Online: March 1999   -   Last update: September 2005

  Spectral Lines

  Lines Search Form

• spectra of interest (e.g., Na I, Na II, Mg I-III).


• lower and upper limits of the wavelength range


• wavelength units.
  Wavelengths may be displayed in ångströms, nanometers, or micrometers. Wavelength units are selected by using the pulldown menu on the Lines Form.

For searches, a variety of output options, optional search criteria, and additional search criteria are available.

Lines searches are either wavelength ordered or multiplet ordered.

Dynamic Plots

This option allows graphical display of two types of dynamically created plots, i.e., line identification plots and Saha-LTE (local thermodynamic equilibrium) plasma emission plots. The plots are created as PDF files and require appropriate software (e.g., Adobe Acrobat Reader or xpdf) for graph display. See the Output Section for the details on the output.

• Line Identification Plot
  
  Selecting this option would produce a PDF file showing positions of all spectral lines within the chosen wavelength range.



• Saha-LTE Spectrum
  
  Selecting this option would produce a PDF file showing line emission from an optically thin plasma having the chosen values of electron temperature and electron density. The plasma emission is generated in arbitrary units. If only one ion is chosen for plot generation, then the populations of the energy levels are calculated according to the Boltzmann formula N_i = N₀/g₀*g_i*exp(-E_i/T_e) where N_i is the level population, N₀ is the population of the ground state level, g_i and g₀ are the statistical weights of the levels, E_i is the energy of the level with respect to the ground state in eV, and T_e is the electron temperature in eV to be entered in the text field. In this case the electron density N_e is not required to be entered.
  
  If several ions are chosen for plot generation (e.g., "C I-V" is entered in the "Spectra" text field), then first the ionization distribution between different ions is calculated according to the Saha formula (see, e.g., H.R. Griem, Principles of Plasma Spectroscopy, 1997), and then within each ion, the populations are calculated using the Boltzmann distribution formula. In this case both electron temperature and electron density are mandatory parameters.
  
  The spectrum may be convoluted with the Doppler (Gaussian) line profile for each of the spectral lines. The number of data points for the spectrum is to be less or equal than 20 000. By default, the entered electron temperature T_e is used for calculation of the line width parameter. An ion temperature T_i may be entered if T_i ≠ T_e.

Java Grotrian Diagrams

• Java subwindow size
  A user can choose the size of the subwindow which shows the Grotrian diagram (GD). There are four sizes available (in pixels): 640×640, 800×640, 1024×768, and 1280×1024.



• Grouping by configuration
  Normally the levels are grouped into series according to their core so that, for instance, in O I the levels belonging to configurations 2p³(³P)nl and 2p³(¹D)nl would be assigned to different series. For ions with multiple cores, it may be more convenient to have such levels grouped according to configuration only, and if such an option is selected by clicking the corresponding checkbox, then for the O I case mentioned above those levels would belong to the same series of 2p³nl.



• Term multiplicity
  This option allows display of the levels belonging only to a particular term subsystem of the ion. The text entered in the text field should be a valid beginning of an atomic term designation. For example, entering "3" would result in display of only triplet levels and transitions between them, while entering "1P" would produce GD only for levels belonging to the ¹P terms and corresponding transitions.



• Show only radiative linked levels
  By default, all levels belonging to the chosen ion are displayed in the GD. Selecting this option would result in display of only those levels which are connected by radiative transitions.



• Make Grotrian Diagram
  Pressing the "Make Grotrian Diagram" button creates a Java Grotrian diagram on the new page.

Output Options

The following options apply to all lines and levels searches and are collectively referred to as output options.

• choice of display using an HTML table or an ASCII table.
• choice of removing Javascript tags in the output (may be convenient for ASCII table when saving the output into a file)
• level units. The user may choose between cm^-1, eV, or Rydberg.
• choice of viewing the (scrollable) data all at once, or one page at a time.
• choice of page size. The number of lines displayed on each page of output may be modified so that for each user's screen, the maximum number of lines may be viewed per screen-full.
• output ordering. The output can be sorted according to either wavelength or multiplet order. The multiplet order is available for one ion only.
  

  Wavelength ordering

  All spectra are intermingled according to wavelength ordering. A spectrum must be provided if no wavelength range is indicated.
  

