THE CODE LISE: new version 4.8
20.09.2000

Contents : 1.1. Reactions in a target (stripper)
1.2. Reactions in a wedge
1.3. Reactions in materials
2. Calculation of the secondary reactions contribution in a fragment output 2.1. Secondary reactions and Optimal target calculations subroutine 3. Other 3.1. New generator of random numbers
3.2. Creation of a file with results of secondary reactions contribution
3.3. Call of a web-homepage of the LISE program from dialogue ABOUT
3.4. Angles of an inclination of a target and a stripper
3.5. Calculation of optimal target thickness from an inclination of a target
3.6. File of transmission calculation (Results)

1. Reduction of a fragment output due to reactions

In the new version of the program losses from reactions in a target, a stripper and a wedge, and also contributions of secondary reactions to outputs of fragments are more accurately investigated. In the previous versions simple dependence of formation of reactions products that is true in a case only thin targets was assumed:

,     /1/ where NF (x) is the number of fragments F produced at thickness x, NP (0) is the beam intensity which is supposed to be constant, x is the target thickness, sP->F is the cross section for producing the fragment F from projectile P.
So for an example usage of new algorithm of fragments outputs calculation with losses due to responses in a target and in wedge reduce in 4 times a 40Ti output in reaction 58Ni (500AMeV) + Be (W.Liu et al, PRC 58, 1998, 2677) in comparison with the previous version of the program.

1.1. Reactions in a target (stripper)

As the target thickness is increased, the probabilities of destroying the fragment of interest and the projectile become significant. These probabilities are governed by the total cross sections of the fragment sF and accordingly the projectile sP. Taking this into account, the number of fragments F is determined as:

.      /2/ In a case F=P the equation /2/ assumes the following:    .      /3/ In the program was entered the new coefficient of transmission to number 22 which shows the ratio of the lost fragments to number derived in target and stripper after target (from equation /1/). Number of lost fragment is defined as the difference between outputs of fragments counted on the Formulas /1/ and /2/. This coefficient is calculated at any modes (options: secondary reactions, charge states etc.) also can be observably also on a plot of transmission at calculation of optimal target thickness. The curve describing the given coefficient is marked on Fig.1 with arrows of red color.

1.2. Reactions in a wedge

In the new version of the program losses of number of fragments due to responses in a wedge also are taken into account. The new coefficient 23 showing the ratio of lost fragments to a total number got in a wedge (x is its thickness) is entered .

Fig.1.

1.3. Reactions in materials

The user also can see the considering of reactions in materials in dialogue "GOODIES" which represented on Fig.2. It is possible to observe as loss in the given material (À), and how many percent of fragments has remained from a beginning number got in a telescope.

Fig.2. Dialogue "GOODIES": calculation of reactions in materials

2. Calculation of the secondary reactions contribution in a fragment output

In version 4.7 the user only could make the plot of the contribution of secondary reactions for one fragment. In the new version Possibility to take into account the contribution of secondary reactions for all selected products of projectile fragmentation has appeared directly at calculation of transmission. To apply the calculation of secondary responses it is necessary to include an appropriate option (A) in menu PREFERENCES (see Fig.3).

Fig.3. Dialogue “Preferences”

In the mode of the calculation of secondary reactions in an upper right corner of SETTINGS window the green flag SEC will appear (see Fig.4). The number under this flag designates quantity of fragments involved for calculation of the secondary reaction contribution.

Fig.4. Flag of secondary reaction calculations is set.

Allocations of fragment outputs after a target depending on target thickness are kept in memory. They are deleted, if thickness of a target or has decreased in 5 times, or has increased in 2 times and also if the energy of an initial beam has varied on 10 percents. If new thickness of a target satisfies to the above-stated conditions an output of fragments are interpolated from the saved arrays. When the user sets area of nuclei (Ftop,right , Fbottom,left) for transmission calculation, the program determines new square for calculation of secondary reactions in view of that the projectile (P) also should enter into this area, and then expands the given square on one unit in all sides:

,     /4/ where N and Z are numbers of neutrons and protons correspondingly. After the given stage the program fills in arrays of outputs depending on thickness of a target for all nuclei of this square and only after that starts to count transmission. If after calculation of transmission of isotopes in the given square the user will decide to count transmission of an isotope outside of this square the program will calculate in addition arrays of outputs to the same principle defining square.

