CHIPS muon capture in Geant4

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CHIPS muon capture in Geant4

• Mikhail Kosov, ACAT07

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Welcome to CHIPS World
CHiral Invariant Phase Spase (CHIPS) is the first
3D low energy parton model
Quark exchange
Quark fusion
(E,p)
q
q
(E,p)
k
k
Mesons
Fragments
Clusterization
Quasmon NpartonsM/2Tc
1. Asymptotic freedom of quark-partons 2.
Critical temperature Tc of virtual gluons 3.
Quark fusion makes secondary mesons 4. Quark
exchange provides nuclear fragments 5. Nuclear
clusterization (nucleon clusters) 6.
Energy-momentum charge conservation 7. Smooth
transition from low to high energies dW/kdk(1-2
k/M)n-3 ? dW/xdx(1-x)n-2
Feynman diagrams
Isgur diagrams
N
N
N.Isgur, Nucl.Phys.,A497(1989)91
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Quark exchange (E) kME q (p) k p
q 2k pE-M
k
M
q
(fragments)
Quark fusion kqE (E) k- qp
(p) 2kEp
E,p
k
q
(mesons)
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Neutron spectra in m--capture reactions

• Since 60s there exists a problem of high energy
  neutrons in muon capture reactions
• Maximum neutron energy in the m-(p,n)nm reaction
  is Tnm2m/2(mNmm)5.3 MeVltEsplit
• Absolute normalization of nuclear m--capture
  depends on a nuclear capture rate Lc1/tc
  .45(H)12610(U)ms-1 and on a decay rate Ld
• As muons are bounded, the decay rate Ld is
  reduced by Huff factor (H) LdH/tmH455 ms-1
• For light nuclei LcltltLd, heavy nuclei LcgtgtLd

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Parameterization of atomic coefficients

• The Huff factor (l.W. Huff, Ann.Phys. (N.Y.) 16
  (1961) 288) was investigated in I.M. Blair et
  al., Proc.Phys.Soc. London 80 (1962) 938
  H10.82(U)
• In CHIPS H is tabulated till 19F and for Zgt9 it
  is parameterized as a function of Z (only)
• Isotope variation of the nuclear capture rate can
  be estimated by a Primakoff formula
• Lc(A,Z) C(Z)(1.-3.125(A-Z)/2A)
• In CHIPS Lc is tabulated till 19F and for Zgt9 it
  is parameterized as a function of Z (only)

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CHIPS approximation of the Huff factor
Table
Fit
1-
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CHIPS fit of m- nuclear capture rate (Lc)
Table
Fit
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Simulation of decay of bounded muon

• The effective nuclear charge Zeff and the nuclear
  mass A can be used for simulation of the bounded
  muon decay
• Recently electron spectra
• were accurately calculated in
• Atomic Data and Nuclear Data
  Tables,v.54(1993)165
• The electron spectrum can exceed a free mm/2
  threshold, because the momentum can be
  transferred to the recoil nucleus.
• For simulation geant4/tests/test29 is made

g
m-
Atomic x-rays
Atomic e-
nm
K shell

ne
e-
recoil nucleus
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Geant4 processes for muon capture

• The inherited from GEANT3 (FLUKA) process
  G4MuonMinusCaptureAtRest was substituted (in
  G4.8.0.) by a process with the same name
• The algorithm of this process is precompound
  deexcitation after m-(pbound,nfree)nm reaction
• An alternative process is G4QCaptureAtRest
  process of the G4 CHIPS physics package
• It is based on the CHIPS deexcitation after 97.5
  m-(d,u)nm and 2.5 m-?dunm reactions
• On pictures old blue curves, new (CHIPS) red
  curves, dots are published Tables/Data

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(test29)
G4MuonMinusCaptureAtRest (all physics lists 8.2)
G4MuonMinusCaptureAtRest (8.2.ref-02, fixed bug)
CHIPS G4QCaptureAtRest (new development)
Data Tables 54(1993)165
Decay bug
m-
(nenm)

e-
The same direction
A
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(test29)
G4MuonMinusCaptureAtRest (8.2)
Atomic x-rays
G4MuonMinusCaptureAtRest
CHIPS G4QCaptureAtRest
Data Tables 54(1993)165
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Spectra of nucleons in nuclear m--capture

• In addition to classic E. Segre data for Ca (?)
  (Experimental Nuclear Physics, N.-Y., Wiley,1953)
  and R.M. Sudelin, R.M. Edelstein measurements
  (Phys.Rev. C7 (1973) 1037) on Si, S, and Ca ()
  There are recent data for neutron spectra
• for 16O (Nucl.Phys. A408 (1983) 573)
  16O(m-,nmxn)
• for 165Ho (Phys. Lett., B137 (1984) 339) ()
• for O, Si, Ca, Pb (Nucl. Phys. A436 (1985) 717)
  (?)
• for 40Ca (Phys. Lett., B177 (1986) 21) ()
• The only m-nuclear (Ca, Y) spectra of protons are
  W.J.Cumming, Nuclear Muon Capture in Extreme
  Kinematics, Stanford University, Thesis (Ph.D),
  1992 (o)
• Spectra of d and t (Si) Sov.Phys.JETP,33(1971)11,
  Sov.J.Nucl.Phys,28(1978)297 (Si(d) o, ?, Si(t)
  ? )

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CHIPSG4QCaptureAtRest(test29,m-Ca)
Filled points - neutrons Open points - protons
m-u?nmd
(m-?p-)
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m-?nm ud
m-p?nmn (8.2) G4MuonMinusCaptureAtRest
PCAC mmm-Bm-MiMf-me r(p,E)c?r(pi,Ei)d(mEi
-En-E)d3(pi-pn-p)d3pid3pn
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CHIPSG4QCaptureAtRest(test29, m-Si)
kd(mm/2)
kt(mm/2)
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CHIPS G4QCaptureAtRest (test29,p-C)
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Conclusion

• A bug was found in electron spectra simulated by
  the G4MuonMinusCaptureAtRest class electron is
  radiated in muon momentum direction
• The m-(pbound,nfree)nm capture is unrealistic. On
  hadron level the PCAC mechanism is better
  J.Bernabeu, T.E.O. Ericson, C.Jarlskog, Phys.
  Lett., 69B (1977) 161
• Precompound model cannot reproduce the difference
  between proton and neutron spectra
• CHIPS with 2.5 parameter for m-?qqnm decay
  fits both m decay and m nuclear capture

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