LISE++

1. General description

LISE is a program for calculating 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 predict settings, rates, and contaminants, but also during the run, for the identification of different nuclei and charge states, and to allow the experimenter to recalculate quantities quickly and easily if some parameter of the experiment has 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. It also adapts to a Wien filter installed after the spectrometer. It allows free adjustment of the geometrical and momentum acceptances, as well as of the slits, to determine the selectivity of the whole apparatus. Stacks of up to 7 different materials can be placed at the focal plane of the spectrometer (or Wien filter) in order to simulate slowing-down and/or implantation media for the different transmitted nuclei. The parameters related to the production mechanism simulated in the program can also be adjusted. For example, a realistic cross section for a different reaction process used in the experiment can be specified.
2.2. Calculations performed
The program can calculate the Bρ settings of the spectrometer and the electric (or magnetic) field of the Wien filter for the best transmission of a given fragment. It can calculate the Bρ of any charge state of any transmitted nucleus (especially useful for keeping track of beam charge states). It can also calculate the transmission of any fragment at a given field setting. These numbers are then multiplied by the beam intensity, target thickness, and 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 program can also determine 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 in 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 can be performed using a charge state of the beam and the Bρ at which the ion is centered at the dispersive focal plane. A similar feature is provided for calibrating the wedge thickness using any transmitted nucleus. The program also includes the possibility of calculating 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 view results 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 from the nuclear chart. If a new nucleus has been added, the automatic calculation of rates will take it into account. The chart of the nuclides is updated each time the program is terminated. One of the main features of this program is the production of 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 quantities such as the high frequency of an accelerator (cyclotron) if it is used as a time reference (this method usually leads to a wraparound of the identification plot). A plot of energy loss versus total kinetic energy can also be displayed under 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 slit 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 Bρ 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, if it is used). The implantation distribution can also be displayed in any of the 7 selected 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. At present, the only way to copy the graphic screens produced by LISE is to use the “Print Screen” key and hope that the PC has been correctly configured to produce a valid screen dump. 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 that relies on the mouse to select commands and functions. Different parameters also appear in these menus, and they are constantly updated. They can be changed simply by 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 described, 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 energies (above a few hundred MeV/u), the reaction mechanism changes to energy-relaxation processes such as deep-inelastic or incomplete-fusion reactions 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 data (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 in the predicted rates arising from the lack of data in the cross-section fit for the production of nuclei close to the drip lines. Therefore, the possibility of entering cross sections directly for a given reaction is included, provided they have actually been measured or calculated with 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 gives only a qualitative estimate, and a better estimate of the cross section is needed in order to obtain reasonable yield predictions. Once the cross sections are entered manually into 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 that is dispersive, and a second part in which the fragments are refocused, thus providing achromatism. At the focal plane of the first section (called the “intermediate focal plane”), the horizontal position (perpendicular to the beam axis) of the fragments depends only on Bρ and on their horizontal position at the target. Therefore, the two optical parameters that determine the horizontal distribution at this focal plane are the dispersion and the magnification. A wedge can be installed at the intermediate focal plane. This wedge is assumed to be achromatic (i.e. to provide the same dispersion after it as before it). The proper slope can be calculated in the program. Since the focal plane of the second section is achromatic, there is no momentum dependence of the final horizontal position (nor of the vertical position). Consequently, the only optical parameter 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 nuclei transmitted through the spectrometer is separated into three steps corresponding to three different criteria. The first section of the spectrometer provides a Bρ 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. If 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 on the dispersion of the second section. This provides a second selection criterion that also depends on the horizontal size of the beam spot on target (“Object size”), the magnification, and the 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 optional Wien filter. Here again, the relevant optical parameters are the magnification and the dispersion. Since this third selection criterion is different from the two previous ones, it allows a further selection of 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 and vertical planes. The maximum Bρ acceptance of the device can also be set and is used as an upper limit for the slits at the intermediate focal plane. In all the calculations mentioned above, both 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 finite range of the particles, limit the maximum thickness that can be accepted before particles begin to be lost. 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 and the decrease due to the slowing down of the fragments, which reduces the actual momentum acceptance and increases angular and energy straggling. The command “Optimal target” calculates the dependence of the fragment yield on target thickness and finds the “best” target thickness, i.e. the one that gives the maximum rate. The second compromise concerns the wedge thickness and is a balance between better selectivity—the images of different nuclei move farther apart as the wedge thickness increases—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 or range calculation needs to be performed, the program looks on disk for the range table corresponding to the beam-absorber pair. If it does not already exist, the program calculates it (a display appears on the screen) and stores it on disk (files TABZ1Z2.RAN in the sub-directory “\RANGE”). Thus, the range-data tables are built up over time. These range tables are calculated using Simpson’s rule for integration, and the energy losses are deduced by inverse interpolation on the range. The starting point for the integration is given by the 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 so as to match 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 either mouse button (they are equivalent) opens the main menu, and the mouse is automatically placed at the top center of this new menu. By moving the mouse up and down with the buttons released, one can select an item in the menu, which appears highlighted on a black background while the smiling face disappears. Once an item has been selected, clicking activates the corresponding action. This allows the user to move down through the menu structure. To go up (that is, 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 the nuclides, one simply points to and clicks 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 changes into an arrow) and click. If the button is held down, the chart scrolls faster after a fraction of a second. Placing the mouse at any corner of the chart makes it scroll diagonally (thus allowing “isospin” and “isobaric” scrolling). Once an action has been performed, the program again displays at the top line the choice between “Previous menu” and “Main menu.” One can jump back to the depth from which the last action was executed by selecting “Previous menu,” or start again 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 the user clicks again to request 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 terminate the entry by pressing 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 are reformatted to fit into the menu (this means that the format in which they appear in the menu might be different from the format in which they were entered).

