paul scherrer institut

CH-5232 Villigen PSI, Switzerland

KINETIC ENERGY OF pi¯p-ATOMS IN LIQUID AND GASEOUS HYDROGEN

A. Badertscher¹, M. Daum°, P.F.A. Goudsmit¹, M. Janousch¹, P.-R. Kettle°, J. Koglin²°, V.E. Markushin°, J. Schottmüller³° and Z. G. Zhao¹

° PSI, Paul-Scherrer-Institut, CH-5232 Villigen-PSI, Switzerland
¹ IPP, Institut for Particle Physics, ETH Zürich, CH-8093 Zürich, Switzerland
² Physics Department, University of Virginia, Charlottesville, Virginia 22901, USA
³ Physik-Institut der Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland

Abstract

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We have measured the Doppler broadening of neutron time-of-flight spectra from the reaction pi¯ p -> pi° + n in atomic states. From the data, we infer that the kinetic energy distribution of pi¯p-atoms in liquid and gaseous hydrogen contains discrete `high-energy' components with energies as high as 200 eV attributed to Coulomb de-excitation. In liquid hydrogen, evidence for Coulomb de-excitation transitions with delta n = 2 has been found.

Introduction

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Evidence for a substantial fraction of highly energetic (>>1 eV) pi¯p-atoms in the charge exchange (CEX) reaction pi¯ p -> pi° + n, in liquid hydrogen, was seen in our previous experiments [1-3]. The effect is observed as a Doppler broadening of the neutron time-of-flight (TOF) peak, which is related to the kinetic energy distribution f(Tpi p) of pi¯p-atoms at the instant of the CEX-reaction. Later experiments gave further evidence for such `high-energy' components in both liquid and gaseous hydrogen [4,5]. A precise knowledge of the kinetic energy distribution of the pionic hydrogen atoms is important for the determination of the strong interaction width of the ground state in pionic hydrogen from the measurement of pionic X-ray transitions [6-9].
The observed Doppler broadening of the TOF-spectra [1-5] can be attributed to Coulomb de-excitation [10] (pi¯ p)n + p -> (pi¯ p)n' + p ¹, where the de-excitation energy associated with the transition is shared as kinetic energy between the collision partners. Other cascade processes, such as external Auger effect, are only able to cause a moderate acceleration of the pionic atom (~ 1 eV) [14].
The kinetic energy of the pi¯p-atom after a Coulomb de-excitation transition is given by

neglecting the initial kinetic energy of the pionic atom. Here delta Enn' is the energy difference of the two atomic states n and n'; Mpi p and mp are the masses of the pi¯p-atom and the proton, respectively. The corresponding idealized energy distribution f(Tpi p) is shown in Fig.1, where only transitions with delta n =1 are considered. For the sake of simplicity, the low energy part of f(Tpi p) is approximated by a uniform distribution between 0 and T1. This Tpi p-distribution (Fig.1a) leads to the step-like neutron TOF-distribution shown in Fig.1b, where tau is the difference between TOF (t) and the mean TOF (t0). The times tau1 and taunn' in Fig.1b are related to the kinetic energies T1 and Tnn' as follows [15]:

Here, l is the length of the flight path, and v0 = 0.894 cm/ns is the neutron velocity for pi¯p-atoms undergoing the CEX-reaction at rest. At this point we assume that the pi¯p-atoms are not significantly decelerated between Coulomb de-excitation and nuclear capture. This assumption is supported by cascade calculations [5] for atoms with a kinetic energy of T >= 50 eV. Therefore, a signature for Coulomb de-excitation would be a step-like structure visible in the TOF-spectra of neutrons from the CEX-reaction. For atoms with T <= 20 eV the deceleration is important, and the Coulomb peaks are expected to be smeared out.

¹ It is not excluded that Coulomb de-excitation is part of some new mechanism, e.g. the formation of a resonant state, as was suggested for n = 2 [11-13].

The new experiment

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The present experiment was performed at the piE1-channel of PSI; the experimental setup is shown in Fig.2. The following improvements to the previous experiments [1-4] were made: (i) a reduction of the background by introducing several neutron collimators as well as using specially selected low noise photomultiplier (PM) tubes for the neutron counters; (ii) improvement of the time resolution of the neutron counters by placing them in adjustable holders so as to point radially at the target for the different neutron flight-paths; (iii) increased counting statistics by enlarging the solid angle of the neutron detector and using a new beamline setup.
Pions of 117 MeV/c passed the beam counter S1 (see Fig.2) and a carbon degrader, the thickness of which was optimized for a maximal stop rate in the hydrogen target. The liquid target (LH2) had a length of 9.3 cm in the direction of the pion beam and a thickness of 0.5 cm in the direction of the neutron flight path perpendicular to the pion beam. The 40 bar gas target was operated at room temperature and had a length of 21.2 cm in the direction of the pion beam and a diameter of 14 mm. Neutrons from the hydrogen target were detected after a flight path of variable length (3 - 11 m) in a detector array consisting of 36 scintillator disks coupled directly to PM-tubes. For the measurements in liquid hydrogen, we used PILOT-U scintillators with a thickness of 5 mm, whereas for the measurements in gas, NE102A scintillators with a thickness of 15 mm were used in order to partially compensate for the lower pion stop density. The neutrons from the CEX-reaction in the target were accepted only if coincident with a suitably delayed pi-stop signal and a corresponding gamma-ray signal from pi°-decay in a NaI-calorimeter [16].

