Atomic and molecular spectra emitted by normal liquid ⁴He excited by corona discharge

The liquid ⁴He at fixed temperature 4.2 K and different pressures up to 8 MPa was excited by corona discharge of both negative and positive polarity. Emission of He I atomic lines and He₂ molecular bands are observed. In negative corona the lines spectra show a distinct blue-shift and line-broadenin...

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Дата:	2011
Автори:	Li, Z.-L., Bonifaci, N., Denat, A., Atrazhev, V.M., Shakhatov, V.A., von Haeften, K.
Формат:	Стаття
Мова:	English
Опубліковано:	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2011
Назва видання:	Физика низких температур
Теми:	8th International Conference on Cryocrystals and Quantum Crystals
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Цитувати:	Atomic and molecular spectra emitted by normal liquid ⁴He excited by corona discharge / Z.-L. Li, N. Bonifaci, A. Denat, V.M. Atrazhev, V.A. Shakhatov, K. von Haeften // Физика низких температур. — 2011. — Т. 37, № 5. — С. 484–490. — Бібліогр.: 37 назв. — англ.

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spelling	irk-123456789-1185672017-05-31T03:08:35Z Atomic and molecular spectra emitted by normal liquid ⁴He excited by corona discharge Li, Z.-L. Bonifaci, N. Denat, A. Atrazhev, V.M. Shakhatov, V.A. von Haeften, K. 8th International Conference on Cryocrystals and Quantum Crystals The liquid ⁴He at fixed temperature 4.2 K and different pressures up to 8 MPa was excited by corona discharge of both negative and positive polarity. Emission of He I atomic lines and He₂ molecular bands are observed. In negative corona the lines spectra show a distinct blue-shift and line-broadening, which becomes stronger with the pressure increasing. The rotational structure of molecular bands is resolved at pressures (0.1–0.2) MPa. The blue shift of the Q-branch maximum at different pressures was observed. Rotational temperature of 900 K has been estimated for the d³Σ⁺u-b³Πg molecular band. A positive corona was realized on a point anode for fewer radii of the electrode and larger voltage than in the negative corona. Electric currents in both negative and positive corona differ weakly. Spectral analysis of the radiation from the positive corona shows qualitative differences of spectral features of these discharges. The spectra observed in the positive corona have marked nonsymmetric shape. The asymmetric atomic and molecular spectra show an increased intensity of their long-length (red) wings. 2011 Article Atomic and molecular spectra emitted by normal liquid ⁴He excited by corona discharge / Z.-L. Li, N. Bonifaci, A. Denat, V.M. Atrazhev, V.A. Shakhatov, K. von Haeften // Физика низких температур. — 2011. — Т. 37, № 5. — С. 484–490. — Бібліогр.: 37 назв. — англ. 0132-6414 PACS: 36.40.Mr, 71.35.Aa, 73.20.–r, 78.40.–q http://dspace.nbuv.gov.ua/handle/123456789/118567 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
topic	8th International Conference on Cryocrystals and Quantum Crystals 8th International Conference on Cryocrystals and Quantum Crystals
spellingShingle	8th International Conference on Cryocrystals and Quantum Crystals 8th International Conference on Cryocrystals and Quantum Crystals Li, Z.-L. Bonifaci, N. Denat, A. Atrazhev, V.M. Shakhatov, V.A. von Haeften, K. Atomic and molecular spectra emitted by normal liquid ⁴He excited by corona discharge Физика низких температур
description	The liquid ⁴He at fixed temperature 4.2 K and different pressures up to 8 MPa was excited by corona discharge of both negative and positive polarity. Emission of He I atomic lines and He₂ molecular bands are observed. In negative corona the lines spectra show a distinct blue-shift and line-broadening, which becomes stronger with the pressure increasing. The rotational structure of molecular bands is resolved at pressures (0.1–0.2) MPa. The blue shift of the Q-branch maximum at different pressures was observed. Rotational temperature of 900 K has been estimated for the d³Σ⁺u-b³Πg molecular band. A positive corona was realized on a point anode for fewer radii of the electrode and larger voltage than in the negative corona. Electric currents in both negative and positive corona differ weakly. Spectral analysis of the radiation from the positive corona shows qualitative differences of spectral features of these discharges. The spectra observed in the positive corona have marked nonsymmetric shape. The asymmetric atomic and molecular spectra show an increased intensity of their long-length (red) wings.