4.3. Description of each command following the menu structure

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

Projectile: calls the projectile menu.

• Nature, mass and charge: the program displays the chart of nuclides surrounding the current projectile (⁴⁰Ar by default) and asks the user to click on the desired new projectile (one can scroll the chart in any direction to access a different area). The new projectile then flashes red on the chart, and the program asks for its ionic charge (this parameter is used only to convert enA into pps). Any previous transmission calculation is cleared by this command. The program then automatically asks for the energy and intensity, assuming that these parameters are different for a different projectile.
• Energy: asks for the energy of the projectile (in MeV/nucleon). Previous calculations are cleared.
• Intensity: asks for the primary beam intensity. The unit can be enA or pps, depending on how the intensity-unit option is set (see the Options menu). The default is enA. Previous calculations are cleared.

• Nature: selects the periodic-table menu to choose the element corresponding to the target. It then automatically asks for the thickness. The mass used corresponds to the natural abundance of the selected element (this also holds for the wedge and the material(s)). Previous calculations are cleared.
• Thickness: asks for the thickness of the target. The unit can be mg/cm² or µm depending on how the thickness-unit option is set (see the Options menu). Previous calculations are cleared.

• Nature: same entry as for the target.
• Thickness: same entry as for the target. The thickness entered here corresponds to the thickness seen by the particles traveling on the beam axis (i.e. at the middle of the dispersive focal plane).

Material \#1..7: selects the material on which the action will take place.
• Add: calls the periodic-table menu to choose the element of the material, and then asks for its thickness. This command allows the user to add or insert a new material.
• Remove: removes the specified material.
• Change: changes the nature and/or thickness of the material by first calling the periodic-table menu and then asking for a new thickness.

• v_opt/v₀: sets the ratio of the velocity corresponding to the maximum of the momentum distribution to the beam velocity. The default value is 1.
• Sigma0: sets the reduced width of the momentum distribution. The final width is calculated according to the Goldhaber formula:  where A_F and A_P are the fragment and projectile masses respectively. The default value is 90 MeV/c.

Spectrometer: calls the spectrometer menu.
 

Slits: calls the slits menu.

• Object size (2 sigma): this command asks for the size of the beam spot on the target. The beam spot is assumed to be gaussian in both horizontal and vertical directions with the same width. The number entered is sigma. This parameter plays a very important role in the wedge selection, since it determines the size of the images corresponding to different nuclei at the first focus. The smaller these images are, the better the selection can be by closing the slits. Previous calculations are cleared when issuing this command.
• calls the spectrometer menu. sets the slit width at the dispersive focal plane. These slits determine the Br acceptance of the spectrometer, which is automatically calculated and displayed in %. The maximum opening is set by the maximum momentum acceptance parameter (see the Acceptance menu). Previous calculations cleared.
• Slits first focus (after wedge): sets the slit width at the first focal point. These slits are important when a wedge is used, since the images corresponding to different nuclei are spread out in position. Closing the slits will therefore allow a better selection of the nuclei which are focused at or close to the center. Previous calculations cleared.
• command asks for the size of the beam spot on the target. The beam spot is assumed to be Gaussian in both the horizontal and vertical directions, with the same width. The number entered is σ. This parameter plays a very important role in wedge selection, since it determines the size of the images corresponding to different nuclei at the first focus. The smaller these images are, the better the selection obtained by closing the slits. Previous calculations are cleared when this command is issued.sets the slit width at the second focal point, which is the focal point of the Wien filter. They therefore set the velocity acceptance of the filter, allowing to select more or less nuclei, depending on the velocity dispersion. Only valid if the Wien filter has been enabled (see the Options menu). Clears previous calculations.

