Radiative lifetime measurements and transition probability calculations in lanthanide ions

Journal of Alloys and Compounds 344 (2002) 255–259

L

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Radiative lifetime measurements and transition probability calculations in lanthanide ions a,b ´ P. Quinet a,b , *, P. Palmeri a , E. Biemont , Z.S. Li c , Z.G. Zhang c , S. Svanberg c a

Astrophysique et Spectroscopie, Universite´ de Mons-Hainaut, B-7000 Mons, Belgium b ` , B-4000 Liege ` , Belgium IPNAS, Universite´ de Liege c Department of Physics, Lund Institute of Technology, S-22100 Lund, Sweden

Abstract We have undertaken a systematic investigation of spectroscopic properties of lanthanide ions (Z557–71). Using time-resolved laser-induced fluorescence following one- or two-photon excitations, a large number of radiative lifetimes have been measured at the Lund Laser Centre for singly, doubly and trebly ionized atoms. These new measurements have been used for testing theoretical calculations performed within the framework of a relativistic Hartree–Fock approach taking core-polarization effects into account. Using the experimental lifetimes (when available) and the theoretical branching fractions, a large number of transition probabilities, most of them of astrophysical interest, have been deduced and are stored in a new database (DREAM). Up to now, the results obtained concern the following ions: La 21 , Ce 1 , Ce 31 , Pr 21 , Ho 21 , Er 21 , Tm 1 , Tm 21 , Yb 1 , Yb 21 , Yb 31 , Lu 1 and Lu 21 .  2002 Elsevier Science B.V. All rights reserved. Keywords: Radiative lifetime measurements; Transition probability; Lanthanide ions

1. Introduction The neutral and lowly ionized lanthanides (Z557–71) are characterized by the progressive filling of the 4f subshell of their electronic configurations. They possess the common feature of a xenon structure with in addition two or three outer electrons. The energy and spatial extension of the 4f-eigenfunction drop suddenly at the beginning of the lanthanide sequence. Indeed, in lanthanum (Z557), the 4f eigenfunction is still essentially located outside the xenon structure, whereas in neodymium (Z560) it has contracted in such a way that its maximum lies inside the 5s 2 5p 6 closed subshells. In view of the imperfect screening of the 4f electrons, this contraction is very rapid with increasing atomic number, i.e. with the increasing number of 4f electrons. Due to their complexity, these configurations have been rather little investigated so far. The laboratory analyses and the theoretical studies are

*Corresponding author. E-mail address: [email protected] (P. Quinet).

still very fragmentary, or missing, for many lanthanide ions. Nevertheless, there is an increasing need for accurate spectroscopic data, in particular radiative transition rates (oscillator strengths, transition probabilities, radiative lifetimes), for rare-earth ions. Such data are essential in studies of chemically peculiar stars and other problems in stellar structure. As an example, many lines of neutral, singly and doubly ionized lanthanides have been identified in the extreme peculiar star HD 101065 (Przybylski star) [1]. Outside of astrophysics, the lighting-research community is interested in rare-earth elements because of their rich emission spectra in the visible. Rare-earth salts are used in many commercial metal-halide high-intensity discharge (HID) lamps. In that field, accurate atomic data are required in the models used for lamp design and diagnostics. For these reasons, we have decided to perform new experimental and theoretical investigations of many transitions belonging to the first ionization stages of the lanthanide elements. In the present paper, we give a brief description of the methods used and a summary of the results obtained in the recent past.

0925-8388 / 02 / $ – see front matter  2002 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 02 )00363-8

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2. Lifetime measurements

surface, and the delay times between the ablation and excitation pulses.

The lifetime of an excited atomic state i, ti , can be measured by observing the fluorescence decay from this state using the following expression of the intensity: I(t) 5 I(0)e 2t / ti

(1)

A very direct way of investigating atomic lifetimes is to use short-pulse laser excitation and subsequent fast timeresolved detection of the fluorescence light. This is sometimes referred to as time-resolved laser-induced fluorescence (LIF). A typical setup is shown in Fig. 1. Slight modifications of the basic setup are needed for experiments in different ions.

