O2scl_part Documentation

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Particles

These classes in the library o2scl_part calculate the thermodynamic properties of interacting and non-interacting quantum and classical particles.

The class part is the basic structure for a particle:

The data members part::ms and part::nu allow one to specify modifications to the mass and the chemical potential due to interactions. This allows one to calculate the properties of particle due to interactions so long as the basic form of the free-particle dispersion relation is unchanged, i.e.

\[ \sqrt{k^2+m^2} - \mu \rightarrow \sqrt{k^2+m^{* 2}} - \nu \]

Typically, if the particle is non-interacting, then mu and m are copied to nu and ms, computations are performed with nu and ms, and then, if necessary, the result for nu is copied back to mu.

If part::inc_rest_mass is true (as is the default), then all functions include the rest mass energy density in the energy density, the "mu" functions expect that the rest mass is included in part::mu or part::nu as input and the "density" functions output part::mu or part::nu including the rest mass.

When inc_rest_mass is true, antiparticles are implemented by choosing the antiparticle chemical potential to be $ - \mu $, and when inc_rest_mass is false, antiparticles are implemented by choosing the chemical potential of the antiparticles to be $ - \mu - 2 m $.

The thermodynamic identity used to compute the pressure for interacting particles is

\[ P = -\varepsilon + s T + \nu n \]

where nu is used. This way, the particle class doesn't need to know about the structure of the interactions to ensure that the thermodynamic identity is satisfied. Note that in the o2scl_eos library, where in the equations of state the normal thermodynamic identity is used

\[ P = -\varepsilon + s T + \mu n \]

Frequently, the interactions which create an effective chemical potential which is different than mu thus create extra terms in the pressure and the energy density for the given equation of state.

At zero temperature, fermions and bosons can be treated exactly in the classes fermion and boson. quark is a descendant of the fermion class which contains extra data members for the quark condensate and the contribution to the bag constant. classical is a descendant of both fermion and boson and calculates everything in the classical limit.

At finite temperature, there are a couple different approaches. The approximation scheme from Johns96 is used in eff_boson, eff_fermion, and eff_quark. An exact method is used in rel_boson and rel_fermion, but these are necessarily quite a bit slower.

The class nonrel_fermion can be used to assume a non-relativistic dispersion relation for fermions and includes zero-temperature methods and an exact method for finite temperatures.


Units:

Factors of $ \hbar, c $ and $ k_B $ have been removed everywhere, so that mass, energy, and temperature all have the same units. Number densities have units of mass cubed (or energy cubed), and entropy is unitless.


Atomic nuclei

Nuclei

Atomic nuclei, class nucleus, are implemented as descendants of classical. This class sets the value of nucleus::inc_rest_mass to false by default.

Nuclear mass formulas are given as children of nuclear_mass. The class mnms95_mass provides the mass formula from Moller95, and the class ame_mass provides the mass formula from Audi95 or Audi03.

The class nuclear_dist provides an experimental generic base class for a collection of several nuclei with an STL-like iterator. The sole descendant, simple_dist, provides a simple collection of nuclei.


Other Todos and Bugs

Only more general items which aren't particular to a specific class are listed here. See the full lists at Todo List and Bug List.

Bug:

Bibliography

Some of the references which contain links should direct you to the work referred to directly through dx.doi.org.

Audi95: G. Audi and A. H. Wapstra, Nucl. Phys. A 595 (1995) 409-480.

Audi03: G.Audi, A. H. Wapstra and C. Thibault, Nucl. Phys. A729 (2003) 337.

Eggleton73: P.P. Eggleton, J. Faulkner, and B.P. Flannery, Astron. and Astrophys. 23 (1973) 325.

Johns96: Johns, P.J. Ellis, and J.M. Lattimer, Astrophys. J. 473, (1996) 1020.

Moller95: P. Moller, J.R. Nix, W.D. Myers, and W.J. Switecki, At. Data Nucl. Data Tables 59 (1995) 185.


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