Atomic Database

General Description

The database system used by XSTAR version 2 attempts to separate, as much as possible, the numerical quantities which determine the various atomic rates from the Fortran code which actually performs the calculation. The goal is make the atomic data modular, so that new data can be adopted or tested without requiring extensive modifications to the code. The way this is done is to separate the data from the code itself, and store the data in a database which is designed specifically for use by XSTAR. The database is divided into “records”, each of which corresponds to a given physical process affecting a given level or pair of levels. An example is the radiative decay of hydrogen from the 2p to the 1s level. Each record contains numerical constants needed to calculate the rate for the process, in this example simply the Einstein \(A\) value for the transition, together with various other associated quantities. Chief among these are two integers which describe the how the constants are to be used. The first integer is denoted the “data type”, and describes the fitting formula to be used in order to calculate a rate from the constants. The second integer is the “rate type”, which describes how XSTAR uses the rates calculated. The list of data types is already quite long and is expected to grow and change as new data is adopted into the database, but not all data types are used by the current database. In order to interpret the various data types, XSTAR contains one central data calculating subroutine, denoted ucalc.f, which branches to various segments of code (and calls to specialized subroutines) which are tailored to each data type. ucalc.f returns the rates in a standard form for use by the other XSTAR subroutines. It is expected that ucalc.f will require additions in order to handle new data types as they are adopted. The list of rate types is not intended to grow, since such changes could require changes to the rest of the XSTAR code structure.

The XSTAR database system can be divided into 2 parts:

First, and most important, is the ASCII file containing all the data. That is, this file contains all the numerical data and labels required for calculation of all atomic rates and resultant quantities. This includes all level excitation energies, statistical weights and spectroscopic names, all element names and abundances, all ion names, and of course all photoionization cross sections, collision rates, recombination rates, fluorescence yeilds, and line wavelengths. This file is separated into records, corresponding crudely to lines of text, although many records extend over more than one line. Each record consists of a header, followed by the data. The header currently consists of 6 integers: the data type, the rate type, a continuation flag (currently unused), the number of reals in the record, the number of integers in the record, and the numbers of characters in the record. Then follows the real data, the integer data, and the character data. The various fields within the record are separated by one or more spaces. The record is terminated with a \(\%\), and the entire database is terminated by a single line containing \(\%\%\%\%\). Each record can currently contain up to 2000 of any of the types of constants: real, integer, or character. In the XSTAR source tree this file is named atdat.text and currently is approximately 3 GB in size.

The second part of the database is the subroutine ucalc.f. This routine, when passed the contents of a record, returns the result of the rate calculation for the corresponding process. ucalc therefore contains all of the various arithmetic expressions corresponding to rates for various physical processes. ucalc returns generally 4 real rates and two integers. The rates are: rate, inverse rate, heating rate, and cooling rate. The integers are indeces of the levels involved, lower and upper. Not all data types return all 4 rates.

Rate types

The list of rate types currently included in ucalc are as follows:

01

Ground state ionization.

03

Bound-bound collision.

04

Bound-bound radiative.

05

Bound-free collision (level).

06

Total recombination.

07

Bound-free radiative (level).

08

Total recombination, forces norm.

09

2-photon decay.

11

Element data.

12

Ion data.

13

Level data.

14

Bound-bound radiative superlevel-spectroscopic level.

15

Collisional ionization total rate.

40

Bound-bound collisional superlevel-spectroscopic level.

41

Non-radiative Auger transition.

42

Inner shell photoabsorption followed by autoionization.

Data types

01

Radiative recombination rate coefficient of \(N\)-electron recombined ion [1, 2]: \(\mathtt{r1} =A_\text{rad}~(\text{cm}^3\,\text{s}^{-1})\); \(\mathtt{r2}=\eta\); \(\mathtt{i1}=ion_N\).

02

\(\text{H}^0\) charge exchange rate coefficient of \(N\)-electron recombined ion [34]: \(\mathtt{r1}= a~(10^{-9}\,\text{cm}^3\,\text{s}^{-1})\); \(\mathtt{r2}= b\); \(\mathtt{r3}= c\); \(\mathtt{r4}= d\); \(\mathtt{r5}= T_1\) (K); \(\mathtt{r6}= T_2\) (K); \(\mathtt{r7}=\Delta E/k~(10^4\,\text{K})\); \(\mathtt{i1}=ion_N\); \(\mathtt{s1}=\) recombining ion identifier.

