- Email: [email protected]
Determination of the strong interaction shift in pionic hydrogen with a high resolution crystal spectrometer system
Volume 261, number 1,2
PHYSICS LETTERS B
23 May 1991
Determination of the strong interaction shift in pionic hydrogen with a high resolution crystal spectrometer system W . Beer, M . B o g d a n , P . F . A . G o u d s m i t , H . J . L e i s i , A.J. R u s i E1 H a s s a n i , D . Sigg, St. T h o m a n n , W. Volken :
lnstitutJ~r Mittelenergiephysik der ETHZ, CH-5232 Villigen PSI, Switzerland D . B o v e t , E. B o v e t z, D . C h a t e l l a r d , J.-P. Egger, G . F i o r u c c i 2
Institut de Physique de l'UniversitO, Breguetl, CH-2000 Neuch(tteL Switzerland K. G a b a t h u l e r a n d L . M . S i m o n s
Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland Received 15 January 1991
The 3P-IS X-ray transition energy was measured in pionic hydrogen with a double focussing silicon crystal spectrometer in combination with a cyclotron trap and CCD detectors: E = 2885.98 +_0.17 (stat.) + 0.15 (syst.) eV. The corresponding strong interaction shift ~ts = - 7.12 + 0.32 eV (attractive) yields the scattering length combination ] (2a: + a 3) = 0.086 _+0.004 m~ i.
The p i o n - n u c l e o n strong interaction can be studied at zero energy by measuring the strong interaction shift ~lS and the strong interaction b r o a d e n i n g F~s o f the 1S level in pionic hydrogen. The S-wave scattering lengths al (isospin ½) a n d a 3 (isospin 3) are o b t a i n e d directly from ~ls and F~s through the Deser formula [ 1 ] 4Els ~,s = - - (2a, 3rB
-t-a3)
,
ffls = 1 6 a E l s ( l + l ) ( a l - - a 3 ) 2 9ra where E~s is the binding energy o f the 7t- in the IS orbit, rB the corresponding Bohr radius, Q a reduced mass factor and P the Panofsky ratio. The scattering lengths can also be o b t a i n e d indirectly from dispersion relations using phase shifts from low energy 7tN scattering and charge exchange d a t a and extrapolating to zero energy [2 ]. This proDeceased. 2 Also at Ecole d'Ing6nieurs, CH-2610 St. Imier, Switzerland. 16
cedure is indirect in the sense that extensive theoretical treatments o f the experimental d a t a are necessary. Moreover, results from different scattering experiments lead to solutions for the low-energy parameters which are mutually inconsistent [ 3 ]. The first pionic hydrogen experiment with a clear signal and adequate signal to background ratio was published in 1985 [4]. This m e a s u r e m e n t o f the strong interaction shift els yielded a direct determination of2a~ + a 3 = 0 . 1 7 8 + 0 . 0 1 9 m~-1 . The present experiment ~l is a first step in an att e m p t to d e t e r m i n e both s-wave scattering lengths directly, from a measurement o f the shift E~s and the b r o a d e n i n g F~s in pionic hydrogen. In this letter we report on a m e a s u r e m e n t o f e ~s to a precision o f five percent. An accurate d e t e r m i n a t i o n o f the X-ray transition energies in pionic hydrogen is not an easy task on account o f the low energy o f the corresponding X-rays and the weak signal associated with the necessary use o f a gaseous target. There are several possibilities to i m p r o v e u p o n the previous measure~l An earlier version of this experiment is described in ref. [5 ].
