Geissel, H.

Gilg, H.

Gillitzer, C. G.

Hayano, R. S.

Hirenzaki, S.

Itahashi, K.

Iwasaki, M.

Kienle, P.

Münch, M.

Münzenberg, G.

Schott, W.

Suzuki, K.

Tomono, D.

Weick, H.

Yamazaki, T.

Yoneyama, T.

Gillitzer, A.

Hayano, R.

GSI Repository

Deeply Bound 1s and 2p Pionic States in $^{205}Pb$ and Determination of the s-Wave Part of the Pion-Nucleus Interaction

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VOLUME 88, NUMBER 12 P H Y S I C A L R E V I E W L E T T E R S 25 MARCH 2002Deeply Bound 1s and 2p Pionic States in 205Pb and Determination of the s-Wave Partof the Pion-Nucleus InteractionH. Geissel,1 H. Gilg,2 A. Gillitzer,3 R. S. Hayano,4 S. Hirenzaki,5 K. Itahashi,6 M. Iwasaki,6 P. Kienle,2 M. Münch,2G. Münzenberg,1 W. Schott,2 K. Suzuki,4 D. Tomono,6 H. Weick,1 T. Yamazaki,7 and T. Yoneyama61Gesellschaft für Schwerionenforschung, D-64291 Darmstadt, Germany2Physik-Department, Technische Universität München, D-85747 Garching, Germany3Institut für Kernphysik, Forschungszentrum Jülich, D-52425 Jülich, Germany4Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan5Department of Physics, Nara Women’s University, Kita-Uoya, Nishimachi, Nara 630-8506, Japan6Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan7RI Beam Science Laboratory, RIKEN, 2-1 Hirosawa, Wako-shi, Saitama 351-0198, Japan(Received 27 April 2001; revised manuscript received 5 July 2001; published 11 March 2002)We observed well-separated 1s and 2p p2 states in 205Pb in the 206Pbd, 3He reaction at Td 604.3 MeV. The binding energies and the widths determined are B1s  6.762 6 0.061 MeV, G1s 0.76410.17120.154 MeV, B2p  5.110 6 0.045 MeV, and G2p  0.32110.06020.062 MeV. They are used to deducethe real and imaginary strengths of the s-wave part of the pion-nucleus interaction, which translates intoa positive mass shift of p2 in 205Pb.DOI: 10.1103/PhysRevLett.88.122301 PACS numbers: 36.10.Gv, 13.75.Gx, 14.40.Aq, 25.45.HiIn a recent experiment at GSI, we have discovered thedeeply bound 2p state and an indication of the 1s stateof negative pions in 207Pb in the 208Pbd, 3He reaction[1–4]. This experiment has demonstrated that (i) thedeeply boundp2 states (1s and 2p) in heavy nuclei indeedexist with narrow widths and that (ii) they are produced inthe (d, 3He) reaction, as theoretically predicted [5–8]. Thenarrowness of these deeply bound states despite the strongpion absorption in nuclei is well understood as being dueto the halolike pionic structure, which is accommodated ina potential pocket provided by the long-range Coulomb at-traction and the short-range nuclear repulsion [5,6,9]. The(d, 3He) reaction produces deeply bound states of configu-rations nlp n0l0j021n at small momentum transfer. Theobserved spectrum in the previous experiment showed adistinct but skewed 2pp peak due to the presence of the3p12 and 3p32 neutron hole states separated in energy by0.90 MeV. The 1sp state was observed as a bump at theshoulder of the 2pp peak accordingly. In the present pa-per, we report on a new experiment using a 206Pb target,which was purposely undertaken in view of the smallercontribution of the 3p12 hole and, consequently, a betterseparation of the 1sp and 2pp states. This expectationwas supported by a theoretical study [10].The experiment was performed with the Fragment Sepa-rator (FRS) [11] using a Td  604.3 MeV deuteron beamfrom the SIS-18 synchrotron at GSI, Darmstadt. Thedetailed description of the experimental procedures andanalyses are found in Refs. [3,4,12]. The beam intensitywas 1.5 3 1011spill at 1 s spill duration and 3 s