I want to simulate the 2nd order quadrupolar effect. I found out that
when I only use 1st order quadrupolar interaction, the results keep
more or less constant when I change the gamma angles. However, when I
use 2nd order quadrupolar interaction, the results change much when I
change the gamma angles, such as change from 31 to 32.

I don't know why. Could anybody tell me the reasons.



spinsys {
channels 23Na
nuclei 23Na
quadrupole 1 2 1.2e6 0.6 0 0 0
}

par {
spin_rate 8000
variable tsw 0.25
sw 1.0e6/tsw
np 20
crystal_file rep30
gamma_angles 31
start_operator I1z
detect_operator I1p
proton_frequency 400e6
variable rf 80000
variable srf 10000
verbose 1101
use_cluster 1
}

proc pulseq {} {
set DEBUG 0
global par

maxdt 0.5
#matrix set detect elements { {2 1} {4 3} }
matrix set 111 totalcoherence {1 -1}
matrix set 112 totalcoherence {2 -2}
matrix set 113 totalcoherence {0}

set h1 1
set s180 [expr 1.0e6/($par(srf)*2.0)/2.0]
set s90 [expr $s180/2.0]

if {$DEBUG>0} {
puts "s180=$s180"
puts "s90=$s90"
}

reset
for {set i 1} {$i < $par(np)} {incr i 1} {
set h2 [expr $i*$par(tsw)]
reset
pulse $h1 $par(rf) 0
filter 111

delay [expr 1.0e6/$par(spin_rate)-$h1/2.0-$s180/2.0]
pulse $s180 $par(srf) 0
filter 112

delay [expr 1.0e6/$par(spin_rate)-$s180/2.0-$h2/2.0]
pulse $h2 $par(rf) 0
filter 113

delay [expr 1.0e6/$par(spin_rate)-$h2/2.0-$s90/2.0]
pulse $s90 $par(srf) 0
acq
}
}

proc main {} {
global par

fsave [fsimpson] $par(name).fid
}