For the registration of the secondary reaction contribution the new coefficient of transmission at number 24 is entered. The algorithm of calculation of the secondary reaction contribution also counts losses of outputs in a target and in a stripper. However and the coefficient 22 (look the previous paragraph) takes into account it. To avoid the repeated registration of losses thanking responses in targets, coefficient 24 it is written as follows:

C24=SecReact / Nsimple / (1-C22)  ,       /5/ where SecReact is number of the interest nucleus calculated by an algorithm which was demonstrated in previous version 4.7, Nsimple is output without any corrections calculated with equation /1/. Summary coefficient K is a result of all three coefficients (22-24) which gives in the table of transmission in an output file of results: K=C24 (1-C22) (1-C23) .                       /6/ If the option "Secondary Reactions" is switched off, coefficient 24 is equal to one.

2.1. Secondary reactions and Optimal target calculations subroutine

The new version of the program also allows to take into account the contribution of secondary responses at calculation of an optimal target thickness. If the energy of an initial beam is more 200 AMeV or the option "Secondary Reactions" is set, the program will offer automatically to calculate thickness in view of secondary reactions. The user has possibility to disable the given option (see Fig.5). For matching on a graphics outputs of a fragment are shown depending on target thickness as well as in view of secondary responses, and without them (see Fig.6).

Fig.5.

Fig.6. Optimal target plot with contribution of secondary reactions.

3. Other

3.1. New generator of random numbers

In the new version of the program the generator random numbers was replaced on more advanced. A range of the new generator up to 232-1, that best allows to feign bidimensional plots in a mode of Monte Carlo acquisition. The reference to generators of random numbers: http://www.ulib.org/webRoot/Books/Numerical_Recipes/bookcpdf/c7-0.pdf

3.2. Creation of a file with results of secondary reactions contribution

Using the plot "Output of products from a target with the contribution of secondary reactions" through the menu "Utilities", the user can get access to a file of results of calculations of fragments outputs in view of the contribution of secondary reactions (see Fig.7). The given file is in root directory LISE and called "contribution.txt".

Fig.7. Call of a file of results through plot "Output of products from a target with the contribution of secondary reactions".

The given file allows to see what fragments give the greater contribution through secondary reactions in a fragment of interest and also to analyze a difference between fragments outputs without amendments on the basis of the formula /1/ with outputs in view of secondary reactions. Whence it is possible to draw a conclusion on an example what fragments has advantage at relativistic energies with use of a thick target.

The example of the given file for a fragment 31F gives below:

LISE CALCULATIONS Version 4.8.1
Date : 9/19/2000 Time : 12:28:10
Projectile : 40Ar 18+ at 1000 MeV/u - Intensity : 1e+12 pps
Target : Be Thickness : 30000 mg/cm2 (162338 microns)
Settings calculated on 31F
Methods: Cross Section=4 NP=128

