Decay Width

Functions
template<typename T >
T	EGXPhys::DecayWidth (const T &energyUncertainty)
	Calculates the decay width, \(\Gamma\), of a radioactive substance via the uncertainty in energy, \(\Delta E\). The decay width is also known as line width, natural line width and decay FWHM. More...
template<typename T >
T	EGXPhys::DecayWidthViaDecayConstant (const T &decayConstant)
	Calculates the decay width, \(\Gamma\), of a radioactive substance via the decay constant, \(\lambda\). The decay width is also known as line width, natural line width and decay FWHM. More...
template<typename T >
T	EGXPhys::DecayWidthViaHalfLife (const T &halfLife)
	Calculates the Decay Width, \(\Gamma\), of a radioactive substance via the half life, \(t_{\frac{1}{2}}\). The decay width is also known as line width, natural line width and decay FWHM. More...
template<typename T >
T	EGXPhys::DecayWidthViaMeanLifetime (const T &meanLifetime)
	Calculates the Decay Width, \(\Gamma\), of a radioactive substance via the mean lifetime, \(\tau\). The decay width is also known as line width, natural line width and decay FWHM. More...

Detailed Description

Calculates the decay width, \(\Gamma\), of a radioactive substance.

Function Documentation

DecayWidth()

template<typename T >

T EGXPhys::DecayWidth

(

const T &

energyUncertainty

)

Calculates the decay width, \(\Gamma\), of a radioactive substance via the uncertainty in energy, \(\Delta E\). The decay width is also known as line width, natural line width and decay FWHM.

The decay width is the full width half maximum of the energy distribution of a decay when fit using a Breit-Wigner distribution.

\[\Gamma=2\Delta E\]

See http://quantummechanics.ucsd.edu/ph130a/130_notes/node428.html, http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/parlif.html

Equation taken from "On the Relationship between the Natural Line Width and Lifetime of X-Ray Transitions" (Croft, 2015), https://www.osti.gov/scitech/servlets/purl/1214016 and "Mössbauer Spectroscopy and Transition Metal Chemistry" (Gütlich,2011) p 9 https://doi.org/10.1007/978-3-540-88428-6

Parameters

energyUncertainty

\(\Delta E\ (eV)\) Energy uncertainty. The uncertainty in the release energy from the decay of a radioactive substance.

Returns

\(\Gamma\ (eV)\) Decay width also known as line width, natural line width and decay FWHM. The FWHM of the uncertainty in the measured energy of the radioactive decay.

See also

DecayWidthViaDecayConstant() to calculate decay width using decay constant, \(\lambda\).

DecayWidthViaHalfLife() to calculate decay width using half life, \(t_{\frac{1}{2}}\).

DecayWidthViaMeanLifetime() to calculatedecay width using mean lifetime, \(\tau\).

DecayWidthViaDecayConstant()

template<typename T >

T EGXPhys::DecayWidthViaDecayConstant

(

const T &

decayConstant

)

Calculates the decay width, \(\Gamma\), of a radioactive substance via the decay constant, \(\lambda\). The decay width is also known as line width, natural line width and decay FWHM.

The decay width is the full width half maximum of the energy distribution of a decay when fit using a Breit-Wigner distribution.

\[\Gamma \approx \hbar \lambda \]

See http://quantummechanics.ucsd.edu/ph130a/130_notes/node428.html, http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/parlif.html

Equation taken from "On the Relationship between the Natural Line Width and Lifetime of X-Ray Transitions" (Croft, 2015), https://www.osti.gov/scitech/servlets/purl/1214016 and "Mössbauer Spectroscopy and Transition Metal Chemistry" (Gütlich,2011) p 9 https://doi.org/10.1007/978-3-540-88428-6

Parameters

decayConstant

\(\lambda\ (\frac{1}{s})\) Decay constant. Fraction of radioactive substance that decays in 1 second.

