I'm one of the people advocating the discussed method. I agree with Simon
that it is sort of "poor man's Montecarlo", however it is by far more
efficient for the primary goals of extracting physics observables like
e.g. G_En.
>
> I think what Aaron did (and what I did in the white generator in DGen) is a
> 'white' spectra in the 5-fold phase space above the reaction threshold. Or
> in more detail, electron scattering angle, electron energy transfer and
> proton scattering angle in CMS frame are picked at random then all the
> particles are transformed into BLAST frame. each event is physically
> possible, not just a arbitrary combination of vectors in Blast LAB
> frame. So I hope the deuteron binding energy constraint would not render
> any of the events useless.
>
About the binding energy issue (which is equivalent that deuteron
disintegration happens only above breakup threshold):
There is the possibility to generate the electron in the coordinates
(W,Q^2,phi_e) instead of (omega,theta_e,phi_e). In this way one can
require W > W_thr (= M_deut + 2.2MeV) and generate up to some W_max.
The above coordinate transformation involves one (trivial) Jacobian.
> We (in fact Vitaliy first) also realize the role of Jacobians here. In
> order to reproduce the event distributions that simulate what we observe
> in experiment, we need to weight the events generated in "white" spectrum
> by the product of Jacobian and cross section. Because for each individual
> event, both cross section and Jacobian (I count two non-trivial Jacobians
> for dee'pn, for the proton polar angle in CMS and the electron polar angle
> in LAB). Zilu, please do let us know if I am missing important issues.
>
I don't quite understand why a Jacobian for the electron polar angle
in LAB is needed.
> At this moment, genereting events in "standard" formalism in dee'pn
> channel requires 5-dimensional lookup tables of cross sections and their
> integrals. this makes the program very memory intense. It easily takes up
> 300M memory. To add Z-dependent spin angle and/or readiative
> correction(which requires some perturb of beam energy)
> would require even more degrees of freedom on top of these 5 dimensions.
> This would make our computers constantly swapping and crawling. So I am
> afraid MCEEP way of "generate events uniformly and weight each by cross
> section" approach is anyway in order. The large acceptance of ours makes
> it harder to implement such method.
>
I have one more difficulty with the "5" dimensional phase space. In fact,
the deuteron disintegration cross section has five dimensions though,
however two of these dimension are trivial as they are related to the
electron only and characterize the "leptonic" vertex, quantifiable by the
Mott cross section and kinematic factors or "virtual photon
flux and polarization" and exactly/analytically calculable for each
generated electron). The "structure" of the cross section is entirely
given by Arenhoevel's "f's", and those depend on three coordinates only.
Therefore, only three-dimensional lookup tables are actually necessary,
and from these it is possible to contruct cross sections for any beam
energy. A reduction of the dimension from 5 to 3 would make the code much
less memory-expensive.
A final comment on the interpolation of the cross section: The steepest
slopes in cross section usually occur in the Mott cross section term,
whereas the f's show rather smooth variations. Therefore I believe that
after a reduction of the dimensions it would be sufficient to linearly
interpolate the grid for the f's in order to evaluate the cross section
weights.
Regards,
Michael
--+-------------------------------------+--------------------------+ | Office: | Home: | |-------------------------------------|--------------------------| | Dr. Michael Kohl | Michael Kohl | | Laboratory for Nuclear Science | 5 Ibbetson Street | | MIT-Bates Linear Accelerator Center | Somerville, MA 02143 | | Middleton, MA 01949 | U.S.A. | | U.S.A. | | | - - - - - - - - - - - - | - - - - - - - - -| | Email: kohlm@mit.edu | K.Michael.Kohl@gmx.de | | Work: +1-617-253-9207 | Home: +1-617-629-3147 | | Fax: +1-617-253-9599 | Mobile: +1-978-580-4190 | | http://blast.lns.mit.edu | | +-------------------------------------+--------------------------+
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