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Physics Procedia 17 (2011) 69-76 Physics of Fundamental Symmetries and Interactions - PSI2010

Pionic Hydrogen

D. Gottaa, F. D. Amarob, D. F. Anagnostopoulosc, A. Buhlerd, D. S. Covitab,g, H. Gorkee, A. Gruberd, M. Hennebacha, A. Hirtld, P. Indelicatof, T. Ishiwatarid, E.-O. Le Bigotf, J. Martond, M. Nekipelova, J. M. F. dos Santosb, S. Schlesserf, Ph. Schmidd, L. M. Simonsg, Th. Straucha, M. Trassinellif, J. F. C. A. Velosoh, J. Zmeskald

aInstitutfUr Kernphysik (IKP), Forschungszentrum Jülich, D-52425 Jülich, Germany b Department of Physics, Coimbra University, P-3000 Coimbra, Portugal c Department of Material Science and Engineering, University of Ioannina, Ioannina, GR-45110, Greece dStefan Meyer Institut, Austrian Academy of Sciences, A-1090 Vienna e Zentralinstitut für Elektronik (ZEL), Forschungszentrum Jülich, D-52425 Jülich, Germany fLaboratoire Kastler Brossel (LKB), UPMC-Paris 6, ENS, CNRS; Case74, 4 place Jussieu, F-75005 Paris, France gLaboratory for Particle Physics (LTP), Paul Scherrer Institut, Villigen PSI, CH-5232 Villigen, Switzerland hI3N, Department of Physics, Aveiro University, P-3810 Aveiro, Portugal

Abstract

K X-rays from pionic hydrogen and deuterium as well as muonic hydrogen have been measured using a highresolution crystal spectrometer at the nE5 beam line of the Paul Scherrer Institut. From the ground-state level shifts and broadenings of the hydrogen isotopes, caused by the strong interaction, low-energy parameters of QCD become accessible as are the pion-nucleon scattering lengths and the threshold production strength of pions in nucleon-nucleon collisions. Muonic hydrogen allows important insights in the de-excitation cascade of such exotic atoms, the understanding of which is essential for a precision determination of the above-mentioned quantities. First experimental results are discussed in the context of recent results from theoretical efforts within the approach of chiral pertubation theory and atomic cascade calculations.

Keywords: exotic atoms, pion-nucleon scattering lengths, crystal spectrometer

1. Introduction

X-ray spectroscopy of hadronic atoms measures the influence of the strong interaction by means of an energy shift

6 and a line broadening r of the low-lying atomic states (Fig. 1). For the elementary systems formed with hydrogen, the ground-state parameters yield the particle-nucleon scattering lengths [1, 2, 3].

In the pion-nucleon case (nN), the two independent scattering lengths maybe expressed as the isospin even (isoscalar) and odd (isovector) combinations a+ and a- in terms of elementary nN ^ nN reactions or the isospin amplitudes I = 1/2 and I = 3/2 by

a+ - i (an-p—n~p + p—n+ p) - 3 (ai/2 + 2^3/2),

a - 2 (an-p—p - an+ p—p) - 3 (a1/2 - a3/2).

Email address: d.gotta@fz-juelich.de (D. Gotta)

1875-3892 © 2011 Published by Elsevier B.V. Selection and/or peer-review under responsibility of the Organising Committee of the 2nd International

Workshop on the Physics of fundamental Symmetries and Interactions

doi:10.1016/j.phpro.2011.06.019

n Stark mixing capture

1=0 1 2 : : n-1

^ ... Coulomb de-excitation

7 .-T-T T rs

^ -r- — 4TT. v- t-r —

_ * _i"' [l '^L-ih-Ji: external Auqer effect

r ^ Mm//

4 ^ j Mf

I //// f/ X-radiation

Figure 1: De-excitation cascade in pionic hydrogen. The hadronic shift is defined here to e1s = Eexp - Eqed. i. e.. a positive (negative) sign as is the case in nH (nD) corresponds to an attractive (repulsive) interaction.

The values for a+ and a-, obtained in the framework of current algebra half a century ago, already suggest the dominant role of chiral symmetry for the low-energy nN interaction [4, 5]. From the scattering lengths, important quantities of the interaction are derived as are the nN <r term [6, 7] and the nN coupling constant by using the Gold-berger-Miyazawa-Oehme sum rule [8, 9, 10].