Returns

\(\Gamma\ (eV)\) Decay width also known as line width, natural line width and decay FWHM. The FWHM of the uncertainty in the measured energy of the radioactive decay.

See also

DecayConstant() to calculate the decay constant, \(\lambda\).

DecayWidth() to calculate decay width using the uncertainty in energy, \(\Delta E\).

DecayWidthViaHalfLife() to calculate decay width using half life, \(t_{\frac{1}{2}}\).

DecayWidthViaMeanLifetime() to calculatedecay width using mean lifetime, \(\tau\).

DecayWidthViaHalfLife()

template<typename T >

T EGXPhys::DecayWidthViaHalfLife

(

const T &

halfLife

)

Calculates the Decay Width, \(\Gamma\), of a radioactive substance via the half life, \(t_{\frac{1}{2}}\). The decay width is also known as line width, natural line width and decay FWHM.

The decay width is the full width half maximum of the energy distribution of a decay when fit using a Breit-Wigner distribution.

\[\Gamma\approx \frac{\hbar \ ln(2)}{t_{\frac{1}{2}}}\]

See http://quantummechanics.ucsd.edu/ph130a/130_notes/node428.html, http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/parlif.html

Equation taken from "On the Relationship between the Natural Line Width and Lifetime of X-Ray Transitions" (Croft, 2015), https://www.osti.gov/scitech/servlets/purl/1214016 and "Mössbauer Spectroscopy and Transition Metal Chemistry" (Gütlich,2011) p 9 https://doi.org/10.1007/978-3-540-88428-6

Parameters

halfLife

\(t_{\frac{1}{2}}\ (s)\) Half life. Time required for the activity of a radioactive substance to decay to half of its initial value.

Returns

\(\Gamma\ (eV)\) Decay width also known as line width, natural line width and decay FWHM. The FWHM of the uncertainty in the measured energy of the radioactive decay.

See also

HalfLife() to calculate the half life, \(t_{\frac{1}{2}}\).

DecayWidth() to calculate decay width using the uncertainty in energy, \(\Delta E\).

DecayWidthViaDecayConstant() to calculate decay width using decay constant, \(\lambda\).

DecayWidthViaMeanLifetime() to calculatedecay width using mean lifetime, \(\tau\).

DecayWidthViaMeanLifetime()

template<typename T >

T EGXPhys::DecayWidthViaMeanLifetime

(

const T &

meanLifetime

)

Calculates the Decay Width, \(\Gamma\), of a radioactive substance via the mean lifetime, \(\tau\). The decay width is also known as line width, natural line width and decay FWHM.

The decay width is the full width half maximum of the energy distribution of a decay when fit using a Breit-Wigner distribution.

\[\Gamma \approx \frac{\hbar}{\tau}\]

See http://quantummechanics.ucsd.edu/ph130a/130_notes/node428.html, http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/parlif.html

Equation taken from "On the Relationship between the Natural Line Width and Lifetime of X-Ray Transitions" (Croft, 2015), https://www.osti.gov/scitech/servlets/purl/1214016 and "Mössbauer Spectroscopy and Transition Metal Chemistry" (Gütlich,2011) p 9 https://doi.org/10.1007/978-3-540-88428-6

Parameters

meanLifetime

\(\Delta E\ (eV)\) Mean lifetime. Average time that a radioactive substance is likely to survive before it decays.

Returns

\(\Gamma\ (eV)\) Decay width also known as line width, natural line width and decay FWHM. The FWHM of the uncertainty in the measured energy of the radioactive decay.

See also

MeanLifetime() to calculate the mean lifetime, \(\tau\).

DecayWidth() to calculate decay width using the uncertainty in energy, \(\Delta E\).

DecayWidthViaDecayConstant() to calculate decay width using decay constant, \(\lambda\).

DecayWidthViaHalfLife() to calculate decay width using half life, \(t_{\frac{1}{2}}\).