Dielectronic recombination rates to the n = 3 singly excited states: The neon sequence

J. Qum.

Pergamon

Specrrosc.

Rotliur.

Trw.$v Vol. 54. No. 4. pp. 737-143. 1995 Elsevier Science Ltd. Printed in Great Brkain

0022-4073(95)00106-9

DIELECTRONIC RECOMBINATION RATES TO THE n = 3 SINGLY EXCITED STATES: THE NEON SEQUENCE ARATI DASGUPTA Radiation Hydrodynamics

Branch, Plasma Physics Division, Naval Research Laboratory, Washington, DC 20375, U.S.A. (Received 21 November 1994)

Abstract-In this work we present the state-specific dielectronic recombination rate coefficients to the n = 3 single excited state of Ar IX, Ti XIII, Fe XVII and Se XXV. Results presented involve detailed calculations of radiative and autoionization rates to ground as well as excited states of the recombining ions. Coeficients of least-squares polynomial fits to the calculated data are also provided for temperature range 0.01-5.0 keV.

INTRODUCTION

Dielectronic recombination (DR) is the process whereby a free electron is captured by an ion into a doubly excited state which subsequently stabilizes by radiative decay to a bound level of the recombined ion. Since the doubly excited state can undergo resonance autoionization to the ground as well as to the excited states of the initial ion, DR involves competing processes of autoionization and radiative transition. DR is a dominant recombination process for ions in laboratory and astrophysical plasmas’-3 and is a significant contributor in the kinetics involved in gain calculations.4-6 Recent interest in extensive theoretical and observational studies of neon-like ions stems from their possible applications for astrophysical plasma diagnostics’ as well as from their importance in improving experiments*-” and calculations6 in obtaining gain for soft x-ray lasers. Even though neon-like selenium was studied extensively since the demonstration of neon-like soft x-ray laser at the NOVA facilities at the Lawrence Livermore Laboratory,“v’2 a number of calculations involving other Ne-like ions have also been carried out for investigating the gain coefficients for these ions.6,‘3 Since the DR process populates the upper lasing level significarltly more than the lower level, it is an important mechanism effecting population inversion. However, as stressed in our earlier work (Dasgupta and Whitney;14 hereafter DW), it is crucial to obtain the DR rate coefficients directly to the specific excited states of theion in order to calculate gain coefficients accurately. Moreover, for any accurate collisional-radiative-equilibrium calculations, one needs to obtain collisional as well as radiative data including DR, at the state-specific level. As mentioned by DW, most calculations however report only total, ground to ground, DR rates as a function of temperature. The DR rates to the n = 3 singly excited states of neon-like ions such as Ar8+, T”+, Fe16+, and Se24+ have already been reported previously (see DW). But in that work, we have included the complete state-specific DR data only for some of the ions and for recombination from the 2s2p6 state, the temperature range does not include the temperature of maximum abundance for some of the ions. In DW, we also presented the Scaling coefficients for DR branching ratios for recombination from the ground 2s22p5state as well as from the An = 0 2s2p6 states to all the n = 3 singly excited states through the most dominant DR channels. One can thus obtain the DR rate coefficient for any temperature of interest by adding the individual rates for each of the DR channels. However the rates thus obtained will include contribution of DR data from doubly excited states with Rydberg electrons in only up to n = 10. The contributions of DR rates using an l/n3 extrapolations to higher levels with 10 < n < 50 for recombination from the ground state 737

738 Table

Arati I. Dielectronic

Temperature (kev) 0.02 0.04 0.06 0.08 0.10 0.20 0.40 0.60 0.80 I .oo 2.00 3.00 4.00 5.00

Dasgupta

recombination rate coefficients ( 10-‘2cm3/sec) to the n = 3 singly excited Ser4+ states. Transitions include both An = 0 and An # 0 for recombination from the around 2~~20~ state.

