wigner_functions.cc File Reference

Wigner symbol interactions. More...

#include "constants.h"
#include "wigner_functions.h"
#include <algorithm>
#include "arts_omp.h"

Go to the source code of this file.

Classes
struct	Wigner3JTriangleLimit

Macros
#define	WIGNER3   wig3jj
#define	WIGNER6   wig6jj

Functions
Numeric	wigner3j (const Rational j1, const Rational j2, const Rational j3, const Rational m1, const Rational m2, const Rational m3)
	Wigner 3J symbol. More...
Numeric	wigner6j (const Rational j1, const Rational j2, const Rational j3, const Rational l1, const Rational l2, const Rational l3)
	Wigner 6J symbol. More...
Numeric	co2_ecs_wigner_symbol (int Ji, int Jf, int Ji_p, int Jf_p, int L, int li, int lf)
	Returns the wigner symbol used in Niro etal 2004. More...
Numeric	o2_ecs_wigner_symbol (int Nl, int Nk, int Jl, int Jk, int Jl_p, int Jk_p, int L)
	Returns the wigner symbol used in Makarov etal 2013. More...
constexpr Wigner3JTriangleLimit	find_wigner3j_limits (const Rational L1, const Rational L2)
	Finds the upper and lower limits of L3 given a Wigner-3J symbol: More...
constexpr Wigner3JTriangleLimit	find_even_limits (const Wigner3JTriangleLimit lim1, const Wigner3JTriangleLimit lim2)
	Combines two limits and return the highest even-numbered low value and the lowest numbered even high value. More...
Numeric	o2_ecs_erot_jn_same (Rational J)
	Energy of the J=N line at J. More...
Numeric	o2_ecs_ql_makarov (Rational L, Numeric T)
Numeric	o2_ecs_adiabatic_factor_makarov (Rational N, Numeric T)
Numeric	o2_ecs_wigner_symbol_tran (const Rational &Ji, const Rational &Jf, const Rational &Ni, const Rational &Nf, const Rational &Si, const Rational &Sf, const Rational &Ji_p, const Rational &Jf_p, const Rational &Ni_p, const Rational &Nf_p, const Rational &n, const Numeric &T)
	Returns the wigner symbol used in Tran etal 2006. More...
Numeric	o2_makarov2013_reduced_dipole (const Rational &Jup, const Rational &Jlo, const Rational &N)
	Returns the reduced dipole moment following Makarov etal 2013. More...
Index	make_wigner_ready (int largest, [[maybe_unused]] int fastest, int size)
bool	is_wigner_ready (int j)
	Tells if the function can deal with the input integer. More...
bool	is_wigner3_ready (const Rational &J)
	Tells if the function is ready for Wigner 3J calculations. More...
bool	is_wigner6_ready (const Rational &J)
	Tells if the function is ready for Wigner 6J calculations. More...

Detailed Description

Wigner symbol interactions.

Author

Richard Larsson

Date

2013-06-19

Definition in file wigner_functions.cc.

Macro Definition Documentation

WIGNER3

#define WIGNER3   wig3jj

Definition at line 36 of file wigner_functions.cc.

Referenced by co2_ecs_wigner_symbol(), o2_ecs_wigner_symbol(), and o2_ecs_wigner_symbol_tran().

WIGNER6

#define WIGNER6   wig6jj

Definition at line 37 of file wigner_functions.cc.

Referenced by co2_ecs_wigner_symbol(), o2_ecs_wigner_symbol(), and o2_makarov2013_reduced_dipole().

Function Documentation

co2_ecs_wigner_symbol()

Numeric co2_ecs_wigner_symbol	(	int	Ji,
		int	Jf,
		int	Ji_p,
		int	Jf_p,
		int	L,
		int	li,
		int	lf
	)

Returns the wigner symbol used in Niro etal 2004.

