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The Iron Project: RADIATIVE ATOMIC PROCESSES IN ASTROPHYSICS

Sultana N. Nahar

Dept of Astronomy, The Ohio State University, Columbus, OH 43210, USA

E-mail: [email protected]

Astronomical objects, such as, stars, galaxies, blackhole environments, etc are studied through their spectra producedby various atomic processes in their plasmas. The positions, shifts, and strengths of the spectral lines provide infor-

mation on physical processes with elements in all ionization states, and various diagnostics for temperature, density,

distance, etc of these objects. With presence of a radiative source, such as a star, the astrophysical plasma is dominatedby radiative atomic processes such as photoionization, electron-ion recombination, bound-bound transitions or photo-

excitations and de-excitations. The relevant atomic parameters, such as photoionization cross sections, electron-ionrecombination rate coefficients, oscillator strengths, radiative transition rates, rates for dielectronic satellite lines etc

are needed to be highly accurate for precise diagnostics of physical conditions as well as accurate modeling, such as,

for opacities of astrophysical plasmas.This report illustrates detailed features of radiative atomic processes obtained from accurate ab initio methods of the

latest developments in theoretical quantum mechanical calculations, especially under the international collaborations

known as the Iron Project (IP) and the Opacity Project (OP). These projects aim in accurate study of radiative andcollsional atomic processes of all astrophysically abundant atoms and ions, from hydrogen to nickel, and calculate

stellar opacities and have resulted in a large number of atomic parameters for photoionization and radiative transition

probabilities. The unified method, which is an extension of the OP and the IP, is a self-consistent treatment for the totalelectron-ion recombination and photoionization. It incorporates both the radiative and the dielectronic recombination

processes and provides total recombination rates and level-specific recombination rates for hundreds of levels for a

wide range of temperature of an ion. The recombination features are demonstrated. Calculations are carried out usingthe accurate and powerful R-matrix method in the close-coupling approximation. The relativistic fine structure effects

are included in the Breit-Pauli approximation. The atomic data and opacities are available on-line from databases atCDS in France and at the Ohio Supercomputer Center in the USA. Some astrophysical applications of the results of

the OP and IP from the Ohio State atomic-astrophysics group are also presented. These same studies, however with

different elements, can be extended for bio-medical applications for treatments. This will also be explained with somepreliminary findings.

Keywords: Photoionization; Electron-ion recombination; Oscillator strengths; Di-electronic satellite lines; Opacities

1. Introduction

The initial study of an astronomical object can bemade via photometry which gives information on lo-cation, size, surroundings, etc alongwith low levelspectroscopy. Figure 1 shows a photometric imageof supernova remnant Cassiopia A1 composed of in-frared data from the Spitzer, visible data from theHubble Space Telescope, and X-ray data from theChandra observatory. A supernova remnant typicallyconsists of an outer, shimmering shell of expelledmaterial and a core skeleton of a once-massive star,called a neutron star. Heavy elements in universe areknown to be formed during a supernova explosion.

However, details such as, temperature, density,speed, composition etc can be obtained only fromprecise spectroscopy. What we see in an astronomicalobject depends on how the nuclear energy (gammarays) produced in the core of the star propagates tothe surface. As the radiation travels outward it goesthrough repeated absorption and emission by atoms

Fig. 1. Photometric picture of Cassiipia A made from obser-vation by Spitzer (infrared), Hubble (visible), and Chandra

(X-ray).1

and molecules and looses energy to become visiblephotons. This process depends on the opacity of theconstituent materials. Stellar opacities give measures


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of radiation transport in the plasmas and are crucialin calculating various quantities and analyzing astro-physical spectra. Opacities depend mainly on oscil-lator strengths and photoionization cross sections ofall transitions in the constituent elements.

About 25 years ago, it was realized that theexisting calculated stellar opacities, obtained usingatomic data from simple approximations, were incor-rect by factors of 2 to 5 resulting in inaccurate stellarmodels. For example, pulsation periods of Cepheidstars, which are used in gauging the distances of as-tronomical objects, could not be modeled. A pleawas made for accurate opacity using accorate atomicparameters. This initiated the international OpacityProject2 for precise study of the radiative processesof all astrophysically abundant atoms and ions, fromhydrogen to iron, and calculate the opacities. Withthe same theme, the Iron Project3 was initiated laterfor both radiative and collisional process, however,for iron-peak elements and with inclusion of finestructure effect in the calculations. The OP and theIP include a very wide energy range, from infrared(IR), optical (O), ultraviolet (UV), extreme ultravi-olet (EUV) to X-rays. The theoretical approach ofR-matrix method using close coupling approxima-tion enables consideration of large number of energylevels, and corresponding transitions, and photoion-ization.

2. Radiative Atomic Processes

Astrophysical plasmas are dominated by three ra-diative atomic processes. (1) Photo-excitation andde-excitation:

X+Z + hν X+Z∗

where X+Z is the ion with charge Z. The emittedor absorbed photon (hν) is observed as a spectralline. The relevant atomic parameters for the directand inverse processes are oscillator strength (f) andradiative decay rate (A-value).