2~~3s

Recombination from 2s22ps state 2ps3p 2p53d 2~2~~3s 2s2p63p 2s2p63d

0.008 0.041 0.108 0.587 0.915 0.851 0.732 0.623 0.316 0.195 0.135 0.100

0.389 0.277 0.215 0.179 0.164 0.303 0.552 0.564 0.510 0.448 0.241 0.152 0.106 0.079

0.035 0.232 0.685 4.378 7.315 7.022 6.155 5.306 2.768 1.724 1.200 0.895

0.017 0.156 0.555 5.055 9.761 9.696 8.611 7.470 3.933 2.456 I.710 I.276

1.248 0.975 0.778 0.641 0.544 0.371 0.335 0.294 0.250 0.212 0.108 0.067 0.046 0.034

I.575 1.307 I.055 0.871 0.739 0.529 0.602 0.594 0.538 0.475 0.262 0.166 0.117 0.088

2~~3s

Recombination from 2s2p6 state 2p53p 2pS3d 2~2~~3s 2s2p03p 2s2pb3d

0.012 0.048 0.104 0.342 0.401 0.340 0.279 0.231 0.111 0.067 0.046 0.034

0.001 0.044 0.229 0.569 2.487 3.341 2.947 2.467 2.066 I.013 0.617 0.424 0.314

0.021 0.142 0.415 2.527 4.130 3.973 3.501 3.033 1.605 1.006 0.702 0.525

0.003 0.017 0.048 0.297 0.500 0.481 0.421 0.363 0.189 0.117 0.082 0.061

0.035 0.230 0.668 4.01 I 6.259 5.760 4.91 I 4.152 2.069 1.267 0.873 0.648

0.020 0.173 0.596 5.043 9.344 9.119 8.012 6.900 3.572 2.215 1.537 1.145

with 15 < n < 100 for the An = 0 state have been found to be substantial in some of the cases. For accurate ionization equilibrium calculations these contributions due to high Rydberg states might be significant. The results reported in this present calculation can thus be regarded as an extension of the DR data to the n = 3 singly excited states presented in our earlier work (DW). We also present convenient least-squares polynomial coefficients fitting the DR rates to each of the n = 3 excited states of AP+, Tin+, Fe16+, and Sez4+. and

CALCULATION

AND

RESULTS

The atomic model and the calculational procedures used in obtaining the DR rates have already been explained in DW. We employed the Hartree-Fock with relativistic corrections (HFR) method of CowanI using an intermediate coupling scheme and single configuration approximation. The DR data for A?+, Ti”+, Fe16+, and Se24+ have been obtained by calculating the autoionization and radiative rates from a large number of resonance autoionizing states. The autoionization process includes all energetically allowed autoionization to the excited states and the radiative process includes all dipole allowed radiative transitions to stable bound states that are below the ionization threshold. The DR rate coefficients to the n = 3 excited neon-like states are presented in Tables l-4. As we can see that the rate coefficients to the inner-shell excited states, i.e., to the 2~2~~31states are much smaller than the rates to the 2~~31states for recombination from the ground 2s22p5 state at the temperatures where there is strong recombination. On the other hand, the reverse is just true for recombination from the An = 0 2s2p6 excited states. We also see that in each case the DR rates to the 2s22p53p and 2s2p63p states are much larger than the recombination rates to the 2s22p53s Table 2. Dielectronic

recombination rate coefficients (IO-l2 cmj/sec) to the n = 3 singly excited Fer6+ states. include both An = 0 and An # 0 for recombination from the ground 2s22ps state.

Temperature (kev)

2~~3s

0.02 0.04 0.06 0.08 0.10 0.20 0.40 0.60 0.80 1.00 2.00 3.00 4.00 5.00

0.021 0.148 0.359 0.577 I.100 0.964 0.722 0.552 0.436 0.189 0.110 0.074 0.054

Recombination from 2s22p5 state 2p53p 2p53d 2~2~~3s 2s2pb3p 2s2p63d

2~~3s

Recombination 2p53p 2p53d

0.183 0.123 0.102 0. I14 0.149 0.339 0.378 0.309 0.247 0.201 0.092 0.054 0.037 0.027

0.01 I 0.051 0.099 0.138 0.211 0.176 0.131 0.100 0.079 0.034 0.020 0.013 0.010

0.077 0.475 1.050 1.583 2.645 2.181 1.604 1.217 0.957 0.410 0.238 0.160 0.1 I7

0.057 0.509 1.384 2.379 5.301 5.164 4.035 3.157 2.53 1 I.128 0.664 0.449 0.329

0.029 0.382 1.256 2.41 I 6.558 6.892 5.491 4.333 3.490 1.569 0.926 0.626 0.459

0.620 0.475 0.379 0.324 0.295 0.273 0.227 0.175 0.136 0.109 0.049 0.029 0.019 0.014

