
l. INTRODUCTION Chromium and zinc in the interstellar medium (ISM) are predominantly once ionized and in the ground level. Accurate absolute transition probabilities (or f-values) for transitions in these elements to the ground level are vital for correct interpretation of data from orbiting observatories. Particularly important for evaluation of the ISM are the resonance multiplets at 206 nm in Zn II and Cr II. These transitions are used not only for elemental abundance determination, but also gas versus grain phase evaluation in the ISM. The Goddard High Resolution Spectrograph (GHRS) on the Hubble Space Telescope (HST) provides an opportunity for much improved astronomical observations at these wavelengths.

Theoreticalf-values exist for transitions in both Zn II (which is isoelectronic with Cu I) and Cr II. Calculations off-values are difficult and are subject to significant errors, particularly for many-electron atoms (Blackwell et al. 1983) . The most reliable and broadly applicable experimental method of determining absolute atomic transition probabilities combines accurately measured branching fractions and radiative lifetimes. Recent works on V I , Sc I and Sc II (Lawler & Dakin 1989) , and Fe I (O'Brian et al. 1991 ) demonstrate the power of this approach using semiautomated techniques. In this paper we combine new experimental radiative lifetimes, measured by time-resolved laser-induced fluorescence, and branching fractions, measured by classical techniques, and determine accurate absolute transition probabilities for 14 transitions from the two 3d 10 (1S)4p 2 P 0 levels of Zn+ and the three 3d 4 (5 D)4p z 6 p 0 levels of Cr+.

The radiance of a spectral line at frequency vu 1 from an optically thin, homogenous length of plasma l is (1) where Au1 is the Einstein A-coefficient (transition probability) corresponding to a transition from an upper level u to a lower level 1, h is Planck's constant, and Nu is the volume density of atoms in level u in the plasma. The ratio of transition probabilities for two lines from the same upper level is equal to Uu1,/(hvur)]/ [Iu1"/(hvur') ]. In our experiment the relative quantities I uif(hvu1), branching ratios, of all significant branches from an upper level are measured; their sum is normalized to the reciprocal of the radiative lifetime: branching fractions 382 (complete sets of branching ratios) are thereby converted directly into absolute transition probabilities. By normalizing the branching fractions with radiative lifetimes, we eliminate any need to determine a plasma temperature or even to produce a plasma in local thermodynamic equilibrium. The absorption oscillator strength,fiu, is related Au1 by the relation

where A.u1 is the wavelength of the transition between the upper and lower levels; g; is the degeneracy of the level, namely g; =
21
; + 1; re is the classical radius of the electron; and c is the speed oflight.
LIFETIME EXPERIMENT
A schematic of the experiment is shown in Figure 1 . The apparatus is that used by O'Brian et al. (1991) . Time-resolved laser-induced fluorescence (LIF) on a slow atomic or ionic beam is recognized as a broadly applicable and accurate method for measuring radiative lifetimes. The atomic/ionic beam source is based on a low-pressure, large-bore hollow cathode discharge. That this source has been successful in producing atomic/ionic beams for over 30 different elements, including refractory metals such as tungsten and niobium as well as nonmetals such as carbon and silicon, demonstrates its versatility. The cathode is lined with the element of interest and a 5-50 mA DC discharge is run in 0.5 torr argon. The number of ions in the discharge is dramatically increased, with minimal heating of the cathode, by superposing on the DC discharge a current pulse of 5 µs duration and up to 20 amps. For the Zn atomic/ionic beam, we use a pure Zn liner in our hollow cathode discharge beam source even though the melting point of Zn is quite low (693 K). The Zn liner is not melted and yet sufficient Zn+ ions are generated in the beam for our measurements. To generate a Cr atomic/ionic beam, we line the cathode with cleaved strips of pure Cr.
