gmass06.f

61 lines · 1 definitions · on GitHub (7be4133)

Python version: gmass06.py, 74 lines, on the right (switch to Python above the code).

Purpose

GMASS06 is the version of GMASS for the 2006 OPAL equation of state. At rp_1 its code was identical to GMASS01 apart from its name; GMASS and GMASS01, for the older tables, are removed since rp_1. It returns the mean mass per nucleus (without electrons), and sets the number fractions of H, He, C, N, O, Ne, the particles per nucleus and the ground-state energy.

How it fits

Called only by ESAC06. No COMMON blocks or modules, no calls.

The method

The metals are split in fixed number proportions $x_\mathrm{C} = 0.2471$, $x_\mathrm{N} = 0.0621$, $x_\mathrm{O} = 0.5284$, $x_\mathrm{Ne} = 0.1624$ (XC, XN, XO, XNE). With atomic masses $A_i$ (AMAS), the number of moles per gram of each species is

$$n_\mathrm{H} = \frac{X}{A_\mathrm{H}},\quad n_\mathrm{He} = \frac{1-X-Z}{A_\mathrm{He}},\quad n_k = f_Z\,x_k,\quad f_Z = \frac{Z}{\sum_k x_k A_k}\ (k = \mathrm{C,N,O,Ne}),$$

and the number fractions are $\mathrm{FRAC}_i = n_i/\sum_j n_j$, stored in the order Ne, O, N, C, He, H (indices 1 to 6). With $Z_i$ the nuclear charges (ANUM) and $E_i$ the ground-state energies of the ions (EION, units not stated in the code),

$$\mathrm{AMOLES} = \sum_i (1+Z_i)\,\mathrm{FRAC}_i,\qquad \mathrm{EGROUND} = \sum_i E_i\,\mathrm{FRAC}_i,\qquad \mathrm{GMASS06} = \sum_i A_i\,\mathrm{FRAC}_i,$$

without the electrons' mass (which GMASS added). FRACZ returns $f_Z$. The mean number of electrons per nucleus, ANUME = AMOLES $- 1$ (line 54 ↗), is computed but not returned (unused?).

Definitions

functionGMASS06

lines 7–61 · GitHub

Mean mass per nucleus, number fractions, particles per nucleus and ground-state energy for a fixed metal mixture (method above).

Called by ESAC06

Change log

The changes since rp_1

Changed since rp_1. Declarations only: IMPLICIT NONE. GMASS and GMASS01, which the method referred to, are removed, so their equations are given here.

1C$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 2C 3C GMASS06 4C 5C$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 6 7 function gmass06(x,z,amoles,eground,fracz,frac) 8C 10/20/26 MHP via Claude 9C code changed to replace implicit typing with IMPLICIT NONE and 10C explicit declarations. 11 IMPLICIT NONE 12 REAL*8 AMAS,AMOLES,ANUM,ANUME,EGROUND,EION,FRAC,FRACZ,GMASS06,X, 13 * * XC,XC2,XH,XHE,XN,XN2,XNE,XNE2,XO,XO2,XTOT,Z 14 INTEGER I 15 16 dimension anum(6),frac(7), amas(7),eion(7) 17 data (eion(i),i=1,6)/-3394.873554D0,-1974.86545D0,-1433.92718D0, 18 x x -993.326315D0,-76.1959403D0,-15.29409D0/ 19 data (anum(i),i=1,6)/10.,8.,7.,6.,2.,1./ 20 save 21 22 xc=0.247137766D0 23 xn=.0620782D0 24 xo=.52837118D0 25 xne=.1624188D0 26 amas(7)=1.0079D0 27 amas(6)=4.0026D0 28 amas(5)=12.011D0 29 amas(4)=14.0067D0 30 amas(3)=15.9994D0 31 amas(2)=20.179D0 32 amas(1)=0.00054858D0 33 34 fracz=z/(xc*amas(5)+xn*amas(4)+xo*amas(3)+xne*amas(2)) 35 xc2=fracz*xc 36 xn2=fracz*xn 37 xo2=fracz*xo 38 xne2=fracz*xne 39 xh=x/amas(7) 40 xhe=(1D0-x -z)/amas(6) 41 xtot=xh+xhe+xc2+xn2+xo2+xne2 42 frac(6)=xh/xtot 43 frac(5)=xhe/xtot 44 frac(4)=xc2/xtot 45 frac(3)=xn2/xtot 46 frac(2)=xo2/xtot 47 frac(1)=xne2/xtot 48 eground=0.0D0 49 amoles=0.0D0 50 do i=1,6 51 eground=eground+eion(i)*frac(i) 52 amoles=amoles+(1D0+anum(i))*frac(i) 53 enddo 54 anume=amoles-1D0 55 gmass06=0D0 56 do i=2,7 57 gmass06=gmass06+amas(i)*frac(i-1) 58 enddo 59 60 return 61 end