0.858 0.682 0.541 0.455 0.412 0.420 0.410 0.335 0.270 0.220 0.102 0.061 0.041 0.030

0.03 1 0.277 0.738 1.251 2.731 2.654 2.073 1.622 1.300 0.579 0.341 0.230 0.169

Transitions

from 2s2p6 state 2~2~~3s 2s2p63p 2s2p63d 0.010 0.070 0.168 0.270 0.517 0.455 0.342 0.262 0.207 0.090 0.052 0.035 0.026

0.055 0.475 I.256 2.112 4.396 4.019 3.049 2.346 1.861 0.811 0.473 0.319 0.233

0.033 0.416 I.326 2.488 6.382 6.406 5.002 3.903 3.121 1.381 0.81 I 0.547 0.401

Dielectronic Table

3. Dielectronic

Temperature (kev) 0.02 0.04 0.06 0.08 0.10 0.20 0.40 0.60 0.80

I -00 2.00 3 .oo 4.00 5.00

recombination

739

rates

recombination rate coefficients (IO-” cm’/sec) to the n = 3 singly excited Ti” ’ states. include both An = 0 and An # 0 for recombination from the ground 2s’2ps state. 2~~3s

0.002 0.114 0.405 0.694 0.903 1.108 0.758 0.518 0.377 0.289 O.Il8 0.067 0.045 0.032

Recombination from 2s’2ps state 2p53p 2pS3d 2~2~~3s 2s2p63p 2s2p63d 0.002 0.254 1.095 2.073 2.874 4.114 3.092 2.188 1.624 I.260 0.524 0.301 0.201 0.146

0.176 1.000 2.161 3.230 5.264 4.159 2.983 2.228 1.734 0.727 0.419 0.280 0.204

0.030 0.037 0.061 0.105 0.154 0.273 0.232 0.170 0.129 0.101 0.043 0.025 0.017 0.012

0.107 0.129 0.126 0.133 0.145 0.171 0.130 0.093 0.070 0.054 0.023 0.013 0.009 0.006

0.154 0.187 0.167 0.152 0.143 0.119 0.078 0.054 0.040 0.031 0.013 0.007 0.005 0.003

Transitions

2~~3s

Recombination from 2~2~” state 2pS3p 2pS3d 2~2~~3s 2s2ph3p 2s2p03d

0.028 0.071 0.105 0.127 0.139 0.092 0.063 0.045 0.035 0.014 0.008 0.005 0.004

0.004 0.275 0.860 1.368 I.698 1.903 1.248 0.841 0.609 0.465 0.188 0.107 0.071 0.051

0.001 0.146 0.605 I.117 1.520 2.077 1.512 1.056 0.778 0.601 0.248 0.142 0.095 0.069

0.056 0.195 0.327 0.419 0.501 0.338 0.230 0.167 0.128 0.052 0.030 0.020 0.014

0.002 0.229 0.947 1.737 2.349 3.111 2.200 1.518 1.111 0.855 0.349 0.200 0.133 0.096

0.188 1.028 2.163 3.170 4.908 3.743 2.648 I.963 1.522 0.632 0.363 0.242 0.176

and 2~2~~3s states for recombination from the ground and An = 0 states respectively and thus helping population inversion by substantially populating the upper lasing levels in comparison to the lower levels. We further notice that the DR rates to the 2s22p53d and 2s2p63d states are even larger than the rates to the 2s22p53p and 2s2ph3p states which can thus be also pumped by radiative cascades from these 2s22p53d and 2s2p63d states and thus being populated even further in addition to already being pumped significantly by collisional excitations from the ground and the 2s2ph states. Thus the data presented in these tables will help for any accurate plasma diagnostics and gain calculations where direct state-specific rates to these n = 3 excited states are needed. In Tables 5-8, we present the coefficients for least-squares fits to the data contained in Tables l-4 by using a polynomial of order five. In order to get the best fits, the data were fitted in two temperature intervals for most of the curves except for DR rates to the 2~~31 states of Fei6+ for recombination from the ground state a single polynomial fitting was sufficient for the entire temperature interval of 0.01-5.0 keV. The coefficients for the DR rates given in these tables were obtained by fitting polynomials to the logarithms of the actual data. Thus the DR rate aDR at a particular temperature T, is computed from the polynomial fit given by: log,, CxDR= 2 A, log,,[T,(keVIY )I= 0 where the A,s given in Tables 5-8 are to be drawn from the appropriate temperature interval. In most cases these fits reproduce the directly computed data to within 0.1% for the temperature intervals given in these tables. Figure 1 shows the curves obtained by direct computation and by fitting these data by polynomial in four different cases where the discrepancies were the most. We Table 4. Dielectronic