format	Article
author	Li, Z.-L. Bonifaci, N. Denat, A. Atrazhev, V.M. Shakhatov, V.A. von Haeften, K.
author_facet	Li, Z.-L. Bonifaci, N. Denat, A. Atrazhev, V.M. Shakhatov, V.A. von Haeften, K.
author_sort	Li, Z.-L.
title	Atomic and molecular spectra emitted by normal liquid ⁴He excited by corona discharge
title_short	Atomic and molecular spectra emitted by normal liquid ⁴He excited by corona discharge
title_full	Atomic and molecular spectra emitted by normal liquid ⁴He excited by corona discharge
title_fullStr	Atomic and molecular spectra emitted by normal liquid ⁴He excited by corona discharge
title_full_unstemmed	Atomic and molecular spectra emitted by normal liquid ⁴He excited by corona discharge
title_sort	atomic and molecular spectra emitted by normal liquid ⁴he excited by corona discharge
publisher	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
publishDate	2011
topic_facet	8th International Conference on Cryocrystals and Quantum Crystals
url	http://dspace.nbuv.gov.ua/handle/123456789/118567
citation_txt	Atomic and molecular spectra emitted by normal liquid ⁴He excited by corona discharge / Z.-L. Li, N. Bonifaci, A. Denat, V.M. Atrazhev, V.A. Shakhatov, K. von Haeften // Физика низких температур. — 2011. — Т. 37, № 5. — С. 484–490. — Бібліогр.: 37 назв. — англ.
series	Физика низких температур
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first_indexed	2025-07-08T14:15:06Z
last_indexed	2025-07-08T14:15:06Z
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fulltext	© Z.-L. Li, N. Bonifaci, A. Denat, V.M. Atrazhev, V.A. Shakhatov, and K. von Haeften, 2011 Fizika Nizkikh Temperatur, 2011, v. 37, No. 5, p. 484–490 Atomic and molecular spectra emitted by normal liquid 4He excited by corona discharge Z.-L. Li, N. Bonifaci, and A. Denat G2E.lab, CNRS et Universite Joseph Fourier, Grenoble, France V.M. Atrazhev Joint Institute for High Temperatures, RAS, Moscow, Russia E-mail: atrazhev@yandex.ru V.A. Shakhatov Topchiev Institute of Petrochemical Synthesis, RAS, Moscow, Russia K. von Haeften Department of Physics and Astronomy, University of Leicester, UK Received December 1, 2010 The liquid 4He at fixed temperature 4.2 K and different pressures up to 8 MPa was excited by corona dis- charge of both negative and positive polarity. Emission of He I atomic lines and He2 molecular bands are observ- ed. In negative corona the lines spectra show a distinct blue-shift and line-broadening, which becomes stronger with the pressure increasing. The rotational structure of molecular bands is resolved at pressures (0.1–0.2) MPa. The blue shift of the Q-branch maximum at different pressures was observed. Rotational temperature of 900 K has been estimated for the 3 3–u gd b+Σ Π molecular band. A positive corona was realized on a point anode for fewer radii of the electrode and larger voltage than in the negative corona. Electric currents in both negative and positive corona differ weakly. Spectral analysis of the radiation from the positive corona shows qualitative dif- ferences of spectral features of these discharges. The spectra observed in the positive corona have marked non- symmetric shape. The asymmetric atomic and molecular spectra show an increased intensity of their long-length (red) wings. PACS: 36.40.Mr Spectroscopy and geometrical structure of clusters; 71.35.Aa Frenkel excitons and self-trapped excitons; 73.20.–r Electron states at surfaces and interfaces; 78.40.–q Absorption and reflection spectra: visible and ultraviolet. Keywords: spectra, liquid normal helium, corona discharge. Introduction Liquid helium is a fascinating substance with many pe- culiarities due to its highly quantum nature. A particular special feature of liquid helium is its intense luminescence in the visible and near infrared spectral range. This lumi- nescence has been observed from superfluid 4He that has been bombarded with high energetic electrons [1,2], from liquid helium excited by a corona discharge [3–5] as well as from 4He and 3He droplets that where excited by mo- nochromatic synchrotron radiation [6–8]. The visible and near infrared luminescence stems from transitions between electronically excited states and the reason why such radia- tive