Data analysis

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The data are in form of TOF (TDC) and pulse-height distributions (ADC). In a first step of the analysis, which is very similar to that of Ref. [4], a lower and an upper ADC-cut were introduced for each neutron counter separately, in order to suppress noise events from the PMs (lower ADC-cut) and accidental events triggered by photons from the pi°-decays or bremsstrahlung from beam electrons (upper ADC-cut). Both ADC-cuts were optimized for a maximal signal-to-noise ratio for each neutron counter separately. Before summing the spectra of all 36 neutron counters, the centre of each neutron peak was shifted by a few TDC-channels to the same channel number, in order to correct for small transit time differences in the PMs and cables as well as small differences in the individual neutron flight paths.
In a second step, cuts were applied to the summed photon energy from the NaI-calorimeter, accepting only events between 60 and 110 MeV. In this way photons from bremsstrahlung and from the pi¯ p -> gamma n reaction were suppressed. These cuts were also optimized for a maximal signal-to-noise ratio. The small remaining background in the TOF-spectra, consisting of a flat component from noise events and accidental peaks from bremsstrahlung and 130 MeV photons from the reaction pi¯ p -> gamma n, was determined and subtracted.
The resulting TOF-spectra, taken at 3.82 m, 8.39 m and 11.10 m between the liquid hydrogen target and the neutron detector and at 3.83 m and 8.40 m in gaseous hydrogen, are displayed in Figs.3 and 4, respectively. In both cases, the expected step in the TOF-distribution from the Coulomb de-excitation transition 3 -> 2 (Tpi p = 209 eV) is clearly visible. From the resulting TOF-spectra we have obtained the kinetic energy distribution f(Tpi p) using three different methods.
In method A, based on the TOF-distribution model (cf. Fig.1b), the three spectra measured in liquid hydrogen were fitted simultaneously by TOF-distributions, generated by a detailed GEANT Monte Carlo programme [17] which accounted for the stopping distribution in the target, geometric effects (intrinsic time resolution) and neutron scattering. Similarly, the two spectra measured in gaseous hydrogen were fitted to their respective Monte Carlo distributions. The fit to the data taken with liquid hydrogen was restricted to a region from -15 to +1 ns at 3.82 m, from -25 to +2 ns at 8.39 m and from -30 to +2 ns at 11.10 m, to minimize the contributions from scattered neutrons. For the data taken with gaseous hydrogen, the corresponding fit regions were from -15 to +2 ns at 3.83 m and from -25 to +2 ns at 8.40 m. The free parameters were (i) four yields corresponding to the Coulomb de-excitation transitions with principal quantum numbers 6 -> 5, 5 -> 4, 4 -> 3, and 3 -> 2; (ii) a yield for all Coulomb de-excitation transitions with n > 6; (iii) an upper energy bound for the above transition; (iv) two yields for the Coulomb de-excitation transitions 6 -> 4 and 5 -> 3 with delta n = 2 (not included for gaseous hydrogen); (v) the energy parameter T1 (cf. Fig.1a); (vi) a distance independent Gaussian time-jitter corresponding to electronic contributions to the time resolution of the detector system; (vii) two (H2 gas) or three (LH2) normalization factors for the ordinates, and (viii) two (H2 gas) or three (LH2) shifts to match the time scales of the experimental histograms.

Table 1
Fitted yields Ann' of Coulomb de-excitation peaks in the kinetic energy distribution f(Tpi p) for the transitions n -> n' in liquid and gaseous hydrogen.