recombination rate coefficients (IO-“cm3/sec) to the n = 3 singly excited A?+ include both An = 0 and An # 0 for recombination from the ground 2s22pS state.

states.

Transitions

Temperature (keV)

2~~3s

Recombination from 2s*2pS state 2p53p 2p53d 2~2~~3s 2s2p63p 2s2p63d

2~~3s

Recombination from 2~2~” state 2ps3p 2p53d 2~2~~3s 2s2p63p 2s2p63d

0.02 0.04 0.06 0.08 0.10 0.20 0.40 0.60 0.80 1.00 2.00 3.00 4.00 5.00

0.024 0.330 0.660 0.841 0.91 I 0.757 0.416 0.263 0.184 0.138 0.053 0.030 0.020 0.014

0.03 I 0.641 I.468 2.004 2.262 2.044 1.173 0.752 0.530 0.399 0.156 0.088 0.058 0.042

0.006 0.043 0.069 0.079 0.080 0.059 0.031 0.019 0.013 0.010 0.004 0.002 0.001 0.001

0.047 0.515 0.910 I .080 1.117 0.841 0.438 0.272 0.189 0.141 0.054 0.030 0.020 0.014

0.017 0.587 1.599 2.372 2.809 2.779 1.664 1.082 0.768 0.580 0.228 0.129 0.085 0.062

0.017 0.030 0.065 0.098 0.120 0.130 0.082 0.054 0.039 0.029 0.012 0.007 0.004 0.003

0.059 0.069 0.083 0.099 0.109 0.103 0.062 0.041 0.029 0.022 0.009 0.005 0.003 0.002

0.057 0.076 0.092 0.112 0.127 0.133 0.086 0.058 0.042 0.032 0.013 0.007 0.005 0.003

0.019 0.373 0.805 1.059 I.165 0.994 0.552 0.350 0.245 0.184 0.07 I 0.040 0.026 0.019

0.013 0.163 0.306 0.375 0.395 0.309 0.164 0.103 0.072 0.053 0.020 0.01 I 0.007 0.005

0.002 0.058 0.179 0.284 0.349 0.367 0.225 0.147 0.105 0.079 0.03 1 0.018 0.012 0.008

0.017 0.059 1.528 2.196 2.544 2.388 1.387 0.892 0.630 0.474 0.185 0.104 0.069 0.050

740

Arati Dasgupta

Table 5. Coefficients for polynomial fits to dielectronic recombination rates to n = 3 singly excited states of Se”+. Both An = 0 and An # 0 transitions are included for recombination from the ground 2sr2n5 state. Temperature (keV) 0.01-0.1

0.1-5.0

0.01-0.2

0.2-5.0

Coeff

2~~3s

A0 A, A, Al A, A5 A, A, A, A, A, A5

-2.834 (0) 4.175(l) 7.580 (1) 6.852 (I) 2.972(l) 5.383 (0) -1.220(l) -7.901(-l) -7.271 (-I) 4.000(-l) -2.264(-I) 1.962(-l)

A0 A, A, A, A, A5 A, A, A, A, A, A,

-1.072(l) 8.563 (0) 1.787 (I) 1.829 (1) 8.807 (0) 2.089 (0) -1.264(l) -9.035(-l) -5866(-l) 3.376 (- 1) -1.768(-l) 9.808 (-2)

