Equation of State Sub-Library: Version 0.910
Public Member Functions | Data Fields
ldrop_mass_skin Class Reference

More advanced liquid drop model. More...

#include <ldrop_mass.h>

Inheritance diagram for ldrop_mass_skin:
ldrop_mass nuclear_mass_fit nuclear_mass_cont nuclear_mass nuclear_mass_info ldrop_mass_pair

Detailed Description

In addition to the physics in ldrop_mass, this includes corrections for

Note:
The input parameter T should be given in units of inverse Fermis -- this is a bit unusual since the binding energy is returned in MeV, but we keep it for now.

Bulk energy

The central densities and radii, $ n_n, n_p, R_n, R_p $ are all determined in the same way as ldrop_mass, except that now $ \delta \equiv I \zeta $, where $ \zeta $ is stored in doi . Note that this means $ N > Z~\mathrm{iff}~R_n>R_p $.

If new_skin_mode is false, then the bulk energy is also computed as in ldrop_mass. Otherwise, the number of nucleons in the core is computed with

\begin{eqnarray*} A_{\mathrm{core}} = Z (n_n+n_p)/n_p~\mathrm{for}~N\geq Z \\ A_{\mathrm{core}} = N (n_n+n_p)/n_p~\mathrm{for}~Z>N \\ \end{eqnarray*}

and $ A_{\mathrm{skin}} = A - A_{\mathrm{core}} $. The core contribution to the bulk energy is

\[ E_{\mathrm{core}}/A = \left(\frac{A_{\mathrm{core}}}{A}\right) \frac{\hbar c}{n_{L} } \left[\varepsilon(n_n,n_p) - n_n m_n - n_p m_p \right] \]

then the skin contribution is

\[ E_{\mathrm{skin}}/A = \left(\frac{A_{\mathrm{skin}}}{A}\right) \frac{\hbar c}{n_{L} } \left[\varepsilon(n_n,0) - n_n m_n \right]~\mathrm{for}~N>Z \]

and

\[ E_{\mathrm{skin}}/A = \left(\frac{A_{\mathrm{skin}}}{A}\right) \frac{\hbar c}{n_{L} } \left[\varepsilon(0,n_p) - n_p m_p \right]~\mathrm{for}~Z>N \]

Surface energy

If full_surface is false, then the surface energy is just that from ldrop_mass , with an extra factor for the surface symmetry energy

\[ E_{\mathrm{surf}} = \frac{\sigma}{n_L} \left(\frac{36 \pi n_L}{A} \right)^{1/3} \left( 1- \sigma_{\delta} \delta^2 \right) \]

where $ \sigma_{\delta} $ is unitless and stored in ss.

If full_surface is true, then the surface energy is modified by a cubic dependence for the medium and contains finite temperature corrections.

Coulomb energy

The Coulomb energy density (Ravenhall83) is

\[ \varepsilon = 2 \pi e^2 R_p^2 n_p^2 f_d(\chi_p) \]

where the function $ f_d(\chi) $ is

\[ f_d(\chi_p) = \frac{1}{(d+2)} \left[ \frac{2}{(d-2)} \left( 1 - \frac{d}{2} \chi_p^{(1-2/d)} \right) + \chi_p \right] \]

This class takes $ d=3 $ .

Todos and Future

Todo:
This is based on LPRL, but it's a little different in Lattimer and Swesty. I should document what the difference is.
Todo:
The testing could be updated.
Idea for Future:
Add translational energy?
Idea for Future:
Remove excluded volume correction and compute nuclear mass relative to the gas rather than relative to the vacuum.
Idea for Future:
In principle, Tc should be self-consistently determined from the EOS.
Idea for Future:
Does this work if the nucleus is "inside-out"?

References

Designed in Steiner08 and Souza09 based in part on Lattimer85 and Lattimer91 .


Definition at line 497 of file ldrop_mass.h.

Public Member Functions

virtual const char * type ()
 Return the type, "ldrop_mass_skin".
virtual int fit_fun (size_t nv, const ovector_base &x)
 Fix parameters from an array for fitting.
virtual int guess_fun (size_t nv, ovector_base &x)
 Fill array with guess from present values for fitting.
virtual double drip_binding_energy_d (double Z, double N, double npout, double nnout, double chi)
 Return the free binding energy of a nucleus in a many-body environment.
virtual double drip_binding_energy_full_d (double Z, double N, double npout, double nnout, double chi, double T)
 Return the free binding energy of a nucleus in a many-body environment.

Data Fields

bool full_surface
 If true, properly fix the surface for the pure neutron matter limit (default true)
bool new_skin_mode
 If true, separately compute the skin for the bulk energy (default false)
double doi
 Ratio of $ \delta/I $ (default 0.8).
double ss
 Surface symmetry energy (default 0.5)
bool rel_vacuum
 If true, define the nuclear mass relative to the vacuum (default true)
double Tchalf
 The critical temperature of isospin-symmetric matter in $ fm^{-1} $ (default $ 20.085/(\hbar c)$.)
Input parameters for temperature dependence
double pp
 Exponent (default 1.25)
double a0
 Coefficient (default 0.935)
double a2
 Coefficient (default -5.1)
double a4
 Coefficient (default -1.1)

The documentation for this class was generated from the following file:
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Documentation generated with Doxygen. Provided under the GNU Free Documentation License (see License Information).

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