========================================================================
CONTRIBUTION OF SECONDARY REACTIONS in output of 31F
=========================================================================
| | |   |   |       A     |        B     |     C      | B/C | relation |
A El| Z | N |contribution | fragment's   | fragment's |     |SECONDARY/|
| | |   |   |from fragment|output with   |output w/out|     | PRIMARY  |
| | |   |   | into 31F    | secondary    |any correct.|     | after    |
| | |   |   |  w/out loss | reactions    |    (pps)   |     | tagget   |
=========================================================================
40Ar| 18| 22| 6.03e-04 | 5.64e+10 | 1.00e+12 | 0.056 | 0.0014 |
42K | 19| 23| 4.45e-07 | 8.59e+07 | 1.56e+09 | 0.055 | 0.1488 |
41K | 19| 22| 7.73e-08 | 1.62e+08 | 2.64e+09 | 0.061 | 0.2596 |
40K | 19| 21| 6.09e-08 | 5.78e+08 | 9.81e+09 | 0.059 | 0.1898 |
41Ar| 18| 23| 9.91e-05 | 5.47e+08 | 9.81e+09 | 0.056 | 0.1356 |
39Ar| 18| 21| 2.18e-06 | 8.10e+09 | 1.40e+11 | 0.058 | 0.1413 |
40Cl| 17| 23| 1.01e-03 | 1.70e+08 | 2.64e+09 | 0.064 | 0.2797 |
39Cl| 17| 22| 1.60e-03 | 2.23e+09 | 3.78e+10 | 0.059 | 0.1577 |
38Cl| 17| 21| 6.16e-05 | 4.07e+09 | 6.35e+10 | 0.064 | 0.2356 |
39S | 16| 23| 3.42e-03 | 1.97e+07 | 2.18e+08 | 0.090 | 0.7564 |
38S | 16| 22| 6.98e-03 | 2.38e+08 | 3.12e+09 | 0.076 | 0.4587 |
37S | 16| 21| 6.57e-04 | 7.68e+08 | 9.93e+09 | 0.077 | 0.4553 |
38P | 15| 23| 7.30e-03 | 1.61e+06 | 9.82e+06 | 0.164 | 2.1123 |
37P | 15| 22| 2.57e-02 | 2.16e+07 | 2.08e+08 | 0.104 | 0.9416 |
36P | 15| 21| 5.29e-03 | 1.03e+08 | 1.10e+09 | 0.094 | 0.7220 |
37Si| 14| 23| 1.39e-02 | 1.22e+05 | 3.77e+05 | 0.323 | 4.9994 |
36Si| 14| 22| 7.52e-02 | 1.70e+06 | 1.13e+07 | 0.151 | 1.7554 |
35Si| 14| 21| 2.94e-02 | 1.02e+07 | 8.44e+07 | 0.121 | 1.1659 |
36Al| 13| 23| 2.09e-02 | 8.29e+03 | 1.13e+04 | 0.737 | 12.3321 |
35Al| 13| 22| 1.46e-01 | 1.12e+05 | 4.21e+05 | 0.266 | 3.7289  |
34Al| 13| 21| 8.22e-02 | 7.37e+05 | 3.95e+06 | 0.187 | 2.2621  |
35Mg| 12| 23| 2.17e-02 | 4.95e+02 | 1.92e+02 | 2.582 | 44.5410 |
34Mg| 12| 22| 1.79e-01 | 6.30e+03 | 9.49e+03 | 0.664 | 10.5002 |
33Mg| 12| 21| 9.95e-02 | 4.27e+04 | 1.18e+05 | 0.363 | 5.1821  |
34Na| 11| 23| 1.47e-02 | 2.60e+01 | 2.01e+00 |12.901 | 220.689 |
33Na| 11| 22| 1.80e-01 | 3.16e+02 | 1.38e+02 | 2.289 | 37.6172 |
32Na| 11| 21| 9.39e-02 | 2.11e+03 | 2.36e+03 | 0.895 | 13.8098 |
32Ne| 10| 22| 1.40e-01 | 1.40e+01 | 1.39e+00 |10.077 | 164.348 |
31Ne| 10| 21| 6.90e-02 | 9.01e+01 | 3.20e+01 | 2.819 | 44.3615 |
31F | 9| 22| 4.68e-02 | 5.39e-01 | 9.62e-03 |56.013 | 892.3932 |
=========================================================================
Characteristics of fragment output ( 31F ) after target
Total output 5.39e-01
Primary fragments output 6.03e-04
Secondary fragments output 5.38e-01
Lost fragments 7.28e-01
Output without corrections 9.62e-03

3.3. Call of a web-homepage of the LISE program from dialogue ABOUT

Pressing the left key of a mouse on dialogue About, the user automatically causes a brouser and loads the homepage of program LISE located to the address: http://http:"//lise.nscl.msu.edu. In the following versions it is planned to make automatic check on presence of the new version of program LISE on the appropriate servers, and also access through the INTERNET to various bases to the data (on an example on a database of isomers to the address: http://www.ganil.fr/LISE/isom.html)

3.4. Angles of an inclination of a target and a stripper

In the new version the user can establish in the menu "Preferences" (see Fig.3, ellipse B) an option of simultaneous turn of a target and stripper, taking place for a target. If the user has changed an angle of an inclination of a target automatically there will be a change of an inclination of a stripper, and the user will receive the message on it. If this option is established, Optimum thickness of a target from an inclination of a target will be calculated also under condition of a simultaneous inclination of a target with a stripper (see the following paragraph).

3.5. Calculation of optimal target thickness from an inclination of a target

In the new version the user can calculate an optimum corner of an inclination of a target (simultaneously with a stripper and without it: see above). Through menu "Calculations" (Fig.8) it is possible to call the given utility. For calculation initial thickness of detectors are accepted at an inclination in 0 degrees. This procedure works can work also with options "Secondary reactions" and "Charge states". The example of calculations is given in figure 9.

Fig.8.

Fig.9. Plot of optimal target thickness from an an inclination of a target

3.6. File of transmission calculation results

In a file of transmission calculation results the angles of an inclination of a target (stripper, wedge, materials) and according to their thickness under zero of degrees now are deduced. The factor K (equation /6/), showing change of an output of fragments due to reactions in a target (stripper, wedge) also is added.