2~53~

2p53d

2~2~~3s

Recombination from 2s22p5 state 1.188 (I) I .649(O) a.757 (1) 5.092 (I) 1.325 (2) 6.970 (I) 9.926 (I) 4.670 (1) 3.574 (I) 1.556(l) 5.514 (0) 2.073 (0) -1.113(l) -1.235(l) -7.108(-l) -7.558(-t) -8.155(-l) -8.094(-l) 4.389 (- I) I .230 (0) -2.916(-I) -2.774(-l) 2.904(-I) -1.113(O) Recombination from 2s2p6 state -9.626 (0) - 9.990 (0) -4.246 (0) 9.339 (0) 7.114(O) 3.749 (I) 1.936 (1) 1.515 (1) 6.883 (I) 2.003 (1) 1.656(l) 6.210(l) 9.709 (1) 8.302 (0) 2.639 (I) 2.324 (0) 2.167 (0) 4.678 (0) -1.168(I) -1.244(t) -1.152(l) -8.631(-l) -7.202(-l) -7.481(-l) -6.500(-l) -7.538(-l) -7.661 (-I) 3.961 (-I) 4.064 (- 1) 4.693 (- I) -2.086(-I) -2.121(-l) -2.314(-l) 1.129 (- 1) 1.393 (- 1) 1.066(-l)

4.500 (1) 2.188 (2) 3.379 (2) 2.584 (2) 9.688 (I) 1.472 (1) -1.127(l) -7.321 (--I) -7.700(-l) 3.552 (- 1) -2.153(-l) 2.774(-l)

2s2p63p

2s2p63d

-1.151 (I) 5.808 (0) 1.092(l) a.744 (0) 3.403 (0) 5.326 (- I) -1.270(l) -7.780(-l) -7.566(-l) 1.571(- 1) 4.023 (- 1) -1.576(-l)

-1.086(l) 7.775 (0) 1.382(f) I.083 (I) 4.143 (0) 6.404(-l) -1.232(I) -6.125(-I) -9.810(-I) 2.281 (-I) 5.667 (- I) -2.463 (- I)

- 1.341 (I) - 1.173 (1) -2.356(l) -2.273(l) -1.140(l) - 1.746 (0) -1.138(t) -8.250(-l) -7.106(-l) 4.630 (- I) -2.630(-l) 1.345(-l)

-1.246(l) - 7.839 (0) -1.590(l) -1.497(l) -7.653 (0) -9.773 (- I) -1.116(l) -7.522 (- 1) -7.906(-l) 5.270 (- 1) -2.961 (- 1) 1.395(-l)

notice from this figure that even in these worst situations there is very close agreement between the actual and the fitted data. One can thus use the polynomial coefficients given in Tables 5-8 to obtain with good accuracy the DR rates to the n = 3 excited states of Ar8+, Ti”+, Fei6+, and Se”+ for any temperature between 0.01 and 5.0keV. Table 6. Coefficients for polynomial fits to dielectronic recombination rates to n = 3 singly excited states of Fe16+. Both An = 0 and An # 0 transitions are included for recombination from the ground 2s22ns state. Temperature (keV) 0.01-0.1t

0.1-5.0

Coeff A, A, A, A, A, A5 Ail A,

2~~3s -1.236(l) -1.107(O) -5.045(-l) 2.639 (- 1) -2.000(-2) 1.998(-i)

4 A, A, A5 0.01~.15

0.15-5.0

A0 A, A, A, A, A5 A0 A, A, A, A, A5

- 1.023 (1) 1.086(l) 1.946(l) 1.719 (1) 7.549 (0) I .577 (0) -1.311(l) - 1.OlO(0) -4.326(-l) 2.881 (-I) -1.115(-l) 1.348 (-2)

2~53~

2p53d

2~2~~3s

Recombination from 2s22p5 state - 1.161 (1) - 1.145 (1) 7.576 (0) - I .030 (0) -1.013(O) 5.474 (I) -5.569(-l] -6.234(-l) 5.488 (I) 2.065 (- I) 2.424 (- 1) 2.558 (I) -4.125(-21 -4.727(-3) 5.440 (0) 2.390 (- 1) 3.012(-l) 3.969 (- 1) -1.270(l) - 1.009 (0) -5.429(-I) 5.405 (- I) -2.362(-l) -1.711(-l) Recombination from 2s2p6 state - 8.896 (0) - 8.248 (0) -1.529(l) 1.232(l) 1.426 (1) -1.307(l) 2.269 (I) 2.554 (1) -2.192(l) 2.041 (I) 2.289 (I) -1.834(t) a.999 (0) 1.009 (1) -7.815 (0) 1.863 (0) 2.101 (0) - 1.049 (0) - I .202 (I) -1.189(i) -1.268(l) -1.121(O) - 1.045 (0) - 1.096 (0) -4.119(-l) -4.984(-l) -4.403(-l) 2.838 (- I) 3.429(-l) 3.059(-l) -1.427(-l) -1.529(-l) -1.637(-l) 4.900(-2) 4.879 ( - 2) 6.026 (- 2)

