List of changes in the program MCNelectron
Contents
1. that can be generated by the Fibonacci series generator using a given seed specified after the keyword SEED is still equal to 31329 Consequently the random number streams with sequence numbers from 31330 to 2 31329 62658 will be generated using the next seed i e the seed that exceeds the specified seed by 1 and the streams with sequence numbers from 62659 to 65536 will be generated using the seed that exceeds the specified seed by 2 if the seed value obtained by adding 1 or 2 is greater than 30081 then it is reduced by 30082 Added four CUDA specific keywords use CUDA skip CUDA r CUDA and em CUDA which allow to use lists of CUDA devices as well as to assign device workload ratios for individual CUDA devices see the updated user manual for more details Added a CUDA specific keyword bankModeThr CUDA which controls the bank mode when option heap CUDA 2 is used The term bank mode refers to the choice of an electron that has to be banked after an impact ionization event the banked electron may be either the lower energy one the so called secondary or knock on electron or the higher energy one the primary electron Normally when option heap CUDA 2 is used the knock on electron is the one that is banked However this may cause an overflow of the banked particles buffer in the case of high energies of source particles and thick targets Consequently2. the bank mode is changed when the filling fraction of the banked particles buffer exceeds a certain value That threshold value of the filling fraction is specified after this keyword Its default value is 0 8 i e the bank mode will be changed when the banked particles buffer is more than 80 full In the case heap CUDA 0 or heap CUDA 1 this keyword is ignored in those cases the primary electron is always the one that is banked Added four command line keywords NSTREAMS SEED N and E The first three ones are equivalent to corresponding keywords specified in the input file and allow overriding the number of random number streams the seed of the Fibonacci series random number generator and the number of source particles specified in the input file respectively The keyword E makes it possible to replace the definition of the source energy spectrum specified in the input file by a source of monoenergetic particles Added three command line keywords in out and alt that must precede the names of the input file the output file and the file with alternative cross sections information respectively previously the file names were entered without any keywords Moved subfolders W value and X rays into a new subfolder Simulations Added a subfolder Simulations Backscattering with results of simulations of electron backscattering from a thick layer of gold at i
3. were updated correctly This bug could have a noticeable effect only when electron energy is comparable to the photon cutoff energy 1 eV by default and when particle coordinates are tracked 1 1 0 2015 06 20 1 Plane crossing tallies have been added together with corresponding keywords ETALLY and PTALLY for electron and photon plane crossing tallies respectively 2 Removed restrictions on the angle of incidence and on the position of the starting point of the incident beam it may be inside the layer 3 Added an option to use inner shell electron impact ionization cross sections calculated using the distorted wave Born approximation DWBA The latter cross sections are the same ones that are used by the PENELOPE code system They are calculated using the code by D Bote F Salvat A Jablonski and C J Powell which was published in 2009 That code has been translated from FORTRAN into C using f2c exe and incorporated into MCNelectron it is contained in the file IonCS cpp 4 Added CUDA support together with 18 new keywords ending with CUDA 15 of them may be used both in the input file and on the command line the remaining 3 keywords are command line only As a result Nvidia graphics processing units GPU can now be used for simulations in parallel with the CPU There are now two variants of MCNelectron the CPU only one executable file name MCNelectron exe and the one with CUDA support executable file name MC
4. 4 09 26 4 Fixed a bug that caused too small energies of Compton recoil electrons when tracking of secondary photons was turned off TRACK P 0 2014 09 27 5 Fixed a bug that caused the failure to start the file W value MakeTable exe if the runtime components of Visual C libraries i e the Microsoft Visual C Redistributable are not installed on the computer 1 0 9 2014 10 02 l Simulation of several physical effects has been added a non isotropic angular distribution of bremsstrahlung photons b partial suppression of positron bremsstrahlung in comparison with electron bremsstrahlung c non isotropic angular distribution of photoelectrons d non uniform distribution of positron and electron energies during pair production e angular distribution of electrons and positrons created in pair production events Doppler broadening of energy distribution of incoherently scattered photons For each of those effects there is a keyword in the input file which allows turning on or turning off simulation of the effect By default all those effects are simulated If any of those effects is turned off then it will be replaced by a simplified model e g isotropic bremsstrahlung or neglected completely as in the previous version of MCNelectron For some of those effects there are other keywords controlling some details of the simulation see the updated README file for more informa