1"""Python version of gmass06.f (YREC 7be4133): the mean mass per nucleus 2and number fractions for the 2006 OPAL equation of state.""" 3 4import numpy as np 5 6# DATA: the ground-state energies of the ions and the nuclear charges, in 7# the order Ne, O, N, C, He, H. 8eion = np.zeros(7 + 1) 9eion[1:7] = [-3394.873554, -1974.86545, -1433.92718, -993.326315, 10 -76.1959403, -15.29409] 11anum = np.zeros(6 + 1) 12anum[1:7] = [10., 8., 7., 6., 2., 1.] 13amas = np.zeros(7 + 1) 14 15 16def gmass06(x: float, z: float, amoles: float, eground: float, fracz: float, frac: np.ndarray) -> tuple[float, float, 17 float, float]: 18 """Split Z in fixed number proportions among C, N, O and Ne, and 19 compute the number fractions frac (Ne, O, N, C, He, H), the 20 particles per nucleus amoles, the ground-state energy eground and the 21 mean mass per nucleus (without electrons). 22 23 Translates: gmass06.f#GMASS06 (7be4133) 24 25 Arguments: x, z; amoles, eground, fracz are only set. 26 Array changed in place: frac (indices 1-6). 27 28 Returns (gmass06, amoles, eground, fracz). 29 30 """ 31 32 # The metals' number fractions and the atomic masses (Fortran lines 33 # 22–32). 34 xc = 0.247137766 35 xn = .0620782 36 xo = .52837118 37 xne = .1624188 38 amas[7] = 1.0079 39 amas[6] = 4.0026 40 amas[5] = 12.011 41 amas[4] = 14.0067 42 amas[3] = 15.9994 43 amas[2] = 20.179 44 amas[1] = 0.00054858 45 46 # The number fractions (Fortran lines 34–47). 47 fracz = z / (xc * amas[5] + xn * amas[4] + xo * amas[3] + xne * amas[2]) 48 xc2 = fracz * xc 49 xn2 = fracz * xn 50 xo2 = fracz * xo 51 xne2 = fracz * xne 52 xh = x / amas[7] 53 xhe = (1.0 - x - z) / amas[6] 54 xtot = xh + xhe + xc2 + xn2 + xo2 + xne2 55 frac[6] = xh / xtot 56 frac[5] = xhe / xtot 57 frac[4] = xc2 / xtot 58 frac[3] = xn2 / xtot 59 frac[2] = xo2 / xtot 60 frac[1] = xne2 / xtot 61 62 # Ground-state energy and particles per nucleus (Fortran lines 48–54). 63 eground = 0.0 64 amoles = 0.0 65 for i in range(1, 6 + 1): 66 eground = eground + eion[i] * frac[i] 67 amoles = amoles + (1.0 + anum[i]) * frac[i] 68 anume = amoles - 1.0 # noqa: F841 (unused in the Fortran too) 69 70 # The mean mass per nucleus (Fortran lines 55–58). 71 gmass = 0.0 72 for i in range(2, 7 + 1): 73 gmass = gmass + amas[i] * frac[i - 1] 74 return gmass, amoles, eground, fracz