Quantities defined in X_s.F

[hplan]

Dear Developers:
My question is still about the response function programmed in TDDFT module of yambo.
I looked through two subroutines :O_driver.F and X_s.F, and have a confusion about quantities defined in X_s.F . Would you please do me a favor for this issue ?

I learned from X_s.F that it solves Dyson equation for $\chi$ from $\chi_0$ which is stored in X_mat. My confusion is about the last description for $\chi$:

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 X_mat(i1,i2,iw)=X_mat(i1,i2,iw)*4.*pi/bare_qpg(iq,i1)/bare_qpg(iq,i2)

As far as i know, the solution for Dyson equation should be
$\chi=(1-\chi_0\upsilon-\chi_0 f_{xc})^{-1}\chi_0$.
My question is why we need multiply a quantity like Coulomb potential

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4.*pi/bare_qpg(iq,i1)/bare_qpg(iq,i2)

for X_mat ? In this situation, does X_mat store the exact information for the response function $\chi$ ? Or other attentions need pay to ?
In O_driver.F , I found the expression the $\epsilion_M$

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X_epsilon(2,fr(1):fr(2))=1./(X_mat(1,1,:)*bare_qpg(iq,1)**2/Q_sq_modulus+1.)

exactly follows the formula $\epilsion_M=1/(1+\upsilon\chi)$ . Therefore, in X_s.F why we perform a more calculation over X_mat as

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 X_mat(i1,i2,iw)=X_mat(i1,i2,iw)*4.*pi/bare_qpg(iq,i1)/bare_qpg(iq,i2)

Thanks in advance!
Regards,
Hai-Ping

[myrta gruning]

Dear Hai-Ping,

The output of X_s, X_mat, is Chi(q,G,G') (from the solution of the Dyson equation) multiplied by 4\pi/[(q+G)(q+G')].

This quantity corresponds to a "symmetrized" inverse microscopic dielectric function \epsilon^{-1}.
I am not sure (Andrea can confirm/correct this), but I think the reason is that this quantity can be directly/conveniently used in several expressions involving the microscopic dielectric function (e.g. for the evaluation of the mass operator).

Regards,

Myrta

[andrea marini]

I think the reason is that this quantity can be directly/conveniently used in several expressions involving the microscopic dielectric function (e.g. for the evaluation of the mass operator).

You're right. The symmetrized expression is used in the evaluation of the mass operator and of the Bethe-Salpeter kernel.