The isoscalar and isovector scattering lengths are directly related to the hadronic 1s level shift and broadening of pionic hydrogen [11]:

rf x 1s

An p^n p

1 + n ) (an-p^n°n)

For pionic deuterium the level shift and broadening maybe written as a complex energy E = e-i r/2 being proportional to the also complex pion-deuteron scattering length anD. The energy shift then reads

n p^n p

+ a, 2a

n n^n n +

a+ + a

Consequently, the nD experiment yields a constraint on a+ and a- as obtained from the nH experiment. Ellipsis stand for higher order terms from Coulomb bound-state corrections, both electromagnetic and strong isospin-breaking contributions, and, in the case of nD for multiple scattering, absorptive, and few-body corrections. These corrections have been evaluated, e. g., in the framework of effective field theories like chiral perturbation theory (xPT) at the few per cent level in the case of e1s and to less than 1% in the case of r1s for the ground state of the pionic hydrogen isotopes H and D [13, 14,15,16,17,18]. The factor (1 + p) takes into account radiative capture, where P = p^-p^^ denotes the Panofsky ratio measured to be 1.546 ± 0.009 [19].

Different to the case of nH, the broadening in nD is determined by the two-nucleon absorption nNN ^ NN on the deuteron's isospin 0 nucleon-nucleon pair. Hence, the imaginary part of the pion-deuteron scattering length anD describes an absorption instead of a scattering process

rnD <* 3 anD

<* (1 + }) • a, (5)

where a denotes the strength for pion production at threshold for the NN transition pp ^ n+d. Production and absorption, i. e., a and 3 anD, are unambiguously related by detailed balance assuming charge symmetry [20, 21]. The factor (1 + 1) with S = r(KKy)+(™,le+e-) = 2.76 ± 0.04 [22] corrects again for the contribution of radiative capture n-d ^ nny.

The aim of the described experiments is a new precision determination of e1s and broadening r1s at or below the per cent level by means of ultimate resolution X-ray spectroscopy of low-lying K transitions in pionic hydrogen (nH - experiment R-98.01) and deuterium (nD - experiment R-06.03) [23].

2. Cascade effects

The precise determination of the strong-interaction shift e1s and broadening r1s in exotic hydrogen is hindered by the occurrence of atomic collision processes during the de-excitation cascade. The formation of metastable hybrid molecules like [(ppn)p]ee molecules in nH + H2 collisions, as observed in the case of muonic hydrogen [24, 25], may lead to satellite lines if radiative decay out such complex' occurs [26, 27]. Because collision and formation rate are expected to be proportional, a study of the density dependence of the X-ray line energy may reveal radiative de-excitation.

A non-radiative process, so called Coulomb transitions [28], leads to an acceleration of the still excited exotic atom. Here, the energy of one de-excitation step is converted into kinetic energy during a collision with an H or D atom (bound in a molecule). Hence, subsequent X-ray emission occurs from a moving source leading to Doppler broadening. Coulomb de-excitation was unambiguously identified in muonic [29, 30] and pionic hydrogen [31,32,33] and found to occur several times during the atomic cascade. Consequently, the Doppler contribution contains several components and, therefore, depends on the initial state of the X-ray transition. A sufficiently precise correction of the Doppler width is essential for the determination of r1s. Therefore, the standard cascade model [34] has been extended in order to include the development of the kinetic energy distribution during the cascade (ESCM - extended standard cascade model [35]).

3. Experiment

The improvements achieved in the recent experiment compared to earlier ones [36, 37, 38, 39] are based on the measurement of several transitions at various conditions (Tab. 1), a new method to determine the spectrometer's response, and a significantly better background suppression.

