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/RMF [ Modules ]

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NAME

module RMF

PURPOSE

Includes all information about relativistic mean-field potential for baryons and mesons.

NOTES

  • When hyperon coupling is scaled by the well known factor of 2/3, the kaons are scaled by the factor 1/3 in order to compensate the missing self energy between incoming and outgoing channel. This is because the threshold condition, e.g. for pi N->YK, sqrt(s*)>m*_y+m*_k, in the medium assumes no changes in the self energy between initial and final states (cf. https://inspirehep.net/literature/748586)
  • This prescription should better not be used at energies near the kaon-production threshold, since in this method the kaon potential is not consistent within Chiral Perturbation Theory or One-Boson-Exchange models.
  • The same non-trivial feature appears if the baryon self energies depend on isospin. Presently no isospin-dependent part is included in the baryon fields.
  • Going beyond this simple approximation means to explicitly include different threshold conditions for all channels considered in the collision term.

RMF/RMF_flag [ Global module-variables ]

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SOURCE

  logical, save :: RMF_flag = .false.

PURPOSE

If .true. then use relativistic mean fields.

RMF/N_set [ Global module-variables ]

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SOURCE

  integer, save :: N_set = 1

PURPOSE

Select parameter set to use:

  • 1 --- NL1 [Lalazissis] (K=211.29 MeV, m*/m=0.57)
  • 2 --- NL3 [Lalazissis] (K=271.76 MeV, m*/m=0.60)
  • 3 --- NL2 [Lang] (K=210 MeV, m*/m=0.83)
  • 4 --- NLZ2 [Bender] (K=172 MeV, m*/m=0.583)
  • 5 --- NL3* [Lalazissis, priv. comm.] (K=258.28 MeV, m*/m=0.594)
  • 6 --- Same as N_set=3, but including the rho meson.
  • 7 --- NL1 [Lee] (K=212 MeV, m*/m=0.57)
  • 8 --- NL2 [Lee] (K=399 MeV, m*/m=0.67)
  • 9 --- Set I [Liu] (K=240 MeV, m*/m=0.75)
  • 10 --- NL1 [Lang] (K=380 MeV, m*/m=0.83)
  • 11 --- NL3 [Lang] (K=380 MeV, m*/m=0.70)
  • 31 --- Parity doublet model Set P3 [Zschiesche] (K=374 MeV)
  • 32 --- Parity doublet model Set P2 [Zschiesche] (K=374 MeV)
  • 33 --- Parity doublet model Set 1 [Shin] (K=240 MeV)
  • 34 --- Parity doublet model Set 2 [Shin] (K=215 MeV)

References:

  • Bender et al., PRC 60, 34304 (1999)
  • Lalazissis et al., PRC 55, 540 (1997),
  • Lang et al., NPA 541, 507 (1992)
  • Lee et al., PRL 57, 2916 (1986)
  • Liu et al., PRC 65, 045201 (2002)
  • Shin et al., arXiv:1805.03402
  • Zschiesche et al., PRC 75, 055202 (2007)

RMF/grad_flag [ Global module-variables ]

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SOURCE

  logical, save, public :: grad_flag = .false.

PURPOSE

If .true. then include space derivatives of the fields

RMF/lorentz_flag [ Global module-variables ]

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SOURCE

  logical, save, public :: lorentz_flag = .true.

PURPOSE

If .false. then the space components of the omega and rho fields are put to zero

RMF/Tens_flag [ Global module-variables ]

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SOURCE

  logical, save, public :: Tens_flag = .false.

PURPOSE

If .true. then compute the energy-momentum tensor and four-momentum density field (not used in propagation)

RMF/flagCorThr [ Global module-variables ]

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SOURCE

  logical, save, public :: flagCorThr=.false.

PURPOSE

If .true. then the srtfree of colliding particles is corrected to ensure in-medium thresholds of BB -> BB and MB -> B

RMF/fact_pbar [ Global module-variables ]

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SOURCE

  real, save :: fact_pbar    = 1.

PURPOSE

Modification factor for the antiproton coupling constants

RMF/fact_Delta [ Global module-variables ]

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SOURCE

  real, save :: fact_Delta    = 1.

