3.74(-2)

4-3 7274.58 M1,E2 1.14(-2)

4-2 7139.54 E2 2.10(-2)

3-3 7567.42 M1,E2 2.61(-3)

3-2 7421.40 E2 1.46(-2)

3-1 7255.95 E2 1.10(-2)

2-2 7642.31 E2 6.10(-3)

2-1 7466.98 E2 1.59(-2)

1-2 7794.01 M1,E2 1.30(-3)

1-1 7611.74 E2 1.30(-2)

a⁵F-a³G 5-5 5470.72 M1 3.73(-1)*

5-4 5357.89 M1 2.17(-2)

4-5 5681.65 M1 7.54(-2)

4-4 5560.05 M1 2.11(-1)

4-3 5437.53 M1 1.37(-2)

3-4 5729.51 M1 9.24(-2)

3-3 5599.50 M1 8.43(-2)

2-3 5724.35 M1 6.46(-2)

 

Multiplet J-J' Type A_ki

a⁵F-b³P 3-2 5123.15 M1,E2 9.18(-3)

2-2 5227.47 M1,E2 1.33(-3)*

2-1 5175.25 M1,E2 2.97(-3)

1-2 5298.00 M1 1.15(-3)

1-1 5244.37 M1,E2 1.60(-3)

a⁵F-c³P 3-2 4918.49 M1,E2 3.98(-2)

2-2 5014.56 M1,E2 5.30(-3)*

2-1 4908.42 M1 3.63(-2)

1-2 5079.43 M1,E2 4.60(-3)

1-1 4970.56 M1,E2 2.57(-2)

a⁵F-a³H 5-5 4145.02 M1,E2 2.05((-3)

4-5 4264.99 M1,E2 1.03(-3)

4-4 4187.59 M1,E2 1.08(-3)*

a⁵F-a⁵D 5-4 2676.94 E2 1.42(+1)

5-3 2633.32 E2 6.64(+0)

4-4 2726.47 E2 5.61(+0)

4-3 2681.23 E2 4.99(+0)

4-2 2651.08 E2 1.06(+1)

3-4 2766.60 E2 1.12(+0)

3-3 2720.03 E2 7.14(+0)

3-2 2689.00 E2 9.22(-1)

3-1 2669.57 E2 1.34(+1)

2-4 2796.74 E2 9.24(-2)

2-3 2749.16 E2 2.49(+0)

2-2 2717.47 E2 6.70(+0)

1-3 2768.55 E2 2.30(-1)

1-2 2736.41 E2 3.42(+0)

1-1 2716.29 E2 8.27(+0)

a⁵F-a³D 4-3 4262.17 M1 5.36(-1)

3-3 4361.05 M1 1.20(-2)

3-2 4244.86 M1 6.98(-1)

2-3 4436.41 M1 2.53(-2)

2-2 4316.23 M1 6.10(-2)*

2-1 4110.89 M1 3.02(-1)

1-2 4364.21 M1 6.34(-2)

1-1 4154.39 M1 1.41(-1)

a⁵F-a¹P 2-1 4416.68 M1 3.60(-1)

1-1 4466.92 M1 1.65(-1)

a⁵F-b¹D 3-2 3752.87 M1 5.90(-3)

a⁵F-c³F 5-3 2663.82 E2 1.94(-3)

5-4 2651.98 M1,E2 2.67(-1)

4-3 2712.87 M1,E2 3.87(-2)

4-4 2700.58 M1,E2 7.94(-2)*

3-2 2760.83 M1 5.86(-3)

3-3 2752.59 M1,E2 3.30(-2)*

3-4 2739.95 M1,E2 2.93(-2)

2-2 2790.84 M1 3.02(-2)

2-3 2782.43 M1,E2 6.37(-2)

1-2 2810.82 M1,E2 1.03(-1)

1-3 2802.29 E2 1.28(-3)

b³F-b³F 4-3 111637.78 M1 1.67(-2)

3-2 162957.42 M1 7.26(-3)

b³F-a¹G 4-4 10661.30 M1 6.89(-3)

3-4 11786.95 M1 2.82(-3)

b³F-a³G 4-5 8463.87 M1 3.57(-2)

4-4 8196.81 M1 4.33(-2)*

4-3 7933.29 M1 3.06(-3)

3-3 8540.19 M1 3.79(-2)

2-3 9012.51 M1 2.27(-2)

 

Multiplet J-J' Type A_ki

b³F-b³P 4-2 7009.88 E2 3.02(-2)

