Thermal Velocity Effect

According to Nozawa, Itoh, and Koihyama (1998 astro-ph/9804051) the 1st order and 2nd order thermal velocity effect is

[Graphics:SoftComptongr651.gif]
where
[Graphics:SoftComptongr652.gif]
[Graphics:SoftComptongr653.gif]
where
[Graphics:SoftComptongr654.gif]
and
[Graphics:SoftComptongr655.gif]

[Graphics:SoftComptongr656.gif]

[Graphics:SoftComptongr657.gif]

[Graphics:SoftComptongr658.gif]

[Graphics:SoftComptongr659.gif]

[Graphics:SoftComptongr660.gif]

[Graphics:SoftComptongr661.gif]

[Graphics:SoftComptongr662.gif]

[Graphics:SoftComptongr663.gif]

[Graphics:SoftComptongr664.gif]

[Graphics:SoftComptongr665.gif]

[Graphics:SoftComptongr666.gif]

[Graphics:SoftComptongr667.gif]

[Graphics:SoftComptongr668.gif]

[Graphics:SoftComptongr669.gif]

[Graphics:SoftComptongr670.gif]

[Graphics:SoftComptongr671.gif]

[Graphics:SoftComptongr672.gif]

[Graphics:SoftComptongr673.gif]

[Graphics:SoftComptongr674.gif]

[Graphics:SoftComptongr675.gif]

[Graphics:SoftComptongr676.gif]

[Graphics:SoftComptongr677.gif]

[Graphics:SoftComptongr678.gif]

[Graphics:SoftComptongr679.gif]

[Graphics:SoftComptongr680.gif]

[Graphics:SoftComptongr681.gif]

[Graphics:SoftComptongr682.gif]

[Graphics:SoftComptongr683.gif]

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