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Functions
void	hex_initialize_ (const char *dbname)
	Initialize the environment. More...

void	hex_initialize (const char *dbname)

void	hex_new_ ()
	Create new database. More...

void	hex_new ()

void	hex_import_ (const char *sqlname)
	Import SQL batch file. More...

void	hex_import (const char *sqlname)

void	hex_update_ ()
	Update integral and complete cross section. More...

void	hex_update ()

void	hex_optimize_ ()
	Optimize the SQLite database file. More...

void	hex_optimize ()

void	hex_dump_ (const char *dumpname)
	Dump contents of the T-matrix table. More...

void	hex_dump (const char *dumpname)

void	hex_scattering_amplitude_ (int ni, int li, int mi, int nf, int lf, int mf, int S, int nEnergies, double energies, int nAngles, double angles, double result, double *extra)
	Scattering anplitude (Fortran). More...

void	hex_scattering_amplitude (int ni, int li, int mi, int nf, int lf, int mf, int S, int nEnergies, double energies, int nAngles, double angles, double result, double extra)
	Scattering anplitude (C). More...

void	hex_scattering_amplitude_dir_ (int ni, int li, int mi, int nf, int lf, int mf, int S, double E, int N, double alpha, double beta, double gamma, double angles, double result)
	Scattering anplitude for non-aligned impact direction (Fortran). More...

void	hex_scattering_amplitude_dir (int ni, int li, int mi, int nf, int lf, int mf, int S, double E, int N, double alpha, double beta, double gamma, double angles, double result)
	Scattering anplitude for non-aligned impact direction (C). More...

void	hex_differential_cross_section_ (int ni, int li, int mi, int nf, int lf, int mf, int S, int nEnergies, double energies, int nAngles, double angles, double dcs, double *extra)
	Differential cross section (Fortran). More...

void	hex_differential_cross_section (int ni, int li, int mi, int nf, int lf, int mf, int S, int nEnergies, double energies, int nAngles, double angles, double dcs, double extra)
	Differential cross section (C). More...

void	hex_complete_cross_section_ (int ni, int li, int mi, int nf, int lf, int mf, int N, double energies, double ccs, int Nall, int npws, int pws)
	Complete cross section (Fortran). More...

void	hex_complete_cross_section (int ni, int li, int mi, int nf, int lf, int mf, int N, double energies, double ccs, int Nall, int npws, int pws)
	Complete cross section (C). More...

Function Documentation

◆ hex_complete_cross_section()

void hex_complete_cross_section	(	int	ni,
		int	li,
		int	mi,
		int	nf,
		int	lf,
		int	mf,
		int	N,
		double *	energies,
		double *	ccs,
		int *	Nall,
		int	npws,
		int *	pws
	)

C prototype.

Parameters

ni	Initial atomic principal quantum number.
li	Initial atomic orbital quantum number.
mi	Initial atomic magnetic quantum number.
nf	Final atomic principal quantum number.
lf	Final atomic orbital quantum number.
mf	Final atomic magnetic quantum number.
N	Sample count.
energies	Real array of impact energies in Rydbergs.
ccs	Real array of length N to contain the cross sections.
Nall	Number of energies available in database; will be set if `ccs` is set to null pointer.
pws	List of requested partial waves (or null pointer for all).
npws	Size of `pws`.

◆ hex_complete_cross_section_()

void hex_complete_cross_section_	(	int *	ni,
		int *	li,
		int *	mi,
		int *	nf,
		int *	lf,
		int *	mf,
		int *	N,
		double *	energies,
		double *	ccs,
		int *	Nall,
		int *	npws,
		int *	pws
	)

Fortran prototype equivalent to

subroutine complete_cross_section (ni,li,mi,nf,lf,mf,N,energies,ccs,Nall)
  integer, intent(in)  :: ni,li,mi
  integer, intent(in)  :: nf,lf,mf
  integer, intent(in)  :: n
  double precision, dimension(N)   :: energies
  double precision, dimension(2*N) :: ccs
  integer, intent(out) :: nall

Parameters

ni	Initial atomic principal quantum number.
li	Initial atomic orbital quantum number.
mi	Initial atomic magnetic quantum number.
nf	Final atomic principal quantum number.
lf	Final atomic orbital quantum number.
mf	Final atomic magnetic quantum number.
N	Sample count.
energies	Real array of impact energies in Rydbergs.
ccs	Real array of length N to contain the cross sections.
Nall	Number of energies available in database; will be set if `ccs` is set to null pointer.
pws	List of requested partial waves (or null pointer for all).
npws	Size of `pws`.

◆ hex_differential_cross_section()

void hex_differential_cross_section	(	int	ni,
		int	li,
		int	mi,
		int	nf,
		int	lf,
		int	mf,
		int	S,
		int	nEnergies,
		double *	energies,
		int	nAngles,
		double *	angles,
		double *	dcs,
		double *	extra
	)

C prototype.

