CHINESt JOURNAL OF PHYSICS
VOL. 26, NO. 5
DECEMBER 1988
Analysis of Mg IX 2s3d-2s4f Transition of Beam-Foil Spectra
K. Ando, S. Kohmoto, Y. Awaya,
T. Tonuma and S. Tsurubuchi*
The Institute of Physical and Chemical Research, Wako,
Saitama 351-01, Japan
and
*Tokyo University of Agriculhue and Technology,
Koganeishi, Tokyo 184, Japan
(Received November 25, 1988)
The transition array of Mg IX 2s3d-2s4f is identified in beam-foil
spectra. The energy parameters are obtained from the least square fits
of the observed level energies. The ratio of fitted to Hartree-Fock
values was ascertained to be within reasonable values.
I. INTRODUCTION
Be-like ions have a simple electron configuration, but their energy levels are known
only below the principal quantum number of 3. Above n = 4, the term energies have not
fully analyzed, and a wavelength region around few hundred Angstom, which occurs from
the transitions from n = 4 to 3, is blank in wavelength tables. However, that wavelength
region is important in experiments on high-density plasmas.
The transition array of 2s3d - 2s4f has been identified for Be I to F IV, and for Al X
and Si XI, but, for the latter two elements, only lines of 3d 3 D - 4f 3 F have been identified.
A problem of identification of the singlet transition is that this transition array is overlapped with the other transition array of 2p3d - 2p4f, as shown in theoretical spectra
calculated with the multiconfiguration Dirac-Fock. Also, the 2s4f configuration has a configuration interaction with the 2p3d, as described by Edlen’. This configuration interaction
results in another difficulty of identification of the singlet line. We analyzed the 2s4f configuration, taking the configuration interactions into account.
The lower levels of 2s3d were already known and their energies were obtained from the
Grotorian Diagram2.
303
304
ANALYSIS OF Mg IX 2s3d-2s4f TRANSITION OF BEAM-FOIL SPECTRA
II. EXPERIMENTS
The beam-foil experiment was performed with the Heavy Ion Accelerator in RIKEN
(RILAC). Spectra for Mg beam energies of 12, 19 and 32 MeV were measured with a 2.2 m
grazing incidence spectrometer (McPherson 247) with a grating of 600 grooves/mm. The
entrance slit was placed 10 mm from the beam. and the width was set to obtain sufficiently
good resolution.
The cathode of a detector was coated with CsI to increase the quantum efficiency, and
secondary electrons emitted from it were amplified by a channel electron multiplier
(CERATRON).
In the case of spectrum analysis, observed spectral lines were fitted to the Gaussian
profile by use of the half width determined from strong lines. Spectral wavelengths were
calibrated by the known spectral lines of magnesium ions.
Intensities of spectral lines were normalized to charge collected in the Faraday cup.
The beam current was a few 100 nA.
III. ANALYSIS OF LEVELS OF 2s4f CONFIGURATION
An isoelectronic sequence of the transition 2s3d - 2s4f was obtained from the data of
C III to F VI, Al X, and Si x12*3. The wavelength of the triplet transition 2s3d 3 D - 2s4f
3 F was estimated from the isoelectronic sequence. Also, we calcualted a spectrum of this
transition array with Grant’s multiconfiguration Dirac-Fock (MCDF) computer code4,
where the 2s4f and 2p3d configurations for odd parity and the 2s3d, 2pz , and 2p4f configurations for even parity are included in order to take the interaction configurations into
account. From this calculation, the spectral lines that occurred from the levels of the 3 F,
(J = 2,3,4) overlapped in almost the same wavelength within 0.1 A as shown in Fig. 1, so
that these lines looked like one line. From this estimate, the strong line observed at 2 18.45
A was identified the transition 2s3d3 D, 2 3 - 2s4p F, 3 4.
The upper configuration 2s4f has a’configuration interaction with the 2p3d, so that the
two configurations must be coupled in the least squares fitting of the level energies.
Especially, the l F, of the 2s4f configuration is strongly coupled with that of the 2p3d configuration.’