2s2p63p

2s2p63d

-3.166(O) 3.303 (I) 4.481 (I) 2.956 (1) 9.683 (0) 1.27I (0) -1.296(l) - 1.063 (0) -4.870 (- I) 4.620 (- I) -2.697(-2) -3.441(-l)

- i ,585 (0) 3.825 (I) 5.215(l) 3.457 (1) 1.137(I) 1.502 (0) -1.266(l) -9.937 (- 1) -5.757 (- 1) 6.047(-I) -3.628(-2) -4.944 (- I)

-1.926(l) -3.355(l) -5.538 (I) -4.494 (1) - I .a07 (0) -2.537 (0) -1.173(l) - 1.086 (0) -4.577(-l) 3.156(-I) -1.694(-l) 7.782 (-2)

- 1.838 (I) -3.037(l) -4.938 (1) -3.917 (1) - 1.538 (1) - 2.000 (0) -1.151 (1) - 1.053(0) -4.943(-l) 3.501(- 1) -2.027(-l) 9.398 (-2)

TFitting coefficients for recombination from the 2sz2p5 state to the 2p53s,2p53p and 2p53d states were obtained in one (the entire) temperature range 0.01-5.0 keV.

Dielectronic Table

741

rates

7. Coefficients for polynomial fits to dielectronic recombination rates to n = 3 singly excited states of Ti”+. An = 0 and An # 0 transitions are included for recombination from the ground 2~~2~’ state.

Temperature (keV) O.Ol-O.lt

0.1-5.0:

0.01-0.1

O.lL5.0

tFitting coefficients O.Oi-O.05 keV. IFitting coefficients 0.05-5.0 keV.

Table

Coeff

2~~3s

A0 A, Al A, A, A, A,, A, A? A, A, A,

-1.068(l) 3.997 (0) 4.688 (0) I .909 (0) -8.608(-2) 5.408 (-2) -1.254(l) -1.219(O) -3.148 i-1) 2.174(-l) -1.233(-l) 6.852 (-2)

- 1.021 (1) 2.785 (0) 1.866(0) -6.402(-l) -1.128(O) -7.923(-2) -1.190(l) -1.175(O) -3.636(-l) 2.542(-l) -1.357(-l) 6.234(-2)

A0 A, A> A, A, A, A0 A, A? A? A, ‘4,

-1.190(l) 4.972 (0) I.018 (I) 9.818 (0) 4.659 (0) I ,044
- 8.932 (0) 1.223 (I) 2.135(l) I.812 (I) 7.662 (01 1.501 (oj - 1.233 (1) - 1.235 (0) -2.955 (2.048 (-1.147(-l) 5.732(-2)

2~2~~3s

2pS3d

2~53~

2s2ph3p

Both

2s2ph3d

Recombination from 2s22pS state 1.222 (2) - I.501 (I) - 8.472 (0) 9.301 (0) 3.562 (2) - 1.437 (I) 1.230(l) 4.021 (2) -2.831 (I) 7.682 (0) 2.263 (2) -2.405 (I) 2.124 (0) 6.364 (I) -9.236 (0) 4.571 (‘I) 7.194ioj - 1.295 iOj -1.176(l) - I.301 (I) -1.326(l) -1.160(O) -1.160(O) -1.169(O) -3.833(-l) -2.403(-l) -3.735(-l) 2.630(-l) 5.255 (- I) 3.716(-l) -1.532(-l) -5.073(-l) -1.374(-i) 8.923 (- 2) -3.029(-l) -1.332(-l) Recombination from 2s2p6 state -2.789-(l) -8.818 (0) -3.063(l) 1.247 (I) -5.746(l) -7.077(l) 2.203 (I j -8.346(l) - 1.030 (2) I.919 (1) -6.012 (I) -7.412(l) 8.295 (0) -2.140(l) -2.629 (I) 1.665 (0) -2.795 (0) -3.435 (0) -1.222(l) -1.289(l) - 1.207 (I) -1.192(O) - 1.221(0) - 1.208 (0) I) -3.438(-I) -3.074 (- I) -3.269(-l) 1) 2.423 (- I) 2.101 (-I) 2.280 (- I) -1.255(-l) -1.395(-l) -1.388(-l) 6.263 (- 2) 6.369(-2) 7.451 (-2)