The measurements were performed at the high intensity pion channel nE5 of the Paul Scherrer Institut (PSI) (Fig. 2). The pion beam of 85 MeV/c momentum was stopped in a target cell centered in the cyclotron trap. The cyclotron trap winds up the range curve of the pions in a weakly focusing magnetic field thus increasing the stop density by a factor of about 200 compared to a linear stop arrangement [40]. The necessary energy resolution of about 10-4 in the few keV range is achieved with a Bragg spectrometer using spherically bent quartz and silicon crystals of 10 cm in diameter with a radius of curvature of about 3 m [3]. As a two-dimensional position-sensitive focal plane

Figure 2: Setup for the nH(2p - 1s) experiment in the nE5 area at PSI. The roof of the concrete shielding is omitted to show the vacuum system connecting the cyclotron trap (upper right), crystal chamber (upper left) and the cryostat of the X-ray detector (bottom left). The concrete shielding suppresses substantially the pion-induced neutron background.

detector an array of six charge-coupled devices was used [41, 42]. Typical count rates for K transitions from exotic hydrogen are 20 to 50 per hour depending on initial state and target density.

The experiment comprises a series of measurements to studying the influence of the cascade effects depending on target density and initial state as well as muonic hydrogen and pionic deuterium.

• At first, the nH(3p - 1s) transition was measured at the densities equivalent to pressures of 3.5, 28 and 785 bar, which corresponds to liquid hydrogen. The density was adjusted by means of temperature using a cryogenic target.

• The dependence of the Doppler broadening on the principle quantum number of the initial state was studied for the transitions nH(4p - 1s), nH(3p - 1s), and nH(2p - 1s) at an equivalent density of 28 bar. Corrected for the experimental resolution, a significant increase of the X-ray line width is observed with decreasing principle quantum number of the initial state [33].

• In order to determine the quality of cascade codes predicting the kinetic energy distribution at the time of X-ray emission, the (3p - 1s) line of muonic hydrogen was measured at 10 bar target density. Here, without strong interaction, any broadening exceeding the experimental response must be attributed to Coulomb de-excitation.

• The hydrogen experiments were completed by high statistics studies of the nH(4p - 1s) and nH(2p - 1s) transitions, were the Doppler broadening was found to be minimal and maximal, respectively.

Finally, the experiment was performed with pionic deuterium using the (3p -1 s) transition at equivalent densities 3, 10, and 20bar.

Table 1: Energies of exotic-atom transitions (upper half) and calibration lines used for the shift measurement (lower half), Bragg crystal, reflecting plane, and Bragg angle of the various measurements.

X-ray transition energy / eV reflecting plane Bragg angle

juH(3p - 1 s) 2250 Si(111) 61.51°

nH(2p - 1s) 2436 Si(111) 54.23°

nH(3p - 1s) 2886

Si(111) / quartz 10-1 43.24° / 39.98°

nH(4p - 1s) 3043 Si(111) 40.52°

nD(3p - 1s) 3075.52 Si(111) 40.00°

X-ray transition nO(6h - 5f) Ga Ka2

energy / eV 2881 9224.464

reflecting plane Si(111) / quartz 10-1 Si (333)

Bragg angle 43.34° / 40.02° 40.01°

The resolution function of the crystal spectrometer and other crystal parameters were determined with X-rays from helium-like sulphur, chlorine and argon as outlined in [43, 44, 45] (Fig. 3 - left). In these highly ionised atoms, the energies of the M1 transitions (2430, 2765, and 3104 eV) coincide almost perfect with the energies of the pionic hydrogen and helium lines. The response for the juH(3p - 1s) transition is obtained by extrapolation. The resolution was found to be of the order of 500 meV. This is close to the theoretical limit given by the convolution of the intrinsic width as calculated from dynamical diffraction theory [46] and geometrical effects taken into account by means of a Monte Carlo ray-tracing code.

Figure 3: Left: M1 line from helium-like sulphur (S14+) used to determine the spectrometer response at the energy of the nH(2p - 1s) transition. Right: line shape of the ¡j.H(3p - 1s) transition (from [30]).