3-2 7479.54 E2 5.74(-3)

3-1 7373.09 E2 3.04(-2)

2-1 7722.50 M1,E2 2.30(-2)

2-0 7637.67 E2 2.74(-2)

b³F-c³P 4-2 6632.28 E2 2.04(-2)

3-2 7051.19 M1,E2 1.03(-2)

2-2 7370.09 M1 1.63(-2)

2-1 7143.09 M1,E2 4.37(-3)

2-0 6875.85 E2 1.53(-3)

b³F-b¹G 4-4 6519.48 M1 1.84(-1)

3-4 6923.83 M1 1.06(-1)

2-4 7231.07 E2 2.48(-3)

b³F-a³H 4-4 5526.56 M1 7.44(-3)*

3-4 5814.40 M1 3.87(-3)

b³F-a³D 4-3 5657.21 M1 1.07(-1)

3-3 5959.20 M1 6.24(-2)*

3-2 5744.35 M1 8.88(-3)

3-1 5386.29 E2 2.25(-3)

2-3 6185.39 M1,E2 7.66(-3)

2-2 5954.24 M1 3.44(-2)

2-1 5570.41 M1,E2 4.43(-2)

b³F-a¹P 3-1 5923.64 E2 3.83(-3)

2-1 6147.09 M1,E2 3.00(-2)

b³F-b¹D 3-2 4878.82 M1 5.38(-1)

2-2 5029.40 M1,E2 3.12(-1)

b³F-a⁵D 4-3 3173.56 E2 6.70(-3)

3-3 3266.42 M1,E2 1.06(-3)*

3-2 3221.78 E2 4.44(-3)

2-2 3286.76 M1,E2 1.45(-3)

2-1 3257.78 M1,E2 2.62(-3)

b³F-c³F 4-3 3217.97 M1,E2 1.59(-2)

4-4 3200.70 M1,E2 3.24(-3)*

3-2 3325.43 M1,E2 2.18(-2)

3-3 3313.49 E2 2.29(-3)

3-4 3295.18 M1 2.00(-2)

2-3 3382.27 M1,E2 2.43(-2)

2-4 3363.19 E2 1.21(-2)

b³F-a¹F 3-3 2994.71 M1 9.77(-3)*

2-3 3050.78 M1,E2 1.69(-1)

a¹D-a³P 2-2 62122.27 M1 2.96(-2)

2-1 57029.52 M1 2.55(-2)

a¹D-a¹G 2-4 13261.38 E2 1.80(-3)

a¹D-b³P 2-2 8047.29 M1,E2 8.56(-3)*

2-1 7924.21 E2 5.20(-2)

2-0 7834.91 E2 6.39(-2)

a¹D-c³P 2-2 7553.59 M1,E2 2.68(-2)*

2-1 7315.32 M1,E2 7.23(-3)*

2-0 7035.30 E2 1.18(-3)

a¹D-b¹G 2-4 7407.62 E2 7.14(-2)

a¹D-a³H 2-4 6151.81 E2 1.44(-2)

a¹D-a³D 2-3 6314.12 M1,E2 6.24(-3)

2-2 6073.44 M1,E2 3.92(-3)*

2-1 5674.60 E2 3.29(-1)

a¹D-a¹P 2-1 6274.22 E2 1.67(-1)

a¹D-b¹D 2-2 5114.18 M1,E2 9.88(-1)

a¹D-a⁵D 2-4 3442.05 E2 2.72(-3)

 

Multiplet J-J' Type A_ki

a¹D-c³F 2-2 3433.13 E2 4.80(-2)

2-3 3420.40 E2 2.57(-1)

2-4 3400.90 E2 5.41(-1)

a¹D-a¹F 2-3 3081.77 E2 3.93(+0)

a³P-a⁵P 2-3 22162.28 M1 1.04(-3)

2-2 20954.77 M1 1.53(-3)*

1-1 20260.69 M1 2.89(-3)

a³P-b³P 2-2 9244.88 E2 9.36(-3)

2-1 9082.80 M1,E2 3.90(-2)

2-0 8965.67 E2 7.37(-2)

1-2 9369.40 M1,E2 1.91(-2)*

1-1 9202.96 M1,E2 1.83(-2)

0-2 9538.20 E2 7.98(-3)

a³P-c³P 2-2 8599.20 M1,E2 1.74(-2)*

2-1 8291.74 M1,E2 2.21(-3)*

1-2 8706.82 E2 2.48(-2)

