Page 61 out of 81 total pages , Page 4 out of 12 pages in this chapter

5.10 Spherical Spatial Tensor Functions

5.10.1 A0, A20

Usage:


#include <IntG.h>
complex IntG::A0() const
complex IntG::A20() const
complex IntG::A0(double theta, double phi) const
complex IntG::A20(double theta, double phi) const

Description:

The functions A0 and A20 are used to obtain the G interaction spatial tensor component A2,0. If no arguments are given the functions return the value of the tensor component at the current interaction orientation. If the arguments theta and phi are given the returned tensor component is for the orientation at theta degrees down from the interactions PAS z-axis and phi degrees over from the interactions PAS x-axis. The values of theta and phi are assumed in Hz.

Note that GAMMA uses a scaling on all spatial tensor components which is independent of the interaction type1. This component can also be related to the Cartesian tensor components for any arbitrary orientation.

Return Value:

A complex number.

Example:


IntG G(1.5, 3.e5, 0.2, 45.0, 45.0); // Make a G interaction.
complex A20 = G.A20(); // This is at theta=phi=45 degrees
cout << G.A20(15.6, 99.3); // This is at theta=15.6 and phi=99.3 degrees.

See Also: A1, A21, Am1, A2m1, A2, A22, Am2, A2m2

5.10.2 A1, A21

Usage:


#include <IntG.h>
complex IntG::A1() const
complex IntG::A21() const
complex IntG::A1(double theta, double phi) const
complex IntG::A21(double theta, double phi) const

Description:

The functions A1 and A21 are used to obtain the G interaction spatial tensor component A2,1. If no arguments are given the functions return the value of the tensor component at the current interaction orientation. If the arguments theta and phi are given the returned tensor component is for the orientation at theta degrees down from the interactions PAS z-axis and phi degrees over from the interactions PAS x-axis. The values of theta and phi are assumed in Hz.

Note that GAMMA uses a scaling on all spatial tensor components which is independent of the interaction type2. This component can also be related to the Cartesian tensor components for any arbitrary orientation.

Return Value:

A complex number.

Example:


IntG G(1.5, 3.e5, 0.2, 45.0, 45.0); // Make a G interaction.
complex A20 = G.A20(); // This is at theta=phi=45 degrees
cout << G.A20(15.6, 99.3); // This is at theta=15.6 and phi=99.3 degrees.

See Also: A1, A21, Am1, A2m1, A2, A22, Am2, A2m2

5.10.3 Am1, A2m1

Usage:


#include <IntG.h>
complex IntG::Am1() const
complex IntG::A2m1() const
complex IntG::Am1(double theta, double phi) const
complex IntG::Am21(double theta, double phi) const

Description:

The functions Am1 and A2m1 are used to obtain the G interaction spatial tensor component A2,1. If no arguments are given the functions return the value of the tensor component at the current interaction orientation. If the arguments theta and phi are given the returned tensor component is for the orientation at theta degrees down from the interactions PAS z-axis and phi degrees over from the interactions PAS x-axis. The values of theta and phi are assumed in Hz.

Note that GAMMA uses a scaling on all spatial tensor components which is independent of the interaction type3. This component can also be related to the Cartesian tensor components for any arbitrary orientation.

Return Value:

A complex number.

Example:


IntG G(1.5, 3.e5, 0.2, 45.0, 45.0); // Make a G interaction.
complex A20 = G.A20(); // This is at theta=phi=45 degrees
cout << G.A20(15.6, 99.3); // This is at theta=15.6 and phi=99.3 degrees.

See Also: A1, A21, Am1, A2m1, A2, A22, Am2, A2m2

5.10.4 A2, A22

Usage:


#include <IntG.h>
complex IntG::A2() const
complex IntG::A22() const
complex IntG::A2(double theta, double phi) const
complex IntG::A22(double theta, double phi) const

Description:

The functions A2 and A22 are used to obtain the G interaction spatial tensor component A2,1. If no arguments are given the functions return the value of the tensor component at the current interaction orientation. If the arguments theta and phi are given the returned tensor component is for the orientation at theta degrees down from the interactions PAS z-axis and phi degrees over from the interactions PAS x-axis. The values of theta and phi are assumed in Hz.