5. 5 07 15 17 The error messages displayed after detecting an invalid command line parameter have been made more informative 2015 08 21 18 Fixed a bug in the CUDA version of MCNelectron that sometimes caused overflow of the banked particles buffer when the option heap CUDA 2 was used Now that overflow is prevented by controlling which of the two electrons existing after an impact ionization event is banked when the banked particles buffer is less than 80 full the banked electron is the lower energy one i e the secondary or knock on electron and if the banked particles buffer is more than 80 full then the banked electron is the higher energy one i e the primary electron In the case heap CUDA 0 or heap CUDA 1 the banked electron is always the primary one as before 1 1 1 2015 10 02 1 Added an option to use elastic scattering cross sections obtained from relativistic Dirac partial wave calculations Those cross sections were calculated using the code ELSEPA by F Salvat A Jablonski and C J Powell which was published in 2005 These are the same cross sections that are used by the PENELOPE 2014 code system Their values are stored in files Data ElasticDPW_totalCS dat and Data ElasticDPW_angularDistr dat in binary format The latter file contains angular distributions which were calculated for electron energies from 10 eV to 1 GeV on a logarithmic scale the increment of the
6. A devices with automatic workload balancing this bug was caused by rounding errors when converting a floating point number to an integer number 2015 11 12 7 Fixed a bug that caused exclusion of forced interactions from the sampled interaction types during analog tracking of particles with weights below the cutoff value This bug could affect the simulation results only when at least one of parameters FORCING _WT_MIN or CUT_WT was not equal to zero which is the default value of those parameters 2015 12 02 8 Fixed a bug in MCNelectron CUDA that caused failure to terminate a CPU only simulation after the minimum maximum or average relative standard deviation of a control tally became less than the target error 9 Fixed a bug in MCNelectron CUDA that caused incorrect value of the current minimum maximum or average relative standard deviation when checking for a termination condition in a two dimensional control tally 10 Corrected the language in several error messages 2015 12 07 11 Fixed a bug that could cause a crash or incorrect results when the specification of the target error of a control tally was not the last entry of the line with the tally definition in the input file 10
7. List of changes in the program MCNelectron Below is the list of changes for each version of MCNelectron that was available for download from http web vu lt ff a poskus mcnelectron up to the current version 1 1 2 1 0 1 2014 06 29 l In the current version electron positron pair production is simulated However a very simplistic model is used both the electron and the positron continue in the direction of the incident photon and positron energy distribution is assumed to be uniform In the current version positron annihilation is simulated Each annihilation event occurs when positron energy drops below the low energy cutoff value In the current version the source can emit positrons PART E Fixed a bug in the procedure that is used to determine if a particle has escaped from the layer The current version implements a more realistic method of sampling of angular deflections of the two electrons existing after an electroionizatoin event Their deflection angles are calculated from conservation of momentum The search for energy values in cross section tables has been made faster this has been achieved by keeping in memory the current position in each table and using it as the starting position for the next search As a result the total simulation time has decreased by 20 30 1 0 2 2014 07 01 l In the current version simulation of incoherent scattering at low energies when atomic binding ef
8. Nelectron CUDA exe The file MCNelectron CUDA exe can perform GPU only CPU only or hybrid CPU GPU computations in CPU only mode MCNelectron CUDA exe produces the same results as MCNelectron exe 5 Changed the random number generator The new random number generator is the original Fibonacci series generator published by George Marsaglia and Arif Zaman in 1987 In addition simulations using CUDA devices may optionally use the XORWOW random number generator from the cuRAND library the latter generator can not be used on the CPU The CPU random number generator was changed because the previous generator which was a derivative of the one by G Marsaglia and A Zaman was less suited for generation of a large number 30 000 of independent random number streams 6 Added an option to apply a diffusion model of elastic scattering at extremely low electron energies when the elastic scattering cross section is much larger than cross sections of other types of interactions When the diffusion model is applied the program first generates the distance to the next inelastic interaction event i e the path traveled to that event not the displacement and samples the electron coordinates corresponding to that event from a Gaussian distribution with a root mean square displacement proportional to the square root of the generated path This reduces the electron trapping effect which could otherwise slow the simulation significantly at the expense o
