Pressure broadening and shift of the rubidium

D1 transition and potassium D2 by various gases with

comparison to other alkali rates

Greg A. Pitza,⇤, Andrew J. Sandovala, Ti↵any B. Tafoyaa, Wade L.Klennertb, David A. Hostutlera

aAir Force Research Laboratory 3550 Aberdeen Ave SE, Kirtland Air Force Base, New

Mexico 87117

bThe Boeing Company, 4411 The 25 Way NE #350, Albuquerque, NM 87109

Abstract

The pressure broadening and shift rates for the potassium D2 (42P3/2 42S1/2) transition with the noble gases, N2, CH4, C2H6, C3H8, and n-C4H10 wereobtained for pressures up to 80 Torr and at a temperature of 55�C by means oflaser absorption spectroscopy. Additionally, the broadening and shift ratesfor the rubidium D1 (52P1/2 52S1/2) for He, CH4, C2H6, C3H8, and n-C4H10 were obtained utilizing the same techniques and under similar condi-tions. The potassium D2 collisional broadening rate, �

L

, for He, Ne, Ar, Kr,Xe, N2, CH4, C2H6, C3H8, and n-C4H10 are 19.84, 8.88, 18.65, 19.17, 22.19,18.98, 27.78, 27.60, 27.70, and 33.48 MHz/Torr, respectively. The uncer-tainty in the broadening rates is typically less than 2.1%. The correspondingpressure induced shift rates, �, are 0.52, -2.06, -5.52, -5.42, -7.01, -5.66, -8.38,-8.04, -9.22, and -9.37 MHz/Torr with a uncertainty of less than 1.8%. Therubidium D1 collisional broadening rates for He, CH4, C2H6, C3H8, and n-C4H10 are 20.80, 32.78, 30.49, 33.05, and 29.61 with uncertainties typicallyless that 2.2%. The collisional shift rates for the rubidium D1 transition are5.80, -6.96, -7.88, -8.61, and -9.43 with uncertainties on the order of 1.1%.A comparison with the other alkali broadening and shift cross-sections ispresented.

Keywords: Pressure Broadening, Pressure Shift, Potassium, Rubidium,

⇤Corresponding author.Email address: AFRL.RDLC.SCI.org@kirtland.af.mil (Greg A. Pitz)

Preprint submitted to Journal of Quantitative Spectroscopy & Radiative TransferApril 1, 2013

Laser Absorption, Spectroscopy, DPAL

1. Introduction

With the reinvigoration of alkali-based lasers by Krupke and Beach in2003, the alkali D1 and D2 transitions and their corresponding line shapes asa function of temperature and pressure have become under higher scrutiny[1]. The Diode Pumped Alkali Laser (DPAL) optically pumps the alkalialong the D2 transition. The population is then collisionally moved from theP3/2 to the P1/2 state, from which it lases along the D1 transition returningthe population to the ground state S1/2. The performance of these lasersystems will depend on how well they absorb the diode light and how theypropagate through the atmosphere. The D2 line shape will enable a highfidelity prediction of the absorption of the diode light, while theD1 line shapewill enable an understanding of the atmospheric absorption characteristicsof a DPAL system.

The collisional broadening and shift rates for the alkali D-lines and theircorresponding hyperfine structure has been studied since the mid twentiethcentury in various experiment and theoretical treatises. [2, 3, 4, 5, 6, 7, 8, 9,10, 11, 12, 13, 14, 15, 16, 17, 18, 19] In addition, numerous general reviewsof the atomic hyperfine profiles due to collisions are available [20, 21, 22].

One of the most recent studies was accomplished by Zameroski et.al.[5].This work employed laser absorption spectroscopy and limited itself to onlythe D2 transition. Another recent work on potassium D1 transition wasaccomplished by Pitz et.al.[23]. This current work was accomplished to sup-plement these prior works with the missing broadening rates by employingsimilar techniques.

Prior to the work by Zameroski, the rubidium D1 and D2 broadeningand shift rates were measured by Rotodaro and Perram in 1995 [6]. Whilethis work measures the broadening rates for many di↵erent gases, it did notmeasure the rates for the more complex hydrocarbons which were of interestas possible spin-orbit mixing gases for DPAL systems; prior to the work ofPitz, the most recent work on the potasium D-lines was accomplished byEfthimiopoulos et.al.. This work employed a broadband white light sourceand a spectrometer. This technique did not have the resolution needed for ac-curate absorption predictions in DPAL numeric models, and in addition, thiswork did not measure the rates of the hydrocarbon gases. Both Efthimiopou-los and Lwin both observed asymmetries in the line shape for potassium-rare

2

gas collisions, a fact that might play a significant role in the modeling anddevelopment of high pressure DPAL systems.