After determination of the 3 F levels, the parameters of the energy expressions for the
2s4f and 2p3d configurations, which included the configuration interaction mentioned
above, were fitted by the least squares method5S7. The parameters used were average
energies, Slater direct- and exchange-radial integrals (Fk, Gk), spin-orbit interactions ({) for
the 2s4f and 2p3d configuration, respectively, and configuration interaction-radial integrals
(Rk) between two configurations. The initial values of these parameters were calculated
with the Hartree-Fock program code of MCHF778. From the least squares fitting, the
energy of th,- ’ F state was obtained, and the wavelength of the transition of 2s3d ’ D-2s4f
K.ANDO,S.KOHMOTO,Y.AWAYA,
FIG. 1
T.TONUMA,ANDS.TSURUBUCHI
305
A theoretical spectrum of two transition arrays of 2s3d-2s4f and 2p3d-2p4f, calculated by the
relativistic Dirac-Fock multiconfiguration. The upper configurations include 2s4f and 2p3d, and
the lower configurations 2s3d, 2p*, and 2p4f. The transition of 2s3d-2s4f is indicated in the
figure; other spectral lines come from the transition 2p3d-2p4f.
’ F was estimated. An isolated spectral line was found near this estimated wavelength, and
was identified as the singlet transition of 2s3d ’ D-2s4f’ F.
An isoelectronic sequence of the transition energies of this transition is plotted in Fig.
2, were the scaled transition energy was calculated from uS = a,‘{ - aH * C. u, is the
km’1
I
o*
t
;
2s3d ‘D -
2t4f
‘F
3000 .
2000 -
:
s
‘G
‘3
1000 -
ii
o-
c
P,
7 -1000 sf
Atomic
FIG. 2
Number
Isoelectronic sequence of the transition energies of the 2s3d-2s4f
wavenumber of the transition energy, au the corresponding wavenumber of the hydrogen
atom, and { is the net charge. The observed spectrum is shown in Fig. 3. were the identified
lines are indicated. The results of identification and classification are given in Table 1.
The parameters are determined from the observed energy levels by means of the least
%_ . . . . ,:
ANALYSIS OF I@ IX 2s3d-2s4f TRANSITION OF BEAM-FOIL SPECTR A
306
FIG. 3
A spectrum obtained by a beam-foil experiment at 19 MeV, in which the newly identified transition of 2s3d-2s4f is indicated. Numbers at the bottom are uncalibrated wavelengths, which are
different by about -1.5 A from the real ones. The + marks show the observed intensities.
TABLE 1.
Intensity
Observed Lines of the 2s3d-2s4f Transition in Mg IX
kavelength
( .J, 1
Wavenumbe r
Combination
(cm-l)
960
218.15
J3r -__- I /o
2s3d 3D1,2,3
- 2s-if 3F.3-, 3 , J
170
229.07
436550
2s3d ID2
- 2s4f IF3
squares fits7. Table 2 shows the fitting values, Hartree-Fock values, and ratio of the fitted
value to Hartree-Fock for each parameter. The energy levels and designations of the 2s4f
and 2p3d configurations are shown in Table 3. The standard deviation of experimental
energies is 695 cm-’ for 13 experimental levels included in the 2s4f and 2p3d configuration.
The differences of the experimental and the fitted level energies are small for the levels of
th 2s4f, but for 2p3d, they are slightly large, especially for 3 P levels. This means that the 3 P
levels may have a configuration interaction with the other configurations. The energy level
diagram of the obtained levels is shown in Fig. 4.
-__.
K. ANDO, S. KOHMOTO, Y. AWAYA, T. TONUMA,
TABLE 2.