The other two are the inverse processes of (2)photoionization (PI) and (3) electron-ion recombina-tion. In direct photoionization and radiative recom-bination (RR), an electron is ejected with absorptionof a photon or recombines to a ion with emission ofa photon:

X+Z + hν X+Z+1 + ε

Photoionization and recombination can also occurvia an intermediate state as:

e + X+Z (X+Z−1)∗∗

e + X+Z AIX+Z−1 + hν DR

where an electron colliding with a target of charge+Z excites it as well as attaches itself to form a dou-bly excited quasi-bound state known as an autoion-izing state. This state is short-lived and leads eitherto autoionization (AI) where the electron goes freeand target drops to ground state or to dielectronicrecombination (DR) where the electron gets boundby emission of a photon. The autoionizing state man-ifests as an enhancement or resonance in the process.Photoionization resonances can be seen in absorptionspectra while recombination resonances can be seenin emission spectra. The relevant atomic parametersfor these processes are photoionization cross sections(σPI), recombination cross sections (σRC) and ratecoefficients (αRC).

3. Theory

The relativistic Hamiltonian of a multi-electron sys-tem in Breit-Pauli R-matrix (BPRM) method isgiven by,

HBPN+1 = HNR

N+1 + HmassN+1 + HDar

N+1 + HsoN+1, (1)

where the non-relativistic Hamiltonian is,

HNRN+1 =

N+1∑i=1

−∇2i −

2Z

ri+

N+1∑j>i

2rij

(2)

and the three one-body relativisitc terms are masscorrection, Hmass = −α2

4

∑i p4

i , Darwin term,

HDar = α2

4

∑i∇2

(Zri

), and spin-orbit interation

term, Hso =[

Ze2~2

2m2c2r3

]L.S. However, the effects of

higher order terms, especially the two-body terms,in the Breit-Pauli Hamiltonian,

12

N∑i 6=j

[gij(so + so′) + gij(ss′) + gij(css′) + gij(d) + gij(oo′)].(3)

where the notation are c for contraction, d for Dar-win, o for orbit, s for spin and a prime indicates’other’ can improve the energies and weak transi-tions. We include full Breit interaction,

HB =∑i>j

[gij(so + so′) + gij(ss′)] (4)

for the weak forbidden transitions.


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The energies and wavefunctions of the (N+1)-electron system can be obtained from solving

HBPN+1Ψ = EΨ. (5)

The close coupling (CC) approximation for wave-function describe an atomic process as a target or thecore ion of N electrons interacting with the (N+1)thelectron (e.g. Seaton4). Total wavefunction expan-sion is expressed as:

ΨE(e + ion) = AN∑i

χi(ion)θi +∑

j

cjΦj(e + ion)

where χi is the target ion or core wavefunction atstate i, θi is the interacting electron wavefunction,which is a continuum state wavefunction ΨF when E≥ 0 or bound state function ΨB when E < 0. Φj isa correlation function of (e+ion) compensating theshort-range correlation and orthogonality condition.The complex resonant structures in the atomic pro-cesses are introduced through couplings of bound andcontinuum channels in the transition matrix. Substi-tution of ΨE(e+ion) in Hamiltonian equation resultsin a set of coupled equations which are solved by R-matrix method.

R-matrix method divides the space in two re-gions, the inner and the outer regions, of a sphere ofradius ra with the ion at the center. ra is large enoughfor electron-electon interaction potontial to be zerooutside the boundary; wavefunction at r > ra isCoulombic due to perturbation from the long-rangemultipole potentials. In the inner region, the partialwave function of the interacting electron is expandedin terns of a basis set, called the R-matrix basis,

Fi =∑

akuk

which satisfies[d2

dr2− l(l + 1)

r2+ V (r) + εlk

]ulk+

∑n

λnlkPnl(r) = 0.

(6)and are made continuous at the boundary by match-ing with the Coulomb functions outside the bound-ary.

For radiative processes, the transition matrixelements < ΨB ||D||ΨB′ > for bound-bound transi-tions and < ΨB ||D||ΨF > for photoionization andrecombination are obtained with dipole operator,D =

∑i ri, where i is the number of electrons. The

generalized line strength, S, can be obtained as

S =

∣∣∣∣∣∣⟨

Ψf |N+1∑j=1

rj |Ψi

⟩∣∣∣∣∣∣2

(7)

The oscillator strength (fij) and radiative decayrate (Aji) for a dipole bound-bound transition arethen obtained as

fij =[Eji

3gi

]S, Aji(sec−1) =

[0.8032× 1010

E3ji

3gj

]S

(8)The photoionization cross section, σPI , is related

to S as

σPI =[4π

3c

1gi

]ωS, (9)

where ω is incident photon energy in Rydberg unitsand gi is the statistical weight factor of the initialstate.

Recombination cross section, σRC , for any levelcan be obtained from σPI using principle of detailedbalance (Milne relation) as

σRC = σPIgi

gj

h2ω2

4π2m2c2v2. (10)

These can be summed for the total σRC . Recombina-tion rate coefficient in terms of photoelectron energyis given by

αRC(E) = vσRC

The recombination rate coefficient, αRC(T ), atvarious temperatures is obtained as

αRC(T ) =∫ ∞

0

vf(v)σRCdv, (11)

where f(v, T ) = 4√π( m2kT )3/2v2e−

mv22kT is the

Maxwellian velocity distribution function. The to-tal αRC is obtained from summed contributions ofinfinite number of recombined states.

