Decay Constant

Functions
template<typename T >
T	EGXPhys::DecayConstant (const T &countInitial, const T &countFinal, const T &time)
	Calculates the decay constant, \(\lambda\), of a radioactive substance via the uncertainty in energy, \(\Delta E\). More...
template<typename T >
T	EGXPhys::DecayConstantViaHalfLife (const T &halfLife)
	Calculates the decay constant, \(\lambda\), of a radioactive substance via the half life, \(t_{\frac{1}{2}}\). More...
template<typename T >
T	EGXPhys::DecayConstantViaMeanLifetime (const T &meanLifetime)
	Calculates the decay constant, \(\lambda\), of a radioactive substance via the mean lifetime, \(\tau\). More...
template<typename T >
T	EGXPhys::DecayConstantViaDecayWidth (const T &decayWidth)
	Calculates the decay constant, \(\lambda\), of a radioactive substance via the decay width, \(\Gamma\). More...

Detailed Description

Todo:

decay constant in terms of dN/dt

Function Documentation

DecayConstant()

template<typename T >

T EGXPhys::DecayConstant	(	const T &	countInitial,
		const T &	countFinal,
		const T &	time
	)

Calculates the decay constant, \(\lambda\), of a radioactive substance via the uncertainty in energy, \(\Delta E\).

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

\[\frac{dN}{dt}=-\lambda N\]

\[\lambda=-\frac{\frac{dN}{dt}}{N}\]

\[\lambda=-\frac{\frac{N_t-N_0}{dt}}{N_0}\]

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

countInitial	\(\Delta E\)(dimensionless) Count Initial.
countFinal	\(\Delta E\)(dimensionless) Count Final.
time	\(t\ (s)\) Time.

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

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

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

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

DecayConstantViaDecayWidth()

template<typename T >

T EGXPhys::DecayConstantViaDecayWidth

(

const T &

decayWidth

)

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

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

\[\lambda = \frac{\Gamma}{\hbar} \]

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

decayWidth

\(\lambda\ (\frac{1}{s})\) 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, \(\Gamma\).

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

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

DecayConstantViaHalfLife()

template<typename T >

T EGXPhys::DecayConstantViaHalfLife

(

const T &

halfLife

)

Calculates the decay constant, \(\lambda\), of a radioactive substance via the half life, \(t_{\frac{1}{2}}\).

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

\[\lambda = \frac{ln(2)}{t_{\frac{1}{2}}}\]

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, \(\Delta E\).

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

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

DecayConstantViaMeanLifetime()

template<typename T >

T EGXPhys::DecayConstantViaMeanLifetime

(

const T &

meanLifetime

)

Calculates the decay constant, \(\lambda\), of a radioactive substance via the mean lifetime, \(\tau\).

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

\[\lambda = \frac{1}{\tau}\]

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, \(\Delta E\).

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

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