393 lines
13 KiB
Fortran
393 lines
13 KiB
Fortran
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!
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!=======================================================================
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!
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MODULE PAIR_DISTRIBUTION
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!
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USE ACCURACY_REAL
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!
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CONTAINS
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!
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!
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!=======================================================================
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!
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SUBROUTINE PAIR_DISTRIBUTION_3D(R,RS,T,RH_TYPE,R2)
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!
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! This subroutine computes the pair distribution function rho2(r)
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! for 3D systems.
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!
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!
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! Input parameters:
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!
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! * R : grid point (in units of a_0)
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! * RS : Wigner-Seitz radius (in units of a_0)
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! * T : temperature in SI
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! * RH_TYPE : pair distribution function approximation (3D)
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! RH_TYPE = 'CDI' chain diagram improved
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! RH_TYPE = 'CEG' classical electron gas
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! RH_TYPE = 'DEB' Debye electron gas
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! RH_TYPE = 'FUA' correct to order 2 in epsilon
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! RH_TYPE = 'SDC' short-distance correlations
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! RH_TYPE = 'WDA' watermelon diagrams summed
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!
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! Output parameters:
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!
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! * R2 : value of the pair correlation function
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 4 Jun 2020
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!
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!
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!
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IMPLICIT NONE
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!
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CHARACTER (LEN = 3) :: RH_TYPE
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!
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REAL (WP) :: R,RS,T,R2
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!
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IF(RH_TYPE == 'CDI') THEN !
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R2=CDI_PDF(R,RS,T) !
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ELSE IF(RH_TYPE == 'CEG') THEN !
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R2=CEG_PDF(R,RS,T) !
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ELSE IF(RH_TYPE == 'DEB') THEN !
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R2=DEB_PDF(R,RS,T) !
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ELSE IF(RH_TYPE == 'FUA') THEN !
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R2=FUA_PDF(R,RS,T) !
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ELSE IF(RH_TYPE == 'SDC') THEN !
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R2=SDC_PDF(R,RS,T) !
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ELSE IF(RH_TYPE == 'WDA') THEN !
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R2=WDA_PDF(R,RS,T) !
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ENDIF !
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!
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END SUBROUTINE PAIR_DISTRIBUTION_3D
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!
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!=======================================================================
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!
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FUNCTION CDI_PDF(R,RS,T)
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!
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! This function computes the electron gas pair distribution function
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! rho2(r) for 3D systems, with a chain diagram improved
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!
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! References: (1) A. Isihara, "Electron Liquids", 2nd edition,
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! Springer Series in Solid-State Sciences 96,
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! (Springer, 1998) p. 33
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!
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! Input parameters:
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!
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! * R : grid point in unit of a_0
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! * RS : Wigner-Seitz radius (in units of a_0)
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! * T : temperature in SI
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 2 Jun 2020
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!
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!
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USE REAL_NUMBERS, ONLY : ONE,TWO
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USE CONSTANTS_P1, ONLY : BOHR,E,K_B
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USE SQUARE_ROOTS, ONLY : SQR2
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USE SCREENING_VEC, ONLY : DEBYE_VECTOR
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USE UTILITIES_1, ONLY : RS_TO_N0
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USE EXT_FUNCTIONS, ONLY : ERFC ! Error function
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!
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IMPLICIT NONE
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!
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REAL (WP) :: R,RS,T
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REAL (WP) :: CDI_PDF
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REAL (WP) :: X,EPS,ALP,BETA
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REAL (WP) :: N0,KD_SI
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!
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REAL (WP) :: DSQRT,DEXP
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!
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N0=RS_TO_N0('3D',RS) !
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!
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! Computing the Debye screening vector
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!
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CALL DEBYE_VECTOR('3D',T,RS,KD_SI) !
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!
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X=KD_SI*R*BOHR !
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EPS=E*E*KD_SI/(K_B*T) ! ref. (1) eq. (1.1.2)
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BETA=ONE/(K_B*T) !
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ALP=KD_SI*DSQRT(BETA) !
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!
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CDI_PDF=N0*N0*( ONE -EPS*( & !
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DEXP(-X)/X - & !
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DEXP(-X/(TWO*ALP))/X + & ! ref. (1) eq. (3.3.14)
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SQR2*ERFC(X/(SQR2*ALP))/ALP & !
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) & !
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) !
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!
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END FUNCTION CDI_PDF
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!
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!=======================================================================
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!
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FUNCTION CEG_PDF(R,RS,T)
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!
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! This function computes very dilute classical electron gas
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! pair distribution function rho2(r) for 3D systems
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!