0370-2693/91/$ 03.50 © 1991 - Elsevier Science Publishers B.V. ( North-Holland )
Volume 26 l, number 1,2
PHYSICS LETTERS B
ment [4 ] which was performed using crystal diffraction. By replacing the graphite crystal with Si ( 111 ) crystals, the energy resolution could be improved by almost an order o f magnitude. The corresponding loss in luminosity was partly compensated by an elaborate device for maximizing the pion stopping rate in the low-density hydrogen target: the cyclotron trap. Furthermore background was minimized by using CCDs as X-ray detectors. The experiment was carried out at PSI (Paul Scherrer Institute, formerly SIN) at the hE3 channel tuned to deliver 85 M e V / c n - with an intensity o f typically 2.5 × 106/~- s-1. The setup is presented in figs. I and 2. It consists o f a cyclotron trap [ 6 ], a high resolution double focussing silicon crystal spectrometer of the reflection type [ 7 ] and position sensitive C C D X-ray detectors [ 8 ]. Target, crystals and detectors are located on a 3 m diameter focal circle (see fig. 1). The principle o f the cyclotron trap is to wind up the range curve of the 85 M e V / c pion beam in a weakly focussing magnetic field. This field with a central value o f 2.5 T is produced by a superconducting split coil magnet. After radial injection the pions spiral towards the center while loosing energy in a few thin degraders and finally the target gas. One o f the thin degraders was a scintillator used as a monitor for incoming pions. The pions entered the cylindrical
,
®
Fig. I. Schematic layout: (l)argon source for calibration, (2) hydrogen target, ( 3 ) crystal assembly, (4) CCD detector system at argon focus position, (5) CCD detector at hydrogen focus position (fis focal distance), (6) Braggangle, ( 7 ) Rowlands circles.
23 May 1991
Fig. 2. Schematic view of the experimental setup: ( 1) position of H2 target cell at 1 atm. and 20.6 K (15psTp), (2) cyclotron trap, ( 3 ) cooling system for the H 2 gas target, (4) n - beam trajectory, (5) argon gas stability monitor, (6) crystal assembly, (7) laser for alignment and adjustments, (8) example of X-ray trajectory, (9) soft flange between helium tube and CCD support, (10) 3 CCDs mounted in the vertical focal plane ( T= 170 K, p= 10-~ Torr), ( 11 ) liquid N2 container, (12) stepping motors for precision moving of CCD support.
target cell which was placed coaxially with the cyclotron trap through a cylindrical mylar window o f 40 m m diameter and 50 ~m thickness. The cooled cell was filled with saturated hydrogen vapor o f 1 atm pressure corresponding to 15pSTP. Since the low stopping rates at small hydrogen gas pressures are partially compensated by an increased X-ray yield, this low gas density was used to minimize the cell windows. The number o f pions stopping in the target was approximately 2 X 105 s - 1 for a primary beam o f 100 ~A. A fraction o f the pionic X-rays left the target cell at one of its faces through a 12 ~m thick Kapton foil and entered the crystal spectrometer which was filled with He gas through an identical window. The crystal arrangement o f the spectrometer confjsists o f 13 spherically bent Si ( 111 ) crystals, 100 p.m thick, with a diameter o f 5 cm each. These crystals were obtained from Philips Research Laboratories, Eindhoven. The crystal curvatures were achieved by mounting them under v a c u u m onto glass supports 17
Volume 261, number 1,2
PHYSICS LETTERS B
with the required curvatures. Special care was taken to align each individual crystal. Integral reflectivity was 8% and overall energy resolution approximately 3 eV FWHM. The 3P-1S pionic X-rays were scattered through a Bragg angle of 43.37 °. They entered the X-ray detector module through a 12 ~tm Kapton window. The 3P-1S transition was chosen for its higher X-ray energy and nearby calibration line after yield measurements showed that this possibility existed. The position sensitive detector consisted of three CCD ~2 mounted in a vertical row. Their size is 8.5 m m × 12.7 m m (385X576 pixels, 20 ~tm×20 ~tm each, separated by 2 ~tm). For charge transfer and readout a special electronics was built [ 8 ]. In order to minimize thermal noise the CCDs are operated at - 100°C. The advantages of using CCDs lie in their excellent intrinsic position resolution (in our case 22 ~tm), together with good energy resolution ( ~<220 eV F W H M ) which helped to reduce background by imposing an adequate energy window. The CCD background rejection capabilities are excellent. They are based on the fact that, in most cases, an X-ray in the 2-3 keV energy range deposits its energy in a single pixel. The whole spectrometer set-up was precisely aligned and temperature stabilized. For on-line stability checks a cell filled with argon gas was moved in front of the hydrogen target. The nearby argon I ~ Xrays, obtained by irradiation with 55Mn X-rays from a SSFe source, were monitored. For this the detector module was moved a few cm to the appropriate focal plane position using remotely controlled stepping motors. To this end the arms connecting target, crystals and detectors contained soft rubber bellows. An IBM PC was used for data acquisition and linked to a SUN work station which controlled spectrometer movement, position, temperature etc. Data were taken in units of 6 h [4 pionic hydrogen runs of 80 min each and a 40 min argon run during which the routine maintenance inside the area (helium and nitrogen refills etc.) was carried out]. Data were stored on the IBM disk and an on-line analysis was performed. In the off-line analysis only runs with a sufficient number of stopped pions were included. The excel~2 EEV (EnglishElectricValve),WaterhouseLane,Chelmsford, Essex, CM1 2QU, England.
