state_to_state_cross_sections_mod – the SCATTERING code

This module provides functions and subroutines for calculating and analyzing state-to-state cross-sections. It is divided into three parts:

(1) Calculating cross-sections: Functions for computing state-to-state cross-sections based on quantum states, S-matrix, and scattering parameters ("calculate_state_to_state_cross_section", "compute_individual_cross_section", "get_block_indices", "sum_cross_section_contributions", "compute_real_component", "compute_imag_component") (2) Printing cross-sections: Subroutines to output the largest partial cross-sections, providing both basic and detailed information. ("print_largest_partial_cross_sections", "print_basic_cross_section_info", "print_detailed_cross_section_info") (3) Threshold checking: Subroutine to check if the computed cross-sections meet specified convergence conditions ("check_cross_section_thresholds")

Uses

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Used by

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Graph Key

Nodes of different colours represent the following:

Solid arrows point from a submodule to the (sub)module which it is descended from. Dashed arrows point from a module or program unit to modules which it uses. Where possible, edges connecting nodes are given different colours to make them easier to distinguish in large graphs.

Functions

compute_imag_component compute_individual_cross_section compute_real_component get_block_indices sum_cross_section_contributions

Subroutines

add_cross_sections calculate_state_to_state_cross_section check_cross_section_thresholds determine_largest_cross_sections initialize_cross_section_arrays print_cross_sections_for_jtot print_final_cross_sections print_largest_partial_cross_sections save_partial_xs_file_header save_partial_xs_single_block print_all_cross_sections print_basic_cross_section_info print_detailed_cross_section_info

Functions

private function compute_imag_component(initial_index_, final_index_, s_matrix_imag_) result(imag_contribution_)

Computes the imaginary part of the cross-section contribution for given indices.

Arguments

Type	Intent		Name
integer(kind=int32),	intent(in)	::	initial_index_	index pointing to the basis element involving initial state
integer(kind=int32),	intent(in)	::	final_index_	index pointing to the basis element involving final state
real(kind=dp),	intent(in)	::	s_matrix_imag_(:,:)	imaginary part of the S-matrix

Return Value real(kind=dp)

(output) contribution to the cross-section from imaginary part of the S-matrix

private function compute_individual_cross_section(initial_state_, final_state_, open_basis_levels_, basis_wavevectors_, s_matrix_real_, s_matrix_imag_, channel_indices_, channel_l_values_, total_angular_momentum_) result(cross_section_)

Calculates cross-section for a given initial and final state.

Arguments

Type	Intent		Name
integer(kind=int32),	intent(in)	::	initial_state_	index pointing to the intial state in basis arrays
integer(kind=int32),	intent(in)	::	final_state_	index pointing to the final state in basis arrays
integer(kind=int32),	intent(in)	::	open_basis_levels_(:)	holds indices to the basis arrays which correspond to open channels
real(kind=dp),	intent(in)	::	basis_wavevectors_(:)	holds wavevectors k_{i}
real(kind=dp),	intent(in)	::	s_matrix_real_(:,:)	real and imaginary parts of the S-matrix
real(kind=dp),	intent(in)	::	s_matrix_imag_(:,:)	real and imaginary parts of the S-matrix
integer(kind=int32),	intent(in)	::	channel_indices_(:)	holds the indices pointing to the basis arrays
integer(kind=int32),	intent(in)	::	channel_l_values_(:)	holds all values of l
integer(kind=int32),	intent(in)	::	total_angular_momentum_	total angular momentum

Return Value real(kind=dp)

(output) cross-section

private function compute_real_component(initial_index_, final_index_, l_initial_, l_final_, s_matrix_real_) result(real_contribution_)

Computes the real part of the cross-section contribution for given indices.

Arguments

Type	Intent		Name
integer(kind=int32),	intent(in)	::	initial_index_	index pointing to the basis element involving initial state
integer(kind=int32),	intent(in)	::	final_index_	index pointing to the basis element involving final state
integer(kind=int32),	intent(in)	::	l_initial_	pre-collisional \(l\) value
integer(kind=int32),	intent(in)	::	l_final_	post-collisional \(l\) value
real(kind=dp),	intent(in)	::	s_matrix_real_(:,:)	real part of the S-matrix

Return Value real(kind=dp)

(output) contribution to the cross-section from real part of the S-matrix

private function get_block_indices(v_, j_, channel_indices_) result(block_indices_)

Returns indices from channel_indices_ that match the specified quantum state.

