Version 2.2 - June 8, 1992

1. General description

LISE is a program to calculate the transmission and yield of fragments produced and collected in a zero degree achromatic spectrometer. This method has been used for several years to produce and select radioactive nuclei far from stability, and is now opening a new era in nuclear physics research through the production of radioactive secondary beams. The program is designed to be as user-friendly as possible, and to be used not only before an experiment to forecast the settings, rates and contaminants, but also during the run for the identification of the different nuclei and charge states, and to allow the experimenter to recalculate anything quickly and easily in case some parameter of the experiment has been changed (different selected nucleus, different detector, ...).

2. List of features

2.1. Simulation of experimental conditions
The program adapts to any spectrometer operating in the achromatic mode by adjusting the relevant optical parameters.Adapts to a Wien filter installed after the spectrometer.Free adjustment of the geometrical and momentum acceptances as well as slits to determine the selectivity of the whole apparatus.Stacks of up to 7 different materials at the focal plane of the spectrometer (or Wien filter) in order to simulate the slowing down and/or implantation media for the different transmitted nuclei.Adjustment of the parameters related to the production mechanism simulated in the program. E.g. a realistic cross section of a different reaction process used in the experiment can be specified.
2.2. Calculations performed
The Br settings of the spectrometer and electric (or magnetic) field of the Wien filter for the best transmission of a given fragment.The Br of any charge state of any transmitted nucleus (specially useful to keep track of the beam charge states).The Transmission of any fragment at a given setting of the fields. These numbers are then multiplied by the beam intensity, the target thickness and the cross sections to give an estimate of the rates. Angular and energy straggling are taken into account in the transmission calculations.The optimal target thickness can be calculated.The kinetic energy, the energy loss in a given material thickness, the range and both angular and energy straggling at different positions in the spectrometer. The range and energy loss calculations can be performed at any energy (although the valid range is from 2.5 MeV/u to 500 MeV/u) for elements Li through U into materials Be through U. The program `remembers' the range tables whenever they are calculated by storing them on disk.Calibration of either the beam energy or the target thickness using a charge state of the beam and the Br at which the ion is centered on the dispersive focal plane. The same feature for calibrating the wedge thickness using any transmitted nucleus is provided.The program includes the possibility to calculate the charge state distribution of any fragment and the corresponding transmission.
2.3. Display
The results of the calculations are displayed on a "chart of the nuclides" which can be scrolled in order to see the results obtained for a different region of nuclei (the screen contains 7´ 7 nuclei). Two pieces of information per nucleus can be chosen from the list of transmission, charge state distribution, cross section and final rate.It is possible to add (or remove) any nucleus to the nuclear chart. If a new nucleus has been added, the automatic calculation of rates will take it into account. The chart of nuclides is updated each time the program is terminated.One of the main features of this program is to produce an identification plot (Energy loss vs Time Of Flight). The parameters of this plot can be adjusted. They include the material in which the particles lose their energy, the flight path length, and other things such as the High Frequency of an accelerator (cyclotron) in case it is used as a time reference (this method usually leads to a wrap around of the identification plot).Display of Energy loss vs Total Kinetic Energy using the same conditions as for the identification plot.The distributions calculated for the transmission of the fragments can be displayed together with the acceptances or slits positions in order to visualize the selections and cuts created by the spectrometer. These include the angular distributions after both the target and the wedge, the Br distributions at the dispersive focal plane, the position distributions at the first focal plane (after the wedge) and at the second focal plane (after the Wien filter in case it is used).The implantation distribution can also be displayed in any of the 7 chosen materials.
2.4. Files and results output
Any set of parameters and calculations can be saved in a file and later recalled.The results of the calculations can be stored in a separate file. This file is automatically printed when a printer is connected to the computer. Right now, the only way to copy the graphic screens produced by LISE is by using the "Print Scrn" key and hope that the PC has been correctly configured to produce a valid screendump. Postscript files of the graphic screen will be available in the next version.
2.5. User-friendly features
The program uses a pop-up menu structure relying on the mouse to select the commands and functions. Different parameters also appear in these menus and they are constantly updated. They can be changed by simply selecting the corresponding item and then entering the new value. Once a command has been issued, one can recall the last submenu, or start again from the root.

