We present the results of laser magnetic resonance measurements performed on the ground ^2P state of singly

ionized atomic carbon (C_II). The 2^P_(3/2) ← ^2P_(1/2) fine-structure intervals of both ^(12)C^+ and ^(13)C^+ have been determined with a precision of approximately 1 ppm, and the g_J factors to approximately one part in 10^4.

Specifically, we find that g_(J=(1/2)) = 0.66576(11) and g_(J=(3/2)) = 1.33412(11), while for ^(12)C^+ ΔE_0(^2P_(3/2) ← ^2P_(1/2))= 1900536.9(1.3) MHz, with ΔE_0(^2P_(3/2) ← ^2P_(1/2)) = 1900545.8(2.1) and ΔE(^2P(3/2) ← ^2P_(1/2), F = 2 ← 1) = 1900466.1(2.3) MHz in ^(13)C^+. The highly precise values of the ^(12)C_II and ^(13)C_II fine-structure intervals verify the already secure far-infrared astronomical identification of C^+ and should allow the interstellar (^(12)C / ^(13)C) ratio to

be unambiguously determined in a number of environments

Blake, Geoffrey A.

Cooksy, Andrew L.

Saykally, Richard J.

English

Caltech Authors - Main

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THE ASTROPHYSICAL JOURNAL, 30S:L89-L92, 1986 June 15 
~· 1986. The American Astronomical Society. All rights reserved. Printed in U.S.A. 
DIRECT MEASUREMENT OF THE FINE-STRUCTURE INTERVAL AND gJ FACTORS OF 
SINGLY IONIZED ATOMIC CARBON BY LASER MAGNETIC RESONANCE 
ANDREW L. COOKSY, GEOFFREY A. BLAKE/AND RICHARD J. SAYKALLY 2 
Department of Chemistry, University of California, Berkeley 
Received 1986 February 3; accepted March 12 
ABSTRACT 
We present the results of laser magnetic resonance measurements performed on the ground 2P state of singly 
ionized atomic carbon (C II). The 2P312 +- 2 P112 fine-structure intervals of both 12 ~+ and 13 C+ ha~e been 
determined with a precision of approximately 1 ppm, and the gJ factors to approXImately one part m 104 • 
Specifically, we find that gJ= 1; 2 = 0.66576(11) and gJ= 3; 2 = 1.33412(11), while for 12 C+ !lEoeP3!2 +- 2 P1;2) 
= 1900536.9(1.3) MHz, with !lE0eP312 +- 2 Pl/2 ) = 1900545.8(2.1) and !lEeP312 +- 2 P~/2• F= 2 ~ 1) = 
1900466.1(2.3) MHz in 13 C+. The highly precise values of the 12 C II and 13 C II fine-structure mtervals venfy the 
already secure far-infrared astronomical identification of C + and should allow the interstellar 12 C / 13 C ratio to 
be unambiguously determined in a number of environments. 
Subject headings: laboratory spectra -line identification- molecular processes 
I. INTRODUCTION 
Observations made possible by the dramatic improvements 
in astronomical instrumentation during the past decade have 
now confirmed the theoretical expectation that the far-infrared 
(FIR) fine-structure lines of atomic carbon and oxygen in 
various ionization states would provide an important cooling 
mechanism for the interstellar gas (Dalgarno and McCray 
1972). These species have energy levels and excitation densi-
ties that are well matched to the physical state of both the 
neutral and ionized regions in which they are prevalent and 
are therefore quite efficient sources of energy loss. Particularly 
important are the transitions of 0 (0 I) and c+ (C II) which, 
because of their high abundance in the warm photodissocia-
tion regions commonly associated with giant molecular cloud 
complexes, may contain up to 1% of the total bolometric 
luminosity of "typical" gas-rich galaxies (Watson 1984; 
Crawford eta/. 1985). Measurement of the intensities and 
velocity profiles of FIR fine-structure emission lines can also 
yield considerable insight into the chemistry and dynamics of 
molecular clouds, star formation processes, and galactic mor-
phology. Indeed, the detection of intense 610 p.m neutral 
carbon (C I) emission by Phillips eta/. (1980) has led to a 
number of revisions in the chemical modelling of dense inter-
stellar clouds, while the 158 p.m [C II] line has been used, 
among other things, to examine the validity of CO as a tracer 
of H 2 (Crawford eta/. 1985). The detailed structure of the 
c+ ;c;co transition in molecular clouds can profoundly 
influence the chemical composition of dense clouds and there-
fore the star formation process, but it must usually be probed 
indirectly via velocity shifts and line profiles because the 
transition regions are often spatially unresolved. For detailed 
1 Berkeley Miller Research Fellow. 
2 Berkeley Miller Research Professor. 
L89 
studies of the dynamics and chemistry of such objects it is 
therefore imperative to know the rest frequencies of the 
transitions under study to considerably better accuracy than 
the currently available spectral resolution. 
