1. CHIPS muon capture in Geant4 Mikhail Kosov, ACAT’07

2. M.Kosov. G4 Muon capture, ACAT072 April 23-27,2007 k k (E,p) q q Quasmon: N partons =M/2T c Fragments Mesons CHiral Invariant Phase Spase (CHIPS) is the first 3D low energy parton model Quark exchangeQuark fusion Quark exchange Barrier 1. Asymptotic freedom of quark-partons 2. Critical temperature T c 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~(1-2k/M) n-3 → dW/xdx~(1-x) n-2 Clusterization  Feynman diagramsIsgur diagrams N.Isgur, Nucl.Phys.,A497(1989)91 N N

3. M.Kosov. G4 Muon capture, ACAT073 April 23-27,2007 Quark exchange (E:) k+M=E +q (p:) k =p – q 2k = p+E-M M E,p q k Quark fusion k+q=E (E:) k- q=p (p:) 2k=E+p k q E,p (fragments) (mesons)

4. M.Kosov. G4 Muon capture, ACAT074 April 23-27,2007 Neutron spectra in  - -capture reactions Since 60’s there exists a problem of high energy neutrons in muon capture reactions Maximum neutron energy in the  - (p,n)  reaction is T n =m 2  /2(m N +m  )=5.3 MeV<E split Absolute normalization of nuclear  - -capture depends on a nuclear capture rate  c =1/  c [.45(H)÷12610(U)  s -1 ] and on a decay rate  d As muons are bounded, the decay rate  d is reduced by Huff factor (H):  d =H/   =H ∙455  s -1 For light nuclei:  c >  d

5. M.Kosov. G4 Muon capture, ACAT075 April 23-27,2007 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 : H=1÷0.82(U) In CHIPS H is tabulated till 19 F and for Z>9 it is parameterized as a function of Z (only) Isotope variation of the nuclear capture rate can be estimated by a Primakoff formula:  c (A,Z) = C(Z) ∙ ( 1. - 3.125 ∙ (A - Z)/2A ) In CHIPS  c is tabulated till 19 F and for Z>9 it is parameterized as a function of Z (only)

6. M.Kosov. G4 Muon capture, ACAT076 April 23-27,2007 TableFit 1-1- CHIPS approximation of the Huff factor

7. M.Kosov. G4 Muon capture, ACAT077 April 23-27,2007 CHIPS fit of  - nuclear capture rate (  c ) TableFit

8. M.Kosov. G4 Muon capture, ACAT078 April 23-27,2007 Simulation of decay of bounded muon The effective nuclear charge Z eff 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 m  /2 threshold, because the momentum can be transferred to the recoil nucleus. For simulation geant4/tests/test29 is made -- recoil nucleus Atomic e - e-e-  e ~ K shell Atomic x-rays

9. M.Kosov. G4 Muon capture, ACAT079 April 23-27,2007 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  - (p bound,n free )  reaction An alternative process is G4QCaptureAtRest process of the G4 CHIPS physics package It is based on the CHIPS deexcitation after 97.5%  - ( d, u )  and 2.5%  - → d + u +  reactions On pictures: old – blue curves, new (CHIPS) – red curves, dots are published Tables/Data _

10. M.Kosov. G4 Muon capture, ACAT0710 April 23-27,2007 G4MuonMinusCaptureAtRest (8.2.ref-02, fixed bug) CHIPS G4QCaptureAtRest (new development) Data Tables 54(1993)165 G4MuonMinusCaptureAtRest (all physics lists 8.2) Decay bug: A -- e-e- ( e +  ) ˜ The same direction (test29)

11. M.Kosov. G4 Muon capture, ACAT0711 April 23-27,2007 G4MuonMinusCaptureAtRest (8.2) CHIPS G4QCaptureAtRest Data Tables 54(1993)165 G4MuonMinusCaptureAtRest Atomic x-rays (test29)

12. M.Kosov. G4 Muon capture, ACAT0712 April 23-27,2007 Spectra of nucleons in nuclear  - -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 16 O ( Nucl.Phys. A408 (1983) 573 ) 16 O(  -,  x n)  for 165 Ho ( Phys. Lett., B137 (1984) 339 ) (■)  for O, Si, Ca, Pb ( Nucl. Phys. A436 (1985) 717 ) (●)  for 40 Ca ( Phys. Lett., B177 (1986) 21 ) (■) The only  -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): ▲ )

13. M.Kosov. G4 Muon capture, ACAT0713 April 23-27,2007 (-→-)(-→-)  - +p*→  +n (8.2) G4MuonMinusCaptureAtRest  - +u→  +d  - →  + u+d Filled points - neutrons Open points - protons _ CHIPS:G4QCaptureAtRest(test29,  - Ca) “PCAC”:  *=m  -B  -M i +M f -m e  (p,E)=c ∫  (p i,Ei)  (  *+E i -E -E)  3 (p i -p -p)d 3 p i d 3 p

14. M.Kosov. G4 Muon capture, ACAT0714 April 23-27,2007 CHIPS:G4QCaptureAtRest(test29,  - Si) k d (m  /2) k t (m  /2)

15. M.Kosov. G4 Muon capture, ACAT0715 April 23-27,2007 CHIPS: G4QCaptureAtRest (test29,  - C)

16. M.Kosov. G4 Muon capture, ACAT0716 April 23-27,2007 Conclusion A bug was found in electron spectra simulated by the G4MuonMinusCaptureAtRest class: electron is radiated in muon momentum direction The  - (p bound,n free )  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  - →q+q+  decay fits both  * decay and  nuclear capture _