Homepage of Petra Ruth Kapralova

Gases in Extreme UV Radiation

Full Title: Ionization and excitation of atomic and molecular gases exposed to intense extreme ultraviolet radiation: theory and experiment

Project No. P205/11/0571, 2011-2014


Photoionization in gases exposed to intense short-wavelength radiation plays an important role in astrophysics, planetology, fusion research, and the development of 4th generation short-wavelength sources.

New strong lasers

For several decades, photoionization of gases has been studied using sources of ionizing electromagnetic radiation with low peak brightness (e.g., Henkes tubes, synchrotron radiation sources, etc.). New extreme ultraviolet (XUV) and soft X-ray (SXR) lasers enable high-amplitude, ultra-high-frequency electromagnetic radiation.

New phenomena

These lasers make it possible to study photoionization of isolated atoms and molecules, as well as collective processes (e.g., instabilities, recombination, etc.) in the photoionized gas.

Project details

The project deals both with theoretical and experimental investigations of the ionization and excitation dynamics in atomic and molecular gases exposed to nanosecond and femtosecond pulses of radiation with a wavelength of 50 nm and intensities of 109-1016 W/cm2 delivered by a capillary discharge laser and a free-electron laser, respectively.

Progress (the theoretical part only)


  • A study on a distorting effect of complex scaling on wavefunctions was published (No. 21). Topic: Fundamental theory. Use: This work is needed to understand how to develop basis sets for electronic resonances that are essential in description of interaction of ionizing radiation. Short abstract: Principles and numerical consequencies of wavefunction distortion by complex scaling transformation. Study based on Wigner phase space representation. Journal: J. Chem. Phys.
  • Coding of dynamical calculations of atomic Floquet states in linearly polarized field (finished).
  • Development of a theoretical method for dynamical simulation of atoms in finite laser pulses based on nonadiabatic coupling between Floquet states (finished).
  • Development of Gaussian basis sets for quatitative calculations of helium Rydberg states and resonances (prolonged to 2012).


  • Development of exponentially tempered Gaussian basis set was finished for helium and published (No.22). Topic: Quantum chemistry. Use: Special Gaussian basis sets are needed for complex scaling applications as long as the standard basis sets do not allow for enough stability of resonance energies with the complex scaling parameter. The Gaussian basis sets will allow calculations of molecular interactions with ionining radiation. Short abstract: It was shown that the ExTG basis sets are the only suitable set of functions for complex scaling calculations among standard Gaussian basis sets. The precision of the basis set was tested for helium S-states including resonances up to the 5s7s state. Journal: J. Chem. Phys.
  • Calculation of Floquet states for helium based on ExTG basis sets is in progress. This study will include a comparison of measured and calculated absorption wavelengths in IR region, comparison of Einstein coefficients with more exact theory and calculations of absorption coefficients, ionization rates, etc. for various wavelengths in XUV and laser strengths.
  • Other calculations that are also in progress will be announced as soon as they get published.

Developed codes (incomplete account)

I am publishing the codes for our internal use only. (I.e. the description of the codes is severely incomplete for one not developping the code.)


Matlab codes for basis set optimizations.


A version for complex scaled calculations of the He atom:



This code analyses results obtained from KAPRFCI: complex energies and transition dipole moments. It consists of two codes working within Matlab: findres and epatab2. findres finds (classifies) bound states and doubly excited resonances, while epatab2 calculates transitions between the classified states (frequecies, Einstein coefficients and oscillator strengths).

The input for the codes includes directories that are designated by the capital letters S,P,D,F,G,.... Each directory includes output files from KAPRFCI, namely the files of the forms: th+0.00000h1De.dat and th+0.35000d3Fo3De.dat. The files starting at th+0.00000 may be replaced by the files without the initial part, such as h1De.dat. The inidividual directories include files obtained in different KAPRFCI runs and pertain to different number of partial waves, e.g. S would include the results for the ExTG5S basis set, P would include the results for the ExTG5P basis set, etc. Here is a following comment to be taken into account: "Pozor: To, co oznacuje helium jako 1Pe je vlastne 3Pe, 1Do je 3Do atd. - plati pro vazane stavy nad druhym thresholdem."

findres is an interactive code that would ask you for 'Naboj jadra analyzovaneho atomu/iontu: ', 'Term ve formatu, jak se znaci vystupni soubory: ' (i.e. '1De' etc.), 'Cislo analyzovane serie dle ionizacniho thresholdu (N=1,2,...): '. It will find all bound states/resonances that are available in the calculated spectrum and are of the symmetry and threshold given in the interactive input. It will calculate their theta-trajectories from their complex energies for every basis set (i.e. for every input directory), separately for the real and imaginary parts of the energies, where the results include the variational values and error estimates. The results will appear in the output file o, which is the grounds for construction of the files of the type EPAPS_1_1Po. Here is a following comment to be taken into account: "EPAPSy konstruujeme pomoci findres, ktery vypise soubor o. To je zaklad pro EPAPS. Je potreba umazat vyssi nezkonvergovane rezonance a seradit rezonance podle energie do sloupcu (tj. odsadit nektere radky)"

epatab2 uses the tables of the type EPAPS_1_1Po as the input files. The tables EPAPS_1_1Po must be changed by the user prior to the epatab2 run by including two lines after the lines starting as ExTG7F : the user must define the 'Best' results by coppying them from the machine created output (typically combines F-limit for higher excitations and G-limit for lower excitations); and the user must include the 'Bench' line, with results obtained from NIST and similar.