06

Data attributes of the \(i\)-th level of \(N\)-electron ion: \(\mathtt{r1} =E(i)\) (eV); \(\mathtt{r2} = (2J+1)\); \(\mathtt{r3} = \nu\) (effective quantum number); \(\mathtt{r4} =E(\infty)\) (eV); \(\mathtt{i1} = n\); \(\mathtt{i2}=(2S+1)\); \(\mathtt{i3}=L\); \(\mathtt{i4}=Z\); \(\mathtt{i5}=i\); \(\mathtt{i6}=ion_N\); \(\mathtt{s1}=\) level configuration assignment.

07

Dielectronic recombination rate coefficient of \(N\)-electron recombined ion [1, 2]: \(\mathtt{r1} =A_\text{di}~(cm^3\,\text{s}^{-1}\,\text{K}^{3/2})\); \(\mathtt{r2} =B_\text{di}\); \(\mathtt{r3}=T_0\) (K); \(\mathtt{r4}=T_1\) (K); \(\mathtt{i1}=ion_N\).

14

Ionization potential of \(N\)-electron ion: \(\mathtt{r1} =E(\infty)\) (eV); \(\mathtt{i1} = Z-N+1\); \(\mathtt{i2} = Z\); \(\mathtt{i3}=ion_N\); \(\mathtt{s1}=\) ion identifier.

22

Dielectronic recombination rate coefficient of the \(N\)-electron recombined ion [42]: \(\mathtt{r1}= a\); \(\mathtt{r2}= b\); \(\mathtt{r3}= c\); \(\mathtt{r4}= d\); \(\mathtt{r5}= e\); \(\mathtt{r6}= f\); \(\mathtt{i1}=ion_N\).

30

Total radiative recombination rate (hydrogenic) for \(N\)-electron recombined ion [21]: \(\mathtt{i1}=Z\); \(\mathtt{i2}=ion_N\).

38

Total radiative recombination rate coefficient of \(N\)-electron recombined ion [http://amdpp.phys.strath.ac.uk/tamoc/DATA/RR/]: \(\mathtt{r1} =A (\text{cm}^3\,\text{s}^{-1})\); \(\mathtt{r2} =B\); \(\mathtt{r3} =T_0\) (K); \(\mathtt{r4} =T_1\) (K); \(\mathtt{r5} =C\); \(\mathtt{r6} =T_2\) (K); \(\mathtt{i1}=Z\); \(\mathtt{i2}=N-1\); \(\mathtt{i3}=M\); \(\mathtt{i4}=W\); \(\mathtt{i5}=ion_N\).

39

Total dielectronic recombination rate coefficient of \(N\)-electron recombined ion [http://amdpp.phys.strath.ac.uk/tamoc/DATA/DR/]: \(\mathtt{r1{-}rj_{max}} =(C(j),j=1,j_\text{max}) (\text{cm}^3\,\text{s}^{-1}\,\text{K}^{3/2})\); \(\mathtt{rj_{max+1}{-}rj_{2*max}} =(T(j),j=1,j_\text{max})\) (K); \(\mathtt{i1}=Z\); \(\mathtt{i2}=N-1\); \(\mathtt{i3}=M\); \(\mathtt{i4}=W\), \(\mathtt{i5}=ion_N\).

49

Partial photoionization cross section of \(i_N\)-th level of the \(N\)-electron ion leaving the (\(N-1\))-electron ion in the \(k_{N-1}\)-th level: \(\mathtt{r1{-}rj_{2*max}} =(E(j),\sigma(E(j)),j=1,j_\text{max})\) (Energy in Ryd relative to \(E(\infty)\), cross section in Mb); \(\mathtt{i1} = n\); \(\mathtt{i2}=L\); \(\mathtt{i3}=2J\); \(\mathtt{i4}=Z\); \(\mathtt{i5}=k_{N-1}\); \(\mathtt{i6}=ion_{N-1}\); \(\mathtt{i7}=i_N\); \(\mathtt{i8}=ion_N\).

