Skip to main content
SpringerLink
Log in

\(^1S_0\) Pairing in Neutron Matter

  • Published:
Journal of Low Temperature Physics Aims and scope Submit manuscript

Abstract

We report calculations of the superfluid pairing gap in neutron matter for the \(^1S_0\) components of the Reid soft-core \(V_6\) and the Argonne \(V_{4}'\) two-nucleon interactions. Ground-state calculations have been carried out using the central part of the operator-basis representation of these interactions to determine optimal Jastrow–Feenberg correlations and corresponding effective pairing interactions within the correlated basis formalism, the required matrix elements in the correlated basis being evaluated by Fermi hypernetted-chain (FHNC) techniques. Different implementations of the Fermi hypernetted-chain Euler–Lagrange (FHNC-EL) method agree at the percent level up to nuclear matter saturation density. For the assumed interactions, which are realistic within the low density range involved in \(^1S_0\) neutron pairing, we did not find a dimerization instability arising from divergence of the in-medium scattering length, as was reported recently for simple square-well and Lennard–Jones potential models (Fan et al. in Phys Rev A 92:023640, 2015).

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.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. J. Bardeen, L.N. Cooper, J.R. Schrieffer, Phys. Rev. 108, 1175 (1957)

    Article  ADS  MathSciNet  Google Scholar 

  2. R. Broglia, V. Zelevensky, Fifty Years of Nuclear BCS (World Scientific, Singapore, 2013)

    Book  Google Scholar 

  3. A. Bohr, B.R. Mottelson, D. Pines, Phys. Rev. 110, 936 (1958)

    Article  ADS  Google Scholar 

  4. L.N. Cooper, R.L. Mills, A.M. Sessler, Phys. Rev. 114, 1377 (1959)

    Article  ADS  MathSciNet  Google Scholar 

  5. J.R. Schrieffer, Theory Of Superconductivity (Advanced Books Classics), revised edn. (Perseus Books, New York, 1999)

  6. R.L. Mills, A.M. Sessler, S.A. Moszkowski, D.G. Shankland, Phys. Rev. Lett. 3, 381 (1959)

    Article  ADS  Google Scholar 

  7. R.V. Reid Jr., Ann. Phys. (NY) 50, 411 (1968)

    Article  ADS  Google Scholar 

  8. J.M.C. Chen, J.W. Clark, R.D. Davé, V.V. Khodel, Nucl. Phys. A 555, 59 (1993)

    Article  ADS  Google Scholar 

  9. V.A. Khodel, V.V. Khodel, J.W. Clark, Nucl. Phys. A 598, 390 (1996)

    Article  ADS  Google Scholar 

  10. J.W. Clark, C.H. Yang, Lett. Nuovo Cimento 3, 272 (1970)

    Article  Google Scholar 

  11. C.H. Yang, J.W. Clark, Nucl. Phys. A 174, 49 (1971)

    Article  ADS  Google Scholar 

  12. C.H. Yang, Ph.D. thesis, Washington University, 1971

  13. J.W. Clark, in Progress in Particle and Nuclear Physics, vol. 2, ed. by D.H. Wilkinson (Pergamon Press Ltd., Oxford, 1979), pp. 89–199

    Google Scholar 

  14. N.C. Chao, J.W. Clark, C.H. Yang, Nucl. Phys. A 179, 320 (1972)

    Article  ADS  Google Scholar 

  15. E. Krotscheck, in Introduction to Modern Methods of Quantum Many-Body Theory and their Applications, Advances in Quantum Many-Body Theory, vol. 7, ed. by A. Fabrocini, S. Fantoni, E. Krotscheck (World Scientific, Singapore, 2002), pp. 267–330

    Google Scholar 

  16. E. Krotscheck, R.A. Smith, A.D. Jackson, Phys. Rev. B 24, 6404 (1981)

    Article  ADS  Google Scholar 

  17. E. Krotscheck, J.W. Clark, Nucl. Phys. A 333, 77 (1980)

    Article  ADS  Google Scholar 

  18. H.H. Fan, E. Krotscheck, T. Lichtenegger, D. Mateo, R.E. Zillich, Phys. Rev. A 92, 023640 (2015)

    Article  ADS  Google Scholar 

  19. J.W. Clark, A. Sedrakian, M. Stein, X.G. Huang, V.A. Khodel, V.R. Shaginyan, M.V. Zverev, J. Phys. Conf. Ser. 702, 012012 (2016)