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! References: (1) A. Isihara, "Electron Liquids", 2nd edition,
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! Springer Series in Solid-State Sciences 96,
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! (Springer, 1998) p. 33
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!
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! Input parameters:
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!
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! * R : grid point in unit of a_0
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! * RS : Wigner-Seitz radius (in units of a_0)
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! * T : temperature in SI
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 30 Jul 2020
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!
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!
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USE CONSTANTS_P1, ONLY : BOHR,E,K_B
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USE UTILITIES_1, ONLY : RS_TO_N0
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!
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IMPLICIT NONE
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!
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REAL (WP) :: R,RS,T
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REAL (WP) :: CEG_PDF
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REAL (WP) :: N0
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!
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REAL (WP) :: DEXP
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!
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N0=RS_TO_N0('3D',RS) !
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!
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CEG_PDF=N0*N0*DEXP(-E*E/(R*BOHR*K_B*T)) ! ref. (1) eq. (3.1.1)
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!
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END FUNCTION CEG_PDF
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!
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!=======================================================================
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!
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FUNCTION DEB_PDF(R,RS,T)
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!
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! This function computes Debye electron gas
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! pair distribution function rho2(r) for 3D systems
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!
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! References: (1) A. Isihara, "Electron Liquids", 2nd edition,
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! Springer Series in Solid-State Sciences 96,
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! (Springer, 1998) p. 33
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!
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! Input parameters:
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!
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! * R : grid point in unit of a_0
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! * RS : Wigner-Seitz radius (in units of a_0)
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! * T : temperature in SI
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 4 Jun 2020
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!
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!
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USE REAL_NUMBERS, ONLY : FOUR
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USE CONSTANTS_P1, ONLY : BOHR
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USE PI_ETC, ONLY : PI
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USE UTILITIES_1, ONLY : RS_TO_N0
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USE SCREENING_VEC, ONLY : DEBYE_VECTOR
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!
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IMPLICIT NONE
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!
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REAL (WP) :: R,RS,T
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REAL (WP) :: DEB_PDF
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REAL (WP) :: RA
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REAL (WP) :: N0,KD_SI
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!
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REAL (WP) :: DEXP
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!
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N0=RS_TO_N0('3D',RS) !
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!
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! Computing the Debye screening vector
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!
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CALL DEBYE_VECTOR('3D',T,RS,KD_SI) !
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!
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RA=R*BOHR ! r in SI
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!
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DEB_PDF=N0*N0 - N0*KD_SI*KD_SI*DEXP(-KD_SI*RA)/(FOUR*PI*RA) ! ref. (1) eq. (3.1.4)
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!
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END FUNCTION DEB_PDF
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!
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!=======================================================================
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!
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FUNCTION FUA_PDF(R,RS,T)
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!
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! This function computes the electron gas pair distribution function
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! rho2(r) for 3D systems, correct to order 2 in epsilon, the plasma
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! parameter
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!
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! References: (1) A. Isihara, "Electron Liquids", 2nd edition,
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!C (Springer, 1998) p. 33
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!
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! Input parameters:
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!
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! * R : grid point in unit of a_0
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! * RS : Wigner-Seitz radius (in units of a_0)
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! * T : temperature in SI
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 21 Jul 2020
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!
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!
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USE REAL_NUMBERS, ONLY : TWO,THREE,HALF,THIRD,FOURTH
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USE CONSTANTS_P1, ONLY : BOHR,E,K_B
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USE UTILITIES_1, ONLY : RS_TO_N0
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USE SCREENING_VEC, ONLY : DEBYE_VECTOR
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USE EXT_FUNCTIONS, ONLY : DEI
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!
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IMPLICIT NONE
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!
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REAL (WP) :: R,RS,T
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REAL (WP) :: FUA_PDF
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REAL (WP) :: ARG_E
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REAL (WP) :: X,EPS,TX
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REAL (WP) :: N0,KD_SI
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!
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REAL (WP) :: DEXP,DLOG
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!
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N0=RS_TO_N0('3D',RS) !
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!
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! Computing the Debye screening vector
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!
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CALL DEBYE_VECTOR('3D',T,RS,KD_SI) !
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!
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X=KD_SI*R*BOHR !
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EPS=E*E*KD_SI/(K_B*T) ! ref. (1) eq. (1.1.2)
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TX=THREE*X !
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!
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ARG_E=EPS*DEXP(-X)/X + HALF*EPS*EPS/X * ( & !
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DEXP(-X)*( -THREE*FOURTH*DLOG(THREE) + & !
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X*FOURTH*DLOG(THREE) - THIRD ) + & !
