Abstract
Integrals arising in the calculation of 2-phonon processes in hte absorption of light by free continuum polarons [E. Kartheuser, R. Evrard, J. Devreese, "Mechaism of absorption of light by free continuum polarons" Phys. Rev. Letters 22, 94 (1969)], are evaluated numerically.
A method to calculate
∫∫∫dk/k2 ∫∫∫dk'/k'2 k'2jθ'cos2iθ δ ((k+k')2-ε2)e-xk'2-yk'2 (α)Numerically for all x, y > 0 and with positive integers i and j is described. Also a power series development in ε and an asymptotic expansion for the case x=y=2 and i = j = 0 are derived. Finally the calculation of (α) is carried out analytically.
A method to calculate
∫∫∫dk/k2 ∫∫∫dk'/k'2 k'2jθ'cos2iθ δ ((k+k')2-ε2)e-xk'2-yk'2 (α)Numerically for all x, y > 0 and with positive integers i and j is described. Also a power series development in ε and an asymptotic expansion for the case x=y=2 and i = j = 0 are derived. Finally the calculation of (α) is carried out analytically.
Original language | English |
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Publisher | SCK CEN |
Number of pages | 52 |
State | Published - Nov 1969 |
Externally published | Yes |
Publication series
Name | SCK CEN Reports |
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Publisher | SCK CEN |
No. | BLG-439 |