ULTRAVIOLET BANDS OF POTASSIUM DIMER

IC/2001/36 United Nations Educational Scientific and Cultural Organization and International Atomic Energy Agency THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS ULTRAVIOLET BANDS OF POTASSIUM DIMER K. Ahmed 1 Spectroscopy Research Laboratory, Department of Physics, University of Karachi, Karachi-75270, Pakistan and The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy, LA. Khan and S.S. Hassan Spectroscopy Research Laboratory, Department of Physics, University of Karachi, Karachi- 75270, Pakistan. Abstract The ultraviolet band spectra of potassium dimer have been investigated. The studies were performed in absorption in the second order of a 3.4 m Ebert spectrograph with a reciprocal dispersion of 2.6 A/mm. A number of new bands in the electronic states G and H not previously reported have been observed. The vibrational analysis is performed and molecular constants are evaluated. MIRAMARE - TRIESTE May 2001 1 Regular Associate of the Abdus Salam ICTP. E-mail: drkamalahmed@yahoo.com

1. Introduction Potassium is the second most abundant matter present in the earth's crust and is desired to be investigated heavily. In comparison with the other homonuclear alkali dimers, potassium molecule is the least investigated by the spectroscopists. During the past decade, important experimental efforts have been devoted to the laser spectroscopy of the ground gerade and ungerade excited states (in moderate energy range) of K2 dimer. Different laser spectroscopic techniques such as single photon absorption were used and many excited states have been characterized experimentally [1-4]. Only, the Stwalley research group has observed a number of gerade high lying excited states in UV region by optical-optical double resonance technique [5]. Up till now, the experimentally available information regarding electronic states of potassium molecule is not satisfactory, because of the so many discrepancies present in the experimentally observed and theoretically predicted result [6]. Due to lack of available UV tunable laser sources, it is difficult for laser spectroscopists to investigate Rydberg ungerade states in UV region of these molecules. Therefore, one has to depend on the conventional absorption spectroscopic methods to investigate the electronic states near the ionization potential of potassium dimer. Potassium molecule has been studied since 1930's. First of all, Yoshinaga [7] worked in UV region and performed the vibrational analysis of the bands observed in absorption. Later, Sinha [8] worked in the same region and concluded that previous work was not satisfactory but he did not perform vibrational analysis. In our previous reported work [9,10] we observed new electronic transition named H X system and later we also found some new bands in the F X and G X (designated as systems IV and V by Yoshinaga [7] respectively). In the present work, we have observed new data regarding potassium dimer, while we were trying to record the spectra of KLi molecule. The present paper describes the work extended in G X and H X transitions. These new bands are observed due to less miscible property of lithium atoms. The analysis has been performed to evaluate improved molecular constants.

2. Experimental The vapor of potassium molecules was generated by heating spectroscopically pure, lithium and potassium metal loaded with a ratio 1:6 inside a 1.5 meter long stainless steel tube in an atmosphere of argon gas at 300 torr. This tube was directly heated by a high current low voltage transformer providing 950 A at 10 V. Before introducing the sample in the tube, it was thoroughly evacuated and was heated to about 200 C. Later, the loaded furnace was heated to a temperature of 750 C. Both ends of the furnace tube were water cooled to avoid vapor condensation at the quartz windows. The ultraviolet absorption spectrum of potassium molecule was photographed in second order of a 3.4 m Ebert spectrograph equipped with 1200 lines/mm plane grating. The background source of radiation was a 450 W high-pressure xenon arc lamp. The spectra were recorded on the Q-2 plates at 2.6 A/mm reciprocal dispersion with an exposure time of about two hours. The photo-densitometer trace of the recorded absorption spectrum covering the wavelength region 320 to 337 nm is shown in Fig.-l. The wavelength calibration was achieved by superimposing the iron arc spectrum, which possesses sharp lines covering this spectral region. The measurements of the band heads were made on Zeiss Abbe comparator by comparison with iron arc lines to an accuracy of ±0.2 A. The wavelengths were calculated using Chebychev polynomial fit of comparator readings with the reference iron lines. The iron wavelengths have been marked from MIT tables [11]. The vacuum wavenumbers of the wavelengths were obtained by a computer program using Edlen's dispersion formula [12]. 3. Results and Discussion The spectrum was photographed in the region 320 to 360 nm. It revealed new vibrational bands in G X and H X systems of K2 molecule. Actually, we were interested to record the new electronic states of KLi molecule in the UV-region, will be submitted for publication in future. Due to the less miscible property of lithium [13], we also observed a number of bands of G X and H X systems of K2 molecule. A number of bands

