R-functions for the HRS

Update 8/3/05: Error found and corrected in description of the dipole exit used to generate the with-septum files.

Update 3/11/04: Data files added for the Right and Left arms as used in the Hypernuclear (E94-107) experiment

Update 10/9/03: Data files added for the Right arm at 6° (i.e. with septum) and collimation as used in Small Angle GDH

Update 4/29/02: Data files changed to reflect a new, improved spectrometer model.

(A way to make cuts on data and optimally use the full acceptance)

John J. LeRose 8/03/05

There now exists a subroutine/function package that can be used to generate cuts in HRS data. These routines use a so-called r-function to evaluate where a given trajectory (characterized by y₀, d, theta₀, and phi₀) lies with respect to the boundaries of the acceptance of the spectrometer. As such, the r-function value can be used as a parameter for placing a systematic cut on data or simulations without artificially excluding too much acceptance.

The entire r-function package (source code and both new and old data files, both arms with septum too!) is included in a single tar file, which you can get HERE

tar file contents:

Fortran Source files: see http://www.jlab.org/~lerose/r-functions/r-function.f & http://www.jlab.org/~lerose/r-functions/test-r-function.f

In the CUE the files can also be found in: home/lerose/public_html/r-functions/r-function.f and test-r-function.f. Comments regarding usage can be found in the source files. The first file, r-function.f, contains the source code for the routines needed to use the r-functions. They are:

• init_rfunction - This subroutine initializes the arrays needed to evaluate the r-function.
• getindex - This subroutine is called inside rfunction. It is used to determine where in the lookup tables to get the correct parameters for the r-function. The user only uses it indirectly when rfunction is invoked (see next)
• rfunction - This function actually evaluates the r-function and returns a value equal to the distance, in units of radians, of the input trajectory, specified by y₀, d, q₀, & f₀, from the boundary of the nominal acceptance. R-function = 0 defines the boundary of the nominal acceptance. Negative values of the r-function indicate that the trajectory is outside nominal acceptance. e.g. Making at cut requiring rfunction > 0 would include everything inside the "nominal acceptance", which is defined by my SNAKE based model and isn't exactly correct. Making a cut requiring rfunction > 0.005 would include only the trajectories that lie 5 mrad or more inside the solid angle defined by the model for the specified y₀ and d.

Data files: see :

http://www.jlab.org/~lerose/r-functions/New-Left/collimator/ for left arm with collimator

http://www.jlab.org/~lerose/r-functions/New-Left/no-collimator/ for left arm without collimator

http://www.jlab.org/~lerose/r-functions/New-Right/collimator/ for right arm with collimator

http://www.jlab.org/~lerose/r-functions/New-Right/no-collimator/ for right arm without collimator

http://www.jlab.org/~lerose/r-functions/Right_6degree/collimator/ for right arm at 6 degrees (septum) with collimation for GDH

http://www.jlab.org/~lerose/r-functions/left_septum_hypernuclear/ for left arm at 6 degrees (septum) with collimation for Hypernuclear (E94-107)

http://www.jlab.org/~lerose/r-functions/right_septum_hypernuclear/ for right arm at 6 degrees (septum) with collimation for Hypernuclear (E94-107) 

old data files with older spectrometer models can still be found at:

http://www.jlab.org/~lerose/r-functions/leftarm/collimator/ for left arm with collimator

http://www.jlab.org/~lerose/r-functions/leftarm/no-collimator/ for left arm without collimator

http://www.jlab.org/~lerose/r-functions/rightarm/collimator/ for right arm with collimator

http://www.jlab.org/~lerose/r-functions/rightarm/no-collimator/ for right arm without collimator

At each of these locations there are 15 files entitled:

Information.dat (general information about the files)

dy-dd.dat (parameters of the lookup table)

min-max.dat (rfunnction parameters)

linei.dat (i = 1,12) (more rfunction parameters)

Re choice of data files: In general the differences between left and right are very small, except of course for left and right with septum. As a practical matter, for a generic HRS (no septum) one could use the left or right r-function equally well with either arm. With and without collimator, however, are significantly different.

General Discussion:

The solid angle acceptance of the HRS is a complicated function of y₀ and d (DW = F(y,d)). The r-function tells you, for the solid angle acceptance appropriate for a given value of y₀ and d, where in relation to the boundary of that solid angle acceptance, a given value of q₀ and f₀ lie. The r-function provided above uses a lookup table approach to determine the boundaries of the solid angle at (y₀, d). These boundaries take the form of 16 straight lines, whose parameters are contained in the files linei.dat and min-max.dat. The r-function then evaluates the distance between a given point (q₀, f₀) and each of those lines. The minimum of those distances is then returned as the r-function value.

The 16 straight lines are shown in the figure below along with the actual points that are the edges of the acceptance at y₀ = d = 0.

A contour plots of a sample r-functions appear below:

Enjoy!

Please send comments or questions to John LeRose: lerose@jlab.org