• sets the slit width at the first focal point. These slits are important when a wedge is used, since the images corresponding to different nuclei are spread out in position. Closing the slits therefore provides better selection of nuclei focused at or close to the center. Previous calculations are cleared. this command allows the user to enter the Br of the first section. This is useful when an experimental value has been determined (e.g. by centering a charge state of the beam on the dispersive focal plane), and one wants to calibrate either the beam energy or the target thickness (see the Calibrations menu). The Br of the second section is automatically recalculated for the best transmission of the selected fragment. Clears previous calculations.
• sets the slit width at the second focal point, which is the focal point of the Wien filter. They therefore set the velocity acceptance of the filter, allowing the user to select more or fewer nuclei depending on the velocity dispersion. This is valid only if the Wien filter has been enabled (see the Options menu). Previous calculations are cleared. allows the user to enter the Br of the second section (after the wedge). It can be used to calibrate the wedge thickness when the image of a beam charge state or of an identified nucleus has been experimentally centered at the first focal point (see also the Calibrations menu). Clears previous calculations.
• Radius 1: radius of the first section dipole(s). Used to display the value of the magnetic field on the screen. The default value is the radius of the GANIL LISE dipoles.
• Radius 2: radius of the second section dipole(s).

 
• allows the user to enter the Bρ of the second section (after the wedge). It can be used to calibrate the wedge thickness when the image of a beam charge state or of an identified nucleus has been experimentally centered at the first focal point (see also the Calibrations menu). Previous calculations are cleared. sets the electric field of the filter in kV/m (the user has to know the gap between the electrodes). Calculates the magnetic field for the best transmission of the selected fragment and the dispersion. All these calculations are then updated on the screen. Clears previous calculations.
• Magnetic field: sets the magnetic field of the filter in Gauss, calculates the electric field for the best transmission of the selected fragment and the dispersion. Clears previous calculations.
• Dispersion coefficient: coefficient used to calculate the velocity dispersion in mm/% according to the formula: D=KE/(Br _2b) where E is the electric field in kV/m, Br₂ the Br of the second section of the spectrometer in Tm, and (the velocity of the particle. This coefficient depends on the field set on the quadrupoles used to focus the beam after the filter. Clears previous calculations.
• coefficient used to calculate the velocity dispersion in mm/% according to the formula: D = K E /(Bρ2 β) where E is the electric field in kV/m, Bρ2 is the Bρ of the second section of the spectrometer in Tm, and β is the velocity of the particle. This coefficient depends on the field set on the quadrupoles used to focus the beam after the filter. Previous calculations are cleared. vertical magnification between the object (target position) and the filter. Clears previous calculations.
• Electric length: effective electric length of the filter taking into account the fringe fields. Clears previous calculations.
• Magnetic length: effective magnetic length of the filter taking into account the fringe fields. Clears previous calculations.

•  Maximum momentum acceptance: This parameter is used as an upper limit for the setting of the slits at the intermediate focal plane.
• Target q acceptance: horizontal angular acceptance after the target (in degree). Clears previous calculations.
• This parameter is used as an upper limit for the setting of the slits at the intermediate focal plane. vertical angular acceptance after the target (in degree). Clears previous calculations.
• Wedge q acceptance: horizontal angular acceptance after the wedge (in degree). Clears previous calculations.
• Wedge f acceptance: vertical angular acceptance after the wedge (in degree). Clears previous calculations.

• Dispersion 1: horizontal dispersion of the first section of the spectrometer in mm/%. Clears previous calculations.
• Dispersion 2: horizontal dispersion of the second section of the spectrometer in mm/%. Clears previous calculations.
• Magnification 1: horizontal magnification of the first section of the spectrometer. Clears previous calculations.
• Magnification 2: horizontal magnification of the second section of the spectrometer. Clears previous calculations.
• q magnification: horizontal angular magnification at the wedge position. This parameter is used in conjunction with the wedge (acceptance to calculate the transmission. Clears previous calculations.
• horizontal angular magnification at the wedge position. This parameter is used in conjunction with the wedge acceptance to calculate the transmission. Previous calculations are cleared. vertical angular magnification at the wedge position used with the (acceptance. Clears previous calculations.
• vertical angular magnification at the wedge position, used with the vertical acceptance. Previous calculations are cleared.Offset of the angular distributions at the target position in the case the beam is tilted with respect to the spectrometer axis. Clears previous calculations.

