[next] [tail] [up]

A.1 CBB Transitions

A.1.1 van-Regemorter Formula (Allowed Dipole Transitions)

------ |_ ( ) _| 2 V~ -8k-- V ~ -- EH-- 2 - u0 Cij = pa0 ne T |_ 14.5fij _| u0e G(u0) pme E0

u u0 = hnij/kT , E0 = hnij, G(u0) = max[g, 0.276e 0E1(u0)]

g = 0.2 for n’/=n else = 0.7. EH is the ionization energy of the hydrogen ground state.

------ 8k pa02V~ ----- = 5.465 .10 -11 pme
2 input parameters: fij, g

A.1.2 Forbidden Transitions

-6 8.631-.10---- -u0 Cij = gi V~ T nee _O_

NF IT _O_ = sum a .xi -1 i=1 i
NFIT+1 input parameters: NFIT, a1, ... , aNFIT
for the effective collision strength. Is only one parameter supplied (explicitly: 1), then _O_ = 1 is set.

A.1.3 Hydrogen

following Mihalas

------ ( )2 2 V~ -8k-- V ~ -- EH--- Cij = 4pa0 pm ne T hn u0fij (E1(u0) + 0.148u0E5(u0)) g e ij

g = b + 2(a - b)/Dn for Dn > 1, and g = 1 else b = 3 - 1.2/n , a = 1.8- 0.4/n2 i i
no input parameter

A.1.4 He II

following Mihalas & Stone

------ ( )2 2 V~ -8k-- V ~ -- EH--- ( - u0 ) Cij = pa0 pme ne T hnij u0fije e ln 2 + E1(u0) g

[ n - 1 ] g = min [ni, 1.1] .min Dni, ni - ------- Dn
no input parameter

A.1.5 He I: Allowed Transitions from its Ground State

following Mihalas & Stone

------ 8k V~ -- ( E )2 C1j = 4pa02V ~ -----ne Tf1j --H-- u0E1(u0) pme hn1j
1 input parameter: f1j

A.1.6 He I: Allowed Transitions but not from its Ground State
following Mihalas & Stone

------ 8k V ~ -- ( EH )2 ( u0 ) Cij = 4pa02V~ -----ne T fij ----- u0 E1(u0) - ---e- 0.2(E1(u1) pme hn1j u1

u1 = u0 + 0.2
1 input parameter: fij

A.1.7 He I: Forbidden Transitions from its Ground State
following Mihalas & Stone

------ 8k V ~ -- a 1 [ ] Cij = pa02V~ -----ne T -----3u0 ----2- a0E1(u0) + a1u0e -b1u0x1 + a2u0e - b2u0x2 pme neff pa0

( -1) bi-u0-+--c1--+-2-- xi = ( 1-)3 u0 + ci

------ E neff = ZV ~ --H-- (Z = 1) hnth
8 input parameters: a, ai, bi, ci (found in tabular form in M&S; Attention: their equation A16 is wrong!)

A.1.8 He I: Forbidden Transitions between its n = 2 Sublevels
following Mihalas & Stone

------ 2 V~ -8k-- V ~ -- -E0/kT Cij = pa0 pm ne T e Gij(T ) e

E0 = hnij

-2 log G = c0 + c1 log T + c- 2 (log T )
3 input parameters: c0, c1, c-2 (in tabular form by M&S)

A.1.9 Unknown Collisional Cross-Sections

------ V~ -- C = pa 2 V~ --8k- n T e- u0 (1 + u ) ij 0 pme e 0
no input parameter

A.1.10 _O_-Fit of 3rd Degree
like A.1.2, but:

sum 4 i-1 _O_ = ai (log T ) i=1
4 input parameters: a1, a2, a3, a4

A.1.11 Mg II: Allowed Transitions from its Ground State
following Mihalas (1972)

------ 8k V ~ -- EH 2 ( ) Cij = pa02V ~ -----ne T 4fij---- u0 aE1(u0) + be-u0 pme E0
2 input parameters: a, b

A.1.12 van-Regemorter: Combined Levels of Complex Ions

------ C = pa 2 V~ -8k--n V~ T-e -u0G (T ) ij 0 pme e ij
2 3 log Gij(T ) = a0 + a1x + a2x + a3x , x = log kT [in eV ]
4 input parameters: a0, a1, a2, a3

A.1.21 He I: Transition between its Levels with s < 4
D. Hummer, priv. comm.
no input parameter

A.1.25 _O_-Fit in Temperature, General Case
equal to DETAIL Formula No. 25,
8 input parameters

A.1.26 _O_-Fit in log T, General Case
equal to DETAIL Formula No. 26,

NF IT _O_ = sum a (log T - T )i-1 i=1 i 1
NFIT+2 input parameters: T1, NFIT, a1, ..., aNFIT

[next] [front] [up]