168
OPTICS
LETTERS
/ Vol.
9, No.
5
/ May
1984
Quasi-metastable
quartet
levels
in
alkalilike
atoms
and
ions
S.
E.
Harris,
D.
J. Walker,
R.
G.
Caro,
and
A.
J. Mendelsohn
Edward
L. Cinzton
Laboratory,
Stanford
University,
Stanford,
California
94305
R.
D.
Cowan
Los
Alamos
National
Laboratory,
Los
Alamos,
New
Mexico
87545
Received
January
5,
1984;
accepted
February
14,
1984
We
describe
the
properties
of
a subclass
of
quartet
levels
of
alkalilike
atoms
and
ions
that
often
retain
metastability
against
autoionization
and
may
have
large
radiative
yields.
Gain
cross
sections
for
XUV
lasers
with
wavelengths
between
20
and
100
nm are
given.
It is
well
known
that,
in
many
cases,
the
quartet
level
of
highest
J
of
a given
configuration
of
an
alkalilike
atom
or
ion
is
metastable
against
both
autoionization
and
against
radiation
in the
extreme
ultraviolet
(XUV).
This
occurs
sincu,
irrespective
of the
extent
to
which
LS
coupling
holds,
there
is
no
doublet
level
in the
config-
uration
to
which
the
quartet
level
may
couple.
1
In
this
Letter
we
note
the
existence
of
a
subclass
of
quartet
levels
that,
even
in
heavier
elements,
often
re-
tain
relative
metastability
against
autoionization
and
are
radiatively
allowed.
In elements
such
as
Cs
and
Ba
these
levels
are
candidates
for
the
upper
level
of XUV
lasers.
In
lighter
alkalilike
atoms
and
ions
they
provide
storage
levels
for
store
and
transfer
lasers,
which
require
orders-of-magnitude
less
transfer
laser
power
than
an
earlier
proposed
Li
system.
2
The
distinguishing
property
of, these
quasi-meta-
stable
levels
is that
the
selection
rules
on
the
spin-orbit
matrix
elements
allow
nonzero
matrix
elements
only
to
doublet
basis
levels,
which
are
themselves
prohibited
from
autoionizing.
In
second
order,
through
the
di-
agonalization,
these
levels
do
develop
components
of
autoionizing
doublet
levels
and
therefore
do
autoionize,
but
often
sufficiently
slowly
that
the
branching
ratio
for
XUV
radiation
remains
large.
To
illustrate
this
idea,
consider
the
2
p
53
s3p
config-
uration
of
Na.
First,
the
pure
doublet
levels
that
may
not
autoionize
are
2
p
5
3s3p
2
P
1
/
2
,
3
/
2
; their
doing
so
would
not
allow
simultaneous
conservation
of parity
and
an-
gular
momentum.
One
then
tabulates
the
possible
quartet
and
doublet
levels
of
this
configuration:
4S3/2,
4P
1
/2,32,5/
2
)
4
D1/
2
,
3
/
2
,
5
J
2
,
7
/
2
, 2S1/2,
2
P
1
/
2
,
3
/
2
,
2
D
3
/
2
,
5
/2.
The
pertinent
selection
rule
on
the
spin-orbit
element
is
AL
-0,
+
1.
Therefore,
of
the
possible
quartet
levels,
those
that
couple
only
to
the
nonautoionizing
2PI/2,3/
2
levels
are
4S3/2
and
4DI/
2
.
We
term
these
levels
quasi-meta-
stable.
Table
1 lists
the
quartet
levels
of
the
2p
5
3s3p
con-
figuration
and
their
autoionizing
rates
as predicted
by
the
atomic-physics
code
RCN/RCG,
3
with
only
this
configuration
included.
Single
and
double
stars
in the
left-hand
column
denote
predicted
quasi-metastability
and
metastability,
respectively.
The
nonzero
au-
toionizing
rates
of
the
quasi-metastable
levels
result
from
small
components
of autoionizing
doublet
levels,
which
are
acquired
in
second
order
through
the
diago-
nalization.
The
code
expansion
of
the
quasi-metastable
2p
5
3s3p
4S3/2
level
of
Na
is
4S3/2
=
0.98
4S3/2
-
0.15
4P
3
/
2
+
0.07(lPj2P
31 2
+
0.04(
3
P)2P
31 2
-
0.OO1(lP)
2
D
3
/
2
-
.O-OI(3P)
2
D
3
/
2
-
(1)
The
(0.001)2
components
of
2
D
3
/
2
result
in
the
micro-
second-time-scale
autoionizing
rate.