cycletime. We employed a 1.5 mm wide and 25 mgcm2 thick206Pb target. The 3He momentum spectrum was measuredat excitation energies covering the bound p2 region.The obtained excitation spectrum, namely, the doubledifferential cross section versus the excitation energy (Ex)122301-1 0031-90070288(12)122301(4)$20.00above the ground state of 205Pb, is shown in Fig. 1. The ex-citation energy of a bound-pion peak is related to the p2binding energy Bnl as Ex  Mx 2 M205Pbc2 mp2c2 2 Bnl 1 Enn0l0j0, where Mx is the mass of thereaction product, M205Pb is the ground-state mass of205Pb, mp2  139.570 MeVc2 is the pion mass, andEnn0l0j 0 is the excitation energy of 205Pb (neutron hole05101520125 130 135 140 145206Pb(d,3He)(3p,3d,4p...)ππ0π- thresholdd2σ/(dE dΩ)   [µb/(MeV sr)]Excitation Energy   [MeV](1s)π( f5 / 2 ,p1 / 2 , p3 / 2 )n-1-1(2p)π( f5 / 2 ,p1 / 2 , p3 / 2 )nFIG. 1. Double differential cross section measured in the206Pbd, 3He reaction at incident deuteron energy Td 604.3 MeV as a function of the excitation energy above the205Pb ground state. The peak at 140 MeV designated as “p0”is due to the reaction pd, 3Hep0.© 2002 The American Physical Society 122301-1VOLUME 88, NUMBER 12 P H Y S I C A L R E V I E W L E T T E R S 25 MARCH 2002state of 206Pb [13]). The most important contributionsare from the ground state (2f52), the 0.002 MeV state(3p12), the 0.260 MeV state (3p32), and the 1.770 MeVstate (2f72).The spectrum consists of three contributions, whichoriginate from (i) quasifree pion production, (ii) forma-tion of bound pionic states, and (iii) nonpionic nuclearexcitation. The quasifree p2 production forms a contin-uum which opens above the emission threshold at Ex 139.570 MeV shown by the vertical dashed line. Thepeak above the p2 threshold at Ex  140 MeV resultsfrom the pd, 3Hep0 reaction on a small hydrogen con-tamination in the target. Nuclear excitation processes notassociated with pion production contribute at a nearlyconstant level d2sdEdV  4 mbMeV sr in the con-sidered excitation energy range, and dominate at Ex ,130 MeV. The central part between 130 and 140 MeV hasstructures associated with the formation of pionic states.The largest peak at Ex  135 MeV corresponds to thebound 2pp state coupled dominantly to the three neutronhole states 2f52, 3p12, 3p3221n . The well-separatedpeak at Ex  133 MeV below the 2pp peak is 1sp ,which is also composed of contributions from the threehole states. The region between the 2pp peak and thethreshold (Ex  136  139 MeV) is due to the formationof higher states 3p, 3d, 4p, . . .p . The overall structureagrees remarkably well with the theoretical one [10]. Theexperimental resolution and the uncertainty in the absoluteenergy scale are estimated to be 0.374 6 0.050 MeV(FWHM) and 0.040 MeV, respectively (see Ref. [12]).In order to determine the binding energies and widths,we decomposed the region of interest (see Fig. 2) into1sp and 2pp components and a linear background by aleast squares fit in a similar manner as in Ref. [4]. The fit-ting region is between Ex  120.0 and 136.2 MeV wherethe contribution from states other than 1sp and 2pp isnegligible. In the final analysis each pionic state nlp iscoupled to ten neutron hole states with calculated strengthsas listed in Table II of Ref. [10]. The fitting parameters arethe binding energies (Bnl), widths (Gnl), and intensities(Inl ) of both 1sp and 2pp , and the slope and the offsetof the linear background. The result of this fitting is excel-lent (the x2 is 98.0 for NDF  124), but we find a smalldiscrepancy near the tiny structure