There is the following comment that should be taken into account:" Ted jsem zakomentovala serazeni jedn. LLIM vedle sebe, protoze rozdily energii D- a F- limity jsou velke kvuli chybe na bosem a meni se tim znamenka prechodu. Az se spravi problem na bosem, bude vhodne odkomentovat."



This code is intended to sort and select complex energies that will be coupled by linearly polarized electric field in a subsequent dynamical propagation.

Input includes the tables of the type EPAPS_1_1Po and EPAPS_2_1Po, and the files of the type th+0.00000h1De.dat and th+0.35000d3Fo3De.dat.

The code is interactive, using a graphical interface. The user is asked to designate the highest Rydberg states before the ionization limits. The process is repeated for every rotational limit separately. It saves data for each of the limit in the course of the run, as sometimes restarts are necessary due to crashes of the engine if the designated ionization limit is not consistent (in whatever sense).

The output includes the selected energies sorted into groups of bound/resonance states that are classified due to finding them in the EPAPS tables, bound/resonance states that are not classified, and the ionization states that include also the doubly excited states. Each one of the groups is further divided according to the ionization threshold to which it pertains. The groups of the ionization states include singly excited states for different ionization limits (He+ ground/excited states), while the last group inlcudes the doubly ionized states. All is written in a form readable by KAPRDYN in the files th+0.35000SEI.mat.


This is a code that implements a "stairs"-method for an exact simulation of atoms (or anything) driven by strong chirped laser pulses. (t,t')-method is used for the Floquet calculations. Input parameters are passed through binary matlab files, inp.mat, inp0.mat, inp2.mat, nozero.mat. To make things simpler, one can set all parameters within the script job.m and run it before running the code itself (i.e. propag.m).

An additional input for KAPRDYN includes energies of the field-free states and the transition dipole moments. These are included in files th+0.25000SEI.mat and the like (the number in the filename stands for a value of the complex scaling parameter). (The field-free states are coupled by the field as if atoms coupled by linearly polarized field.)

The code is implemented in Matlab. It can be used on computers running Matlab as is. However, I am going to summarize instructions for running it on a server-client cluster. I suppose that Matlab compiler and Octave are installed on the server.

  1. Create a directory for running the jobs - JOBDIR. Create a structure of directories: JOBDIR/TH, JOBDIR/SRC_DYN.
  2. Unfold KAPRDYN.tar.gz in JOBDIR/SRC_DYN and compile. run_run.sh and other files are created by the engine.
  3. Now take files th+0.25000SEI.mat and the like that you get from other codes and copy them to JOBDIR/TH.
  4. Unfold the scripts KAPRDYN0.tar.gz in JOBDIR. Rename job.m as you like to name your job (e.g. he_test.m), while keeping the file extension. Change the parameters within this file.
  5. Adjust the last line in rundyn.sh to match with the actual queueing system.
  6. Lunch the job by typing ./rundyn.sh "job" (replace "job" by the name of the job, such as "he_test"). Directory JOBDIR/OUTPUT_DYN_"job" will be created for the output, which includes: a report on the calculations including contour calculations (if applicable), convergence of (t,t') calculations, and numbers of pulse lengths, all in output.txt; quasienergies and other variables in th+0.25000NEAD0.mat (or the like); populations of field-free and instantenious Floquet states in the course of the pulse and after its finishing in propout.mat


KAPREP0.tar.gz, KAPREP.tar.gz

This code finds complex degeneracies (usually identical with exceptional points) in atoms (or anything) driven by a strong cw laser. (t,t')-method is used for the Floquet calculations. Input parameters are passed through binary matlab files, inp.mat, inp0.mat, inp2.mat, nozero.mat. The program finds the nearest complex degeneracy to I0,omega if these parameters are assigned values in inp2.mat. Otherwise, the initial guess of I0,omega is based on a 2x2 approximation to the Floquet matrix, where ENE,LSYM,THR define the excited state coupled to the ground state by one photon.

The code needs the files of the type th+0.25000SEI.mat and can be executed from Matlab environment by exceppoint. It can be run on a server-client cluster in a analogy to KAPRDYN (see the instructions above). The only difference is represented by using a second parameter, when submitting to a queue, pointing to the directory including the files th+0.25000SEI.mat: ./runep.sh job dir_SEI

The output includes stdout (included in output.txt in a cluster run), all iterations are also in EPtab.txt, and the final result in EPparam.mat. The results include the following parameters of the exceptional point: frequency and intensity; degenerate complex energy up to eight digits (or less if number of iterations exceeded 199), the parameters of the energy split a,b,a2,b2,c1,c2.