Deeply Bound Pionic States

1
Deeply Bound Pionic StatesThe Pion-Nucleon
Interaction in the Medium

• Introduction
• Pionic transfer reactions
• Deeply bound states in Pb nuclei
• Access to the chiral condensate ?
• Pionic 1s states in Sn nuclei
• Conclusions

A. Gillitzer Gießen, 23.5.02
2
p-nucleon interaction

• weak s-wave interaction spontaneous ChSB
• Goldstone boson
• strong p-wave interaction D resonance
• s-wave pN scattering lengths
• pionic hydrogen and pionic deuterium data
  (PSI)
• H.C. Schröder et al., PLB 469 (1999) 25, D.
  Sigg et al., NPA 609 (1996) 310
• P. Hauser et al., PRC 58 (1998) R1869
• isoscalar a (-1.7 1.0) 10-3 mp-1
• isovector a- (90.0 1.6) 10-3 mp-1
• T.O.E. Ericson, B. Loiseau, A.W. Thomas,
  preprint hep-ph/00009812

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p-nucleus interaction

• optical potential (Ericson-Ericson type)
• effective scattering lengths b0 , b1
• 2mUopt(r) - 4p b(r) e2 B0 r2(r)
• 4pÑ c(r) e2-1C0r2(r) C1r(r)
  Dr(r)L(r)Ñ
• b(r) e1 b0r(r) b1Dr(r)
• c(r) e1-1 c0r(r) c1Dr(r)
• r(r) rn(r) rp(r) , Dr(r) rn(r) - rp(r)
• L(r) 1 4/3 pl c(r) e2-1C0r2(r)
  C1r(r)D(r)-1
• M. Ericson and T.O.E. Ericson, Ann. Phys. 36
  (1996) 323
• T.O.E. Ericson and W. Weise, Pions in Nuclei
  (1988)
• goal better understanding of s-wave interaction

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Pionic atoms conventionally
Capture of stopped p-
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Heavy pionic atoms

• Repulsive s-wave interaction
• binding energy reduced in 2p and 1s states
• width significantly reduced
• nuclear-pionic halo states

• E. Friedman and G. Soff,
• J. Phys. G 11 (1985) L37
• H. Toki and T. Yamazaki,
• Phys. Lett. B 213 (1988) 129

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Sensitivity to s and p wave potential

• strong interaction shift
• shallow states have attractive shift, p wave
  part dominant
• 1s and 2p states have repulsive shift
• 1s state almost exclusively determined by s
  wave part

Y. Umemoto, PhD thesis, Nara, Jan. 2000, Y.
Umemoto, S. Hirenzaki, K. Kume, and H.
Toki, Prog. Theo. Phys. 103 (2000)
337 Phys. Rev. C62 (2000)
024606
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Formation of deeply bound states

• use recoilfree pion transfer reactions

• K. Kilian, PANIC 1984, Heidelberg
• H. Toki, T. Yamazaki, PLB 213 (1988) 129

• angular momentum matching l q . r
• q 0 lp ln (substitutional)
• 300 MeV/u d 208Pb 3He 207Pbp Þ (2p)p(
  p1/2,3/2 )n-1l0 dominant

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Experimental technique

• need
• good energy resolution ( dE/E lt 10-3 )
• high luminosity ( L 1030 . . . 1031/cm2s )
• good background suppression
• (2.1011d /spill, 105p /spill, 0.3 3He /spill)
• use Fragment Separator at SIS (GSI)

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3He identification

• use sections 1 2 of FRS to precisely measure
  particle momenta
• use sections 3 4 of FRS to reject protons and
  identify 3He

• change of Br at F2 by degrader
• most protons are rejected
• measure time-of-flight and
• energy loss at F4
• 3He is unambiguously
• identified

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Energy calibration I

• focal plane x Þ 3He kinetic energy T3He Þ
  pion binding energy Bp
• Method (1)
• use p (d,3He) p0 reaction
• problems
• need to know pd
• peak position affected by
• instrumental effects