9. base 10 logarithm of energy is equal to 0 1 Usage of those cross sections is controlled by the switch ELASTIC DPW By default that switch is on i e those cross sections are used instead of the ENDF B elastic scattering cross sections 10 11 The default state of the switch ION DWBA is on i e 1 previously its default state was off i e 0 Now in order to avoid replacement of available ENDF B data by third party data it is necessary to specify the following three options in the input file ION DWBA 0 ELASTIC DPW 0 BREMS POSITRON CORRECTION 0 the latter option has an effect only when pair production is possible or when the source emits positrons Added an option to reduce the size of the tables with values of the angular CDF of elastic scattering by removing some points from them see the updated user manual for more details Added an option to speed up the process of searching for values in tabular data by mapping the tables to index arrays corresponding to sets of equidistant values see the updated user manual for more details Added a range type THETA corresponding to the angle between the particle s momentum vector and the normal vector of a tallying plane see the updated user manual for more details Increased the maximum number of random number streams from 31329 to 2 65536 However the maximum number of unique random number streams
10. d prevent this from occurring anyway 2014 11 29 14 Fixed a bug that prevented periodic redistribution of random number streams among the threads to equalize their workload because of that bug the mentioned redistribution was only done once per simulation 15 Increased the maximum allowed number of random number streams from 256 to 2048 2014 11 30 16 Fixed a bug that sometimes caused incorrect value of the positron bremsstrahlung suppression factor although inequality 0 02 lt lt 1 was still always satisfied as it should This bug rad only showed up when there was non zero probability of pair production by photons and the target material consisted of more than one chemical element or when the source emitted positrons 2014 12 03 17 Fixed a bug that could cause an infinite loop in the part of the code that simulates photon Doppler energy broadening during incoherent scattering Such a situation occurred when the binding energy of the selected atomic subshell happened to be greater than the incident photon energy This bug has been fixed by rejecting such subshells i e by selecting only subshells with binding energy less than the incident photon energy 2015 05 15 18 Fixed a bug that prevented update of components of the electron momentum vector after a bremsstrahlung event when energy of the emitted photon was below the photon cutoff energy the absolute value of that vector and the electron energy
11. f fidelity of the simulated electron trajectory when its energy is only a few electronvolts above the ionization threshold of the material or when it is below the ionization threshold The transition to the diffusion model occurs at a user specified value of the total to inelastic cross section ratio The mentioned threshold value of that ratio is specified by the keyword DIFFUSION TOTAL TO INELASTIC RATIO THR The allowed values of that threshold are from 10 to 10 and the default value is 100 The diffusion model of elastic scattering is never applied if the distance from the electron to the nearest surface of the layer is less than the mean free path times the square root of this parameter In order to turn off application of the diffusion model this parameter must be set to any sufficiently large value e g to the maximum possible value 1e18 7 The above mentioned Gaussian distribution is only exact when the electron is at a depth d large enough to make the probability that the electron escapes from the layer before the next inelastic collision occurs practically zero Consequently the diffusion model of elastic scattering may introduce significant errors when estimating the moment and position of electron s escape from the layer if the electron is close to the surface In order to decrease those errors a single diffusion step mentioned above is replaced by a sufficiently large number of shorter diffusion steps which are less than
12. fects become important is more realistic The changes only affect the recoil electron First the atomic subshell is randomly selected on the basis of the number of electrons in each subshell The energy of the ejected electron is obtained by subtracting the binding energy of the selected subshell from the energy loss of the photon If the resulting energy is negative then the electron is not ejected from the atom Otherwise the direction of its motion is the same as in the case of a free electron only the energy is reduced as explained above In previous versions when tracking of particle position and direction was turned on TRACKPOS 1 the effect of binding on the recoil electron energy was ignored only the angular deflection included the effects of binding via the form factor In the output file a new row backscatter has been added under photon loss and electron loss It contains the number and energy of particles that escaped from the layer through the surface that is exposed to the incident beam The number and energy of photons or electrons that escaped from the other surface can be obtained by subtracting the values in the row backscatter from the corresponding values in the row escape Fixed a bug that caused absence of angular deflection after coherent scattering of a photon 1 0 3 2014 07 04 1 2 The current version simulates Compton fluorescence In the output file the number and ener