2. Experimental details

This experiment utilized the experimental apparatus employed by Pitzet.al. and Zameroski et.al. with the exception of the laser [23, 5]. The lasersemployed for this work were New Focus Velocity lasers centered at 766nmand 790nm. These lasers were able to scan over 20GHz across the K D2 andthe Rb D1 hyperfine spectrum respectively. The laser was split into fourchannels as shown in Fig. 1, one of which monitored the scan rate with afabry-perot etalon (Coherent spectrum analyzer model #33-6248-000) witha 300 Mhz free spectral range. The other three channels, incident intensity,the reference spectrum, and the broaden spectrum, were all observed withlarge area photo-receiver (New Focus model 2031). The output of the photo-receivers and etalon were connected to an oscilloscope (Agilent MS06104A)to measure and record data.

Figure 1: Experimental apparatus for laser absorption spectroscopy.

The gas handling system was the same as that employed by Pitz et.al. [23].This allowed for continuous measurement of the bu↵er gas pressure through-out the experiment with simultaneous measurement of the gas temperature.The cell length for these experiments was 3.25 inches for both K and Rb. It

3

was placed in an aluminum block oven with a Watlow temperature controllerto maintain the temperature of the cell within 1�C. The vapor pressure atthe highest temperature (328 K) was .048±.039 µTorr and 5.36±0.44 µTorrfor K and Rb, respectively [24, 25].

The recorded transmitted intensities, I, were divided by the incident in-tensity, I0, which removed the low frequency power fluctuation from the laser.A small linear background was observed over the 15-20 GHz scan of the laser,which had a relatively small slope in comparison to its o↵set, on the order of10�3%. This was mathematically removed from the known absorption profileduring the numerical fitting of the spectrum.

3. Results

The resulting spectral profiles for the K D2 and Rb D1 are shown in Fig.2(a) and 2(b), respectively. The hyperfine spectrum for the rubidium D1 pro-file is mostly resolved at low pressures. On the other hand, the potassiumD2 hyperfine spectrum can not be resolved at any pressure. This is due tothe relatively small hyperfine ground state of potassium (461.7 MHz - 39K,254.0 - 41K) compared to the rubidium spacing (3035.7 MHz - 85Rb, 6834.7MHz - 87Rb).

1.0

0.8

0.6

0.4

0.2

0.0

Abs

orba

nce,

A (-

Ln(I/

I 0))

6000400020000-2000-4000Frequency, ν (MHz)

(a)

1.0

0.8

0.6

0.4

0.2

0.0

Abs

orba

nce,

A (-

Ln(I/

I 0))

-6000 -4000 -2000 0 2000 4000 6000Frequency, ν (MHz)

(b)

Figure 2: Data samples of the potassium D2 profile (a) and the rubidium D1 (b) profile forpressures between 5-80 Torr.

The resultant spectral profiles can be described by a summation of Voigtprofiles for each hyperfine component,

A=�Ln✓I

I0

◆= c0 + c1⌫ +

4

Table 1: Potassium and rubidium hyperfine transition strengths for the D2 and D1 tran-sition, respectively and for both isotopes.

Alkali SF F0Strength

(Transition) (unitless)

S1 1 1/687Rb(52P1/2 52S1/2) S1 2 5/6

S2 1 1/2S2 2 1/2

S2 2 2/985Rb(52P1/2 52S1/2) S2 3 7/9

S3 2 5/9S3 3 4/9

S1 0 1/6S1 1 5/12

39,41K(42P3/2 42S1/2) S1 2 5/12S2 1 1/20S2 2 1/4S2 3 7/10

+ c2X

iso

4,6X

i=1

ai,iso

V (⌫i,iso

+ �⌫,�⌫L

; �D

), (1)

where c0 and c1 correspond to the slight linear background observed. Theline strength, a

i,iso

, and the line center of each hyperfine component, ⌫i,iso

,are independent of pressure and are shown in Table 1. The primary measuredfactors within this line shape are the collisional shift, �⌫, and the lorentzianwidth, �⌫

L

, which corresponds to the collisional broadening. The final factorwithin the Voigt profile is the Doppler width, �

D

, which is 394 and 262 MHzat 328K for K and Rb, respectively.