The
much
larger
(0.07)2
component
of
(1P)2P3/
2
causes
no
autoionization
and
leads
to
a
radiative
rate
of
7.7
X
106
on
the
transi-
tion
2p
5
3s3p
4S
3
/
2
-
2p
6
3p
2
P
31 2
at
41.5
nm.
The
quasi-metastable
4D
1 1
2
level
lies
higher
in
the
configuration
and
couples
more
closely
to
nearby
dou-
blet
levels.
In
second
order
it
acquires
a
(-0.014)2
component
of (
1
P)
2
8
11 2
, which
in
turn
leads
to
its
au-
toionizing
rate
of
2
X
109
sec-'.
Table
2
tabulates
the
quasi-metastable
quartet
levels
of
all
sp,d
configurations
of
the
alkalilike
atoms
and
ions.
The
requirement
for
quasi-metastability
is
summarized
by
I J-L
I
=
3/2;
parity
and
angular
mo-
mentum
must
be
both
even
or
both
odd.
Table
3 tabulates
the
calculated
single
configura-
tional
autoionizing
rate
and
dominant
XUV
radiation
rate
for
the
lowest-energy
quasi-metastable
level
for
the
elements
of
columns
I and
II.
In
general,
the
selection
Table
1.
Single
Configurational
Autoionizing
Rates
of
Quartet
Levels
in
the
Sodium
2p
5
3s3p
Configuration
Autoionizing
Level,
Rate
(sec-')
*4S312
6.06
X 105
4
P
1
/
2
10.1
X
1010
4p,1/2
4.5
x
1010
4P
5/2
2.67
x
1010
*4D
12
0.181
X
1010
4Ds/2
1.25
x 10"0
4Ds,52
0.99
x 1010
**4D7/2
0
a
Single
and
double
stars
indicate
predicted
quasi-metastability
and
metastability,
respectively.
0146-9592/84/050168-03$2.00/0
©
1984,
Optical
Society
of
America
May 1984 / Vol. 9, No. 5 / OPTICS LETTERS 169
rule on quasi-metastability
holds better and is less af-
fected
by the inclusion
of other
configurations
for col-
umn
I than for
column II elements.
As expected,
it also
tends
to hold better
in lighter
elements and
for low-lying
levels.
We have
made multiconfigurational
code
runs on
several
elements.
In
sodium,
the inclusion
of the
2p
53
s3p,
2p
5
3s4p,
2p
5
3p4s, and
2p
5
3p3d
configura-
tions
changes the
single configurational
(Table
1)
2p
5
3s3p
4S3/2
autoionizing
rate
to 4.1
X 10i sec-'
and
the 2p
5
3s3p 4Dl/2
rate to 1.1
X 109 sec-
1
.
In Ca+ the
inclusion
of the
3p
5
3d4s,
3p
5
4d4s,
3p
5
5d4s,
and 3p
5
3d
2
configurations
changes
the 3p
5
3d4s 4P
5
/
2
autoionizing
rate
(Table 3) to 1.03
X 106 sec-'. Bat
does particularly
poorly.
The
5p
5
5d6s
and 5p
5
5d
2
configurations
are
strongly mixed,
and the
autoionizing
rate of
the 4P
5
/
2
level can
be made
to vary
between
1012 and
107, de-
pending
on the choice
of the relative
average
energy of
the
two configurations.4
On the
other hand,
Cs is rel-
atively
insensitive
to
the relative
energy
position and
has a multiconfigurational
autoionizing
rate
of 7.46 X
107 sec-'.
Radiation in the XUV
has been observed and
at-
tributed
to the 4S3/2
and 4P5/2
levels in several
column
I
and column II
metals by Aleksakhin
et al.
5
and by
Table 2. Quasi-metastable Quartet Levels of
Alkalilike Configurations
Metastable
Configuration Quasi-metastable
Levels Levels
p
5
sp
4S3/2, 4D1/2
4D7/2
p
5
sd 4P
5 1 2
, "F
3
/
2
4F
9
/
2
p6pd 4S3/2, 4DD/
2
, 4D
7
/
2
, 4G5/
2
"G11
12
p5p2
4P5/
2
p
5
d
2
4P
512
. 4F
31 2
, "F
9
/
2
-
138798 //S
//~''CS+ 5p56S
[I I 0
107219 5p
5
5d6S
4
P
5
/
2
107.5 nm
3 1 307 1/_// / e,//Z CS+ 5p
6
1r
3
14597
. - 5p
6
5d
2
D
5 12
0
5p
6
6S
2
S
1
/2
Fig. 1. Energy-level diagram for 107.5-nm Cs laser.
