EXPERIMENTALLY MEASURED RADIATIVE LIFETIMES AND OSCILLATOR STRENGTHS IN NEUTRAL VANADIUM

The experimental set-up used for our radiative lifetime measurements is shown schematically in Figure 1. A pure vanadium foil was placed on a rotating target in a vacuum chamber at a pressure between 10⁻⁴ and 10⁻³ Pa. This was then irradiated perpendicularly by ablation pulses of 10 ns duration and energies between 2 and 10 mJ, emitted from a Nd:YAG laser (Continuum Surelite) of 532 nm wavelength at a repetition rate of 10 Hz. These pulses entered the top of the vacuum system through a fused-silica window, and were focused vertically onto the surface of the rotating vanadium foil, producing a plasma of both neutral and ionized atoms that expanded into an interaction zone at the center of the chamber, about 10 mm above the foil. The ionized atoms traverse the chamber much faster than the neutrals, meaning that after a short delay, the plasma in the interaction zone contains only neutral atoms. At this moment, an excitation laser beam from a tunable nanosecond laser system intersects the plasma at right angles. This beam was linearly polarized and tuned in wavelength to the resonant transition of an upper state of interest.

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The tunable laser system consisted of an injection-seeded and Q-switched Nd:YAG laser (Continuum NY-82), a stimulated Brillouin scattering (SBS) temporal compressor, a DCM dye laser (Continuum Nd-60), a potassium dihydrogen phosphate (KDP) crystal, retarding plate (RP) and β-barium borate (BBO) crystal, and a stimulated Stokes Raman scattering (SSRS) cell.

The Nd:YAG seeded laser produced pulses of light at 532 nm wavelength, 8 ns duration, and 400 mJ energy, at a repetition rate of 10 Hz. These pulses were shortened in length to approximately 1 ns duration using an SBS compressor, and then sent to pump a DCM dye laser. To obtain the ultraviolet radiation needed to excite the vanadium atoms, light from the dye laser was passed through a frequency-doubling KDP crystal, producing second harmonic radiation that was mixed with the fundamental laser frequency in a BBO crystal to produce light at the third harmonic frequency. Finally, to expand the spectral range of the laser light, both the second and third harmonic radiation was focused onto a SSRS hydrogen cell at a pressure of 10⁶ Pa, in which different orders of stimulated Stokes and anti-Stokes Raman scattering were produced.

Depending on the excitation requirements of a particular measurement, the appropriate component of the excitation laser was selected with a CaF₂ Pellin–Broca (PB) prism, passed through two apertures and sent horizontally into a vacuum chamber where it struck the expanding plasma produced by the ablation laser. The two Nd:YAG lasers were controlled externally by a digital delay generator (Stanford Research Systems Model 535), which adjusted the delay between the ablation and excitation laser pulses, ensuring that the excitation laser met with the vanadium plasma only after the fast moving ionized atoms had traversed the laser interaction zone.

Fluorescence from the spontaneous decay of the targeted excited levels was focused by a fused-silica lens onto the entrance slit of a 1/8 m monochromator (resolution 6.4 nm mm⁻¹), that was used as a filter to select a particular fluorescence line and to block stray light. This selected light was then detected by a Hamamatsu 1564U microchannel-plate photomultiplier tube (PMT, 200 ps rise time and sensitive between 200 and 600 nm), which was connected to a digital transient oscilloscope (Tektronix Model DSA 602), triggered by a Thorlabs SV2-FC photodiode (120 ps rise time) driven by a reflection from the excitation laser beam. These fluorescence signals were averaged in the oscilloscope and sent to a computer, where the level radiative lifetimes were measured. For the shorter lifetimes the temporal shape of the exciting laser pulses was recorded after the ablation beam was blocked and the decay curves then analyzed by deconvolving the observed signal and the laser pulse using the computer program DECFIT (Palmeri et al. 2008). The longer lifetimes were obtained by fitting a single exponential decay, and a background function, to the region after the pulse had expired.

Many systematic effects were considered and accounted for. A static magnetic field of approximately 100 G, provided by a pair of Helmholtz coils surrounding the laser interaction zone, was used to eliminate potential Zeeman quantum beat effects for long-lived states. Flight-out-of-view effects are also important, particularly for long lifetimes. During the experiment, the position and width of the monochromator entrance slit and the delay times between the ablation and the excitation pulses were adjusted to identify and eliminate the possible influence of such flight-out-of-view effects.