1-1 8391.77 M1 1.06(-3)*

0-2 8852.42 E2 7.86(-3)

a³P-b¹G 2-4 8410.52 E2 1.17(-2)

a³P-a³H 2-4 6827.97 E2 2.53(-3)

a³P-a³D 2-3 7028.51 M1,E2 1.83(-2)

2-2 6731.56 M1,E2 2.06(-2)

2-1 6245.07 M1,E2 1.70(-1)

1-3 7100.25 E2 1.11(-2)

1-2 6797.34 M1,E2 5.86(-3)

1-1 6301.64 M1,E2 1.02(-2)*

0-2 6885.75 E2 1.57(-2)

a³P-a¹P 2-1 6979.10 M1,E2 5.33(-2)

1-1 7049.83 M1,E2 3.37(-2)*

0-1 7144.98 M1 2.53(-3)*

a³P-b¹D 2-2 5572.98 E2 2.06(-1)

1-2 5617.98 M1,E2 4.40(-3)*

0-2 5678.24 E2 4.50(-3)

a³P-a⁵D 2-4 3643.96 E2 7.50(-3)

2-3 3563.61 M1,E2 2.19(-3)

2-1 3477.49 M1,E2 1.64(-3)*

1-3 3581.96 E2 2.99(-3)

1-2 3528.34 M1,E2 3.30(-3)

0-1 3518.19 M1 1.87(-3)

a³P-c³F 2-2 3633.96 E2 1.14(-1)

2-3 3619.71 E2 5.26(-1)

2-4 3597.87 E2 1.70(+0)

1-2 3653.04 E2 9.04(-1)

1-3 3638.64 E2 1.25(+0)

0-2 3678.43 E2 8.20(-1)

a³P-a¹F 2-3 3242.64 E2 8.79(-1)

1-3 3257.83 E2 8.10(-3)

a⁵P-a⁵P 2-1 325485.09 M1 1.18(-3)

a⁵P-b³P 3-2 15861.40 M1 4.84(-3)

2-2 16543.69 M1 2.00(-3)*

2-1 16031.75 M1 1.03(-3)

1-2 17429.60 M1 1.18(-3)

1-1 16862.30 M1 2.44(-2)

1-0 16463.02 M1 4.75(-2)

a⁵P-c³P 3-2 14051.25 M1 1.72(-1)

2-2 14584.08 M1 9.32(-2)

1-2 15268.20 M1 1.93(-2)

1-1 14325.09 M1 1.42(-1)

1-0 13289.29 M1 1.49(-1)

 

Multiplet J-J' Type A_ki

2-3 10575.80 M1 1.21(-2)

2-2 9917.51 M1 4.02(-2)

1-2 10229.20 M1 1.07(-2)

1-1 9146.48 M1 4.70(-3)

a⁵P-a¹P 2-1 10464.33 M1 1.49(-3)

1-1 10811.93 M1 2.46(-2)

a⁵P-b¹D 3-2 7445.18 M1 2.48(-3)

a⁵P-a⁵D 3-4 4361.04 E2 5.13(-1)

3-3 4246.44 E2 6.36(-1)

3-2 4171.30 E2 4.60(-1)

3-1 4124.73 E2 1.88(-1)

2-4 4411.05 E2 3.92(-1)

2-2 4217.04 E2 2.72(-1)

2-1 4169.44 E2 7.97(-1)

1-3 4351.26 E2 3.70(-1)

1-2 4272.39 E2 3.56(-1)

1-1 4223.55 E2 1.62(-1)

a⁵P-c³F 3-3 4326.34 M1,E2 1.22(-3)

3-4 4295.18 M1,E2 3.50(-3)

2-3 4375.56 E2 1.93(-3)

1-2 4456.60 M1,E2 1.65(-3)

1-3 4435.19 E2 3.27(-3)

a¹G-b¹G 4-4 16781.66 M1,E2 2.76(-3)

a¹G-a³H 4-5 12075.42 M1,E2 3.58(-3)

4-4 11474.94 M1,E2 5.19(-3)*

a¹G-a¹H 4-5 8787.06 E2 1.19(-1)

a¹G-b¹D 4-2 8324.52 E2 1.61(-2)

a¹G-c³F 4-3 4609.27 M1,E2 8.06(-3)

4-4 4573.92 M1,E2 4.28(-3)*

a¹G-a¹F 4-3 4014.80 E2 3.99(+0)

a³G-a³G 5-4 259784.18 M1 1.27(-3)