Configuration
2slf
Parameter
E av
H-F Value
Fit/H-F
2085141
2051455
1.016
3285
4266
0.770
15
1.000*
Fitted Value
15
5 (4f)
Configuration
307
Energy Parameters (cm-’ )
C3(2s,4f)
2p3d
AND S. TSURUBUCHI
1808032
1766807
1.023
F2(2p,3d)
73697
68475
1.076
Gl(2pJd)
62654
64321
0.974
G3(2p,3d)
32766
373'52
0.877
<(2P)
2179
2582
c (3d)
107
107
1.000*
Rl(sf,pd)
-95502
-50657
1.885
R2(sf,dp)
-9302
-14435
0.644
E av
0.844
Interaction
* c(4f)"and {(3d)
were not varied in the Least squares fitting,
because these values were small.
IV. CONCLUSION
The levels of the 2s4f configuration were analyzed by taking into account the configuration interaction with the 2p3d configuration: the transition array of the 2s3d-2s4f was
identified. The energies of the levels were obtained from the wavelengths. The parameters
in the energy expressions were determined from the experimental level energies; their ratios
to Hartree-Fock values are within the limits of reasonable values.
-
i- *_ __
ANALYSIS OF Me IX 2s3d-2s4f TRANSITION OF- BEAM-FOIL SPECTRA
308
Energy levels and designations of 2s4f and 2p3d in Mg IX
T.4BLE 3.
Config.
Desig
2
ievel Energ:li cm -11
Exp.
2slf
Cal.
(
x)
2
2088710-s
20&8750
9913F;,
1(3F,2p3d)
3
2088980+x
2088790
99i3Fi,
U3F,2p3d)
1
2089140-s
2088840
99f3F),
1(3F,2p3d)
1F
3
2091110
2091720
98?F),
2(lF,2p'3d)
3P
0
1813291+y
1816679
1
1816276+y
1816289
99(3P),
U3D)
2
1816804+y
1815528
97(3P),
3(3D)
1P
1
1811286
18-110-13
3D
1
1807436ty
1807735
99(3D),
l(3P)
2
1808929ty
1808212
9i(3D),
3(3P)
3
1808924ty
1809066
1D
2
1789287
1789533
86(1D),
14(3F)
3F
2
1786422
85(3F),
l?('D)
3F
2p3d
Component
lOO(3P)
lOO(lP)
100(3D)
1(3F,2s4f)
1F
3
1787999
98(3~),
1(3F,2s4f)
4
1789646
99(3F),
1(3F,2s4f)
1837465
98?F),
2?F,2s4f)
3
1837337
Standard deviation of 13 experimental energies:696
In
a
column of the component,
configuration
configuration
interaction
.,.
the
same
is shok-n by only a term name in a parenthesis
name
with
the
unknown energy shifts.
_
level mixing within
cm-l
in
a
parenthesis
principal
means
configuration.
and
configuration
x
and
y
are
K. ANDO, s. KOHMOTO, Y. AWAYA,
T. TONUMA, AND S. TSURUBUCHI
309
'F-
2.0
3.0
4.0
J value
FIG. 4
Energy diagram of 2s4f obtained from the experiment.
ACKNOWLEDGEMENTS
We especially thank Miss. Yoko Aikawa for help in this analysis. We thank the
operators and staff of RILAC for operation in the experiments. This work was supported
by the Science and Technology Agency.
REFERENCES
1. B. Edlen, Encyclopedia ofPhysics, Vol. 27 (Springer-Verlag, Berlin, 1964) p. 80.
2. S. Bashkin and J. 0. Stoner, Jr., Atomic Energy Levels and Grotorian Diagrams, Vol.
1 (North-Holland Pub. Co., Amsterdam, 1975).
3. R. L. Kelly, J. Phys. Chem. Ref. Data, 16 (1987) Supplement No. 1.
4. I. P. Grant, B. J. McKenzie, P. H. Norrington, D. F. Mayers, and N. C. Pyper, Comput.
Phys. Commun. 21,207 (1980).
5. R. D. Cowan, Phys. Rev. 163, 54 (1963).
6. R. D. Cowan and D. C. Griffin, J. Opt. Sot. Am. 66, 1010 (1976).
7. R. D. Cowan, The Theory of Atomic Structure and Atomic Spectra (University of
California Press, California, 198 1).
8. C. F. Fischer, Comput. Phys. Commun. 14, 145 (1978).