Because of the reactive nature of most atoms and the 
relative lack of intense radiation sources in the FIR, atomic 
fine-structure lines have proven difficult to study in the 
laboratory. Far-infrared laser magnetic resonance (FIR LMR) 
spectroscopy is an extremely powerful tool for the study of 
molecular rotational spectra but is less applicable to the 
investigation of atomic species due to the small number of 
fine-structure transitions in any given species and the incom-
plete coverage of even the most versatile FIR LMR spec-
trometers. Nevertheless, to date the fine-structure lines of C 
(Saykally and Evenson 1980; Cooksy eta/. 1986), 0 (Davies 
eta/. 1978; Saykally and Evenson 1979), and Si (Inguscio 
eta/. 1984) have been measured in the FIR, while several 
isotopes of a (Dagenis, Johns, and McKellar 1976), Hg 
(Johns, McKellar, and Riggin 1977), and metastable Kr and 
Xe (Sears and McKellar 1982) have been detected with in-
frared systems. The inherently high sensitivity of the LMR 
technique was essential for the detection of these electric 
dipole-forbidden transitions, but the extension of LMR spec-
troscopy to ionic species such as c+ has proven difficult due 
to their extreme reactivity under normal laboratory condi-
tions. Utilizing advances in ion production technology, we 
have recently detected the first ionic fine-structure transition 
in the laboratory, the 3 P2 +- 3 P1 121 p.m line of N+ (N II) 
(Cooksy, Hovde, and Saykally 1986). In this Letter we report 
the detection of the 158 p.m 2 P312 +- 2 P112 transitions of 
12 c+ and 13 c+ with similar techniques, thereby confirming 
the astronomical detection of this feature (Russell eta/. 1980). 
It is hoped that the measurement of these lines will permit an 
accurate determination of the interstellar 12 C j 13 C and 
14Nj15 N isotopic rations free from the deleterious effects of 
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fractionation that plague molecular tracers of the dense inter-
stellar gas. 
II. EXPERIMENTAL 
The LMR spectrometer used in our study of the c+ and 
N+ ions has been described in detail elsewhere (Ray, Lubic, 
and Saykally 1982). Briefly, the spectrometer consists of an 
optically pumped far-infrared molecular laser containing an 
intracavity sample cell placed between the pole pieces of a 
0-20 kilogauss Varian 15" electromagnet, a liquid-helium 
cooled Ga:Ge bolometer, and associated detection electron-
ics. A rotatable polyproplylene beam splitter set at the 
Brewster angle separates the gain and sample regions of the 
FIR laser cavity. The FIR gain cell is transversely pumped by 
a 80 watt C02 laser, with power coupled out to the bolometer 
by an adjustable copper mirror inserted into the laser mode. 
If necessary, an iris may be used to suppress higher order 
transverse modes in the FIR laser. By superposing a 2-6 kHz 
sinusoidal magnetic field of about 30 G onto the slowly swept 
DC field any absorption from paramagnetic species is con-
verted into a phase coherent signal which is detected by the 
bolometer and processed in a lock-in amplifier. For the 
weakest transitions studied here it was necessary to signal 
average several scans in order to accurately measure the line 
position. The resonant fields were measured and calibrated to 
an accuracy of ± 2 G with an NMR gaussmeter probe. 
Like N+, the C + ions were generated in a 12-17 kHz AC 
discharge between two brass shimstock electrodes housed in 
the sample cell. The simple reaction 
He+ + CO --+ c+ + 0 + He 
proceeds quite rapidly to produce c+ and has the added 
advantage that the less reactive neutral oxygen species may be 
used to estimate optimum reaction conditions. As judged 
initially by the [0 1] line at 145 p.m and subsequently by the 
158 p.m [C II] transition, optimized conditions for c+ produc-
tion were approximately 50-70 millitorr of CO in 900 milli-
torr of He, with a discharge current of about 50 rnA. The 
search problem for the 158 p.m line was greatly reduced by 
the astronomical rest frequency estimate of Crawford et a/. 
(1985), determined from observations of the Orion molecular 
cloud. Figure 1 shows a recording of the MJ = - 3/2 -+ 
-1/2 component of the [C II] line under typical operating 
conditions. 
III. THEORY 
The effective Hamiltonian employed in our analysis of c+ 
has been thoroughly described in our study of N+ (Cooksy, 
Hovde, and Saykally 1986). We give here a brief summary of 
the perturbations treated and the results for the case of c+ 
that differ from our earlier work. The effective Hamiltonian is 
written as 
(1) 
where H0 is the phenomenological fine structure Hamilto-
nian, Hz is the Zeeman term, and H M is the magnetic 
hyperfine term. 
2p c+ 
J,MJ =3/2,-312-1/2,-1/2 
900 950 1000 
8 (Gauss) 
FIG. I.-Signal-averaged LMR spectrum of the MJ = -3/2 +-
-1/2 fine-structure transition in 2P 12 C+ at 1898.2799 GHz and 
967.0 G. 
The diagonal elements of Hz may be explicitly expressed 
as 
{2) 
where a is the nuclear shielding constant and XI is the 
isotropic diamagnetic Zeeman interaction. If we neglect the 
anisotropic diamagnetic Zeeman effect (the term in XA), the 
!l.MI = 0 selection rule implies that, for allowed transitions, 
only the first term of expression (2) has a first-order effect on 
the transition energy in a magnetic field. For a 2 P atom, the 
gyromagnetic factors are approximately 8J-l/Z = 2/3 and 
gJ_ 312 = 4/3. Because the gJ are significantly different for 
the two J levels, the energies of the MJ components of the 
2 P312 +- 2 P112 transition will change at different rates in a 
magnetic field. Lines of lower tunability [which is simply 
P.B(8J-3f2MJ=J/Z - 8J-t;2 MJ=t;2 )] will be broader and will 
appear at higher magnetic fields than their faster tuning 
counterparts. 