-9.360 (0) 1.067(l) 1.195(l) 6.038 (0) I .505 (0) 1.916(-l) -1.351 (I) - I .2Ol (0) -3.329(-l) 3.017(-l) -5.705(-2) -1.573(-l) -2.792(l) -6.100(l) -8.766(l) -6.193 (I) -2.149(l) - 2.643 (0) -1.182(l) -1.177(O) -3.629(-l) 2.482(-Ij -1.532(-l) 9.296 ( - 2)

for recombination

from the 2s22vs state to the 2~2~~3s state were obtained

in the temverature

ranee

for recombination

from the 2s’2ps state to the 2~2~~3s state were obtained

in the temperature

range

8. Coefficients for polynomial fits to dielectronic recombination rates to n = 3 singly excited states of A?‘. An = 0 and An # 0 transitions are included for recombination from the ground 2s22ps state.

Temperature (kcV)

Coeff

0.014.lt

A0 A, A2 ‘4, A4 A5

O.l-5.02

A0 A, A? A, A, A,

0.01-0.

recombination

I

0.1-5.0

TFitting coefficients O.Oi-O.05 keV. fFitting coefficients 0.05-5.0 keV.

‘40 A, 4 A, Al A5 A0 A,

2~~3s

2p53d

2~53~

-1.842(l) -2.184(l) -2.997 (1) -2.089(l) - 7.250 (0) -8.568(-I) -1.286(l) -1.317(O) -2.046(-l) 1.479(-l) -9.662(-2) 4.738(-2) -1.199(l) 7.368 (0) 1.495 (1) 1.335(l) 5.746 (0) I .078 (0) -1.401 (lj - 1.340 (0) -1.811(-l) 1.313(-l) -7.923(-2) 3.712(-2)

’

Recombination -1.502(l) -1.176(l) -1.564(l) -1.072(l) - 3.703 (0) -3.309(-l) -1.224(l) - 1.284 (0) -2.446(-I) 1.741 f-1.125(-tj 6.690 (Recombination -9.828 (0) 1.080 (1) 2.004fl) 1.725 ilj 7.252 (0) 1.360 (0) -1.274(l) -1.314(O) -2.076(1.500(-l) -1.012(-l) 2) 5.245 (-

-1.820(l) -2.287 (1) -3.170(l) -2.223 (I) -7.767 (0) -9.198(-l) -1.240(l) - I .299 (0) - 2.265 (- 1) 1.579(-l) -i.o06i-Ij 6.058 ( - 2) - 1.071 (I) 7.730 (0) 1.528 (I) 1.343 (ij 5.749 (0) 1.102 (0) -1.285(l) - 1.340 (0) -1.785(-l) 1.311(-l) -8.684(-2) 4.523 (-

2~2~~3s

1) 2)

1)

2)

from 2s!2p* state -3.562(l) -6.313 (I) -5.955(l) -1.949(l) 6.328 (- 1) 1.016(O) -1.353(l) - 1.263 (0) -2.688(-I) 1.923(-l) -1.229i-Ij 6.942 (-2) from 2s2p6 state -1.480(l) - 6.286 (0) - 6.003 (0) -2.565 {Oj -2.293(-l) 2.192(-l) -1.327(l) - I.330 (0) -1.914(-I) 1.331 (- 1) -8.513 (-2) 5.210(-2)

2s2p63p -4.208 (I) - 1.048 (2) - 1.427 (2) -9.400 (I) - 3.006 (1) - 3.727 (0) -1.366(l) - I.276 (0) -2.540(-I) 2.092 ( -l.ln-lj I.l05(-2)