3. Calculations

3.1. Reaction mechanism and cross sections
The production reaction mechanism assumed in this program is the so-called projectile fragmentation, as pictured for example by the abrasion model followed by sequential evaporation by both projectile and target spectators (fragments). Although this picture has been shown to be fairly accurate at high energy (above a few hundred MeV/u), the reaction mechanisms goes over to energy relaxation processes such as deep-inelastic or incomplete fusion in the intermediate energy range (between 30 MeV/u and 200 MeV/u). Therefore the model may produce incorrect cross sections.In the program the cross sections are calculated according to a global fit to fragmentation (fit by K. Sümmerer [1]) with no energy dependence. For the production cross sections of nuclei far from stability, the values provided by this fit are valid only within one to two orders of magnitude: we have observed systematic deviations of the predicted rates coming from the lack of data in the cross section fit for the production of nuclei close to the drip-lines. Therefore the possibility to input directly the cross sections for a given reaction is included, provided these were actually measured or calculated by more sophisticated codes. It is also possible to calculate the transmission and rates for transfer products (i.e. for "fragments" having more protons and/or neutrons than the projectile). In these cases the fit based on target fragmentation only gives a qualitative guess, and a better estimate of the cross section is needed in order to obtain reasonable yield predictions. Once the cross sections are manually input in the program they are automatically saved whenever a set of calculations is saved in a file.
3.2. Beam optics
The spectrometer is assumed to function in the achromatic mode. This statement implies the following:The spectrometer is composed of two sections : a first part which is dispersive, and a second part in which the fragments are refocused, providing the achromatism.At the focal plane of the first section (called "intermediate focal plane") the horizontal position (perpendicular to the beam axis) of the fragments only depends on B( and their horizontal position at the target. Therefore, the two optical parameters which determine the horizontal distribution at this focal plane are the dispersion (x/d r /r ) and the magnification (x/x).A wedge can be installed at the intermediate focal plane. This wedge is assumed to be achromatic (i.e., providing the same dispersion after as before). The proper slope can be calculated in the program.The focal plane of the second section being achromatic, there is no momentum dependence of the final horizontal position (as well as vertical). Consequently, the only optical paramenter taken into account in the determination of the final image size is the magnification from the target to the achromatic focal plane(called "image 1").In addition to the achromatic spectrometer previously described, the program can calculate the selection provided by an additional Wien filter (velocity filter). The velocity dispersion created by this device is assumed to occur in the vertical plane, the resulting image (called "image 2") is determined by the magnification and the dispersion of the filter (this last parameter is automatically calculated from the physical dimensions as well as the electrical and magnetic fields set on the filter).
3.3. Acceptance and transmission calculations
The selection of the nuclei transmitted through the spectrometer is separated in three steps corresponding to three different criteria:The first section of the spectrometer provides a B( selection depending on the Av/Q ratio of each nucleus (A being the mass, v the velocity and Q the ionic charge). The horizontal slits at this first section focal plane ("Slits intermediate focal plane") set the momentum acceptance.In case an achromatic wedge is used at the dispersive focal plane, different nuclei are refocused at different horizontal positions at the second focal plane, depending on the different amounts of energy they lose in the wedge, and the dispersion of the second section. This provides a second selection criteria which depends also on the horizontal size of the beam spot on target ("Object size"), the magnification, and setting of the horizontal slits at the second section focal plane ("Slits first focus (after wedge)").Finally, the third selection is the velocity selection provided by the Wien filter (optional). Here again the relevant optical parameter are the magnification and the dispersion. This third selection criteria being different from the two previous ones, allows a further selection of the nuclei after the slits (called "Slits second focus (after Wien)").The other acceptances taken into account for the calculation of the transmission are the geometrical acceptances after the target and after the wedge. Their values can be set in both the horizontal (q ) and the vertical (f ) planes. The maximum Br acceptance of the device can also be set and is used as an upper limit for the slits of the intermediate focal plane.In all the calculations mentionned above, both the energy and angular straggling in the target and the wedge are taken into account. The effect of the energy loss in the wedge on the size of the image at the first focus is also included [2]. These effects, in addition to the fixed range of the particles, limit the maximum thickness one can accept before starting to lose particles. The best target and wedge thicknesses result from two compromises. The first is the balance between the rate increase due to a larger number of interacting nuclei in the target, versus the decrease due to the slowing down of the fragments which reduces the actual momentum acceptance, and the angular and energy straggling. The command "Optimal target" calculates the dependence of the fragment yield on the target thickness, and finds the "best" target thickness with the maximum rate. The second compromise concerns the wedge thickness and is a balance between better selectivity - the images of different nuclei are further apart when increasing the wedge thickness - and rate loss due to angular straggling, secondary reactions (which are not taken into account), and image broadening.
3.4. Energy loss and range tables
The energy losses are calculated according to the latest functions provided by F. Hubert et al. [3]. These calculations are valid between 2.5 MeV/u and 500 MeV/u. Whenever an energy loss and range calculation needs to be performed, the program looks for the range table corresponding to the beam-absorber pair on disk. If it doesn't already exist, the program calculates it (a display appears on the screen) and stores it on the disk (files TABZ1Z2.RAN in the sub-directory "\RANGE"). Thus, the tables of range data are built up over time. These range tables are calculated using Simpson's rule for integration, and the energy losses are deduced by inverted-interpolation on the range.The starting point for the integration is given by range tables of Northcliffe and Schilling [4] at 2.5 MeV/u (files NORTH*.RAN in the sub-directory "\RANGE").Between 0 and 2.5 MeV/u the range is calculated linearly, matching the value at 2.5 MeV/u. Above 500 MeV/u a power function fit is used as an extrapolation from the last points of the table.