18
23 May 1991
lent two dimensional position resolution of the CCDs allows for a sophisticated highly efficient pattern-recognition algorithm that reduces background almost to zero [ 9 ]. We demanded that a single pixel X-ray lies in an appropriate energy window and that the surrounding eight pixels are only charged by the intrinsic electronic and thermal noise of the CCDs. Charged particles, high-energy ?-rays and neutrons charge in general at least one neighbouring pixel. In order to reject multi-pixel events the eight neighbouring pixels of the one-pixel events must have an energy below a low-level limit normally chosen just above the noise level. In addition we applied cuts on the mean value, the standard deviation and the center of gravity of the eight surrounding pixels, decreasing thereby the background level by an order of magnitude. A less elaborate analysis [ 10 ] yields the same hydrogen peak position within statistics. For calibration we used the argon K~ and K~: lines (E=2957.790+0.009 and 2955.661+0.012 eV) [ 11 ]. Since the experimental energy resolution was not sufficient to fully separate the double line, the lines were unfolded by representing the I ~ line by a polygon and adjusting it into the measured line using the fact that the energy difference (2.13 eV) and the intensity ratio (2 : 1 ) of the I ~ l and I~a lines are known (see fig. 3). In order to equalize the source
m~
1
2
3
4
5
6
7
8
100 80
6O -p
5 o
u 40
20
10 20 30 40 50 60 70 channet Fig. 3. Argon K~ X-ray position spectrum. The two lines, I ~ and K~2, separated by 2.13 eV are unfolded with polygons as described in the text.
Volume 261, number
1,2
PHYSICS
LETTERS
B
23 May 1991
Table 1 Measured pionic hydrogen 3P-1S transition energy, calculated electromagnetic value and deduced strong interaction shift of the 1S state. Pionic hydrogen
8
(eV )
&_,s, measured 2885.98~0.17(stat.)+O.l5(syst.) &,_ts, calculated point nucleus (Klein-Gordon) 2875.70 ‘) vacuum polarization (Uehling) 3.24 finite size -0.06 higher order corrections -0.02 total electromagnetic transition energy 2878.86 strong interaction shift t,s - 7.12? 0.32 a) Based on pion mass m,= 139.5688?0.0013
10 20 30 40 50 60 70
MeV/c*
[ 121.
channel Fig. 4. Pionic hydrogen 3P-IS X-ray position spectrum with titted line shape from the argon &, calibration line. Signal to background ratio is z 15. See text for further details.
eIs
the 7t-p scattering
a&P=f(2a,
length
+a,)=a,++a~+
=0.086+0.004 m;’ , geometries for the hydrogen and the argon measurewhere a$+ and a, are the isospin-even and -odd Sments, the argon calibration experiment was perwave scattering lengths, respectively. The pionic hyformed at the end of the run by tilling the hydrogen drogen result, as opposed to pion scattering, is the only target cell with argon gas, moving it with the cyclodirect zero-energy on the pion-nucleon tron trap to the argon source position aJMLDSFJLJDSGLJGSDLJDSnd irradiating information scattering lengths. it with X-rays as described above. The &, polygon A most useful analysis of the low-energy scN scatthus obtained was then fitted to the hydrogen spectering data has been performed by Gasser et al. trum. Both the natural line width of argon and the [ 13,3]. The two scattering lengths a$+ and a F+ are assumed hydrogen value are approximately the same chosen as independent parameters. It is shown that (0.8 eV); therefore only the shift and the height of data from different scattering experiments contrathe polygon was left free (see fig. 4 ). dict each other significantly; the value for agYp given The 3P- 1S transition energy obtained is given in above favors the solution which is based on the data table 1 (first line), together with the calculated elecof Bet-tin et al. [ 141 (see ref. [ 31). The Karlsruhetromagnetic value of the transition energy (sixth Helsinki phase shift solution [ 151 yields ul;Yp= line). The difference between the two is the strong 0.082-tO.004 m;‘, which is in agreement with our interaction shift of the pionic hydrogen 1S level: result. It should be stressed that the Karlsruhe-Helsinki value does not contain the normalization errors e,,=-7.12+0.17(stat.)fO.l5(syst.) eV. of the experimental data sets used [ 16 ] _ This value differs from the previous measurement An important application of the xN threshold parameters is the investigation of the low-energy struc[ 41 by 2.5 standard deviations #‘. ture of QCD through the calculation of the pion-nuWith Deser’s formula [ 1 ] we deduce from the shift clean o-term. An up-to-date summary of the present situation may be found in ref. [ 3 1. (13 The result of ref. [ 4 ] does not include a small refraction correction of -0.25 0.3( syst.) eV.