The absorbance, A, is measured from the ratio of the transmitted in-tensity, I, and the incident intensity, I0. The absorbance is defined as theproduct of the absorption cross-section, the length of the cell, and the num-ber density of the absorber (�LN). The number density throughout theseexperiments was on the order of 1.4⇥ 109 and 1.6⇥ 1011 cm�3 for K and Rb,

5

respectively.Examples of the fit of equation 1 to the K D2 and the Rb D1 transition,

both broadened by helium, are shown in Fig. 3. The residuals associatedwith these fits are on the order of 3% and 2% for K and Rb in the wings,respectively. On the other hand, the core of the line shape fits less accuracyand may be due to Dicke Narrowing.[26] This e↵ect can be seen in cesiumand rubidium.[15, 16, 5]

1.0

0.8

0.6

0.4

0.2

0.0

Abs

orba

nce,

A (-

Ln(I/

I 0))

-5000 -4000 -3000 -2000 -1000 0 1000 2000 3000 4000 5000Frequency, ν (MHz)

6040200

-20-40 R

esid

uals

( x10

-3)

(a)

0.8

0.6

0.4

0.2

0.0

Abs

orba

nce,

A (-

Ln(I/

I 0))

-6000 -4000 -2000 0 2000 4000 6000Frequency, ν (MHz)

-20

0

20

Res

idua

ls ( x

10-3)

(b)

Figure 3: A sample of the resultant fits with residual for the potassium D2 (a) and therubidium D1 (b) transition under the influence of helium at 15, 45, 60 Torr.

The resulting shifts, �⌫, and widths, �⌫L

, are shown as a function of thepressure of various atomic and molecular collision partners in Fig. 4, 5, and6. A linear fit was performed on this data to extract the broadening andshift rates. This is related to the following formula for the lorentzian widthand the total shift,

�⌫L

=�P + �N

, (2)

�⌫=�P, (3)

where � and � are the broadening and shift rates. The natural width, �N

associated with this fit was allowed to vary to allow for the inaccuracy of thezero of the pressure gauge. The shifts should have a y-intercept of zero, butthis again was allowed to vary in the fit to account for the lack of an absolutezero on the pressure measurement.

The resultant rates are shown in Tables 2,3,4,5,6,7,8, and 9 with thecorresponding numerical fit errors and a comparison to previously measured

6

16001200

800400

Lore

ntzi

an W

idth

, Δν L

(MH

z)

8070605040302010Pressure, P (Torr)

600400200

1200

800

400

16001200

800400

16001200

800400

Helium

Neon

Argon

Krypton

Xenon

(a)

1600

1200

800

400

Lore

ntzi

an W

idth

, Δν L

(MH

z)

908070605040302010Pressure, P (Torr)

2000

1500

1000

500

1600

1200

800

400

2000

1500

1000

500

3000

2000

1000

Butane

Propane

Ethane

Methane

Nitrogen

(b)

Figure 4: Potassium D2 hyperfine profilebroadening as a function of pressure of (a)the noble gases and (b) various molecularcollisional partners.

7

5040302010

Freq

uenc

y Sh

ift, δν

(MH

z)

8070605040302010Pressure, P (Torr)

-120

-80

-40

0-400

-300

-200

-100

-400

-300

-200

-100

-500-400-300-200-100

Xenon

Krypton

Argon

Neon

Helium

(a)

-500-400-300-200-100

Freq

uenc

y Sh

ift, δν

(MH

z)

908070605040302010Pressure, P (Torr)

-600

-400

-200

-500-400-300-200-100

-600

-400

-200

-600

-400

-200

Butane

Propane

Ethane

Methane

Nitrogen

(b)

Figure 5: Potassium D2 hyperfine profilebroadening as a function of pressure of (a)the noble gases and (b) various molecularcollisional partners.

8

200015001000

500

Lore

ntzi

an W

idth

, Δν L

(MH

z)

8070605040302010Pressure, P (Torr)

2500200015001000

500

200015001000

500

2500200015001000

500

16001200

800400

Helium

Methane

Propane

Butane

Ethane

(a)

400

300

200

100

8070605040302010Pressure, P (Torr)

-500-400-300-200-100

Freq

uenc

y Sh

ift, δν

(MH

z)

-600

-400

-200

0

-600

-400

-200

-600

-400

-200

Helium

Methane

Ethane

Propane

Butane

(b)

Figure 6: Rubidium D1 hyperfine profilelorentzian widths (a) and shifts (b) as afunction of pressure of helium and varioushydrocarbons.