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Energy calibration II

• Method (2)
• use attenuated d beam at same magnetic
  rigidity
• pd(cal) p3He /2 pd(exp) /2
• problems
• corresponding d kinetic energy very low ( 85
  MeV/u )
• need exact beam energies
• drift chamber response for d and 3He different
• Method (3)
• use non-pionic (d,3He) transfer d AZ
  (A-1)(Z-1)g.s. 3He
• problems
• large momentum transfer Þ small cross section
• same beam energy Þ much higher 3He momentum
• same FRS setting Þ lower beam energy
• need exact beam energies

A. Gillitzer Gießen, 23.5.02
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Excitation energy spectra in Pb
208Pb (d,3He) 207Pbp
206Pb (d,3He) 205Pbp

• rich structure below the free pion emission
  threshold
• peaks interpreted as p- bound states (2p)p and
  (1s)p
• much better separation of (1s)p and (2p)p in
  205Pb p

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The 206Pb experiment

• n-holes 3p3/2, 3p1/2, 2f5/2
• B2p 5.110 0.045 MeV
• G2p 0.3210.060 MeV
• B1s 6.762 0.061 MeV
• G1s 0.7640.171 MeV

• Interpreted spectrum
• discrete bound states
• nuclear background
• free p- production
• p (d,3He) p0 peak

-0.062
-0.062
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Constraints to the pion-nucleus potential

• 1s state fully determined by the s-wave
  potential
• solve Klein-Gordon equation
• with Us(r) V(r) i W(r)
• deduce potential depth at r 0
• ( i.e. r r0 )
• V(0) 27.1 1.7 MeV
• W(0) -14.0 3.8 MeV
• 27 MeV repulsive mass shift
• of the p- in nuclear matter
• ( r r0 , rn/rp 1.5 )
• H. Geissel et al., Phys.Rev.Lett. 88 (2002)
  122301-1

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Chiral symmetry breaking of QCD

• hadron mass spectrum
• Mhadron gtgt mu,d
• no parity doublets
• 1 GeV mass gap
• spontaneous symmetry breaking
• finite quark condensate in QCD ground
• state
• p lowest collective excitation
• r,w dipole excitations of the vacuum
• experimental access to medium effects
• vector meson masses at r gt 0
• fp pion decay constant
• chiral order parameter
• DEG Ö2 mV 4p fp

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Comparison with chiral dynamics

• chiral dynamics calculations (R. Leisibach, W.
  Weise)
• use free and medium-modified fp

W. Weise, Nucl. Phys. A690 (2001) 98c

• include multi-scattering and
• absorption effects
• 205Pbp U0 27 MeV
• free T() double scattering
• U0 16 MeV

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Measurement of b1
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Search for 1s states in Sn isotopes

• long chain of stable isotopes Þ large
  variation of N/Z
• low lying (s1/2)n states Þ enhanced (1s)p
  states
• DWIA calculations
• ASn(d,3He) at Td 500 MeV, dEinstr 300 keV
• predicted Q value spectra Ex -Q c1 mp -
  Bp en
• expect clear 1s peak contributions from other
  n hole states small !
• Y. Umemoto, S. Hirenzaki, K. Kume and H. Toki,
  Phys. Rev. C62 (2000) 024606

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Precision and resolution

• measurement of B1s
• determine pbeam , p3He
• determine USIS
• dUSIS 1cm Þ dBp 10 keV
• measurement of G1s
• determine dEinstr
• energy calibration
• p ( d,3He ) p0 on (CH2)n
• d beam at p/q ( p/q)ref
• non-pionic ( d,3He ) transfer
• instrumental resolution
• non-pionic ( d,3He ) transfer
• ASn ( d,3He ) A-1Ing.s. ( g.s. g9/2 )
• ( p/q)3He ( p/q)ref Þ Td 187 MeV/u

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Pionic 1s states in Sn nuclei

• focal plane 3He kinetic energy spectra (
  preliminary )
• Td 503.388 MeV
• targets 20 mg/cm2 ASn ( 1.5 mm strip ) with
  thin mylar layer
• p (d,3He) p0 calibration peak indicated as p0
• corrected for acceptance, ion optics, long term
  energy drift
• no pionic peak observed in the 112Sn (d,3He)
  reaction
• single particle strength for (3s1/2)n-1 in
  111Sn known to be small