eV and is therefore eIS= -5.15rt:O.4(stat.)
f
We are indebted
to the Philips
Research
Labora19
Volume 26 1, number 1,2
PHYSICS LETTERS B
tories, Eindhoven, for providing us with the silicon crystals used in this experiment. We are grateful to L. Knecht and B. Leoni for very competent technical assistance. This research was partially supported by the Swiss National Science Foundation. We wish to dedicate this paper to the memory of William Volken who died in a delta glider accident in his beloved Swiss Alps shortly after the completion of the experiment. It would have been his Ph.D. thesis.
References ] S. Deser, M.L. Goldberger, K. Baumann and W. Thirring, Phys. Rev. 96 (1954) 774. :]O. Dumbrajs et al., Nucl. Phys. B 216 (1983) 277, and references therein. ,] J. Gasser, H. Leutwyler and M.E. Sainio, Phys. Lett. B 253 ( 1991) 252, and references therein.
20
23 May 1991
[4] E. Bovet, L. Antonuk, J.-P. Eager, G. Fiorucci, K. Gabathuler and J. Gimlett, Phys. Lett. B 153 (1985) 231. [5] G. Fiorucci, these de doctorat, Universitt de Neuchltel (1990). (61 L.M. Simons. Phys. Ser. T22 (1988) 90. [ 71 W. Beer et al., Nucl. Instrum. Methods, to be published. [8] G. Fiorucci et al., Nucl. Instrum. Methods A 292 ( 1990) 141; D. Varidel, J.-P. Bourquin, D. Bovet, G. Fiorucci and D. Schenker, Nucl. Instrum. Methods A 292 ( 1990) 147. [9] D. Sigg, Diplomarbeit, ETHZ-IMP (1990). [ lo] D. Chatellard, travail de diplbme, Universite de Neuchltel (1990). [ 111 R.D. Deslattes and E.G. Kessler jr., in: Atomic inner-shell physics, ed. B. Crasemann (Plenum, New York, 1985); E.G. Kessler, private communication ( 1987). [ 121 St. Thomann, Ph.D. thesis, ETHZNo. 9198 (1990); internal report ETHZ-IMP RP-91-01. [ 13 ] J. Gasser, H. Leutwyler, M.P. Lecher and M.E. Sainio, Phys. Lett.B213(1988)85. [ 141 P.Y. Bertin et al., Nucl. Phys. B 106 (1976) 341. [ 151 R. Koch, Nucl. Phys. A 448 ( 1986) 707. [ 161 R. Koch and E. Pietarinen, Nucl. Phys. A 336 (1980) 331.
PHYSICS LETTERS B
23 May 1991
Determination of the strong interaction shift in pionic hydrogen with a high resolution crystal spectrometer system W . Beer, M . B o g d a n , P . F . A . G o u d s m i t , H . J . L e i s i , A.J. R u s i E1 H a s s a n i , D . Sigg, St. T h o m a n n , W. Volken :
lnstitutJ~r Mittelenergiephysik der ETHZ, CH-5232 Villigen PSI, Switzerland D . B o v e t , E. B o v e t z, D . C h a t e l l a r d , J.-P. Egger, G . F i o r u c c i 2
Institut de Physique de l'UniversitO, Breguetl, CH-2000 Neuch(tteL Switzerland K. G a b a t h u l e r a n d L . M . S i m o n s
Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland Received 15 January 1991
The 3P-IS X-ray transition energy was measured in pionic hydrogen with a double focussing silicon crystal spectrometer in combination with a cyclotron trap and CCD detectors: E = 2885.98 +_0.17 (stat.) + 0.15 (syst.) eV. The corresponding strong interaction shift ~ts = - 7.12 + 0.32 eV (attractive) yields the scattering length combination ] (2a: + a 3) = 0.086 _+0.004 m~ i.