of 2pp 2f7221n at136.2 MeV, although this is located mostly outside thefitting region. A 40% reduction of the f-hole contribu-tions, 2f52 and 2f7221n , compared with the theoreticalones removes this discrepancy, and yields binding ener-gies B1s and B2p which are slightly larger by 0.024 and0.026 MeV, respectively (the x2 is 93.1 for NDF  123).The fit result of this option is shown in Fig. 2a). In the in-terval 130 MeV , Ex , 136 MeV, the solid curve showsthe obtained fit function, and the dashed and the dottedcurves are the 1sp and 2pp contributions, respectively.The peak intensity of 1sp relative to 2pp is 73% largerthan the theoretical prediction. The contributions of the122301-2130 131 132 133 134 135 136 137 138 139Excitation Energy   [MeV]051015d2σ/(dE dΩ)   [µb/(MeV sr)] ( 3p,3d,4p,...)π(3p1/2)n(3p3/2)n-1(2f7/2)n(2f5/2)n(a)(b)(1s)π( f5/ 2,p1/ 2,p3/ 2 )n-1-1(2p)π( f5/ 2,p1/ 2,p3/ 2 )n-1-1-1FIG. 2. (a) The experimental spectrum and the best fit curveobtained in the fit region indicated by the horizontal arrow. Thedashed, dotted, and dash-dotted curves are the 1sp , 2pp , andhigher-nlp components, respectively. (b) The partial contribu-tions of the most dominant neutron hole states, shown in thesame scale as (a).shallower states 3p, 3d, 4p, . . .p were not considered inthe fitting procedure because they are located outside theregion relevant for the deduction of the 1sp and 2ppbinding energies and widths. Using the theoretical val-ues from Ref. [10] for the relative strength of the shal-lower states as compared to the 2pp state, their summedcontribution was obtained, as presented by the dash-dottedcurve. This contribution is included in the solid curve inaddition to the fit function in order to demonstrate that theexcitation spectrum is well understood also in the regionof shallow bound pionic states.122301-2VOLUME 88, NUMBER 12 P H Y S I C A L R E V I E W L E T T E R S 25 MARCH 2002The deduced binding energies and widths are presentedin Table I, where we adopt the average values resultingfrom the two fit options described above. The systematicuncertainties due to the choice of the f-hole contributionare 60.012 and 60.013 MeV for B1s and B2p, respec-tively. The systematic errors are obtained from a quadraticsum of the evaluated uncertainties, which are dominatedby the uncertainty of the absolute energy scale for B andby the uncertainty of the experimental resolution for G.The present values are much more precise than the formerones obtained for p2 ≠ 207Pb [4].In Fig. 3 the experimental data are presented in the B-Gplanes with the 1s contours for the statistical errors andwith the bars for the total (statistical 1 systematic) errors.Here we compare the experimental results with those cal-culated by using a pion-nucleus potential of the Ericson-Ericson type [14] with various potential parameter setswhich were obtained from fitting observed strong interac-tion shifts and widths in pionic atoms (see Refs. [4,15,16]).The pion-nucleus potential consists of the s-wave (local)part (Us) and the p-wave (nonlocal) part (Up). Whereasthe known strong interaction shifts in most of the shallowstates in pionic atoms are due to the combination of at-tractive Up and repulsive Us terms, the 1sp states aredominated by the s-wave part (see Fig. 1 of Ref. [17]).This part is given byUsr  22pmpe1b0rr 1 b1Drr	 1 e2B0r2r ,(1)where rr  rnr 1 rpr, Drr  rnr 2rpr, e1  1 1 mpM  1.147, and e2  1 1mp2M  1.073 with M being the nucleon mass. Weassumed the two-parameter Fermi distributions for theneutron density rnr and the proton density