Symbol: / \ / \ / \ | Ji_p L Ji | | Jf_p L Jf | | Ji Jf 1 | | | | | < > (2L + 1) | li 0 -li | | -lf 0 lf | | Jf_p Ji_p L | \ / \ / \ /

Note: The wigner library takes two times the physical values so, e.g., the 1 must be 2. This hold true for all user inputs as well!

Reference: Spectra calculations in central and wing regions of CO2 IR bands between 10 and 20 mcrons. I: model and laboratory measurements. F. Niro, C. Boulet, J.-M. Hartmann. JQSRT 88 (2004) 483 – 498. Equation 4 page 488.

Note: Ignore typos, the above is tested in relmat

Warning: Must have called wig_temp_init(j) with appropriate j before using this function. Failure to do so will cause segfault.

Parameters

[in]	Ji	as above times 2
[in]	Jf	as above times 2
[in]	Ji_p	as above times 2
[in]	Jf_p	as above times 2
[in]	L	as above times 2
[in]	li	as above times 2
[in]	lf	as above times 2

Returns

Numeric Symbol value

Definition at line 88 of file wigner_functions.cc.

References WIGNER3, and WIGNER6.

find_even_limits()

constexpr Wigner3JTriangleLimit find_even_limits	(	const Wigner3JTriangleLimit	lim1,
		const Wigner3JTriangleLimit	lim2
	)

Combines two limits and return the highest even-numbered low value and the lowest numbered even high value.

Parameters

[in]	lim1	Limit 1
[in]	lim2	Limit 2

Returns

More limited limit

Definition at line 136 of file wigner_functions.cc.

References Wigner3JTriangleLimit::lower, and Wigner3JTriangleLimit::upper.

Referenced by o2_ecs_wigner_symbol_tran().

find_wigner3j_limits()

constexpr Wigner3JTriangleLimit find_wigner3j_limits	(	const Rational	L1,
		const Rational	L2
	)

Finds the upper and lower limits of L3 given a Wigner-3J symbol:

/ \

L1 L2 L3
M1 M2 M3

\ /

Based on abs(L1-L2) <= L3 <= L1+L2, where L1 and L2 are positives

Parameters

[in]	L1	As in Wigner symbol
[in]	L2	As in Wigner symbol

Returns

The limits

Definition at line 122 of file wigner_functions.cc.

References abs.

Referenced by o2_ecs_wigner_symbol_tran().

is_wigner3_ready()

bool is_wigner3_ready

(

const Rational &

J

)

Tells if the function is ready for Wigner 3J calculations.

Parameters

[in]

J

Largest input into a Wigner 3J function call

Returns

true If is_wigner_ready(3J + 1) does

false Otherwise

Definition at line 319 of file wigner_functions.cc.

References is_wigner_ready(), and Rational::toInt().

is_wigner6_ready()

bool is_wigner6_ready

(

const Rational &

J

)

Tells if the function is ready for Wigner 6J calculations.

Parameters

[in]

J

Largest input into a Wigner 6J function call

Returns

true If is_wigner_ready(4J + 1)

false Otherwise

Definition at line 325 of file wigner_functions.cc.

References is_wigner_ready(), and Rational::toInt().

is_wigner_ready()

bool is_wigner_ready

(

int

j

)

Tells if the function can deal with the input integer.

Parameters

[in]

j

Returns

true If j is less than max allowed j

false Otherwise

Definition at line 313 of file wigner_functions.cc.

Referenced by is_wigner3_ready(), and is_wigner6_ready().

make_wigner_ready()

Index make_wigner_ready	(	int	largest,
		[[maybe_unused] ] int	fastest,
		int	size
	)

Definition at line 276 of file wigner_functions.cc.

Referenced by test_ecs20(), test_hitran2017(), Wigner3Init(), and Wigner6Init().

o2_ecs_adiabatic_factor_makarov()

Numeric o2_ecs_adiabatic_factor_makarov	(	Rational	N,
		Numeric	T
	)

Definition at line 196 of file wigner_functions.cc.

References Conversion::angstrom2meter(), o2_ecs_erot_jn_same(), and Constant::pow2().