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FOURTH*DEXP(X)*(X*DEI(-TX)) + & ! ref. (1) eq. (3.1.13)
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FOURTH*DEXP(-X)*(X*DEI(-X)) + & !
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THREE*FOURTH*DEXP(X)*DEI(-TX)- & !
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THREE*FOURTH*DEXP(-X)*DEI(-X)+ & !
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THIRD*DEXP(-TWO*X) ) !
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!
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FUA_PDF=N0*N0*DEXP(-ARG_E) ! ref. (1) eq. (3.1.12)
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!
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END FUNCTION FUA_PDF
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!
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!=======================================================================
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!
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FUNCTION SDC_PDF(R,RS,T)
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!
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! This function computes the electron gas pair distribution function
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! rho2(r) for 3D systems, for short-distance correlations
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!
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!
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! --> Warning: valid if T >> k_B * (a_0 / 2)^2
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!
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!
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! References: (1) A. Isihara, "Electron Liquids", 2nd edition,
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! Springer Series in Solid-State Sciences 96,
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! (Springer, 1998) p. 33
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!
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! Input parameters:
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!
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! * R : grid point (in units of a_0)
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! * RS : Wigner-Seitz radius (in units of a_0)
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! * T : temperature in SI
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 4 Jun 2020
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!
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!
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USE REAL_NUMBERS, ONLY : ONE,TWO,HALF,THIRD
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USE CONSTANTS_P1, ONLY : BOHR,K_B
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USE PI_ETC, ONLY : PI
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USE UTILITIES_1, ONLY : RS_TO_N0
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USE SCREENING_VEC, ONLY : DEBYE_VECTOR
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!
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IMPLICIT NONE
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!
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REAL (WP) :: R,RS,T
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REAL (WP) :: R2,R3
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REAL (WP) :: SDC_PDF
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REAL (WP) :: BETA,DELTA
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REAL (WP) :: N0,KD_SI
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!
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REAL (WP) :: DSQRT
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!
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R2=R*R*BOHR*BOHR ! r^2 in SI
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R3=R2*R*BOHR ! r^3 in SI
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!
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N0=RS_TO_N0('3D',RS) !
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!
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! Computing the Debye screening vector
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!
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CALL DEBYE_VECTOR('3D',T,RS,KD_SI) !
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!
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BETA=ONE/(K_B*T) !
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DELTA=TWO*DSQRT(BETA)/BOHR ! ref. (1) eq. (3.3.7)
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!
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SDC_PDF=HALF*N0*N0*( & !
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ONE - DSQRT(HALF*PI)*DELTA + & !
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HALF*R + HALF*R2/BETA - & !
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TWO*THIRD*DSQRT(HALF*PI)*R2 / ( & ! ref. (1) eq. (3.3.10)
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BOHR*DSQRT(BETA) ) - & !
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HALF*R3/(BOHR*BETA) & !
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) !
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!
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END FUNCTION SDC_PDF
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!
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!=======================================================================
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!
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FUNCTION WDA_PDF(R,RS,T)
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!
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! This function computes watermelon diagrams-summed electron gas
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! pair distribution function rho2(r) for 3D systems
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!
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! References: (1) A. Isihara, "Electron Liquids", 2nd edition,
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! Springer Series in Solid-State Sciences 96,
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! (Springer, 1998) p. 33
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!
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! Input parameters:
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!
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! * R : grid point in unit of a_0
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! * RS : Wigner-Seitz radius (in units of a_0)
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! * T : temperature in SI
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 4 Jun 2020
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!
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!
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USE CONSTANTS_P1, ONLY : BOHR,E,K_B
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USE UTILITIES_1, ONLY : RS_TO_N0
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USE SCREENING_VEC, ONLY : DEBYE_VECTOR
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!
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IMPLICIT NONE
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!
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REAL (WP) :: R,RS,T
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REAL (WP) :: WDA_PDF
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REAL (WP) :: PHI_D,RA
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REAL (WP) :: N0,KD_SI
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!
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REAL (WP) :: DSQRT
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!
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N0=RS_TO_N0('3D',RS) !
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!
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! Computing the Debye screening vector
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!
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CALL DEBYE_VECTOR('3D',T,RS,KD_SI) !
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!
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RA=R*BOHR ! r in SI
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!
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PHI_D=E*E*DEXP(-KD_SI*RA)/RA ! ref. (1) eq. (3.1.7)
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!
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WDA_PDF=N0*N0*DEXP(-PHI_D/(K_B*T)) ! ref. (1) eq. (3.1.5)
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!
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END FUNCTION WDA_PDF
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!
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END MODULE PAIR_DISTRIBUTION
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