transitions are observed in liquid helium is its negative electron affinity. Usually, in condensed matter systems tran- sitions between electronically excited states are fast and non-radiative. This is not the case for liquid helium be- cause after electronic excitation the energy localizes in Rydberg-type He atoms or excimer molecules and due to the negative electron affinity a repulsive force establishes between the Rydberg electron orbital and the surrounding Atomic and molecular spectra emitted by normal liquid 4He excited by corona discharge Fizika Nizkikh Temperatur, 2011, v. 37, No. 5 485 ground state helium atoms. As a consequence the sur- rounding helium atoms are pushed away within a short time [9,10] creating a cavity around the He and 2He [11], which is often referred as a “bubble” and which has typical radii between 10 and 20 Å depending on the elec- tron’s orbital radius [12]. Bubbles of similar type are well known to enclose electrons in liquid [13] and even dense gaseous helium [14]. Within the confinement of these cavi- ties the perturbation by surrounding ground state helium atoms is low and the electronic life time of the excited atoms or excimers is almost similarly long as for free spe- cies in the vacuum. The remaining perturbation by the ground state helium atoms surrounding the bubble is nev- ertheless strong enough to cause broadening and wave- length shifts of the atomic and molecular lines and the magnitude of the widths and shift was found to depend on the applied pressure [3,15]. The hydrostatic pressure was also found to affect the line intensity distribution of the rotational spectrum of the confined * 2He [3] as well as the total luminescence yield. For instance, at high pressures exceeding 40 bar no luminescence was observed [3]. To obtain a better understanding of these effects we have initiated a systematic spectroscopic investigation of liquid helium in a cell which is excited by a corona dis- charge [16,17]. The corona discharges have the potential for a relatively simple and versatile excitation source to investigate electronic excitations and luminescence in liq- uid helium as they allow changes over pressures and densi- ties over a very wide range. The liquid 4He under fixed temperature 4.2 K and different pressures up to 8 MPa was excited by corona discharge on sharp tungsten tips of both a negative and a positive polarity. Emission He I atomic lines 706.8 nm and 728.1 nm and He2 molecular bands 660 nm and 640 nm has been observed and analyzed. All spectra show a distinct blue-shift and line-broadening which become stronger with increasing pressure. The rota- tional structure of the molecular bands is resolved at the pressures (0.1–0.2) MPa. The non-resolved profile of the bands recorded at 0.6 MPa resembles the one from [1] where superfluid helium was bombarded with high ener- getic electrons. Shift of the bands Q-branch maximum was studied at different pressures. The shift measured is in a good agreement with experimental data [15] obtained in superfluid He II at 1.7 K. The rotational structure of the singlet band 1 1D Bu g +Σ − Σ (660 nm) resolved for pressures < 0.2 MPa is similar to that observed in luminescence of liquid droplet excited by synchrotron radiation [7]. The corona discharge on point anode (positive corona) was realized if a radius of the electrode was small enough, 0.45 µm, and voltage was some larger than that in the case of the negative corona. The mobility of electrons and posi- tive ions are close each other in LHe. Therefore, electric currents of both negative and positive corona differ weak- ly. However the spectral analysis of the radiation from the positive corona shows qualitative differences of spectral features of these discharges. Both atomic lines and molecu- lar bands were observed. The spectra observed in the posi- tive corona have marked non-symmetric shape. The spectra show an increased intensity of their long-length wings. Such “red satellites” have been observed in the vicinity of both atomic and molecular lines. In positive corona this ef- fect is more significant than in spectra of negative corona. Experiment The experimental set up has been described elsewhere [3] and we will give only a brief summary of the main fea- tures. 