• Wien filter: switch used to enable or disable the calculations for the Wien filter. Clears previous calculations.
• Thickness unit: toggles between mg/cm² and µm for the unit used in all thicknesses entries. The default is mg/cm².
• Intensity unit: toggles between enA and pps for the beam intensity entry. The default is enA.
• Display 1: calls the display menu to select the first line of information displayed on the chart of nuclides. The default is the total transmission.
• Angular transmission: displays the angular transmission (in %) as the first number displayed for each nucleus of the chart for which a calculation has been performed. The angular transmission is the product of the target and the wedge angular transmission, both being calculated as the average between horizontal (q ) and vertical (f) transmissions.
• toggles between analytical (cross sections calculated automatically) and file (cross sections entered manually and stored in a file) for the cross sections used in the calculations. Previous calculations are cleared. displays the Br or momentum transmission (in %) calculated at the intermediate focal plane.
• Wedge transmission: displays the transmission (in %) calculated at the first focus (after the wedge).
• Wien transmission: displays the transmission (in %) calculated at the second focus (after the Wien filter).
• lower limit of the production rate. Calculations are neither displayed nor stored if the rate is below this threshold.displays the total transmission (in %) which is the product of the four transmissions cited above.
• Cross section: displays the cross section (in mb) used in the calculation of the production rate.
• Charge state ratio: displays the charge state fraction (in %) corresponding to the charge state selected on the chart (see the Charge state displayed option).
• the program waits for the selection of a nucleus from the chart and then prompts for the value of its cross section in mb. This value will be used only if the cross-section option is set to “File.”displays the production rate (in pps) estimation based on the transmission, cross section, beam intensity, charge state ratio and target thickness.
• Display 2: calls the display menu to select the second line of information displayed on the chart of nuclides. The default is the production rate.
• Cross section: toggles between analytical (cross sections automatically calculated) and file (cross sections entered manually and stored on file) for the cross sections used in the calculations. Clears previous calculations.
• Charge states: enables or disables the calculation of the charge state distributions and their corresponding transmissions. Clears previous calculations.
• the program asks the user to click on the nucleus that will be removed. selects the charge state (entered as C in Q=Z-C) displayed on the chart of nuclides.
• Calculation threshold: lower limit of the production rate. The calculations are neither displayed nor stored if the rate is below this threshold.
 

• Enter a value: the program waits for the selection of a nucleus from the chart and then prompts for the value of its cross section in mb. This value will only been used if the cross section option is set on "File".
• Read a value: displays the cross section (analytical value or both analytical and file values if this last has been entered) of the selected nucleus.

• calculates the Bρ values and Wien magnetic field for any charge state of any nucleus. This is especially useful for calculating the Bρ values of the beam charge states. It can also be used to set the spectrometer to a charge state different from that of the fully stripped fragment. One then has to record the calculated values and enter them manually via the command “Settings → Spectrometer → Dipoles → Brho 1 or 2”. calls the menu used to select the type of nucleus. Once this selection has been made, the program asks the user to click on the position of the new isotope on the chart of nuclides. The chart is automatically stored whenever the program is terminated.

• calls the transmission-and-rates menu. The results of the calculations are automatically updated on the chart of the nuclides, showing the information lines selected in the menu “Options → Display 1 or 2” for each fragment. If nothing appears after a calculation has been completed, it means that the rate of this particular nucleus is below the threshold (see also the “Options” menu). selects a stable isotope (grey).
• b ^- decay: selects a b ^- emitter (blue).
• b ⁺ decay: selects a b ⁺ emitter (red).
• b ^- and b ⁺ decay: selects a b^- and b ⁺ emitter (cyan).
• a decay: selects an a emitter (green).
• asks the user to choose a nucleus from the chart and then calculates its energy and β at the specified position.⁺ decay: selects an a and b ⁺ emitter (orange).
• Proton decay: selects a direct proton emitter (purple).
• Remove a nucleus: the program asks the user to click on the nucleus which will be removed.
• Read characteristics: not yet implemented.
• asks the user to choose a nucleus from the chart, and then starts to calculate and draw the dependence of the production rate of this nucleus on target thickness. For each target-thickness step, the program recalculates the settings for the best transmission. One can clearly see the saturation and then the decrease of the production rate as the energy of the fragment decreases and the straggling increases. The results are shown on the graphic screen. not yet implemented.