Parameters

ni	Initial atomic principal quantum number.
li	Initial atomic orbital quantum number.
mi	Initial atomic magnetic quantum number.
nf	Final atomic principal quantum number.
lf	Final atomic orbital quantum number.
mf	Final atomic magnetic quantum number.
S	Total spin (0 = singlet, 1 = triplet).
E	Impact energy in Rydbergs.
N	Sample count.
angles	Real array of length N containing scattering angles.
dcs	Real array of length N to contain the cross sections.

◆ hex_differential_cross_section_()

void hex_differential_cross_section_	(	int *	ni,
		int *	li,
		int *	mi,
		int *	nf,
		int *	lf,
		int *	mf,
		int *	S,
		int *	nEnergies,
		double *	energies,
		int *	nAngles,
		double *	angles,
		double *	dcs,
		double *	extra
	)

Fortran prototype equivalent to

subroutine hex_differential_cross_section (ni,li,mi,nf,lf,mf,S,E,N,angles,dcs)
  integer, intent(in)  :: ni,li,mi
  integer, intent(in)  :: nf,lf,mf
  integer, intent(in)  :: s,n
  double precision, intent(in)     :: e
  double precision, dimension(N)   :: angles
  double precision, dimension(2*N) :: dcs

Parameters

ni	Initial atomic principal quantum number.
li	Initial atomic orbital quantum number.
mi	Initial atomic magnetic quantum number.
nf	Final atomic principal quantum number.
lf	Final atomic orbital quantum number.
mf	Final atomic magnetic quantum number.
S	Total spin (0 = singlet, 1 = triplet).
E	Impact energy in Rydbergs.
N	Sample count.
angles	Real array of length N containing scattering angles.
dcs	Real array of length N to contain the cross sections.

◆ hex_dump()

void hex_dump ( const char * dumpname )

◆ hex_dump_()

void hex_dump_ ( const char * dumpname )

The output can be used to construct an equivalent table. The corresponding code is

sqlite> .mode insert

sqlite> select * from tmat

◆ hex_import()

void hex_import ( const char * sqlname )

◆ hex_import_()

void hex_import_ ( const char * sqlname )

The effect of this function should be equivalent to direct use of sqlite3 program:

sqlite3 hex.db < batchfile.sql

The function uses one line at a time and splits the lines into statements on semicolons. For this reason it does not allow multi-line statements. The statements produced by computational modules have always one statement per line.

Parameters

sqlname Zero-terminated character string.

◆ hex_initialize()

void hex_initialize ( const char * dbname )

◆ hex_initialize_()

void hex_initialize_ ( const char * dbname )

The function will open existing database with path specified in "dbname". If the database does not exist, a new empty database will be created. Also, all registered variables will be given chance to initialize by the function

Variable::initialize (sqlitepp::session & db)

This can be used to register special functions needed later in the SQL statements. For example the variable IntegralCrossSection registeres two functions: the simple square root and a more complicated numerical integrator that uses ClenshawCurtis quadrature.

The function "initialize" also disables journalling to speed up insertion of data.

Parameters

dbname Zero-terminated character string.

◆ hex_new()

void hex_new ( )

◆ hex_new_()

void hex_new_ ( )

This will create the necessary table structure in a new empty database. It is necessary to call initialize first, so that the databse file is created and opened. The tables are created by the call to

Variable::SQL_CreateTable();

for every registered variable. The return value is a vector of SQL statement which are executed.

◆ hex_optimize()

void hex_optimize ( )

◆ hex_optimize_()

void hex_optimize_ ( )

Reduces the occupied space using the VACUUM statement.

◆ hex_scattering_amplitude()

void hex_scattering_amplitude	(	int	ni,
		int	li,
		int	mi,
		int	nf,
		int	lf,
		int	mf,
		int	S,
		int	nEnergies,
		double *	energies,
		int	nAngles,
		double *	angles,
		double *	result,
		double *	extra
	)

C prototype.

Parameters

ni	Initial atomic principal quantum number.
li	Initial atomic orbital quantum number.
mi	Initial atomic magnetic quantum number.
nf	Final atomic principal quantum number.
lf	Final atomic orbital quantum number.
mf	Final atomic magnetic quantum number.
S	Total spin (0 = singlet, 1 = triplet).
nEnergies	Number of supplied impact energies.
energies	Real array of length `nEnergies` containing impact energies in Rydbergs.
nAngles	Number of supplied angles.
angles	Real array of length `nAngles` containing scattering angles.
result	Complex array of length `nEnergies*nAngles` (or real array of twice that length) to contain the amplitudes.
extra	Extrapolated result (w.r.t. partial waves); optional - can be set to zero.