99.9999% helium is extra purified by passing it through a series of cold traps and activated charcoal. The purified helium is then immersed into a high pressure cell that allows pressure variations up to 10 MPa. The cell is equipped with two windows and attached to a liquid he- lium bath cryostat that provides temperatures down to 4.2 K. Two electrodes were inside the cell, the first of which is a sharp tungsten tip and the second, which is a flat plate 8 mm apart from the end of the tip. The tips have been pro- duced by electrolytic etching and had radii 0.45 µm and 2.5 µm. Electrodes were supported by Marcor insulators. High voltage from a dc stabilized power supply (Spell- manRHSR/20PN60) is applied to the electrodes. Light emitt- ed from the region close to the point electrode is collected on the entrance slit of a spectrograph (SpectraPro-300i, 300 mm focal length, aperture f/4.0), equipped with 3 grat- ings (150 gr/mm and two of 1200 gr/mm blazed at 750 nm and 300 nm respectively). The 2D-CCDTKB-UV/AR detec- tor is located directly in the exit plane of the spectrograph. Its dimensions are 12.3×12.3 mm with 512×512 pixels of 24×24 µm for each pixel. In order to reduce the dark cur- rent, the detector was cooled to a temperature of 153 K (dark current < 1 e/pixel/heure at 153 K). The instrumental broadening measured by recording profiles of argon lines from a low pressure discharge lamp is ∆λ = 0.1 nm for a 1200 gr/mm grating. Results and discussion Current of corona discharge Corona initiation has a threshold nature both for nega- tive and positive polarity. For negative corona, above a threshold voltage Vinit a mean current with a magnitude of 10−12 A is observed in the external circuit. With voltage increasing the current varies steeply up to a value of 10–8 A. Then a slower current growth with the voltage is recorded which corresponds to a space charge limited current re- gime [17]. On decreasing the applied voltage after corona initiation, the extinction of the corona current occurs at a voltage Vext < Vinit. The large difference observed between Vinit and Vext is specific to liquid helium. This hysteresis has also been observed in LHe by Goncharov et al. [18]. A positive corona was observed for small radius of a tip elec- Z.-L. Li, N. Bonifaci, A. Denat, V.M. Atrazhev, V.A. Shakhatov, and K. von Haeften 486 Fizika Nizkikh Temperatur, 2011, v. 37, No. 5 trode rp = 0.4 μm only. For the positive corona Vinit is higher than that of the negative one and it equals 4 kV compared with 0.5 kV for cathode with the same tip radius. In the point-plane electrodes geometry, outside the re- gion of charge generation, which is very close to the point, the field strength is too low to maintain the ionization process. Then, the charge carriers (electrons or positive ions) injected from ionization zone, move through the drift region under the action of the field. This field is modified by the space charge of the carriers. Therefore, the space- charge-limited current is a quadratic function of an applied voltage V (or I1/2 vs. V is a straight line) for constant mo- bility of the charge carrier [19]. The square root of the mean current I0.5 is a linear function of the applied voltage V and the I1/2(V) straight line has a slope which is propor- tional to a mobility µ of charge carriers [20]. Pressure de- pendence of the slope means that the mobility of charge carriers in liquid He depends on hydrostatic pressure. The mobility µ of negative charge carriers, extracted from cur- rent-voltage characteristics, is very small and it cannot be related to the mobility of free electrons. Its variation with pressure P is a non-monotonous function. At first, µ in- creases with P, then goes through a maximum near P = 1 MPa, and finally decreases with raising pressure. These mobility values and their pressure variation show a great similarity to the results obtained from the time-of- flight method [21]. The measured µ(P) variation can be explained by the theoretical model (see, for example, [22]) which assumes that electrons in LHe are trapped in empty cavities. The cavity is a