- Generated on Thu May 16 2024 14:51:07 for Multidip by
1.9.1
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Multidip
1.0
Multi-photon matrix elements
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Routines related to outer region asymptotic channels. More...
Functions/Subroutines | |
| subroutine | test_outer_expansion (filename, moldat, irr, ck, ap, Etot) |
| Evaluate wfn in channels for inside and outside of the R-matrix sphere. More... | |
| subroutine | evaluate_fundamental_solutions (moldat, r, irr, nopen, Ek, S, C, Sp, Cp, sqrtknorm) |
| Evaluate asymptotic solutions at boundary. More... | |
| subroutine | calculate_k_matrix (moldat, nopen, irr, Etot, S, C, Sp, Cp, Kmat) |
| Calculate (generalized) K-matrix. More... | |
Routines related to outer region asymptotic channels.
| subroutine multidip_outer::calculate_k_matrix | ( | type(moleculardata), intent(in) | moldat, |
| integer, intent(in) | nopen, | ||
| integer, intent(in) | irr, | ||
| real(wp), intent(in) | Etot, | ||
| real(wp), dimension(:), intent(in) | S, | ||
| real(wp), dimension(:), intent(in) | C, | ||
| real(wp), dimension(:), intent(in) | Sp, | ||
| real(wp), dimension(:), intent(in) | Cp, | ||
| real(wp), dimension(:, :), intent(inout) | Kmat | ||
| ) |
Calculate (generalized) K-matrix.
Alternative to RSOLVE. Calculates the K-matrix without propagation, simply by projecting the inner wave function on the asymptotic channels. Unlike RSOLVE, though, this subroutine can include the long-range dipole potential. Only permanent dipoles (diagonal couplings) are considered.
First, the R-matrix is calculated from boundary amplitudes and R-matrix poles. Next, the asymptotic standing wave solutions of the asymptotic potential (including monopole and dipole potentials) are evaluated using the subroutine COULCC. Asymptotic radial wave-function for a given partial wave is represented as a linear combination of Coulomb functions with generalized (generally complex) angular momenta that diagonalize the sum of the centrifugal and dipole potentials, neglecting the transition dipoles.
Finally, the generalized K-matrix is obtained by solution of the standard matrix equation
\[ (C - R C') K = R S' - S \,. \]
In this equation the diagonal matrices S and C consist of the regular and irregular solutions of the dipole-coupled outer region asymptotic equations.
| [in] | moldat | Molecular data class. |
| [in] | nopen | Number of open channels. |
| [in] | irr | Irreducible representation index. |
| [in] | Etot | Total energy of the whole system. |
| [in] | S | Value of the regular asymptotic solution per partial wave channel. |
| [in] | C | Value of the irregular asymptotic solution per partial wave channel. |
| [in] | Sp | Derivative of the regular asymptotic solution per partial wave channel. |
| [in] | Cp | Derivative of the irregular asymptotic solution per partial wave channel. |
| [in,out] | Kmat | Kmatrix to calculate. |
Definition at line 199 of file multidip_outer.f90.
| subroutine multidip_outer::evaluate_fundamental_solutions | ( | type(moleculardata), intent(in) | moldat, |
| real(wp), intent(in) | r, | ||
| integer, intent(in) | irr, | ||
| integer, intent(in) | nopen, | ||
| real(wp), dimension(:), intent(in) | Ek, | ||
| real(wp), dimension(:), intent(inout) | S, | ||
| real(wp), dimension(:), intent(inout) | C, | ||
| real(wp), dimension(:), intent(inout) | Sp, | ||
| real(wp), dimension(:), intent(inout) | Cp, | ||
| logical, intent(in), optional | sqrtknorm | ||
| ) |
Evaluate asymptotic solutions at boundary.
Obtain amplitudes and derivatives of the fundamental solutions at region boundary.
The evaluated functions use the same normalization as ASYWFN in cfasym.f. That is, the amplitudes contain an extra factor of 1/sqrt(k) in addition to the standard normalization of Coulomb functions. Similarly, the derivatives contain the same factor of 1/sqrt(k). Because the functions are differentiated with respect to 'r', this 1/sqrt(k) factor combines with the 'k' coming from derivative of the argument, giving sqrt(k) compared to standard normalization of the derivative of the Coulomb functions.
| [in] | moldat | Molecular data class. |
| [in] | r | Evaluation radius. |
| [in] | irr | Irreducible representation index. |
| [in] | nopen | Restrict evaluation of solutions to this number of (open or closed) partial wave channels. |
| [in] | Ek | Photoelectron kinetic energy in each channel. |
| [in,out] | S | Regular solution amplitude per partial wave channel. |
| [in,out] | C | Irregular solution amplitude per partial wave channel. |
| [in,out] | Sp | Regular solution derivative per partial wave channel. |
| [in,out] | Cp | Irregular solution derivative per partial wave channel. |
| [in] | sqrtknorm | Set to .false. to avoid adding the 1/sqrt(k) factor discussed above. |
Definition at line 124 of file multidip_outer.f90.
| subroutine multidip_outer::test_outer_expansion | ( | character(len=*), intent(in) | filename, |
| type(moleculardata), intent(in) | moldat, | ||
| integer, intent(in) | irr, | ||
| real(wp), dimension(:, :), intent(in) | ck, | ||
| real(wp), dimension(:, :), intent(in) | ap, | ||
| real(wp), intent(in) | Etot | ||
| ) |
Evaluate wfn in channels for inside and outside of the R-matrix sphere.
Obtain the single-electron radial wave function amplitudes in channels by projecting the inner wave function at all sampling radii contained in molecular_data. Continue these to twice the R-matrix radius by evaluating the outer expansion in the outer region. The outer expansion assumes only outgoing (or exponentially decaying real) radial functions.
The results are saved into a text file, which has the radial distance in the first column and sampled radial wave-functions in the remaining columns, one per partial wave channel. Every first column gives real part, every second the imaginary part.
| [in] | filename | Name of a text file to write. |
| [in] | moldat | Molecular data class. |
| [in] | irr | Inde xof irreducible representation in molecular_data. |
| [in] | ck | Inner region expansion coefficients (in terms of inner region eigenstates). |
| [in] | ap | Outer region expansion coefficients (in terms of partial wave channel eigenfunctions). |
| [in] | Etot | Total energy of the system. |
Definition at line 54 of file multidip_outer.f90.
1.9.1