Title:
Tutorial example - exterior complex scaling
The purpose of this exercise is to
(1) get introduced to exerior complex scaling
(2) have a look at the scaled spectrum
[TASK] plot real vs. imaginary part of eigen energies (file 05irECS/00xx/eig)
for various theta and R0, observe the changes
# piece-wise specification of discretization with exponential tails at both ends
Axis: name,nCoefficients,lower end, upper end,functions,order
X,20,-Infty,-20,polExp[0.5]
X,15,-20,-15,polynomial,15
X,60,-15, 15,polynomial,10
X,15, 15, 20,polynomial,15
X,20, 20, Infty,polExp[0.5]
# define exterior complex scaling
# theta ...scaling radius
# upper ...the place R0 where scaling starts
Absorption: kind, axis, theta, upper
ECS,X,0.3,10.
# NOTE: upper (=R0) MUST coincide with an element boudary (ANY of the boundaries)
!!! otherwise it is mathematically wrong and fails numerically !!!
for this reason, the code stops with an error in this case
# NOTE: with a double-sided axis like X,
by default scaling at the lower radius -R0 is assumed
Operator: hamiltonian='0.5-<1/sqrt(Q*Q+2)>'
# NOTE: we do not use truncation,
i.e. the complete operator is complex scaled,
not only the potential or kinetic energy alone
# we will print the lowest eigenvalues and stop
Eigen: select=SmallReal[10]