• Brho1, Brho2, B_Wien: calculates the Br of the two sections of the spectrometer and the magnetic field of the Wien filter (if it has been enabled) for the best transmission of the setting fragment. The current settings of the spectrometer are updated to these new values. Clears previous calculations.
• Brho charge state: calculates the Br s and Wien magnetic field for any charge state of any nucleus. Specially useful calculating the Br s of the beam charge states. Can also be used to set the spectrometer on a charge state different than the fully stripped fragment. Then one has to record the calculated values and enter them manually via the command "Settings Spectrometer Dipoles Brho 1 or 2".
• used to calibrate the thickness of the wedge during an experiment, once a charge state or identified fragment has been centered at the first focus. Bρ2 is then entered manually, and the program asks the user which nucleus corresponds to this Bρ (and for its charge state if it is the projectile). The calculated thickness is the thickness seen on the beam axis of the spectrometer. calls the transmission and rates menu. The results of the calculations are automatically updated on the chart of nuclides, showing the information lines selected in the menu "Options Display 1 or 2" for each fragment. If nothing appears after a calculation has been done, it means that the rate of this particular nucleus is below the threshold (see also the "Options" menu).
• This command is used to calculate the amount of material #i needed to implant a given nucleus at a given depth in #j. #i and #j are first specified by selecting “material” and “implantation in,” respectively, and then the program asks for the nucleus and depth for which the calculation will be performed when selecting “thickness.” If the nucleus does not reach material #j, the command is ignored. One can easily check the average range by calculating the range after material #(j-1) using the command “Calculations → Goodies → Range”. the program asks the user to click on the nucleus in the chart for which the calculation will be performed.
• Area of nuclei: the program asks the user to click on the upper rightmost nucleus first, and then on the lower leftmost nucleus second, in order to define the area of nuclei to calculate.
• All nuclei: the program automatically starts the calculation for all nuclei displayed in the chart from the projectile down to the lithium isotopes. Be aware that you cannot interrupt this command once it has been issued.
• Goodies: calls the goodies menu.creates or updates a result file that has the same name as the current settings file, but with the extension “.liz”. This file is stored under the directory “\RESULT” and is automatically sent to the printer manager via the DOS command “Print,” whether one is installed or not (if none is installed, DOS only issues an error message—no big deal!). This file contains the parameters of the spectrometer and the results of the transmission and rate calculations.clicking on this arrow will open the menu used to select the spectrometer position for which the following calculations will be performed. The default is after the wedge.
• this command is used to copy the program to any other disk or directory. The program asks for the DOS path corresponding to the destination, creates the necessary directories, and copies all required files, including this manual. this selection means that the calculations will be performed assuming the fragments have a kinetic energy determined by the B(of the first section.
• After wedge: with this selection, the kinetic energy is taken after the energy loss in the wedge, not regarding whether the fragment is actually transmitted by the second section or not. That way, the calculations for the fragments which are not centered at the first focus are more realistic than assuming that their kinetic energy corresponds to the Br of second section, which is only true at first approximation within the Br acceptance.
• Into material: in this case, the kinetic energy is taken after the energy losses in the wedge and the 1st to (i-1)-th material(s) where i is the number of the selected material. This allows calculation, for instance, of the energy loss in a detector after the fragments have been slowed down by some other material(s).
• used to start plotting once all parameters have been set to their correct values. Only the fragments for which a transmission calculation has been performed appear on the screen. Once the plot has been completed, the mouse can be moved to any nucleus to read its time of flight and energy loss, as well as the corresponding channels on the actual spectrum if the calibrations have been entered (see below). The time-of-flight axis is reversed, as in most experiments in which the start detector has a much greater counting rate than the stop detector. Reversing start and stop therefore prevents starting the TAC or TDC without stopping it. same as "Into material" but the energy loss into the i-th material is included to deduce the kinetic energy. Adds more flexibility to the calculational possibilities.
• Energy and b: asks the user to pick a nucleus of the chart and then calculates its energy and b at the specified position.
• Energy loss: calls the periodic table menu to pick an element, and then asks for its thickness, and finally the fragment for which the calculation has to be performed. If the position "Into material \#i" is selected, the program only asks to pick a fragment and calculates the energy loss in this material.
• Energy straggling: displays the energy straggling at the specified position after a fragment has been chosen.
• Angular straggling: same as for the energy straggling.
• Range: same as in the energy loss calculation but for the range.
• Optimum target: asks the user to pick a nucleus from the chart, and then starts to calculate and draw the dependence of the production rate of this nucleus versus the target thickness. For each step of target thickness, the program recalculates the settings for the best transmission. One can clearly see the saturation and then decrease of the production rate as the energy of the fragment decreases and the straggling increase. The results are shown on the graphic screen.
• Wedge slope: calculates the slope of an achromatic wedge in % of Br /Br .

• the program asks the user first in which material these distributions should be drawn. It then displays the range distributions for the fragments that actually stop in this material. These distributions are drawn only on a linear scale.calculates the beam energy from Br 1, which has to be input manually, and its corresponding charge state. This command is used during an experiment when one has centered a known charge state of the beam at the intermediate focal plane, and knows precisely the thickness of the target (or doesn't have any target).
• toggles between “lin” and “log” for the display of the distributions. The default is “lin”. same as above, but this time the beam energy is precisely known, and one wants to measure the thickness of the target.
• selects how many distributions will be drawn on the plots. The program always starts with the distributions of the selected fragment and then adds the most intense contaminants. Only nuclei for which a transmission and rate calculation has been performed are displayed. used to calibrate the thickness of the wedge during an experiment, once a charge state or identified fragment has been centered at the first focus. B(2 is then entered manually, and the program asks the user which nucleus corresponds to this B((and its charge state if it is the projectile). The calculated thickness is the thickness seen on the beam axis of the spectrometer.
• Material \#i thickness for implantation in \#j: This command is used to calculate the amount or material \#i needed to implant a given nucleus at a given depth in \#j. \#i and \#j are first specified by selecting `material' and `implantation in' respectively, and then the program asks for which nucleus and at which depth the calculation will be performed when selecting `thickness'. If the nucleus doesn't make it through to the material \#j, the command is ignored. One can check easily the average range by calculating the range after the material \#j-1 using the command "Calculations Goodies range".