The magnetic hyperfine Hamiltonian is (Abragam and Pryce 
1951) 
HM = 2g1p.~{ (r1- 3 )(L ·I) 
+(r,- 3 )€[L{L + 1){S ·I)- t(L · S)(L ·I) 
- HL ·l)(L 0 S)] + t'ITIV(0)1 2 (S ·I)}' 
{3) 
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No.2, 1986 SINGLY IONIZED ATOMIC CARBON L91 
where 
(2/ + 1) - 4S 
~ = S(2/- 1)(2/ + 3)(2L- 1) . 
The matrix elements are functions of the constants (evaluated 
here for 2 P atoms) 
and 
2[2 -3 1 -3 16'1T 2] 
A3/2I/2=giiLB 3(rt )-3(rs )--9-1'1'(0)1 · (4) 
We currently lack the precision to determine the constant 
off-diagonal in J, A 112 312 , but have included it in our analy-
sis by utilizing the ab initio values of Schaefer and Klemm 
(1970) for (r1- 3 ), (rs- 3 ), and 1'1'(0)1 2 • It is worth noting that 
due to the ·magnitude of the diagonal constants A 112 and 
A 312 , terms off-diagonal in M1 and M1 are by no means 
negligible, contributing energies of as much as 50 MHz to the 
LMR transitions observed at low magnetic fields. 
IV. RESULTS AND DISCUSSION 
Four laser lines were available with which to investigate the 
LMR spectrum of c+. The transitions resonant with each of 
these frequencies were the two A M1 = -1 and the A M1 = 
0, M1 = -1/2 components as pictured for 13 C+ in Figure 2. 
Of these, the M1 = -3/2 ...- -1/2 line has the greatest 
intensity and tunability. The M1 = -1/2 ...- -1/2 compo-
nent has only one-third of this intensity and is broader by 
nearly a factor of four, and it could not be resolved in this 
study. 
The data obtained are given in Table 1. Measurements 
taken for both isotopes were combined in a least-squares 
analysis, the results of which comprise Table 2. We have 
failed thus far to resolve the hyperfine components of the 
M1 = -1/2 ...- 1/2 transition in 13 C + and therefore cannot 
adequately evaluate the independent parameters A 112 and 
A 312 . We have been able to determine the value of the 
coupled term 1j4A112 - 3j4A312 to within small uncertainty, 
however, and can use this to precisely predict the frequency of 
the J, F = 3j2, 2 ...- 1/2,1 transition, the strongest of the 
zero-field 2 P312 ...- 2 P112 components. The ab initio hyperfine 
constants of Schaefer and Klemm (1970) have proved capable 
of reproducing experimental measurements in 2 P atoms to 2% 
or better, and we have therefore used these calculations to 
estimate the frequencies of the weaker zero-field transitions, 
which are listed together with the 3 j2, 2 ...- 1/2, 1 frequency 
in Table 3. Schaefer and Klemm's constants predict the 
measured combination of the hyperfine constants to with-
in 2.5%, from which we estimate a 2 cr uncertainty of 
± 10-15 MHz for the weaker zero-field hyperfine lines. The 
TABLE 1 
A. RESONANT FIELDS FOR 12 C II MEASURED IN THIS WORK 
Transition Lasing Laser Frequency Field 
Ml <- MJ' Gas (GHz) (G) 
-3/2 <- -1.2 .............. 13 CH30H 1898.2799 967.0 
-1/2 <- 1/2 ................ 13 CH30H 1898.2799 1613.2 
- 3/2 <- - 1/2 ............. CH 2F2 1891.2743 3968.4 
- 3/2 <- - 1/2 ............. CH2DOH 1882.9063 7556.0 
-1/2 <- 1/2 ................ CH2DOH 1882.9063 12650.5 
-3/2 <- -1/2 ............. CH30H 1877.5085 9872.1 
-1/2 <- 1/2 ................ CH30H 1877.5085 16544.1 
B. RESONANT FIELDS FOR 13 C II MEASURED IN THIS WORK 
Transition Lasing Laser Frequency 
M;, MJ', M1 Gas (GHz) 
- 3/2, -1/2, -1/2 ........ CH2DOH 1882.9063 
-3/2, -1/2,1/2 ........... CH2DOH 1882.9063 
-3/2, -1/2, -1/2 ........ CH30H 1877.5085 
-3/2, -1/2,1/2 ........... CH30H 1877.5085 
J 
TABLE2 
CONSTANTS FOR C II DETERMINED BY LMR 
Constant 
E( 12 C+ 2P3;2 <- 2 P1;2) 
E(13 C+ 2P3;2 <- 2 P112) 
gJ~lj2· .................... . 
gJ~3j2· .................... . 
~(Al/2-3A3/2) .. · ...... · .. 
Value 
1900.5369(13) GHz 
1900.5458(21) GHz 
0.66576(11) 
1.33412(11) 
80.3(7) MHz 
NOTE.-Numbers in parenthesies represent 2 
a, 95% confidence limits. 