PURPOSE

Modification factor for the Delta(1232) coupling constants

RMF/fact_hyp [ Global module-variables ]

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SOURCE

  real, save :: fact_hyp     = 1.

PURPOSE

Modification factor for the hyperon coupling constants

RMF/fact_antihyp [ Global module-variables ]

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SOURCE

  real, save :: fact_antihyp = 1.

PURPOSE

Modification factor for the antihyperon coupling constants

RMF/fact_Xi [ Global module-variables ]

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SOURCE

  real, save :: fact_Xi      = 1.

PURPOSE

Modification factor for the Xi and XiStar coupling constants

RMF/fact_antiXi [ Global module-variables ]

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SOURCE

  real, save :: fact_antiXi  = 1.

PURPOSE

Modification factor for the antiXi and antiXiStar coupling constants

RMF/fact_kaon [ Global module-variables ]

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SOURCE

  real, save :: fact_kaon    = 0.

PURPOSE

Modification factor for the Kaon and antikaon coupling constants

RMF/kaonpot_flag [ Global module-variables ]

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SOURCE

  logical, save, public :: kaonpot_flag = .false.

PURPOSE

This switch turns on the Kaon potential in RMF mode

RMF/flagVectMod [ Global module-variables ]

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SOURCE

  logical, save, public :: flagVectMod=.true.

PURPOSE

This switch turns on the modification factors for vector couplings

RMF/ModificationFactor [ Functions ]

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NAME

real function ModificationFactor(Id,antiFlag)

PURPOSE

Returns the modification factor of the RMF coupling constants for a given particle

INPUTS

  • integer :: Id -- Id of particle
  • logical :: antiFlag -- if .true. the particle is an antiparticle
  • logical, optional :: vectFlag -- if .true. the modification for vector couplings

RMF/getRMF_flag() [ Functions ]

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NAME

logical function getRMF_flag()

PURPOSE

return the value of the variable RMF_flag. Ensures that jobcard is read.

RMF/getRMF_parSet() [ Functions ]

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NAME

integer function getRMF_parSet()

PURPOSE

return the value of the variable N_set. Ensures that jobcard is read.

RMF/init [ Subroutines ]

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NAME

subroutine init

PURPOSE

Reads input switches. Initializes the mean field parameters.

RMF/RMF_input [ Namelists ]

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NAME

NAMELIST /RMF_input/

PURPOSE

Includes the following input switches:

RMF/waleckaShift [ Functions ]

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NAME

function waleckaShift(rhobar,em0,rhoscalar,endens,S,V,potential) return(shift)

PURPOSE

Determine the mass shift of the nucleon in equilibrated isospin symmetric nuclear matter at zero temperature within Walecka model with nonlinear sigma-coupling.

INPUTS

  • real :: rhobar ! -- baryon density (fm^-3)
  • real, optional :: em0 ! -- starting value of mass for iterations (GeV)

OUTPUT

  • real :: shift ! = m - m^* -- mass shift (GeV)
  • real, optional :: rhoscalar ! -- scalar density (fm^-3)
  • real, optional :: endens ! -- energy density (GeV/fm^3)
  • real, optional :: pressure ! -- pressure (GeV/fm^3)
  • real, optional :: S ! -- scalar potential (GeV)
  • real, optional :: V ! -- vector potential (GeV)
  • real, optional :: potential ! -- Schroedinger equivalent potential (GeV)

NOTES:

  • The SE potential is for a particle at rest, so there is no gamma factor E/m_N in front of U_v

RMF/fshift [ Functions ]

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NAME

real function fshift(rho)

PURPOSE

Fit of the nucleon mass shift m - m* for the various RMF parameter sets.

INPUTS

  • real :: rho -- baryon density (fm**-3)

OUTPUT

  • real :: fshift -- m - m* (GeV)

NOTES

This is a very rough fit which is only good to provide the starting value for iterations in walecka. The density rho must be in the interval from 0 up to 12*rhoNull.

RMF/PD [ Subroutines ]

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NAME

subroutine PD(mubStar,sigma,shift,flagPlot,sigma_inp,mub,rhoPlus,rhoMinus,rhoscalar,endens,pressure,S,V,potential)

PURPOSE

Determine the scalar field and mass shifts of the nucleon and its negative parity partner in equilibrated isospin symmetric nuclear matter at zero temperature within parity doublet model.