9

Table 2: The alkali D1 broadening rates for the rare gases.

Alkali Bu↵er � Temp. Press. Range Ref.(Transition) Gas (MHz/Torr) (K) (Torr)

K (42P1/2 42S1/2) He 13.08±0.05 328 5-80 [23]Rb (52P1/2 52S1/2) 18.9±0.2 394 0-300 [6]

20.80±0.02 328 5-80 This WorkCs (62P1/2 62S1/2) 24.13±0.07 323 0-300 [15]

K (42P1/2 42S1/2)3He 17.46±0.12 328 5-80 [23]

Rb (52P1/2 52S1/2) — — — —Cs (62P1/2 62S1/2) 26.00±0.05 323 0-300 [15]

K (42P1/2 42S1/2) Ne 6.14±0.03 328 5-80 [23]Rb (52P1/2 52S1/2) 9.84±0.1 394 0-300 [6]Cs (62P1/2 62S1/2) 10.85±0.03 313 0-300 [15]

K (42P1/2 42S1/2) Ar 19.45±0.06 328 5-80 [23]Rb (52P1/2 52S1/2) 18.1±0.2 394 0-300 [6]Cs (62P1/2 62S1/2) 18.31±0.06 313 0-300 [15]

K (42P1/2 42S1/2) Kr 16.64±0.05 328 5-80 [23]Rb (52P1/2 52S1/2) 17.1±0.4 394 0-300 [6]Cs (62P1/2 62S1/2) 17.82±0.05 313 0-300 [15]

K (42P1/2 42S1/2) Xe 20.02±0.10 328 5-80 [23]Rb (52P1/2 52S1/2) 18.6±0.2 394 0-300 [6]Cs (62P1/2 62S1/2) 19.74±0.08 328 0-300 [15]

rates for the other alkalis. The most significant contribution to the error wasthe measurement of the pressure which has an error of 0.5%. This produceda maximum error of 2.2% on the measurement of the rates.

4. Discussion

The broadening rates for the rubidium D1 transition are shown in Table2 and 3 alongside the most recent measurement of these values by Ronton-daro and Perram.[6] The discrepancies between this work and the previouswork can be first accounted for by the temperature di↵erence. The first stepis to assume that the broadening cross-section is independent of tempera-ture, which has been shown to be reasonable in the past for cesium.[15] This

10

Table 3: The alkali D1 broadening rates for various molecular collision partners.

Alkali Bu↵er � Temp. Press. Range Ref.(Transition) Gas (MHz/Torr) (K) (Torr)

K (42P1/2 42S1/2) H2 22.15±0.12 328 5-80 [23]Rb (52P1/2 52S1/2) 17.3±0.2 394 0-300 [6]Cs (62P1/2 62S1/2) 20.81±0.09 328 0-300 [15]

K (42P1/2 42S1/2) HD 19.36±0.11 328 5-80 [23]Rb (52P1/2 52S1/2) —Cs (62P1/2 62S1/2) 20.06±0.12 318 0-300 [15]

K (42P1/2 42S1/2) D2 17.47±0.16 328 5-80 [23]Rb (52P1/2 52S1/2) 14.1±0.4 394 0-300 [6]Cs (62P1/2 62S1/2) 18.04±0.04 318 0-300 [15]

K (42P1/2 42S1/2) N2 17.78±0.07 328 5-80 [23]18.82±0.23 400-420 x-XX [17]

Rb (52P1/2 52S1/2) 16.3±0.4 394 0-300 [6]Cs (62P1/2 62S1/2) 16.36±0.02 323 0-300 [15]

K (42P1/2 42S1/2) CH4 29.35±0.12 328 5-80 [23]Rb (52P1/2 52S1/2) 29.1±0.08 394 0-300 [6]

32.78±0.02 328 0-300 This WorkCs (62P1/2 62S1/2) 29.00±0.10 333 0-300 [15]

K (42P1/2 42S1/2) C2H6 26.63±0.10 328 5-80 [23]Rb (52P1/2 52S1/2) 30.492±0.04 328 5-80 This WorkCs (62P1/2 62S1/2) 26.70±0.03 331 0-300 [15]

K (42P1/2 42S1/2) C3H8 27.27±0.21 328 5-80 [23]Rb (52P1/2 52S1/2) 33.05±0.05 328 5-80 This WorkCs (62P1/2 62S1/2) — — — —

K (42P1/2 42S1/2) n-C4H10 27.85±0.19 328 5-80 [23]Rb (52P1/2 52S1/2) 29.61±0.04 328 5-80 This WorkCs (62P1/2 62S1/2) — — — —

11

Table 4: The alkali D1 shift rates for the rare gases.