4-3 246767.08 M1 1.70(-3)

a³G-b¹G 5-4 28379.33 M1 1.44(-2)

4-4 31859.76 M1 1.86(-3)*

3-4 36582.93 M1 1.05(-2)

a³G-a³H 5-6 18238.80 M1 4.18(-2)

5-5 17105.46 M1 4.14(-2)*

5-4 15924.97 M1 5.34(-3)

4-5 18311.16 M1,E2 1.97(-3)

4-4 16964.94 M1 7.16(-2)

3-4 18217.36 M1 3.19(-2)

a³G-a¹H 5-5 11179.22 M1 1.10(-1)*

4-5 11681.93 M1 4.66(-2)

a³G-a⁵D 5-4 5242.12 M1,E2 1.19(-3)

a³G-c³F 5-3 5192.06 E2 1.79(-2)

5-4 5147.26 M1,E2 1.19(-1)

4-2 5328.54 E2 1.97(-2)

4-3 5297.95 M1,E2 2.79(-2)

4-4 5251.30 M1,E2 4.86(-2)*

3-2 5446.14 M1,E2 1.01(-1)

3-3 5414.19 M1,E2 7.07(-2)

3-4 5365.49 M1,E2 3.69(-3)

a³G-a¹F 5-3 4449.86 E2 1.90(-3)

4-3 4527.41 M1,E2 1.09(-1)

3-3 4612.03 M1 6.89(-2)

b³P-c³P 2-1 80425.36 M1 2.86(-2)

1-2 161506.86 M1 3.02(-3)

1-0 62716.98 M1 8.84(-3)

 

Multiplet J-J' Type A_ki

b³P-a³D 2-3 29317.43 M1 8.63(-3)

2-2 24761.29 M1 1.39(-2)

2-1 19246.36 M1 2.05(-2)

1-2 26004.16 M1 1.63(-3)

1-1 19988.94 M1 1.23(-2)*

0-1 20580.64 M1 2.35(-2)

b³P-a¹P 2-1 28476.50 M1 2.39(-2)

1-1 30132.78 M1 3.08(-2)

0-1 31497.89 M1 3.22(-2)

b³P-b¹D 1-2 14422.01 M1 1.79(-2)

b³P-c³F 2-2 5987.62 M1,E2 2.02(-3)

2-3 5949.02 M1,E2 3.26(-3)

2-4 5890.27 E2 3.81(-3)

1-2 6057.63 E2 1.62(-3)

0-2 6110.87 E2 2.28(-3)

b³P-a¹F 1-3 5043.14 E2 2.30(-3)

c³P-c³P 1-0 183790.32 M1 5.46(-3)

c³P-a³D 2-3 38480.06 M1 1.24(-2)

2-2 30994.59 M1 1.88(-2)

2-1 22812.32 M1 5.63(-2)

1-2 35775.97 M1 1.17(-3)

1-1 25301.09 M1 5.33(-2)

0-1 29340.14 M1 1.18(-2)

c³P-a¹P 2-1 37044.23 M1 1.35(-3)

1-1 44086.30 M1 1.75(-2)

0-1 57998.59 M1 2.32(-3)

c³P-b¹D 2-2 15836.13 M1 1.36(-1)

1-2 16996.75 M1 1.02(-2)

c³P-c³F 2-2 6293.69 M1,E2 4.64(-3)*

2-3 6251.06 M1,E2 1.46(-2)

2-4 6186.22 E2 1.67(-2)

1-2 6469.25 M1,E2 1.67(-2)

1-3 6424.22 E2 8.60(-3)

0-2 6705.28 E2 6.96(-3)

b¹G-a³H 4-5 43059.03 M1 1.65(-2)

4-4 36287.74 M1 1.78(-2)

b¹G-a¹H 4-5 18445.18 M1,E2 3.59(-3)

b¹G-c³F 4-2 6398.75 E2 2.56(-3)

4-3 6354.69 M1,E2 4.29(-2)

4-4 6287.69 M1 6.49(-2)

b¹G-a¹F 4-3 5277.37 M1,E2 1.27(-3)*

a³H-a³H 5-4 230756.04 M1 1.88(-3)

a³H-a¹H 6-5 28882.17 M1 1.11(-2)

4-5 37513.36 M1 5.74(-3)

a³H-c³F 6-4 7171.06 E2 3.57(-2)

