Semi-empirical mass formula. More...
#include <nucmass.h>
Inheritance diagram for o2scl::nucmass_semi_empirical:
Detailed Description
A simple semi-empirical mass formula of the form
![\[ E/A = B + S_s \frac{1}{A^{1/3}}+E_c \frac{Z^2}{A^{4/3}} + S_v \left(1-\frac{2Z}{A}\right)^2+E_{\mathrm{pair}}(Z,N) \]](form_219.png)
where the pairing energy is given by
![\[ E_{\mathrm{pair}}(Z,N) = - \frac{E_{\mathrm{pair}}}{2 A^{3/2}} \left[ \cos \left( \pi Z \right)+\cos \left( \pi N \right) \right] \]](form_220.png)
which is equivalent to the traditional prescription
![\[ E_{\mathrm{pair}}(Z,N) = \frac{E_{\mathrm{pair}}}{A^{3/2}} \times \left\{ \begin{array}{rl} -1 & \mathrm{N~and~Z~even} \\ +1 & \mathrm{N~and~Z~odd} \\ 0 & \mathrm{otherwise} \end{array} \right. \]](form_221.png)
when 
and 
and integers.
- Note
- The default parameters are arbitrary, and are not determined from a fit.
There is an example of the usage of this class given in Nuclear mass fit example.
Public Types | |
| typedef boost::numeric::ublas::vector< double > | ubvector |
 Public Types inherited from o2scl::nucmass_fit_base | |
| typedef boost::numeric::ublas::vector< double > | ubvector |
Public Member Functions | |
| virtual const char * | type () |
Return the type, "nucmass_semi_empirical". | |
| virtual double | mass_excess_d (double Z, double N) |
Given Z and N, return the mass excess in MeV. | |
| virtual double | mass_excess (int Z, int N) |
Given Z and N, return the mass excess in MeV. | |
| virtual int | fit_fun (size_t nv, const ubvector &x) |
| Fix parameters from an array for fitting. | |
| virtual int | guess_fun (size_t nv, ubvector &x) |
| Fill array with guess from present values for fitting. | |
| Public Member Functions inherited from o2scl::nucmass | |
| virtual bool | is_included (int Z, int N) |
| Return false if the mass formula does not include specified nucleus. | |
| virtual int | get_nucleus (int Z, int N, nucleus &n) |
Fill n with the information from nucleus with the given neutron and proton number. More... | |
| virtual double | electron_binding (double Z) |
| Return the approximate electron binding energy in MeV. | |
| virtual double | binding_energy (int Z, int N) |
| Return the binding energy in MeV. More... | |
| virtual double | binding_energy_d (double Z, double N) |
| Return the binding energy in MeV. More... | |
| 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. | |
| virtual double | atomic_mass (int Z, int N) |
| Return the atomic mass of the nucleus in MeV (includes electrons and their binding energy) | |
| virtual double | atomic_mass_d (double Z, double N) |
| Return the atomic mass of the nucleus in MeV (includes electrons and their binding energy) | |
| Public Member Functions inherited from o2scl::nucmass_info | |
| int | parse_elstring (std::string ela, int &Z, int &N, int &A) |
| Parse a string representing an element. More... | |
| int | eltoZ (std::string el) |
| Return Z given the element name abbreviation. More... | |
| std::string | Ztoel (size_t Z) |
| Return the element name abbreviation given Z. More... | |
| std::string | Ztoname (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. More... | |
Public Attributes | |
| double | B |
| Binding energy (negative and in MeV, default -16) | |
| double | Sv |
| Symmetry energy (in MeV, default 23.7) | |
| double | Ss |
| Surface energy (in MeV, default 18) | |
| double | Ec |
| Coulomb energy (in MeV, default 0.7) | |
| double | Epair |
| Pairing energy (MeV, default 13.0) | |
| Public Attributes inherited from o2scl::nucmass_fit_base | |
| size_t | nfit |
| Number of fitting parameters. | |
| Public Attributes inherited from o2scl::nucmass | |
| double | m_neut |
Neutron mass in  (defaults to o2scl_mks::mass_neutron converted into MeV) | |
| double | m_prot |
| Proton mass in (defaults to o2scl_mks::mass_proton converted into MeV) | |
| double | m_elec |
| Electron mass in (defaults to o2scl_mks::mass_electron converted into MeV) | |
| double | m_amu |
| Atomic mass unit in (defaults to o2scl_mks::unified_atomic_mass converted into MeV) | |
Additional Inherited Members | |
| Protected Types inherited from o2scl::nucmass_info | |
| typedef std::map< std::string, int, std::greater< std::string > >::iterator | table_it |
| A convenient typedef for an iterator for element_table. | |
| Protected Attributes inherited from o2scl::nucmass_info | |
| std::vector< std::string > | name_list |
| Element names. | |
| std::map< std::string, int, std::greater< std::string > > | element_table |
| A map containing the proton numbers organized by element abbreviation. | |
| std::string | element_list [nelements] |
| The list of elements organized by proton number. | |
| Static Protected Attributes inherited from o2scl::nucmass_info | |
| static const int | nelements =119 |
| The number of elements (proton number) | |
The documentation for this class was generated from the following file:
- /home/awsteiner/wcs/o2scl/src/nuclei/nucmass.h