Alkali Bu↵er � Temp. Press. Range Ref.(Transition) Gas (MHz/Torr) (K) (Torr)

K (42P1/2 42S1/2) He 1.63±0.01 328 5-80 [23]Rb (52P1/2 52S1/2) 4.71±0.04 394 0-300 [6]

5.80±0.02 328 5-80 This WorkCs (62P1/2 62S1/2) 4.24±0.02 323 0-300 [15]

K (42P1/2 42S1/2)3He 6.82±0.02 328 5-80 [23]

Rb (52P1/2 52S1/2) — — — —Cs (62P1/2 62S1/2) 6.01±0.01 323 0-300 [15]

K (42P1/2 42S1/2) Ne -1.27±0.01 328 5-80 [23]Rb (52P1/2 52S1/2) -0.90±0.02 394 0-300 [6]Cs (62P1/2 62S1/2) -1.60±0.01 313 0-300 [15]

K (42P1/2 42S1/2) Ar -6.44±0.01 328 5-80 [23]Rb (52P1/2 52S1/2) -6.77±0.12 394 0-300 [6]Cs (62P1/2 62S1/2) -6.47±0.03 313 0-300 [15]

K (42P1/2 42S1/2) Kr -5.24±0.01 328 5-80 [23]Rb (52P1/2 52S1/2) -5.12±0.10 394 0-300 [6]Cs (62P1/2 62S1/2) -5.46±0.01 313 0-300 [15]

K (42P1/2 42S1/2) Xe -6.54±0.02 328 5-80 [23]Rb (52P1/2 52S1/2) -5.84±0.12 394 0-300 [6]Cs (62P1/2 62S1/2) -6.43±0.01 313 0-300 [15]

was discussed by Pitz, Fox, and Perram and can be determined from therelationship between the broadening rate and the cross-section:

� (T ) = �

8k

b

T

⇡µ

!1/2

, (4)

where � is the broadening rate in terms of number density, � is the cross-section, k

b

is the Boltzmann constant, T is the temperature, and µ is thereduced mass.[16] � can be easily converted to be in terms of pressure butthe use of the ideal gas law (PV = nk

b

T ), which results in follow equation:

� (T ) = �

8

⇡µkb

T

!1/2

. (5)

12

Table 5: The alkali D1 shift rates for various molecular collision partners.

Alkali Bu↵er � Temp. Press. Range Ref.(Transition) Gas (MHz/Torr) (K) (Torr)

K (42P1/2 42S1/2) H2 -5.34±0.02 328 5-80 [23]Rb (52P1/2 52S1/2) -2.17±0.04 394 0-300 [6]Cs (62P1/2 62S1/2) 1.11±0.01 328 0-300 [15]

K (42P1/2 42S1/2) HD -5.10±0.02 328 5-80 [23]Rb (52P1/2 52S1/2) —Cs (62P1/2 62S1/2) 0.47±0.03 318 0-300 [15]

K (42P1/2 42S1/2) D2 -4.70±0.03 328 5-80 [23]Rb (52P1/2 52S1/2) -2.22±0.06 394 0-300 [6]Cs (62P1/2 62S1/2) 0.00009±0.00004 318 0-300 [15]

K (42P1/2 42S1/2) N2 -6.80±0.02 328 5-80 [23]Rb (52P1/2 52S1/2) -7.41±0.12 394 0-300 [6]Cs (62P1/2 62S1/2) -7.71±0.01 323 0-300 [15]

K (42P1/2 42S1/2) CH4 -7.41±0.02 328 5-80 [23]Rb (52P1/2 52S1/2) -7.92±0.10 394 0-300 [6]

-6.96±0.01 328 0-300 This WorkCs (62P1/2 62S1/2) -9.28±0.02 333 0-300 [15]

