Precision Lifetime Measurements of He in a Cryogenic Electrostatic Ion-Beam Trap

P. Reinhed, A. Orbán, J. Werner, S. Rosén, R.D. Thomas, I. Kashperka, H.A. B. Johansson, D. Misra, L. Brännholm, M. Björkhage, H. Cederquist, and H. T. Schmidt* Department of Physics, Stockholm University, AlbaNova University Center, 10691 Stockholm, Sweden Manne Siegbahn Laboratory, Stockholm University, Frescativägen 28, 11418 Stockholm, Sweden (Received 2 October 2009; published 18 November 2009)

The He ground state cannot bind an additional electron to form a stable bound state.However, the He À ion has been reported in beam experiments since 1925 [1].In 1955, Holøien and Midtdal [2] established theoretically that the metastable 1s2s2p 4 P o J state in He À is bound with respect to the lowest excited state of neutral He, 1s2s 3 S e (cf.Fig. 1).Since then, results have been reported from both experimental [3][4][5][6][7][8][9][10][11][12][13] and theoretical studies [11,[14][15][16][17][18][19][20][21][22] aimed at a more refined description of the energetics and metastabilities of this intriguing, highly correlated, He À state.In general, doubly excited three-electron systems attract significant attention as precise measurements of their various properties are particularly well suited to test theoretical descriptions of electron-electron interactions.In this context, He À takes a special place as the noncentral parts of the interaction potential for the electrons are much more important on a relative scale than in the corresponding neutral and positively charged atomic systems.Furthermore, due to the weak interaction with the nucleus, the wave functions of He À extend to large distances, and as subtle details in atomic wave functions may control the corresponding decays, calculations of the relaxation of excited states in He À are particularly demanding and important.
In Coulomb autodetachment processes, the total angular momentum quantum number, J, the parity, and the total energy of the system are conserved.In addition, as spinorbit interactions are weak, the total orbital angular momentum, L, and the total spin, S, are also fairly good quantum numbers.For energetic reasons, the 1s2s2p 4 P o J state in He À can only autodetach to the neutral He ground state 1s 2 1 S e , and thus the only available continua are 1s 2 l 2 L with parities ðÀ1Þ l and total angular momenta J ¼ l AE 1=2.Thus, neglecting weak radiative processes, the 1s2s2p and the 1s 2 f 2 F o 5=2 continuum.However, the main contribution to the decay is due to spin-spin and spin-otherorbit interactions (i.e., to direct relativistic couplings) between the 4 P o 5=2 level and the 2 F o 5=2 continuum.It has been known for quite some time that the J ¼ 1=2 and J ¼ 3=2 levels have lifetimes of the order of 10 s, and that the lifetime of the 4 P o 5=2 level is 30-40 times longer.However, all experimental studies up to this point have been performed under conditions requiring substantial corrections for instrumental effects and direct, high-precision measurements have until now not been possible.
Here, we present the first direct high-precision measurement of the 4 P o 5=2 lifetime, where we have effectively eliminated all instrumental influences on the result by using a cryogenic, compact, and purely electrostatic ion- The American Physical Society beam trap.In [23] (and references therein), the design of larger, cryogenically operated, ion storage rings are described.Cryogenic traps and rings are very useful for studies of stabilities of, and reactions with, loosely bound atomic and molecular systems.Such methods are essential when photodetachment by blackbody radiation influences ion stabilities under normal (room temperature) laboratory conditions.
The electrostatic ion-beam trap, ConeTrap [24], consists of two cone-shaped electrodes, where the cone openings face each other from opposite sides of a centered, grounded, box-shaped electrode (cf.Fig. 2).The trap, of total length 175 mm, is mounted inside a cryogenically cooled aluminum vacuum chamber, surrounded by a copper heat shield and an outer stainless steel vacuum chamber.This arrangement and a resistive heater allow us to regulate the common trap and inner chamber temperature to within AE1 K down to 10 K and, furthermore, to keep the system in thermal equilibrium.When ions are injected in the trap, the entrance cone electrode is kept on ground potential, and the exit cone on a potential which is slightly higher than the 2.5 kV beam acceleration voltage.The ion beam is reflected, and focused, by the electric field between the center electrode and the exit cone.During this reflection, the entrance cone is switched (rise time %100 ns) to the same value as the exit cone, thus trapping the 0:8 s long He À ion pulse.The trap is operated in the storage mode [24] giving trajectories that fill the volume indicated in the lower part of Fig. 2 (calculated by means of the SIMION package [25] for a 4 mm diameter ion beam).In order to shield the stored He À ions from thermal radiation from the beam line, the trap is mounted at an angle of 20 with respect to the incident beam (Fig. 2).Neutral He atoms leaving the trap through the hole in the exit cone are detected by a microchannel plate (MCP) detector, and we obtain decay curves through the rate of detected neutrals as a function of time.Note that the recordings of the decay curves are relative measurements, and hence knowledge of the exact value of the detection efficiency (about 50% for 2.5 keV He) is not needed for the extraction of the lifetimes.Recently, MCP detectors have been successfully tested under cryogenic conditions [26].
The 4 He À ions are produced in double collisions ( 4 He þ þ Cs ! 4 He Ã , 4 He Ã þ Cs ! 4 He À ) of 2.5 keV 4 He þ in a cesium charge exchange cell, which is out of sight from the ConeTrap interior.Approximately 0.1% of the He þ ions are converted to He À yielding typical currents of 50 pA.The period for the He À ion motion in the trap is 1:6 s, and injections are made at a repetition rate of 280 Hz, allowing 3.5 ms long measuring cycles with few He À ions in the trap.
The measured decay rate for the population of a given J level is, in general, where Àð 4 P o J Þ is the true autodetachment rate, and À BB is the rate due to photodetachment by blackbody (BB) radiation.À coll , À ion-ion , À fields , and À instr refer to the depletions due to collisions with the residual-gas, ion-ion scattering, electric and magnetic fields, and any other unknown instrumental effects, respectively.Here, we will argue that all terms on the right hand side of Eq. (1), except Àð 4 P o J Þ, are negligibly small for temperatures below 100 K.
The 1s2s2p 4 P o J state of He À is bound by only 77.5 meV relative to the 1s2s 3 S e state of He [9,11] (Fig. 1).Thus, any room temperature lifetime measurement needs to be corrected for photodetachment by BB radiation photons.Such corrections rely on calculated cross sections for photodetachment and accurate knowledge of the photon energy distribution-i.e., of the temperature (or distribution of temperatures)-that the He À ions experience throughout the measurements.