13. gy of the Compton fluorescence photons is shown separately from other fluorescence photons However the number and energy of electrons emitted during atomic relaxation after an incoherent scattering event is grouped with Auger electrons emitted after photoelectric absorption similarly to MCNP6 output Fixed a bug that caused incorrect number of pair production events in the output file 3 Added the keywords COH_THR E_UNIT and E CONTIGUOUS to the input file see the updated README file for more information 1 0 4 2014 07 13 1 2 Added more information to the README file Added a subfolder Test with six MCNelectron input files and six MCNP6 input files corresponding to identical simulation conditions together with respective output files Additional information about those files and instructions on running the tests are in the file Test _ Test info pdf 1 0 5 2014 07 19 l 3 Added the keyword NSTREAMS to the input file It is used to specify the number of independent streams of random numbers For optimum performance NSTREAMS should be a multiple of the number of threads see below The maximum allowed number of streams is 256 Added multithreading capability The number of threads is specified on the command line in the same way as for MCNP i e as tasks lt number_of threads gt If there is no keyword tasks on the command line then MCNelectron will run in single thread mode On mult
14. i processor or multi core systems multithreading can significantly reduce simulation time The number of threads can be assigned any value that does not exceed the number of streams of random numbers see above However there is no point in using a number of threads that is greater than the number of logical processors in the system a further increase of the number of threads will not cause a decrease of the simulation time The final results of the simulation do not depend on the number of threads that was used during the simulation Updated the README file 2014 07 26 4 Updated the batch file W value Make W tables bat which is used to build the final tables of W values The previous version of that file worked correctly with MCNelectron v1 0 4 output files but it did not work with MCNelectron v1 0 5 output files The updated version of Make W tables bat works correctly both with v1 0 4 and with v1 0 5 output files 2014 08 13 5 Fixed a bug that could in extremely rare cases cause a crash after a positron annihilation event probability of such a crash was less than 0 01 1 0 6 2014 08 23 l Log log interpolation of photon cross sections and form factors has been made faster This has been achieved by calculating their natural logarithms before the simulation and then using those logarithms for linear linear interpolation with natural logarithm of photon energy or of the change of photon momentum as i
15. l and in the file X rays _info_ pdf which is in the same subfolder 2015 06 25 12 Fixed a bug that caused the seed of the XORWOW random number generator from the cuRAND library to be always equal to the seed of the Fibonacci series random number generator which is used on the CPU 13 Fixed a bug that caused a CUDA error invalid argument after pressing any of the keys or J during simulation using options emFirst_ CUDA 1 and emLast_CUDA 1 on a computer with two or more CUDA devices i e when the CUDA device No 1 was being emulated by the CPU while the CUDA device No 2 was not being emulated 2015 06 27 14 The inner shell electron impact ionization cross sections calculated using the DWBA approximation are now stored in the file Data lonDWBA dat in binary format instead of being recalculated at the start of each simulation Accordingly the code for calculating those cross sections has been removed from MCNelectron 15 Fixed a bug that caused incorrect values of inner shell positron impact ionization cross sections when the option ION_DWBA 1 was specified in the input file 2015 07 03 16 Added the file randomlib c with the original code of the Fibonacci series random number generator to the distribution package inserted a comment line with a reference to that file at the beginning of files RandGen cpp RandGen cu and RandGen_CUDA cu 201
16. ncident electron energies from 200 eV to 15 MeV obtained with MCNelectron_CUDA using the option ELASTIC_DPW 1 12 MCNelectron and MCNelectron_CUDA are now distributed as WinRAR self extracting archives The names of those files are MCNelectron_install exe and MCNelectron CUDA _install exe respectively They are contained in WinZip archives MCNelectron_install zip and MCNelectron_CUDA install zip respectively they replace the files MCNelectron zip and MCNelectron CUDA zip which were used previously 13 Updated the user manual 2015 10 10 14 Fixed a bug that caused inconsistent sign of a bin count increment 1 when a range type MU was used in the specification of a two dimensional plane crossing tally before fixing this bug the mentioned sign depended on the direction of crossing whereas for this range type the sign should be always positive 15 Fixed a bug in the CUDA version of MCNelectron that caused inconsistent sign of a bin count increment 1 when a range type THETA was used in the specification of a two dimensional plane crossing tally before fixing this bug the mentioned sign depended on the direction of crossing whereas for this range type the sign should be always positive This bug affected only the 2D tallies calculated on CUDA devices but not the tallies calculated on the CPU 2015 10 14 16 Fixed incorrect interpretation of a negative value of the inpu