To make sure that the experimental lifetimes were not affected by collisions and radiative trapping—a particular concern when the delay between ablation and excitation pulses is short—the intensity of the ablation pulse was varied and the delay time adjusted within the range 2.8–5.5 μs, changing the plasma atomic density and temperature at the time of excitation. The resulting LIF signal intensities varied, but the lifetime values were found to be nearly constant, implying that the effects of collisional quenching and radiation trapping were negligible.

To avoid saturation effects and to ensure that the response of the detection system is linear, the fluorescence signals were detected with different neutral density filters inserted in the path of the exciting laser light.

A smooth fluorescence decay curve was obtained for each lifetime measurement by averaging fluorescence photons from 1000 pulses to obtain a sufficiently high signal-to-noise ratio (S/N). Between 10 and 20 curves were recorded for each level under the different experimental conditions listed above, and the averaged measured lifetime taken as the final value reported in Table 1. The errors quoted include the statistical scattering between the different recordings and different curve fittings, as well as any remaining systematic effects.

Accurate experimental log(gf) values can be obtained by combining the radiative lifetime of a level, τ, with radiative transition branching fractions (BFs) derived from the relative intensity of all spectral lines emanating from transitions linked to that level (Huber & Sandeman 1986). For the log(gf) values reported in Table 4, BFs were obtained from V i emission line spectra measured by FT spectrometry in several overlapping regions between 2000 cm⁻¹ and 34,500 cm⁻¹ (between 5000 and 290 nm). These spectra are listed in Table 2.

Spectra A to C were measured at Lund Observatory, Sweden, on a Bruker IFS-125HR infrared FT spectrometer, which has a resolving power R = 10⁶ at 5 μm. The V i emission was generated from a vanadium cathode (99.9% pure) mounted in a water-cooled hollow cathode lamp (HCL) running at currents of up to 500 mA in a neon atmosphere at a pressure between 220 and 230 Pa. Each of the three spectra were constructed from up to 20 repeated measurements, coadded together to improve the S/N of lines of interest. In spectrum B many target lines were observed to be very strong (S/N ≳ 1000). Spectrum C was thus taken across the same spectral range, but at a lower lamp current of 200 mA, to verify that these strong lines were free from any self-absorption.

The spectrum of a tungsten lamp calibrated by the Swedish National Laboratory—with spectral radiance known to ±3% between 400 and 800 nm, and ±5% between 800 and 2500 nm—was also measured before each of the listed vanadium spectra to obtain the response function of the spectrometer as a function of wavenumber. The response functions are shown in Figure 2.

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Spectra D to G were measured at Imperial College (IC) London, UK, on a Chelsea Instruments FT spectrometer based on an IC prototype design (Thorne et al. 1987; Thorne 1996) with spectral range down to 135 nm. The V i emission was generated using an HCL of similar design to that employed at Lund, again operated at currents of up to 500 mA, but in an argon atmosphere at a pressure 30 Pa. Spectrum F contained many target lines with S/N ≳ 1000, so as with the Lund measurements, Spectrum G was acquired under similar conditions, but with a lower lamp current of 300 mA, to allow any effects from self-absorption to be corrected.

The spectrometer response functions for spectra D and E were again obtained from a calibrated W lamp, measured before and after each HCL measurement. Uncertainties in the relative spectral radiance of the W lamp used at IC, and calibrated by the UK National Physical Laboratory (NPL), do not exceed ±1.4% between 410 and 800 nm, and rise to ±2.8% at 300 nm. Spectra F and G extended too far into the ultraviolet to be calibrated from the measurement of a W standard lamp alone. For these spectra, an additional measurement was made of a deuterium lamp before and after each HCL measurement. This lamp was calibrated by the Physikalisch-Technische Bundesanstalt (PTB), Germany, and has a relative spectral radiance known to ±7% between 170 and 410 nm. The spectrometer response function obtained from this lamp was combined with that from the W lamp such that the final response function used to calibrate the vanadium line spectrum was defined at longer wavelengths by the W lamp and at shorter wavelengths by the deuterium lamp. The response functions for spectra D to G are also shown in Figure 2.

Of the 39 upper energy levels for which we report log(gf) values, 25 linked to lower energy levels through transitions that produced spectral lines contained entirely within the range of a single spectrum listed in Table 2. For the remaining levels, the spectral lines spanned at least two spectra. In these cases, the intensities of lines observed in regions of overlap between any two spectra were compared, and the intensity scale of all required spectra adjusted to match the spectrum that contributed most to the total upper-level branching fraction. This process of intensity calibration of several spectra overlapping in wavelength is given in more detail in Pickering et al. (2001a, 2001b).