Both

2s2p63d

11

4.044(l) 1.959 (2) 2.851 (2) 2.027 (I) 7.010(l) 9.572 (0) -1.310(l) - 1.278 (0) -2.510(-l) 1.777 (- 1) -1.252(-l) 7.860(-2)

1.036(l) 5.658 (I) 5.125(l) 2.114(l) 3.774 (0) 2.247(-l) -1.350(l) - 1.266 (0) -1.832(-l) 3.700 (-3.210(-lj -2.157(-2)

I)

- 1.507 (1) -1.083(l) -1.280(l) - 7.395 (0) - 1.920 (0) 2.976(-2) - 1.232 (I) - I .296 (0) -2.319(-I) 1.565(-l) -1.040(-l) 7.390(-2)

for recombination

from the 2s22p5 state to the 2s2v63d state were obtained

in the temperature

range

for recombination

from the 2s22ps state of the 2s2p63d state were obtained

in the temperature

range

742

Arati

Dasgupta

r

r -12.4 -12.2 -12.5

-12.4

-

_

B a 0

-12.4 --I-T-

(d)

-I

-12.6 -

$ -12.8 -

-132 -

-136 -

-13.6

\

-14.0 -2.0

IL -1.5

-1.0

-0.5

0.0

0.5

IO

-2.0

-1.5

-1.0

-0.5

0.0

I

-L-i 0.5

10

loglo (T) WV

Fig. 1. Comparisons of calculated dielectronic-recombination (DR) rate coefficients vs least-squares fitted data obtained using the calculated DR rate coefficients to the n = 3 excited states of neon-like ions for the four cases where the differences were the maximum. The results shown are for recombination from the 2s22p5 state to the (a) 2~~3s and (b) 2p63d states of Sez4+, (c) 2~~3s state of Ti’*+, and (d) 2~~3s state of A?+. The solid curves represent the calculated rate coefficients while the dashed-chained curves represent the polynomial fits to these rates.

Acknowledgemenr-This

work was supported

in part by the 6.1 program

of the Naval

Research

Laboratory

REFERENCES 1. A Burgess, Asrrophys. J. 139, 776 (1964); 141, 1589 (1965). 2. M. J. Seaton and P. J. Storey, in Atomic Processes and Applications, P. G. Burke and B. L. Moiseiwitsch, eds., p. 133, North Holland, Amsterdam (1976). 3. J. Dubau and S. Volonte, Rep. Prog. Phys. 43, 199 (1980). 4. J. P. Apruzese, J. Davis, M. Blaha, P. C. Kepple, and V. L. Jacobs, Phys. Rev. Left. 55, 1877 (1985). 5. B. L. Whiten, A. U. Hazi, M. H. Chen, and P. L. Hagelstein, Phys. Rev. A 33, 2171 (1986). 6. R. A. London, M. D. Rosen M. S. Maxon, D. C. Eder, and P. L. Hagelstein, J. Phys. B 22,3363 (1989). 7. H. R. Rugge and D. L. McKenzie, Asrrophys. J. 297, 338 (1985). 8. C. J. Keane, N. M. Ceglio, B. J. MacGowan, D. L. Matthews, D. G. Nilson, J. E. Trebes, and D. A. Whealan, J. Phys. B 22, 3343 (1989). 9. T. N. Lee, E. A. McLean, and R. C. Elton, Phys. Rev. Left. 59, 1185 (1987). 10. T. N. Lee, E. A. McLean, J. A. Stamper, H. R. Griem, and C. K. Manka, Bull. Am. P&s. Sot. 33, 1920 (1988). 11. D. L. Matthews et al, Phys. Rev. Lett. 54, 110 (1985).

Dielectronic recombination rates

743

12. M. D. Rosen et al, Phys. Rev. Lett. 54, 106 (1985). 13. P. B. Holden, S. B. Healy, M. T. M. Lightbody, G. J. Pert, J. A. Plowes, A. E. Kingston, E. Robertson, C. L. S. Lewis, and D. Neely, J. P&s. B 27, 341 (1994). 14. A. Dasgupta, K. G. Whitney, M. Blaha, and M. Buie, Phys. Rev. A 46, 5973 (1992). 15. R. D. Cowan, The Theory of Atomic Structure and Spectra, The University of California Press, Berkeley, CA (1981).