50

Line (\(k-i\)) radiation rates of \(N\)-electron ion: \(\mathtt{r1} =\lambda~(\AA)\); \(\mathtt{r2} = gf(i,k)\); \(\mathtt{r3} = A(k,i)~(\text{s}^{-1}\)); \(\mathtt{i1} = i\) (lower level); \(\mathtt{i2}=k\) (upper level); \(\mathtt{i3}=Z\); \(\mathtt{i4}=ion_N\).

51

Electron-impact effective collision strength for the \(k - i\) transition of \(N\)-electron ion (CHIANTI fit [12, 17]): \(\mathtt{r1} =\Delta E\) (Ryd); \(\mathtt{r2} =C\); \(\mathtt{r3{-}r7} =(\Upsilon_\text{ red}(j),j=1,5)\) (reduced effective collision strength); \(\mathtt{i1} = it\) (transition type); \(\mathtt{i2} = i\) (lower level); \(\mathtt{i3} = k\) (upper level); \(\mathtt{i4} = Z\); \(\mathtt{i5}=ion_N\).

53

TOPbase partial photoionization cross section (resonance averaged) of \(i_N\)-th level of the \(N\)-electron ion leaving the (\(N-1\))-electron ion in the \(k_{N-1}\)-th level: \(\mathtt{r1{-}rj_{2*max}} =(E(j),\sigma(E(j)),j=1,j_\text{max})\) (Energy in Ryd relative to \(E(\infty)\), cross section in Mb); \(\mathtt{i1} = n\); \(\mathtt{i2}=L\); \(\mathtt{i3}=2J\); \(\mathtt{i4}=Z\); \(\mathtt{i5}=k_{N-1}\); \(\mathtt{i6}=ion_{N-1}\); \(\mathtt{i7}=i_N\); \(\mathtt{i8}=ion_N\).

54

Radiative transition probability \(A_{ki}\) for the \(k - i\) transition of \(N\)-electron ion computed by quantum defect theory (or hydrogenic): \(\mathtt{r1} =0.0E+0\); \(\mathtt{i1} = i\) (lower level); \(\mathtt{i2}=k\) (upper level); \(\mathtt{i3}=Z\); \(\mathtt{i5}=ion_N\).

56

Electron-impact effective collision strengths for the \(k - i\) transition of \(N\)-electron ion: \(\mathtt{r1{-}rj_{max}} =(\log T_e(j), j=1, j_\text{max})\) (K); \(\mathtt{rj_{(max+1)}{-}rj_{(2*max)}} =(\Upsilon(T_e(j)),j=1,j_\text{max})\) (effective collision strength); \(\mathtt{i1} = i\) (lower level); \(\mathtt{i2}=k\) (upper level); \(\mathtt{i3}=Z\); \(\mathtt{i5}=ion_N\).

57

Effective ion charge for \(i\)-th level of \(N\)-electron ion: \(\mathtt{r1} =Z_{\rm eff}\); \(\mathtt{i1} = n\); \(\mathtt{i2}=L\); \(\mathtt{i3}=2J\); \(\mathtt{i4}=Z\); \(\mathtt{i5}=i\); \(\mathtt{i6}=ion_N\)

59

Partial photoionization cross section of \(i_N\)-th level of the \(N\)-electron ion leaving the (\(N-1\))-electron ion in the \(k_{N-1}\)-th level [51]: \(\mathtt{r1} =E(th)\) (eV); \(\mathtt{r2} =E(0)\) (eV); \(\mathtt{r3} =\sigma(0)\) (Mb); \(\mathtt{r4} =y(a)\); \(\mathtt{r5} =P\); \(\mathtt{r6} =y(w)\) ; \(\mathtt{i1} = N\); \(\mathtt{i2}=n\) (shell principal quantum number); \(\mathtt{i3}=l\) (orbital quantum number of the subshell); \(\mathtt{i4}=k_{N-1}\); \(\mathtt{i5}=ion_{N-1}\); \(\mathtt{i6}=i_N\); \(\mathtt{i7}=ion_N\); \(\mathtt{s1}=\) shell-ion identifier.

60

Analytic fits for effective collision strengths in H-like ions [14]: \(\mathtt{r1{-}rj_{max}} =\) coefficients; \(\mathtt{i1} = i\) (lower level); \(\mathtt{i2}=k\) (upper level); \(\mathtt{i3}=1\); \(\mathtt{i8}=ion_N\); \(\mathtt{s1}=\) Transition.