  Multiplet ordering

  Multiplets are transitions that share the same term and configuration. Multiplets have been ordered in the transition probability compilations according to energies and g values of the lower and upper levels, and have been assigned arbitrary multiplet numbers that reflect this order.

  To view multiplet ordered data, the user must select the "multiplet ordering" radio box.

  In some cases, a multiplet is missing from the numbered list. In general, this is because some property of a compiled wavelength or level involved is not consistent with other more recent compilations, such as the NIST energy level data. Note that with multiplet ordering, only those lines with transition probability values will be displayed. Moreover, the output will always be for vacuum wavelengths.

  Only the lines with energy level classification are displayed in the multiplet-ordered output, and therefore the total number of lines shown at the top of the page may be different for wavelength and multiplet orderings.

The default is to display output in its entirety as an HTML formatted table. By default, levels are displayed in cm^-1.

For instructions on how to modify options associated with viewing data, refer to the section options for viewing data.

Optional Search Criteria

The following search criteria may be specified:

• maximum lower level energy.
• maximum upper level energy.
• preference of whether the transition strength bounds will apply to A_ki (default), f_ik, S, or log(gf) values.
• minimum transition strength.
• maximum transition strength.
• accuracy minimum for A_ki (default), f_ik, S, and log(gf).
• relative intensity minimum.

Additional Search Criteria

There are numerous options that apply for lines searches. The following options apply to all lines searches and are collectively referred to as additional search criteria options.

• interest in displaying either:
  • all lines of data meeting the search criteria,
  • only lines with transition probability data,
  • only lines with energy level classifications, or
  • only lines with observed wavelengths.

  The default is to display all lines of data meeting the search criteria, regardless of whether the lines contain transition probability data or energy level classifications.

• choice of bibliographic information output

  If the corresponding radio box is selected, the bibliographic references for transition probabilities (TP) and spectral lines will be shown in two separate columns.

• choice of display of wavelength data:
  • observed wavelength
  • Ritz wavelength
  • The default is to suppress the display of the "observed-Ritz" column of data. Checking the "observed-Ritz" option will cause that column of data to be generated in the output.
• choice of wavelength units.

  The default is to display wavelengths in:
  Vacuum (< 2,000 Å), Air (2,000 Å to 10,000 Å), Vacuum (> 10,000 Å).

  For wavelength ordered output, the wavelengths are output in one column, with table headings changing as needed to reflect the change in units.

  For multiplet ordered output, the wavelength are ALWAYS given in vacuum.

  Alternative choices are:

• Vacuum (< 2,000 Å), Air (2,000 Å to 10,000 Å), Wavenumber (> 10,000 Å)
• Vacuum (< 10,000 Å), Wavenumber (> 10,000 Å)
• Vacuum (< 2,000 Å), Air (2,000 Å to 20,000 Å), Vacuum (> 20,000 Å)
• Vacuum (all wavelengths)
• Air (all wavelengths)
• Wavenumber (all wavelengths)

To change the default, the user simply needs to click on one of the radio buttons. The user will also need to check appropriate checkboxes if individual columns of wavelength information are desired

• choice of display of transition strength information. The default is to display the following columns of data:
  • A_ki (or g_kA_ki)
  • Accuracy
  • Relative intensity.

  By default, A_ki (or g_kA_ki) are displayed in units of s^-1. They can be displayed in units of 10⁸ s^-1 if a proper checkbox is checked.
  
  To suppress display of the Relative Intensity columns of data, the corresponding checkbox can be unchecked.

  Although f_ik, S, and log(gf) values are not displayed by default, if the corresponding checkboxes are clicked, then those data values will be displayed.

• choice of transition type
  
  By default, both electric dipole-allowed (E1) and forbidden (M1, E2, M2,...) transition are displyed in the output. To diplay only one type of transition, a user must uncheck the corresponding checkbox.
  
  
• choice of levels information: For lines output, the default is to display:
  • Configurations,
  • Terms,
  • Energies,
  • J values, and
  • g values.

  To suppress display of the information listed above, the corresponding checkbox can be unchecked. If the user has selected the "Only lines with transition probability data" interest option, then the g values will be suppressed.

  Selecting Spectra for Lines Searches

If the user has not provided enough information to specify spectra, an error message will be displayed.

