Thank you so much dear Caterina for answering
1. My first question was surmounted with your help.
2. My mean of the second problem is:
EPSILON_XXX.OUT of "BSE-singlet" shows some excitonic features below the band gap. But with a shifting equal to the difference between the first peak in "RPA" and the first one in "BSE", my "BSE" and "RPA" spectra were graphically very similar and coincided. Not only for MgTe, but also for more organic and inorganic cases that I tested.
I understand that for some cases it is reasonable (for example in Anthracene, as pointed in C. Hummer et al work), but not for all structures.
For a better conclusion, I have brought my input files:
input file of MgTe for "BSE-singlet":
<input>
<title>MgTe_BSE_Singlet</title>
<structure speciespath="/opt/exciting/species" autormt="false">
<crystal scale="12.3153454079">
<basevect>0.0 0.5 0.5</basevect>
<basevect>0.5 0.0 0.5</basevect>
<basevect>0.5 0.5 0.0</basevect>
</crystal>
<species speciesfile="Mg.xml" rmt="2.2">
<atom coord="0.00 0.00 0.00"/>
</species>
<species speciesfile="Te.xml" rmt="2.0">
<atom coord="0.50 0.50 0.50"/>
</species>
</structure>
<groundstate
rgkmax="8"
gmaxvr="14"
xctype="GGA_PBE"
nempty="30"
ngridk="10 10 10"
maxscl="300">
</groundstate>
<xs xstype="BSE"
rgkmax="7"
ngridq="4 4 4"
ngridk="4 4 4"
vkloff="0.05 0.097 0.14"
nempty="100"
lmaxapwwf="3"
gqmax="2.7"
broad="0.003674933"
tevout="true" nosym="true">
<energywindow intv="0.0 2.0"
points="2400" />
<screening screentype="full"
nempty="120" />
<BSE bsetype="singlet"
nstlbsemat="1 13 1 16"
nstlbse="1 13 1 16"
aresbse="false"/>
<qpointset>
<qpoint>0.0 0.0 0.0</qpoint>
</qpointset>
</xs>
</input>
and input file of MgTe for "RPA":
<input>
<title>MgTe_Indipendent_Particle_Approximation</title>
<structure speciespath="/opt/exciting/species" autormt="false">
<crystal scale="12.3153454079">
<basevect>0.0 0.5 0.5</basevect>
<basevect>0.5 0.0 0.5</basevect>
<basevect>0.5 0.5 0.0</basevect>
</crystal>
<species speciesfile="Mg.xml" rmt="2.2">
<atom coord="0.00 0.00 0.00"/>
</species>
<species speciesfile="Te.xml" rmt="2.0">
<atom coord="0.50 0.50 0.50"/>
</species>
</structure>
<groundstate
rgkmax="8"
gmaxvr="14"
xctype="GGA_PBE"
nempty="30"
ngridk="10 10 10"
maxscl="300">
</groundstate>
<xs xstype="BSE"
rgkmax="7"
ngridq="4 4 4"
ngridk="4 4 4"
vkloff="0.05 0.097 0.14"
nempty="100"
lmaxapwwf="3"
gqmax="0.0"
broad="0.003674933"
tevout="true" nosym="true">
<energywindow intv="0.0 2.0"
points="2400" />
<screening screentype="full"
nempty="120" />
<BSE bsetype="IP"
nstlbsemat="1 13 1 16"
nstlbse="1 13 1 16"
aresbse="false"/>
<qpointset>
<qpoint>0.0 0.0 0.0</qpoint>
</qpointset>
</xs>
</input>