Transition probabilities for the 3s-4p transitions of Nei

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Transition probabilities for the 3s-4p transitions of Nei

A. Czernichowski, A. Holys, J.R. Roberts

To cite this version:

A. Czernichowski, A. Holys, J.R. Roberts. Transition probabilities for the 3s-4p transitions of Nei.

Journal de Physique, 1977, 38 (9), pp.1065-1069. �10.1051/jphys:019770038090106500�. �jpa-00208672�

TRANSITION PROBABILITIES FOR THE 3s-4p TRANSITIONS OF NeI (*)

A. CZERNICHOWSKI and A.

HO0142Ys

Institute of

Inorganic Chemistry

^and

Metallurgy

^{of Rare}

Elements,

Technical

University of Wroc0142aw,

^50-370

Wroc0142aw,

^Poland

and J. R. ROBERTS Institute of Basic Standards

National Bureau of

Standards, Washington,

^D.C.

20234,

^U.S.A.

(Reçu

^{le 30 décembre}

1976,

^{revise le 2 mai}

1977, accepte

^{le 12 mai}

1977)

Résumé. ²⁰¹⁴ On a mesuré les

probabilités

de transition des raies correspondant ^aux transitions

3s-4p ^{de NeI dans un arc} stabilisé par paroi. L’arc fonctionnait dans une

atmosphère

^{de néon}

( 5 % H2) ^{à la}

pression atmosphérique ;

^les

probabilités

de transition de 27 raies émises par ^ce

plasma ^{d’arc ont été} ajustées ^en valeur absolue en utilisant les durées de vie connues de deux niveaux

supérieurs différents. Les résultats obtenus ont été comparés ^{aux autres travaux} théoriques ^{et contrôlés}

par la règle ^{de sommation sur} les J. Les résultats indiqués ^{ici sont} incompatibles ^{avec la} règle ^de

sommation sur les J.

Abstract. ²⁰¹⁴ Transition

probabilities

for the lines of the 3s-4p transition array of NeI ^were measured in a wall-stabilized arc. The arc

operated

^{in neon} ( ⁵ % H2) ^{at one} atmosphere pressure and the relative transition

probabilities

of 27 lines emitted from this arc

plasma

^were

placed

^{on an absolute}

scale

using

lifetimes of two different upper levels. The results ^are

compared

^{to other} theoretical results and were checked with the J-file sum rule. The results presented ^{here are} inconsistent with the J-file

sum rule.

Classification

Physics ^Abstracts

32.20J

1. Introduction. ^- Unlike the

popular 3s-3p

^tran-

sitions,

^the

3s-4p

^{lines of NeI} have received little attention. To observe if the

3s-4p

transitions exhibit the

same well-behaved

relationship

^to the J-file sum rule

as the

3s-3p transitions,

^{and to} compare these

relatively strong

^{uv lines to recent} theoretical calculations

[1-5],

an

experiment

^{to measure} their emission transition

probabilities

^was undertaken. Relative transition pro- babilities were determined

by

measurements of relative line intensities emitted from a wall-stabilized arc. The absolute scale for the transition

probabilities

^{is based}

on lifetime measurements

[6],

^and

compared

^with

other lifetime measurements

[6, 7, 8, 9].

This method of relative emission measurements combined with upper ^state lifetime measurements for an absolute scale

produces

^{some of the} most accurate values for absolute transition

probabilities ^{[10, 11].}

^{Because all}

the lines

originate

^from upper levels with

nearly

^the

same energy, the relative line intensities are

practically

(*) ^Work supported by ^the Maria Curie-Skxodowska Founda- tion, grant number NBS (G)-181.

independent

^{of source}

conditions,

e.g.,

temperature

and local

thermodynamic equilibrium,

and therefore the relative transition

probabilities

^{can be}

quite accurately

determined. The accuracy of the absolute scale will therefore

depend mainly

^{on the} accuracy of the _upper state lifetimes.

Because this is

by

^{now a standard}

experimental technique,

^the

history

^{of Ne}

experiments

^{and details of}

arc construction and

experimental apparatus

^{will not} be discussed. A more

complete

summary of this material will be found in reference

[10].

2.

Experimental

^{method. - The standard}

equation assuming

^an

optically

^thin

emitting layer

^{and the}

establishment of local

thermodynamic equilibrium

^is

used to determine the relative emission transition

probabilities, A,

^i.e.

where g

^{is the} upper level statistical

weight (=

^{2 J +}

1),

I is the emitted line

intensity, A

^{is the line}

wavelength,

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019770038090106500

1066

Eu

^{is the} upper ^state energy, and T is the

temperature.

In this

equation, 1 represents

the unknown lines and 2 the reference line

(e.g.,

^{3 520.5}

A, 3s’[1/2]O-4p’[1/2]

line).