Examples of Spectral Notation (Case Insensitive)

  Plotting Java Grotrian diagrams

Working with the Grotrian diagram plot

Basically, only a computer mouse and a space bar are used for interaction with this plot.

    Default view
    Initially all levels and transitions are shown on the plot. Each energy level is shown by a horizontal bar. The colors (black and blue) have no meaning and used simply to help with visualization of the plot. The X-axis corresponds to different level series, and the Y-axis shows the level energy in cm^-1. The radiative transitions between the levels are shown as the gray lines. The ionization limits are shown as the magenta horisontal lines. On the top of the plot, the total number of levels, lines and ionization limits is displayed. This parameters are automatically updated when zooming in or out. In the bottom right part of the plot, the maximal and minimal values of the transition probability for the displayed lines are given in the input text fields. The "Submit" and "Reset" buttons are used for setting the limits for transition probabilities while the "Isolate" button is used to single out one level and all relevant transitions. The green field ("zoom field" below) next to the Y-axis is use for zooming in and out. Below, the top right part of the plot will be referred to as the "info field".

• Selecting, deselecting and cycling over objects
  
  Mouse:
  
  • Clicking on any level colors it and all relevant transitions in red. In addition, the basic data on this level, e.g., energy, configuration, etc., are displayed in the info field.
  • Clicking on any line colors the line and the lower and upper level in red. In addition, the basic data on the levels and line (wavelengths, transition probability, etc.) are shown in the info field.
  • Consecutive clicking on two levels is equivalent to clicking on the corresponding spectral line. If there is no line connecting the levels, no Line information is shown in the info field although the data on both levels is displayed.
  • Clicking anywhere in the white background of the GD subwindow deselects the already selected object(s).
  
  
  
  Space bar:
  
  • If no objects have been selected, pressing a space bar selects a first spectral line in the following order: the levels are assumed to be arranged first according to the X-axis label (from left to right) and then according to the level energy. Since the ground state always has a zero energy, pressing the bar would normally highlight the line originating from the ground state.
  
  
  • If a line has been selected, pressing a space bar cycles over all spectral lines on the plot in the above described order, that is, (i) for the same lower level, the upper level is updated, and (ii) after all lines for a particular lower level are cycled, the lower level is updated, and so on.
  
  
  • If a level has been selected, pressing a space bar cycles over all energy levels within the levels series.
  • The data shown in the info field is the same as for the mouse selection.
  
  
• Zooming in and out
  
  The zoom field to the right of the Y-axis is used for zooming in. The upper and lower limits for the energy levels are set up by clicking the mouse in the zoom field. The upper and lower limits are shown by the horizontal blue lines. When both limits are selected, the "Zoom" button above the Y-axis becomes highlighted and clicking on it with the mouse results in subwindow update. This procedure can be repeated infinitely. After zooming in, the "Reset" button on the above the Y-axis becomes highlighted, and clicking on it restores the original plot.



• Filtering A-values
  
  To choose the limits for the radiative transition probabilities, a user must enter new values in the "minA" and "maxA" text fields in the bottom right part of the plot and press the "Submit" button. By default, the minimal and maximal values of transition probabilities for all lines shown on the plot are displayed in those fields. The "Reset" button restores the default limits.



• Isolating a level
  
  In order to isolate one energy level with all radiatively connected levels one has first to select a level by a mouse click. Then, the "Isolate" button in the bottom right part of the plot becomes highlighted, and pressing it would result in display of the red group of levels and lines only. If necessary, a user can then perform zoom or transition probability limit procedures on this subset of the levels. After isolating a level, the "Isolate" button changes its label to "Show All", and pressing this new button would show all available levels and transitions.

  Output for Lines

The output on the screen is graphical by default, but a significantly faster ASCII format may also be selected.

Help popup windows

The output may contain some symbols or combinations thereof colored in red. This means that moving a mouse over such symbols would result in appearance of a small popup window showing some explanatory text provided Javascript language is enables in the browser options or preferences. Moving the mouse out would remove the popup window unless a user clicked on the red symbols. In that case, the popup window remains visible until the next mouse click on the same symbols. For the Ritz wavelengths, such popup windows appear also for brown asterisk and pink plus symbols (see below).