belong to H X system in the region 320 to 337 nm along with Lithium (2S-3P) and potassium (4S-7P) atomic transitions can be seen in the spectrum Fig.-l. A large number of bands of good quality are obtained in both transitions. This is also due to the improved design of the absorption column and suitable experimental conditions in comparison of our previous work [9, 10]. Thermally only three vibrational levels in the ground state were able to populate. We have observed a total of 83 bands in the region 320 to 360 nm belonging to G X and H X systems of K2 dimer (Fig.-l). The G X system: In the region 340 nm to 360 nm a total 40 bands of G X system of K2 molecule have been observed out of which 11 bands are new (Fig.-l). The band heads of similar intensity are found to belong to mainly three distinct sets of red degraded bands indicating that these bands mainly belong to three progressions (v 1, 0), (v 1, 1) and (v 1, 2). The general appearance of the band heads helps in making the tentative assignment of vibrational numbers v', v" to the bands. Later, the exact assignment of vibrational quantum numbers to the band heads is conveniently done by the already assigned values of reported bands in literature [7-10]. Table-1 shows the assignment of the newly observed band heads. The term values of the upper vibrational state are constructed for all observed bands using the data of the X ground vibrational state [14, 15] and is presented in Table - 2. The vibrational quantum numbers as well as the vibrational constants are determined by using the computer methods incorporating least square fit to find the values of Te, cue, toexe, etc. for the G and H states. The relation [16] used is: T = T e The vibrational quantum number of the upper state is allowed to vary until the residual variance becomes minimum. The values of AG(v+l/2) obtained in both progressions agree within the accuracy of measurements (Tables-3 and 4). The vibrational constants

obtained are compared with those of previously reported [7,9,10] work and are listed in Table-5. The H X transition: we have recorded 43 bands in the region 320 to 342 nm, the bands of all these systems are red degraded and the bands of this system have been found to belong to (v\ 0) and (v\ 1) progressions (Fig.-l). The progression belonging to (v 1, 0) bands lie at the same frequencies as those of previously reported work (Rafi et al. [9]). It has provided an extension in the vibrational progression (v', 1) and thus newly observed 23 bands along with previously reported bands are presented in Table-6. There are few band heads that could not be measured reliably. These band heads are therefore not reported. The upper state terms are built by adding wave numbers of the band heads to X ground vibrational level [14,15] Table-4. The vibrational assignment and evaluation of constants were made in a manner as described in the case of G-X bands of potassium dimer. The vibrational constants are compared with those of previous work and given in (Table-5). The D e of the X ground state of K2 molecule is estimated to be 4451 ±1.5 cm" 1 [14], which is correlating it with the separated ground atomic states K(4 2 S)+K(4 2 S). The correlation diagram is already presented and discussed in previous work of Rafi et. al [9]. The K2 excited molecular G and H states are comfortably correlated with the excited atomic states K(5 2 P)+K(4 2 S) and K(4 2 D)+K(4 2 S) respectively [9]. These atomic states have the average energies of 24710.82 cm" 1 and 29003.50 cm" 1 respectively. The dissociation energies D e of both G and H excited states of K2 dimer can be determined from the correlation diagram using the following relation (Table-6). D e = D e + r L s (atomic states) - T e The dissociation energies are also calculated using the Birge-Sponer formula for both states and are shown in Table-6 [16]:

4ft) The dissociation energy D e of the G state using correlation diagram is less than Birgesponer formula (BSF). The correlation-diagram suggests, the maximum vibration quantum number of 20 that can be observed whereas we have seen vibrational band up to v'=15. In Figure-2 AG versus band number v' has been plotted for both the G and H states of potassium molecule. It is seen that G state has larger slope than for the H state. The extrapolation is supported by the calculated value for G state which suggests the dissociation at v'=20. For the H state of K 2 molecule the dissociation energy D e calculated using BSF is quite large in comparison of correlation diagram value Table-6. The correlation diagram in Rafi et. al [9] suggest the largest vibrational quantum number of 33 whereas we have seen vibrational bands for v' up to 22. The extrapolation (in Figure-2) is also supported by the calculated value using the available vibrational constants for H state which gives dissociation around v=33. Our analysis indicates both G and H states are not perturbed or predissociated by other neighbouring states. The reduced mass of the K2 molecule is quite large, so the rotational structure is very close and congested and could not be resolved under the present experimental facilities. To get more information about rovibrational structure and precise values of dissociation energies of G and H states of K2 dimer, high-resolution spectroscopy is desired. Acknowledgments We acknowledge the Pakistan Science foundation for the financial assistance to carry out this work under research grant S-KU-Phys(72). We are indebted to Professor M. A. Baig, Department of Physics, Quaid-I-Azam University, Pakistan for the use of photodensitometer. We are grateful Professor Dr. M. Rafi for his enthusiasm, initiating this experiment and useful discussion during this analysis. K. Ahmed also thanks the Abdus