K (42P1/2 42S1/2) C2H6 -8.32±0.02 328 5-80 [23]Rb (52P1/2 52S1/2) -7.88±0.01 328 5-80 This WorkCs (62P1/2 62S1/2) -8.54±0.01 331 0-300 [15]

K (42P1/2 42S1/2) C3H8 -8.59±0.04 328 5-80 [23]Rb (52P1/2 52S1/2) -8.61±0.02 328 5-80 This WorkCs (62P1/2 62S1/2) — — — —

K (42P1/2 42S1/2) n-C4H10 -8.80±0.04 328 5-80 [23]Rb (52P1/2 52S1/2) -9.43±0.02 328 5-80 This WorkCs (62P1/2 62S1/2) — — — —

13

Table 6: The alkali D2 broadening rates for the rare gases.

Alkali Bu↵er � Temp. Press. Range Ref.(Transition) Gas (MHz/Torr) (K) (Torr)

K (42P3/2 42S1/2) He 19.84±0.02 328 5-80 This Work12.83 500 Theoretical [19]

15.44±0.30 400-420 3-600 [17]Rb (52P3/2 52S1/2) 20.0±0.14 394 0-300 [6]

20.3±0.3 314 5-80 [5]Cs (62P3/2 62S1/2) 20.59±0.06 313 0-300 [16]

K (42P3/2 42S1/2)3He — — — —

Rb (52P3/2 52S1/2) — — — —Cs (62P3/2 62S1/2) 22.35±0.05 313 0-300 [16]

K (42P3/2 42S1/2) Ne 8.88±0.02 328 5-80 This Work8.69±0.30 400-420 3-600 [17]

Rb (52P3/2 52S1/2) 9.47±0.1 394 0-300 [6]Cs (62P3/2 62S1/2) 9.81±0.06 313 0-300 [16]

K (42P3/2 42S1/2) Ar 18.65±0.03 328 5-80 This Work17.67 500 Theoretical [19]

14.84±0.22 400-420 3-600 [17]Rb (52P3/2 52S1/2) 17.7±0.2 394 0-300 [6]Cs (62P3/2 62S1/2) 16.47±0.18 313 0-300 [16]

K (42P1/2 42S1/2) Kr 19.17±0.06 328 5-80 This Work18.67 500 Theoretical [19]

17.32±0.37 400-420 3-600 [17]Rb (52P1/2 52S1/2) 17.2±0.4 394 0-300 [6]Cs (62P1/2 62S1/2) 15.54±0.05 313 0-300 [16]

16.83±0.30 295 0-150 [14]10.94±0.90 295 10-150 [8]

K (42P1/2 42S1/2) Xe 22.19±0.03 328 5-80 This Work21.44 500 Theoretical [19]

20.62±0.22 400-420 3-600 [17]Rb (52P1/2 52S1/2) 17.8±0.2 394 0-300 [6]Cs (62P1/2 62S1/2) 18.41±0.07 313 0-300 [16]

14

Table 7: The alkali D2 broadening rates for various molecular collisional partners.

Alkali Bu↵er � Temp. Press. Range Ref.(Transition) Gas (MHz/Torr) (K) (Torr)

K (42P1/2 42S1/2) H2 — — — —Rb (52P1/2 52S1/2) 26.4±0.2 394 0-300 [6]Cs (62P1/2 62S1/2) 27.13±0.02 313 0-300 [16]

59.66±7.94 295 10-150 [8]

K (42P1/2 42S1/2) HD — — — —Rb (52P1/2 52S1/2) —Cs (62P1/2 62S1/2) 20.06±0.12 328 0-300 [15]

K (42P1/2 42S1/2) D2 — — — —Rb (52P1/2 52S1/2) 20.6±0.4 394 0-300 [6]Cs (62P1/2 62S1/2) 22.84±0.16 313 0-300 [16]

K (42P1/2 42S1/2) N2 18.98±0.03 328 5-80 This Work18.37±0.23 400-420 3-600 [17]

Rb (52P1/2 52S1/2) 18.3±0.4 394 0-300 [6]Cs (62P1/2 62S1/2) 19.18±0.06 313 0-300 [16]

K (42P1/2 42S1/2) CH4 27.78±0.03 328 5-80 This WorkRb (52P1/2 52S1/2) 26.2±0.08 394 0-300 [6]

28.0±0.4 314 0-300 [5]Cs (62P1/2 62S1/2) 25.84±0.09 313 0-300 [16]