Here, we have measured the depletion of the three finestructure levels of the 1s2s2p 4 P o state of He À at 10, 50, and 296 K.At 10 K (Fig. 3) and 50 K, we measured decay rates for the J ¼ 5=2 level corresponding to lifetimes of 358:8 AE 0:7 s and 362 AE 2 s, respectively (statistical errors, 1 standard deviation).As the BB radiation driven photodetachment rate is negligible at both 10 and 50 K (see below), our low-temperature result for J ¼ 5=2 is the weighted average: ¼ 359:0 AE 0:7 s.Using this result and the photodetachment cross sections [22], we calculate the BB contributions to the total decay rate as a function of temperature and obtain the curve shown in Fig. 4.This curve yields an expected 296 K lifetime of 297:3 s, in agreement with our room temperature measurement of 296 AE 4 s.In Fig. 4, we show the present measured J ¼ 5=2 lifetimes for 10, 50, and 296 K, and results by Pedersen et al. [13] and Wolf et al. [12] at intermediate and high temperatures.The most recent theoretical result, by Miecznik et al. [20], is shown at 0 K.Note that the (measured) lifetime is independent of limited temperature variations at 10 and 50 K as, in fact, the thermal photodetachment rate is negligible for all temperatures below 100 K.In contrast, the only previous measurements below room temperature [13] required careful measurements of the full temperature distribution in order to deduce a value for the 0 K lifetime.
We measured the pressure in our cold chamber in a room temperature volume (directly connected to the cold region) to be 1:5 Â 10 À10 mbar at 10 K, 1:7 Â 10 À10 mbar at 50 K, and 4:0 Â 10 À10 mbar at 296 K.In addition, we made a room temperature measurement at a hundred times higher pressure of 4:0 Â 10 À8 mbar yielding a measured lifetime of 290 AE 10 s for J ¼ 5=2.Ascribing the full difference between the low (296 AE 4 s) and the high (290 AE 10 s) pressure results to residual-gas collisions, we determine À coll ¼ 0:26 AE 0:48 s À1 at 1:5 Â 10 À10 mbar, which is negligible compared to the measured decay rate, À measured , for J ¼ 5=2 of 2784 AE 5 s À1 .Having shown that a residual-gas density of 10 8 cm À3 does not significantly affect the measured lifetime, we may safely ignore losses due to interactions with other stored ions as, on average, only 3-4 ions are trapped per injection cycle.
As the trap is electrostatic, there is no Zeeman-mixing between the J levels.With magnetic storage devices, such mixings may contribute substantially to the depletion and have to be corrected for [10].In principle, electric fields may also induce decays.This may be through electric field induced tunneling, which is negligible at the present trap field strengths below 200 kV=m [27], and/or through Stark mixing of the J levels.However, the field induced shifts of the 4 P o J levels are only a few neV [28,29], which is negligible in relation to the fine-structure splittings (Fig. 1).In order to determine any remaining limitations in the storage time, 2.5 keV He þ ions were stored in ConeTrap.At 4:0 Â 10 À10 mbar, the storage lifetime is 6 AE 2 s, corresponding to an upper limit for contributions from other instrumental effects of À instr % 0:17 AE 0:06 s À1 .Thus, all terms of the sum in Eq. ( 1) are negligibly small except for the spontaneous autodetachment rate, and we conclude that our low-temperature measurement for the 1s2s2p 4 P o 5=2 He À level represents the true intrinsic lifetime 5=2 ¼ 359:0 AE 0:7 s.
Pedersen et al. [13] used the electrostatic heavy-ion storage ring ELISA to measure the lifetime of the 1s2s2p 4 P o 5=2 level of He À at temperatures down to below À50 C. From the average of ten temperature measurements at different positions in ELISA and the photodetachment cross sections [21,22], they determined the contribution to the measured decay rate from BB radiation, and indirectly deduced a 0 K result of 365 AE 3 s.This is significantly longer than what we report here from a direct measurement at low, well defined, temperatures and at thermal equilibrium.Most likely, the ELISA result [13] was somewhat limited in precision due to the uncertainties in their estimate of the temperature distribution.Wolf et al. [12] used an electrostatic ion-beam trap at room temperature and corrected for BB radiation by means of the photodetachment cross sections [18], and indirectly deduced a 0 K result of 343 AE 10 s for J ¼ 5=2.Miecznik et al. [20] used the multiconfiguration Hartree Fock approximation to calculate a lifetime of 345 AE 10 s.
Although the statistical quality of the present data is high, we cannot directly, in a three-component fit (with seven free parameters, including background), extract separate values for the two short lifetimes.With a double-exponential fit to the data in Fig. 3, the average lifetime for J ¼ 1=2 and J ¼ 3=2 is 10:8 AE 0:8 s (cf.Table I).Notably, this fit does yield results consistent with 213002-3 a 1:1 statistical population, at the time of production of the ions, between on one side the J ¼ 1=2 and J ¼ 3=2 levels together and, on the other side, the J ¼ 5=2 level.Assuming that all three fine-structure levels are populated in proportion to their statistical weights (1:2:3 for J ¼ 1=2, 3=2, and 5=2), a new two-component fit yields an average lifetime of 10:8 AE 0:1 s.An analysis based on different starting points for three-component fits yields separate J ¼ 3=2 and J ¼ 1=2 lifetimes of 12:3 AE 0:5 s and 7:8 AE 1:0 s under the rather well-founded assumption of a strict statistical population of the three fine-structure levels at the time of production in the cesium cell (cf. the row marked by an a in Table I).
In this work, we have used a novel technique based on a purely electrostatic ion-beam trap which may be operated at room temperature and at cryogenic temperatures down to 10 K to perform the first correction-free measurements of the lifetime of the 1s2s2p 4 P o J ¼ 5=2 fine-structure level in He À .All previous experimental studies of this lifetime have been hampered by the need to accurately measure the temperature distribution in the apparatus, and by the need to make theory based, substantial, corrections of the results.Our new, direct, high-precision measurement of the 4 P o J ¼ 5=2 lifetime of 359:0 AE 0:7 s presents a serious challenge for advanced theories describing, in detail, the properties of the spatially extended wave functions of He À (dipole polarizability 8169.1 a 3 0 [29])the lightest atomic three-electron system.
We thank Liu and Starace for providing us with their calculated photodetachment cross sections.This work is supported by the Knut and Alice Wallenberg Foundation and the Swedish Research Council.[20] 345 AE 10 a Result when the relative initial populations of the J ¼ 1=2, J ¼ 3=2, and J ¼ 5=2 levels are assumed to be 1=6, 1=3, and 1=2, respectively, (cf.text).