The unified theory for electron-ion recombina-tion considers all infinite recombining levels andsubsumes RR and DR in unified manner5–7 incontrast to existing methods that treat RR andDR separately and the total rate is obtained fromαRC = αRR + αDR neglecting the interference be-tween RR and DR. The unified method divides therecombined states in to two groups. The contribu-tions from states with n ≤ 10 (group A) are ob-tained from σPI using principle of detailed balance,while the contributions from states with 10 < n ≤ ∞


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(group B), which are dominated by narrow dense res-onances, are obtained from an extension of the DRtheory:6,8

Ω(DR) =∑Jπ

∑n

(1/2)(2J + 1)P Jπn (DR). (12)

where the DR probability P Jπn in entrance channel

n is, P Jπn (DR) = (1 − S†

eeSee)n, See is the matrixfor electron scattering including radiation damping.The recombination cross section, σRC in Megabarns(Mb), is related to the collision strength, ΩRC, as

σRC(i → j)(Mb) =πΩRC(i, j)

(gik2i )

(a2o/1.× 10−18),

(13)where k2

i is in Rydberg. The method provides self-consistent set of σPI , σRC , and αRC as they obtainedusing the same wavefunction. It also provides level-specific recombination rate coefficients and photoion-ization cross sections for many bound levels.

Under the IP, f , S, and A-values for fine struc-ture forbidden transitions, and allowed for some com-plex ions, are treated with relativistic configurationinteraction atomic structure calculations using codeSUPERSTRUCTURE (SS).9 The allowed and for-bidden transitions are as summarized as: Allowedelectric dipole (E1) transtitions are of two types: (i)same-spin multiplet (∆ j=0,±1, ∆L = 0, ±1, ±2,∆S = 0, parity π changes), (ii) intercombination (∆j=0,±1, ∆L = 0, ±1, ±2, ∆S 6= 0, π changes):

Aji(sec−1) = 0.8032× 1010E3

ji

3gjSE1, fij =

Eji

3giSE1(ij)

(14)where SE1(ij) is the line strength for E1 transition.

Forbidden transitions, which are usually muchweaker than the allowed transitions, are of higherorder magnetic and electric poles.i) Electric quadrupole (E2) transitions (∆ J =0,±1,±2, parity does not change):

AE2ji = 2.6733× 103

E5ij

gjSE2(i, j) s−1, (15)

ii) Magnetic dipole (M1) transitions (∆ J = 0,±1,parity does not change):

AM1ji = 3.5644× 104

E3ij

gjSM1(i, j) s−1, (16)

iii) Electric octupole (E3) transitions (∆ J= ±2, ±3,parity changes):

AE3ji = 1.2050× 10−3

E7ij

gjSE3(i, j) s−1, (17)

iv) Magnetic quadrupole (M2) transitions (∆ J =±2, parity changes):

AM2ji = 2.3727× 10−2s−1

E5ij

gjSM2(i, j) . (18)

The lifetime of a level can be calculated from theA-values, τk(s) = 1/

∑i Aki(s−1)

4. Results

Results with various features on oscillator strengthsand radiative decay rates for bound-bound transi-tions, photoionization cross sections and recombina-tion rate coefficients are illustrated below.

4.1. Radiative Transitions: f , S,

A-values

Under the IP, E1 transitions are calculated for levelsgoing up to n=10 and l ≤ 9 while weaker forbiddentransitions are considered up to n ≤ 5 in general. Theadvantage of BPRM method is that a large numberof energy levels and transitions can be calculated,however, without spectroscopic identification. Theo-retical spectroscopy for level identification, which isa major task, is carried out using quantum defectanalysis, percentage of channels contributions, andangular momenta algebra.

For example, a recent BPRM calculations forFe VX11 has resulted in 507 fine structure levels andcorresponding 27,812 transitions of type E1. The en-ergies are found be within 1% in agreement withthe observed values available in NIST12 compiled ta-ble. Table 1 presents an example set of identified en-ergy values grouped together as fine structure com-poments of Fe XV.

Close coupling approximation with R-matrixmethod does not optimize individual transitions.Hence, consistent accuracies are expected in gen-eral. Table 2 presents comparison of BPRM transi-tion probabilies of Fe XV11 with the available values.Good agreement can be seen for most transitions.However, some differences are also exist. Table 2 alsopresents comparison of A-values for forbidden tran-sitions in Fe XV,11 obtained from relativistic Breit-Pauli approximation using SUPERSTRUCTURE,9

with those available in NIST compilation.12 Goodagreement is found between SS and NIST for E2,M1 transitions. Variable agreement is noted betweenSS and NIST for M2 transitions.


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Table 1. Sample set of fine structure energy levels of Fe XVgrouped as sets of LS term components. Ct is the coreconfiguration, ν is the effective quantum number.

Ct(StLtπt) Jt nl 2J E(Ry) ν SLπ

Eqv electron/unidentified levels, parity: e2p63s2 0 -3.35050E+01 0.00 1 S e

Nlv(c)= 1 : set complete

Nlv= 3, 3Lo: P ( 2 1 0 )

2p63s (2Se) 1/2 3p 0 -3.13740E+01 2.68 3 P o2p63s (2Se) 1/2 3p 1 -3.13214E+01 2.68 3 P o2p63s (2Se) 1/2 3p 2 -3.11951E+01 2.69 3 P o


Nlv= 1, 1Lo: P ( 1 )

2p63s (2Se) 1/2 3p 1 -3.02823E+01 2.73 1 P o


Eqv electron/unidentified levels, parity: e2p63p2 0 -2.84377E+01 0.00 3 P e2p63p2 2 -2.83981E+01 0.00 3 P e2p63p2 1 -2.83502E+01 0.00 3 P e