consequence of strong exchange repulsion between the electron and He atoms. Electron moves through the normal liquid He together with its cavi- ty. Its drift velocity is determined in the hydrodynamic regime by the Stokes’ law. The cavity radius decreases with the pressure increasing. This leads to the electron mo- bility increasing with pressure observed for P < 1 MPa. For larger pressures, the electron mobility decreases with pres- sure increasing due to viscosity increasing with the pres- sure [21]. The positive charge carrier mobility, extracted from the current-voltage characteristics of a positive co- rona also exhibits pressure dependence. The ionic field strength is high enough to compress the liquid into solid phase near the ion, and the ion is surrounded by “snow- ball” of solid helium [23,24]. The radius of the ionic snow- ball increases slightly with pressure growth and the mobili- ty of positive ions trapped in the snowball decreases monotonically with pressure increasing. In the issue of the low mobility of charges in the drift zone the electric current of corona in LHe is very small and less than that in high electron mobility liquids such as LAr [25]. Close toward tip electrode the current density in- creases. For corona in LAr the Joule heating by the current leads to create a region of a gaseous plasma in the ioniza- tion zone with a temperature higher than the temperature of 84 K in a bulk liquid. In the case of corona in LHe the cur- rent density is less and we assume that the ionization zone is filled with liquid He at the temperature of 4.2 K. Spectra of corona discharge The light emitted from the corona region was collected and spectra in the range 500–1080 nm were recorded. Seve- ral atomic lines and molecular bands were identified. These lines correspond to radiative transitions between excited states of He atoms and 2He excimer molecules. At low pressure the lines are sharp and their peak position match the atomic lines and molecular bands of helium from gas phase experiments. These lines are listed in Table 1. A strong background continuum from 490 to 1100 nm ap- pears in spectra at pressures above P = 4.0 MPa. Moreover, the width of the lines increases with pressure and their relative intensity decreases. No lines and bands can be ob- served in spectra if the pressure exceeds 5.0 MPa. Table 1. Transitions observed in liquid helium (T = 4.2 K, P = = 0.1 MPa). Atomic lines Molecular bands λ, nm Upper-Lower λ, nm Upper-Lower 492.19 4d 1D-2p 1P 462.24 1 1J Bu gΔ − Π 587.56 3d 3D-2p 3P 464.95 3 3e ag u +Π − Σ 706.52* 3s 3S-2p 3P 573.49 ( )3 3f (v 0) b v 0u gΔ = − Π = 728.13 3s 1S-2p 1P 575.00 3 3f (v 1) b (v 1) u gΔ = − Π = 1083.02 2p 3P-2s 3S 577.00 3 3f (v 2) b (v 2)u gΔ = − Π = 588.70 3 3f bu g −Π − Π 639.60* 3 3d bu g +Σ − Π 659.55 1 1D Bu g +Σ − Π 913.61 1 1C Ag u + +Σ − Σ 918.30 3 3c ag u + +Σ − Σ Comments : * Features of spectra of these transitions are dis- cussed in the present paper. Let us consider spectra observed in negative corona discharge. Blue shift and broadening of the lines were rec- orded in a range of the pressure (0.1–3) MPa. Figure 1 shows normalized intensities of the atomic line at 706 nm 3 3(3s S 2p P→ transition) being broadened and shifted with increasing pressure towards smaller wavelengths (blue shift), but with no significant changes in the symmetry of the line shape. The retained symmetric character of the line allowed us to quantify the width using the magnitude of the full width at half maximum (FWHM). The magnitude of the shift was derived from the position of the maximum Atomic and molecular spectra emitted by normal liquid 4He excited by corona discharge Fizika Nizkikh Temperatur, 2011, v. 37, No. 5 487 relative to line peak at 0.1 MPa. The measured shift and width of the 706 nm line are pressure dependent as shown in Figs. 2 and 3. In a low density gas, the line profile can be accurately explained by the theory of pressure broadening [26]. Both shift and width of lines are proportional to gas density and are adequately explained by repulsive interaction between an excited He atom and surrounded ground state He atoms caused by the Pauli principle. The repulsion leads to blue