• Read: calls the directory menu and asks the user to select a file to read. If the number of files is greater than 50, a second page of files can be selected by clicking on "Page". Going back to the previous page is just like going back to the previous menu: move the mouse out of any selection and click. Once a file has been selected, the program displays the title and asks for a confirmation. Striking any key but "n" or "N" will be interpreted as yes. The screen and internal parameters are then updated according to the file data.
• Write: writes the current settings and calculations to a specified file or a new file. If a filename has been selected, the program asks for confirmation to overwrite it. If it is a new file, the program prompts for a filename (the extension ".fic" is automatically added) and a title.
• Remove: erases the specified file (with confirmation).
• Results: creates or updates a result file which has the same name as the current setting file, but with the extension ".liz". This file is stored under the directory "\\RESULT" and is automatically sent to the printer manager via the DOS command "Print" whether one is installed or not (if it is not, the DOS will only issue an error message, no big deal !). This file contains the parameters of the spectrometer and the results of the transmission and rate calculations.
• Spawn: this command is used to copy the program to any other disk or directory. The program asks for the DOS path corresponding to the destination, creates the needed directories, and copies all the necessary files including this manual.

• Table isotopes: this command is used to browse through the chart of nuclides in order to look at different areas of nuclei.
• Plot (E-TOF: calls the identification spectrum menu.
• Go !: used to start the plotting once all parameters are set to their correct values. Only the fragments for which a transmission calculation has been performed will appear on the screen. Once the plot has been completed, the mouse can be moved to any nucleus to read its time of flight and energy loss, as well as the corresponding channels on the actual spectrum if the calibrations have been entered (see the following). The time of flight axis is reversed as in most experiments in which the start detector has a much greater counting rate than the stop detector. Reversing start and stop therefore prevents starting the TAC or TDC without stopping it.
• Detector: selects which material will be used to calculate the energy loss.
• TOF calibration (ns): once the identification has been made, one can calculate a calibration of the time of flight. Using this calibration, the program displays the channel number on the horizontal axis.
• (E calibration (MeV): same as for the energy loss.
• Length start wedge: flight base length between start detector (target if the HF of a cyclotron is used) and wedge.
• Length wedge stop: flight base length between wedge and stop detector.
• Start of TOF: toggles between "Detector" (the default) and "RF" for the start of the time of flight measurement. In case "RF" is selected, the plot shows the wrap around due to the periodicity of the cyclotron radiofrequency.
• RF frequency: used to input the radiofrequency of the cyclotron.
• Identification: selects whether the identification of the plotted nuclei is directly displayed on the screen or not. This option has to be turned off in case a lot of nuclei are being displayed, in which case all the characters are overlapping and it becomes very difficult to distinguish one isotope from the other. In both cases (identification on or off), the nature of the nuclei is displayed whenever the mouse is moved on them.
• Threshold: one can set a display threshold corresponding to the rate below which the nuclei are not plotted.
• Plot d E-E: plots a d E-E spectrum using the parameters set for the d E-TOF spectrum.
• Angular distributions: displays the angular distributions (q and f after both target and wedge) for the setting fragment and the most intense contaminants. The different angular acceptances as well as the angular transmission for each fragment are shown on the plot. The distributions plotted are s W as a function of q (or f ). They can be drawn on a linear or log scale, and their total number is fixed (see the two last selections of the Plot menu).
• Br selection plot: displays the distributions at the intermediate focal plane, where the Br selection occurs. The momentum acceptance of the spectrometer is also shown. Same display comments apply as for the angular distributions.
• Wedge selection plot: displays the distributions at the first focus, where the images corresponding to different nuclei are selected by the slits at this position. Same display possibilities as for the angular distributions.
• Wien selection plot: displays the distributions at the second focus, which is the dispersive focal plane of the Wien filter. Only valid if the Wien filter has been enabled. Same display possibilities as for the angular distributions.
• Range distributions: the program asks the user first in which material these distributions should be drawn. Then it displays the range distributions for the fragments which actually stop in this material. These distributions are only drawn on a linear scale.
• Display: toggles between "lin" and "log" for the display of the distributions. The default is "lin".
• Number of distributions: selects how many distributions will be drawn on the plots. The program always starts with the distributions of the selected fragment, and then adds the most intense contaminants. Only the nuclei for which a transmission and rate calculation has been performed will be displayed.

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 illustrate most of its different features. The calculations performed in this example are stored in three different files, “example1”, “example2”, and “example3”, provided on the diskette. Each corresponds 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 secondary beam.