Referenced by o2_ecs_wigner_symbol_tran().

o2_ecs_erot_jn_same()

Numeric o2_ecs_erot_jn_same

(

Rational

J

)

Energy of the J=N line at J.

Parameters

[in]

J

Rotational quantum number

Returns

O2 energy at this level

Definition at line 159 of file wigner_functions.cc.

References Constant::pow2(), and Constant::pow3().

Referenced by o2_ecs_adiabatic_factor_makarov(), and o2_ecs_ql_makarov().

o2_ecs_ql_makarov()

Numeric o2_ecs_ql_makarov	(	Rational	L,
		Numeric	T
	)

Definition at line 183 of file wigner_functions.cc.

References beta, o2_ecs_erot_jn_same(), and pow().

Referenced by o2_ecs_wigner_symbol_tran().

o2_ecs_wigner_symbol()

Numeric o2_ecs_wigner_symbol	(	int	Nl,
		int	Nk,
		int	Jl,
		int	Jk,
		int	Jl_p,
		int	Jk_p,
		int	L
	)

Returns the wigner symbol used in Makarov etal 2013.

Symbol: / \ / \ / \ / \ | Nl Nk L | | L Jk Jl | | L Jk_p Jl_p | | L Jk Jl | | | < > < > < > | 0 0 0 | | 1 Nl Nk | | 1 Nl Nk | | 1 Jl_p Jk_p | \ / \ / \ / \ /

Note: The wigner library takes two times the physical values so, e.g., the 1 must be 2. This hold true for all user inputs as well!

Reference: D.S. Makarov, M.Yu. Tretyakov, C. Boulet, Line mixing in the 60-GHz atmospheric oxygen band: Comparison of the MPM and ECS model, Journal of Quantitative Spectroscopy and Radiative Transfer, Volume 124, 2013, Pages 1-10, ISSN 0022-4073, https://doi.org/10.1016/j.jqsrt.2013.02.019. (http://www.sciencedirect.com/science/article/pii/S0022407313000745) Abstract: Precise profiles of the 60-GHz molecular oxygen band recorded earlier in a wide temperature range by means of a resonator spectrometer at atmospheric pressure were treated. High signal-to-noise ratio allows careful study of the band shape taking into consideration the mixing effect. Comparative analysis of the band profile calculated by an extended MPM (Millimeter-wave Propagation Model) and by the ECS (Energy Corrected Sudden) approximation model is presented. Some limitations of the MPM approach are discussed on the basis of the comparison of the two models. Interbranch coupling is shown to make a noticeable contribution to absorption which means that it should be taken into account as it is expected to improve band profile modeling accuracy. Keywords: Molecular oxygen; Microwave spectroscopy; Profile shape modeling; Collisional coupling

Note: The ARTS implementation has not been tested in detail

Warning: Must have called wig_temp_init(j) with appropriate j before using this function. Failure to do so will cause segfault.

Parameters

[in]	Nl	as above times 2
[in]	Nk	as above times 2
[in]	Jl	as above times 2
[in]	Jk	as above times 2
[in]	Jl_p	as above times 2
[in]	Jk_p	as above times 2
[in]	L	as above times 2

Returns

Numeric Symbol value

Definition at line 94 of file wigner_functions.cc.

References WIGNER3, and WIGNER6.

o2_ecs_wigner_symbol_tran()

Numeric o2_ecs_wigner_symbol_tran	(	const Rational &	Ji,
		const Rational &	Jf,
		const Rational &	Ni,
		const Rational &	Nf,
		const Rational &	Si,
		const Rational &	Sf,
		const Rational &	Ji_p,
		const Rational &	Jf_p,
		const Rational &	Ni_p,
		const Rational &	Nf_p,
		const Rational &	n,
		const Numeric &	T
	)

Returns the wigner symbol used in Tran etal 2006.