17. nput As a result the simulation time in problems where most of the time is spent for sampling photon interactions e g a beam of photons incident on a thin layer has become less than a half of the simulation time with MCNelectron v1 0 5 When sampling the distance to collision expression 1 pRand gt random has been replaced by pRand gt random Although statistically the former expression is correct too because it also corresponds to a uniform distribution it involves one extra operation subtraction which is not necessary This replacement has been done in two places in the code one for photons and one for electrons Because of this change simulation results when some of the particles can escape from the layer are not exactly identical to the results obtained with the previous versions although they are identical statistically Added an optional command line keyword output_cs When that keyword is used on the command line files with values of excitation and electroionization cross sections are created before starting the 2 simulation In such a case MCNelectron creates a folder Cross sections in the current folder with subfolders for each of the chemical elements that are present in the target material Each of those subfolders contains a text file with values of the total excitation cross section as well as text files with electroionization cross sections for each subshell Each of those files contain
18. s section is created in addition to the files with ionization cross sections for individual subshells If the ENDF data folder name which is specified in the input file after the keyword DIR does not contain the full path i e if it does not start with the backslash and does not contain the colon then it is now assumed to be a subfolder of the folder where the MCNelectron executable is rather than a subfolder of the current folder The same applies to the keyword BREMS_ ANGULAR DISTR _ DIR which is used to specify location of text files with bremsstrahlung angular distribution data when the mentioned binary file Data Brems_angular_prob_dens dat is not used 7 Updated the README file 2014 10 03 8 Multiple pulse height tallies are now allowed 9 If a value of absorbed energy exceeds the bin boundary of a pulse height tally by 10 of the bin width or less then that energy value is treated as though it is equal to that boundary In a special case when that boundary is the low energy limit of the tally energy range the source particle is not counted 2014 10 05 10 Added the keyword INCOH_ IGNORE BINDING E to the input file see the updated README file for information about that keyword 11 Renamed the keyword DOPPLER BROADENING to INCOH_DOPPLER in order to be consistent with the naming convention of the other keywords that control simulation of physical effects the first par
19. s two columns of numbers energy values eV and corresponding cross section values in barns 1 0 7 2014 08 26 1 Interpolation of cross sections has been made faster by calculating the slope coefficients for each energy sub interval before the simulation and using their stored values for interpolation in previous versions of MCNelectron the slope coefficients were recalculated during each step of the simulation In addition sampling of energy transfer during electroionization and bremsstrahlung as well as sampling of angular deflection during elastic scattering of electrons has been made faster using a similar approach As a result of those changes the simulation time has decreased by 10 to 20 in comparison with MCNelectron v1 0 6 2014 08 28 2 Fixed a bug that appeared after the most recent change described in previous paragraph That bug caused incorrect simulation results when alternative cross sections were used because then the corresponding slope coefficients were not recalculated instead their values corresponding to the original cross sections were used After fixing that bug the slope coefficients are recalculated using the updated set of cross sections 3 Merged source files thread cpp thread h and MCNelectron h with MCNelectron cpp Consequently the total number of source files decreased from 6 to 3 1 0 8 2014 08 30 1 In the current version of MCNelectron the values of cross
20. sections form factors and other quantities that only depend on electron or photon energy are only recalculated when the particle energy changes As a result of this modification the simulation time in problems where particle energy changes relatively infrequently i e when most collisions are without energy change or when the source emits monoenergetic particles and the average number of energy loss collisions per source particle is much less than 1 has decreased by 10 to 40 in comparison with MCNelectron v1 0 7 In W value problems i e when both elastic scattering of electrons and coherent scattering of photons are switched off and the target is infinite in all directions TRACKPOS 0 the computational overhead associated with this modification causes an increase of the simulation time by up to 10 2014 09 06 2 The runtime components of Visual C libraries i e the Microsoft Visual C Redistributable are no longer required to be installed on a computer in order to run MCNelectron before this fix absence of the mentioned files caused the error message The program can t start because MSVCR100 dll is missing from your computer after attempting to run MCNelectron 2014 09 12 3 Fixed a bug that caused an error message about incorrect format of the ENDF file when the target material contained elements with atomic number greater than 86 i e the elements that are after radon in the periodic table 201