• Start the program by typing "LISE".
• Click on either "Previous menu" or "Main menu" to open the main menu.
• Select the “Settings” submenu by moving the mouse over it until it is highlighted, and then click.
• Select the "Projectile" submenu.
• Select the option "Nature, mass and charge". The program then asks to choose the projectile from the chart of nuclides. The default projectile being ⁴⁰Ar, it flashes red in the middle of the screen. Move the mouse to the right side until it changes to an arrow, and then click to scroll the chart to the left. Scroll down the chart by moving the mouse to the top and clicking until you see the krypton isotopes appear. Once you see ⁸⁴Kr on the screen, move the mouse at its position and click to select it. Then the program asks to enter successively the ionic charge, energy and intensity. Enter the numbers 25 for the charge, 60 for the energy and 200 for the intensity using the numeric keypad (it is easier) and "Enter". Once all of this has been done, the information related to the projectile is displayed in red on the right side of the screen, and ⁸⁴Kr flashes red on the chart of the nuclides. The program again displays the bar “Previous menu? Main menu”. Click on “Previous menu” (the default mouse position) to recall the projectile submenu.
• Since all information related to the projectile has been entered, go back to the setting menu by clicking once the smiling face appears (it automatically appears on top of the submenu when "Previous menu" has been selected).
• Select the target submenu.
• Select the option “Nature”. The program displays the periodic-table submenu. Move the mouse to “Be” until it appears highlighted and click. The target element is then displayed in green on the right side of the screen. Enter the target thickness (100 mg/cm²) and go back to the previous submenu depth (select "Previous menu").
• To return to the setting submenu, click to go back to the target submenu, then move the mouse out of the "Nature" selection (the smiling face should reappear) and click.
• Scroll down to the "Setting fragment" selection and click. As for the choice of the projectile, scroll the chart of nuclides until ⁶⁸Co appears, then click on it.
• Return to the Setting submenu using "Previous menu", and select the Spectrometer submenu.
• Select “Slits” and then “Slits intermediate focal plane”. Enter the opening of the slits (±15 mm). This value appears on the right side of the screen, followed by the corresponding momentum acceptance (±0.9%).

• Select the "Calculations" submenu from the main menu.
• Select the “Brho1, Brho2, B_Wien” option. The program starts to calculate the field settings of the spectrometer. It first calculates the range tables of krypton and cobalt in beryllium (a flashing box appears on the screen for each energy). Once these tables are calculated, they are automatically stored on disk (see 3.4). Then the Bρ values of the two sections of the spectrometer, as well as the corresponding magnetic fields, are displayed on the right side of the screen.
• Click on "Previous menu" to return to the calculation submenu.
• Select the "Transmission and rate" submenu.
• Choose the "One nucleus" option. Select the ⁶⁸Co from the chart. The program then calculates and displays two numbers: 11.60%, which is the total transmission (first line of information by default), and 2.8e+01, which is an estimate of the rate in pps (second line of information by default).

• Select “Main menu → Settings → Options”.
• Select "Calculation threshold" in the Options submenu. The cursor appears in the submenu. Enter the number 1.67e-2. To verify that this value has been effectively taken into account, select "Previous menu": the value displayed for the calculation threshold is now 1.7e-02. Only the format of the number has been changed, and the value in memory is still 1.67e-2.
• Go back to the main menu using the smiling face, and select “Calculations → Transmission and rate → All nuclei”. The program will calculate the rate for all possible fragments, starting from projectile-like nuclei with fewer neutrons and going down to the lithium isotopes. During this process, it calculates and stores the range tables of all these elements in beryllium (except for cobalt, which has already been calculated). All this may take a while (depending on the computer speed) and can be interrupted only by resetting the system, so it is probably time for a coffee break!
• For each nucleus transmitted at a rate larger than one per minute, the program displays the total transmission in % and the rate in pps. A lot of nuclei are transmitted together with the ⁶⁸Co because the only selection used is the Br selection of the first section of the spectrometer.
• Select “Main menu → Settings → Options → Display1 → Angular transmission”. The first line of information now displays the angular transmission (or geometrical transmission due to the horizontal and vertical acceptances after the target and wedge positions). It is possible to display any of the quantities listed in the Display1 or Display2 submenu.
• Select “Main menu → Plots → Table isotopes”. Browse through the chart of the nuclides in order to look at different regions of transmitted nuclei. Click on any nucleus to return to the menu.

• Select "Main menu Settings Options Thickness unit". This command toggles the thickness unit to µm.
• Go back to the Settings submenu and select “Material(s) → Material #1 → Add → Si”. Then enter the thickness in µm (enter 100 µm).
• Select "Main menu Plots Plot d E-TOF Detector". Enter the material number of the detector used to measure the energy loss (this is obviously 1).
• Return to the Plot dE-ToF submenu and turn Identification off. This prevents the names of the nuclei from being plotted on the screen when too many of them overlap and therefore become impossible to read.
• Select "Go !". This will start generating the plot. The screen stays erased until the energy loss calculations are performed. If the range tables of elements Krypton through Lithium into Silicon are not yet calculated, the program will generate them and store them on disk (this might take a little more time). Once the plot is produced, the mouse appears as a cross. The name, transmission and rate of any nucleus appears on the right side of the screen whenever the cross is pointing on it. One can clearly see the isospin lines on the plot (the most obvious one is the N=Z straight line), as well as the tilted Z lines which flatten for the lighter elements. To return to the menu, click anywhere and strike any key.

• Select "Main menu Settings Options Thickness unit" to toggle back to mg/cm².
• Select “Previous menu → Go back → Wedge → Nature → Al” and enter the thickness of the wedge (50 mg/cm²). As soon as this entry is made, the calculations are cleared.