62

Analytic fits for effective collision strengths in H-like ions [14]: \(\mathtt{r1{-}rj_{max}} =\) coefficients; \(\mathtt{i1} = i\) (lower level); \(\mathtt{i2}=k\) (upper level); \(\mathtt{i3}=1\); \(\mathtt{i8}=ion_N\); \(\mathtt{s1}=\) Transition.

63

Collisional transition probability \(C_{ik}\) for \(N\)-electron ion computed by quantum defect theory (or hydrogenic): \(\mathtt{i1} = 1\); \(\mathtt{i2} = i\) (lower level); \(\mathtt{i3}=k\) (upper level); \(\mathtt{i4}=Z\); \(\mathtt{i5}=ion_N\).

66

Fits to fine-structure collision strengths for He-like ions [32]: \(\mathtt{r1{-}rj_{max}} =\) coefficients; \(\mathtt{i1} = i\) (lower level); \(\mathtt{i2}=k\) (upper level); \(\mathtt{i3}=Z\); \(\mathtt{i4}=ion_N\).

67

Analytic fits for effective collision strengths in He-like ions [33]: \(\mathtt{r1{-}rj_{max}} =\) coefficients; \(\mathtt{i1} = i\) (lower level); \(\mathtt{i2}=k\) (upper level); \(\mathtt{i3}=Z\); \(\mathtt{i4}=ion_N\).

68

Analytic fits for effective collision strengths in He-like ions [53]: \(\mathtt{r1{-}rj_{max}} =\) coefficients; \(\mathtt{i1} = i\) (lower level); \(\mathtt{i2}=k\) (upper level); \(\mathtt{i3}=Z\); \(\mathtt{i8}=ion_N\).

69

Fits to \(LS\) collision strengths for He-like ions [32]: \(\mathtt{r1{-}rj_{max}} =\) coefficients; \(\mathtt{i1} = i\) (lower level); \(\mathtt{i2}=k\) (upper level); \(\mathtt{i3}=Z\); \(\mathtt{i8}=ion_N\).

70

Coefficients for recombination and photoionization cross sections of superlevels: \(\mathtt{r1{-}rj_{nd}} =(n_e(j),j=1,j_{nd})\); \(\mathtt{rj_{nd+1}{-}rj_{nd+nt}} =(T_e(j),j=1,j_{nt})\); \(\mathtt{rj_{nd+nt+1}{-}rj_{ nd+nt+nt*nd}} =((\log\alpha(j,j'),j'=1,j'_{nd}),j=1,j_{nt})\); \(\mathtt{rj_{nd+nt+nt*nd+1}-rj_{nd+nt+nt*nd+2*nx}} =(E(j),\sigma(j),j=1,j_{nx})\); \(\mathtt{i1} = nd\); \(\mathtt{i2} = nt\); \(\mathtt{i3} = nx\); \(\mathtt{i4} = n\); \(\mathtt{i5}=L\); \(\mathtt{i6}=2S+1\); \(\mathtt{i7}=Z\); \(\mathtt{i8}=k_{N-1}\); \(\mathtt{i9}=ion_{N-1}\); \(\mathtt{i10}=i_N\); \(\mathtt{i11}=ion_N\).

71

Radiative transition rates from superlevels to spectroscopic levels: \(\mathtt{r1{-}rj_{nd}} =(n_e(j),j=1,j_{nd})\); \(\mathtt{rj_{nd+1}{-}rj_{nd+nt}} =(T_e(j),j=1,j_{nt})\); \(\mathtt{rj_{nd+nt+1}{-}rj_{ nd+nt+nt*nd}} =((A(j,j'),j'=1,j'_{nd}),j=1,j_{nt})\); \(\mathtt{r_{nd+nt+nt*nd+1}} =\lambda~(\AA)\); \(\mathtt{i1} = nd\); \(\mathtt{i2} = nt\); \(\mathtt{i3} = i\) (lower level); \(\mathtt{i4} = k\) (upper level); \(\mathtt{i5}=Z\); \(\mathtt{i6}=ion_N\).