Eqv electron/unidentified levels, parity: e2p63p2 2 -2.81990E+01 0.00 1 D e


Eqv electron/unidentified levels, parity: e2p63p2 0 -2.74705E+01 0.00 1 S e


Nlv= 3, 3Le: D ( 3 2 1 )

2p63s (2Se) 1/2 3d 1 -2.72920E+01 2.87 3 D e2p63s (2Se) 1/2 3d 2 -2.72822E+01 2.88 3 D e2p63s (2Se) 1/2 3d 3 -2.72669E+01 2.87 3 D e


Nlv= 1, 1Le: D ( 2 )

2p63s (2Se) 1/2 3d 2 -2.65180E+01 2.88 1 D e


Nlv= 9, 3Lo: P ( 2 1 0 ) D ( 3 2 1 ) F ( 4 3 2 )

2p63p (2Po) 1/2 3d 2 -2.50182E+01 2.88 3 PDF o2p63p (2Po) 1/2 3d 3 -2.49282E+01 2.88 3 DF o2p63p (2Po) 1/2 3d 4 -2.48254E+01 2.86 3 F o2p63p (2Po) 1/2 3d 1 -2.45113E+01 2.89 3 PD o2p63p (2Po) 1/2 3d 2 -2.45045E+01 2.88 3 PDF o2p63p (2Po) 1/2 3d 3 -2.44046E+01 2.88 3 DF o2p63p (2Po) 1/2 3d 0 -2.43943E+01 2.88 3 P o2p63p (2Po) 1/2 3d 1 -2.43941E+01 2.89 3 PD o2p63p (2Po) 1/2 3d 2 -2.43929E+01 2.88 3 PDF o


Nlv= 3, 1Lo: P ( 1 ) D ( 2 ) F ( 3 )

2p63p (2Po) 1/2 3d 2 -2.48346E+01 2.88 1 D o2p63p (2Po) 1/2 3d 3 -2.37794E+01 2.84 1 F o2p63p (2Po) 3/2 3d 1 -2.36558E+01 2.85 1 P o


Consideration of large number of transitions isneeded for opacity calculations, spectral modeling ofastrophysical plasmas. Figure 2 shows modeling ofFe I, Fe II, and Fe III lines observed in spectra of ac-tive galaxy 1 Zwicky 1. With large number oscillatorstrengths of Fe I-III in various modelings, agreementis good in general except in shorter wavelength re-

Table 2. Comparison of present A-values in unit of sec−1 for E1transitions with those in NIST12 compilation from references. Thealphabetic letter is NIST accuracy rating.

λ A:Ac A(Present) C SLπ gA NIST BPRM SS i-j i-j i-j

52.911 2.94e+111: C 2.28e+11 2.38e+11 3s2 -3s4p 1S- 1P 1-359.404 3.4e+112 : C 2.40e+11 2.23e+11 3s3p -3s4d 1P-1D 3-5307.73 4.91e+093:C 4.78E+09 4.91E+09 3s3p -3p2 3P-3P 3-365.370 3.2e+102 : C 3.70e+10 3.52e+10 3s3p -3s4s 3P-3S 1-365.612 9.8e+102 : C 1.14e+11 1.06e+11 3s3p -3s4s 3P-3S 3-366.238 1.6e+112 : C 1.95e+11 1.82e+11 3s3p -3s4s 3P-3S 5-3224.754 1.38e+104:C 1.35e+10 1.40e+10 3s3p -3s3d 3P-3D 1-3227.206 1.8e+104:C 1.76e+10 1.83e+10 3s3p -3s3d 3P-3D 3-5227.734 9.8e+094:C 9.68e+09 1.0e+10 3s3p -3s3d 3P-3D 3-369.66 1.9e+115 : C 2.18e+11 2.16e+11 3s3p -3s4s 1P-1S 3-1243.794 4.2e+104:D 4.09e+10 4.25e+10 3s3p -3s3d 1P-1D 3-563.96 1.6e+112 : E 4.61e+10 1.97e+11 3p2 -3s4f 1D- 1F 5-7194.067 3.8e+085:E 1.04e+08 3.85e+08 3p2 -3p3d 1D-1P 5-3231.68 1.5e+105:E 1.43e+10 1.58e+10 3p2 -3p3d 3P- 3P 3-3231.87 2.1e+105:E 2.04e+10 2.13e+10 3p2 -3p3d 3P-3P 3-1242.100 2.3e+105:D 6.30e+09 2.56e+10 3p2 -3p3d 3P- 3D 5-768.849 9.2e+116 : C 9.15e+11 8.66e+11 3p3d -3p4f 3F-3G 9-1169.945 7.4e+112 :C 7.25e+11 7.29e+11 3s3d -3s4f 3D-3F 3-569.987 7.9e+112 :C 7.67e+11 7.72e+11 3s3d -3s4f 3D-3F 5-770.054 8.8e+112 :C 8.63e+11 8.70e+11 3s3d -3s4f 3D-3F 7-970.224 4.13e+115:C 4.23e+11 4.12e+11 3p3d -3p4f 3P-3D 1-373.199 8.8e+115 :C 6.89e+11 7.95e+11 3p3d -3p4f 1F-1G 7-973.473 6.2e+112 :C 6.01e+11 6.12e+11 3s3d -3s4f 1D-1F 5-7312.556 1.1e+093 :E 3.51e+09 1.01E+09 3s3p -3p2 3P-1D 3-5238.114 3.2e+084:E 2.85e+08 2.81e+08 3s3p -3p2 3P-1S 3-1191.408 3.5e+084:E 3.53e+08 2.67e+08 3s3p -3s3d 3P-1D 3-5196.741 1.6e+074:E 1.45e+07 8.49e+06 3s3p -3s3d 3P-1D 5-5304.998 3.0e+074: E 2.20e+07 1.17e+07 3s3p -3s3d 1P-3D 3-5305.889 2.6e+074: E 2.63e+07 2.34e+07 3s3p -3s3d 1P-3D 3-338.95 1.69e+111: C 7.4e+10 1.56e+11 3s2- 3s5p 1S- 1P 1-3