LIFETIME EXPERIMENT
The discharge is sealed from the scattering chamber except for a 1.0 mm hole in the bottom of the cathode which is flared outward at 45° to serve as a nozzle for the atomic/ionic beam. A 10 cm diffusion pump keeps the scattering chamber at a much lower pressure (10-4 torr argon) than the discharge, forming a weakly collimated, optically thin beam which is ideal for laser excitation studies in the scattering chamber. The beam contains neutral and singly ionized species distributed in the ground and virtually all metastable levels. In particular, the metastable 3d 4 (5D)4sa 6 D levels in Cr II, at -12,300 cm-1 above the ground level, are populated sufficiently for laser excitation out of those levels into the three upper Cr II levels included in this study. Neutral species in the beam have kinetic energies slightly above thermal; ions have kinetic energies less than 0.5 eV. Two different pump lasers are used in this experiment, depending on the wavelength of radiation required. For A.> 205 nm, we use a N 2 pumped dye laser, designed and built in our lab, which produces a 3 ns duration pulse (FWHM) of 0.2 cm -l bandwidth and up to 40 kW peak power at a 50 Hz repetition rate. A set of beta barium borate (BBO) and potassium dihydrogen phosphate (KDP) frequency doubling crystals extend the lower wavelength limit to 205 nm in the ultraviolet. For A.< 205 nm, we use a Nd:YAG pumped dye laser, which produces a 10 ns pulse (FWHM) of 0.3 cm -1 bandwidth and up to 10 MW peak power at a roughly 27 Hz repetition rate. We frequency triple this radiation in BBO to the edge of the vacuum ultraviolet (VUV). When necessary, VUV radiation is generated via stimulated Raman scattering in liquid nitrogen-cooled hydrogen gas (O'Brian & Lawler 1992) .
LIFETIME EXPERIMENT
Tunable pulsed laser radiation crosses orthogonally the atomic beam 1.0 cm below the nozzle. Light baffies are placed along the axis of the laser beam, both inside and outside of the scattering chamber, to reduce scattered laser light. Orthogonal to both the laser and atomic/ionic beams, a photomultiplier tube (PMT) is used to detect the LIF. The N 2 pumped laser system uses an RCA 1P28A PMT; the Nd:YAG pumped laser system uses a Hamamatsu R1220 PMT. For the relatively short lifetimes reported here, two fused silica or MgF 2 lenses comprising an f/1 system focus the intersection of the atomic/ ionic and laser beams onto the active region of the photocathode of the PMT. A different fluorescence collection system is used when measuring longer radiative lifetimes to prevent systematic error due to atoms or ions escaping from the detection region before radiating (Marsden et al. 1988) .
LIFETIME EXPERIMENT
The signal from the PMT is recorded and averaged using a Tekronix SCDlOOO transient waveform digitizer, which has an analog bandwidth of 1 GHz and a sampling rate of up to 200 GHz. The leading edge and first few ns of the signal from the PMT is a convolution of the laser pulse and the LIF. By beginning our analysis of the signal after the laser pulse has ended (about 5 ns after the peak of the fluorescence decay signal), we avoid a deconvolution of the two components. The signal is analyzed using a least-squares fit to a single exponential. Whenever possible, at least two laser wavelengths are used to excite an upper level. This provides confidence that the level is correctly identified and that the lines are not blended. This is not possible for the two 3d 10 ( 1 S)4p 2 P 0 levels of Zn II for which only one decay branch exists. Reported lifetimes are an average of over 12,000 individual fluorescence decay curves. Statistical uncertainty is less than 0.5% (1 u) when signals are strong.
LIFETIME EXPERIMENT
The lifetime experiment has a dynamic range from roughly 2 ns to 2 µs. Near the 2 µsend of the range, systematic effects due to atomic motion dominate. An excited atom or ion in the beam can leave the field of view of the light detection apparatus before radiating, artificially shortening the lifetime. This systematic error is completely negligible for the short-lived levels studied here. The finite electrical bandwidth of the detection apparatus is a concern near the 2 ns end of the range. The base of the PMT is wired for very low overall inductance in order to maintain the full electronic bandwidth of the tube. The base includes bypass capacitors in order to provide good linearity to 10 mA of peak anode current and includes small damping resistors to reduce ringing (Harris, Lytle, & McCain 1976) . The electrical bandwidth of the detection system has previously been tested by measuring the lifetimes of the 3 1 P1 and 4 1 P1 levels of He 1 which are known to ± 1 % from very sophisticated calculations (Salih, Lawler, & Whaling 1985; Wiese, Smith, & Glennon 1966) . We also measure the lifetime of the 2s2p 1 Pi-level of Be I to test the bandwidth of our experiment. We think there is enough evidence to conclude that the radiative lifetime of the 2s2p 1 P1 level is 1.85 ± 0.05 ns. The Sims & Whitten (1973) calculation of the 2s2p 1 Pi-2s 2 1 S 0 transition probability in Be 1 approaches the reliability of the best calculations in He 1. This and other calculations on Be 1 are surveyed by Moccia & Spizzo (1985) . Accurate (± 1 %) experimental lifetimes in the 3 to 4 ns range are available from fast-beam laser measurements on Fe n (Biemont et al. 1991) , some of which we also measure to test the electrical bandwidth of our detection apparatus.