The p i o n - n u c l e o n strong interaction can be studied at zero energy by measuring the strong interaction shift ~lS and the strong interaction b r o a d e n i n g F~s o f the 1S level in pionic hydrogen. The S-wave scattering lengths al (isospin ½) a n d a 3 (isospin 3) are o b t a i n e d directly from ~ls and F~s through the Deser formula [ 1 ] 4Els ~,s = - - (2a, 3rB
-t-a3)
,
ffls = 1 6 a E l s ( l + l ) ( a l - - a 3 ) 2 9ra where E~s is the binding energy o f the 7t- in the IS orbit, rB the corresponding Bohr radius, Q a reduced mass factor and P the Panofsky ratio. The scattering lengths can also be o b t a i n e d indirectly from dispersion relations using phase shifts from low energy 7tN scattering and charge exchange d a t a and extrapolating to zero energy [2 ]. This proDeceased. 2 Also at Ecole d'Ing6nieurs, CH-2610 St. Imier, Switzerland. 16
cedure is indirect in the sense that extensive theoretical treatments o f the experimental d a t a are necessary. Moreover, results from different scattering experiments lead to solutions for the low-energy parameters which are mutually inconsistent [ 3 ]. The first pionic hydrogen experiment with a clear signal and adequate signal to background ratio was published in 1985 [4]. This m e a s u r e m e n t o f the strong interaction shift els yielded a direct determination of2a~ + a 3 = 0 . 1 7 8 + 0 . 0 1 9 m~-1 . The present experiment ~l is a first step in an att e m p t to d e t e r m i n e both s-wave scattering lengths directly, from a measurement o f the shift E~s and the b r o a d e n i n g F~s in pionic hydrogen. In this letter we report on a m e a s u r e m e n t o f e ~s to a precision o f five percent. An accurate d e t e r m i n a t i o n o f the X-ray transition energies in pionic hydrogen is not an easy task on account o f the low energy o f the corresponding X-rays and the weak signal associated with the necessary use o f a gaseous target. There are several possibilities to i m p r o v e u p o n the previous measure~l An earlier version of this experiment is described in ref. [5 ].
0370-2693/91/$ 03.50 © 1991 - Elsevier Science Publishers B.V. ( North-Holland )
Volume 26 l, number 1,2
PHYSICS LETTERS B
ment [4 ] which was performed using crystal diffraction. By replacing the graphite crystal with Si ( 111 ) crystals, the energy resolution could be improved by almost an order o f magnitude. The corresponding loss in luminosity was partly compensated by an elaborate device for maximizing the pion stopping rate in the low-density hydrogen target: the cyclotron trap. Furthermore background was minimized by using CCDs as X-ray detectors. The experiment was carried out at PSI (Paul Scherrer Institute, formerly SIN) at the hE3 channel tuned to deliver 85 M e V / c n - with an intensity o f typically 2.5 × 106/~- s-1. The setup is presented in figs. I and 2. It consists o f a cyclotron trap [ 6 ], a high resolution double focussing silicon crystal spectrometer of the reflection type [ 7 ] and position sensitive C C D X-ray detectors [ 8 ]. Target, crystals and detectors are located on a 3 m diameter focal circle (see fig. 1). The principle o f the cyclotron trap is to wind up the range curve of the 85 M e V / c pion beam in a weakly focussing magnetic field. This field with a central value o f 2.5 T is produced by a superconducting split coil magnet. After radial injection the pions spiral towards the center while loosing energy in a few thin degraders and finally the target gas. One o f the thin degraders was a scintillator used as a monitor for incoming pions. The pions entered the cylindrical
,
®
Fig. I. Schematic layout: (l)argon source for calibration, (2) hydrogen target, ( 3 ) crystal assembly, (4) CCD detector system at argon focus position, (5) CCD detector at hydrogen focus position (fis focal distance), (6) Braggangle, ( 7 ) Rowlands circles.