The predicted transitions from each target upper energy level to lower energy levels were taken from the semi-empirical calculations of Kurucz (2007). Emission lines associated from these transitions were then identified in our vanadium HCL spectra, and the XGREMLIN package (Nave et al. 2015) was then used for making center-of-gravity (COG) fits to the observed profiles (Thorne et al. 2011). The V i spectrum is affected by hyperfine structure (Thorne et al. 2011), and all hyperfine components of a given line were included in the COG fit to obtain the total observed intensity of the line, as shown in the example in Figure 3.

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The results from the XGREMLIN line-fitting process (relative line intensities, line S/N) together with the experimental spectra were then transferred to the FAST package (Ruffoni 2013), which was then used to calculate the BFs.

$$\begin{eqnarray}&&{\mathrm{BF}}_{{ul}}=\displaystyle \frac{{I}_{{ul}}}{{\sum }_{l}{I}_{{ul}}},\end{eqnarray} \tag{ 1 }$$

where the subscript u denotes a target upper energy level, and ul, a transition from this level to a lower level, l, resulting in a line of intensity I_ul.

Spectra B and F were preferred over spectra C and G, respectively, for lines in those spectral regions, because the higher HCL running current produced lines of greater S/N. However, in cases where any one hyperfine component of a line was observed to have a very large S/N, the BF measurement was repeated using the line profile observed in spectrum C or G to ensure that the final BF value was not affected by self-absorption.

Lines that were too weak to be observed—typically those predicted by Kurucz (2007) to contribute less than 1% of the total BF—were not considered, nor were lines that were either blended or outside the measured spectral range. Their predicted contribution to the total BF was assigned to a "residual" value, which was used to scale the sum over l of I_ul. The predicted BFs of Kurucz (2007) are used because we found these to be more reliable than those of Wang et al. (2014) due to the strong cancellation effect reported by Wang et al. (2014) affecting some of the transitions, in particular those depopulating the lowest excited odd-parity levels. Figure 4 shows comparisons of our measured BFs with those of Kurucz (2007) and Wang et al. (2014). For the majority of levels for which we report BFs, the residuals are less than 1%, with the least complete set being 94%.

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The final BF values were then combined with the measured radiative lifetime of upper level u to obtain the transition probability, or Einstein A coefficient of the transition:

$$\begin{eqnarray}&&{A}_{{ul}}=\displaystyle \frac{{\mathrm{BF}}_{{ul}}}{{\tau }_{u}}\;({{\rm{s}}}^{-1}).\end{eqnarray} \tag{ 2 }$$

This is equivalent to its log(gf) value, which was obtained from the expression (Thorne et al. 2007)

$$\begin{eqnarray}&&\mathrm{log}({gf})=\mathrm{log}[{A}_{{ul}}{g}_{u}{\lambda }^{2}\times 1.499\times {10}^{-14}],\end{eqnarray} \tag{ 3 }$$

where λ is the wavelength of the line in nm, and g_u the statistical weight of the upper level.

The uncertainty in each log(gf) value quoted in Table 4 arose from a combination of the uncertainty in its BF and that in its upper-level lifetime.

$$\begin{eqnarray}&&{\left(\displaystyle \frac{{\rm{\Delta }}{{BF}}_{{ul}}}{{\mathrm{BF}}_{{ul}}}\right)}^{2}=(1-2{\mathrm{BF}}_{{ul}}){\left(\displaystyle \frac{{\rm{\Delta }}{I}_{{ul}}}{{I}_{{ul}}}\right)}^{2}+\displaystyle \sum _{j=1}^{n}{\mathrm{BF}}_{{uj}}^{2}{\left(\displaystyle \frac{{\rm{\Delta }}{I}_{{uj}}}{{I}_{{uj}}}\right)}^{2},\end{eqnarray} \tag{ 4 }$$

where ΔI_ul is the sum of uncertainties in intensity of a line due to its measured S/N, the uncertainty in calibrating the intensity scale of the spectrum, and the uncertainty in the factor used to place two overlapping spectra on a common intensity scale (Ruffoni 2013). The uncertainty in A_ul, following from Equation (2), is then given by

$$\begin{eqnarray}&&{\left(\displaystyle \frac{{\rm{\Delta }}{A}_{{ul}}}{{A}_{{ul}}}\right)}^{2}={\left(\displaystyle \frac{{\rm{\Delta }}{\mathrm{BF}}_{{ul}}}{{\mathrm{BF}}_{{ul}}}\right)}^{2}+{\left(\displaystyle \frac{{\rm{\Delta }}{\tau }_{{ul}}}{{\tau }_{{ul}}}\right)}^{2}\;,\end{eqnarray} \tag{ 5 }$$

where Δτ_ul is the uncertainty in the upper-level lifetime. Thus, the uncertainty in log(gf) of a particular line is given by

$$\begin{eqnarray}&&{\rm{\Delta }}\mathrm{log}({gf})=\mathrm{log}\left(1+\displaystyle \frac{{\rm{\Delta }}{A}_{{ul}}}{{A}_{{ul}}}\right)\;.\end{eqnarray} \tag{ 6 }$$

