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Nucleon-deuteron breakup differential cross sections derived from

Nucleon-deuteron breakup differential cross sections derived from the quark-model NN interaction. Y. Fujiwara and K. Fukukawa, Kyoto University. 1. Motivation 2. From Sharp cut-off Coulomb to “practical” screening Coulomb 4. Application to 3-body Coulomb problem

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Nucleon-deuteron breakup differential cross sections derived from

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  1. Nucleon-deuteron breakup differential cross sections derived from the quark-model NN interaction Y. Fujiwara and K. Fukukawa, Kyoto University 1. Motivation 2. From Sharp cut-off Coulomb to“practical” screening Coulomb 4. Application to 3-body Coulomb problem 5. Coulomb effect onthebreakupdifferential cross sections 6. Results ( comparison with Kyushu data, KVI data etc.) 7. Conclusion

  2. Motivation nd and pd scattering based on quark-model baryon-baryon interaction fss2 Accurate estimation of Coulomb effects is crucial to compare with experimental data (5-10% in low energies Elab<10 MeV) If disagree with experiment  which is bad, Coulomb treatment or the nuclear force? Standard treatment in momentum representation : “screening and renormalization approach” E. Alt, W. Sandhas and H. Ziegelmann,Phys. Rev. C17, 1981 (1978) , … many papers, … A. Deltuva, A. C. Fonseca and P. U. Sauer, Phys. Rev. C71, 054005 (2005); C72, 054004 (2005) with n=4, R=20 fm not easy to solve AGS equation

  3. Based on the Taylor’s Theorem for screening Coulomb potential Nuovo Cimmento 23B, 318 (1974); M.D. Semon and J. R. Taylor, ibid. 26A, 48 (1975) Case ofsharp cut-off for pd scattering with ℓN =0 phase shift difference ratio of Jost functions Elab=3MeV ℓ = 0 - 4 Elab=3MeV ℓ = 0 - 4 for the regular screened Coulomb wave function Convergence is very slow !

  4. Recent improvement R. Skibiński, J. Golak, H. Witala and W. GLöckle, Euro. Phys. J . A40, 215 (2009) H. Witala, R. Skibiński, R. Skibiński, and W. GLöckle, Euro. Phys. J . A41, 369 (2009) H. Witala, R. Skibiński, R. Skibiński, and W. GLöckle, Euro. Phys. J . A41, 385 (2009) include T=3/2, no partial wave expansion for high j (=I), full Coulomb half on-shell t-matrix  many nice features butvery complicated formulation Our approach C.M. Vincent and S.C. Phatak, Phys. Rev. C10, 391 (1974) based on Vincent-Phatak method for the sharp cut-off Coulomb • sharp cut-off Coulomb (1/r)(-r) on the quark level • error function Coulomb (1/r){erf(r)-1/2[erf((r+)+erf((r-)]} • on the nucleon level • sharp cut-off *)  folded Coulomb potential on the pd level • (Problems still remains) • channel dependence on the truncation of the model space • (NN relative angular mom. should be large enough: Imax= 4 ) • quasi singular nature of screened Coulomb force • (not easy to solve AGS equation accurately:  = 8 – 9 fm） *) K. Fukukawa and Y. Fujiwara, Prog. Theor. Phys. 125 (2011) 729

  5. The two-cluster folding potential is rewritten as C(R) (R)short range Screening function should be consistently derived from the introduced cut-of Coulomb force pd folded Coulomb potential and the screening factor Coulomb region connection “practical” screening Coulomb function no Coulomb region realistic case (ℓ Sc) J=1/2+ , but almost channel independent !

