Precision determination of the strong interaction shifts and widths of the 1s level in pionic 6Li, 7Li, and 9Be

Nuclear Physics B66 (1973) 125-134. North Holland Publishing Company

PRECISION DETERMINATION OF THE STRONG INTERACTION SHIFTS AND WIDTHS OF THE 1 s LEVEL IN PIONIC 6Li, 7Li, AND 9Be G. BACKENSTOSS *, I. BERGSTROM **, J. EGGER *** R. HAGELBERG *, C.J. H E R R L A N D E R **, H. KOCH *, H. P. POVEL *, R.H. PRICE +, A. SCHWlTTER *** and L. TAUSCHER *

CERN, Geneva, Switzerland Received 8 June 1973 (Revised 1 October 1973)

Abstract: The strong-interaction shifts of the ls level in pionic ~Li, 7Li, and 9Be have beendetermined with an accuracy of better than 1%. The corresponding widths were determined with an accuracy of better than 6%. Significant deviations from the theory are observed as far as the absolute values as well as the systematics of the isospin dependence are concerned.

1. Introduction During recent years a considerable amount of work has been done on the stronginteraction effects in pionic atoms for pions in the Is, 2p, 3d, and 4f levels. A detailed summary of the available data was given by one of us (G.B.), ref. [ 1]. An analysis of these data shows that the n - - n u c l e a r interaction can be described by a nonlocal optical potential [2, 3]. Although the general agreement between theory and experiment is fairly good, also some exceptions have been observed as in the case of the shifts and widths of 160 and 180 (cf. ref. [1]) which have been explained on a microscopic basis [4]. For the lighter elements, however, the accuracy o f the measurements done so far [5, 6] was not sufficient (i) to check to what extent if at all - the optical potential is valid for very light nuclei; and if it is, whether the 1/A terms in the n-nuclear interaction as indicated in ref. [2], which have been neglected up to now, would describe the experimental results sufficiently well; (ii) to establish isotopic spin effects also for light nuclei with high significance.

* Visitor at CERN from Karlsruhe. ** Visitor at CERN from Stockholm. *** Visitor at CERN from ETH-SIN. + Present address: TRIUMF, University of Victoria, Victoria, Canada.

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G. Backenstoss et aL, Pionic atoms

The fast development of high resolution silicon and germanium X-ray detectors makes it now possible to perform very accurate measurements in the energy region between 5 and 50 keV. Relative accuracies of better than 10% can now be expected for line broadenings as low as 200 eV and, owing to special calibration methods, accuracies of better than 10 -4 may be achieved for the energy determination down to 20 keV. This experimental situation encouraged us to try to improve the pionic data on 6Li, 7Li and 9Be by an order of magnitude in order to study the above questions.

2. Experimental procedure The experiments were carried out at the muon channel of the CERN 600 MeV Synchrocylotron. The experimental layout was similar to the one described in ref. [1 ]. The targets had an area of about 6 × 6 cm 2, but varied in thickness from 2 to 18 g/cm 2. The 6Li and 7Li targets also contained 4% 7Li and 7.4% 6Li, respectively. Each target was measured between 5 and 24 hours. Two detectors were used, namely a 0.6 × 2.0 cm 3 Ge(Li) X-ray detector, having an in-beam energy resolution of 550 eV at 42 keV, and a 5 × 30 mm 3 Si(Li) detector with optical feedback giving a resolution of 300 eV at 25 keV and 180 eV at 4 keV under beam conditions. The Ge(Li) detector was used only in the Be measurements.

3. Data analysis The pionic X-ray spectra of 6Li, 7Li, and 9Be are shown in figs. 1-3. The data evaluation was concerned with problems of contamination lines, gamma scattering background, line shapes, calibration of the detector resolution, and energy calibration. 3.1. C o n t a m i n a t i o n lines

Corrections due to contamination had to be introduced because the Li targets were not isotopically pure. Knowing the isotopic abundance, these corrections could easily be handled. Other contamination lines originating from C, N, O, F, and A1 were also identified and considered in the analysis. Since the pion beam contained muons of the same range, muonic lines were also present in the pionic spectra, Therefore the muonic X-ray spectra were measured separately in order to determine the muonic contribution to the background, especially since the muonic Lyman series limit has about the same energy as the pionic 2 -~ 1 transition.