λ A:Ac A(sec−1) C SLπ gA NIST SS i-j i-j i-j

E2,M1,M2

131.216 1.6e+06:D 1.73e+06 2p63s2 -3s3d 1S-1D 1-5 E2171.913 4.3e+041:E 3.81e+04 2p63s2 -3p2 1S-3P 1-5 E2178.702 4.1e+051:E 1.59e+05 2p63s2 -3p2 1S-1D 1-5 E220080 4.4e-01:E 4.13e-01 3p2 -3p2 1D-3P 5-3 M1847.43 1.90e+02:E 1.70e+02 3s3p -3s3p 3P-1P 1-3 M1975.84 3.0e+01:E 2.70e+01 3p2 -3s3d 1S- 1D 1-5 E2999.63 2.70e+02:E 2.70e+02 3p2 -3p2 1D-1S 5-1 E21019.43 1.40e+02:E 1.24e+02 3s3p -3s3p 3P-1P 5-3 M11052.00 1.400e+03:E 1.25e+03 3p2 -3p2 3P- 1S 3-1 M11283.09 2.4e+01 :E 2.13e+01 3p2 -3p2 3P- 1S 5-1 E2224.278 1.2e+00:D 31.9 3s3p -3s3d 3P-3D 1-5 M2226.372 1.98e+00:C 26.3 3s3p -3s3d 3P-3D 3-7 M2246.423 4.2e+00:D 40.3 3s3p -3p2 3P-1S 2 5-1 M2303.494 6.4e+00:C 7.88e+00 3s3p -3s3d 1P-3D 3-7 M2393.980 3.39e+00:C 3.38e+00 2p63s2 -3s3p 1S-3P 1-5 M2

gion.

4.2. Photoionization - Cross sections

and Resonances

Similar to oscillator strenghts, IP considers photoion-ization cross sections σPI for the ground and largenumber of excited bound states with n ≤ 10 andl ≤ 9. CC approximation enables inclusion of ex-tensive resonances in σPI that are not possible withcentral field approximation. Resonances exist inher-


6

0

0.5

1

1.5

2

Fe III

Rel

ativ

e Fl

ux

FeII with Lyα Obs10 m310 p010 p320 m320 p020 p340 m340 p040 p3

2200 2300 2400 2500 2600 2700 2800 2900 3000 31000

0.5

1

1.5

2

Fe III

Wavelength (Angstroms)

Rel

ativ

e Fl

ux

FeII without Lyα Obs10 m310 p010 p320 m320 p020 p340 m340 p040 p3

Fig. 2. Modeling of emission spectra of Fe I-III in active

galaxy 1 Zwicky 1. Dots - observation; curves - various mod-els with 1000 energy levels, millions of transitions. With (top)

and without (bottom) Lyman-alpha fluorescent excitation of

Fe II by recombining H-atoms. The models reproduce manyof the observed features.

ently in photoionization and recombination processesfor all atomic systems with more than one electron.Hence, with no core in hydrogen σPI is smooth, butit shows resonances in two electron helium atom. Fig.3 presents σPI for the ground states of H13 and He.14

Photon Energy (Ry)

σ PI (M

b)

2 3 4 5 610-1

100

101

He I (1s2 1S) + hν -> He II + e

(Nahar, unpublished) n=2 threshold

of the core

5 10 15 20

10-3

10-2

10-1

100

101

H I (1s 2S) + hν -> H II + e

(Nahar 1996)

Fig. 3. Photoionization cross sections of ground state ofH (top) and He (bottom). While σPI for hydrogen decays

smoothly, helium shows resonances due to core excitations.

Resonances converge to the excited core threshold; arrowpoints at n=2 threshold.

Resonant features in photoionization can be of

several types. i) The resonances due to Rydberg se-ries of autoinizing states forming at energies Ep,

(Et − Ep) = z2/ν2

where Et is an excited core state or threshold and ν

is the effective quantum number of the state. Eachexcited core state corresponds to a Rydberg seriesalthough the resonances may not be prominent forthe particular state. These resonances are usuallynarrow and more common. ii) The resonances dueto photoexcitation-of-core, PEC, forming at excitedstates of the core that are dipole allowed by the coreground state. PEC or Seaton (who interpreted andnamed them PEC16) resonances exist in valence elec-tron excited states only, that is, no PEC resonancefor the ground or equivalent electron states, and of-ten are enhanced and wider. iii) Overlapped resonantfeatures forming from Rydberg series of states thatbelong to closely spaced core levels. iv) Resonancesfrom quasibound equivalent electron states, usuallybroad, from Coulumb attraction and require atomicstructure calculations for their identification. Theyoccur not common. v) Fine structure effects can in-troduce narrow resonances which are allowed in finestructure, but not allowed in LS coupling.