During the analysis it was found that in the cases of three transitions of interest it was possible to find BF values for transitions that were blends with other V i transitions by fitting the observed hyperfine structure (hfs) of the lines involved in the blends using the hfs A_hfs splitting factor of each energy level involved in the transition. The three transitions appeared in two blended features: at 4408 Å (22,677 cm⁻¹) with transitions ${(}^{5}D)4s\ {a}^{6}{D}_{3/2}-{(}^{5}D)4p\ {y}^{6}{F}_{3/2}$ and ${(}^{5}D)4s$ ${a}^{6}{D}_{1/2}-{(}^{5}D)4p$ ${y}^{6}{F}_{1/2}$ and at 3813 Å (26,215 cm⁻¹) with transitions expected to contribute significantly to the blend $3{d}^{3}4{s}^{2}$ ${a}^{4}{F}_{5/2}-{(}^{5}D)4p$ ${y}^{4}{D}_{5/2}$ and ${(}^{5}D)4s\ {a}^{6}{D}_{3/2}\ -{(}^{4}P)4s4p\ {x}^{6}{D}_{3/2}$.

An example of one of the blended features is given in Figure 5. However, initially in each case only one of the two A_hfs factors involved in a transition was known, and so in order to estimate the relative intensity of each transition, the unknown A_hfs factor had to be found. Following methods reported in Pickering (1996) and Blackwell-Whitehead et al. (2005), new A_hfs factors were found by analysing other spectral lines observed that involve the same level (full details may be found in Holmes 2016). The A_hfs factors together with their uncertainties used to find the BFs of three transitions are shown in Table 3. The value for level ${x}^{6}{D}_{3/2}$ has not previously been published and is new. Our new measurements of A_hfs for levels ${y}^{6}{F}_{1/2}$ and ${y}^{6}{F}_{3/2}$ are compared with those recently published by Güzelçimen et al. (2014) and are found to have reasonable agreement considering the given experiment uncertainties.

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Table 3.  V i New and Previously Published Hyperfine Structure Splitting Factors, A_hfs and B_hfs, Used in Fitting of the 22,677 and 26,215 cm⁻¹ Blended Features

Level	Level Energy	Ahfs	Bhfs	Source
	(cm−1)	(×10−3 cm−1)	(×10−3 cm−1)
$3{d}^{3}4{s}^{2}\ \ {a}^{4}{F}_{5/2}$	137.383	10.7159 ± 0.0001	0.132 ± .001	CPGC
${(}^{5}D)4s\ \ {a}^{6}{D}_{1/2}$	2112.282	25.0685 ± 0.0002	0	CPGC
${(}^{5}D)4s\ \ {a}^{6}{D}_{3/2}$	2153.221	13.5309 ± 0.0001	−0.2330 ± 0.0004	CPGC
${(}^{5}D)4p\ \ {y}^{6}{F}_{1/2}$	24789.401	28.3a ± 0.4	0	new
${(}^{5}D)4p\ \ {y}^{6}{F}_{3/2}$	24830.221	7.1a ± 0.2	0	new
${(}^{5}D)4p\ \ {y}^{4}{D}_{5/2}$	26352.634	0.51 ± 0.03	0	PBAG
${(}^{4}P)4s4p\ {x}^{6}{D}_{3/2}$	28368.753	22.5 ± 0.2	0	new

Notes. Source column: source of published hyperfine structure splitting factors: CPGC, Childs et al. (1979); PBAG, Palmeri et al. (1995); "new," newly found in this work.

^aWe note that Güzelçimen et al. (2014) also report new values of A_hfs of (27.9 ± 0.6) × 10⁻³ cm⁻¹ for the level at 24,789 cm⁻¹ and (6.7 ± 0.1) × 10⁻³ cm⁻¹ for the level at 24830 cm⁻¹. Energy level values are from Thorne et al. (2011).

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