G. Backenstoss et al., Pionic atoms

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In most cases these bumps could be handled by introducing a background, consisting either of a sequence of straight lines, a third-order polynomial, or a broad Gaussian distribution. For the two 9Be spectra used in the analysis, the gamma-scattering distribution was also quantitatively calculated. This was done considering the single Compton and Thompson scattering of the X-rays in the target, taking the proper target geometry into account. The calculation was done in the following way: from all X-rays of energy E 0 originating from an infinitesimal volume P of the target, only a fraction reaches a second infinitesimal volume D in the target, owing to solid angle and absorption. Of these a fraction undergoes Compton or Thompson scattering in the volume D, resulting in an angular distribution with respect to the vector pointing from P to D. Those scattered X-rays escaping from D and hitting the detector, have a certain energy E, determined by the scattering angle. By integrating over-

G. Backenstoss et aL, Pionic atoms

129

all scattering volumes D and all source volumes P in the target, the energy distribution of the scattered X-rays and its intensity with respect to the non-scattered peak is obtained. Details of these calculations will be published by one of us (J.E.), ref. [7]. The calculations are quantitatively consistent with the measurement, with respect to both the shape of the scattering distribution and the intensity of this distribution relative to that of the photopeak. It turned out that the natural line widths are quite sensitive to the different approaches of the background, whereas the line positions are only slightly affected. In the case of 9Be (spectrum of fig. 3b), where the effect is most pronounced, the difference in width of the pionic 2p-~l s transition using once the best empirical background and once the calculated gamma-scattering distribution, is 5 standard deviations, whereas the difference in line position is only 2.6 standard deviations. 3.3. Line shapes

The line shape was studied using the muonic lines, unperturbed impurity lines, and the line of an 241Am source fed by accidental coincidences, in the pionic spectra. These lines could be fitted by pure Gaussian distributions without any additions (e.g. tails). The Gaussian widths thus obtained for the different lines were used to calibrate the instrumental resolution as a function of energy. In cols. 8 and 9 of table 1 the detector resolutions (FWHM) obtained from these calibration curves are listed for the different detectors. 3.4. Energy calibration

The usual method of calibration of a Ge or Si spectrometer is a calibration with radioactive sources, where special care has to be taken to accumulate the calibration spectrum under the same conditions as the X-ray spectrum, i.e. under beam conditions. Otherwise systematic shifts in energy and line shape deteriorations may occur [8]. In the present experiments, where the energies are always below 60 keV, we used the muonic lines in the pion spectra and some of the muonic and pionic lines of the target contamination as calibration standards. The advantage of this method is that these lines are generated under conditions which are identical to those for the pionic lines of interest. On the other hand, the energieslof these muonic and pionic lines can be calculated very accurately. The only sources of uncertainty are the correction due to the finite size of the nucleus, the uncertainties of the 7r- and/amasses, and the uncertainty of the fine structure constant a. A possible uncertainty, which could be due to the still unexplained discrepancies in muonic atoms [9, 10], has been neglected. The constants used are a -1 = 137.03602, m u = 105.6594 MeV, rn~ = 139.570 MeV. The energy values were calculated by numerical integration of the Dirac or KleinGordon equation. Corrections were calculated in perturbation. All possible correc-

G. Backenstoss et al., Pionic atoms

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Table-2 Energy calibration values Spectrum studied

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tions except the vacuum polarization of order a(o~) and a2(oug) and the nuclear polarization are below the 0.1 eV level and hence negligible. The strong interaction in the pionic transitions in 12C, 14N, 160, and 27A1 lead also to a negligible shift, as does the finite size of these nuclei. Details of the calculations are described elsewhere [11]. The calibration standards thus obtained are listed in table 2. A small quadratic correction had to be applied to the linearity of the detector system. Since, however, the energy range of interest is small and well defined by calibration lines, the errors originating from interpolation or extrapolation of the calibration curve do not contribute significantly.

4. Experimental results Table 1 shows the experimental results. The measured energies are given in col. 2. The errors are mainly due to statistics and calibration, but include also the uncertainties of the fitting procedure. In those cases, where several lines of the muonic Lyman series were used in the calibration, the finite size error enters only once of course, since it originates from the ls level. The energies listed in col. 3 were calculated [11] for pure electromagnetic interaction. Corrections were applied for vacuum polarization, nuclear polarization, and the pion form factor correction [12] which is 7 and 19 eV for Li and Be, respectively. The charge distribution was assumed to be a harmonic well distribution with the r.m.s, radii of col. 1. The uncertainty of these energies is mainly due to the finite size effect, which is about twice as large as for muons.

132

G. Backenstoss et aL, Pionic atoms

The experimental strong interaction shifts, i.e. the difference between the measured transition energies (col. 2) and the calculated electromagnetic energies (col. 3) are listed in col. 4. The errors are the same as in col. 2 since the uncertainties of the pionic finite size effect and the muonic one, which enters through the energy calibration, are systematically correlated and cancel partly. For comparison, the best values measured so far [5] are listed too. It should be pointed out that the equality of the experimental strong interaction shifts of the 1s levels for the different n p - 1s transitions in each element demonstrates the consistency of the calibration procedure applied. The experimental ~vidths of the ls level, i.e. the Lorentzian widths of the transitions, are listed in col. 6. The errors reflect mainly the uncertainties involved in fitting the background. The strong n-nucleus interaction was calculated with an optical potential by Ericson and Ericson [2] and Krell and Ericson [3]: V(r) ~

