Laser Spectroscopy Measurements of Metastable Pionic Helium Atoms at Paul Scherrer Institute

We review recent experiments carried out by the PiHe collaboration of the Paul Scherrer Institute (PSI) that observed an infrared transition of three-body pionic helium atoms by laser spectroscopy. These measurements may lead to a precise determination of the charged pion mass, and complement experiments of antiprotonic helium atoms carried out at the new ELENA facility of CERN.


Experimental Method
In the experiment, 800-ps long laser pulses of wavelength λ ≈ 1631 nm excited a transition from a pionic state (n, ) = (17, 16) with a nanosecond-scale lifetime, to a resonance daughter state (17, 15) with a τ = 5 ps lifetime against Auger decay [1] (Fig. 1). The two-body π 4 He 2+ ion [34][35][36][37] that remained after Auger decay [38,39] was destroyed in collisions with helium atoms. The laser resonance of π 4 He + was detected as a peak in the rate of neutrons, protons, and deuterons that emerged from the resulting π − absorption. The signal was superimposed on a background of π 4 He + that decayed with a lifetime of τ ≈ 7 ns [1,33].
For this experiment the πE5 beamline [40] of PSI produced a π − beam of momentum p = 83-87 MeV/c and intensity N π = (2 − 3) × 10 7 s −1 . A Wien filter and slit collimator removed most of the contaminant e − in the beam which had an intensity > 3×10 9 s −1 . The purified π − beam traversed a segmented plastic scintillator plate before entering the experimental helium target. The π − arrived in bursts at intervals t = 19.75 ns which corresponded to the f a = 50.63 MHz accelerating radiofrequency of the cyclotron. Each RF cycle contained on average N π / f a ≈ 0.4 − 0.6 π − , which were distinguished from μ − and e − by the time-of-flight and energy loss in the scintillator plate.
The resonant laser pulses of energy E = 10 mJ and repetition rate f r = 80.1 Hz were generated [2] by an injection-seeded, optical parameteric generator (OPG) and amplifier (OPA) laser system which were based on magnesium oxide doped periodically-polled lithium niobate (MgO:PPLN) and potassium titanyl phosphate Layout of the experiment. The π − beam traverses a segmented scintillation counter before coming to rest in the helium target, and the resulting metastable π 4 He + atoms are irradiated with t = 800 ps long laser pulses. The resulting neutrons, protons, and deuterons that emerge from the π − absorption in the helium nuclei are detected by 140 plastic scintillation counters that surround the target. b: Schematic layout of the laser system. From Ref. [2] (KTP) crystals (see Fig. 2 (b)). The linewidth of the narrowband component of the laser excluding the amplified spontaneous emission (ASE) was around ≈ 10 GHz. A 3 GHz uncertainty in the optical frequency of the laser pulses was introduced by the OPG and OPA processes.
The laser beam of diameter d = 25 mm entered the target chamber and irradiated > 60% of the π 4 He + atoms at a time t = 9 ns after π − arrival. We assumed that about 2.3% [33] of the π − that stopped in the superfluid helium target ( Fig. 2 (a)) formed the long-lived atoms. The estimated production rate > 3 × 10 5 s −1 of the atoms ensured that the probability of coincidence of a laser pulse irradiating an atom would be around 10 −3 .
The neutrons, protons, deuterons, and tritons that emerged from the π − absorptions tended to follow anticollinear [1,41,42] trajectories and had kinetic energies of a few tens of MeV. The arrival times and energy depositions of these nuclear fragments were measured by an array of 140 plastic scintillation counters that covered a solid angle of ≈ 2π steradians around the target. The size 40 ×35×34 mm 3 of the counters provided a < 10% detection efficiency for signal E ≥ 25 MeV neutrons [1]. We rejected most of the background e − that either arrived in the particle beam or were produced by μ − decays by removing events with small energy depositions. The waveforms [43][44][45][46][47] of the signals from the scintillation counters were recorded using some data acquisition electronics developed by us. A prototype was used earlier in an experiment to determine the limits on the annihilation cross sections σ A of antiprotons of kinetic energy E ≈ 125 keV in thin target foils [46,48,49]. The results were compared with other measurements of σ A for antiprotons of energy E = 5.3 MeV [47,[50][51][52].