72

Autoionization rates for satellite levels: \(\mathtt{r1} = A_a(k,i)~(\text{s}^{-1})\); \(\mathtt{r2} =E(k)\) (eV above ionization limit); \(\mathtt{r3} = (2J+1)\); \(\mathtt{i1}=(2S+1)\); \(\mathtt{i2}=L\); \(\mathtt{i3}=k\) (level); \(\mathtt{i4}=i\) (continuum level); \(\mathtt{i5}=Z\); \(\mathtt{i6}=ion_N\); \(\mathtt{s1}=\) level configuration.

73

Fit to effective collision strengths for satellite levels of He-like ions [47]: \(\mathtt{r1{-}rj_{7}} =\) fit coefficients; \(\mathtt{i1}=i\) (lower level); \(\mathtt{i2}=j\) (upper level); \(\mathtt{i3}=Z\); \(\mathtt{i4}=ion_N\).

74

Delta functions to add to photoionization cross sections to match ADF DR rates: \(\mathtt{r1} = E(\infty)\) (eV); \(\mathtt{r1{-}rj_{m}} =(E(j),j=1,j_{m})\) (eV); \(\mathtt{rj_{m+1}{-}rj_{2m}} =(f(j),j=1,j_{m})~(\text{cm}^2)\); \(\mathtt{i1} = n\); \(\mathtt{i2}=L\); \(\mathtt{i3}=2S+1\); \(\mathtt{i4}=Z\); \(\mathtt{i5}=k_{N-1}\); \(\mathtt{i6}=ion_{N-1}\); \(\mathtt{i7}=i_N\); \(\mathtt{i8}=ion_N\)

75

Autoionization rates for Fe XXIV satellites [8]: \(\mathtt{r1} = A_a(k,i)~(\text{s}^{-1})\); \(\mathtt{r2} =E(k)\) (eV above ionization limit); \(\mathtt{i1}=ion_N\), \(\mathtt{i2}=k_{N}\); \(\mathtt{i3}=ion_{N-1}\); \(\mathtt{i4}=i_{N-1}\); \(\mathtt{i5}=ion_N\).

76

Two-photon radiation rate for (\(k-i\)) transition of \(N\)-electron ion: \(\mathtt{r1} = A(k,i)~(\text{s}^{-1})\); \(\mathtt{i1} = i\) (lower level); \(\mathtt{i2}=k\) (upper level); \(\mathtt{i3}=1\); \(\mathtt{i4}=ion_N\); \(\mathtt{s1}=\) transition identifier.

77

Collision transition rates from superlevels to spectroscopic levels: \(\mathtt{r1{-}rj_{nd}} =(n_e(j),j=1,j_{nd})\); \(\mathtt{rj_{nd+1}{-}rj_{nd+nt}} =(T_e(j),j=1,j_{nt})\); \(\mathtt{rj_{nd+nt+1}{-}rj_{ nd+nt+nt*nd}} =((C(j,j'),j'=1,j'_{nd}),j=1,j_{nt})~(\text{s}^{-1})\); \(\mathtt{rj_{nd+nt+nt*nd+1}}=\lambda~(\AA)\); \(\mathtt{i1} = nd\); \(\mathtt{i2} = nt\); \(\mathtt{i3} = i\) (lower level); \(\mathtt{i4} = k\) (upper level); \(\mathtt{i5}=Z\); \(\mathtt{i6}=ion_N\).

81

Collision strengths for Fe XIX [10]: \(\mathtt{r1} = \Upsilon(k,i)\); \(\mathtt{i1} = i\) (lower level); \(\mathtt{i2} = k\) (upper level); \(\mathtt{i3}=Z\); \(\mathtt{i4}=ion_N\).

82

Decay rates for Fe UTA [24]: \(\mathtt{r1} =\lambda~(\AA)\); \(\mathtt{r2} =E(k)\) (eV); \(\mathtt{r3} = gf(i,k)\); \(\mathtt{r4} = A_r(k,i)~(\text{s}^{-1})\); \(\mathtt{r5} = A_a(k,i)~(\text{s}^{-1})\); \(\mathtt{i1} = i\) (lower level); \(\mathtt{i2}=k\) (upper level); \(\mathtt{i4}=ion_N\).

83

Level data for Fe UTA [24]: \(\mathtt{r1} =E(i)\) (eV); \(\mathtt{r2} = (2J+1)\); \(\mathtt{r3} = 0.0\); \(\mathtt{r4} =0.0\); \(\mathtt{i1} = 1\); \(\mathtt{i5}=i\) (level); \(\mathtt{i6}=ion_N\); \(\mathtt{s1}=\) level configuration assignment.