4. Detailed operating description

4.1. Mouse handling in menus
As soon as the program is started the mouse appears as a small smiling face enclosed in the active area of the menu. Clicking on either of the mouse buttons (they are equivalent) opens the main menu, and the mouse is automatically placed at the top center of this new menu. By scrolling the mouse up and down with the buttons released, one can select an item of the menu, which appears high-lighted on a black background, the smiling face dissapearing. Once an item has been selected, clicking will activate the corresponding action. This allows the user to go down in the menu structure. To go up (go back to previous menus), just move the mouse out of any selection to make the smiling face reappear and click.When a nucleus is required from the chart of nuclides, one has just to point to and to click on the desired nucleus. To scroll the chart in any direction, move the mouse to the side from which the chart has to appear (the face will change into an arrow), and click. If the button is held down, the chart will scroll faster after a fraction of a second. Placing the mouse at any corner of the chart will make it scroll diagonally (hence allowing "isospin" and "isobaric" scrolls).Once an action has been performed, the program displays again on the top line the choice between "Previous menu" or "Main menu". One can jump back to the depth from which the last action was executed by selecting "Previous menu", or start from the root by selecting "Main menu". Some calculated results are displayed in a window centered on the screen. This window is automatically suppressed when clicking again to ask for another action.
4.2. Keyboard entries
Some information is entered via the keyboard. In every case, one can erase characters using the "delete" key, and terminates the entry by striking either "return" or "enter". This is also true when entering data directly into the menus : the cursor is placed where the entry should occur, and the data is reformatted to fit into the menu (this means that the format in which it appears in the menu might be different from the format in which it has been entered).

4.3. Description of each command following the menu structure

Previous Menu: returns to the menu previous depth.
Main Menu: goes to the root menu.
Settings: calls the settings menu.

Projectile: calls the projectile menu.

Target: calls the target menu. Wedge: calls the wedge menu.
  Material(s): calls the material(s) menu. Production mechanism: calls the production mechanism menu. Setting fragment: allows the user to pick the fragment on which the field calculations will be performed. The program places the chart of nuclides on the previous setting fragment and waits for a new one. Once it has been selected (same entry style as for the projectile), it flashes purple at the center of the screen. Clears previous calculations.

Spectrometer: calls the spectrometer menu.

Slits: calls the slits menu.

Dipoles: calls the dipole menu.
  Wien filter: calls the Wien filter menu. The following commands are valid only if the Wien filter has been enabled (see the Options menu). Acceptances: calls the acceptances menu. Optics: calls the optics menu. Options: calls the options menu. Cross sections: calls the cross section menu. Isotopes: calls the isotope menu. Calculations: calls the calculation menu. Calibrations: calls the calibrations menu. The precision of the calibrations relies on the absolute energy loss calculation precision which is around 2%. Files: calls the files menu. Plots: calls the plot menu. End: terminates the program and returns to DOS. The chart of nuclides is automatically updated.