The energy shift observed in Ref.[4] can be accounted for and made to vanish in our present analysis if we include the delta n = 2 Coulomb de-excitation transitions. Then the resultant energies Tnn' [cf. Eq. (1.1)] for n <= 6 perfectly match the theoretical values derived for Coulomb de-excitation, and do not have to be taken as free parameters. These fits gave a chi²/DOF of 0.96 with 739 degrees of freedom (DOF) for the measurements in liquid hydrogen and a chi²/DOF of 0.93 with 432 degrees of freedom for the measurements in hydrogen gas; this corresponds to confidence levels of 76.2 % and 84.1 %, respectively. In the gaseous hydrogen fit, the components with delta n = 2 were not included because the statistics were not sufficient to resolve these transitions. The values for the relative yields Ann' of the transitions are listed in Table 1. For the low energy component of f(Tpi p), we found T1 = (1.0 ± 0.2) eV for liquid hydrogen and T1 = (1.6 ± 0.3) eV for gaseous hydrogen. The upper energy bound for the sum of all Coulomb de-excitation transitions with n > 6 is Tn>6 = (7 ± 1) eV for liquid hydrogen and Tn>6 = (7 ± 2) eV for gaseous hydrogen.
For comparison, a fit to the liquid hydrogen data was made without the Coulomb de-excitation components with delta n = 2 (see Table 1). This fit gave a chi²/DOF of 1.06 with 741 degrees of freedom, which corresponds to a confidence level of 12.4 %. The difference in the chi²/DOF between the two fits in liquid hydrogen is not very significant; however, there is a strong hint for components with delta n = 2 from two other model independent methods (B,C) used to extract the kinetic energy distribution f(Tpi p) from the data.
In method B, no assumptions about the positions of the peaks were made. Here, the data measured in liquid and gaseous hydrogen were fitted using a kinetic energy distribution consisting of 16 energy bins (from Ti-1 to Ti); this corresponds to 16 equidistant time bins (from taui-1 to taui). The kinetic energy distribution f(Tpi p) was assumed to be constant within each bin. The relationship between the times taui and the energies Ti is given by as in Eq. (1.2) with Ti [eV] = (i = 1,...,16). The fit was restricted to the same regions in the TOF-spectra as described above. The resulting kinetic energy distributions are shown in Fig.5. The yields Ai correspond to the height of the respective bins. In both kinetic energy distributions, a sharp decrease after the transition 4 -> 3 and indications for discrete peaks due to Coulomb de-excitation can be seen. Moreover, in the kinetic energy distribution for liquid hydrogen, a small peak in the region between 100 eV and 121 eV is visible which could be assigned to the Coulomb de-excitation transition 5 -> 3 corresponding to an energy of 107 eV. In the distribution for gaseous hydrogen, the error bars are larger due to the lower statistics.
Method C is based on the direct reconstruction of the kinetic energy distribution from the deconvoluted TOF-spectra. Here, the TOF-spectra are deconvoluted with Monte Carlo generated TOF-distributions, taking into account neutron scattering and the intrinsic time resolution, as well as a distance independent Gaussian time-jitter corresponding to electronic contributions to the time resolution. From these monotonously decreasing, deconvoluted TOF-distributions F(tau), we have calculated the cumulative energy distributions W(Tpi p), which are given by

with

For the calculation of W(Tpi p), only the fast side of the neutron TOF-spectra was used to minimize contributions from scattered neutrons. Finally, the kinetic energy distributions f(Tpi p) can be calculated as follows:

The final results in Fig.6 were obtained by averaging the kinetic energy distributions for the three different distances in liquid and the two distances in gaseous hydrogen. The shapes of these distributions are consistent with those of Fig.5.

Conclusions

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We have confirmed the existence of strong `high-energy' components (Tpi p >>1 eV) in the kinetic energy distribution f(Tpi p) of pi¯p-atoms in both liquid and gaseous hydrogen at the instant of the CEX-reaction. The results obtained with three different methods of reconstruction of the energy distributions are self-consistent. These `high-energy' components contain about half of the pi¯p-atoms (see Table 1), and about four percent have kinetic energies as high as ~200 eV. The shapes of the energy distributions strongly support the Coulomb de-excitation like origin of the `high-energy' components and further give evidence for delta n = 2 Coulomb de-excitation transitions. The inclusion of the delta n = 2 Coulomb de-excitation components in the present analysis made the previously claimed energy shifts in Tnn' [4] vanish. Our results favour the recent calculations of the Coulomb de-excitation process [18,19], which predict relatively high rates and resolve a long standing discrepancy between past calculations [10,14,20-22].

Acknowledgments

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We thank Z. Hochman, L. Knecht and H. Obermeier for their very competent technical assistance. The support from the Hallendienst and many other PSI staff members is gratefully acknowledged. This experiment was supported by the Schweizerischer Nationalfonds zur Förderung der wissenschaftlichen Forschung.

References

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Pictures of the NTOF-Experiment

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NTOF LH2Target (112 kB)

NTOF-Crew (110 kB)

Neutron detector (DIOGENES) (102 kB)

The NTOF beam line (98 kB)

The piE1 beam line

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