F MF MJ M1 
l/2c= 
-~~ 
3/2 -1/2 
2--
l/2c= 
1/2 -1/2 
-2 
3/2--
-1/2 
~E-112 1/2 
1-- 0 
-I 
-1/2 
-3/2 1/2 
_fE 
1/2 
1-- 1/2 -1/2 
1/2--
0-- 0-- -1/2 
-1/2 1/2 
(a) (b) (c) (d) 
2PI3c+ ENERGY LEVELS 
Field 
(G) 
7525.3 
7604.0 
9841.9 
9917.3 
FIG. 2.-Energy level diagram of 2P 13 C+. (a) The unperturbed 
fine-structure levels. (b) The zero-field doublet hyperfine splitting. (c) 
The Zeeman effect in a weak magnetic field. (d) The Zeeman effect in a 
strong field, with the transitions observable at the available laser frequen-
cies illustrated. 
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L92 COOKSY, BLAKE, AND SAYKALLY Vol. 305 
TABLE3 
EsTIMATED ZERO-FlEW 'TRANSITION FREQUENCIES FOR 13 C II 
Transition Frequency Relative 4(13 C II 12 C II) 
F' +- F" (GHz) Intensity (km s- 1 ) 
2 <- 1 ....... 1900.4661(23)8 44.4% -11.2 
1 <- 1 ....... 1900.136(10)b 20.0 -63.2 
1 <- 0 ....... 1900.950(15)b 35.6 65.2 
• Determined in this work. 
bEstimated using values of A112 and A312 obtained from the 
ab initio constants of Schaefer and Klemm 1970. 
F = 2 +- 1 [13 C II] component lies only 14 km s- 1 from the 
[12 C II] fine-structure line and will therefore be difficult to 
observe even in the most narrow-line sources. However, as 
Table 3 shows, the weaker hyperfine satellites still retain 
nearly 50% of the transition intensity and lie some 60-70 
km s- 1 from the stronger [12 C II] line. 
In view of Veseth's recent theoretical work on isotopic 
shifts in atomic fine-structure states (Veseth 1985), we have 
also analyzed the [~E0 (13 C)- ~E0 (12 C)] shift in 2P c+ and 
obtain a value of 8.9(1.5) MHz for this parameter. Because 
further investigation into the theory of fine-structure shifts is 
at present hampered by the paucity of precise experimental 
data, we hope such data will encourage continuing efforts in 
the field. 
The variation of the 13 Cj12 C and N/0 isotopic ratios with 
galactic radius strongly constrains models of star formation 
and mass exchange between stellar interiors and the interstel-
lar medium. Molecular tracers of dense interstellar gas can be 
strongly affected by chemical fractionation processes that 
render the accurate determination of isotopic ratios extremely 
difficult. For example, the molecular 13 C and D content in the 
cores of cool, dense interstellar clouds may be strongly en-
hanced or depleted by the exothermic reactions 
13 c+ + 12 co -+ 12 c+ + 13 co + 35 K 
and 
Hj + HD-+ H 2 D+ + H 2 + 298 K. 
Atomic species are largely unaffected by these processes be-
cause of the higher temperatures and low molecular abun-
dances in the H II regions and photodissociation zones where 
such species are prevalent. Thus, the far-infrared fine struc-
ture lines of C, N, and 0 should be excellent tracers of atomic 
abundances and isotope ratios throughout the galaxy. Indeed, 
Lester eta/. (1983) have used the [N III] and [0 III] lines to 
examine the large scale galactic N/0 abundance gradient. 
The present work and our recent investigation of the labora-
tory spectra of C 1 and N II provide the necessary rest 
frequencies for a more thorough investigation of the 13 C 1 12 C 
and N /0 galactic abundance ratios which is now possible 
with the advent of high-resolution far-infrared astronomical 
receivers and airborne observing platforms. 
To summarize, far-infrared laser magnetic resonance spec-
troscopy has been used to precisely determine the g1 factors 
and fine-structure intervals of the 12 C and 13 C isotopes of 
singly ionized atomic carbon. The resulting transition fre-
quencies will be of considerable use in detailed investiga-
tions of atomic abundances, iostope ratios, molecular cloud 
morphology, interstellar mass exhange, and star-formation 
processes. 
This work was supported by the National Science Founda-
tion, Structure and Thermodynamics Program (grant CHE 
8402861). A. Cooksy thanks Chevron for a graduate fellow-
ship, and G. Blake and R. Saykally gratefully acknowledge 
financial support provided by the Berkeley Miller Research 
Insitute. 
REFERENCES 
Abragam, A., and Pryce, M. H. C. 1951, Proc. Roy. Soc. London, A20S, 
135. 
Cooksy, A. L., Hovde, D. C., and Saykally, R. J. 1986, J. Chern. Phys., 
submitted. 
Cooksy, A. L., Saykally, R. J., Brown, J. M., and Evenson, K. M. 1986, 
Ap. J., submitted. 
Crawford, M. K., Genzel, R., Townes, C. H., and Watson, D. M. 1985, 
Ap. J., 291, 755. 
Dagenis, M., Johns, J. W. C., and McKellar, A. R. W. 1976, Canadian J. 
Phys., 54, 1438. 
Dalgarno, A. and McCray, R. M. 1972, Ann. Rev. Astr. Ap., 10, 375. 
Davies, P. B., Handy, B. J., Murray Lloyd, E. K., and Smith, D. R. 1978, 
J. Chern. Phys., 68, 1135. 
Inguscio, M., Evenson, K. M., Beltran-Lopez, V., and Ley-Koo, E. 1984, 
Ap. J. (Letters), 278, L127. 
Johns, J. W. C., McKellar, A. R. W., and Riggin, M. 1977, J. Chern. 