Experimental Results
The blue time spectrum in Fig. 3 (a) shows the distribution of scintillator arrivals measured without laser irradiation. The peaks at t = 0 and 19.75 ns correspond to consecutive π − arrivals and contain the > 97% majority of π − that underwent immediate nuclear absorption. The remaining (2.1±0.7)% produced a spectrum of the long-lived π 4 He + that decayed with a lifetime τ = (7 ± 2) ns in the intervals between the π − arrivals.
This spectrum roughly agreed with the expected signal according to a Monte Carlo simulation [1], and with the results of a previous experiment [33] carried out using a liquid helium target. We searched for the transition (n, l) = (16, 15) → (17, 14) using a combined dye and Ti:Sapphire [53] laser to scan over a 200 GHz region around the theoretical transition frequency ν th = 781052.6(2.0) GHz [1], but no significant signal was observed. Calculations show that the daughter state (17,14) of this resonance couples to an electronically-excited π 4 He + state which leads to large polarizabilities [6] that destabilize the state against atomic collisions. We also unsuccessfully searched for the (16, 15) → (16, 14) resonance which is expected to have a large width A = 640 GHz. The reason for the non-observation is not understood, but and without (blue filled histogram) laser irradiation at time t = 9 ns. The peak in the former spectrum at t = 9 ns corresponds to the resonance signal of (17, 16) → (17,15). b: Profile of the resonance measured by scanning the laser frequency over a 500 GHz wide region and plotting the normalized counts under the peaks. From Ref. [2] atomic collisions may destroy the population in the resonance parent state (16,15). Similar effects have been observed in several pHe + states [54,55]. An alternative explanation is that the state (16,15) is not populated during the formation of the atom [24,[56][57][58][59][60]. Theoretical calculations of the formation process involve solving the dynamics of a four-body system and are complicated.
We then searched for the transition (17, 16) → (17, 15). The time spectrum shown using filled circles in Fig. 3 (b) represents data collected from 2.5 × 10 7 π − arrivals, with the OPG laser wavelength tuned to λ ≈ 1631.4 nm. We consequently detected a peak at time t = 9 ns which contained 300 events with a signalto-noise ratio of 4 and a statistical significance of > 7 standard deviations. The experimental detection rate of 3 h −1 resonant π 4 He + events is compatible with the implied production rate > 3 × 10 5 s −1 of the atoms, and with Monte Carlo simulations [1] that assume that most of the metastable pionic population occupies the parent state (17,16). The signal decreased and disappeared as expected when the laser was detuned off the resonance frequency.
The resonance profile shown in Fig. 3(b) was obtained by scanning the laser frequency and plotting the number of arrival events under the peak induced by the laser. Each data point contains experimental data collected over a 20-30 h period. The vertical error bars indicate the statistical uncertainty arising from the finite numbers of the resonant π 4 He + events. The ≈ 100 GHz width of the observed resonance is consistent with a convolution of the Auger width A = 33 GHz of state (17,15) [1] , collisional [7] and power broadening (≈ 50 GHz) effects, and the linewidth (≈ 10 GHz) of the narrowband component of the OPG laser pulses. Atomic collisions that shorten [6,54] the lifetime of the daughter state (17, 15) may cause additional broadening of the resonance. The 3.0 GHz spacing [1] between the fine structure sublines that arise from the interaction between the electron spin and the orbital angular momentum of π − is much smaller than the 33 GHz natural width of the resonance and so cannot be resolved. The best fit (blue curve) of two overlapping Lorentzian functions which take these hyperfine sublines into account had a reduced χ 2 value of 1.0, with a resonance centroid ν exp = 183760(6)(6) GHz. The statistical uncertainty of 6 GHz here arises from the finite number of detected π 4 He + , whereas the systematic uncertainty of 6 GHz contains contributions related to the selection of the fit function (5 GHz), the calibration of the laser frequency, and the uncertainty related to the OPG and OPA laser processes (3 GHz). The experimental transition frequency is larger than the calculated frequency [1] ν th = (183681.8 ± 0.5) GHz. This ν = (78 ± 8) GHz deviation is believed to be due to atomic collisions in the experimental target that shift the resonance frequency [6,7]. Collisional shifts of similar magnitude have previously been observed [54,61] for some laser resonances of pHe + . The gradient of this shift in targets of temperature T = 4 K was calculated as dν/dρ = (4.4 − 6.5) × 10 −21 GHz·cm 3 using the impact approximation of the binary collision theory of spectral lineshapes [7]. At the superfluid target density ρ = 2.18 × 10 22 cm −3 used in these experiments, the predicted blueshift corresponds to a value between ν = 96 and 142 GHz, which roughly agrees with the experimental result.
In the future we will search for other laser transitions such as (n, l) = (17, 16) → (16,15), which is predicted to be narrower by a factor of at least 10 −3 compared to the transition (17,16) → (17,15) which was recently detected [1]. The experiments will be carried out using gas targets so that the collisional shifts will be smaller. The precision of the theoretical transition frequency ν th is now limited by the experimental uncertainty of the π − mass. The precision of the calculations themselves [1], however, can be improved to better than 10 −8 for some transitions as in the HD + [62][63][64] and pHe + [17,18] cases. These experiments will complement two-photon laser spectroscopy measurements on pHe + [65] carried out at the new ELENA facility [66,67] of CERN.