K (42P1/2 42S1/2) C2H6 27.60±0.08 328 5-80 This WorkRb (52P1/2 52S1/2) 28.1±0.4 314 5-80 [5]Cs (62P1/2 62S1/2) 26.14±0.08 313 0-300 [16]

K (42P1/2 42S1/2) C3H8 27.70±0.08 328 5-80 This WorkRb (52P1/2 52S1/2) 30.5±0.6 314 5-80 [5]Cs (62P1/2 62S1/2) — — — —

K (42P1/2 42S1/2) n-C4H10 33.48±0.15 328 5-80 This WorkRb (52P1/2 52S1/2) 31.3±0.6 314 5-80 [5]Cs (62P1/2 62S1/2) — — — —

15

Table 8: The alkali D2 shift rates for the rare gases.

Alkali Bu↵er � Temp. Press. Range Ref.(Transition) Gas (MHz/Torr) (K) (Torr)

K (42P3/2 42S1/2) He 0.52±0.01 328 5-80 This Work0.90±0.15 400-420 3-600 [17]

Rb (52P3/2 52S1/2) 0.37±0.06 394 0-300 [6]0.39±0.06 314 5-80 [5]

Cs (62P3/2 62S1/2) 0.69±0.01 313 0-300 [16]

K (42P3/2 42S1/2)3He — — — —

Rb (52P3/2 52S1/2) — — — —Cs (62P3/2 62S1/2) 0.60±0.01 313 0-300 [16]

K (42P3/2 42S1/2) Ne -2.06±0.01 328 5-80 This Work-2.32±0.08 400-420 3-600 [17]

Rb (52P3/2 52S1/2) -2.44±0.02 394 0-300 [6]Cs (62P3/2 62S1/2) -2.58±0.01 313 0-300 [16]

K (42P3/2 42S1/2) Ar -5.52±0.01 328 5-80 This Work-5.69±0.15 400-420 3-600 [17]

Rb (52P3/2 52S1/2) -5.76±0.04 394 0-300 [6]Cs (62P3/2 62S1/2) -6.18±0.02 313 0-300 [16]

K (42P1/2 42S1/2) Kr -5.42±0.02 328 5-80 This Work-4.35±0.15 400-420 3-600 [17]

Rb (52P1/2 52S1/2) 5.50±0.20 394 0-300 [6]Cs (62P1/2 62S1/2) -6.09±0.01 313 0-300 [16]

K (42P1/2 42S1/2) Xe -7.01±0.01 328 5-80 This Work6.71±0.22 400-420 3-600 [17]

Rb (52P1/2 52S1/2) -6.19±0.12 394 0-300 [6]Cs (62P1/2 62S1/2) -6.75±0.01 313 0-300 [16]

16

Table 9: The alkali D2 shift rates for various molecular collisional partners.

Alkali Bu↵er � Temp. Press. Range Ref.(Transition) Gas (MHz/Torr) (K) (Torr)

K (42P1/2 42S1/2) H2 — — — —Rb (52P1/2 52S1/2) -3.83±0.12 394 0-300 [6]Cs (62P1/2 62S1/2) -4.83±0.04 313 0-300 [16]

K (42P1/2 42S1/2) HD — — — —Rb (52P1/2 52S1/2) —Cs (62P1/2 62S1/2) -4.49±0.03 313 0-300 [16]

K (42P1/2 42S1/2) D2 — — — —Rb (52P1/2 52S1/2) -4.09±0.08 394 0-300 [6]Cs (62P1/2 62S1/2) -4.54±0.03 313 0-300 [16]

K (42P1/2 42S1/2) N2 -5.66±0.02 328 5-80 This WorkRb (52P1/2 52S1/2) -5.79±0.10 394 0-300 [6]Cs (62P1/2 62S1/2) -6.2±0.01 313 0-300 [16]

K (42P1/2 42S1/2) CH4 -8.38±0.01 328 5-80 This WorkRb (52P1/2 52S1/2) -7.00±0.20 394 0-300 [6]

-8.4±0.1 314 0-300 [5]Cs (62P1/2 62S1/2) -8.86±0.02 313 0-300 [16]

K (42P1/2 42S1/2) C2H6 -8.04±0.02 328 5-80 This WorkRb (52P1/2 52S1/2) -8.8±0.2 314 5-80 [5]Cs (62P1/2 62S1/2) -9.38±0.02 313 0-300 [16]