shift. The “impact” approximation in the framework of the theory predicts strong broadening compare with shift of a line and its ratio of 7.1 [26]. Our data shows the ratio close to unity. Moreover, the calculation of the pressure broadening in helium gas at 4.2 K for different pressures and in a vapor along the liquid-gas saturated line gives more large width of the λ0 = 706 nm line, Fig. 3. It means that a perturbation of radiator by surrounding atoms is less than that in homogeneous gas with low density. Previous theoretical and experimental studies have pro- vided convincing evidence for the existence of microscopic cavities “bubble” with diameter of 1 nm surrounding ex- cited atomic and molecular species in superfluid helium at 1.7 K [27,28]. The origin of the bubble around an excited state of atom or molecule is a balance between the repul- sive interaction Eint between a closed shell He atoms and the Ridberg electron of He and the pressure bpV and the surface tension bSσ of liquid. The medium is then not homogeneous around the excited atom and the theory of the pressure broadening is not valid. The shift of the spec- tral lines and their width depend on the size of the bubble which is pressure dependent. When the bubble size de- creases with pressure the interaction between the surround- ing atoms increases due to the reduction of distance be- tween the radiator and the perturbing ground state atoms and this ultimately leads to an increase of the line width with pressure. The well-known calculation of the atomic line shape in LHe at 1.7 K has been published in [28]. We carried out such calculations for conditions of our experi- ments at 4.2 K using the same simple model with a spheri- cal bubble of radius Rb and a trial function ( )n R [29,30] of a “soft” profile of its boundary He[1 (1 )e ], ( ) 0( ) 0, 0 x bn x x R Rn R x −⎧ − + = α − ≥⎪= ⎨ <⎪⎩ . (1) Here nHe = 2.2·1022 cm–3 is the number density of the liq- uid helium and the parameter α was chosen as 1 Å–1. Be- cause of a reduction of the surface tension a contribution of the “kinetic” term [29] in the energy balance is important ( ) ( ) 3 2 tot int kin 4 ( ) 4 ( ) 3 b b R E E n R p R E n R π = + + πσ + . (2) The term was calculated using the boundary profile (1) as ( )22 2 2 2 kin He He He ( ) 4 1.67 4 . 8 ( ) 8 b b R n R E R dR n R M n R M ∞ ∇ = π = π α∫ (3) Fig. 1. Normalized intensities of the 706 nm atomic line for dif- ferent pressures. 690 694 698 702 706 710 714 0 0.2 0.4 0.6 0.8 1.0 T = 4.2 K= 0.1 MPaP = 1.4 MPaP = 2.3 MPaP In te n si ty , ar b . u n it s �� nm 0.5 1.0 1.5 2.0 2.5 3.00 1 2 3 4 5 6 7 8 9 Bubble model Present data Calculations Bubble model Gas at 4.2 K Saturated vapor Pressure, MPa F W H M , n m Fig. 3. Full-Width-Half-Maximum (FWHM) of the 706 nm atom- ic line vs. pressure. Points — experimental data. Lines — calcu- lations. Fig. 2. Shift of 706 nm atomic line in LHe at 4.2 K for different pressures. Points — experimental data. Line — calculation in frame of “bubble” model. 0.5 1.0 1.5 2.0 2.5 3.00 1 2 3 4 5 6 7 8 Bubble model. 706nm Present results [15] [4] Calculation Pressure, MPa S h if t, n m Z.-L. Li, N. Bonifaci, A. Denat, V.M. Atrazhev, V.A. Shakhatov, and K. von Haeften 488 Fizika Nizkikh Temperatur, 2011, v. 37, No. 5 The interaction between an excited atom with surround- ing atoms in the ground state was simulated using the one parameter repulsion potential 12 12( )U R C R= with C12 = 10–99 erg·cm12 0.5 2 12 He12 int 12 8.54 ( ) 0.126 b bR C nC E R n R dR R R ∞ α = π =∫ . (4) The total energy of the system ( *He + cavity), Eq. (2), has a minimum for an equilibrium radius of the cavity. The radius decreases from 10.6 Å at p = 0 down to 8.6 Å at p = 3 MPa. The line shape I(ω) was described in frame of the “stat- ic” approximation [31] ( )2( ) exp 4 ( ) 1 exp ( ) . bR I i dRR n R i U R d ∞ ∞ −∞ ⎡ ⎤ ⎢ ⎥ω ∝ ωτ− π − − τΔ τ⎡ ⎤⎣ ⎦⎢ ⎥ ⎣ ⎦ ∫ ∫ (5) Here ( ) ( ) ( )i fU R U R U RΔ = − is the difference between the interaction potentials of the excited atom in initial and final electronic states. The initial state is more extensive and its cavity has greater radius. The cavity is invariable during the radiative transition and it is larger than the