Semi-Empirical Mass Formula

Functions
template<typename T >
double	EGXPhys::SemiEmpericalBindingEnergyKrane (const T &atomicNumber, const T &massNumber)
	Calculates the binding energy, \(BE_{SEMF}\), used in the semi-emperical mass formula for determining the mass of a nucleus using Krane's method. More...
template<typename T >
double	EGXPhys::SemiEmpericalMassFormula (const T &atomicNumber, const T &massNumber)

Detailed Description

Todo:

Add reference to Decay Width.

Approximate the mass, \(m_{SEMF}\), of a nucleus.

Function Documentation

SemiEmpericalBindingEnergyKrane()

template<typename T >

double EGXPhys::SemiEmpericalBindingEnergyKrane	(	const T &	atomicNumber,
		const T &	massNumber
	)

Calculates the binding energy, \(BE_{SEMF}\), used in the semi-emperical mass formula for determining the mass of a nucleus using Krane's method.

The semi-emperical binding energy calculates the binding energy formula.

\[BE_{SEMF} = a_V A - a_S A^{2/3}-a_C Z(Z-1)A^{-1/3}-a_{sym}\frac{(A-2Z)^2}{A}+\delta(Z,A)\]

Where \(\delta(Z,A)\):

\[\delta(Z,A)=\begin{cases} a_pA^{-3/4} & \text{ if } Z,N\text{ even }\\ 0 & \text{ if } A \text{ odd }\\ -a_pA^{-3/4} & \text{ if } Z,N \text{ odd } \end{cases}\]

Constants used:

\[a_V = 15.5\ MeV\]

\[a_S = 16.8\ MeV\]

\[a_C = 0.72\ MeV\]

\[a_{sym} = 23.0\ MeV\]

\[a_p = 34.0\ MeV\]

Equation taken from "Introductory Nuclear Physics" (Krane, 1987), p. 68

Parameters

atomicNumber	\(Z\ (1)\) Atomic number. The number of protons in the nucleus of an atom.
massNumber	\(A\ (1)\) Mass number. The number of protons and neutrons in the nucleus of an atom.

Returns

\(B_{SEMF}\ (MeV)\) Binding Energy.

See also

MassDefectInMeVPercSquared() to calculate mass defect, \(\Delta m\) in megaelectron volts per c squared.