  6. 1  2 (P) W (P) 3 =3 Application to 3-body Coulomb problem Step 1. 2-body t-matrix (sharp cut-off at quark level) : error function Coulomb isospin formalism  for I=1 pair (2/3)(tpp)+ (1/3)tnp : short range Step 2. AGS (Alt-Grassberger-Sandhas) equation

  7. : short range force Wave functions where reduction to the components for the deuteron channel Asymptotic forms are used to establish the connection condition for the pd elastic scattering amplitudes

  8. connection condition for finite  Step 3. 2-potential formula approximation comes in ! renormalize and take    limit in the first term Step 4. elastic differential cross sections Step 5. breakup cross sections Opp=(1+z(1))/2 (1+z(2))/2 common phase factors ( : should be large enough) pp and np half off-shell t-matrices approximation comes in ! phase spacefactor

  9. k1 k3 q3 p3 k2 =3 breakup differential cross sections (Various breakup configurations) • QFS (quasi-free scattering) k=0 • FSI (final-state interaction) p=0 • COLL (collinear) q=0 • SS (standard space star) 120 perpendicular • COP, CST (coplanar star) 120 coplanar • non-standard: othernon-specific configurations Kyushu data • 13 MeVp + d (p incident） • n + d (n incident） • 16 MeVd + p (d incident) Experimental data nd J. Strate et al., Nucl. Phys. A501 (1989) 51 pd G. Rauplich ey al., Nucl. Phys. A535(1991)313 F.D. Correll et al., Nucl. Phys. A475 (1987) 407 • 130 MeVd + p (d incident)KVI data: St. Kistryn et al., Phys. Rev.C72, • 044006 (2005); Phys. Lett. B641 (2006) 23 comparison with meson-exchange predictions

  10. 1 QFS k30 39 39 3 2 lab. Breakup differential cross sections at Ep=13 MeV p n p red with Coulomb H. Witala et al., Eur. Phys. J. A41, 385 (2009)

  11. H. Witala et al., Eur. Phys. J. A41, 385 (2009) 13 MeV 3.4 3.4 3.4 S. Kimura et al. This conference

  12. ● present 19 MeV ○ Koeln ― pd pd+Δ nd QFS S [MeV] Calc. by A. Deltuva et al. (2005) 19 MeV too large S. Kimura et al. This conference 2.8 2.8 red with Coulomb

  13. 22.7 MeV 22.7 MeV data seem to have normalization problems.

  14. np FSI p20 1 39 3 37 62.5 lab. p20 2 p10 J. Kuroś-Żolnierczuk et al., Phys. Rev. C66, 024004 (2002)

  15. 1 COLL2 116 3 q30 98 2 c.m. J. Kuroś-Żolnierczuk et al. (2002)

  16. SS 1 120 50.5 3 50.5 50.5 120 120 2 c. m. lab. J. Kuroś-Żolnierczuk et al. (2002) serious problem !

  17. red Coulomb with  = 8 fm Ed= 16 MeV deuteron incident (Ep= 8 MeV) Exp: F.D. Correll et al., Nucl. Phys. A475 (1987) 407 some improvement !

  18. pp FSI 20 1 p30 2 68 lab. 3 Coulomb force is very important ! Comparison with KVI data 13  = 8 fm E12= 0.61 0.18 0.66 MeV  = 20 fm ? by Deltuva St. Kistryn et al., Phys. Rev.C72, 044006 (2005); Phys. Lett. B641 (2006) 23

  19. 1=2=13 12=40 12=60 12=80 12=140 12=160 12=120 problem in nuclear force ?

  20. 1=30 2=25 seem to be almost right 12=40 12=80 12=60 12=100 12=120 12=140

  21. Conclusion • Our quark-model NN interaction fss2 can reproduce • overall characteristics of the nd and pd scattering. • For the elastic scattering, the screening Coulomb force is • treated by the Vincent and Phatak method, in a consistent • way with the sharp cut-off Coulomb force introduced at • the quark level. • For the breakup differential cross sections, the screening • Coulomb approach improves agreement with the pd data • on the whole. However, further improvement is necessary • when the Coulomb effect is very large as in thepp final • state interaction. The Coulomb effects of the quasi-free • and symmetric space star configurations at 13 MeV are • not improved either.

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