equi- librium cavity for the final state of the excited atom. It al- lowed us to use the one parameter repulsive potential C12/R12 in Eq. (5) and the analytical expression for the profile of the line has been obtained ( )Re ( ) 0 ( ) e cos Im ( )VI V d ∞ − τω ∝ ωτ− τ τ∫ . (6) Here Re V(τ) and Im V(τ) are real and imaginary parts of the phase function V(τ) 12 122 0 ( ) 4 ( ) 1 e Ci RV n R R dR ∞ τ⎛ ⎞ ⎜ ⎟τ = π −⎜ ⎟⎜ ⎟ ⎝ ⎠ ∫ . (7) The Im V(τ) and Re V(τ) calculated using the cavity boun- dary Eq. (1) are linear and quadratic functions of the para- meter τ, correspondingly. It gives the Gaussian shape for the spectral line, Eq. (5). Its width and shift have a weak dependence of a magnitude of the interaction parameter C12. We obtained with accuracy of a numerical factor that 1 2 5 5 18 230 12 He 9 1 2 4 42 460 12 21 19 He Shift , 2 . 2 C n p c C p FWHM c n ⎡ ⎤λ ∝ ⎢ ⎥ π α⎢ ⎥⎣ ⎦ ⎡ ⎤λ ∝ ⎢ ⎥ π α⎢ ⎥⎣ ⎦ (8) The more strong dependence of the parameters was found of the diffuse boundary parameter of the cavity α which was chosen as 1 Å–1. The results of the calculation are shown in Figs. 2 and 3 as the “bubble model” lines. The calculated radii of the cavity have been founded from 10.6 Å at zero pressure to 8.6 Å at 3 MPa. The analysis showed that the ratio Shift/FWHM is a function of the pa- rameter 3 1/2 He b( )n R and is closed to 3 as observed in our experiment. This is strong argument confirmed the “bubble” nature of observed spectra, because the impact interaction between radiator and surrounding atoms in a gas leads to the Shift/FWHM = 0.14. The spectral species with a structure of molecular bands have been observed in the experiments. Figure 4 shows the experimental spectrum of the 3 3d S b Pu g + − triplet transi- tion. The spectrum shows (i) a distinct blue-shift and (ii) line-broadening, which become stronger with increasing pressure. At 0.6 and 1.4 MPa, individual rotational lines cannot be resolved anymore. The profile of the band rec- orded at 0.6 MPa resembles the one reported in [1,15] in a superfluid helium bombarded with high energetic elec- trons. Thus, we can conclude that, in our experiments, he- lium excimer molecules reside within a bubble of a diame- ter similar to the one reported in [15]. The 3 3d S b Pu g + − triplet transition is the most intense fluorescence band ob- served in the superfluid LHe excited by femtosecond laser pulses with intensity below a threshold of laser-induced breakdown of LHe [32]. No resolution of the rotational structure of the band was recorded in those experiments. The measurements were carried out for conditions with different temperatures from 1.4 K up to 2.8 K under satu- rated vapor pressures. The strong broadening (2.5 nm) cen- tral peak with red shift (2 nm) was recorded. The sign of the shift is in contradiction with our data and the results obtained in [1,15]. At pressures less than 0.2 MPa the spectrum has a well resolved rotation structure which is a subject of the numer- ical simulation. The upper molecular term 3d u +Σ of the transition has the rotational levels (Hund case b) with odd R-branch P-branch = 2.1 nm�� = 4.6 nm shift 3.3 nm shift 1.0 nm b d-- triplet LHe T = 4.2 K = 0.1 MPaP = 0.6 MPaP = 1.4 MPaP 625 630 635 640 645 650 0 0.2 0.4 0.6 0.8 1.0 1.2 In te n si ty , ar b . u n it s �, nm Fig. 4. Normalized intensity of molecular band 3 3d bu g +Σ − Π in LHe at 4.2 K for different pressures. Atomic and molecular spectra emitted by normal liquid 4He excited by corona discharge Fizika Nizkikh Temperatur, 2011, v. 37, No. 5 489 numbers of K which is the total momentum of the mole- cule rotation without spin. The spin-splitting of the levels of the 3Σ-term of He2 molecule is very narrow [33,34] and their separation does not resolved in our measurements. The transitions between different rotation levels are go- verned by the selection rule which determined three differ- ent branches of rotation lines in the molecular band such as the central Q-branch together with the R-branch in the red site and the P-branch in the blue side. Our calculations taking into account contributions of general and satellite transitions give the simple formulae for intensity of the Q-, P-, and R-branches