5-3 7454.90 E2 2.70(-2)

5-4 7362.86 M1,E2 3.72(-3)

4-2 7768.63 E2 2.42(-2)

4-3 7703.78 M1,E2 4.20(-3)

a³H-a¹F 5-3 6014.53 E2 2.21(-3)

a³D-a³D 3-2 159331.81 M1 4.42(-3)

2-1 86413.59 M1 2.74(-2)

a³D-b¹D 3-2 26911.21 M1 2.50(-2)

2-2 32380.25 M1 6.74(-3)

1-2 51784.59 M1 1.68(-3)

 

Multiplet J-J' Type A_ki

a³D-c³F 3-2 7524.36 M1,E2 1.52(-3)

3-3 7463.51 M1,E2 1.06(-2)*

3-4 7371.27 M1,E2 2.01(-2)

2-2 7897.31 M1,E2 1.20(-2)

2-3 7830.31 M1,E2 4.24(-3)

2-4 7728.84 E2 4.76(-3)

1-2 8691.65 M1,E2 2.90(-3)

a³D-a¹F 3-3 6020.13 M1,E2 8.23(-3)*

2-3 6256.53 M1,E2 6.09(-3)

1-3 6744.88 E2 5.19(-3)

a¹P-a³D 1-2 189791.64 M1 1.09(-3)

1-1 59378.22 M1 1.24(-2)

a¹P-b¹D 1-2 27661.02 M1 1.79(-2)

a¹P-c³F 1-2 7581.83 M1,E2 4.62(-3)

1-3 7520.05 E2 3.90(-3)

a¹P-a¹F 1-3 6056.86 E2 5.39(-3)

a¹H-a¹F 5-3 7392.46 E2 3.19(-2)

b¹D-c³F 2-2 10444.72 M1 2.46(-3)

2-3 10327.83 M1,E2 5.09(-3)

a⁵D-a⁵D 4-3 161611.29 M1 7.67(-3)

3-2 235729.18 M1 4.80(-3)

2-1 369448.43 M1 1.85(-3)

c³F-a¹F 2-3 30113.81 M1 2.51(-3)

4-3 32843.85 M1 1.90(-3)

^a Wavelengths, in air, are deduced from the observed energy levels compiled by Sugar & Corliss (1985).
* Cancellation effects present (see text).

The calculation of line strengths and transition probabilities involves the evaluation of the sum of several terms resulting of intermediate coupling and/or configuration interaction mixing of basis states. When strong basis function mixing is present, there frequently are destructive interference effects that cause a weak line to become still weaker or a strong line to nearly disappear. Consequently, in making numerical calculations on individual transitions, it is worthwhile evaluating the cancellation factors, CF, as defined by Cowan (1981). Small values of CF factors (typically CF 0.01) indicate that the corresponding lines may be expected to show large percent errors. Such transitions are indicated by starred A-values in Table 3 (click here).

Although it is well established that the neglect of some configurations is partly overcome by scaling down the Slater integrals and by fitting the calculated energy levels to the observed values, the effects of configurations not included explicitly in our physical model due to computer memory limitations were estimated in separate semi-empirical HFR calculations. In particular, the 3s3p⁶3d⁹, 3s3p⁶3d⁸4s and 3s3p⁶3d⁷4s² configurations were investigated. As mentioned recently by Quinet & Hansen (1995), these configurations, corresponding to the core excitation 3s 3d in 3s²3p⁶3d⁸, 3s²3p⁶3d⁷4s and 3s²3p⁶3d⁶4s², might contribute to the transition probabilities for the forbidden lines considered in the present work. By comparing a three-configuration calculation (including 3d⁸, 3d⁷4s and 3d⁶4s²) with a six-configuration calculation (adding 3s3p⁶3d⁹, 3s3p⁶3d⁸4s and 3s3p⁶3d⁷4s²), the effect on the A-values of the latter three configurations was estimated. In general, for the strongest multiplets (A 0.01 s^-1), both calculations agree within a few percent if we except a³F-b¹G, a³F-a¹P, a³F-b¹D, b³F-a¹P, a³P-c³P, a⁵P-b³P, a⁵P-a³D, a³G-a³G, b³P-a¹P, b³P-b¹D, a³D-a¹F and a¹P-b¹D for which the multiplet A-values were larger when calculated with the six-configuration expansion. Exceptions occur also for the a³F-a⁵D, a¹G-b¹D and c³P-c³F lines for which the transition probabilities were reduced by about 25% when adding the 3s3p⁶3d⁹, 3s3p⁶3d⁸4s and 3s3p⁶3d⁷4s² configurations.