85

Photoionization cross sections for Fe ions obtained by summation of resonances near the K edge [44]: \(\mathtt{r1} =Z_\text{eff}\); \(\mathtt{r2} =E_\text{th}\) (Ryd); \(\mathtt{r3} =f\); \(\mathtt{r4} =\gamma\); \(\mathtt{r5} =\) scaling factor; \(\mathtt{i1} = n\); \(\mathtt{i2}=L\); \(\mathtt{i3}=2J\); \(\mathtt{i4}=Z\); \(\mathtt{i5}=k_{N-1}\); \(\mathtt{i6}=ion_{N-1}\); \(\mathtt{i7}=i_N\); \(\mathtt{i8}=ion_N\).

86

Auger and radiative widths of \(k_N\)-th K-vacancy level: \(\mathtt{r1} =E(k_N)\) (eV, relative to \(E(\infty)\)); \(\mathtt{r2} = A_a(k_N)~(\text{s}^{-1})\); \(\mathtt{r3} = A_a(k_N,i_{N-1})~(\text{s}^{-1})\); \(\mathtt{r4} = A_r(k_N)~(\text{s}^{-1})\); \(\mathtt{i1} = i_{N-1}\); \(\mathtt{i2}=k_N\); \(\mathtt{i3}=Z\); \(\mathtt{i4}=ion_{N-1}\); \(\mathtt{i5}=ion_N\).

88

Photoionization cross section damped excess of \(i_N\)-th level of the \(N\)-electron ion leaving the (\(N-1\))-electron ion in superlevel_[K] \(k_{N-1}\): \(\mathtt{r1{-}rj_{max}} =(E(j),\sigma(E(j)),j=1,j_\text{max})\) (Energy in Ryd relative to \(E(\infty)\), cross section in Mb); \(\mathtt{i1} = n\); \(\mathtt{i2}=L\); \(\mathtt{i3}=2J\); \(\mathtt{i4}=Z\); \(\mathtt{i5}=k_{N-1}\); \(\mathtt{i6}=i_N\); \(\mathtt{i7}=ion_N\).

91

APED line (\(k-i\)) radiation rates [20]: \(\mathtt{r1} =\lambda~(\AA)\); \(\mathtt{r2} = 0.0\); \(\mathtt{r3} = A(k,i)~(\text{s}^{-1})\); \(\mathtt{i1} = i\) (lower level); \(\mathtt{i2}=k\) (upper level); \(\mathtt{i3}=Z\); \(\mathtt{i4}=ion_N\).

92

APED collision strengths [20]: \(\mathtt{r1{-}rj_{max}} =(T_e(j),j=1,j_{max})\) (K); \(\mathtt{rj_{max+1}{-}rj_{2*max}} =(\Upsilon(j),j=1,j_{max})\); \(\mathtt{i1} = 1\); \(\mathtt{i2}=i\) (lower level); \(\mathtt{i3}=k\) (upper level); \(\mathtt{i4}=Z\); \(\mathtt{i5}=ion_N\).

95

Collisional ionization rates for \(N\)-electron ion [11]: \(\mathtt{r1} =E(th)\) (eV); \(\mathtt{r2} =T_0\) (K); \(\mathtt{r3{-}rj_{max+2}} =(\rho(j), j=1,j_{max})\) (effective collision strength); \(\mathtt{i1} = i\) (level); \(\mathtt{i5}=ion_N\).

98

Electron-impact effective collision strengths for the \(k - i\) transition of the \(N\)-electron ion (CHIANTI fit citep{1992:Burgess,1997:Dere}): \(\mathtt{r1} =\Delta E\) (Ryd); \(\mathtt{r2} =C\); \(\mathtt{r3{-}rj_{max+2}} =(\Upsilon_{\rm red}(j),j=1,max)\) (reduced effective collision strength); \(\mathtt{i1} = it\) (transition type); \(\mathtt{i2} = i\); \(\mathtt{i3} = k\); \(\mathtt{i4}=ion_N\).