rprwith a common nuclear radius cp  cn  6.591 fm anda diffuseness parameter zp  zn  0.545 fm for 205Pb,which are taken as the average of the proton parametersfor 204Pb and 206Pb [18]. The central densities for neu-trons [rn0] and protons [rp0] are 0.0961 andTauscherBatty 1Batty 2Batty 3SM 1Konijn 1Konijn 2Konijn 3Konijn 4Konijn 5Nieves 1Ericson 1Ericson 2Ericson 3FG6.7 6.8 7.0 7.16.9(a)Γ 1s [MeV]B1s [MeV]0.00.20.60.80.41.0(b)B2p [MeV]Γ 2p [MeV]5.05 5.10 5.205.15 5.250.200.400.450.300.250.150.350.50FIG. 3. Comparison of the measured binding energy and width for (a) 1sp and (b) 2pp in 205Pb with the corresponding valuescalculated by using various potential parameter sets (abbreviated as in [4] except for FG [16]). When necessary, an isotope shift ofB1s205Pb  B1s207Pb 1 40.5 keV is applied. The small ellipses and the bars show the experimental values with 1s statisticaland total (statistical 1 systematic) errors, respectively.122301-3TABLE I. The binding energies and widths of the 1sp and2pp states of 205Pb obtained in the present experiment.B1s  6.762 60.061 60.045 stat 6 0.041 syst MeVG1s  0.76410.17120.154 10.16220.141 stat 6 10.05520.061 syst MeVB2p  5.110 60.045 60.016 stat 6 0.042 syst MeVG2p  0.321 10.06020.062 60.039 stat 6 10.04520.049 syst MeV0.0640 fm23, respectively. The calculated values of B andG, for which the effect of vacuum polarization is takeninto account, are shown in Fig. 3. Most of them are infair agreement with the experimental values, though theindividual potential parameters are widely distributed.Conversely, we determine the strengths of the real andthe imaginary parts of the s-wave potential, Usr V r 1 iWr, irrespective to the choice of the p-waveparameters, since the 1sp binding energy and widthdepend nearly entirely on the s-wave potential. The well-established Seki-Masutani relation [4,6,19], b0  b0 1e2e1r02 ReB0  const, further implies that the real partof the potential is well represented by its value at thehalf-density radius R0.The theoretical relations of B1s and G1s with V 0[ 2V R0] and 2W0 obtained in this way, while set-ting the insensitive p-wave parameters to the well-knownvalues [15,19], are presented as two-dimensional contourcurves in Fig. 4. The width depends not only on theimaginary part but also on the real part through the overlapof the p2 density with the nucleus. The binding energydepends also on the imaginary part. The experimentalvalues of B1s and G1s presented in the figure yieldV 0  2V R0  27.1 6 1.7 MeV , (2)W 0  214.0 6 3.8 MeV . (3)Thus far, we have assumed that the shapes of rpr andrnr are the same. If the rms radius of the neutrondistribution is larger than that of the proton distribution[20], it would cause a decrease in the calculated 1s bindingenergy [17,21], which results in a decrease of V 0 by about2 MeV.122301-3VOLUME 88, NUMBER 12 P H Y S I C A L R E V I E W L E T T E R S 25 MARCH 2002051520102530282624 29272523 31V0*  [MeV]−W(0)  [MeV]0.56.66.7B1s = 6.8 MeV6.97.0Γ1s = 1.0 MeVFIG. 4. A contour map of B1s and G1s in the plane of V0[ 2V R0] and 2W0. The experimental values with 1sstatistical and total (statistical 1 systematic) errors are shownby the broken and solid ellipses, respectively.The real s-wave potential V r translates into an in-crease of the effective mass of p2 in the nuclear medium[2,22]. The value of V 0 (27 MeV) corresponds to a pionmass shift in the medium of 205Pb, as the half-densityvalue V R0 is extrapolated to the full-density limit2V R0. (Strictly speaking, the potential at r  0 is notV 0 but V0 2 pmpe2 ReB0r02, and thus the