Salam ICTP, Trieste, Italy for giving the opportunity to visit the centre under the regular associate-ship program and for using the library facilities during writing the manuscript of this article. References [I] Kowalczyk P, Katern A and Engelke F 1990 Z. Phys. D, 17, 47 [2] Jastrzebskib W and Kowalczyk P 1993 Chem. Phys. Lett. 206 69 [3] Jastrzebski W and Kowalczyk P 1994 Chem. Phys. Lett. 227 283 [4] L. Li L, Lyrra A M, Luh T H and Stwalley W C 1990 J. Chem. Phys. 93(12) 845: Jong G, Li L, Whang T J, and Stawlley W C 1992 J. Mol. Spectrosc. 1992 155 115 [5] Kim J T, Tsai C C and Stwalley W C 1995 J. Mol. Spectrosc. 171, 200 [6] Magnier S and Millie Ph., 1996 Phys. Rev. 54(1), 204 [7] Yoshinaga M, Proc. Phys. Math. Soc. Jpn. 1937 19,847 [8] Sinha S P 1947 Proc. Phys. Soc. Lond. 59 610 [9] Rafi M, Ahmed K, Khan IA and Husain M R 1991 Z. Phys. D. 18, 379 [10] Rafi M, Naqvi S M, Jahangir S, Mahmood S and Khan IA 1993 Z. Phys. D. 27 61 [II] Harrison G H, M.I.T. Tables 1959 (New York, N.Y.) [12] Edlen B 1953 J. Opt. Soc. Am. 53 339 [13] Breford E J, Engelke F 1979 J. Chem. Phys. 71(5) 1994 [14] Amiot C 1991 J. Mol. Spectrosc, 146, 370 [15] Ross A J, Crozet P, D'Incan J and Effantin C 1986 J. Phys. B. 19L 145 [16] G. Herzberg, Molecular spectra and molecular structure 1950 (Van Nostrand New York, N. Y.).

Table-1. Term values (in cm" 1 ) of G X system of K 2 molecules. Excited state (v) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 28127.4 189.4 251.2 312.9 371.1 430.7 489.2 544.5 599.7 658.4 710.4 763.7 815.0 867.0 916.9 Ground State (v") 28126.6 189.9 249.8 312.4 370.0 429.1 488.9 543.8 600.2 656.5 711.5 764.3 815.6 865.5 916.7 965.7 28126.5 187.5 249.2 371.9 488.8 543.7 710.8 28126.1 656.5 Average 28126.6 188.9 249.9 312.6 371.0 429.9 488.9 544.0 599.9 657.1 710.9 764.0 815.3 866.2 916.8 965.7

Table-2. Term values (in cm" 1 ) of H X system of K 2 molecules. Excited state (V) ow i 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 10 l y 20 21 22 Ground 0 7Q96Q 1 ±*yl\jy. 1 349.2 428.6 508.3 589.5 669.5 750.4 830.5 910.3 989.0 30068.6 146.7 227.1 306.2 383.0 461.2 540.1 617.3 693.5 847.1 924.2 state (v") 1 29351.2 430.9 510.1 591.0 672.3 752.4 832.8 912.9 991.3 30069.7 148.9 227.9 307.0 383.9 462.3 540.5 617.8 694.5 770 S / / w.o 846.7 922.8 998.5 Average 9Q96Q 1 350.2 429.7 509.2 590.2 670.9 751.4 831.6 911.6 990.1 30069.1 147.8 227.5 306.6 383.4 461.7 540.3 617.5 694.0 770 8 / / yj.o 846.9 923.5 998.5