Phys., 66, 3962. 
Lester, D. F., Dinerstein, H. L., Werner, M. W., Watson, D. M., and 
Genzel, R. L. 1983, Ap. J., 271, 618. 
Phillips, T. G., Huggins, P. J., Kuiper, T. B. H., and Miller, R. E. 1980, 
Ap. J. (Letters), 238, L103. 
Ray, D. R., Lubic, K. G., and Saykally, R. J. 1982, Mol. Phys., 46,217. 
Russell, R. W., Melnick, G., Gull, G. E., and Harwitt, M. 1980, Ap. J. 
(Letters), 240, L99. 
Saykally, R. J. and Evenson, K. M. 1979, J. Chern. Phys., 71, 1564. 
__ . 1980, Ap. J. (Letters), 238, L107. 
Schaefer, H. F., and Klemm, R. A. 1970, Phys. Rev. A, _1, 1063. 
Sears, T. J., and McKellar, A. R. W. 1982, Canadian J. Phys., 60, 345. 
Veseth, L. 1985, Phys. Rev. A, 32, 1328. 
Watson, D. M. 1984, in Galactic and Extragalactic Infrared Spectroscopy, 
ed. M. F. Kessler and J. P. Phillips (Dordrecht: Re1del), p. 195. 
GEOFFREY A. BLAKE: Space Sciences Laboratory, University of California, Berkeley, CA 94720 
ANDREW L. COOKSY and RICHARD J. SAYKALLY: Department of Chemistry, University of California, Berkeley, CA 94720 
© American Astronomical Society • Provided by the NASA Astrophysics Data System 


Direct measurement of the fine-structure interval and g_J factors of singly ionized atomic carbon by laser magnetic resonance

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THE ASTROPHYSICAL JOURNAL, 30S:L89-L92, 1986 June 15 
~· 1986. The American Astronomical Society. All rights reserved. Printed in U.S.A. 
DIRECT MEASUREMENT OF THE FINE-STRUCTURE INTERVAL AND gJ FACTORS OF 
SINGLY IONIZED ATOMIC CARBON BY LASER MAGNETIC RESONANCE 
ANDREW L. COOKSY, GEOFFREY A. BLAKE/AND RICHARD J. SAYKALLY 2 
Department of Chemistry, University of California, Berkeley 
Received 1986 February 3; accepted March 12 
ABSTRACT 
We present the results of laser magnetic resonance measurements performed on the ground 2P state of singly 
ionized atomic carbon (C II). The 2P312 +- 2 P112 fine-structure intervals of both 12 ~+ and 13 C+ ha~e been 
determined with a precision of approximately 1 ppm, and the gJ factors to approXImately one part m 104 • 
Specifically, we find that gJ= 1; 2 = 0.66576(11) and gJ= 3; 2 = 1.33412(11), while for 12 C+ !lEoeP3!2 +- 2 P1;2) 
= 1900536.9(1.3) MHz, with !lE0eP312 +- 2 Pl/2 ) = 1900545.8(2.1) and !lEeP312 +- 2 P~/2• F= 2 ~ 1) = 
1900466.1(2.3) MHz in 13 C+. The highly precise values of the 12 C II and 13 C II fine-structure mtervals venfy the 
already secure far-infrared astronomical identification of C + and should allow the interstellar 12 C / 13 C ratio to 
be unambiguously determined in a number of environments. 
Subject headings: laboratory spectra -line identification- molecular processes 
I. INTRODUCTION 
Observations made possible by the dramatic improvements 
in astronomical instrumentation during the past decade have 
now confirmed the theoretical expectation that the far-infrared 
(FIR) fine-structure lines of atomic carbon and oxygen in 
various ionization states would provide an important cooling 
mechanism for the interstellar gas (Dalgarno and McCray 
1972). These species have energy levels and excitation densi-
ties that are well matched to the physical state of both the 
neutral and ionized regions in which they are prevalent and 
are therefore quite efficient sources of energy loss. Particularly 
important are the transitions of 0 (0 I) and c+ (C II) which, 
because of their high abundance in the warm photodissocia-
tion regions commonly associated with giant molecular cloud 
complexes, may contain up to 1% of the total bolometric 
luminosity of "typical" gas-rich galaxies (Watson 1984; 
Crawford eta/. 1985). Measurement of the intensities and 
velocity profiles of FIR fine-structure emission lines can also 
yield considerable insight into the chemistry and dynamics of 
molecular clouds, star formation processes, and galactic mor-
phology. Indeed, the detection of intense 610 p.m neutral 
carbon (C I) emission by Phillips eta/. (1980) has led to a 
number of revisions in the chemical modelling of dense inter-
stellar clouds, while the 158 p.m [C II] line has been used, 
among other things, to examine the validity of CO as a tracer 
of H 2 (Crawford eta/. 1985). The detailed structure of the 
c+ ;c;co transition in molecular clouds can profoundly 
influence the chemical composition of dense clouds and there-
fore the star formation process, but it must usually be probed 
indirectly via velocity shifts and line profiles because the 
transition regions are often spatially unresolved. For detailed 
1 Berkeley Miller Research Fellow. 
2 Berkeley Miller Research Professor. 
L89 
studies of the dynamics and chemistry of such objects it is 
therefore imperative to know the rest frequencies of the 
transitions under study to considerably better accuracy than 
the currently available spectral resolution. 