23 May 1991
Fig. 2. Schematic view of the experimental setup: ( 1) position of H2 target cell at 1 atm. and 20.6 K (15psTp), (2) cyclotron trap, ( 3 ) cooling system for the H 2 gas target, (4) n - beam trajectory, (5) argon gas stability monitor, (6) crystal assembly, (7) laser for alignment and adjustments, (8) example of X-ray trajectory, (9) soft flange between helium tube and CCD support, (10) 3 CCDs mounted in the vertical focal plane ( T= 170 K, p= 10-~ Torr), ( 11 ) liquid N2 container, (12) stepping motors for precision moving of CCD support.
target cell which was placed coaxially with the cyclotron trap through a cylindrical mylar window o f 40 m m diameter and 50 ~m thickness. The cooled cell was filled with saturated hydrogen vapor o f 1 atm pressure corresponding to 15pSTP. Since the low stopping rates at small hydrogen gas pressures are partially compensated by an increased X-ray yield, this low gas density was used to minimize the cell windows. The number o f pions stopping in the target was approximately 2 X 105 s - 1 for a primary beam o f 100 ~A. A fraction o f the pionic X-rays left the target cell at one of its faces through a 12 ~m thick Kapton foil and entered the crystal spectrometer which was filled with He gas through an identical window. The crystal arrangement o f the spectrometer confjsists o f 13 spherically bent Si ( 111 ) crystals, 100 p.m thick, with a diameter o f 5 cm each. These crystals were obtained from Philips Research Laboratories, Eindhoven. The crystal curvatures were achieved by mounting them under v a c u u m onto glass supports 17
Volume 261, number 1,2
PHYSICS LETTERS B
with the required curvatures. Special care was taken to align each individual crystal. Integral reflectivity was 8% and overall energy resolution approximately 3 eV FWHM. The 3P-1S pionic X-rays were scattered through a Bragg angle of 43.37 °. They entered the X-ray detector module through a 12 ~tm Kapton window. The 3P-1S transition was chosen for its higher X-ray energy and nearby calibration line after yield measurements showed that this possibility existed. The position sensitive detector consisted of three CCD ~2 mounted in a vertical row. Their size is 8.5 m m × 12.7 m m (385X576 pixels, 20 ~tm×20 ~tm each, separated by 2 ~tm). For charge transfer and readout a special electronics was built [ 8 ]. In order to minimize thermal noise the CCDs are operated at - 100°C. The advantages of using CCDs lie in their excellent intrinsic position resolution (in our case 22 ~tm), together with good energy resolution ( ~<220 eV F W H M ) which helped to reduce background by imposing an adequate energy window. The CCD background rejection capabilities are excellent. They are based on the fact that, in most cases, an X-ray in the 2-3 keV energy range deposits its energy in a single pixel. The whole spectrometer set-up was precisely aligned and temperature stabilized. For on-line stability checks a cell filled with argon gas was moved in front of the hydrogen target. The nearby argon I ~ Xrays, obtained by irradiation with 55Mn X-rays from a SSFe source, were monitored. For this the detector module was moved a few cm to the appropriate focal plane position using remotely controlled stepping motors. To this end the arms connecting target, crystals and detectors contained soft rubber bellows. An IBM PC was used for data acquisition and linked to a SUN work station which controlled spectrometer movement, position, temperature etc. Data were taken in units of 6 h [4 pionic hydrogen runs of 80 min each and a 40 min argon run during which the routine maintenance inside the area (helium and nitrogen refills etc.) was carried out]. Data were stored on the IBM disk and an on-line analysis was performed. In the off-line analysis only runs with a sufficient number of stopped pions were included. The excel~2 EEV (EnglishElectricValve),WaterhouseLane,Chelmsford, Essex, CM1 2QU, England.
18
23 May 1991
lent two dimensional position resolution of the CCDs allows for a sophisticated highly efficient pattern-recognition algorithm that reduces background almost to zero [ 9 ]. We demanded that a single pixel X-ray lies in an appropriate energy window and that the surrounding eight pixels are only charged by the intrinsic electronic and thermal noise of the CCDs. Charged particles, high-energy ?-rays and neutrons charge in general at least one neighbouring pixel. In order to reject multi-pixel events the eight neighbouring pixels of the one-pixel events must have an energy below a low-level limit normally chosen just above the noise level. In addition we applied cuts on the mean value, the standard deviation and the center of gravity of the eight surrounding pixels, decreasing thereby the background level by an order of magnitude. A less elaborate analysis [ 10 ] yields the same hydrogen peak position within statistics. For calibration we used the argon K~ and K~: lines (E=2957.790+0.009 and 2955.661+0.012 eV) [ 11 ]. Since the experimental energy resolution was not sufficient to fully separate the double line, the lines were unfolded by representing the I ~ line by a polygon and adjusting it into the measured line using the fact that the energy difference (2.13 eV) and the intensity ratio (2 : 1 ) of the I ~ l and I~a lines are known (see fig. 3). In order to equalize the source
m~
1
2
3
4
5
6
7
8
100 80
6O -p
5 o
u 40
20
10 20 30 40 50 60 70 channet Fig. 3. Argon K~ X-ray position spectrum. The two lines, I ~ and K~2, separated by 2.13 eV are unfolded with polygons as described in the text.