4. Results

Figure 3 (right) shows the significant Doppler broadening of the juH(3p - 1s) line caused by the acceleration due to Coulomb de-excitations. The narrower structure, composed of the hyperfine ground-state doublet having a splitting of 183 meV [47], is the calculated response as obtained from the above-mentioned measurement of helium-like low Z atoms and folding in the experiments's geometry. From the deconvolution two (high-energy) Coulomb components, (4 - 3) and (5 - 4), were identified having a relative intensity of about 20% each [30]. About 60% of the juH atoms were found to have kinetic energies of 1 eV or less (low-energy component), i. e., being non accelerated or having been slowed down again during the preceding steps of the atomic cascade. Thus result is about 15% below the first

12010080-

CD 7T H(3p-1 s)

1 quartz 101

o to 1.4 bar T=98K

t= 1 ^ (3.5 bar)

CO cT Jl

2880 2882 2884 2886

energy/eV

Si 111 ®n=40'

7rD(3p-1s) { (10+20bar)

fit .....

response

x/channels

Figure 4: Left: line shape of the nH(3p - 1s) line measured simultanuously with the nO(6 - 5) transitions using a H2/O2(1.9%) gas mixture. Right: the narrow line inserted in the nD(3p - 1s) line shape displays the spectrometer resolution (from [50]).

Table 2: Results for hadronic shifts and broadenings of PSI experiments R-98.01 and R-06.03, which represent an improvement of factors 2 - 5 compared to previous experiments [36, 37, 38, 39].

eu / meV

ris / meV

720 ± 11 2356 ± 31

823 ± 19

+ 23 - 49

+ 5 - 11

R-98.01 R-06.03

[33] [50, 51]

predictions of ESCM. More recent calculations for the atomic cross sections [48] led to a significant improvement in the description of the juH(3p - 1s) line shape [30,49].

In nH and nD, the hadronic broadening dominates the line width of the ground state transitions (Fig. 4). The total line is composed of the natural width r1s, the spectrometer response and a superposition of contributions from Coulomb caused Doppler broadening. In the fit, r1s and up to three Doppler components were treated as free param-

In the nH(3p - 1s) and nH(4p - 1s) transitions, the low-energy component (<1 eV) and the Coulomb transition (high-energy component) preceding the X-ray transition were found to be of comparable weight (about 50% each). No An > 2 or higher lying Coulomb transitions could be identified. For the nH(2p - 1s) transition, however, the high-energy component results from the (5 - 4) Coulomb transition, the one but last step preceding the X-ray emission.

Surprisingly, no evidence for any high-energy component was found in the case of nD at the 10% level [50]. This difference in the cascades of nH and nD is not understood at present. Preliminary results for shift and broadening in nH and the final results for nD are given in Table 2.

The recent data from the nD [51] and nH level shifts together with the nH broadening (preliminary [33] were evaluated in the framework of ^PT yielding for the first time a consistent result for a+ and a- [52] (Fig. 5 - left). Whereas the uncertainty of the bands derived from the level shifts of nH and nD is dominated by the theoretical uncertainty, the error for a~ determined from the nH level width is almost entirely due to the experiment. In particular, the insufficient knowledge of the relative intensity of the various Doppler components contributes about half of the error. A detailed study of the corresponding systematics stemming from the experimental conditions and the cascade effects is ongoing.

The threshold parameter for threshold pion production, determined from the hadronic broadening in nD is compared to results from pion production experiments and to theoretical calculations (Fig. 5 - right). A significant improvement on the theoretical accuracy is expected from forthcoming calculations of higher orders in^PT [53, 54].

i I1' t "1 T 9 ...........,□......... I V V 1 V...... ' v X 7 JT

• this work A previous atom data □ production data v theory

Figure 5: Left: constraints for the isospin-separated pion-nucleon scattering lengths a+ and a- as obtained in an analysis within the framework of ^PT from the hadronic shift and broadening in nH and the hadronic shift in nD (from [52]). Right: threshold parameter a for s-wave pion production as obtained from the hadronic broadening in nD compared to pion-production data (from [50]).

5. Summary

Ultimate X-ray spectroscopy allows the determination of the hadronic shifts in pionic hydrogen and deuterium to well below 1% whenever an appropriate energy calibration line is available. The somewhat larger uncertainty in the case of nD stems from the poor knowledge of the Ga Ka2 calibration line [55], which contributes 90% of the error, but matches sufficiently well enough the accuracy achievable with present theoretical techniques of ^PT.

In the case of the line broadening, the limit of about 3% is determined by the quality of the correction for the Doppler broadening arising from Coulomb de-excitation. Statistics allows an improvement by a factor two, if cascade calculations could be put forward to predict reliably the kinetic energy distribution of the exotic hydrogen atom at the time of X-ray emission. Efforts in obtaining improved cross sections for a better description of the collisional processes are going on.

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