For a complex system, such as neutral cromiumCr I, the resonant features in photoionization can beintriguing as seen in Fig. 4 which presents σPI of3d54s(5P ) state of Cr I.15 The entire energy range isfilled with extensive narrow resonances. Due to largenumber of core excitations, 39 in total, in the energyrange overlapping of series of resonances is obvious.The background cross section has been enhanced bythe first core excited state 3d54s(6D) (pointed byarrow). These structures will provide considerablecontributions to quantities such as photoionizationrates, recombination rates etc, from low to high tem-peratures.

The other prominent type of resonance, Seatonor the PEC (photo-excitation-of-core) resonance,forms at an excited core threshold as the core excitesto an allowed state while the outer electron remainsas a ’spectator’ which is followed by photoionizationand core dropping to the ground state. It is usuallydistinguishable because of its wider width and higherpeak. A PEC or Seaton resonance is illustrated inFig. 5 for excited 3d5 6S4d(7D) state of of Cr I.15

It exhibits non-hydrogenic nature of an excited statecross sections in contrast to hydrogenic that is often


7

Photon Energy (Ry)

σ PI (M

b)

.3 .4 .5 .6 .7 .810-1

100

101

102

103

3d44s 6D

Cr I (3d54s 5P) + hν -> Cr II + e

Fig. 4. Photoionization cross sections of 3d54s(5P ) state of

Cr I15 showing complex resonant structures due to overlap-ping of Rydberg series of resonances. The calculation includes

excitations of the core to 39 states.

assumed. The enhancement in the background dueto a PEC can be orders of magnitude.

Photon Energy (Ry)

σ PI (M

b)

.1 .2 .3 .4 .5 .610-2

10-1

100

101

102

103

3d44p 6PoPEC Resonance

Cr I (3d54d 7D) + hν -> Cr II + e

Fig. 5. Illustration of a PEC or Seaton resonance, due to core

excitation 3d5 6S − 3d44p 6P o at energy 0.442 Ry (pointed

by an arrow), in photoionization cross sections of excited3d5 6S4d7D state of Cr I.15 PEC resonance has enhanced

the background by orders of magnitude.

4.3. Total and Level-Specific

Electron-Ion Recombination

Electron-ion recombination in low temperature isusually dominated by radiative recombination whenthe electron combines with an ion by emission of aphoton. The electron may not be energetic enough toexcite the ion and go through dielectronic recombi-nation. Hence typically the total recombination ratecoefficient (αR) starts high at low temperature due todominance by RR, falls with temperature and thenrises again at high temperature due to dominanceof DR and forms a DR ’bump’ which is followedby monotonic decay at very high temperature. Anexample showing the typical features of αR for re-combination to a Li-like ion, S XIV,17 is presentedin Fig. 6. The solid curve corresponds to the totalunified recombination rate which is being comparedwith other existing separate RR and DR rates.

T (K)

α R (cm3 se

c-1)

10 100 1000 10000 105 106 107 108 10910-14

10-13

10-12

10-11

10-10

10-9

10-8

RR:Verner & Ferland(1996)

DR:Romanik (1988)

Unified Total (Nahar 2008)

e + S XV -> S XIV

Fig. 6. Total recombination rate coefficients (solid curve) for(e+S XV → S XIV) from unified method that is valid forentire temperature range incorporating both RR and DR.17

Existing rates are available individually for RR and DR.

The recombination feature often changes forcomplex atomic systems by forming two or multipleDR ’bump’s. The positions of these bumps depend onthe resonance positions in photoionzation. For exam-ple, one DR bump may form in the low temperatureregion, such as for recombination of Fe II.27 In a rarecase, almost four bumps may form, as seen in Fig. 7


8

for recombination to Ar XIII.19

α dRC

( cm3 se

c-1)

T (K)

10 100 1000 10000 105 106 107 108 109

10-14

10-13

10-12

10-11

10-10

10-9

10-8

RR:Aldrovandi &

Pequignot(1974)

DR:Shull & Steenberg(1982)

DR:Altun et al(2004)

Total Unified: 37-CC

e + Ar XIV -> Ar XIII

(Nahar 2004)

Fig. 7. Unified total recombination rate coefficients of

Ar XIII showing multiple DR bumps.19 Unified rates are com-pared with available RR and DR rates obtained separately by

others.

One important advantage of the unified methodis to have state-specific recombination rate coeffi-cients αR(nLS), including both RR and DR, formany bound levels. These are obtained from integra-tion of state-specific photoionization cross sections asexplained in the Theory section. Fig. 8 shows level-specific recombination rate coefficients for He-likeS XV.17 The rates correspond to (a) the ground leveland four excited levels (b) 2s2p(1P o

1 ), (c) 2s2p(3P o2 ),

(d) 2s2p(3P o1 ), (e) 2s2s(3S1) that form the well-

known diagnostic allowed w, intercombination y, andforbidden x, z lines of He-like ions for high tempera-ture plasmas. The hydrogenic decay of a level-specificrecombination rate changes by a DR bump or shoul-der in the high temperature. These rates are neededfor the cascade matrix and determination of levelpopulations.

