nuclear_mass Class Reference

#include <nuclear_mass.h>

Inheritance diagram for nuclear_mass:

Detailed Description

Nuclear mass formula base [abstract base].

This base class provides some default functionality for the nuclear mass formulas. For typical usage, use ame_mass, mnmsk_mass, mnmsk_mass_exp, or semi_empirical_mass.

Elements 112-118 are named "Uub", "Uut", "Uuq", "Uup", "Uuh", "Uus", and "Uuo", respectively.

The binding energy is defined by

$\mathrm{BE}=Z m_{H} + N m_{n} - m_{\mathrm{nuclide}}$

where $m_{\mathrm{nuclide}}$ is the mass of the nucleus including the mass of the electrons. The mass excess is defined by

$m_{\mathrm{excess}} = m_{\mathrm{nuclide}} - A m_{u}$

For example, for $\mathrm{U}^{238}$ , the binding energy is 1801.695 MeV, the mass excess is 47.30366 MeV, and $m_{\mathrm{nuclide}}$ is 221742.9 MeV. This is consistent with the above, as $m_H$ is 938.7830 MeV, $m_n$ is 939.5650 MeV, and $m_u$ is 931.494 MeV.

Some mass formulas are undefined for sufficiently exotic nuclei. You can use the function is_included() to find if a particular nucleus is included or not.

Warning:: The spin degeneracy is not handled particularly intelligently. The get_nucleus() function simply assumes 0 spin for even A and spin 1/2 for odd A.
The treatment of the electron binding energy contribution is not necessarily consistent at present.

Some common reaction Q-values and separation energies:
$\mathrm{Q}(\beta^{-})=\mathrm{M(A,Z)}-\mathrm{M(A,Z+1)}$ : Beta-decay energy
$\mathrm{Q}(2\beta^{-})=\mathrm{M(A,Z)}-\mathrm{M(A,Z+2)}$ : Double beta-decay energy
$\mathrm{Q}(4\beta^{-})=\mathrm{M(A,Z)}-\mathrm{M(A,Z+4)}$ : Four beta-decay energy
$\mathrm{Q}(\alpha)=\mathrm{M(A,Z)}-\mathrm{M(A-4,Z-2)}- \mathrm{M(He^{4})}$ : Alpha-decay energy
$\mathrm{Q}(\beta-n)=\mathrm{M(A,Z)}-\mathrm{M(A-1,Z+1)} -\mathrm{M(n)}$ : Beta-delayed neutron emission decay energy
$\mathrm{Q}(d,\alpha)=\mathrm{M(A,Z)}-\mathrm{M(A-2,Z-1)} -\mathrm{M(He^{4})}-\mathrm{M(H^{2})}$ : $(d,\alpha)$ reaction energy
$\mathrm{Q}(\mathrm{EC})=\mathrm{M(A,Z)}-\mathrm{M(A,Z-1)}$ : Electron capture decay energy
$\mathrm{Q}(\mathrm{ECp})=\mathrm{M(A,Z)}-\mathrm{M(A-1,Z-2)}$ : Electron capture with delayed proton emission decay energy
$\mathrm{Q}(n,\alpha)=\mathrm{M(A,Z)}-\mathrm{M(A-3,Z-2)} -\mathrm{M(He^{4})}+\mathrm{M(n)}$ : $(n,\alpha)$ reaction energy
$\mathrm{Q}(p,\alpha)=\mathrm{M(A,Z)}-\mathrm{M(A-3,Z-1)} -\mathrm{M(He^{4})}+\mathrm{M(p)}$ : $(p,\alpha)$ reaction energy
$\mathrm{S}(n) = \mathrm{-M(A,Z)}+\mathrm{M(A-1,Z)}+ \mathrm{M(n)}$ : Neutron separation energy
$\mathrm{S}(p) = \mathrm{-M(A,Z)}+\mathrm{M(A-1,Z-1)}+ \mathrm{H^{1}}$ : Proton separation energy
$\mathrm{S}(2n) = \mathrm{-M(A,Z)}+\mathrm{M(A-2,Z)}+ \mathrm{2M(n)}$ : Two neutron separation energy
$\mathrm{S}(2p) = \mathrm{-M(A,Z)}+\mathrm{M(A-2,Z-2)}+ \mathrm{2 M(H^{1)}}$ : Two proton separation energy

Todo:: Make the treatment of the electron binding energy contribution more consistent.

Idea for future:: It might be useful to consider a fudge factor to ensure no problems with finite precision arithmetic when converting double to int.