Arguments

Type	Intent		Name
integer(kind=int32),	intent(in)	::	v_	vibrational quantum number
integer(kind=int32),	intent(in)	::	j_	rotational quantum number
integer(kind=int32),	intent(in)	::	channel_indices_(:)	holds the indices pointing to the basis arrays

Return Value integer(kind=int32), allocatable, (:)

(output) indices that match the specified quantum state

private function sum_cross_section_contributions(init_indices_, final_indices_, s_matrix_real_, s_matrix_imag_, channel_l_values_) result(sum_contributions_)

Sum the contributions to the cross-section from S-matrix components

Arguments

Type	Intent		Name
integer(kind=int32),	intent(in)	::	init_indices_(:)	indices pointing to basis element involving initial state
integer(kind=int32),	intent(in)	::	final_indices_(:)	indices pointing to basis element involving final state
real(kind=dp),	intent(in)	::	s_matrix_real_(:,:)	real and imaginary parts of the S-matrix
real(kind=dp),	intent(in)	::	s_matrix_imag_(:,:)	real and imaginary parts of the S-matrix
integer(kind=int32),	intent(in)	::	channel_l_values_(:)	holds all values of l

Return Value real(kind=dp)

(output) contribution to the cross-section from S-matrix components

Subroutines

public subroutine add_cross_sections(size_, partial_, accumulated_)

Add partial cross-sections to accumulated cross-sections

Arguments

Type	Intent		Name
integer(kind=int32),	intent(in)	::	size_	number of open basis levels (defines the size of both arrays)
real(kind=dp),	intent(in)	::	partial_(size_*size_)	array holding partial cross-sections
real(kind=dp),	intent(inout)	::	accumulated_(size_*size_)	array holding accumulated cross-sections

public subroutine calculate_state_to_state_cross_section(total_angular_momentum_, open_basis_levels_, basis_wavevectors_, s_matrix_real_, s_matrix_imag_, channel_indices_, channel_l_values_, cross_section_array_)

Calculates all state-to-state cross-sections.

Arguments

Type	Intent		Name
integer(kind=int32),	intent(in)	::	total_angular_momentum_	total angular momentum
integer(kind=int32),	intent(in)	::	open_basis_levels_(:)	holds indices to the basis arrays which correspond to open channels
real(kind=dp),	intent(in)	::	basis_wavevectors_(:)	holds wavevectors k_{i}
real(kind=dp),	intent(in)	::	s_matrix_real_(:,:)	real and imaginary parts of the S-matrix
real(kind=dp),	intent(in)	::	s_matrix_imag_(:,:)	real and imaginary parts of the S-matrix
integer(kind=int32),	intent(in)	::	channel_indices_(:)	holds the indices pointing to the basis arrays
integer(kind=int32),	intent(in)	::	channel_l_values_(:)	holds all values of l
real(kind=dp),	intent(inout)	::	cross_section_array_(:)	array holding all XSs

public subroutine check_cross_section_thresholds(largest_elastic_xs_, largest_inelastic_xs_, consecutive_elastic_, consecutive_inelastic_, terminate_)

Checks if the elastic_xs_threshold (threshold for elastic XS) and inelastic_xs_threshold (threshold for inelastic XS) conditions are already fulfilled.

Arguments

Type	Intent		Name
real(kind=dp),	intent(in)	::	largest_elastic_xs_	largest elastic XS in the block
real(kind=dp),	intent(in)	::	largest_inelastic_xs_	largest inelastic XS in the block
integer(kind=int32),	intent(inout)	::	consecutive_elastic_	number of consecutive blocks meeting condition on elastic XS
integer(kind=int32),	intent(inout)	::	consecutive_inelastic_	number of consecutive blocks meeting condition on inelastic XS
logical,	intent(inout)	::	terminate_	flag to indicate termination of loop based on thresholds

public subroutine determine_largest_cross_sections(open_basis_levels_, cross_sections_, max_elastic_cross_section_, max_inelastic_cross_section_, max_elastic_index_, max_inelastic_index_1_, max_inelastic_index_2_)

Determine the largest partial elastic and inelastic cross-sections in a given set of cross-sections.

