the
relativistic kinematics program in Excel
This document describes the spreadsheet CATKIN
written for Microsoft Excel, which performs kinematics
calculations for two-body collisions as well as calculating
various other nuclear physics quantities such as: separation
energy, Q-value, multiple scattering, Brink matching, safe
Coulomb energies, breakup cone sizes, etc. The document requires
nothing other than a copy of Excel on your computer.
For a description and derivation of relativistic
kinematics formulae, see this
link.
A copy of this brief guide is included as a part
of the "Instructions for Use" file that is downloaded as a Word
file along with catkin. That file also includes the development
history.
A general feature is that cells where you enter values are coloured yellow. All other cells in the spreadsheets are protected, so that you cannot accidentally change a formula, etc. Using the ‘tab’ key will automatically move you to the next yellow (data entry) cell.
The two spreadsheets into which you may enter data are: (1) kinematics (where you specify a two-body reaction and the kinematics are calculated), and (2) Calculator (where several additional nuclear physics quantities can be calculated). Several other sheets and charts display kinematics plots. A final sheet holds the mass excess data read in from the Audi web site, and can be updated (see Appendix).
The main two-body reaction spreadsheet is called kinematics and it has several parts
The beam, target and ejectile are specified by their chemical symbol (lower or upper case are acceptable) and the mass number. A mass table on a separate sheet (2000 data) is used to calculate the reaction Q-value and the mass excesses etc.
The other inputs apart from these three particles are the beam energy in the lab, and the excitation energy of the recoil nucleus. There is no facility for explicitly including excitation in the ejectile.
The section where a table gives results for a particular range of angles is given below the input information. Here, the initial angle and the step in angle are specified for the ejectile. The programme uses 11 angles separated by the given step.
Everything else should update automatically. If it doesn’t for some reason, it is possible to force a recalculation in Excel using Tools>Options>Calculation>CalcNow.
Under the font and to the left of the equals sign there is a drop-down list that includes the option Print_table. Selecting this will highlight the top region of the sheet, and this area can be printed on its own by using File>Print and checking selection, then Preview>Setup>Page and check fit to page and landscape and click OK, and the Print or Close depending on whether the print is to proceed.
The summary plots chart includes plots of various quantities derived from the results section in rows 16 to 26. There are 4 plots for each of the two possible kinematic solutions.
The lab angle vs cm chart gives a single plot of the function relating the laboratory and centre of mass angles for ejectile and recoil, cm angle 0 to 180 degrees.
Lab energy vs cm gives the analogous plot for ejectile and recoil energy, for 0 to 180 degree cm angles.
The plectrum plots are plots of lab energy vs lab angle, for the reaction specified in the kinematics sheet. (I call them by this name, because they have the characteristic shape of a guitar plectrum in the case of reactions that ‘fold around’ to give two solutions at forward angles).
The Calculator spreadsheet will calculate the quantities Mass, Separation energy, Q-value, Br , momentum, experimental production rates, Coulomb barriers and safe energies, breakup cone sizes, Brink cluster transfer matching and multiple scattering angles. At the top of the sheet, hyperlinks allow the desired part of the sheet to be easily reached in one click.
The mass table is self explanatory and
contains the mass excess data and the plotting sheet is
simply a scratch pad of intermediate computations.