LIFETIME EXPERIMENT
Selective laser excitation eliminates repopulation of the upper level through radiative cascade which has troubled beam-foil time of flight measurements. Occasionally in our LIF experiment, a high-lying level of interest decays via infrared transitions to nearby levels which then decay to lower levels producing cascade radiation in the spectrally sensitive region of the PMT (200-700 nm). This radiative cascade through BERGESON & LAWLER Vol. 408 lower levels is possible in the three upper levels studied in Cr n. The 3d 5 d 2 D martinezeric@example.org and 47372.53 cm -l could serve as intermediate even parity levels. However, no evidence for cascade through lower levels is observed in this experiment, probably because selection rules and low frequencies suppress the infrared decay channels. Other systematic errors are avoided by the nature and construction of the experiment. In the beam environment, both radiation trapping and collisional quenching are negligible. This is tested by searching for any change in the observed lifetime while varying the beam intensity and background pressure. The magnetic field in the scattering chamber is kept near zero ( < 20 mG) when short lifetimes are measured, such as those included in this study. This eliminates the possibility of observing Zeeman quantum beats. The totality of error we conservatively estimate as the greater of ± 5% or ± 0.2 ns. This uncertainty cannot easily be identified as a 1 a or 3 a uncertainty because photon statistics actually make a negligible contribution to the uncertainty. The uncertainty for these short lifetimes is dominated by the electronic bandwidth, linearity, and overall fidelity of the data acquisition system including the PMT, coaxial cables, and transient digitizer. The previously described "bandwidth tests" of the detection system such as our measurement of short Be 1 and He 1 lifetimes are thus very important. Our goal is to have more than 90% of our lifetime measurements accurate to within one uncertainty. We note that the first ion lifetimes measured using this apparatus were in Nb II (Salih & Lawler 1983 ). These Nb II lifetimes were remeasured by Hannaford et al. (1985) using an experiment of comparable accuracy and precision. The average and root mean squared (rms) difference between Nb n lifetimes measured by Hannaford et al. and lifetimes measured by Salih & Lawler is +0.9% and 3.5%, respectively. All of these lifetimes agreed to within their combined uncertainties.
BRANCHING FRACTION EXPERIMENT
Only one electric dipole decay branch exists for the 3d 10 (1S)4p 2 P~1 2 and 3d 10 (1S)4p 2~1 2 levels in Zn II. Thus the transition probability is the reciprocal of the radiative lifetime.
BRANCHING FRACTION EXPERIMENT
The 3d 4 (5 D)4p z 6 P 0 levels in Cr II have several branches including" allowed" transitions to the 3d 5 a 6 S ground level and the 3d 4 (5 D)4s a 6 D levels ~ 12,300 cm -l above the ground level, and intercombination or spin-forbidden transitions to other low-lying even parity levels as well. Figure 2 is a partial Grotrian diagram showing the decay pattern of the z 6 P~1 2 level. The decay patterns of the other z 6 P° levels are similar. Comprehensive branching fractions measurements of complex spectra are best made on the powerful 1.0 m Fourier transform spectrometer at the National Solar Observatory at Kitt Peak (O'Brian et al. 1991) . However, the measurements for this investigation are few and the spectra are simple, thus we used a simpler apparatus.
BRANCHING FRACTION EXPERIMENT
The emission source in this experiment is the same hollow cathode discharge used in the lifetime experiment, shown schematically in Figure 3 . To avoid possible blends with the Fe 1 and II spectra in the emission source, the cleaved strips of Cr lining the cathode for the lifetime experiment, which left some of the stainless steel cathode exposed, are replaced by a Cr plated hollow cathode. A slightly wedged fused silica window near the anode transmits the uv light from the discharge, which also serves as the source of the atomic/ionic beam described in the previous section, to an Acton Research Corporation 1.0 m vacuum compatible monochrometer. This Czerny-Turner style monochrometer is equipped with a 2400 lines per mm holographic grating. The reciprocal linear dispersion in the focal plane is nominally 0.41 nm mm -1 , the slit widths are adjustable from 5 µm to 3000 µm, and the wavelength scan rate is variable in 9 steps from 0.1 nm per minute to 100 nm per minute. A strip-chart recorder is used to log the signal from a PMT located at the exit slit of the monochrometer. To improve signal to noise in the PMT output, we use an integration circuit with a 0.3 s time constant.