K (42P1/2 42S1/2) C3H8 -9.22±0.03 328 5-80 This WorkRb (52P1/2 52S1/2) -9.7±0.2 314 5-80 [5]Cs (62P1/2 62S1/2) — — — —

K (42P1/2 42S1/2) n-C4H10 -9.37±0.06 328 5-80 This WorkRb (52P1/2 52S1/2) -10.00±0.2 314 5-80 [5]Cs (62P1/2 62S1/2) — — — —

17

A simple ratio of �’s of two di↵erent temperature will result in the correctconversion factor

�2 = �1

✓T1

T2

◆n

, (6)

where n = 1/2. For comparison to the work of Rotondaro and Perram onrubidium, this factor is 1.096 which adjusts their helium rate up to 20.71MHz/Torr and their CH4 value up to 31.90 MHz/Torr. Both of these valuesare well within the error bounds of our experiment. On the other hand, thepotassium D2 rates when compared to the values from Lwin and McCartanare a factor on the order of 1.12 o↵ and there is an average discrepancy of 8%between the rates measured for this work and those previously recorded.[17]While this is concerning, the previous work was at much higher pressuresand asymmetries in the line shape were observed. In addition, in the pres-sure range that was tested, the hyperfine structure may have needed to beaccounted for, but the previous work did not state the total line shape em-ployed for their work. Between the lack of a full hyperfine structure and theasymmetries, this may account for the di↵erence in the values.

The comparison of the shift rates must be done more qualitatively. Thecross-section for the shift are dependent on temperature and therefore thevalue for n in equation 6 does not equal 1/2. The value must be experimen-tally determined, which was beyond the scope of this study. [15]

A comparison between the alkali D1 and D2 broadening cross-sections isshown in figures 7(a) and7(b). This shows nearly linear relationships betweeneach alkali’s cross-section to another’s cross-section. The cross-sections wereconverted from the rates of various references.[6, 15, 16, 23, 27, 19] In thecase of the lithium data, this corresponds to only the S ! P transition anddoes not include the fine splitting of the P state and thus it is repeated be-tween the figures 7(a) and7(b). The figures reveal that with increasing alkalimass there is an increase in the broadening cross-section. This relationshipwas not shown by Pitz, Fox and Perram when they used Lwin’s rates forpotassium.[16, 17] This may show a discrepancy between the values of thiswork and the work of Lwin.[17]

5. Conclusions

The reported values for the potassium D2 pressure broadening and shiftrates with errors less than 2.1% will aid in the accurate modeling of a DPALsystem. The rates for the noble gases are in agreement with previous results.

18

200

180

160

140

120

100

80

60

40Cs 6

2 P 1/2

Cro

ss-s

ectio

n, σ

γ (Å

2 )

200100

Rb 52P1/2

200100

K 42P1/2

200100

Na 32P1/2

200100

Li 22P1/2

He Ne

Ar

Kr

Xe

H2D2

N2

CH4

C2H6

He 3HeNe

Ar

Kr

Xe

H2HDD2

N2

CH4

C2H6

He Ne

Ar

Kr

Xe

He Ne

Ar

Kr

Xe

Cross-section, σγ (Å2)

(a)

180

160

140

120

100

80

60

40 Cs

6 2 P 3

/2 C

ross

-sec

tion,

σγ (

Å2 )

200100

Rb 52P3/2

200100

K 42P3/2

200100

Na 32P3/2

200100

Li 22P3/2

He Ne

Ar

Kr

Xe

H2D2

N2CH4

C2H6

He Ne

Ar

Kr

Xe

N2CH4

C2H6

He Ne

Ar

Kr

Xe

He Ne

Ar

Kr

Xe

Cross-section, σγ (Å2)

(b)

Figure 7: A comparison between thebroadening cross-sections for the D1 (a)and D2 (b) transitions of the various al-kali to that of cesium.

New rates have been measured for CH4, C2H6, C3H8 and n-C4H10. Also, theaddition of the Rb D1 broadening and shift rates for interactions with C2H6,C3H8 and n-C4H10 will aid in propagation studies of rubidium based DPALsystems.

Acknowledgments

Support for this work from the Air Force O�ce of Scientific Research andthe High Energy Laser Joint Technology O�ce is gratefully acknowledged.We also want to thanks Billy Pike and Don Stalnaker for their help in thelaboratory, and Chris Rice and Glen Perram of the Air Force Institute ofTechnology for the use of the laser to study the K D2 transition.

19

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