FIG. 1 .
FIG. 1. Schematic energy diagrams of the ground state and the lowest excited state of 4 He, and the 1s2s2p 4 P o state of 4 He À [7,9,11].

FIG. 2 .
FIG. 2. Upper:A schematic of the chamber with ConeTrap.The inner chamber, ConeTrap, the deflector (and a 4 mm diameter tube in front of it), and the detector are thermally anchored to the cold stage of the cryogenerator and may be cooled down to 10 K. Lower: Expanded view of ConeTrap illustrating simulated ion trajectories (cf.text).

FIG. 4 (
FIG. 4 (color online).Temperature dependence of the measured lifetime of the 1s2s2p 4 P o 5=2 level of4 He À .The effect on the decay rate from photodetachment by blackbody radiation can readily be seen as a decrease in the measured lifetime above 100 K.
of the rapidly autodetaching 1s2s2p 2 P o 1=2 and 2 P o 3=2 levels in the respective J ¼ 1=2 and J ¼ 3=2 levels of the quartet state (this process is often referred to as relativistically induced Coulomb autodetachment).For the 4 P o 5=2 level, autodetachment leads to a final state in which neither L nor S is conserved.Also, here Coulomb autodetachment may be relativistically induced through the very small admixtures of the 1s2pð 1 PÞ3d 2 F o 5=2 and the 1s2sð 1 SÞ4f 4 P o 1=2 level can only decay to the 1s 2 p 2 P o 1=2 continuum, 1s2s2p 4 P o 3=2 only to 1s 2 p 2 P o 3=2 , and 1s2s2p 4 P o 5=2 only to 1s 2 f 2 F o 5=2 .In the former two cases, autodetachment is governed mainly by small admixtures 2 F o 5=2 [20] levels, which have the same J and parity as 4 P o 5=2