The python program is simply run from the 'isov' directory with the following command:

python exe.py

The fortran program may be run directly by entering the 'bin' directory and using the following shell command:

./run

Alternatively the following shell script will save any console printout:

./run.sh

The ISOV program facilates analysis of the nuclear Equation of State. Options for computing the isoscalar and isovector properties from a given input are provided.

Acronyms:

EoS : Equation of State NM : Neutron Matter SNM : Symmetric Nuclear Matter EPA : Energy per Nucleon

Abbreviations :

Den : Density Eng : Energy Phen : Phenomenolgoical Sat : Saturation

The nuclear matter EoS is approximated with the parabolic approximation:

e(rho, alpha) = e0 + esym*alpha*alpha

where,

alpha = (rhon-rhop)/(rhon+rhop)

esym(rho) = e1(rho) - e0(rho)

and,

rho = rhon + rhop.

The pressure expression:

P = rho*rho*(d e)/(d rho)

The parameters:

Slope Parameter : L = 3.0*rho_0*(d e_sym)/(d rho)

Curvature Parameter : K = 9.0*rho_0*rho_0*(d^2 e_sym)/(d^2 rho)

alpha : isospin asymmetry parameter rho : hadron den. rhon : neutron den. rhop : proton den. e : EPA e0 : SNM EPA e1 : NM EPA

rho_0 : Saturation Den. (0.16 fm^-3) rho_1 : Reference Den. = 0.1 fm^-3

ISOV parameter files:

• execpar.don : parameters which govern how the program is executed
• readpar.don : parameters which govern how the program reads in the EoS
• phenpar.don : parameters which govern the phenomenolgoical EoS input

The input files are examined in detail:

• execpar.don

Style : I1 I2 E.g. : 1 1

Description:

I1 : 'nrun' -> [1,2,3] see below for details I2 : 'nprint' -> [ >0 ] see below for details

If nrun = 1

• The Isovector and Isoscalar values for the input EoS are generated

  • If 'nprint' = 1, Then E0(rho), E1(rho), Esym(rho) and the pressures are printed for 'n' number of density if 'n' > 0 these densities corrospond to the densities found in the 'den.don' file, else these quantites are printed for 'n0' number of densities corrosponding to the densities found in the 'e0_nxlo.don' file. These quantites are printed to a file named 'eosvals.don'

  • If 'nprint' = 2, Then the following isoscalar and isovector values are printed to a file titled 'isovals.don', according to the following order:

    • n0 : The number of E0 values
    • rho0 : The saturation density
    • rho1 : The reference density
    • rho2 : Twice saturation density
    • e0o : SNM EoS at saturation density
    • e01 : SNM EoS at reference density
    • e02 : SNM EoS at twice saturation density
    • e1o : NM EoS at saturation density
    • e11 : NM EoS at reference density
    • e12 : NM EoS at twice saturation density
    • esym0 : Symmetry energy at saturation density
    • esym1 : Symmetry energy at reference density
    • esym2 : Symmetry energy at twice saturation density
    • prs0o : SNM Pressure at saturation density
    • prs01 : SNM Pressure at reference density
    • prs02 : SNM Pressure at twice saturation density
    • prs1o : NM Pressure at saturation density
    • prs11 : NM Pressure at reference density
    • prs12 : NM Pressure at twice saturation density
    • bigL : Slope Parameter
    • bigK : Curvature Parameter
    • bigKR : Curvature at reference density
    • bigK0 : SNM Curvature at saturation

If nrun = 2

• The parabolic EoS progression is partitioned into 'nprint' number of divisions with equal incrementing of isospin asymmetry

  • nprint range is [3,]

If nrun = 3

• A phenomenolgoical EoS is generated according to input 'phenpar' parameters

If nprint = 0 If nprint = 1 If nprint = 2

• readpar.don

Style : I1 I2 I3 I4 I5 I6 E.g. : 0 1 0 0 10 10

Description:

I1 : 'n_read' -> [0,1] 0 is a single file (ex) read, 1 is a two file (e0,e1) read I2 : 'nkf_read' -> [0,1] reads the first column of EoS file(s) as: 0 - momenta, 1 - density I3 : 'ndn_read' -> [0,1] reads the first column of 'den.don' file as: 0 - momenta, 1 - density I3 : 'n' -> [>= 0] 0 - no densities read, >0 - number of densities read I4 : 'n0' -> [>= 0] number of SNM values to be read, number of NM values as well if n_read = 0 I5 : 'n1' -> [>= 0] number of NM values to be read if n_read = 1.

If n_read = 0

• 'ex_nxlo.don' : contains n0 entries, formatted as follows: xval, e0, e1

if n_read = 1

• 'e0_nxlo.don' : contains n0 entries, formatted as follows: xval, e0
• 'e1_nxlo.don' : contains n1 entries, formatted as follows: xval, e1

nkf_read determines 'xval':

If nkf_read = 0 : xval is read as fermi momenta (kf) (see conversion below) If nkf_read = 1 : xval is read as density (fm^-3)

For SNM, e0 : den = 2.0*xkf*xkf*xkf/(3.0*pi*pi) For NM, e1 : den = xkf*xkf*xkf/(3.0*pi*pi)

If n > 0 :

• 'den.don' is read for n entries, formatted as follows: dval

ndn_read determines 'dval':

If ndn_read = 0 : dval is read as fermi momenta (kf) (see conversion below) If ndn_read = 1 : dval is read as density (fm^-3)

Note that 'den.don' entries read as momenta are converted to density according to SNM.

• phenpar.don

Style : I1 I2 I3 F1 F2 F3 E.g. : 1 0 0 2.7 220. 0.16

Description:

I1 : 'mic' -> [0,1] 0 SNM EoS is phen., 1 SNM EoS is microscopic I2 : 'isnm' -> [0,1] 0 SNM EoS independent of sat., 1 SNM EoS dependent on sat. I3 : 'isym_emp' -> [0,1] 0 for symmetry energy from e0 and e1, 1 for phen symmetry energy F1 : 'gam' -> [>= 0.] Exponent parameter for phenomenolgoical symmetry energy F2 : 'xk0' -> [>= 0.] Symmetry Curvature (K0) float value for sat. dependent phen EoS F3 : 'rhosat' -> [>= 0.] Saturation Density (rho0) float value for sat. dependent phen EoS

If mic = 0

• The SNM EoS (e0) will be phenomenolgoical, the other inputs in this file determine the parameters if mic = 1
• The SNM EoS (e0) will be microscopic, the other inputs in this file are ignored

If isnm = 0 : The Phenomenolgoical SNM EoS (e0) is parameterized independently from saturation properties If isnm = 1 : The Phenomenolgoical SNM EoS (e0) is dependent on input saturation properties (rho0 and K0)

If isym_emp = 0 : The symmetry energy is determined from the SNM and NM EoS: e1(rho) - e0(rho) If isym_emp = 1 : The symmetry energy is determined from a phen. curve: esym(rho)

gam : Exponent parameter for phenomenolgoical symmetry energy, typically around 2.7

xk0 : the symmetry curvature (K0), typically around 220 MeV.

rhosat : The saturation density is emperically given by 0.16 fm^-3 and is typically between 0.15 - 0.17 fm^-3