4.4. Unified Method Extension for

Dielectronic Satellite Lines

The unified method for total electron-ion recombina-tion has been extended recently20 to study the dielec-tronic satellite (DES) lines. These lines, formed fromradiative decay of autoionizing states, are highly

T(K)

α R (cm3 s-1

)

10 100 1000 10000 105 106 107 108 10910-15

10-14

10-13

10-12

10-11

10-10

10-9

e) 1s2s(3Se1) :z

10-1510-1410-1310-1210-1110-1010-9

d) 1s2p(3Po1) :y

10-15

10-14

10-13

10-12

10-11

10-10

c) 1s2p(3Po2) :x

10-15

10-14

10-13

10-12

10-11

10-10

b) 1s2p(1Po1) :w

10-14

10-13

10-12

10-11

10-10

10-9

a) 1s2(1Se0) :Ground

e + S XIV -> S XV

Fig. 8. Level-specific recombination rate coefficients, includ-

ing RR and DR, of ground and four excited levels, correspond-ing to four diagpositic w, x, y, z lines, of He-like S XV.17

sensitive temperature diagnostics of astrophysicaland laboratory plasma sources. Most common DESlines in astrophysical spectra are formed by col-lision of (e+He-like ion) creating a 3-electron Li-like ion. Among DES lines, the 22 DES lines ofKLL (1s2l2l’) complex below the core excitation1s2(1S0) → 1s2p(1P o

1 ) (w-line) are used most be-cause of higher resolution or separation among them,especially for highly charged ions.

The earlier treatment of DES lines is basedon isolated resonance approximation (IRA), e.g.,21

where rate coefficient of a DES line is obtained as,

αR = a3o

gi

2gf

[4π

T

]e−

εkT

ArAa∑m Aa(m) +

∑n Ar(n)

(19)ε is the DES energy. The single energy point cannot provide the natural shape of the DES lines andhence a line profile (or cross section shape dependingon one’s perspective) is often assumed. IRA treatsthe resonances essentially as bound features, exceptfor the inclusion of dielectronic capture into, and au-toionization out of these levels.

In contrast, the unified method, by includingthe coupling between the autoionizing and contin-uum channels, gives the intrinsic spectrum of DESlines which includes not only the energies and linestrengths as S =

∫ εf

εiσRCdε from the unified σRC

that includes both RR background and DR, but also


9

the natural line (or cross section) shapes. Since uni-fied recombination cross sections (σRC) include boththe resonant and the non-resonant background con-tributions. the DES spectra correspond directly toresonances in σRC . The recombination rate coeffi-cients of DES lines can be calculated from directintegration over the product of the resonant crosssections and temperature-dependent factors.

Using the unified approach, the entire spectraof DES line intensities and recombination rates forthe 22 satellite lines of KLL complexes can be pro-duced. Fig. 9 presents the DES spectra of helium-like Fe XXV20 which is applicable to analysis of Kα

complexes observed in high-temperature X-ray emis-sion spectra. The top panel (a) presents total spec-trum that can be observed and bottom three pan-els (b-d) present individual component states thatcontribute to the total spectrum. Individual spectraprovides the identification of the DES lines. It maybe noted that the natural widths and overlapping oflines are inherently included in the total spectrum.The method was benchmarked by comparing the re-combination rates of the DES lines with the existingrates and very good agreement was found for thestrong lines.

Photoelectron Energy (eV)

σ RC(M

b)

10-510-410-310-210-1100101102103

e + Fe XXV -> Fe XXIV + hν: KLL satellite lines

a) Total

10-5

10-4

10-3

10-2

10-1

100b) Jπ = (1/2)e: 1s2s2p(SLJ) -> 1s22s(2S1/2) resonances

v u r q t s

10-710-610-510-410-310-210-1100101

c) Jπ = (1/2)o: 1s2p2(SLJ) -> 1s22p(2Po1/2) resonances

p i g k d b n

4550 4600 4650 4700

10-610-510-410-310-210-1100101102

d) Jπ = (3/2)o: 1s2p2(SLJ) -> 1s22p(2Po3/2) resonances

o h f e l

c

j a m

Fig. 9. Satellite lines of Fe XXV in the Kα complex.20 The

top panel (a) shows the total spectrum and the lower three

panels show the resolved and identified lines belonging to fi-nal recombined level (b) 1s22s(2S1/2), (c) 1s22p(2P o

1/2), (d)

1s22p(2P o3/2

).

5. X-ray Spectroscopy from Astronomyto Bio-medical Science

Study of atomic astrophysics research is applicableto medical and nanotechnology research because ofsimilarities. However, interest of atomic species is dif-ferent from those in astrophysics. We have extendedthe current investigation to spectral models for X-ray absorption and transmission, and properties ofchemical compounds of high-Z elements for possi-ble bio-medical application. Heavy elements, such asgold, interact very efficiently with X-rays with largeattenuation coefficients. Ionization and excitation ofextended electronic shells have large photoabsorp-tion cross sections up to very high energies. Goldnanoparticles, which are intoxic in living tissues, arebeing used in study of therapy and diagnostics forcancer treatment. Irradiation with gold nanoparti-cles in nice cancer has shown reduction of tumorgrowth.22 Most of the irradiation methods use broad-band radiation that cause sufficient damages. Presentwork aim in narrow band irradiation using resonantenergy ranges.

