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The European Physical Journal A

, Volume 34, Issue 2, pp 185–196 | Cite as

Two-particle scattering on the lattice: Phase shifts, spin-orbit coupling, and mixing angles

  • B. Borasoy
  • E. Epelbaum
  • H. Krebs
  • D. LeeEmail author
  • U. -G. Meißner
Regular Article - Theoretical Physics

Abstract.

We determine two-particle scattering phase shifts and mixing angles for quantum theories defined with lattice regularization. The method is suitable for any non-relativistic effective theory of point particles on the lattice. In the center-of-mass frame of the two-particle system we impose a hard spherical wall at some fixed large radius. For channels without partial-wave mixing the partial-wave phase shifts are determined from the energies of the nearly spherical standing waves. For channels with partial-wave mixing further information is extracted by decomposing the standing wave at the wall boundary into spherical harmonics, and we solve coupled-channels equations to extract the phase shifts and mixing angles. The method is illustrated and tested by computing phase shifts and mixing angles on the lattice for spin-1/2 particles with an attractive Gaussian potential containing both central and tensor force parts.

PACS.

13.75.Cs Nucleon-nucleon interactions (including antinucleons, deuterons, etc.) 21.30.-x Nuclear forces 34.50.-s Scattering of atoms and molecules 

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References

  1. 1.
    H.M. Müller, S.E. Koonin, R. Seki, U. van Kolck, Phys. Rev. C 61, 044320 (2000) nucl-th/9910038.CrossRefADSGoogle Scholar
  2. 2.
    T. Abe, R. Seki, A.N. Kocharian, Phys. Rev. C 70, 014315 (2004)CrossRefADSGoogle Scholar
  3. 3.
    S. Chandrasekharan, M. Pepe, F.D. Steffen, U.J. Wiese, Nucl. Phys. Proc. Suppl. 129, 507 (2004) hep-lat/0309093.CrossRefADSGoogle Scholar
  4. 4.
    S. Chandrasekharan, M. Pepe, F.D. Steffen, U.J. Wiese, JHEP 12, 035 (2003) hep-lat/0306020.CrossRefADSMathSciNetGoogle Scholar
  5. 5.
    D. Lee, B. Borasoy, T. Schäfer, Phys. Rev. C 70, 014007 (2004) nucl-th/0402072.CrossRefADSGoogle Scholar
  6. 6.
    D. Lee, T. Schäfer, Phys. Rev. C 72, 024006 (2005) nucl-th/0412002.CrossRefADSGoogle Scholar
  7. 7.
    M. Hamilton, I. Lynch, D. Lee, Phys. Rev. C 71, 044005 (2005) nucl-th/0412014.CrossRefADSGoogle Scholar
  8. 8.
    R. Seki, U. van Kolck, Phys. Rev. C 73, 044006 (2006) nucl-th/0509094.CrossRefADSGoogle Scholar
  9. 9.
    D. Lee, T. Schäfer, Phys. Rev. C 73, 015201 (2006) nucl-th/0509017.CrossRefADSGoogle Scholar
  10. 10.
    D. Lee, T. Schäfer, Phys. Rev. C 73, 015202 (2006) nucl-th/0509018.CrossRefADSGoogle Scholar
  11. 11.
    B. Borasoy, H. Krebs, D. Lee, U.-G. Meißner, Nucl. Phys. A 768, 179 (2006) nucl-th/0510047.CrossRefADSMathSciNetGoogle Scholar
  12. 12.
    F. de Soto, J. Carbonell, hep-lat/0610040 (2006).Google Scholar
  13. 13.
    B. Borasoy, E. Epelbaum, H. Krebs, D. Lee, U.-G. Meißner, Eur. Phys. J. A 31, 105 (2007) nucl-th/0611087.CrossRefADSGoogle Scholar
  14. 14.
    D. Lee, R. Thomson, Phys. Rev. C 75, 064003 (2007) nucl-th/0701048.CrossRefADSGoogle Scholar
  15. 15.
    J.-W. Chen, D.B. Kaplan, Phys. Rev. Lett. 92, 257002 (2004) hep-lat/0308016.CrossRefADSGoogle Scholar
  16. 16.
    M. Wingate, cond-mat/0502372 (2005).Google Scholar
  17. 17.
    A. Bulgac, J.E. Drut, P. Magierski, Phys. Rev. Lett. 96, 090404 (2006) cond-mat/0505374.CrossRefADSGoogle Scholar
  18. 18.
    D. Lee, Phys. Rev. B 73, 115112 (2006) cond-mat/ 0511332.CrossRefADSGoogle Scholar
  19. 19.
    E. Burovski, N. Prokofev, B. Svistunov, M. Troyer, Phys. Rev. Lett. 96, 160402 (2006) cond-mat/0602224.CrossRefADSGoogle Scholar
  20. 20.
    E. Burovski, N. Prokofev, B. Svistunov, M. Troyer, New J. Phys. 8, 153 (2006) cond-mat/0605350.CrossRefADSGoogle Scholar