2.1. Ion source A laser-produced plasma is utilized as an ion source. This plasma is produced by focussing, on a solid rare-earth target placed in a vacuum chamber, the green beam of a Continuum Surelite Nd:YAG laser, which has a pulse duration of 10 ns and a typically employed energy of about 5–10 mJ. A small plume of plasma is developed after each pulse. The expanding plasma is crossed by an excitation beam (one-step excitation or two-photon excitation) or two excitation beams (two-step excitation) at a position of about 1–2 cm above the target. The delay between the plasma production and the excitation can be varied by externally triggering all the lasers used in the experiment with a digital delay generator. The plasma density and temperature in the observed region can be adjusted by changing the plasma production laser pulse energy, the size of the focus point, the distance above the target

2.2. Excitation laser system Three types of excitation laser systems are used in our work, the first for one-step excitation, the second for two-step excitation and the third for two-photon excitation. A detailed description of these systems can be found, for example, in Refs. [2,13]. For the one-step excitation, green pumping laser pulses coming from a seeder injected Nd:YAG laser (Continuum NY-82) with a pulse duration of about 8 ns is sent to a stimulated Brillouin scattering (SBS) compressor, and the output pulse duration is compressed to about 1 ns. The laser is used to pump a dye laser (Continuum Nd-60). The second or third harmonics of the dye laser is obtained in a nonlinear optical system, consisting of a KDP crystal, a retarding plate and a BBO crystal according to the excitation requirements. Sometimes, the harmonics is focused into a hydrogen cell with 10 bars pressure to produce the desired wavelength by stimulated Raman scattering. For the two-step excitation, another Continuum NY-82 Nd:YAG laser is used to pump another dye laser (Continuum ND-60). Usually, the dye laser or its second harmonic is employed as the first step excitation, and the laser used in the one-step excitation was utilized as the second step excitation. For two-photon excitation, a picosecond laser system is employed. A Q-switched and mode-locked Nd:YAG laser provides 25-mJ green pulses with a duration of 70 ps (measured with a streak camera). A distributed feedback dye (DFDL) laser is pumped with this beam. The output from the DFDL laser is amplified by two linear dye stages and a Ti:sapphire crystal butterfly amplifier, which are pumped by the third Nd:YAG (Continuum NY-82) laser. To reach the required wavelength region, frequency tripling is performed in an optical system, which is similar to the one described in the previous paragraphs.

2.3. Signal observation and analysis

Fig. 1. Experimental setup used in the present work.

All the Nd:YAG lasers are working in the external triggering mode and are activated by the same delay generator, which enables the temporal synchronization of the atomisation and excitation pulses. Fluorescence signals are recorded with a fast detection system, which includes a fast multi-channel-plate (MCP) photo-multiplier-tube and a fast transient digitizer. The digitalized signals are transferred to a personal computer. The lifetime evaluation is carried out by fitting an exponential to the recorded fluorescence curve for the long lifetime or by fitting the recorded fluorescence curve with a convolution between the detected laser pulse and an exponential function with

P. Quinet et al. / Journal of Alloys and Compounds 344 (2002) 255–259

257

fields experienced by the valence electrons gives rise to a two-particle term given by VP2 5 2 ad

r¢ .r¢ O ]]]]]] [(r 1 r )(r 1 r )] i

2 i

i .j

2 c

j

2 j

2 c

3/2

(3)

A further correction, introduced by Hameed and coworkers [4,5] to allow for a more accurate treatment of the penetration of the core by the valence electrons, corresponds in the present formalism to the addition to the integral `

EP

n,

0

r (r)]]]] P (r)dr 2 (r 1 r c2 )3 / 2 n‘ , ’

(4)

in (2) of the core-penetration term Fig. 2. A typical detected fluorescence signal from a 4f 10 6p level in Ho III, with a convolutional fitting.

rc

E

1 ]3 Pn , (r)rPn‘ , ’ (r)dr rc

(5)

0

adjustable parameters for short lifetime. A typical fluorescence curve with a convolutional fit is shown in Fig. 2.

When including the core-polarization and core-penetration in the Hamiltonian, the dipole-moment operator in the transition matrix element has also to be modified for consistency. The dipole radial integral `

EP

3. Theoretical calculations

n,

For heavy complex systems such as lanthanide ions, accurate calculations of atomic structures should allow for both intravalence and core-valence correlation. Simultaneous treatment of both types of effects, within a configuration interaction (CI) scheme, is very complex and reliable only if enough configuration mixing is considered. However, in practice, even a large computer imposes rather severe limitations on the number of interacting configurations that can be considered simultaneously. In particular, the inclusion of core-polarization effects through the consideration of a huge number of configurations with open inner shells is often prevented by computer limitations. Migdalek and Baylis [3] have suggested an approach in which most of the intravalence correlation is represented within CI scheme while core-valence correlation is represented approximately by a core-polarization model potential, VP . For atoms with n valence electrons, the oneparticle operator of this potential can be written as n r 2i 1 ]]] VP1 5 2 ]ad , 2 i 51 (r 2i 1 r 2c )3

O

(2)

where ad is the dipole polarizability of the ionic core and r c is the cut-off radius, which is arbitrarily chosen as a measure of the size of the ionic core. This latter parameter is usually taken as the expectation value of r for the outermost core orbitals. In addition, the interaction between the modified electric

(r)rPn‘ , ’ (r)dr

(6)

0

has to be replaced by `

a E P (r)r F1 2 ]]]] P (r 1 r ) G d

n,

2

0

2 3/2 c

n‘ , ’

(r)dr

rc

ad 2 ]3 rc

EP

n,

(r)rPn‘ , ’ (r)dr

(7)

0

In the present work, the wavefunctions are obtained by the relativistic Hartree–Fock (HFR) method described by Cowan and Griffin [6] using the suite of computer codes written by Cowan [7] in which we have incorporated the core-polarization and core-penetration correction (HFR1 CP) as described above.

