Does the Dimensionless Quantity from These Constants Have Physical Meaning?

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Krakers
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Question: Does the dimensionless quantity derived from the constants below have any physical meaning?

6.6524585580E-29 = Thomson cross section in SI units
2.1001941382E-16 = neutron Compton wavelength / 2pi inSI units
1508.215132 = (Thomson cross section) * (neutron Compton wavelength / 2pi)^-2

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Krakers
 

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Maybe because:
[tex]\frac{55+150 \pi+1867 \pi^2}{4 \pi} = 1508.215132...[/tex]

;)
 
Now I get it. Do you have software that does that for you?
 
The Thomson cross section (= 8 pi r02/3 = 0.66 barns) is the low energy limit of the total Compton cross section (photon scattering on free electrons). r0 is the classical electron radius (2.828 fermi).
 
The dimensionless quantity above is equal to [tex]\frac{8\pi}{3} (\alpha \frac{m_n}{m_e} )^2[/tex].
 
Thank you all for your time and the gift of your knowledge.

Regards,
Krakers