◆ hex_scattering_amplitude_()

void hex_scattering_amplitude_	(	int *	ni,
		int *	li,
		int *	mi,
		int *	nf,
		int *	lf,
		int *	mf,
		int *	S,
		int *	nEnergies,
		double *	energies,
		int *	nAngles,
		double *	angles,
		double *	result,
		double *	extra
	)

Fortran prototype equivalent to

subroutine scattering_amplitude (ni,li,mi,nf,lf,mf,S,E,N,angles,result)
  integer, intent(in) :: ni,li,mi
  integer, intent(in) :: nf,lf,mf
  integer, intent(int) :: s,n
  double precision, intent(in)     :: e
  double precision, dimension(N)   :: angles
  double precision, dimension(2*N) :: result

Parameters

ni	Initial atomic principal quantum number.
li	Initial atomic orbital quantum number.
mi	Initial atomic magnetic quantum number.
nf	Final atomic principal quantum number.
lf	Final atomic orbital quantum number.
mf	Final atomic magnetic quantum number.
S	Total spin (0 = singlet, 1 = triplet).
nEnergies	Number of supplied impact energies.
energies	Real array of length `nEnergies` containing impact energies in Rydbergs.
nAngles	Number of supplied angles.
angles	Real array of length `nAngles` containing scattering angles.
result	Complex array of length `nEnergies*nAngles` (or real array of twice that length) to contain the amplitudes.
extra	Extrapolated result (w.r.t. partial waves); optional - can be set to zero.

◆ hex_scattering_amplitude_dir()

void hex_scattering_amplitude_dir	(	int	ni,
		int	li,
		int	mi,
		int	nf,
		int	lf,
		int	mf,
		int	S,
		double	E,
		int	N,
		double	alpha,
		double	beta,
		double	gamma,
		double *	angles,
		double *	result
	)

C prototype.

See hex_scattering_amplitude_dir_ for theory.

Parameters

ni	Initial atomic principal quantum number.
li	Initial atomic orbital quantum number.
mi	Initial atomic magnetic quantum number.
nf	Final atomic principal quantum number.
lf	Final atomic orbital quantum number.
mf	Final atomic magnetic quantum number.
S	Total spin (0 = singlet, 1 = triplet).
E	Impact energy in Rydbergs.
N	Sample count.
alpha	Impact angle (first of Euler angles).
beta	Impact angle (second of Euler angles).
gamma	Impact angle (third of Euler angles).
angles	Real array of length N containing scattering angles.
result	Complex array of length N (or real array of length 2N) to contain the amplitudes.

◆ hex_scattering_amplitude_dir_()

void hex_scattering_amplitude_dir_	(	int *	ni,
		int *	li,
		int *	mi,
		int *	nf,
		int *	lf,
		int *	mf,
		int *	S,
		double *	E,
		int *	N,
		double *	alpha,
		double *	beta,
		double *	gamma,
		double *	angles,
		double *	result
	)

This function will evaluate the scattering amplitude when the projectile is coming in a direction different from the quantization axis, i.e. when

\[ \mathbf{k}_i \neq (0, 0, k_i) \,. \]

In that case the of the scattering amplitude can be computed using Wigner d-function and all possible amplitudes from scattering between various magnetic levels. The reason for this is that such situation is equivalent to a change of the quantization axis by the same amount. To be precise, it is

\[ T_{n_f l_f m_f \leftarrow n_i l_i m_i} = \sum_{m_i' m_f'} D_{m_i' m_i}^{l_i} D_{m_f' m_f}^{l_f \ast} T_{n_f l_f m_f' \leftarrow n_i l_i m_i'} \,. \]

Fortran prototype equivalent to

subroutine scattering_amplitude (ni,li,mi,nf,lf,mf,S,E,N,angles,result)
  integer, intent(in) :: ni,li,mi
  integer, intent(in) :: nf,lf,mf
  integer, intent(int) :: s,n
  double precision, intent(in)     :: e
  double precision, dimension(N)   :: angles
  double precision, dimension(2*N) :: result

Parameters

ni	Initial atomic principal quantum number.
li	Initial atomic orbital quantum number.
mi	Initial atomic magnetic quantum number.
nf	Final atomic principal quantum number.
lf	Final atomic orbital quantum number.
mf	Final atomic magnetic quantum number.
S	Total spin (0 = singlet, 1 = triplet).
E	Impact energy in Rydbergs.
N	Sample count.
alpha	Impact angle (first of Euler angles).
beta	Impact angle (second of Euler angles).
gamma	Impact angle (third of Euler angles).
angles	Real array of length N containing scattering angles.
result	Complex array of length N (or real array of length 2N) to contain the amplitudes.

◆ hex_update()

void hex_update ( )

◆ hex_update_()

void hex_update_ ( )

This function is used after import of T-matrices. All variables will be given chance to update themselves using the function

Variable::SQL_Update();

which returns SQL statement that should do the update. If a variable uses other variables besides T-matrices for its update, it must be inserted to VariableList AFTER those variables, because the order of update is set by the order in the list.

Functions

Function Documentation

◆ hex_complete_cross_section()

◆ hex_complete_cross_section_()

◆ hex_differential_cross_section()

◆ hex_differential_cross_section_()

◆ hex_dump()

◆ hex_dump_()

◆ hex_import()

◆ hex_import_()

◆ hex_initialize()

◆ hex_initialize_()

◆ hex_new()

◆ hex_new_()

◆ hex_optimize()

◆ hex_optimize_()

◆ hex_scattering_amplitude()

◆ hex_scattering_amplitude_()

◆ hex_scattering_amplitude_dir()

◆ hex_scattering_amplitude_dir_()

◆ hex_update()

◆ hex_update_()