Table-3. Band head positions of G X system of K 2 molecules. (v',v") (0,0) (1,0) (2,0) (3,0) (4,0) (5,0) (6,0) (7,0) (8,0) (9,0) *(10,0) *(H,0) *(12,0) *(13,0) *(14,0) (0,1) (1,1) (2,1) (3,1) (4,1) (5,1) (6,1) (7,1) (8,1) (9,1) (10,1) *(H,1) *(12,1) (13,1) *(14,1) *(15,1) (0,2) (1,2) (2,2) (4,2) (6,2) (7,2) (9,2) (10,2) (0,3) Wavelength V) ( A ) 3560.0 3552.1 3544.4 3536.7 3529.3 3522.0 3514.7 3507.9 3501.2 3593.1 3487.5 3481.2 3474.9 3468.7 3462.7 3571.8 3563.7 3556.1 3548.2 3540.9 3533.6 3526.1 3519.3 3512.3 3505.4 3498.8 3492.2 3485.1 3479.9 3473.7 3467.8 3583.4 3575.6 3567.5 3552.1 3537.5 3530.6 3516.6 3509.9 3595.1 * Observed new bands Wavenumber (obs.) v (vac) (cm" 1 ) 28081.5 143.4 205.2 266.9 326.0 384.8 443.3 498.6 553.7 723.1 665.5 717.7 769.0 821.1 871.0 27989.2 28052.5 112.4 175.0 232.6 291.7 351.5 406.4 462.8 519.0 572.1 626.8 678.2 728.1 779.3 828.3 27898.2 959.0 28022.9 143.6 260.2 315.5 428.7 482.5 27807.5 Wavenumbers (calc.) v (vac ) (cm" 1 ) 28080.5 143.2 204.1 265.8 325.6 384.4 442.3 499.3 555.3 723.3 664.3 717.4 769.5 820.7 870.9 27989.0 28051.8 113.5 174.3 234.1 293.0 350.9 407.8 463.8 518.8 572.9 625.1 678.1 729.3 779.5 828.7 27898.2 960.9 28022.6 143.2 259.9 316.9 427.9 482.0 27807.8 10

Table-4. Band head positions of H X system of K 2 molecules. (v\v") (0,0) (1,0) (2,0) (3,0) (4,0) (5,0) (6,0) (7,0) (8,0) (9,0) (10,0) (11,0) (12,0) (13,0) (14,0) (15,0) (16,0) (17,0) *(18,0) *(20,0) (21,0) 0,1) *(2,1) *(3,1) *(4,1) *(5,1) *(6,1) (7,1) (8,1) *(9,1) (10,1) *(1.1,1) *(12,1) *(13,1) *(14,1) (15,1) *(16,1) *(17,1) *(18,1) *(19,1) (20,1) *(21,1) *(22,1) Wavelength *<*) (A) 3420.9 3411.6 3402.4 3392.2 3383.7 3374.7 3365.5 3356.4 3347.5 3338.7 3329.9 3321.2 3312.3 3303.7 3295.3 3286.9 3278.4 3270.0 3261.1 3245.6 3237.5 3422.0 3412.7 3403.5 3394.2 3384.8 3375.7 3366.5 3357.5 3348.7 3339.9 3331.1 3322.3 3313.6 3305.2 3296.6 3288.2 3279.8 3271.6 3263.5 3255.4 3247.3 3239.4 * Observed new bands Wavenumber (obs.) V( vac ) (cm') 29223.2 303.3 382.7 462.2 544.6 623.6 704.5 784.5 864.4 943.2 30022.6 100.8 181.2 260.3 337.1 415.3 494.2 571.4 647.6 802.0 878.3 29213.8 293.5 373.6 453.6 534.8 614.1 695.4 775.5 853.9 932.3 30011.5 090.5 169.7 246.5 324.9 403.1 480.4 557.0 633.5 694.9 785.4 861.1 Wavenumbers (calc.) v (vac) (cm" 1 ) 29223.3 303.6 383.9 464.3 544.9 624.8 704.5 784.8 864.6 944.2 30023.5 102.6 181.5 260.0 338.3 416.3 493.9 571.2 648.3 801.3 877.4 29212.1 292.5 372.8 453.1 533.3 613.9 693.4 773.2 852.7 932.0 30011.2 090.0 168.8 246.9 324.8 402.5 479.8 556.8 633.5 694.2 785.9 861.6 11

Table-5. Molecular constants (in cm" 1 ) of K 2 molecules. State Te cog (Q e x e co e ye H a 29228.5+0.6 80.70± 0.04 0.037+0.005 0.00263± 0.00005 H b 29228.0+0.4 81.092+0.034 0.094± 0.001 G a 28094.710.5 63.67+0.04 0.49 ± 0.06 G c 28094.310.3 63.78+0.08 0.49± 0.04 a Present work >c Rafietal. [9,10] Table-6. Dissociation energies (in cm" 1 ) of excited G and H states of K dimer. Molecular state H G Atomic state 4D 5P Dissociation Correlation diagram 2620.1 1067 energy (cm" 1 ) Birge-sponer formula 44003.3 2068.3 12

z\ Absorption Intensity i o to CD 1 I o CD U) 00 CD in o' U) CD O P-+- B o O 00 o" o to Li atomic line (2S-3P) K atomic line (4S-7P)

/ - - 80- o eo eo.oo.c a o H -state G-state \. 60- St3s QDtr,.- "" " " \ 40-,- ' \ \\ 20- \ \ \\ \ ] 0-1 i i < i 0 10 20 30 40 Band Number (v 1 ) Fig.-2. Vibrational quanta (AG) as a function of v in the G and H states of K 2