Volume 261, number
1,2
PHYSICS
LETTERS
B
23 May 1991
Table 1 Measured pionic hydrogen 3P-1S transition energy, calculated electromagnetic value and deduced strong interaction shift of the 1S state. Pionic hydrogen
8
(eV )
&_,s, measured 2885.98~0.17(stat.)+O.l5(syst.) &,_ts, calculated point nucleus (Klein-Gordon) 2875.70 ‘) vacuum polarization (Uehling) 3.24 finite size -0.06 higher order corrections -0.02 total electromagnetic transition energy 2878.86 strong interaction shift t,s - 7.12? 0.32 a) Based on pion mass m,= 139.5688?0.0013
10 20 30 40 50 60 70
MeV/c*
[ 121.
channel Fig. 4. Pionic hydrogen 3P-IS X-ray position spectrum with titted line shape from the argon &, calibration line. Signal to background ratio is z 15. See text for further details.
eIs
the 7t-p scattering
a&P=f(2a,
length
+a,)=a,++a~+
=0.086+0.004 m;’ , geometries for the hydrogen and the argon measurewhere a$+ and a, are the isospin-even and -odd Sments, the argon calibration experiment was perwave scattering lengths, respectively. The pionic hyformed at the end of the run by tilling the hydrogen drogen result, as opposed to pion scattering, is the only target cell with argon gas, moving it with the cyclodirect zero-energy on the pion-nucleon tron trap to the argon source position aJMLDSFJLJDSGLJGSDLJDSnd irradiating information scattering lengths. it with X-rays as described above. The &, polygon A most useful analysis of the low-energy scN scatthus obtained was then fitted to the hydrogen spectering data has been performed by Gasser et al. trum. Both the natural line width of argon and the [ 13,3]. The two scattering lengths a$+ and a F+ are assumed hydrogen value are approximately the same chosen as independent parameters. It is shown that (0.8 eV); therefore only the shift and the height of data from different scattering experiments contrathe polygon was left free (see fig. 4 ). dict each other significantly; the value for agYp given The 3P- 1S transition energy obtained is given in above favors the solution which is based on the data table 1 (first line), together with the calculated elecof Bet-tin et al. [ 141 (see ref. [ 31). The Karlsruhetromagnetic value of the transition energy (sixth Helsinki phase shift solution [ 151 yields ul;Yp= line). The difference between the two is the strong 0.082-tO.004 m;‘, which is in agreement with our interaction shift of the pionic hydrogen 1S level: result. It should be stressed that the Karlsruhe-Helsinki value does not contain the normalization errors e,,=-7.12+0.17(stat.)fO.l5(syst.) eV. of the experimental data sets used [ 16 ] _ This value differs from the previous measurement An important application of the xN threshold parameters is the investigation of the low-energy struc[ 41 by 2.5 standard deviations #‘. ture of QCD through the calculation of the pion-nuWith Deser’s formula [ 1 ] we deduce from the shift clean o-term. An up-to-date summary of the present situation may be found in ref. [ 3 1. (13 The result of ref. [ 4 ] does not include a small refraction correction of -0.25 0.3( syst.) eV.
eV and is therefore eIS= -5.15rt:O.4(stat.)
f
We are indebted
to the Philips
Research
Labora19
Volume 26 1, number 1,2
PHYSICS LETTERS B
tories, Eindhoven, for providing us with the silicon crystals used in this experiment. We are grateful to L. Knecht and B. Leoni for very competent technical assistance. This research was partially supported by the Swiss National Science Foundation. We wish to dedicate this paper to the memory of William Volken who died in a delta glider accident in his beloved Swiss Alps shortly after the completion of the experiment. It would have been his Ph.D. thesis.
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