We have calculated the Auger resonant proba-bilities and cross sections of gold ions to obtain to-tal mass attenuation coefficients using detailed reso-nance structures for the K −→ L,M,N,O,P shell tran-sitions. The X-ray mass absorption is shown in Fig.10 for gold nanoparticles with vacancies in 2s, 2p sub-shells. It is seen that X-ray absorption is considerablyenhanced by factors of up to 1000 or more at energiesof K-shell resonances from K-alpha excitation en-ergy, ∼ 67.7 to K-ionization edge at ∼82 keV.? Thisis potentially useful in the calculation of resonantplus non-resonant attenuation coefficients by high-Z elements in plasmas created with high-intensitylasers, monochromatic synchrotron light sources, andelectron-beam-ion-traps.

A simulation was carried out for resonant Kα

X-ray (68 keV) absorption by gold nanoparticles intissues. A phantom is assumed where a thin film ofAu, 1.0mm/g, is deposited in a tumor 10 cm insidefrom the skin. As the 68 keV X-rays pass through thephantom, the percentage depth deposition (relativeto background) of the radiation due to partial Kα

attenuation is found to be in complete absorptionwithin < 1 cm of the Au-layer, as shown in Fig. 11.This relates to the development of novel monochro-matic or narrow-band X-ray sources.


10

1234 np−1Kα Kβ Kγ Kδ Kε

1234 np−2

1234 np−3

1234

log 10

κ [ c

m2 /g]

np−4

1234 np−5

1234 np−6

1234 ns−1 np−6

65 70 75 80 851234

Energy [keV]

ns−2 np−6

K−edge

Fig. 10. X-ray mass absorption (κ) by nano gold particles

with 2s, 2p-subshell vacancies via 1s-np K-shell transitions.The K-complexes of resonances, in E = 67.5 - 79 keV, show

photo-absorption exceeding the background below the K-edgeionization at 82 keV by large factors.?

Per

cent

age

Dep

th D

epos

ition

(%

)

Depth (cm)0 2 4 6 8 10 12 14 16 18 20

0

50

100

150

200

250

300

350

muscle

bone

muscle

Resonant X−Ray AbsorptionBy Gold Nanoparticles

Fig. 11. Percentage depth deposition (relative to back-ground) of 68 keV X-rays irradiated on body tissues where

a film of gold nanoparticles of concentration 1.0mm/g is em-bedded in a tumor 10 cm inside the surface. Deposition due

to partial Kα attenuation by gold show complete absorption

of X-rays within < 1 cm of gold layer.?

6. Conclusion

Dominant radiative atomic processes, such as photo-excitaions and de-excitations, photoionizatioon, andelectron-ion recombination, in astrophyical plasmasare discussed. Features revealed from detailed studyof the processes under the Iron Project are reported.Extensions to total and level-specific electron-ion re-combination and di-electronic satellite lines provideself-consistent set of atomic data for the inverse pro-cesses vio unified theory.

The international collaborations of the Opac-ity Project and the Iron Project have resulted inlarge amount of atomic data for the astrophysi-cally abundant atoms and ions from hydrogen tonickel in various ionization stages. They are avail-able through databases, TOPbase and TIPbase atvizier.u-strasbg.fr/topbase/topbase.html and opaci-ties.osc.edu. New and more updated results on pho-toionization cross sections and recombination crosssections and rates from Ohio State Atomic Astro-physics group (Nahar et al) is available from NORADwebpage at www.astronomy.ohio-state.edu/∼nahar

Acknowledgments

I would like to thank Professors Fayaz Shahin, Lot-fia El-Nadi, and organizers of MTPR08 conferencefor inviting me for a keynote speech and their kindhospitalities. The research is supported partially byNASA APRA program. The computations were car-ried out by various Cray computers at the Ohio Su-percomputer Center.

References

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3. D.G. Hummer et al., Astron. Astrophys. 279, 298(1993)

4. M. J. Seaton, J. Phys. B 20, 6363 (1987)5. S.N. Nahar & A.K. Pradhan, Phys. Rev. Lett. 68,

1488 (1992)6. S.N. Nahar & A.K. Pradhan, Phys. Rev. A 49, 1816

(1994)7. H.L. Zhang, S.N. Nahar, & A.K. Pradhan, J. Phys

B 32, 1459 (1999)8. R.H. Bell and M.J. Seaton, J. Phys. B 18, 1589

(1985)9. W. Eissner, M, Jones, H. Nussbaumer, Comput.

Phys. Commun. 8 270, 1974 (


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10. spn T.A.A. Sigut, A.K. Pradhan, S.N. Nahar, Astro-phys. J. 611, 81 (2004)

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dards and Technology (NIST), compilation atomicdata are available at http : //physics.nist.gov/cgi−bin/AtData/main asd

13. S.N. Nahar, Phys. Rev. A 53, 2417 (1996)14. S.N. Nahar (unpublished)15. S.N. Nahar (in preparation 2008)

16. Yu Y. & M.J. Seaton, J. Phys. B 20, 6409 (1987)17. S.N. Nahar, Open Astron. J. I, 1 (2008)18. S.N. Nahar, Phys. Rev. A 55, 1980 (1997)19. S.N. Nahar, ApJS 156, 93 (2004)20. S.N. Nahar & A.K. Pradhan, Phys. Rev. A 73,

62718-1 (2006)21. A.H. Gabriel, MNRAS 160, 99 (1972)22. Hainfeld J et al. Phys. Med. Biol. 49, N309 (2004)23. A.K. Pradhan et al (in preparation 2008)

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