       Cross sections calculations

• To: mathgroup at smc.vnet.net
• Subject: [mg74009] Cross sections calculations
• From: "Johan Mars" <jmars at uwc.ac.za>
• Date: Mon, 5 Mar 2007 04:56:39 -0500 (EST)

```Dear mathgroup
I am new to math 5.1 and like assistance solving the calculations for
cross sections
I am using (...r-matrix approach---------
parameters: y is cross section, x is energy and t is the angle (in
degrees). The summation of l is from 0 to n=7.
sqrt is the square root. Pl is the cosine of the Legendre polynomial.
j=t/2 and
u=-2.15*ln(sin(j))...)

the equation which is:

y=1+3.4*x*sin^4(j)*[sum(
Bl*Pl)]+[1.86*sqrt(x)*sin^2(j)*(sum(Tl*Pl*cos(u))-sum(Rl*Pl*sin(u))]

Bl, Tl and Rl are unknowns to be calculated from the fit to the data.
This means that 3 sets of data (2D vectors (x and y)) are needed for
the determination.
I have added the data points since I do not have a site on the web to
place them.

t=85.7
t=123.8				                       t=152.6
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
x	              y			                     x
y			                                  x
y
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
1.032919        1.342186    				 1.034540
1.638148    				  1.035617        1.676251

1.038439        1.342024    				  1.039728
1.588318    				  1.040366        1.589682

1.043274        1.341003    				  1.044800
1.508356    				  1.045648        1.502952

1.045025        1.333919    				  1.047154
1.296485    				  1.050777        1.398026

1.046472        1.308382    				  1.048602
1.256833    				  1.053271        1.950580

1.048490        1.308323    				  1.049745
1.208223    				  1.054043        3.166415

1.049061        1.300394    				  1.050890
1.219943    				  1.054630        3.582741

1.049898        1.282787    				  1.051602
1.651101    				  1.055846        3.561088

1.051612        1.255484    				  1.052843
1.994618    				  1.056856        3.159478

1.053020        1.277421    				  1.054796
2.769292    				  1.058560        2.991751

1.054315        1.349470    				  1.055800
2.965068    				  1.059078        2.648054

1.055076        1.384613    				  1.057125
2.777640    				  1.060705        2.428667

1.058312        1.440782    				  1.058296
2.563109    				  1.063215        2.452225

1.060216        1.425781    				  1.060041
2.375554    				  1.065260        2.241832

1.062424        1.424837    				  1.062594
2.314452    				  1.070995        2.100240

1.064442        1.421262    				  1.064609
2.178097    				  1.076282
2.147275
1.068439        1.419386    				  1.069947
2.073923
1.073883        1.419227    				  1.075099
2.066335
1.077386        1.405058

Please note that in literature various other symbols are used for the
cross sections, the energies and angles. Mine here are just for
simplicity.
I hope to hear from you soon. Thanks a million.

Sincere regards

Johan Mars, Dr
Environmental Awareness         Tel.: +27 21 9593050
Department of Chemistry             Fax.: +27 21 9593055
University of the Western Cape     Cell.:+27 72 5043585
Private Bag X17
Bellville, 7535
South Africa
http://www.uwc.ac.za

```

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