  21. 21.
    D. Lee, Phys. Rev. B 75, 134502 (2007) cond-mat/ 0606706.CrossRefADSGoogle Scholar
  22. 22.
    M. Lüscher, Commun. Math. Phys. 104, 177 (1986). zbMATHCrossRefADSGoogle Scholar
  23. 23.
    M. Lüscher, Commun. Math. Phys. 105, 153 (1986).CrossRefADSGoogle Scholar
  24. 24.
    M. Lüscher, Nucl. Phys. B 354, 531 (1991).CrossRefADSGoogle Scholar
  25. 25.
    X. Li, C. Liu, Phys. Lett. B 587, 100 (2004) hep-lat/ 0311035.CrossRefADSGoogle Scholar
  26. 26.
    X. Feng, X. Li, C. Liu, Phys. Rev. D 70, 014505 (2004) hep-lat/0404001.CrossRefADSGoogle Scholar
  27. 27.
    S.R. Beane, P.F. Bedaque, A. Parreno, M.J. Savage, Phys. Lett. B 585, 106 (2004) hep-lat/0312004.CrossRefADSGoogle Scholar
  28. 28.
    K. Rummukainen, S.A. Gottlieb, Nucl. Phys. B 450, 397 (1995) hep-lat/9503028.CrossRefADSGoogle Scholar
  29. 29.
    C.H. Kim, C.T. Sachrajda, S.R. Sharpe, Nucl. Phys. B 727, 218 (2005) hep-lat/0507006.zbMATHCrossRefADSGoogle Scholar
  30. 30.
    I. Sato, P.F. Bedaque, hep-lat/0702021 (2007).Google Scholar
  31. 31.
    S. Sasaki, T. Yamazaki, Phys. Rev. D 74, 114507 (2006) hep-lat/0610081.CrossRefADSGoogle Scholar
  32. 32.
    S.R. Beane, W. Detmold, M.J. Savage, arXiv:hep-lat/ 0707.1670 (2007).Google Scholar
  33. 33.
    R.C. Johnson, Phys. Lett. B 114, 147 (1982).CrossRefADSMathSciNetGoogle Scholar
  34. 34.
    C. Lanczos, J. Res. Nat. Bur. Stand. 45, 255 (1950).MathSciNetGoogle Scholar
  35. 35.
    H.P. Stapp, T.J. Ypsilantis, N. Metropolis, Phys. Rev. 105, 302 (1957).CrossRefADSGoogle Scholar
  36. 36.
    J.M. Blatt, L.C. Biedenharn, Phys. Rev. 86, 399 (1952).zbMATHCrossRefADSGoogle Scholar
  37. 37.
    J.M. Blatt, L.C. Biedenharn, Rev. Mod. Phys. 24, 258 (1952).zbMATHCrossRefADSGoogle Scholar
  38. 38.
    C.A. Regal, C. Ticknor, J.L. Bohn, D.S. Jin, Phys. Rev. Lett. 90, 053201 (2003) cond-mat/0209071v1.CrossRefADSGoogle Scholar
  39. 39.
    J. Zhang, E.G.M. van Kempen, T. Bourdel, L. Khaykovich, J. Cubizolles, F. Chevy, M. Teichmann, L. Tarruell, S.J.J.M.F. Kokkelmans, C. Salomon, Phys. Rev. A 70, 030702(R) (2004).CrossRefADSGoogle Scholar
  40. 40.
    C.H. Schunck, M.W. Zwierlein, C.A. Stan, S.M.F. Raupach, W. Ketterle, A. Simoni, E. Tiesinga, C.J. Williams, P.S. Julienne, Phys. Rev. A 71, 045601 (2005) cond-mat/0407373.CrossRefADSGoogle Scholar
  41. 41.
    J.P. Gaebler, J.T. Stewart, J.L. Bohn, D.S. Jin, cond-mat/ 0703087 (2007).Google Scholar
  42. 42.
    J.G.E. Harris, S.V. Nguyen, S.C. Doret, W. Ketterle, J.M. Doyle, arXiv.org:0705.0713 (2007).Google Scholar
  43. 43.
    J. Doyle, B. Friedrich, R.V. Krems, F. Masnou-Seeuws, Eur. Phys. J. D 31, 149 (2004) physics/0505201.CrossRefADSGoogle Scholar
  44. 44.
    K. Gunter, T. Stoferle, H. Moritz, M. Kohl, T. Esslinger, Phys. Rev. Lett. 95, 230401 (2005) cond-mat/0507632.CrossRefADSGoogle Scholar
  45. 45.
    A. Micheli, G.K. Brennen, P. Zoller, Nat. Phys. 2, 341 (2006) quant-ph/0512222v2.CrossRefGoogle Scholar
  46. 46.
    G.K. Brennen, A. Micheli, P. Zoller, New J. Phys. 9, 138 (2007) quant-ph/0612180.CrossRefADSGoogle Scholar
  47. 47.
    P.F. Bedaque, U. van Kolck, Annu. Rev. Nucl. Part. Sci. 52, 339 (2002) nucl-th/0203055.CrossRefADSGoogle Scholar
  48. 48.
    E. Epelbaum, Prog. Part. Nucl. Phys. 57, 654 (2006) nucl-th/0509032.CrossRefADSGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag 2007

Authors and Affiliations

  • B. Borasoy
    • 1
  • E. Epelbaum
    • 1
    • 2
  • H. Krebs
    • 1
    • 2
  • D. Lee
    • 3
    • 1
    Email author
  • U. -G. Meißner
    • 1
    • 2
  1. 1.Helmholtz-Institut für Strahlen- und Kernphysik (Theorie)Universität BonnBonnGermany
  2. 2.Institut für Kernphysik (Theorie)Forschungszentrum JülichJülichGermany
  3. 3.Department of PhysicsNorth Carolina State UniversityRaleighUSA

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