 

Multiplet J-J' Type A_ki(NS) A_ki(HFR)

a³F-a³F 4-3 10.52 M1 2.23(-2) 2.21(-2)

3-2 15.46 M1 9.73(-3) 9.88(-3)

a³F-a⁵F 4-5 2.984 M1 4.90(-6) 3.09(-6)

a⁵F-a⁵F 5-4 14.74 M1 1.23(-2) 1.03(-2)

4-3 18.80 M1 1.08(-2) 9.27(-3)

3-2 25.67 M1 5.72(-3) 5.00(-3)

2-1 39.26 M1 1.78(-3) 1.57(-3)

a³F-b³F 4-4 1.019 E2 3.85(-2) 5.36(-2)

3-4 1.128 E2 4.91(-3) 6.33(-3)

2-4 1.217 E2 1.54(-4) 2.11(-4)

4-3 0.934 E2 1.63(-2) 2.30(-2)

3-3 1.025 E2 2.58(-2) 3.47(-2)

2-3 1.097 E2 6.97(-3) 8.74(-3)

4-2 0.883 E2 1.38(-3) 1.01(-3)

3-2 0.964 E2 1.87(-2) 2.60(-2)

2-2 1.028 E2 3.09(-2) 3.84(-2)

a⁵F-b³F 5-4 1.547 M1 2.89(-2) 2.66(-2)

4-4 1.728 M1 2.82(-3) 2.98(-3)

3-4 1.903 M1 4.28(-3) 4.81(-3)

4-3 1.497 M1 6.41(-3) 4.17(-3)

3-3 1.626 M1 4.91(-3) 4.53(-3)

2-3 1.736 M1 1.04(-2) 9.59(-3)

3-2 1.479 M1 5.38(-4) 1.99(-4)*

2-2 1.569 M1 5.30(-3) 4.34(-3)

1-2 1.634 M1 1.69(-2) 1.34(-2)

b³F-b³F 4-3 11.16 M1 1.87(-2) 1.67(-2)

3-2 16.30 M1 8.32(-3) 7.26(-3)

Table 4: Comparison of the transition probabilities, A_ki in s^-1, calculated in the present work (HFR) with those obtained by Nussbaumer & Storey (1988b) (NS) for the forbidden lines connecting the lowest three terms in Co II. A(B) stands for A.10^B

* Cancellation effects present (see text).  

A very limited number of transition probabilities has been reported previously for [Co II] lines. To our knowledge, only the results obtained by Nussbaumer & Storey (1988b) for the forbidden transitions involving the first three terms, a³F, a⁵F and b³F, have been published. Their calculations were based on the multiconfiguration expansion of eigenfunctions as implemented in the SUPERSTRUCTURE code of Eissner et al. (1974) and modified by Nussbaumer & Storey (1978). In their study, the individual configurations were constructed from one-electron wavefunctions, the radial parts of which being calculated either in a scaled Thomas-Fermi-Dirac or a scaled Coulomb potential. The scaling parameters in the potentials were chosen to minimize the sum of the energies of the lowest three terms. Table 4 (click here) shows the comparison between the computations of Nussbaumer & Storey (1988b) and the present work. The agreement between the two sets of results is very good (within 15%) for the a³F-a³F, a⁵F-a⁵F, a⁵F-b³F and b³F-b³F magnetic dipole transitions if we except a⁵F₄-b³F₃ and a⁵F₃-b³F₂ for which larger discrepancies are observed. The difference can even reach a factor of three for the latter transition but, in that particular case, the A-value computed in our work is affected by strong cancellation effects and, consequently, could be uncertain. Larger differences () appear also when comparing our results with those obtained by Nussbaumer & Storey (1988b) for the a³F-a⁵F magnetic dipole and a³F-b³F electric quadrupole transitions. For these multiplets, the transitions arise through spin-orbit and configuration interactions and are therefore particularly sensitive to the choice of eigenfunctions. The magnitudes of the coefficients due to spin-orbit and CI depend on the a³F-a⁵F and a³F-b³F term separations. These term separations calculated in our work (3460 and 9757 cm^-1) are in excellent agreement with the observations (3457 and 9774 cm^-1) while the values obtained in intermediate coupling by Nussbaumer & Storey (1988b), i.e. 595 and 7551 cm^-1, are too small.