Skip to main content
SpringerLink
Log in

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

  • Regular Article - Theoretical Physics
  • Published:
The European Physical Journal A Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. H.M. Müller, S.E. Koonin, R. Seki, U. van Kolck, Phys. Rev. C 61, 044320 (2000) nucl-th/9910038.

    Article  ADS  Google Scholar 

  2. T. Abe, R. Seki, A.N. Kocharian, Phys. Rev. C 70, 014315 (2004)

    Article  ADS  Google Scholar 

  3. S. Chandrasekharan, M. Pepe, F.D. Steffen, U.J. Wiese, Nucl. Phys. Proc. Suppl. 129, 507 (2004) hep-lat/0309093.

    Article  ADS  Google Scholar 

  4. S. Chandrasekharan, M. Pepe, F.D. Steffen, U.J. Wiese, JHEP 12, 035 (2003) hep-lat/0306020.

    Article  ADS  MathSciNet  Google Scholar 

  5. D. Lee, B. Borasoy, T. Schäfer, Phys. Rev. C 70, 014007 (2004) nucl-th/0402072.

    Article  ADS  Google Scholar 

  6. D. Lee, T. Schäfer, Phys. Rev. C 72, 024006 (2005) nucl-th/0412002.

    Article  ADS  Google Scholar 

  7. M. Hamilton, I. Lynch, D. Lee, Phys. Rev. C 71, 044005 (2005) nucl-th/0412014.

    Article  ADS  Google Scholar 

  8. R. Seki, U. van Kolck, Phys. Rev. C 73, 044006 (2006) nucl-th/0509094.

    Article  ADS  Google Scholar 

  9. D. Lee, T. Schäfer, Phys. Rev. C 73, 015201 (2006) nucl-th/0509017.

    Article  ADS  Google Scholar 

  10. D. Lee, T. Schäfer, Phys. Rev. C 73, 015202 (2006) nucl-th/0509018.

    Article  ADS  Google Scholar 

  11. B. Borasoy, H. Krebs, D. Lee, U.-G. Meißner, Nucl. Phys. A 768, 179 (2006) nucl-th/0510047.

    Article  ADS  MathSciNet  Google Scholar 

  12. F. de Soto, J. Carbonell, hep-lat/0610040 (2006).

  13. B. Borasoy, E. Epelbaum, H. Krebs, D. Lee, U.-G. Meißner, Eur. Phys. J. A 31, 105 (2007) nucl-th/0611087.

    Article  ADS  Google Scholar 

  14. D. Lee, R. Thomson, Phys. Rev. C 75, 064003 (2007) nucl-th/0701048.

    Article  ADS  Google Scholar 

  15. J.-W. Chen, D.B. Kaplan, Phys. Rev. Lett. 92, 257002 (2004) hep-lat/0308016.

    Article  ADS  Google Scholar 

  16. M. Wingate, cond-mat/0502372 (2005).

  17. A. Bulgac, J.E. Drut, P. Magierski, Phys. Rev. Lett. 96, 090404 (2006) cond-mat/0505374.

    Article  ADS  Google Scholar 

  18. D. Lee, Phys. Rev. B 73, 115112 (2006) cond-mat/ 0511332.

    Article  ADS  Google Scholar 

  19. E. Burovski, N. Prokofev, B. Svistunov, M. Troyer, Phys. Rev. Lett. 96, 160402 (2006) cond-mat/0602224.

    Article  ADS  Google Scholar 

  20. E. Burovski, N. Prokofev, B. Svistunov, M. Troyer, New J. Phys. 8, 153 (2006) cond-mat/0605350.

    Article  ADS  Google Scholar 

  21. D. Lee, Phys. Rev. B 75, 134502 (2007) cond-mat/ 0606706.

    Article  ADS  Google Scholar 

  22. M. Lüscher, Commun. Math. Phys. 104, 177 (1986).

    Article  MATH  ADS  Google Scholar 

  23. M. Lüscher, Commun. Math. Phys. 105, 153 (1986).

    Article  ADS  Google Scholar 

  24. M. Lüscher, Nucl. Phys. B 354, 531 (1991).

    Article  ADS  Google Scholar 

  25. X. Li, C. Liu, Phys. Lett. B 587, 100 (2004) hep-lat/ 0311035.

    Article  ADS  Google Scholar 

  26. X. Feng, X. Li, C. Liu, Phys. Rev. D 70, 014505 (2004) hep-lat/0404001.

    Article  ADS  Google Scholar 

  27. S.R. Beane, P.F. Bedaque, A. Parreno, M.J. Savage, Phys. Lett. B 585, 106 (2004) hep-lat/0312004.

    Article  ADS  Google Scholar 

  28. K. Rummukainen, S.A. Gottlieb, Nucl. Phys. B 450, 397 (1995) hep-lat/9503028.