• Select “Previous menu → Go back → Go back → Spectrometer → Slits → Slits image1” and enter ±2 mm. This opening determines the selectivity of the second section of the spectrometer when a wedge is used.
• Select "Main menu Calculations Brho1, Brho2, B_Wien" to calculate the new settings of the spectrometer corresponding to the best transmission for ⁶⁸Co.

• Select “Previous menu → Go back → Transmission and rate → Area of nuclei” and click on ⁷⁴Ga first (the upper rightmost nucleus) and then on ⁶³Cr (the lower leftmost nucleus). This will start the calculation only for the nuclei located in the square defined by ⁷⁴Ga and ⁶³Cr. Since far fewer nuclei are being transmitted, it is not necessary to calculate the transmission for all of them.

• The insertion of an achromatic wedge has considerably reduced the amount of nuclei transmitted with the ⁶⁸Co. This additional selection can be visualized by looking again at the d E-TOF plot.
• Select “Main menu → Plots → Plot dE-ToF → Identification” to turn identification back on.
• Select “Previous menu → Go!” to start the plot. In an actual experiment, one would use the calibration determined from the previous plot to identify the nuclei on the experimental spectrum. If this calibration is entered in the Plot dE-ToF submenu, the numbers labeled “Ch# X” and “Ch# Y” give the channel numbers corresponding to the mouse position.
• One can also visualize the selection performed by the wedge and the second section of the spectrometer by plotting the positions of the images corresponding to different nuclei at the first focal point. Select “Previous menu → Go back → Wedge selection plot”. The images are spread along the horizontal axis, ⁶⁸Co being centered with respect to the slits. It is interesting to notice that the image of ⁷¹Cu is also rather well centered; therefore, it is impossible to eliminate it using the wedge technique. Another selection criterion, such as that provided by a Wien filter (velocity filter), must be used.

• Select "Main menu Settings Options Wien filter" to enable its use in the calculations. This command clears the previous calculations.
• Select "Previous menu go back Spectrometer Wien filter Electric field" and enter a value of 3000 kV/m. The magnetic field setting of the Wien filter is then automatically calculated for the best transmission of ⁶⁸Co, as well as the dispersion. All this information appears on the right side of the screen.
• Select “Previous menu → Go back → Slits → Slits second image” and enter an opening of ±2 mm.
• Perform the rate calculations (select “Main menu → Calculations → Transmission and rate → Area of nuclei” and click on ⁷⁴Ga then on ⁶³Cr). The amount of ⁷¹Cu is greatly reduced and ⁶⁸Co is now the main component of the beam. However, ⁷⁰Ni is still present at a competitive rate.
• Select “Main menu → Plots → Wien selection plot” to plot the distributions at the second focal point. It then becomes obvious that although the Wien filter is efficient at eliminating ⁷¹Cu, it cannot do the same for ⁷⁰Ni because its velocity is close to that of ⁶⁸Co.
• Select “Previous menu → Wedge selection plot” to look again at the selection provided by the wedge. ⁷⁰Ni appears to be shifted from the slit position. Two solutions are possible to reduce its contamination further: one can close the slits of the first image even more, although this will also decrease the amount of ⁶⁸Co transmitted, or one can also increase the thickness of the wedge in order to shift the image of ⁷⁰Ni farther to the left. This last solution appears to be the best. However, it should be tested, since a thicker wedge will broaden the images and increase angular scattering, resulting in a loss of transmission for ⁶⁸Co.

LISE is DOS-based software that runs on any IBM-compatible PC. It runs under DOS 3.1 and later versions, and requires only 640 kbytes of memory. The speed of the program depends greatly on the CPU type, speed, and configuration. The use of a coprocessor is strongly recommended: the program uses FFT (Fast Fourier Transform) algorithms that contain extensive floating-point operations. The latest version was developed on a 386-SX at 16 MHz with a coprocessor, 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 required for the same calculation!). The program uses a mouse driver loaded at startup. This driver has to be Microsoft-compatible (most of them are). The graphics interface included with the program (file “EGAVGA.BGI”) ensures compatibility with any EGA- or VGA-compatible graphics card. The program automatically looks for the best resolution the card can provide, although it is limited to the maximum standard VGA resolution of 640×480×16 colors. A hard copy of the graphics screen can be made on a printer provided the command “graphics” is executed at startup. The first version of LISE was 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 allows direct control of the mouse driver via software interrupts, in order to create a custom menu system. Turbo C also provides an extensive set of graphics routines. Finally, recursion, the ability to manipulate data structures, and the possibility of allocating and deallocating memory dynamically are major improvements in programming. Today, the C language has evolved even further toward object-oriented programming, producing 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 languages best suited for this task. However, this software is still tightly bound to MS-DOS, and transferring it to other machines running 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 et al., Nucl. Data Tables A7 (1970) 233.