Conflicting definitions of statistical weight in calculation of level-resoled dielectronic recombination

[wtbarnes]

In ch_load_2ion_rates, the level resolved dielectronic capture as well as the dielectronic recombination between the ground states of the recombining and recombined ion is calculated. The latter includes a correction factor to account for the double counting of the level-resolved rates. My understanding is that these contributions are calculated using Eqs. 4 and 5 in the Appendix of Dere et al. (2019) (the v9 paper).

Both equations include the ratio $g_s/g_k$ which I understand to be the ratio of the statistical weights of the autoionizing states ($s$) of the recombined ion and the lower-energy bound states ($k$) of the recombining ion.

In ch_load_2ion_rates, when computing the the dielectronic capture rate, the statistical weights are computed as $2J+1$ (where $J$ is the total angular momentum):

chianti-idl/level_population/ch_load_2ion_rates.pro

Lines 408 to 412 in 0387392

	gs=1.+2.*rates1.ion_data.jj[lvl_s[k]-1]
	; gl is the statistical weight of the level of the recombining ion
	; that produces the dielctronic capture.
	gl=1.+2.*rates2.ion_data.jj[lvl_l[k]-1]

However, when computing the total of the level-resolved dielectronic recombination rates, the statistical weights are computed using the multiplicity, $2S+1$ (where $S$ is the spin):

chianti-idl/level_population/ch_load_2ion_rates.pro

Lines 471 to 484 in 0387392

	gs=rates1.mult[lvl_auto[ii]-1]
	; now check how many levels of the recombining ion are connected to
	; the ground state *******
	ind_this_auto= where(lvl_s eq lvl_auto[ii] and lvl_l eq 1, n_decays)
	if n_decays gt 0 then begin
	; ecms is the energy of the autoionising level
	ecms=rates1.ion_data.ecm[lvl_auto[ii]-1] ; this is either observed or theoretical
	for id=0, n_decays-1 do begin
	gl=rates2.mult[lvl_l[ind_this_auto[id]] -1]

Is this difference intentional? If so, why are the statistical weights defined differently in these two expressions?

[pryoung]

Hi Will, I see the multiplicity (mult) is defined as 2J+1 in ch_load_ion_rates, so the multiplicity is actually the weight. Thus the code is OK, but the variable mult is misnamed! It’s best not to relabel it at this stage, but I’ll insert a comment into ch_load_ion_rates pointing this out. Thanks, Peter From: Will Barnes ***@***.***> Date: Tuesday, February 4, 2025 at 3:27 PM To: chianti-atomic/chianti-idl ***@***.***> Cc: Subscribed ***@***.***> Subject: [EXTERNAL] [BULK] [chianti-atomic/chianti-idl] Conflicting definitions of statistical weight in calculation of level-resoled dielectronic recombination (Issue #9) CAUTION: This email originated from outside of NASA. Please take care when clicking links or opening attachments. Use the "Report Message" button to report suspicious messages to the NASA SOC. In ch_load_2ion_rates, the level resolved dielectronic capture as well as the dielectronic recombination between the ground states of the recombining and recombined ion is calculated. The latter includes a correction factor to account for the double counting of the level-resolved rates. My understanding is that these contributions are calculated using Eqs. 4 and 5 in the Appendix of Dere et al. (2019) (the v9 paper). Both equations include the ratio $g_s/g_k$ which I understand to be the ratio of the statistical weights of the autoionizing states ($s$) of the recombined ion and the lower-energy bound states ($k$) of the recombining ion. In ch_load_2ion_rates, when computing the the dielectronic capture rate, the statistical weights are computed as $2J+1$ (where $J$ is the total angular momentum): https://github.com/chianti-atomic/chianti-idl/blob/0387392a6cba39ce700be0d164f53ab56b2fcd12/level_population/ch_load_2ion_rates.pro#L408-L412 However, when computing the total of the level-resolved dielectronic recombination rates, the statistical weights are computed using the multiplicity, $2S+1$ (where $S$ is the spin): https://github.com/chianti-atomic/chianti-idl/blob/0387392a6cba39ce700be0d164f53ab56b2fcd12/level_population/ch_load_2ion_rates.pro#L471-L484 Is this difference intentional? If so, why are the statistical weights defined differently in these two expressions? — Reply to this email directly, view it on GitHub<#9>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/AEL4UCEEXG34YTAXTHEPOY32OEPBVAVCNFSM6AAAAABWPOTDXOVHI2DSMVQWIX3LMV43ASLTON2WKOZSHAZTCMRRHEZTSNI>. You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

[wtbarnes]

Thanks Peter! I hadn't even thought to check that function and naively assumed it was the same multiplicity in the elvlc files.