    Article  ADS  Google Scholar 

  29. C.H. Kim, C.T. Sachrajda, S.R. Sharpe, Nucl. Phys. B 727, 218 (2005) hep-lat/0507006.

    Article  MATH  ADS  Google Scholar 

  30. I. Sato, P.F. Bedaque, hep-lat/0702021 (2007).

  31. S. Sasaki, T. Yamazaki, Phys. Rev. D 74, 114507 (2006) hep-lat/0610081.

    Article  ADS  Google Scholar 

  32. S.R. Beane, W. Detmold, M.J. Savage, arXiv:hep-lat/ 0707.1670 (2007).

  33. R.C. Johnson, Phys. Lett. B 114, 147 (1982).

    Article  ADS  MathSciNet  Google Scholar 

  34. C. Lanczos, J. Res. Nat. Bur. Stand. 45, 255 (1950).

    MathSciNet  Google Scholar 

  35. H.P. Stapp, T.J. Ypsilantis, N. Metropolis, Phys. Rev. 105, 302 (1957).

    Article  ADS  Google Scholar 

  36. J.M. Blatt, L.C. Biedenharn, Phys. Rev. 86, 399 (1952).

    Article  MATH  ADS  Google Scholar 

  37. J.M. Blatt, L.C. Biedenharn, Rev. Mod. Phys. 24, 258 (1952).

    Article  MATH  ADS  Google Scholar 

  38. C.A. Regal, C. Ticknor, J.L. Bohn, D.S. Jin, Phys. Rev. Lett. 90, 053201 (2003) cond-mat/0209071v1.

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  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.

    Article  ADS  Google Scholar 

  41. J.P. Gaebler, J.T. Stewart, J.L. Bohn, D.S. Jin, cond-mat/ 0703087 (2007).

  42. J.G.E. Harris, S.V. Nguyen, S.C. Doret, W. Ketterle, J.M. Doyle, arXiv.org:0705.0713 (2007).

  43. J. Doyle, B. Friedrich, R.V. Krems, F. Masnou-Seeuws, Eur. Phys. J. D 31, 149 (2004) physics/0505201.

    Article  ADS  Google Scholar 

  44. K. Gunter, T. Stoferle, H. Moritz, M. Kohl, T. Esslinger, Phys. Rev. Lett. 95, 230401 (2005) cond-mat/0507632.

    Article  ADS  Google Scholar 

  45. A. Micheli, G.K. Brennen, P. Zoller, Nat. Phys. 2, 341 (2006) quant-ph/0512222v2.

    Article  Google Scholar 

  46. G.K. Brennen, A. Micheli, P. Zoller, New J. Phys. 9, 138 (2007) quant-ph/0612180.

    Article  ADS  Google Scholar 

  47. P.F. Bedaque, U. van Kolck, Annu. Rev. Nucl. Part. Sci. 52, 339 (2002) nucl-th/0203055.

    Article  ADS  Google Scholar 

  48. E. Epelbaum, Prog. Part. Nucl. Phys. 57, 654 (2006) nucl-th/0509032.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Helmholtz-Institut für Strahlen- und Kernphysik (Theorie), Universität Bonn, Nußallee 14-16, D-53115, Bonn, Germany

    B. Borasoy, E. Epelbaum, H. Krebs, D. Lee & U. -G. Meißner

  2. Institut für Kernphysik (Theorie), Forschungszentrum Jülich, D-52425, Jülich, Germany

    E. Epelbaum, H. Krebs & U. -G. Meißner

  3. Department of Physics, North Carolina State University, 27695, Raleigh, NC, USA

    D. Lee

Authors
  1. B. Borasoy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. Epelbaum
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. Krebs
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. D. Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. U. -G. Meißner
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. Lee.

Additional information

A. Schäfer

Rights and permissions

Reprints and permissions

About this article

Cite this article

Borasoy, B., Epelbaum, E., Krebs, H. et al. Two-particle scattering on the lattice: Phase shifts, spin-orbit coupling, and mixing angles. Eur. Phys. J. A 34, 185–196 (2007). https://doi.org/10.1140/epja/i2007-10500-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epja/i2007-10500-9

PACS.

Search

Navigation