Arguments

Type	Intent		Name
integer(kind=int32),	intent(in)	::	open_basis_levels_(:)	array holding indices to open basis levels
real(kind=dp),	intent(in)	::	cross_sections_(:)	array holding partial cross-sections
real(kind=dp),	intent(out)	::	max_elastic_cross_section_	largest elastic cross-section
real(kind=dp),	intent(out)	::	max_inelastic_cross_section_	largest inelastic cross-section
integer(kind=int32),	intent(out)	::	max_elastic_index_	index pointing to the largest elastic cross-section
integer(kind=int32),	intent(out)	::	max_inelastic_index_1_	first index pointing to the largest inelastic cross-section
integer(kind=int32),	intent(out)	::	max_inelastic_index_2_	second index pointing to the largest inelastic cross-section

public subroutine initialize_cross_section_arrays(size_, partial_block_, partial_jtot_, accumulated_)

allocate arrays keeping accumulated and partial cross-sections in each jtot and parity block

Arguments

Type	Intent	Attributes		Name
integer(kind=int32),	intent(in)		::	size_	number of open basis levels (defines the size of both arrays)
real(kind=dp),	intent(inout),	allocatable	::	partial_block_(:)	array holding partial cross-sections in a parity block
real(kind=dp),	intent(inout),	allocatable	::	partial_jtot_(:)	array holding partial cross-sections in a jtot block
real(kind=dp),	intent(inout),	allocatable	::	accumulated_(:)	array holding accumulated cross-sections

public subroutine print_cross_sections_for_jtot(total_angular_momentum_, open_basis_levels_, cross_sections_)

Prints information about cross-sections at the end of each total angular momentum (jtot) block

Arguments

Type	Intent		Name
integer(kind=int32),	intent(in)	::	total_angular_momentum_	total angular momentum
integer(kind=int32),	intent(in)	::	open_basis_levels_(:)	array holding indices to open basis levels
real(kind=dp),	intent(in)	::	cross_sections_(:)	holds values of the cross-sections

public subroutine print_final_cross_sections(open_basis_levels_, cross_sections_)

Prints information about cross-sections at the end of the program

Arguments

Type	Intent	Optional	Attributes		Name
integer(kind=int32),	intent(in)			::	open_basis_levels_(:)	array holding indices to open basis levels
real(kind=dp),	intent(in)			::	cross_sections_(:)	holds values of the cross-sections

public subroutine print_largest_partial_cross_sections(total_angular_momentum_, largest_elastic_xs_, largest_inelastic_xs_, elastic_index_, inelastic_index_1_, inelastic_index_2_, open_basis_levels_)

Print the largest partial elastic and inelastic state-to-state cross-sections in a given block.

Arguments

Type	Intent		Name
integer(kind=int32),	intent(in)	::	total_angular_momentum_	total angular momentum
real(kind=dp),	intent(in)	::	largest_elastic_xs_	the largest partial elastic state-to-state XS in the block
real(kind=dp),	intent(in)	::	largest_inelastic_xs_	the largest partial inelastic state-to-state XS in the block
integer(kind=int32),	intent(in)	::	elastic_index_	index pointing indirectly to quantum numbers associated with the largest partial elastic state-to-state XS in the block
integer(kind=int32),	intent(in)	::	inelastic_index_1_	indices pointing indirectly to quantum numbers associated with the largest partial inelastic state-to-state XS in the block
integer(kind=int32),	intent(in)	::	inelastic_index_2_	indices pointing indirectly to quantum numbers associated with the largest partial inelastic state-to-state XS in the block
integer(kind=int32),	intent(in)	::	open_basis_levels_(:)	array holding indices to open basis levels

public subroutine save_partial_xs_file_header()

save "header" of the partial cross-sections file: -- label, "itype", number of levels in the basis, reduced mass of the system -- vibrational and rotational quantum numbers -- rovibrational energies -- index pointing to the initial level and the kinetic/total energy

Arguments

None

public subroutine save_partial_xs_single_block(jtot_, block_number_, open_basis_levels_, xs_block)

Arguments

Type	Intent		Name
integer(kind=int32),	intent(in)	::	jtot_
integer(kind=int32),	intent(in)	::	block_number_
integer(kind=int32),	intent(in)	::	open_basis_levels_(:)
real(kind=dp),	intent(in)	::	xs_block(:)

private subroutine print_all_cross_sections(open_basis_levels_, cross_sections_)

Prints information about cross-sections from provided "cross_sections_" array

Arguments

Type	Intent	Optional	Attributes		Name
integer(kind=int32),	intent(in)			::	open_basis_levels_(:)	array holding indices to open basis levels
real(kind=dp),	intent(in)			::	cross_sections_(:)	holds values of the cross-sections

private subroutine print_basic_cross_section_info(total_angular_momentum_, cross_section_value_, type_label_)