Because of the reactive nature of most atoms and the 
relative lack of intense radiation sources in the FIR, atomic 
fine-structure lines have proven difficult to study in the 
laboratory. Far-infrared laser magnetic resonance (FIR LMR) 
spectroscopy is an extremely powerful tool for the study of 
molecular rotational spectra but is less applicable to the 
investigation of atomic species due to the small number of 
fine-structure transitions in any given species and the incom-
plete coverage of even the most versatile FIR LMR spec-
trometers. Nevertheless, to date the fine-structure lines of C 
(Saykally and Evenson 1980; Cooksy eta/. 1986), 0 (Davies 
eta/. 1978; Saykally and Evenson 1979), and Si (Inguscio 
eta/. 1984) have been measured in the FIR, while several 
isotopes of a (Dagenis, Johns, and McKellar 1976), Hg 
(Johns, McKellar, and Riggin 1977), and metastable Kr and 
Xe (Sears and McKellar 1982) have been detected with in-
frared systems. The inherently high sensitivity of the LMR 
technique was essential for the detection of these electric 
dipole-forbidden transitions, but the extension of LMR spec-
troscopy to ionic species such as c+ has proven difficult due 
to their extreme reactivity under normal laboratory condi-
tions. Utilizing advances in ion production technology, we 
have recently detected the first ionic fine-structure transition 
in the laboratory, the 3 P2 +- 3 P1 121 p.m line of N+ (N II) 
(Cooksy, Hovde, and Saykally 1986). In this Letter we report 
the detection of the 158 p.m 2 P312 +- 2 P112 transitions of 
12 c+ and 13 c+ with similar techniques, thereby confirming 
the astronomical detection of this feature (Russell eta/. 1980). 
It is hoped that the measurement of these lines will permit an 
accurate determination of the interstellar 12 C j 13 C and 
14Nj15 N isotopic rations free from the deleterious effects of 
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fractionation that plague molecular tracers of the dense inter-
stellar gas. 
II. EXPERIMENTAL 
The LMR spectrometer used in our study of the c+ and 
N+ ions has been described in detail elsewhere (Ray, Lubic, 
and Saykally 1982). Briefly, the spectrometer consists of an 
optically pumped far-infrared molecular laser containing an 
intracavity sample cell placed between the pole pieces of a 
0-20 kilogauss Varian 15" electromagnet, a liquid-helium 
cooled Ga:Ge bolometer, and associated detection electron-
ics. A rotatable polyproplylene beam splitter set at the 
Brewster angle separates the gain and sample regions of the 
FIR laser cavity. The FIR gain cell is transversely pumped by 
a 80 watt C02 laser, with power coupled out to the bolometer 
by an adjustable copper mirror inserted into the laser mode. 
If necessary, an iris may be used to suppress higher order 
transverse modes in the FIR laser. By superposing a 2-6 kHz 
sinusoidal magnetic field of about 30 G onto the slowly swept 
DC field any absorption from paramagnetic species is con-
verted into a phase coherent signal which is detected by the 
bolometer and processed in a lock-in amplifier. For the 
weakest transitions studied here it was necessary to signal 
average several scans in order to accurately measure the line 
position. The resonant fields were measured and calibrated to 
an accuracy of ± 2 G with an NMR gaussmeter probe. 
Like N+, the C + ions were generated in a 12-17 kHz AC 
discharge between two brass shimstock electrodes housed in 
the sample cell. The simple reaction 
He+ + CO --+ c+ + 0 + He 
proceeds quite rapidly to produce c+ and has the added 
advantage that the less reactive neutral oxygen species may be 
used to estimate optimum reaction conditions. As judged 
initially by the [0 1] line at 145 p.m and subsequently by the 
158 p.m [C II] transition, optimized conditions for c+ produc-
tion were approximately 50-70 millitorr of CO in 900 milli-
torr of He, with a discharge current of about 50 rnA. The 
search problem for the 158 p.m line was greatly reduced by 
the astronomical rest frequency estimate of Crawford et a/. 
(1985), determined from observations of the Orion molecular 
cloud. Figure 1 shows a recording of the MJ = - 3/2 -+ 
-1/2 component of the [C II] line under typical operating 
conditions. 
III. THEORY 
The effective Hamiltonian employed in our analysis of c+ 
has been thoroughly described in our study of N+ (Cooksy, 
Hovde, and Saykally 1986). We give here a brief summary of 
the perturbations treated and the results for the case of c+ 
that differ from our earlier work. The effective Hamiltonian is 
written as 
(1) 
where H0 is the phenomenological fine structure Hamilto-
nian, Hz is the Zeeman term, and H M is the magnetic 
hyperfine term. 
2p c+ 
J,MJ =3/2,-312-1/2,-1/2 
900 950 1000 
8 (Gauss) 
FIG. I.-Signal-averaged LMR spectrum of the MJ = -3/2 +-
-1/2 fine-structure transition in 2P 12 C+ at 1898.2799 GHz and 
967.0 G. 
The diagonal elements of Hz may be explicitly expressed 
as 
{2) 
where a is the nuclear shielding constant and XI is the 
isotropic diamagnetic Zeeman interaction. If we neglect the 
anisotropic diamagnetic Zeeman effect (the term in XA), the 
!l.MI = 0 selection rule implies that, for allowed transitions, 
only the first term of expression (2) has a first-order effect on 
the transition energy in a magnetic field. For a 2 P atom, the 
gyromagnetic factors are approximately 8J-l/Z = 2/3 and 
gJ_ 312 = 4/3. Because the gJ are significantly different for 
the two J levels, the energies of the MJ components of the 
2 P312 +- 2 P112 transition will change at different rates in a 
magnetic field. Lines of lower tunability [which is simply 
P.B(8J-3f2MJ=J/Z - 8J-t;2 MJ=t;2 )] will be broader and will 
appear at higher magnetic fields than their faster tuning 
counterparts. 