99

Coefficients for recombination and photoionization cross sections of superlevels: \(\mathtt{r1{-}rj_{nd}} =(n_e(j),j=1,j_{nd})\); \(\mathtt{rj_{nd+1}{-}rj_{nd+nt}} =(T_e(j),j=1,j_{nt})\); \(\mathtt{rj_{nd+nt+1}{-}rj_{ nd+nt+nt*nd}} =((\alpha(j,j'),j'=1,j'_{nd}),j=1,j_{nt})\); \(\mathtt{rj_{nd+nt+nt*nd+1}-rj_{nd+nt+nt*nd+2*nx}} =(E(j),\sigma(j),j=1,j_{nx})\); \(\mathtt{i1} = nd\); \(\mathtt{i2} = nt\); \(\mathtt{i3} = nx\); \(\mathtt{i4} = n\); \(\mathtt{i5}=L\); \(\mathtt{i6}=2S+1\); \(\mathtt{i7}=Z\); \(\mathtt{i8}=k_{N-1}\); \(\mathtt{i9}=ion_{N-1}\); \(\mathtt{i10}=i_N\); \(\mathtt{i11}=ion_N\).

Utility Programs

The program which translates the ascii database file into the binary fits format used by XSTAR is called bintran.f, and is included with the XSTAR source distribution. Compilation of this program is straightforward, although it requires links to the cfitsio libraries. Execution simply requires the redirection of the input.

Level Labels

New in version 2.21bh is the replacement of all level strings by a uniform system developed for the the uadb database. The following is reproduced from the uadb manual and describes the labeling system.

While level strings from any coupling scheme can be stored and retrieved from uaDB, currently it only supports searching for \(LS\)-coupled level strings. In order to guarantee uniqueness, level strings entered into the database must conform to the rules outlined in this appendix.

All states must have a configuration. Term-averaged or level-resolved states must also include a term string and level-resolved states must specify \(J\). The rules for each part follow.

Configuration strings

Configurations are stored in the database using an unambiguous notation which should be familiar to most users. A configuration consists of a space-delimited list of sub-shells in standard order each having the form, \(nlm\), where \(nl\) is the sub-shell (standard order: 1s, 2s, 2p, 3s, …) and \(m\) is the occupation number. Note that the shorthand notation of omitting \(m\) when unity is not used, e.g. 2s1 not 2s. Configuration strings obey the rules:

• all closed sub-shells starting with 1s and ending just prior to the first open (or last) sub-shell are not part of the configuration string,

• the first open sub-shell is always displayed even if it is empty (\(m=0\)), and

• all empty sub-shells beyond the first open sub-shell are not displayed.

Some examples:

• \(1s^2\,2s^2\,2p^3\) becomes 2p3,

• \(1s^2\,2s^1\,2p^4\) becomes 2s1 2p4

• \(1s^2\,2s^0\,2p^5\) becomes 2s0 2p5, and

• \(1s^1\,2s^2\,2p^4\) becomes 1s1 2s2 2p4.

Using a list of occupation numbers as the configuration label was considered and ultimately rejected due to the impracticality of storing Rydberg levels. Consider the configuration, 1s 200p; whereas only 13 characters are needed to store this configuration in the form described above, nearly 40,000 characters are required if using a list of occupation numbers.

To get the number of electrons of a configuration takes two steps; first you need to calculate the number of electrons in the core and then add up the occupation numbers of the visible sub-shells. To get the number of electrons in the core, \(n_{core}\), take the principal quantum number, \(n\), and the orbital angular momentum, \(l\) of the first open sub-shell and apply the following expression:

\[n_{core} = \frac{1}{3} n (n-1) (2n-1) + 2l^2 .\]

For a configuration of 4p5 5s2 5p1 we have \(n=4\) and \(l=1\). The above expression yields \(n_{core} = 30\) and the total occupation of the visible sub-shells is 8 so this configuration has 38 electrons.

Term strings

The format for term should be familiar to most users. It starts with an integer representing \(2S+1\) followed by the spectroscopic letter representing the total orbital angular momentum, \(L\). An example is \(\mathtt{2P}\) where \(S=1/2\) and \(L=1\).

Level strings

To specify the total angular momentum, \(J\), of a level-resolved state, you append the term string defined above with an underscore and the \(J\) value. If \(J\) is a half-integer then you must use fractional notation. Examples of the term and level strings include: \(\mathtt{2P_1/2}\) and \(\mathtt 1S_0\).