Zhmenyah et al.
6
Also, a single configurational analysis
by McGuire7 predicts slow autoionizing rates for the
4S3/2 levels of Na and Mg
t
.
Table 4 gives the transition wavelength, Doppler
width, and gain cross section a for XUV laser transitions
that originate from the lowest quasi-metastable level
of each element. The Doppler width is calculated at a
Table 3. Single Configurational Autoionizing and Radiative Rates for Quasi-metastable Column I and Column II
Elements
Element Upper Level
Autoionizing Rate Radiative
Rate X (nm) Lower Level
Na
2p
5
3s3p 4S3/2
6.1 X 105
7.7 X 106
41.5
3p
2
P
3
/
2
K
3p
5
3d4s 4Ps/
2
4.6)X
102
3.0
X 106
71.1
3d
2
D
3
/
2
Rb
4p
5
5s5p
4S3/2
8.6 X 107
2.6 X 107
82.1
5p
2
P
3
/2
Cs
5p
5
5d6s
4P
5
/
2
5.1 X 107
4.1
X 107
107.5
5d
2
D
5
/2
Mg+
2p
5
3s3p
4S3/2
9.3 X
104
1.9 X
107
25.6
3p
2
P
3
/
2
Ca+
3p
5
3d4s
4P
5
/
2
9.3 X 105
4.1 X 106
52.9
3d
2D152
Sr+
4p
5
4d5s 4P
51 2
1.4)X 103
5.3 X 107
62.0
4d 2D5/2
Ba4 5p
5
5d6s
4P
512
2.7
X 109
8.8 X 107 77.1
5d 2D5/2
Table 4. Gain Cross Sections of Transitions from Quasi-metastable Levels
Doppler
Element Transition X (nm) Width (cm-') a (cm
2
)
Na
2p
5
3s3p 4S312
- 2p63p
2
P
5
/
2
41.5
1.04
1.6 X 10-16
K 3p
5
3d4s 4P
5
/2 - 3p63d 2P5/
2
71.1 0.43
4.4 X 10-16
Rb
4p
5
5s5p
4S3/2 - 4p65p
2P
3
/
2
82.1
0.24
9.1 X 10-15
Cs
5p
5
5d6s
4P
5
/2
- 5p
6
5d
2D
51 2
107.5
0.15
3.9 X 10-14
Mg+
2p
5 3
s3p 4S3/2 -
2p63p 2P
31 2
25.6
1.78
8.71
X 10-17
Ca+
3p
5
3d4s
4P
51 2
- 3p
6
3d 2D
5
/
2
52.9
0.83
1.72 X
10-16
Sr+
4p
5
4d5s 4P
5
/2 - 4p64d 2D5/2
62.0
0.45 5.6 X 10-15
Bat 5p
5
Sd6s 4P
5
/
2
- 5p
6
5d
2
D
512
77.1 0.27 2.4 X 10-14
170 OPTICS LETTERS / Vol. 9, No. 5 / May 1984
temperature
corresponding to a vapor
pressure of 10
Torr.
Figure 1 is an energy-level diagram for a 107.5-nm Cs
laser.
The 4PP
5 2
level
will be populated
by electron
collisions at a peak excitation cross section that Alek-
sakhin et al.
5
estimate
as 5.8 X 10-17
cm
2
and also by
charge transfer from the Cs+ 5p
5
6s ion. The lower laser
level
5p65d 2D5/2 will
also be excited by
electron colli-
sions but can probably be emptied
by laser excitation
to a
Rydberg level or to the Cs+
Sp" continuum.
Population in the quasi-metastable levels of the col-
umn II elements of Table 4 can be produced by soft-
x-ray photoionization8'
9
of populated
valence levels.
For example, photoionization of atoms in the 5p
6
5d6s
3D level of Ba will produce 5p55d6s 4P
5
/
2
ions with a
statistical branching ratio
of about 7%. A possible ad-
vantage of using column II metals is that the lower laser
level is an excited level of the ion rather than of the
neutral.
The authors gratefully acknowledge helpful discus-
sions with T. Lucatorto, A. W. Weiss, and P. J. K. Wi-
soff.
The research described here was supported by the
U.S. Air Force Office of Scientific Research and the U.S.
Army Research Office.
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