21. t of those keywords is derived from the name of an interaction type 2014 10 30 12 Added the capability to equalize the workload of different threads in multi threading mode When a thread finishes processing of all histories assigned to it the program redistributes all unfinished random number streams among the threads so that the number of active threads stays the same in the previous versions the threads were not restarted after termination This is only possible when the number of unfinished random number streams is not less than the number of threads otherwise each stream of random numbers is assigned to a separate thread so that the number of active threads is equal to the number of unfinished random number streams 2014 11 14 13 Fixed a bug that could in extremely rare cases cause an indeterminate energy value 1 IND of a scattered photon when simulating Doppler energy broadening during incoherent scattering Such an error was possible when the sampled value of the projection of the electron initial momentum to the direction of incident photon is very close to zero resulting in calculation of the square root of a difference of two very close numbers Although the exact value of that difference is always non negative the rounding errors can make it negative however since there are no known cases of this actually happening it is possible that granularity of the random number generator implemented in MCNelectron woul
22. t parameter ELASTIC_PDF_ ERROR in the CPU only version of MCNelectron Before fixing this bug a negative value of ELASTIC_PDF_ ERROR was always interpreted by the CPU only version of MCNelectron as a zero value i e no values were removed from tables with values of elastic scattering angular PDF whereas the correct way is to ignore the mentioned sign when the option ELASTIC_DPW 1 is used as explained in the user manual Note This bug was absent in the CUDA version of MCNelectron 1 1 2 2015 11 10 1 Added an option to use interaction forcing see Section 4 5 in the updated user manual 2 The files with plane crossing and pulse height tally data now include relative standard deviations for each bin in addition to the particle counts 3 Added an option to terminate the simulation when the maximum minimum or average relative standard deviation calculated over all bins of one or more plane crossing or pulse height tallies control tallies becomes less than the target error specified by the user see Section 4 4 in the updated user manual 4 The simulations of electron induced characteristic X ray emission folder Simulations X rays of the distribution packages have been re done using interaction forcing and control tallies 5 Updated the user manual 2015 11 11 6 Fixed a bug in MCNelectron_CUDA that could cause loss of one source particle during a GPU only simulation using two or more CUD
23. the root mean square displacement and also less than d but still greater than the mean free path if d is less than a user specified number of r m s displacements the latter r m s displacement is estimated as described above This number is specified by the keyword DIFFUSION _DIST_TO_RMSPATH_ RATIO THR The allowed values of that number are from 2 to 10 and the default value is 5 8 After an electron impact ionization event the banked electron is the higher energy primary one rather than the knock on electron as in previous versions of MCNelectron As a result the number of banked electrons has been reduced significantly in comparison with previous versions usually by an order of magnitude An exception is a simulation on a CUDA device using the option heap CUDA 2 in this case the banked electron is the lower energy one i e the knock on electron 9 Replaced the keyword INCOH_IGNORE BINDING _E by INCOH_ SUBTRACT _ BINDING E 10 Updated the user manual 2015 06 24 11 Added the subfolder X rays with 99 MCNelectron CUDA input files and the corresponding output files Each of them is used to simulate characteristic X ray emission from a thick target composed of one of those elements C Al Si Ti Fe Cu Zn Ge Zr Sn Sm Ta W Pt Au and Pb bombarded by monoenergetic electrons with energy from 5 keV to 30 keV Information about those files is provided in Section 8 of the user manua
24. tion Simulation of bremsstrahlung angular distribution and Doppler broadening requires additional data files which are included in the MCNelectron distribution package the file Data Brems_angular_prob_dens dat with angular probability densities of bremsstrahlung calculated by integrating analytically over the triply differential cross sections derived by Bethe and Heitler and the file Data ComptonProfiles dat with Compton profiles The data in the file Brems_angular_prob_dens dat is in binary format it is described in the updated README file However there is an executable Data ExtractBremsAngularDistr exe which extracts ASCII data from the binary data and creates a subfolder with human readable files Those text files can be used as input data for the simulation too instead of the mentioned binary file The current version of MCNelectron can calculate a pulse height tally similar to the MCNP F8 tally Added the keyword TRACK X to the input file it controls tracking of X ray photons emitted due to atomic relaxation The energy of the Compton recoil electron is calculated simply as the difference of the incident and scattered photon energies 1 e the recoil electron energy is no longer reduced additionally by subtracting the binding energy of the subshell from which the electron was ejected When the keyword output_cs is specified on the command line a file with values of the total ionization cros
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