of the rotation band (2 1) ( ), ( 2) ( ), ( 1) ( ). Q P KK R K I K N K I K N K I K N K ′′′′ ′′ ′′ ′′ ′′ ′′∝ + ∝ + ′′ ′′∝ − , (9) Here K ′′ is the quantum number of the upper level of the rotational transition. Honl-London factors of the b-d triplet rotation lines calculated in [35,36] and listed in [37] have been used. The analysis allowed us to estimate the population of the rotation levels using the experimental data of the rota- tion lines intensity. The distributions ( )N K ′′ calculated following Eq. (9) and using the measured intensities of both R-branch and P-branch lines, Fig. 4, are presented in Fig. 5 as a function of the quantum number K ′′ of upper rotational levels. The Boltzmann distribution corresponds to a linear function in this semi-logarithmic plot. Figure 5 shows that such distribution is only exhibited for large ,K ′′ The “rotational” temperature of the distribution is 900 K, which is much higher than the temperature of the liquid of 4.2 K. It indicates that the rotating excimer mole- cules are far from being thermalized. Moreover, the popu- lations derived from the P-branch intensities are larger than those calculated from R-branch intensities. This fact can formally be interpreted by the existence of an addition- al source of radiation that located in a range of larger wa- velengths to the spectrum. The simulation of the d-b spec- trum shows the magnitude of the contribution of such a “red satellite” as the difference between measured and si- mulated spectra in the range of the P-branch lines. The comparison of spectra observed in negative and positive corona shows that the additional radiator identified as “red satellite” presents spectral lines recorded for posi- tive corona. Such satellites have been observed near both atomic lines and molecular bands. The phenomenon of “red satellite” is more significant in spectra recorded with positive corona discharges. The satellites were observed for both 706 nm and 728 nm atomic lines. The same “red satellites” were observed in molecular spectra and their spectrum can be shown by subtracting the simulated spec- tra from the measured one. The result of this procedure is presented in Fig. 6. Our calculations show that the “addi- tional radiator” cannot be explained by contributions from higher vibration transitions such as ( 1 v= , 1 v′= ) which band head is located close to 642 nm. Nature of the addi- tional radiator is unclear yet and here we can only tenta- tively explain the red satellite bands as possibly due to a van der Waals bound molecular complex formed by the radiating atom or molecule and single helium atom. Fur- ther calculations and experiments on the nature of the pro- files of the red satellite lines and bands are in progress. Conclusion We have shown that, in liquid helium at 4.2 K, the spectroscopic investigation of localized atomic and mole- cular excited helium states can be created by using a coro- na discharge as excitation source. Spectra were recorded in a large range of applied pressure from 0.1 to 4 MPa. The analysis of the observed shifts and widths show that the classical theory of line broadening (that accurately predicts the experimental line profile for helium gas a 4.2 K) cannot be applied for liquid helium. For pressures under 1 MPa the experimental width of a line is in agreement with pre- dictions of the “bubble” theory. 0 40 80 120 160 200 240 280 320 1E–3 0.01 0.1 b d-- triplet 4.2 K 0.1MPa Trot= 900 K R el at iv e p o p u la ti o n , ar b . u n it s ( +1)K K -branchR -branchP Boltzmann 900 K Fig. 5. Relative population of the rotational levels of the upper term 3d u +Σ (idem to Fig. 4). 634 638 642 646 650 0 0.2 0.4 0.6 0.8 1.0 experiment simulation red satellite Lhe 4.2 K P = 0.43 MPa POSITIVE CORONA shift 0.56 nm broadenning 0.75 nm In te n si ty , ar b . u n it s Wavelength, nm Fig. 6. Rotational spectra of transition 3 3d bu g +Σ − Π of positive corona in LHe, T = 4.2 K, P = 0.142 MPa. Z.-L. Li, N. Bonifaci, A. Denat, V.M. Atrazhev, V.A. 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Atomic and molecular spectra emitted by normal liquid ⁴He excited by corona discharge

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