The magnetic hyperfine Hamiltonian is (Abragam and Pryce 
1951) 
HM = 2g1p.~{ (r1- 3 )(L ·I) 
+(r,- 3 )€[L{L + 1){S ·I)- t(L · S)(L ·I) 
- HL ·l)(L 0 S)] + t'ITIV(0)1 2 (S ·I)}' 
{3) 
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No.2, 1986 SINGLY IONIZED ATOMIC CARBON L91 
where 
(2/ + 1) - 4S 
~ = S(2/- 1)(2/ + 3)(2L- 1) . 
The matrix elements are functions of the constants (evaluated 
here for 2 P atoms) 
and 
2[2 -3 1 -3 16'1T 2] A3/2I/2=giiLB 3(rt )-3(rs )--9-1'1'(0)1 · (4) 
We currently lack the precision to determine the constant 
off-diagonal in J, A 112 312 , but have included it in our analy-
sis by utilizing the ab initio values of Schaefer and Klemm 
(1970) for (r1- 3 ), (rs- 3 ), and 1'1'(0)1 2 • It is worth noting that 
due to the ·magnitude of the diagonal constants A 112 and 
A 312 , terms off-diagonal in M1 and M1 are by no means 
negligible, contributing energies of as much as 50 MHz to the 
LMR transitions observed at low magnetic fields. 
IV. RESULTS AND DISCUSSION 
Four laser lines were available with which to investigate the 
LMR spectrum of c+. The transitions resonant with each of 
these frequencies were the two A M1 = -1 and the A M1 = 
0, M1 = -1/2 components as pictured for 13 C+ in Figure 2. 
Of these, the M1 = -3/2 ...- -1/2 line has the greatest 
intensity and tunability. The M1 = -1/2 ...- -1/2 compo-
nent has only one-third of this intensity and is broader by 
nearly a factor of four, and it could not be resolved in this 
study. 
The data obtained are given in Table 1. Measurements 
taken for both isotopes were combined in a least-squares 
analysis, the results of which comprise Table 2. We have 
failed thus far to resolve the hyperfine components of the 
M1 = -1/2 ...- 1/2 transition in 13 C + and therefore cannot 
adequately evaluate the independent parameters A 112 and 
A 312 . We have been able to determine the value of the 
coupled term 1j4A112 - 3j4A312 to within small uncertainty, 
however, and can use this to precisely predict the frequency of 
the J, F = 3j2, 2 ...- 1/2,1 transition, the strongest of the 
zero-field 2 P312 ...- 2 P112 components. The ab initio hyperfine 
constants of Schaefer and Klemm (1970) have proved capable 
of reproducing experimental measurements in 2 P atoms to 2% 
or better, and we have therefore used these calculations to 
estimate the frequencies of the weaker zero-field transitions, 
which are listed together with the 3 j2, 2 ...- 1/2, 1 frequency 
in Table 3. Schaefer and Klemm's constants predict the 
measured combination of the hyperfine constants to with-
in 2.5%, from which we estimate a 2 cr uncertainty of 
± 10-15 MHz for the weaker zero-field hyperfine lines. The 
TABLE 1 
A. RESONANT FIELDS FOR 12 C II MEASURED IN THIS WORK 
Transition Lasing Laser Frequency Field 
Ml <- MJ' Gas (GHz) (G) 
-3/2 <- -1.2 .............. 13 CH30H 1898.2799 967.0 
-1/2 <- 1/2 ................ 13 CH30H 1898.2799 1613.2 
- 3/2 <- - 1/2 ............. CH 2F2 1891.2743 3968.4 
- 3/2 <- - 1/2 ............. CH2DOH 1882.9063 7556.0 
-1/2 <- 1/2 ................ CH2DOH 1882.9063 12650.5 
-3/2 <- -1/2 ............. CH30H 1877.5085 9872.1 
-1/2 <- 1/2 ................ CH30H 1877.5085 16544.1 
B. RESONANT FIELDS FOR 13 C II MEASURED IN THIS WORK 
Transition Lasing Laser Frequency 
M;, MJ', M1 Gas (GHz) 
- 3/2, -1/2, -1/2 ........ CH2DOH 1882.9063 
-3/2, -1/2,1/2 ........... CH2DOH 1882.9063 
-3/2, -1/2, -1/2 ........ CH30H 1877.5085 
-3/2, -1/2,1/2 ........... CH30H 1877.5085 
J 
TABLE2 
CONSTANTS FOR C II DETERMINED BY LMR 
Constant 
E( 12 C+ 2P3;2 <- 2 P1;2) 
E(13 C+ 2P3;2 <- 2 P112) 
gJ~lj2· .................... . 
gJ~3j2· .................... . 
~(Al/2-3A3/2) .. · ...... · .. 