4. Results The details of the experimental and theoretical procedures used for the lanthanide ions considered up to now can be found in the references listed in Table 1. Numerical results and detailed comparisons between calculated and measured lifetimes obtained in our different works are also given in these original references. Consequently, we will only present here a brief summary. Up to now, 68 radiative lifetimes for levels belonging to lanthanide ions, ranging from 1 to 200 ns, have been measured at the Lund Laser Centre using the LIF tech-

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Table 1 Lanthanide ions for which experimental (time-resolved LIF technique) and theoretical (HFR1CP) data have been obtained in the present work

Table 2 Number of radiative transitions listed for lanthanide ions in the DREAM database

Z

Ion

Method used in our work

Refs.

Z

Ion

57 58

La III Ce II Ce IV Pr III Ho III Er III Tm II Tm III Yb II Yb III Yb IV Lu II Lu III

Experiment1Theory Experiment1Theory Experiment1Theory Experiment1Theory Experiment1Theory Experiment1Theory Theory Experiment1Theory Experiment1Theory Experiment1Theory Theory Theory Theory

[8] [9,10] [11] [12,13] [14] [15] [16] [2] [17,18] [19,20] [21] [22] [8]

Number of transitions

57 58 59 67 68 69

La III Ce II Pr III Ho III Er III Tm II Tm III Yb II Yb III Yb IV Lu II Lu III

131 14 970 18 402 1324 1308 7955 1479 5485 279 2770 107 59

59 67 68 69 70

71

Original references are also given for each ion considered.

nique described in Section 2. More precisely, two experimental values have been obtained in La III, 18 in Ce II, two in Ce IV, eight in Pr III, eight in Ho III, seven in Er III, eight in Tm III, 10 in Yb II and five in Yb III. On the theoretical side, a huge number of oscillator strengths and transition probabilities have been computed using the HFR1CP method for all the ions listed in Table 1. When comparing the radiative lifetimes deduced from our calculations with the LIF measurements, we found a very good agreement in most cases as illustrated in Fig. 3. In fact, the mean deviation between theory and experiment, when available, was equal to 3, 11, 1, 14, 9, 5, 15, 15 and 13%

70

71 Total

54 269

for La III, Ce II, Ce IV, Pr III, Ho III, Er III, Tm III, Yb II and Yb III, respectively.

5. The DREAM atomic database The main purpose of DREAM (database on rare-earths at Mons University) is to provide the scientific community with an updated information concerning the lanthanide atoms and ions. In our tables, the spectra are classified in order of increasing Z values and, for a given Z, according to the ionization degree. For each spectrum, the tables show, respectively: ˚ derived from the experimental The wavelengths (in A) levels; The levels of the transitions (in cm 21 ); The calculated weighted oscillator strengths (log gf ) and transition probabilities ( gA); The cancellation factor (CF ) as defined by Cowan [7]. The different tables are accessible directly through anonymous ftp at the address umhsp02.umh.ac.be / pub / ftp]astro / dream or on the following Web site: http: / / www.umh.ac.be / |astro / dream.shtml Up to now, data are tabulated for the ions La III, Ce II, Pr III, Ho III, Er III, Tm II, Tm III, Yb II, Yb III, Yb IV, Lu II and Lu III and contain informations for more than 50 000 radiative transitions in these ions. Details are given in Table 2.

Acknowledgements Fig. 3. Comparison between experimental and calculated lifetimes obtained in the present work for La III (d), Ce II (j), Pr III (m), Ho III (.), Er III (s), Tm III (h), Yb II (^) and Yb III (,). Only values shorter than 8 ns are shown in the figure.

This work was partly supported by the European Community Access to Large-Scale Facilities programme (contracts ERBFMGECT-950020 and HPRI-CT-1999-00041).

P. Quinet et al. / Journal of Alloys and Compounds 344 (2002) 255–259

Financial support from the Swedish Natural Science Research Council (NFR) and from the Belgian National Fund for Scientific Research (FNRS) is also gratefully acknowledged.

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