^The absolute scale is determined dither from the

relationship

where i is the _upper state

lifetime,

^or

by knowing

^the

absolute transition

probability, A2,

ⁱⁿ eq.

(1).

As stated

previously

the accuracy of the

temperature

determination is not critical for the determination of the relative transition

probability

scale because the difference between

Eu(I)

^and

Eu(2)

^is very small

( 0.1 eV) compared

^{to the}

temperature

^{( ~ 1}

eV), therefore,

^the

exponential

^{factor in} eq.

(1)

^{is near}

unity.

The source for these emission measurements was a

wall-stabilized arc

operating

^{in neon with an admixture}

of

H2 ⁽

⁵

%)

^{at one}

atmosphere

pressure. Gas flow

rates of 10-50

1/h

^{and arc currents}

ranging

^from

40-120 A were used. The arc channel was 7 cm

long

and 4 and 6 mm in diameter and consisted of 8 water- cooled _copper discs. All observations were made end-

on and the arc diameter was

imaged

^{1 : 1 onto a 1 mm}

high

^{slit of a 2 m}

monochrometer/spectrograph.

^With

gratings

^{of 326}

1/mm

^{and 652}

1/mm

this instrument had a

reciprocal

^linear

dispersion

in first order of 14.8

A/mm

^{and 7.0}

A/mm, respectively,

^{in the wave-}

length regions

of interest. The reflection

optical

system

was

apertured

^to

f/50, guaranteeing

the observation of

a uniform

plasma.

The entire

optical

system, ^{arc, and} calibration

lamp

^were

carefully aligned

^{with a laser.}

The slit width and

grating

^{order (1st}

through 4th)

varied

according

^to the mode of

operation

^{of the}

monochromator/spectrograph.

^{In order to observe}

the

integrated intensity

^{of the lines under}

investigation, photographic

exposures of the lines were made at

high dispersion ^(4th order, 1.66 Å/mm,12

pm slit

width)

^to

determine if lines were blended

(and

^if

they

^{were what}

the line

intensity

ratio of the blended lines

was),

^and

what the

experimental

line width was. Once the

experi-

mental line width was determined the entrance slit width

(equivalent

^{to 0.7-3}

A)

^and

grating

^{were chosen}

to

guarantee only

^the

integrated

^line

intensity

^was

observed

(equivalent

^{to the}

height

of the measured line

signal

when the continuum

signal

^{has been}

subtracted).

Both

photographic

^and

photoelectric

measurements’

were made

(a

total of 9

separate experimental runs).

A side-on

monitoring system consisting

^{of a}

1/4

^m

monochromator and

phototube

observed the red Nel lines or

HB.

This monitor was used in the

photoelectric

measurements to observe the arc

stability. Together

the

photographic ^{( ~} 1 j2

^s

exposure)

and the monitor- ed

photoelectric ⁽¹⁵ min)

observations verified that the arc conditions did not

change

because similar results were obtained from both

types

^{of obser-} vations. The

photoelectric

^{results were considered}

more accurate because of the

large

range of intensities of the lines observed. The

spectral

response of the

entire

system

^was calibrated

using

^{a calibrated}

tungsten

^ribbon

lamp.

^{Care was taken to insure no}

overlapping

orders affected calibration measurements

by placing appropriate

filters in the

optical path. ^Also,

scattered

light

^{from the}

spectrograph

^was checked and found to be

negligible.

A

large

range of conditions of

temperature

(9 ^000-13 000

K)

and electron

density (1015-1016 cm- 3)

were used in order to test for

self-absorption

^{of the}

strongest

lines. Each line width was much narrower

than the instrumental width for all conditions observ- ed. All measured

strong-to-weak

line ratios were the

same

(to

^{within 7}

%)

^{for all}

conditions, indicating

^that

the

strongest

^{lines were}

optically

^thin.

Since the temperature ^{factor in} eq.

(1)

^{is not}

exactly unity,

^the temperature ^was determined

by

^two

methods. The first was to use a Boltzmann

plot, i.e., log IAIGA

^vs.

Eu,

for lines of well-known A values and well

separated

ⁱⁿ upper ^state energy. The

slope

^{of this}

plot

^is

equal

^{to - 5}

040/T (K).

The lines chosen of low upper ^state energy ^were the

prominent

^red

lines,

e.g., 6 128

A,

^{6 163}

A,

^{6 217}

A,

^{and 6 334}

^A

^{whose absolute}

transition

probabilities

^are well known

(see

e.g.

ref.

[10]).