Explanation of the Lines Tables

• Ion
• Observed Wavelength, Ritz Wavelength, and Obs.-Ritz Wavelength
• Rel. Int: Relative Intensity
• Transition Strengths, Accuracy
• E_i-E_k: Lower level and upper level energies
• Configurations: Configurations of the lower and upper levels
• Terms : Terms of the lower and upper levels
• J_i-J_k: the total electronic angular momentum of the lower and upper level
• g_i-g_k: Lower level statistical weight (g_i=2J_i+1) - upper level statistical weight (g_k=2J_k+1)
• Type: Transition multipole moment dipole, etc.
• TP Ref.
• Line Ref.
• Line Identification Plots
• Saha-LTE plots

Ion

Observed Wavelength, Ritz Wavelength, and Obs.-Ritz Wavelength

The user may choose to display both Ritz and observed wavelengths. The Obs-Ritz value may also be displayed. By default, wavelengths are given for vacuum wavelengths below 2000 Å and above 20000 Å, with air wavelengths in between.

Indexes of refraction are derived for expressions given by E.R. Peck and K. Reeder, J. Opt. Soc. Am. 62, 958 (1972). These authors fitted data between 1850 Å and 17000 Å. Any transition between air and vacuum entails an ambiguity near the transition point. For example, a wavelength of 2000.648 Å in vacuum corresponds to 2000.000 Å in air (15 °C in "standard air," i.e., 101 325 Pa pressure, with 0.033 % CO₂). Conversely, an air wavelength of 1999.352 Å corresponds to 2000.000 Å in vacuum. In this database, as the default the following convention is adopted in terms of the energy difference or wavenumber, "=E_k-E_i":

      For   50,000 cm-1                  vacuum wavelengths,
      For 5000 cm-1 <  < 50,000 cm-1      air wavelengths, 
      For   5000 cm-1                    vacuum wavelengths.

An explanation of the number of decimal places in each wavelength is provided in the section on significant figures.

  Significant Figures

Ritz wavelengths:

"Ritz" wavelengths are derived from level energies via the Ritz principle: The wavelength in vacuum is equal to the inverse of the difference in energies, , between the upper and lower energy levels of the transition:

 = 1/   ,

where the wavenumber  = E_k - E_i. The energies E_k and E_i are of the upper and lower levels of the transition, respectively. The units of this derived wavelength are the inverse of the energy units. For example, if the energy units are in inverse centimeters (cm^-1), the Ritz wavelength, derived by taking the inverse of E_k - E_i, is in cm. One multiplies a wavelength in cm by 10⁷ to obtain nanometer units, or 10⁸ to obtain ångströms.

The problem addressed here is to express the Ritz wavelength with a precision comparable to that of the energy difference from which it is derived. Because the wavelength and difference in energies are inversely related, a given number of significant figures does not always correspond to the comparable precision for both. For example, if the energy difference is 0.99, an extra significant figure is required to express the Ritz wavelength of comparable precision: 1.01.

The number of significant figures of any number, X, is equal to [log₁₀(X)] + dp +1, where dp indicates the number of decimal places and the square bracket indicates the integer value without roundoff, e.g., [5.6] = 5. Using this, we set the significant figures equal to one another, except for a "shift" between them to account for the fact that they are inversely related:

[log₁₀()] + dp = [log₁₀() + ] + dp   .

Here indicates a shift between the two quantities to account for the fact that they are inversely related. In the above expression, the units of are physically reasonable for values of this shift range from 0 to 1, and the chosen value depends on the criteria one applies. The number of decimal places in the energy difference, dp, is set to the smaller of the dp's for the lower and upper level energies of the transition. Applying the relation between and to the above expression, one obtains:

dp(cm) = [2log₁₀() + ] + dp   .

If  = 0, dp will yield a sufficient number of significant figures such that when the derived wavelength is inverted, in all cases the resulting will be no less precise than the original from which the wavelength was derived. Unfortunately, this choice often yields an overly optimistic precision for the derived wavelength. We have chosen  = 0.5 as a compromise between full inversion precision and realistic precision in the derived wavelength. In the large majority of cases, the error in upon inverting the derived wavelength is at most 1 in the last decimal place. This factor of 0.5 corresponds to a shift of half a decade, which is intuitively reasonable for two quantities that are inversely related. Thus the expression we use in determining the number of decimal places in the derived Ritz wavelength is:

dp(Å) = [2log₁₀() - 7.5] + dp   .