Symbol: / \ / \ / \ / \ / \ | Ni_p Ni L | | Nf_p Nf L | | L Ji Ji_p | | L Jf Jf_p | | L Ji Ji_p | | | | | < > < > < > (2L + 1) (OmegaNi / OmegaL) * QL | 0 0 0 | | 0 0 0 | | Si Ni_p Ni | < Sf Nf_p Nf | | n Jf_p Jf | \ / \ / \ / \ / \ /

Reference: H. Tran, C. Boulet, and J.-M. Hartmann Line mixing and collision-induced absorption by oxygen in the A band: Laboratory mea*surements, model, and tools for atmospheric spectra computations, Journal Of Geophysical Research, Volume 111, 2006, doi:10.1029/2005JD006869.

Note: The ARTS implementation has not been tested in detail

Warning: Must have called wig_temp_init(j) with appropriate j before using this function. Failure to do so will cause segfault.

Parameters

[in]	Ji	Initial J of level
[in]	Jf	Final J of level
[in]	Ni	Initial N of level
[in]	Nf	Final N of level
[in]	Si	Initial S of level
[in]	Sf	Final S of level
[in]	Ji_p	Initial J of pseudo-level
[in]	Jf_p	Final J of pseudo-level
[in]	Ni_p	Initial N of pseudo-level
[in]	Nf_p	Final N of pseudo-level
[in]	L	Coupling to pseudo-level
[in]	n	Order of the tensor (n=1 is magnetic dipole)
[in]	OmegaNi	Adiabatic factor at initial N
[in]	OmegaL	Adiabatic factor at L
[in]	QL	Adiabatic factor at L

Returns

Numeric Symbol value

Definition at line 218 of file wigner_functions.cc.

References even(), find_even_limits(), find_wigner3j_limits(), max, o2_ecs_adiabatic_factor_makarov(), o2_ecs_ql_makarov(), o2_ecs_wigner_symbol_tran(), sqrt(), Rational::toInt(), and WIGNER3.

Referenced by o2_ecs_wigner_symbol_tran().

o2_makarov2013_reduced_dipole()

Numeric o2_makarov2013_reduced_dipole	(	const Rational &	Jup,
		const Rational &	Jlo,
		const Rational &	N
	)

Returns the reduced dipole moment following Makarov etal 2013.

Only for N+ and N- lines

Parameters

[in]	Jup	Upper state's J
[in]	Jlo	Lower state's J
[in]	N	Upp/low states' N

Returns

The reduced dipole moment

Definition at line 267 of file wigner_functions.cc.

References even(), sqrt(), Rational::toInt(), and WIGNER6.

wigner3j()

Numeric wigner3j	(	const Rational	j1,
		const Rational	j2,
		const Rational	j3,
		const Rational	m1,
		const Rational	m2,
		const Rational	m3
	)

Wigner 3J symbol.

Run wigxjpf wig3jj for Rational symbol

/ \

j1 j2 j3
m1 m2 m3

\ /

See for definition: http://dlmf.nist.gov/34.2

Parameters

[in]	j1	as above
[in]	j2	as above
[in]	j3	as above
[in]	m1	as above
[in]	m2	as above
[in]	m3	as above

Returns

Numeric Symbol value

Definition at line 40 of file wigner_functions.cc.

Referenced by Zeeman::Model::Strength().

wigner6j()

Numeric wigner6j	(	const Rational	j1,
		const Rational	j2,
		const Rational	j3,
		const Rational	l1,
		const Rational	l2,
		const Rational	l3
	)

Wigner 6J symbol.

Run wigxjpf wig6jj for Rational symbol

/ \ | j1 j2 j3 | < > | l1 l2 l3 | \ /

See for definition: http://dlmf.nist.gov/34.4

Parameters

[in]	j1	as above
[in]	j2	as above
[in]	j3	as above
[in]	l1	as above
[in]	l2	as above
[in]	l3	as above

Returns

Numeric Symbol value

Definition at line 65 of file wigner_functions.cc.

Referenced by LineRecord::reduced_magnetic_quadrapole(), and Absorption::reduced_magnetic_quadrapole().