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p(O = pn(r) + %(0, Pn, Pp being the neutron and proton distributions, respectively. For pionic s-states only the first (local) part of the potential is of interest. Terms of order 1/A are mentioned in ref. [2], but have not been evaluated so far, though they might have some influence for very light nuclei. In order to compare our results with this theory, we have used the parameters, which were obtained by a least square fit to all previous CERN data on pionic atoms [ 13]. From these calculations we obtained the theoretical shifts given in col. 5 of table 1 and the theoretical widths, given in col. 7. The distributions of neutrons and protons were assumed to be equal harmonic well distributions with the r.m.s. radii of col. 1. The comparison of the experimental shifts and widths with theory shows very pronounced deviations. The calculated shifts are systematically larger than the measured ones, whereas the calculated widths are significantly smaller than the measured widths. In order to analyse these discrepancies qualitatively the parameter b 0 was changed to reproduce the shift of 6Li, since in this case the isospin term b 1 should be of no influence. This results in a change of the pion wave functioo, which yields a somewhat larger overlap with the nucleus. Thus the absorption width changes slightly

133

G. Backenstoss et aL, Pionic atoms

from 125 eV to 136 eV but remains still far below the measured value at 195 eV. Changes of the radii of the nuclear matter distribution by about 5 - 1 0 % do not influence the shift by more than a few eV, but the width may become of the order of the measured width by lowering the r.m.s, radius by about 10% and using the adjusted b 0. The influence of the isospin on the strong interaction shift is well demonstrated in the case of 6Li and 7Li. There is, however, no experimental evidence for an isospin dependence of the width, as would indicate the theoretical values. Using the modified b 0 of the 6Li adaptation and adjusting b 1 to reproduce the 7Li shift properly, the absorption width for 7Li changes from 160 eV to 172 eV, which is still much smaller than the measured value of 195 eV. Also here the shift is rather insensitive to the radius of the nuclear matter distribution. The width, however, may become ~" 200 eV, if one lowers the r.m.s, radius by ~ 6% and uses the proper wave function. This means that the so far accepted absorptive part of the potential is too weak to explain the measured widths. Furthermore it yields different widths for the two Li isotopes, whereas the experiment shows no difference. Fig. 4 shows a reduced plot of the strong interaction shift, e / Z 4 versus the mass number A. The difference between nuclei having isospin T = 0 and T = -~ has been observed earlier (cf. ref. [ 1]) but the high accuracy confirms this effect for the light elements studied here. Moreover, the 6Li data reveal a change in the sytematics for light elements with T = 0, which seems to be confirmed by the preliminary shift value for* 4He. A 5 I

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134

G. Backenstoss et aL, Pionic a t o m s

5. Conclusion The accuracy obtained in this study of the strong interaction effects in light pionic atoms is better than 1% for the strong interaction shifts and better than 6% for the widths. The results show that the optical potential for the ~r--nuclear interaction as used at present is not sufficient for light nuclei. Furthermore, the results show a very pronounced isospin dependence o f the real part of the potential, whereas the absorptive part seems not to be affected by the isospin. Our results therefore emphasize the need for a theoretical analysis which is based on a more detailed microscopic analysis.

This work was supported in part by the Ministerium fi~r Bildung und Wissenschaft of the Federal Republic of Germany.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]

G. Backenstoss, Ann. Rev. Nucl. Sci. 20 (1970) 467. M. Ericson and T.E.O. Ericson, Ann. of Phys. 36 (1966) 323. M. Krell and T.E.O. Ericson, Nucl. Phys. B l l (1969) 521. K. Chung, M. Danos and M.G. Huber, Phys. Letters 29B (1969) 265. R.J. Harris, Jr., W.B. Shuler, M. Eckhouse, R.T. Siegel and R.E. Welsh, Phys. Rev. Letters 20 (1968) 505. R.J. Wetmore, D.C. Buckle, J.R. Kane and R.T. Siegel, Phys. Rev. Letters 19 (1967) 1003. J. Egger, thesis, ETH Ztirich, 1973. G. Backenstoss, H. Daniel, H. Koch, U. Lynch, Ch. v.d. Malsburg, G. Poelz, H.P. Povel, H. Schmitt, K. Springer and L. Tauscher, Phys. Letters 36B (1971) 403. M.S. Dixit, H.L. Anderson, C.K. Hargrove, R.J. McKee, D. Kessler, M. Mes and A.C. Thompson, Phys. Rev. Letters 27 (1971) 878. H.K. Walter, J.H. VuiUeumier, H. Backe, F. Boehm, R. Engfer, A.H.v. Gunten, R. Link, R. Michaelsen, C. Petitjean, L. Schellenberg, H. Schneuwly, W.U. SchrSder and A. Zehnder, Phys. Letters 40B (1972) 197. L. Tauscher, CERN preprint (1973). U.E. Schroeder, Acta Phys. Austriaca 34 (1971) 235. L. Tauscher, Proc. Int. Seminar on n-meson nucleus interactions, Strasbourg, 1971 (CNRS, Strasbourg, 1971) p. 45.