Definition at line 119 of file nuclear_mass.h.


Public Member Functions
virtual const char *	type ()
	Return the type, `"nuclear_mass"`.
virtual bool	is_included (int Z, int N)
	Return false if the mass formula does not include specified nucleus.
int	get_nucleus (int Z, int N, nucleus &n)
	Fill `n` with the information from nucleus with the given neutron and proton number.
virtual double	mass_excess (int Z, int N)=0
	Given `Z` and `N`, return the mass excess in MeV.
virtual double	mass_excess_d (double Z, double N)=0
	Given `Z` and `N`, return the mass excess in MeV.
virtual double	binding_energy (int Z, int N)
	Return the binding energy in MeV.
virtual double	binding_energy_d (double Z, double N)
	Return the binding energy in MeV.
virtual double	total_mass (int Z, int N)
	Return the total mass of the nucleus (without the electrons) in MeV.
virtual double	total_mass_d (double Z, double N)
	Return the total mass of the nucleus (without the electrons) in MeV.
int	eltoZ (std::string el)
	Return Z given the element name.
std::string	Ztoel (size_t Z)
	Return the element name given Z.
std::string	tostring (size_t Z, size_t N)
	Return a string of the form "Pb208" for a given Z and N.
int	parse_elstring (std::string ela, int &Z, int &N, int &A)
	Parse a string of the form "Pb208".
Protected Types
typedef std::map< std::string, int, string_less_than > ::iterator	table_it
	A convenient typedef for an iterator for element_table.
Protected Attributes
std::map< std::string, int, string_less_than >	element_table
	A map containing the proton numbers organized by element name.
std::string	element_list [nelements]
	The list of elements organized by proton number.
Static Protected Attributes
static const int	nelements = 119
	The number of elements (proton number).
Data Structures
struct	string_less_than
	String comparison operator for element_table. More...

Member Function Documentation

int get_nucleus	(	int	Z,
		int	N,
		nucleus &	n
	)			`[inline]`

Fill n with the information from nucleus with the given neutron and proton number.

All masses are given in $\mathrm{fm}^{-1}$ . The total mass (withouth the electrons) is put in part::m and part::ms, the binding energy is placed in nucleus::be, the mass excess in nucleus::mex and the degeneracy (part::g) is arbitrarily set to 1 for even A nuclei and 2 for odd A nuclei.

Definition at line 146 of file nuclear_mass.h.

virtual double binding_energy	(	int	Z,
		int	N
	)			`[inline, virtual]`

Return the binding energy in MeV.

The binding energy is defined to be negative for bound nuclei, thus the binding energy per baryon of Pb-208 is about -8*208 = -1664 MeV.

Definition at line 172 of file nuclear_mass.h.

virtual double binding_energy_d	(	double	Z,
		double	N
	)			`[inline, virtual]`

Return the binding energy in MeV.

The binding energy is defined to be negative for bound nuclei, thus the binding energy per baryon of Pb-208 is about -8*208 = -1664 MeV.

Definition at line 186 of file nuclear_mass.h.

int eltoZ ( std::string el ) [inline]

Return Z given the element name.

Properly handle errors

Definition at line 216 of file nuclear_mass.h.

std::string Ztoel ( size_t Z ) [inline]

Return the element name given Z.

Note that Ztoel(0) returns "n" indicating the neutron and if the argument Z is greater than 118, an empty string is returned.

Definition at line 227 of file nuclear_mass.h.

std::string tostring	(	size_t	Z,
		size_t	N
	)			`[inline]`

Return a string of the form "Pb208" for a given Z and N.

Note that if Z is zero, then and 'n' is used to indicate the a nucleus composed entirely of neutrons and if the argument Z is greater than 118, an empty string is returned (independ.

Definition at line 243 of file nuclear_mass.h.

int parse_elstring	(	std::string	ela,
		int &	Z,
		int &	N,
		int &	A
	)			`[inline]`

Parse a string of the form "Pb208".

Note that this does not correctly interpret dashes, e.g. "Pb-208". will not work.

Idea for future:: Properly ignore dashes and other non-alphanumeric characters.

Definition at line 260 of file nuclear_mass.h.

The documentation for this class was generated from the following file:

nuclear_mass.h

Documentation generated with Doxygen and provided under the GNU Free Documentation License. See License Information for details.

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nuclear_mass Class Reference

Detailed Description

Public Member Functions

Protected Types

Protected Attributes

Static Protected Attributes

Data Structures

Member Function Documentation