Note that GAMMA uses a scaling on all spatial tensor components which is independent of the interaction type4. This component can also be related to the Cartesian tensor components for any arbitrary orientation.

Return Value:

A complex number.

Example:


IntG G(1.5, 3.e5, 0.2, 45.0, 45.0); // Make a G interaction.
complex A20 = G.A20(); // This is at theta=phi=45 degrees
cout << G.A20(15.6, 99.3); // This is at theta=15.6 and phi=99.3 degrees.

See Also: A1, A21, Am1, A2m1, A2, A22, Am2, A2m2

5.10.5 Am2, A2m2

Usage:


#include <IntG.h>
complex IntG::Am2() const
complex IntG::A2m2() const
complex IntG::Am2(double theta, double phi) const
complex IntG::A2m2(double theta, double phi) const

Description:

The functions Am2 and A2m2 are used to obtain the G interaction spatial tensor component A2,-2. If no arguments are given the functions return the value of the tensor component at the current interaction orientation. If the arguments theta and phi are given the returned tensor component is for the orientation at theta degrees down from the interactions PAS z-axis and phi degrees over from the interactions PAS x-axis. The values of theta and phi are assumed in degrees.

Note that GAMMA uses a scaling on all spatial tensor components which is independent of the interaction type5. This component can also be related to the Cartesian tensor components for any arbitrary orientation.

Return Value:

A complex number.

Example:


IntG G(1.5, 3.e5, 0.2, 45.0, 45.0); // Make a G interaction.
complex A20 = G.A20(); // This is at theta=phi=45 degrees
cout << G.A20(15.6, 99.3); // This is at theta=15.6 and phi=99.3 degrees.

See Also: A1, A21, Am1, A2m1, A2, A22, Am2, A2m2



Page 61 out of 81 total pages , Page 4 out of 12 pages in this chapter

1
Because the GAMMA platform accommodates different interaction types, the scaling on all spatial tensors is chosen to be independent of the interaction. Rather, the spatial tensors are related directly to the familiar rank two spherical harmonics . Also, the sign on the term(s) involving will have opposite sign if the common alternative definition of the PAS orientation ( ) is used rather that the definition used in GAMMA ( )
 2
Because the GAMMA platform accommodates different interaction types, the scaling on all spatial tensors is chosen to be independent of the interaction. Rather, the spatial tensors are related directly to the familiar rank two spherical harmonics . Also, the sign on the term(s) involving will have opposite sign if the common alternative definition of the PAS orientation ( ) is used rather that the definition used in GAMMA ( )
 3
Because the GAMMA platform accommodates different interaction types, the scaling on all spatial tensors is chosen to be independent of the interaction. Rather, the spatial tensors are related directly to the familiar rank two spherical harmonics . Also, the sign on the term(s) involving will have opposite sign if the common alternative definition of the PAS orientation ( ) is used rather that the definition used in GAMMA ( )
 4
Because the GAMMA platform accommodates different interaction types, the scaling on all spatial tensors is chosen to be independent of the interaction. Rather, the spatial tensors are related directly to the familiar rank two spherical harmonics . Also, the sign on the term(s) involving will have opposite sign if the common alternative definition of the PAS orientation ( ) is used rather that the definition used in GAMMA ( )
 5
Because the GAMMA platform accommodates different interaction types, the scaling on all spatial tensors is chosen to be independent of the interaction. Rather, the spatial tensors are related directly to the familiar rank two spherical harmonics . Also, the sign on the term(s) involving will have opposite sign if the common alternative definition of the PAS orientation ( ) is used rather that the definition used in GAMMA ( )
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