Value 
1900.5369(13) GHz 
1900.5458(21) GHz 
0.66576(11) 
1.33412(11) 
80.3(7) MHz 
NOTE.-Numbers in parenthesies represent 2 
a, 95% confidence limits. 
F MF MJ M1 
l/2c= 
-~~ 3/2 -1/2 2-- l/2c= 1/2 -1/2 
-2 
3/2--
-1/2 
~E-112 1/2 
1-- 0 
-I 
-1/2 
-3/2 1/2 
_fE 
1/2 
1-- 1/2 -1/2 
1/2--
0-- 0--
-1/2 
-1/2 1/2 
(a) (b) (c) (d) 
2PI3c+ ENERGY LEVELS 
Field 
(G) 
7525.3 
7604.0 
9841.9 
9917.3 
FIG. 2.-Energy level diagram of 2P 13 C+. (a) The unperturbed 
fine-structure levels. (b) The zero-field doublet hyperfine splitting. (c) 
The Zeeman effect in a weak magnetic field. (d) The Zeeman effect in a 
strong field, with the transitions observable at the available laser frequen-
cies illustrated. 
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TABLE3 
EsTIMATED ZERO-FlEW 'TRANSITION FREQUENCIES FOR 13 C II 
Transition Frequency Relative 4(13 C II 12 C II) 
F' +- F" (GHz) Intensity (km s- 1 ) 
2 <- 1 ....... 1900.4661(23)8 44.4% -11.2 
1 <- 1 ....... 1900.136(10)b 20.0 -63.2 
1 <- 0 ....... 1900.950(15)b 35.6 65.2 
• Determined in this work. 
bEstimated using values of A112 and A312 obtained from the 
ab initio constants of Schaefer and Klemm 1970. 
F = 2 +- 1 [13 C II] component lies only 14 km s- 1 from the 
[12 C II] fine-structure line and will therefore be difficult to 
observe even in the most narrow-line sources. However, as 
Table 3 shows, the weaker hyperfine satellites still retain 
nearly 50% of the transition intensity and lie some 60-70 
km s- 1 from the stronger [12 C II] line. 
In view of Veseth's recent theoretical work on isotopic 
shifts in atomic fine-structure states (Veseth 1985), we have 
also analyzed the [~E0 (13 C)- ~E0 (12 C)] shift in 2P c+ and 
obtain a value of 8.9(1.5) MHz for this parameter. Because 
further investigation into the theory of fine-structure shifts is 
at present hampered by the paucity of precise experimental 
data, we hope such data will encourage continuing efforts in 
the field. 
The variation of the 13 Cj12 C and N/0 isotopic ratios with 
galactic radius strongly constrains models of star formation 
and mass exchange between stellar interiors and the interstel-
lar medium. Molecular tracers of dense interstellar gas can be 
strongly affected by chemical fractionation processes that 
render the accurate determination of isotopic ratios extremely 
difficult. For example, the molecular 13 C and D content in the 
cores of cool, dense interstellar clouds may be strongly en-
hanced or depleted by the exothermic reactions 
13 c+ + 12 co -+ 12 c+ + 13 co + 35 K 
and 
Hj + HD-+ H 2 D+ + H 2 + 298 K. 
Atomic species are largely unaffected by these processes be-
cause of the higher temperatures and low molecular abun-
dances in the H II regions and photodissociation zones where 
such species are prevalent. Thus, the far-infrared fine struc-
ture lines of C, N, and 0 should be excellent tracers of atomic 
abundances and isotope ratios throughout the galaxy. Indeed, 
Lester eta/. (1983) have used the [N III] and [0 III] lines to 
examine the large scale galactic N/0 abundance gradient. 
The present work and our recent investigation of the labora-
tory spectra of C 1 and N II provide the necessary rest 
frequencies for a more thorough investigation of the 13 C 1 12 C 
and N /0 galactic abundance ratios which is now possible 
with the advent of high-resolution far-infrared astronomical 
receivers and airborne observing platforms. 
To summarize, far-infrared laser magnetic resonance spec-
troscopy has been used to precisely determine the g1 factors 
and fine-structure intervals of the 12 C and 13 C isotopes of 
singly ionized atomic carbon. The resulting transition fre-
quencies will be of considerable use in detailed investiga-
tions of atomic abundances, iostope ratios, molecular cloud 
morphology, interstellar mass exhange, and star-formation 
processes. 
This work was supported by the National Science Founda-
tion, Structure and Thermodynamics Program (grant CHE 
8402861). A. Cooksy thanks Chevron for a graduate fellow-
ship, and G. Blake and R. Saykally gratefully acknowledge 
financial support provided by the Berkeley Miller Research 
Insitute. 
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Abragam, A., and Pryce, M. H. C. 1951, Proc. Roy. Soc. London, A20S, 
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Crawford, M. K., Genzel, R., Townes, C. H., and Watson, D. M. 1985, 
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Dagenis, M., Johns, J. W. C., and McKellar, A. R. W. 1976, Canadian J. 
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GEOFFREY A. BLAKE: Space Sciences Laboratory, University of California, Berkeley, CA 94720 
ANDREW L. COOKSY and RICHARD J. SAYKALLY: Department of Chemistry, University of California, Berkeley, CA 94720 
© American Astronomical Society • Provided by the NASA Astrophysics Data System 


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Direct measurement of the fine-structure interval and g_J factors of singly ionized atomic carbon by laser magnetic resonance

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