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Preliminary binding energies

• Data analysis in progress
• B1s 4 MeV in Sn isotopes
• B1s smaller for more neutron-rich Sn isotopes
• error in isotope shift dominated by statistics
• absolute uncertainty 50 keV

A. Gillitzer Gießen, 23.5.02
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Conclusions

• recoil-free (d,3He) transfer proven to be
  successful to form deeply bound pionic atoms
• pionic 1s states now seen in 5 nuclei
• 205Pbp data
• deduced potential depth Us 27 MeV
• significantly smaller than derived from free pN
  scattering
• problem of missing repulsion solved with
  reduced fp
• separation of isovector from isoscalar
  component
• study pionic 1s states with different N/Z
• new pionic 1s states in Sn isotopes
• (1s)p peak seen in 115,119,123Sn, not in 111Sn
• preliminary values for binding energies
• B1s 4 MeV with systematic A dependence

A. Gillitzer Gießen, 23.5.02
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S236 Collaboration
Darmstadt - Jülich - München - Nara - Tokyo GSI
Darmstadt H. Geissel, M. Matos, G.
Münzenberg, H. Weick, M.
Winkler FZ Jülich A. Gillitzer TU
München H. Gilg, P. Kienle, L. Maier Nara
Womens University M. Fujita, S.
Hirenzaki Niigata University T.
Ohtsubo University of Tokyo R. Hayano, M.
Shindo, K. Suzuki, T. Suzuki, T.
Yamazaki Tokyo Inst. of Technology K. Itahashi,
M. Iwasaki, M.Sato, T.
Yoneyama presently RI Beam Science Lab., RIKEN
A. Gillitzer Gießen, 23.5.02
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Calibration spectra

• Energy calibration
• p (d,3He) p0 reaction
• 15 mg/cm2 (CH2)n
• target

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Resolution and precision
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Comparison with theory
208Pb (d,3He) experiment H. Gilg et al.,
Phys. Rev. C62 (2000) 025201
DWIA calculation Nuclear background taken
from experiment S. Hirenzaki, H. Toki and T.
Yamazaki, Phys. Rev. C44 (1991) 2472
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The 206Pb (d,3He) experiment

• decomposition of pionic and
• nuclear excitations
• known n-hole spectrum
• relative strength from DWIA
• problem p1/2 - p3/2 doublet

• shell model systematics
• no 3p1/2 neutrons in 206Pb
• better 1s - 2p separation

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Potential parameterizations
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b0 - B0 correlation

• b0 and ReB0 strongly correlated
• (Seki-Masutani relation)
• b0 (e1/e2) reff ReB0 constant
• b0 b0 0.215 ReB0 constant

KLTK90 J. Konijn et al., NPA519 (90) 773
BFG97 C. Batty, E. Friedman and A.
Gal, Phys. Rep. 287 (1997) 385 parameter
sets are global fits to existing pionic atom data
with different b0, b1, ReB0
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Sensitivity to neutron skin
Dnp Öárn2ñ - Öárp2ñ gt 0

• Halo type larger diffuseness
• Skin type larger half density radius

antiprotonic atom data 650 MeV p elastic
scattering data Dnp 0.17 fm
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Predicted Sn(d,3He) spectra

• DWIA calculations
• ASn(d,3He) at Td 500 MeV, dEinstr 300 keV
• substitutional states dominant for A ³ 116
• Y. Umemoto, S. Hirenzaki, K. Kume and H. Toki,
  Phys. Rev. C62 (2000) 024606

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Beam energy dependence

• DWIA calculations
• best population of substitutional 1s state at
  Td 250 MeV/u
• Y. Umemoto, PhD thesis, Nara, Jan. 2000
• Y. Umemoto, S. Hirenzaki, K. Kume and H. Toki,
  Prog. Theo. Phys. 103 (2000) 337

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Isotope shift and b1

• Isotope shift 115Sn - 123Sn
• B1s and DB1s vs. b1
• V0 27 MeV from 205Pbp 1s state
• SM1 Seki-Masutani
• free free pN scattering length

A. Gillitzer Gießen, 23.5.02