If dp is negative, we set the actual number of decimal places to zero and replace the final dp digits in the integer part of the wavelength with zeros.

In general, the uncertainty of the last significant figure can be as large as 9.

When the wavelengths are calculated online from the available energies of the lower and upper levels, either asterisk "*" or plus "+" is appended to the wavelength value. The former simply indicates that this value was calculated online, while the latter points out that a number of zeros in the energies were not accounted for in the wavelengths calculation and therefore the actual accuracy of this particular wavelength may be higher.

Wavenumbers derived from wavelengths:

dp = [2log₁₀()] + dp   .

Relative Intensity

The following points should be kept in mind when using the relative intensities:

1. There is no common scale for relative intensities. The values in the database are taken from the values given by the authors of the cited publications. Since different authors use different scales, the relative intensities have meaning only within a given spectrum; that is, within the spectrum of a given element in a given stage of ionization.
2. The relative intensities are most useful in comparing strengths of spectral lines that are not separated widely. This results from the fact that most relative intensities are not corrected for spectral sensitivity of the measuring instruments (spectrometers, photomultipliers, photographic emulsions).
3. The relative intensities for a spectrum depend on the light source used for the excitation. These values can change from source to source, and this is another reason to regard the values as being only qualitative.

Descriptors to the relative intensities have the following meaning:

     *    Intensity is shared by lines differing only by J.   
     :    Observed value given is actually the Ritz value rounded to 0.1 Å, e.g., Ne I.
     =    Multiply classified line.
     a    Observed in absorption. 
     b    Band head.
     bl   Blended with another line that may affect the wavelength and intensity. 
     B    Line or feature having large width due to autoionization broadening. 
     c    Complex line.
     D    Double line.
     E    Broad due to overexposure in the quoted reference
     f    Forbidden line.
     g    Transition involving a level of the ground term. 
     G    Line position estimated.
     H    Very hazy line.
     hf   Line has hyperfine structure.
     l    Shaded to longer wavelengths; NB: This looks like a "one" at the end 
          of the number!
     m    Masked by another line (no wavelength measurement). 
     p    Perturbed by a close line.
     r    Easily reversed line.
     s    Shaded to shorter wavelengths.
     w,d  Wide, diffuse, hazy, etc.
     x    Extrapolated wavelength.
	 

I_ik N_kA_kih_ik,

h_ik

_ik

Transition Strengths

Either transition probability "A_ki" (s^-1), absorption oscillator strength or f value "f_ik", line strength "S", or "log(gf)" can be displayed. Note that f_ik, S, and log(gf) are not displayed by default. Also note that log(gf) is shorthand for log₁₀(g_i f_ik).

A_ki represents the emission transition probability in units of s^-1.

f_ik is the absorption oscillator strength or f-value.

f_ik = A_ki · 1.4992 10^-16 g_k/g_i ², for all multipole types,

where is the wavelength in ångströms

log(gf) is the log₁₀(g_i f_ik), where g_i = 2J_i + 1.

S is the line strength. It is the electric dipole matrix element squared and is independent of the transition wavelength.

More details on these quantities can be found in this review.

Accuracy

AA	≤	1%
A+	≤	2%
A	≤	3%
B+	≤	7%
B	≤	10%
C+	≤	18%
C	≤	25%
D+	≤	40%
D	≤	50%
E	>	50%.

If the accuracy is followed by a prime (), then a multiplet in the original compilation has been separated into its component lines and the transition probability was derived from the compiled value assuming spin-orbit coupling. This may decrease the listed accuracy, especially for weaker transitions.

E1   Electric dipole                 4.9355·10-19 gk 3
M1   Magnetic dipole                 3.7073·10-14 gk 3
E2   Electric quadrupole             8.9294·10-19 gk 5
M2   Magnetic quadrupole             1.5091·10-13 gk 5

E_i-E_k

Configurations

Terms 

J_i-J_k

g_i-gget_k

Type

TP Ref.

Line Ref.

Line Identification Plot

Saha-LTE Plot

Online: March 1999   -   Last update: September 2005