BRANCHING FRACTION EXPERIMENT
For the emission method we use, no information of plasma parameters, such as the absolute number density of the emitting level or the absolute temperature of the source, is needed. It is also unnecessary for the discharge to be symmetric, homogeneous, or in thermal equilibrium. However, the source must be optically thin and stable over time. When a sample is optically thick, radiation trapping occurs: photons emitted from No. 1, 1993 RADIATIVE LIFETIMES 385 one end of the sourn are reabsorbed by other atoms or ions before they escape th: plasma. When lines tied to the ground level are radiation tra>ped, the other lines from the same upper level appear artificialy strong. We compare branching ratios as a function of DC current, and hence ion density, in the source, and find a lo~·current region over which the branching ratios remain constar888a:dbb7:2d49:b3f6:8605:bf4e:caed:e5a4 we are confident the emission source is optically thin. The eriission source is largely stable over time, but small slow drifts .o occur over the duration of the experiment. We account fo: this approximately linear drift by alternately measuring !ins and averaging the results. The light detection system is li1ear over two orders of magnitude. Linearity of the detectiot system is assessed with tested MellesGriot ultraviolet neutal density filters. The relative respone of the monochrometer-PMT detection system is calibrated as a function of wavelength using an Optronics 0 2 lamp. 11is lamp is a secondary standard of spectral irradiance, not spctral radiance. As such, it has structure in the source and shmld not be imaged onto the entrance slit. This means that onlypart of the monochrometer grating and mirrors are illuminatd in a calibration run. We compensate for this by varying tie position of the 0 2 lamp in a plane perpendicular to the optical axis of the system and find no variations in the perf>rmance of the monochrometer. Uncertainties in the branchng fractions are almost entirely systematic due to the uncetainty in the 0 2 lamp calibration. We cannot describe such mcertainties as 1 a or 3 a.
RESULTS
4.1. Zn II Each of the 3d 10 {1S)4p 2 P levels in Zn II has only one decay branch. The transition probability is the reciprocal of the radiative lifetime. A comparison of radiative lifetimes for these Zn II levels is made in Table 1. The energy levels are from Martin & Kaufman (1970) . The number in parentheses following each entry is the uncertainty in the last digit(s) of the entry. The experimentalists cited in Tables 1 and 2 all made an effort to include potential systematic error in their uncertainties. It is prudent in the absence of other information to assume that the uncertainties in these cited works are 1 a rather than 3 a uncertainties. We are not aware of any previous LIF measurements for these two levels in Zn II. The various experimental methods and theoretical approaches employed are also noted in the Tables 2 and 3 are from Sugar & Corliss (1985) . Vacuum wavelengths calculated from the energy levels are used throughout this work. We note that Martin & Kaufman (1970) (1975) found two very slightly different results for the z 6 P~1 2 level based on which particular decay branch they examined. Both Pinnington et al. (1973) and Engman et al. (1975) used the beam-foil technique which has often yielded erroneously long lifetimes due to cascade repopulation. Corliss & Bozman (1962) values after applying a multiplicative correction of 0.178 to the transition probabilities are listed in the tables. This correction was suggested by Warner (1967 The z 6 P 0 -a 6 D multiplet is definitely not a pure LS multiplet. We make this claim because our measurements of the relative strengths oflines from a common upper level within this multiplet are actually more accurate than indicated by the uncertainties on the branching fractions. The uncertainty on a Table 3 is a listing of branching fractions and absolute transition probabilities for transitions from the three Cr n levels. Uncertainties in our absolute transition probabilities for Tables 2 and 3 . The relative transition probabilities or Aashamar & Luke for the z 6 Po-a 6 D transitions compare well with our values. The average and rms dift"erences for only the z 6 P--a'D transitions is +0.6% and 6.3%, respectively. In their scmiempirical calculations, Kurucz & Peytremann (1975) Morton (1991) derived from Aashamar and Luke, it is argued that Cr is depicted from the gas phase. Our newly measured transition probabilities place this argument on a finner and more quantitative basis. Observations or these lines through the ISM toward other stars using the International Ulrraulolet Explorer and Copernicus already exist (Pwa & Pottasch 1986 ) and, with our data. the determination or the relative depiction or Cr out or the gas phase may be refined. Similarly, extragalactic measurements of the gas versus grain phase can be made. These resonance and near-resonance tran· sitions in Zn 11 and Cr 11 in distant galaxies arc rcdshifted into the optical region when viewed against very distant quasars (Meyer & Roth 1990i High-resolution measurements on these redshiftcd transitions using ground-based telescopes can be made. In this manner, the time evolution of the gas versus grain phase in the universe can be studied.

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