^The

high

upper ^state energy lines chosen were

6 182

A (3p-5s) (ref. [3])

^{and the 6 328}

^A (3p’-Ss’) (ref. [12]). Although

^{the 6 328}

^A

transition

probability

has been

quite accurately

determined ( 5

%

^uncer-

tainty),

it is blended with a weaker 6 330

A

line in our

experiment

^{and was near to the} very

strong

^{6 334}

A line,

^{so it was not used with as much}

weight.

^{The second}

method involved

calculating

^the

temperature

^{from a}

measurement of the electron

density assuming

^Saha

equilibrium, particle quasi-neutrality,

and the idea _gas law. It has been shown for

high density

argon

plas-

mas

[13, 14] (Ne >

^{5 x}

¹⁰¹⁶ cm-3),

^{that the}

tempe-

rature determined this _way is the same as that deter- mined

by

^Boltzmann

plots.

^{For neon}

plasmas

^at

electron densities below

1016 cm- 3

this result _may not be valid because of deviations from local thermal

equilibrium involving

the atom’s

ground

state, ^{as is} assumed in Saha

equilibrium [15].

^This

temperature

determination

is, however,

^an upper limit of the

plasma

electron

temperature

^{and the}

comparison

^{of the}

Boltzmann

plot temperatures

^{to this}

temperature

^will indicate what confidence can be

placed

^{in the} tempe-

rature determined

using

^{the 6 182}

^A

^{and 6 328}

^A

^lines

in the Boltzmann

plot.

^{Table I shows some of the}

results of the two

temperature

determinations for two

representative examples.

The electron

density

^is

determined from the half-width

of Hp ^{[16] using}

^Hill’s

formula

[17].

TABLE I

Temperature comparisons

As was stated

earlier, however,

^the

temperature

need not be known too well for the determination of relative transition

probabilities

^since all the lines

originate

^from

nearly

^{the same} upper energy and therefore the resultant transition

probabilities

^are

relatively

insensitive to the

temperatures.

^{The error in} the relative transition

probabilities

introduced

by

^the

lack of

complete

^local

thermodynamic equilibrium

and an

accurately

determined temperature is therefore estimated as 5

%.

3. Results and discussion. ^- Table II shows the measured results with

comparisons

^{as indicated.}

Column one

gives

^the

wavelength

of the line in

A,

columns two and three the transition

(Paschen

^and

j -

¹

respectively),

columns four and five list the lower and upper energy in eV

respectively,

^columns

six and seven

give

the lower and _{upper g} values res-

pectively,

^column

eight presents

the measured

experi-

mental absolute transition

probability results,

^with

comparisons

in columns

nine,

ten, eleven and twelve.

The values of column nine are obtained from the Coulomb

approximation

^{and L-S}

coupling.

^The

comparison

^{in column ten uses frozen core Hartree-}

Fock wavefunction in an ab initio

configuration

interaction calculation. The values of column eleven

were abtained from

single

^and

multi-configurational approximations

ⁱⁿ intermediate

coupling.

^{The calcu-}

lations of column twelve are obtained

using

^interme-

diate

coupling theory including configuration

^interac-

tion with the absolute scale based on the Coulomb

approximation. Although

the individual relative tran- sition

probabilities

of all blended lines were determined from a

high dispersion (4th order,

12 J.1m slit

width) experiment,

^{it was} felt their values were not as accu- rate as for the isolated lines. The

experimental

^abso-

lute scale has been determined

using

^{two lifetime}

measurements

[6]

^{for the}

4p’[1/2]

^{and the}

4p[1/2]

levels. This scale is found in the

following

^manner

(all

^A values for other than the

3s-4p

transitions are

taken from references

[18,19])

The sums in _eq.

(3)

^{are taken over all lower states.}

A3351.7

^{is not} included in table II because the

intensity

of this transition is so weak so as to make a determi- nation of its A-value

impossible

^{in this}

experiment.

For each of the 9

experiments

^{these two sums are}

performed

^as above. Each sum will determine an

TABLE 11

Experimentally

determined transition

probabilities for

^the

3s-4p

array

1068

independent

absolute scale for the transition _pro- babilities of the _array. Since each scale will be

slightly different,

the final absolute scale is obtained from

averaging

^{the two values}

resulting

from each lifetime.

The final absolute A-values for all other transitions in the

3s-4p

array ^are then obtained from the _average of the 9 individual

experimental

^{runs. The third}

level, 4p’[1-1/2]

of reference

[6],

^{was not} used because this level contained three transitions all of which were

blended with other

4p

levels. Another method to check the absolute transition

probability

^{scale is to use} eq.

(1)

and the absolute A value of the 6 182

A (3p-5s)

^line

of reference

[3]

^for

A2

^{and the}

temperature

^determined from the Boltzmann

plots. Agreement

^{was found}

between the two absolute scales determined

by

^the

lifetime method and the absolute A-value of 6 182 within the stated

uncertainty

^{of ± 40}

%.