INPUTS

  • real :: mubStar ! = sqrt(pf_pm**2+m_pm**2) -- kinetic part of baryon chemical potential (GeV)
  • logical, optional :: flagPlot ! if true: equation for sigma field f(sigma)=0 is not solved, only function f vs sigma is plotted
  • real, optional :: sigma_inp ! -- starting value of sigma field (GeV)

OUTPUT

  • real :: sigma ! -- scalar field (GeV)
  • real :: shift(1:2) ! = m - m^* -- mass shift (GeV), 1 - nucleon, 2 - negative parity partner
  • real, optional :: mub ! -- baryon chemical potential (GeV)
  • real, optional :: rhoPlus ! -- nucleon density (fm^-3)
  • real, optional :: rhoMinus ! -- partner density (fm^-3)
  • real, optional :: rhoscalar ! -- scalar density (fm^-3)
  • real, optional :: endens ! -- energy density (GeV/fm^3)
  • real, optional :: pressure ! -- pressure (GeV/fm^3)
  • real, optional :: S(1:2) ! -- scalar potential (GeV)
  • real, optional :: V(1:2) ! -- vector potential (GeV)
  • real, optional :: potential(1:2) ! -- Schroedinger equivalent pot. (GeV)

NOTES:

  • The SE potential is for a particle at rest, so there is no gamma factor E/m in front of U_v

RMF/mPD [ Functions ]

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NAME

real function mPD

PURPOSE

Computes effective mass (in GeV) in the parity doublet model

INPUTS

  • real :: sigma -- scalar field (GeV)
  • integer :: parity -- +1 for nucleon, -1 for S11_1535

RMF/dmPD [ Functions ]

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NAME

real function dmPD

PURPOSE

Computes derivative of effective mass over sigma field d m/d sigma in the parity doublet model

INPUTS

  • real :: sigma -- scalar field (GeV)
  • integer :: parity -- +1 for nucleon, -1 for S11_1535

RMF/d2mPD [ Functions ]

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NAME

real function d2mPD

PURPOSE

Computes second derivative of effective mass over sigma field d^2 m/d sigma^2 (in GeV^-1) in the parity doublet model

INPUTS

  • real :: sigma -- scalar field (GeV)

RMF/f [ Functions ]

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NAME

real function f(a)

PURPOSE

Computes analytically the expression 3*a*\int_0^1 dx x^2/\sqrt(x^2+a^2)

INPUTS

  • real, intent(in) :: a -- dimensionless parameter equal to m^*/p_F

RMF/fprime [ Functions ]

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NAME

real function fprime(a)

PURPOSE

Computes analytically the derivative of function f(a) with respect to a.

INPUTS

  • real :: a -- dimensionless parameter equal to m^*/p_F

RMF/g [ Functions ]

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NAME

real function g(a)

PURPOSE

Computes analytically the expression \int_0^1 dx x^2*\sqrt(x^2+a^2)

INPUTS

  • real :: a -- dimensionless parameter equal to m^*/p_F

RMF/mDiracNucleon_Approx [ Functions ]

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NAME

real function mDiracNucleon_Approx(rhoBar)

PURPOSE

shortcut to calculate the Dirac mass in Walecka and Parity Doublet Model for the nucleon mass used in 'initNucPhaseSpace'

INPUTS

  • real :: rhobar -- baryon density (fm^-3)

OUTPUT

  • the Dirac mass (in GeV)

NOTES

  • a shortcut to mDirac = mN - waleckaShift(...) resp. mDirac = mPD(sigma,+1)
  • For PDM, the sigma field is only approximated

RMF/mDirac1535_Approx [ Functions ]

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NAME

real function mDirac1535_Approx(rhoBar)

PURPOSE

shortcut to calculate the Dirac mass in Walecka and Parity Doublet Model for the mass of the N*(1535) resonance

INPUTS

  • real :: rhobar -- baryon density (fm^-3)

OUTPUT

  • the Dirac mass (in GeV)

NOTES

  • For PDM, the sigma field is only approximated