5. Tutorial : a sample calculation
The following lines describe an example of a calculation performed for a 84Kr beam at 60 MeV/u fragmented on a Be target in order to produce 68Co. Although it does not explore all the possibilities of the program, this example tries to exhibit most of its different features. The calculations performed in this example are stored in three different files "example1", "example2" and "example3" provided with the diskette. Each correspond to a further cleaning of the 68Co secondary beam using different selection criteria.The first step when starting from scratch is to set the projectile, target and the secondary beam.

The above actions provide the minimum information required to calculate the settings of the spectrometer and the transmissions. The following lines describe an example of these calculations. The program predicts a production rate of 28 68Co per second for a beam intensity of 200 enA. It is now possible to determine which other fragments are transmitted with the 68Co. Let's first set the rate threshold at one count per minute since we are only concerned by the fragments having a larger production rate. Let's now assume that there is a silicon detector at the focal point of the spectrometer. Measuring the energy loss and time of flight of each particle allow to identify them. The plot generated by LISE tries to reproduce the actual bidimensionnal spectrum observed during the experiment. Establishing the correspondance between these two spectra allows to identify the nuclei and get a calibration of both energy loss and time of flight. The second step in the purification of the 68Co beam is performed by the selection of the second section of the spectrometer when an achromatic wedge is inserted at the intermediate dispersive focal plane. Due to their different energy losses in the wedge, different nuclei are focused at different positions at the focal point of the spectrometer, where the opening of the slits determines the transmission. Just by looking at the (E-TOF spectrum obtained with the wedge, it is possible to tell what selection a velocity filter will provide. The cut in velocity will correspond to a cut in TOF centered around 68Co. It will therefore be possible to reduce the amount of 71Cu contamination using a Wien filter. 6. Computer considerations

LISE is a DOS-based software running on any IBM compatible PC. It runs under DOS 3.1 and following versions, and only needs 640 kbytes of memory. The speed of the program depends greatly on the CPU type, speed and configuration. The use of a co-processor is greatly recommended : the program uses FFT (Fast Fourier Transform) algorithms which contain extensive floating-point operations.The last version has been developed on a 386-SX at 16 MHz with a co-processor which provides a reasonable speed (about 1 second per transmission calculation). Trying the program on a 486-based system showed a great improvement (it was impossible to measure the time lapse of the same calculation !).The program uses a mouse driver loaded at the start-up of the computer. This driver has to be Microsoft compatible (most of them are). The graphics interface included with the program (file "EGAVGA.BGI") insures the compatibility with any EGA or VGA compatible graphic card. The program looks automatically for the best resolution the card can provide (although it is limited to the maximum standard VGA resolution 640x480x16 colors). The hardcopy of the graphic screen can be made on a printer provided the command "graphics" is executed at start-up.The first version of LISE has been written in 1987, using the Borland Turbo C compiler. It is written in C for several reasons : it is one of the few languages that allow piloting the mouse driver directly via software interrupts, in order to create one's own menu system. Also, Turbo C provides an extensive number of graphic routines, and finally recursivity, the ability to manipulate data structures, and the possibility to allocate and deallocate memory dynamically are a major improvement in programming. Today, the C language has evolved even further towards Object Oriented Programming, producing the C++. Following this evolution, the latest parts of LISE are written in C++. Portability is always a critical issue in programming, and C++ is certainly one of the best suited language for this task. However, this software is still tightly bound to MS-DOS, and its transfer to other machines running under different systems would require a non negligible amount of time and has not yet been done.

7. References

[1] K. Sümmerer et al., Phys. Rev. C 42 (1990) 2546-2561.
[2] J.P. Dufour et al., Nucl. Instr. and Meth. A248 (1986) 267-281.
[3] F. Hubert et al., Atom. Dat. and Nucl. Dat. Tabl. 46 (1990) 1-213.
[4] L.C. Northcliffe and al., Nucl. Dat. Tabl. A7 (1970) 233.