^{In table III}

comparisons

^are made with other

experimental

^lifetime

data.

The

subjection

^{of the}

experimentally

^determined

A values to the J-file sum rule

[20] requires

^{the conver-}

sion of A to S (the ^line

strength) by

the relation S ⁼ 4.935 x

10-19 9AA3 (a.u.) (4) where g

^{is the} upper ^state statistical

weight, A

^the

emission transition

probability (s-1)

^{and A the wave-}

length (A).

Other authors have made this

analysis

^on

the red

3s-3p

^{neon lines}

(see

e.g. ref.

[10]

^and

[12])

^and

have found _very

good consistency

between the files (rows and

columns)

^and very

good

agreement ^{with the} calculated

U2 (i.e.,

^the radial transition

integral).

^{In the}

central field

approximation

^{it can} be shown for an s-p array

[20]

This J-file is made in table IV.

TABLE III

Lifetime comparisons

TABLE IV

J-file

^{sum rule}

« 0 » Indicates too weak to be measured.

(*) ^Indicates experimentally determined branching ratios from high dispersion experiment.

The theoretical

0’2

in the Coulomb

approximation

for this

3s-4p

array

(assuming

^{it is constant for all}

transitions)

^{is 28.1 x}

^{10- 2}

^a.u.

[21].

^{There seems to}

be some

consistency

^with

the Y Ss,plgs,

^{but not so much}

p

in

the £ Ss,plgp.

s

In

general,

^the

experimental

^{A values} vary

signifi- cantly

^from those determined from the Coulomb

approximation

(column

nine) [5],

^{and are often a factor}

of 10

larger.

^Most

outstanding

is the lack of consis-

tency

^{of the}

3s-4p

array with the J-file sum rule in contrast to the _very

good agreement

^{for the}

3s-3p

array. In the

analogous 4s-5p

transitions in ArI a

similar

inconsistency

^exists.

Taking

^{the ArI line}

strength

values from reference

[18]

^and

summing

^the

J-files,

^the

weighted

^sums

(E Slg)

^{show the same}

tendencies as the

3s-4p

array in NeI. A

possible explanation

of this behaviour in Arl is

presented

ⁱⁿ

reference

[23]

where it is stated the

U2

for the

4s-5p

array is small and this _array is

subject

^to

possible configuration

interaction. The variation of

62

across

arrays in rare gases ^{as an}

explanation

of such discre-

pancies

is also mentioned in reference

[25].

^The

3s-4p

array of Nel suffers from strong cancellation in the radial transition

integral, ⁶² (see

footnote of ref.

[3]).

The ratio of the ^« +

» and « - » parts

^{of the}

integrand

of this

integral,

calculated

using

^{the Coulomb}

approxi-

mation

(now assuming ^Q2

^{not to be constant over the}

entire

array),

lies between 0.6 and 0.9

indicating large

cancellations and the resultant

Q2

varies from transi- tion-to-transition

by

^{as much as a factor of 10}

(1).

^This

cancellation is the

major

^{cause of the} variation of

U2

across the _array

and, therefore,

invalidates the J-file

sum rule which can be seen from table IV. This

probably

^{accounts for the}

discrepancy

between the measured A values and the

theoretically

^determined

ones which assume a constant

62

for the entire array

[3, 4, 5]. Comparison

^of

lifetimes,

calculated

using

eq.

(2)

with those of references

[24, 25, 26] (also assuming

^{a constant}

U2),

indicates similar discre-

pancies.

^The

exception

^{of the}

assumption

^{of a cons-}

tant

U2

is reference

[1],

where the relative

agreement

^is

quite good. Unfortunately

^not all transitions were

calculated so a

complete comparison

^{could not be}

made.

4. Conclusions. ^- The absolute transition

probabi-

lities have been determined for the

3s-4p

^transition

array in NeI

by

^the measurement of relative A values in emission combined with the

experimental

^lifetime

measurements to

provide

^an absolute scale. The data

are

compared

^to other theoretical data and

significant

deviations are found. The data are also submitted to the J-file sum rule and here too,

significant

^deviations

are noted. The effect of strong cancellation in the radial transition

integral giving

^{rise to} variations in

62

for each transition in the

3s-4p

array is seen as a

possible explanation

^{for these}

significant

deviations.

It is felt that the relative A values determined are accurate to within

10 %

^{for the} stronger ^{lines and} within 15

%

for the weaker and blended ones. The absolute scale is

dependent

^{on the} average of two lifetime measurements

plus

^the

uncertainty

^{in the}

relative A values. The total

uncertainty

estimate is therefore put ^at ± 35

%

^for

strong

lines and ± 40

%

for weak and blended lines.

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