pionmass shift at the center of the nucleus may have an am-biguity as much as 2–8 MeV, if ReB0  20.05 6 0.03 isinvoked [16].) It is to be noted that the measured repulsivepotential V 0 is significantly larger than V 0  16 MeV,which we expect from the free pN scattering lengths afterthe correction for double scattering (b0  20.017 andb1  20.090) [14,23]. The difference between the ob-served value (27 MeV) and the expected value (16 MeV)can be attributed either to an additional isoscalar repulsion[the ReB0rr2 term], as claimed in [16], or to a repulsiondue to an increase of the isovector strength jb1j in thenuclear medium. Such an increase of jb1j is expected as aconsequence of the partial restoration of chiral symmetryat finite nuclear density along with a reduction of thechiral order parameter fp (or the quark condensate)[24,25]. Further studies of pionic 1s states in various Snisotopes to distinguish between the two interpretations arein progress.122301-4The authors thank Professor H. Toki and Dr. Y. Ume-moto for fruitful discussions and theoretical support, andthe staff of GSI for the continuous efforts to provide superbexperimental conditions. This work is supported by theGrant-in-Aid for Scientific Research of Monbukagakusho(Japan), by the Bundesministerium für Bildung, Wissen-schaft, Forschung und Technologie (Germany), and by theGesellschaft für Schwerionenforschung, Darmstadt.[1] T. Yamazaki et al., Z. Phys. A 355, 219 (1996).[2] T. Yamazaki et al., Phys. Lett. B 418, 246 (1998).[3] H. Gilg et al., Phys. Rev. C 62, 025201 (2000).[4] K. Itahashi et al., Phys. Rev. C 62, 025202 (2000).[5] H. Toki and T. Yamazaki, Phys. Lett. B 213, 129 (1988).[6] H. Toki, S. Hirenzaki, T. Yamazaki, and R. S. Hayano,Nucl. Phys. A501, 653 (1989).[7] H. Toki, S. Hirenzaki, and T. Yamazaki, Nucl. Phys. A530,679 (1991).[8] S. Hirenzaki, H. Toki, and T. Yamazaki, Phys. Rev. C 44,2472 (1991).[9] E. Friedman and G. Soff, J. Phys. G 11, L37 (1985).[10] S. Hirenzaki and H. Toki, Phys. Rev. C 55, 2719 (1997).[11] H. Geissel et al., Nucl. Instrum. Methods Phys. Res.,Sect. B 70, 286 (1992).[12] K. Suzuki, Master thesis, University of Tokyo, 2000.[13] R. Tickle and J. Bardwick, Phys. Rev. 178, 2006 (1969).[14] M. Ericson and T. E. O. Ericson, Ann. Phys. (N.Y.) 36, 323(1966); T. E. O. Ericson and W. Weise, Pions and Nuclei(Oxford Science Publications, New York, 1988).[15] C. Batty, E. Friedman, and A. Gal, Phys. Rep. 287, 385(1997).[16] E. Friedman and A. Gal, Phys. Lett. B 432, 235 (1998).[17] Y. Umemoto, S. Hirenzaki, K. Kume, and H. Toki, Phys.Rev. C 62, 024606 (2000).[18] H. de Vries, C. W. de Jager, and C. de Vries, At. Data Nucl.Data Tables 36, 495 (1987).[19] R. Seki and K. Masutani, Phys. Rev. C 27, 2799 (1983).[20] A. Trzcin´ska, J. Jastrze¸bski, P. Lubin´ski, F. J. Hartmann,R. Schmidt, T. von Egidy, and B. Kłos, Acta Phys. Pol. B32, 917 (2001); (unpublished).[21] H. Toki, S. Hirenzaki, and T. Yamazaki, Phys. Lett. B 249,391 (1990).[22] T. Waas, R. Brockman, and W. Weise, Phys. Lett. B 405,415 (1997).[23] T. E. O. Ericson, B. Loiseau, and A. W. Thomas, Nucl.Phys. A684, 380 (2001).[24] W. Weise, Acta Phys. Pol. B 31, 2715 (2000).[25] P. Kienle and T. Yamazaki, Phys. Lett. B 514, 1 (2001).122301-4

Deeply bound 1s and 2p pionic states in 205Pb and determination of the s-wave part of the pion-nucleus interaction

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Deeply bound 1s and 2p pionic states in 205Pb and determination of the s-wave part of the pion-nucleus interaction

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