Prints basic information about the largest elastic and inelastic state-to-state xs (print_level <= 2)

Arguments

Type	Intent		Name
integer(kind=int32),	intent(in)	::	total_angular_momentum_	total angular momentum
real(kind=dp),	intent(in)	::	cross_section_value_	value of the cross-section
character(len=*),	intent(in)	::	type_label_	"elastic" or "inelastic"

private subroutine print_detailed_cross_section_info(total_angular_momentum_, cross_section_value_, index_1_, index_2_, open_basis_levels_, type_label_)

Prints detailed information about the largest elastic and inelastic state-to-state xs (print_level >= 3)

Arguments

Type	Intent		Name
integer(kind=int32),	intent(in)	::	total_angular_momentum_	total angular momentum
real(kind=dp),	intent(in)	::	cross_section_value_	value of the cross-section
integer(kind=int32),	intent(in)	::	index_1_	indices pointing indirectly to quantum numbers associated with the largest partial XS in the block
integer(kind=int32),	intent(in)	::	index_2_	indices pointing indirectly to quantum numbers associated with the largest partial XS in the block
integer(kind=int32),	intent(in)	::	open_basis_levels_(:)	array holding indices to open basis levels
character(len=*),	intent(in)	::	type_label_	"elastic" or "inelastic"

state_to_state_cross_sections_mod Module

Contents

Functions

Subroutines

Uses

Used by

Contents

Functions

Subroutines

Functions

private function compute_imag_component(initial_index_, final_index_, s_matrix_imag_) result(imag_contribution_)

Arguments

Return Value real(kind=dp)

private function compute_individual_cross_section(initial_state_, final_state_, open_basis_levels_, basis_wavevectors_, s_matrix_real_, s_matrix_imag_, channel_indices_, channel_l_values_, total_angular_momentum_) result(cross_section_)

Arguments

Return Value real(kind=dp)

private function compute_real_component(initial_index_, final_index_, l_initial_, l_final_, s_matrix_real_) result(real_contribution_)

Arguments

Return Value real(kind=dp)

private function get_block_indices(v_, j_, channel_indices_) result(block_indices_)

Arguments

Return Value integer(kind=int32), allocatable, (:)

private function sum_cross_section_contributions(init_indices_, final_indices_, s_matrix_real_, s_matrix_imag_, channel_l_values_) result(sum_contributions_)

Arguments

Return Value real(kind=dp)

Subroutines

public subroutine add_cross_sections(size_, partial_, accumulated_)

Arguments

public subroutine calculate_state_to_state_cross_section(total_angular_momentum_, open_basis_levels_, basis_wavevectors_, s_matrix_real_, s_matrix_imag_, channel_indices_, channel_l_values_, cross_section_array_)

Arguments

public subroutine check_cross_section_thresholds(largest_elastic_xs_, largest_inelastic_xs_, consecutive_elastic_, consecutive_inelastic_, terminate_)

Arguments

public subroutine determine_largest_cross_sections(open_basis_levels_, cross_sections_, max_elastic_cross_section_, max_inelastic_cross_section_, max_elastic_index_, max_inelastic_index_1_, max_inelastic_index_2_)

Arguments

public subroutine initialize_cross_section_arrays(size_, partial_block_, partial_jtot_, accumulated_)

Arguments

public subroutine print_cross_sections_for_jtot(total_angular_momentum_, open_basis_levels_, cross_sections_)

Arguments

public subroutine print_final_cross_sections(open_basis_levels_, cross_sections_)

Arguments

public subroutine print_largest_partial_cross_sections(total_angular_momentum_, largest_elastic_xs_, largest_inelastic_xs_, elastic_index_, inelastic_index_1_, inelastic_index_2_, open_basis_levels_)

Arguments

public subroutine save_partial_xs_file_header()

Arguments

public subroutine save_partial_xs_single_block(jtot_, block_number_, open_basis_levels_, xs_block)

Arguments

private subroutine print_all_cross_sections(open_basis_levels_, cross_sections_)

Arguments

private subroutine print_basic_cross_section_info(total_angular_momentum_, cross_section_value_, type_label_)

Arguments

private subroutine print_detailed_cross_section_info(total_angular_momentum_, cross_section_value_, index_1_, index_2_, open_basis_levels_, type_label_)

Arguments