    Article  Google Scholar 

  20. L. Gorkov, T.K. Melik-Barkhudarov, Sov. Phys. JETP 13, 1018 (1961)

    Google Scholar 

  21. H. Heiselberg, C.J. Pethick, H. Smith, L. Viverit, Phys. Rev. Lett. 85, 2418 (2000)

    Article  ADS  Google Scholar 

  22. G.E. Pavlou, E. Mavrommatis, C. Moustakidis, J.W. Clark, Eur. Phys. J. A 53, 96 (2017)

    Article  ADS  Google Scholar 

  23. R.B. Wiringa, V.G.J. Stoks, R. Schiavilla, Phys. Rev. C 51, 38 (1995)

    Article  ADS  Google Scholar 

  24. A. Gezerlis, C.J. Pethick, A. Schwenk, in Novel Superfluids, vol. 2, ed. by K.H. Bennemann, J.B. Ketterson (Oxford University Press, Oxford, 2014). Chap. 22

    Google Scholar 

  25. R.B. Wiringa, S.C. Pieper, Phys. Rev. Lett. 89, 182501 (2002)

    Article  ADS  Google Scholar 

  26. J.W. Clark, in Fifty Years of Nuclear BCS, ed. by R.A. Broglia, V. Zelevinsky (World Scientific, Singapore, 2013), pp. 360–376. Chap. 27

    Chapter  Google Scholar 

  27. A.D. Jackson, A. Lande, R.A. Smith, Phys. Rep. 86(2), 55 (1982)

    Article  ADS  Google Scholar 

  28. A.D. Jackson, A. Lande, R.A. Smith, Phys. Rev. Lett. 54, 1469 (1985)

    Article  ADS  Google Scholar 

  29. R.F. Bishop, in Condensed Matter Theories, vol. 10, ed. by M. Casas, J. Navarro, A. Polls (Nova Science Publishers, Commack, New York, 1995), pp. 483–508

    Google Scholar 

  30. E. Krotscheck, Phys. Lett. A 190, 201 (1994)

    Article  ADS  Google Scholar 

  31. E. Feenberg, Theory of Quantum Fluids (Academic, New York, 1969)

    Google Scholar 

  32. E. Krotscheck, J. Low Temp. Phys. 119, 103 (2000)

    Article  ADS  Google Scholar 

  33. J. Egger, E. Krotscheck, R.E. Zillich, J. Low Temp. Phys. 165, 275 (2011)

    Article  ADS  Google Scholar 

  34. E. Krotscheck, Ann. Phys. (NY) 155, 1 (1984)

    Article  ADS  Google Scholar 

  35. E. Krotscheck, J.W. Clark, Nucl. Phys. A 328, 73 (1979)

    Article  ADS  Google Scholar 

  36. S.T. Beliaev, in Lecture Notes of the 1957 Les Houches Summer School, ed. by C. DeWitt, P. Nozières (Dunod, Paris, 1959), pp. 343–374

  37. S. Fantoni, Nucl. Phys. A 363, 381 (1981)

    Article  ADS  Google Scholar 

  38. A. Fabrocini, S. Fantoni, A.Y. Illarionov, K.E. Schmidt, Phys. Rev. Lett. 95, 192501 (2005)

    Article  ADS  Google Scholar 

  39. A. Fabrocini, S. Fantoni, A.Y. Illarionov, K.E. Schmidt, Nucl. Phys. A 803, 137 (2008)

    Article  ADS  Google Scholar 

  40. C.J. Pethick, H. Smith, Bose–Einstein Condensation in Dilute Gases, 2nd edn. (Cambridge University Press, Cambridge, 2008)

    Book  Google Scholar 

  41. A.L. Fetter, J.D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, New York, 1971)

    Google Scholar 

  42. O. Benhar, G.D. Rosi, G. Salvi, J. Low Temp. Phys. (2017). (This volume, arXiv:1305.4659)

  43. B.D. Day, Phys. Rev. C 24, 1203 (1981)

    Article  ADS  Google Scholar 

  44. S. Gandolfi, A. Illarionov, K.E. Schmidt, F. Pederiva, S. Fantoni, Phys. Rev. C 79, 054005 (2009)

    Article  ADS  Google Scholar 

  45. M. Baldo, A. Polls, A. Rios, H.J. Schulze, I. Vidaña, Phys. Rev. C 86, 064001 (2012)

    Article  ADS  Google Scholar 

  46. G. Brown, J. Gunn, P. Gould, Nucl. Phys. 46, 598 (1963)

    Article  Google Scholar 

  47. P. Quentin, H. Flocard, Ann. Rev. Nucl. Part. Sci. 28, 523 (1978)

    Article  ADS  Google Scholar 

  48. E. Krotscheck, R.A. Smith, A.D. Jackson, Phys. Lett. B 104, 421 (1981)

    Article  ADS  Google Scholar 

  49. G.E. Brown, C.J. Pethick, A. Zaringhalam, J. Low Temp. Phys. 48, 349 (1982)

    Article  ADS  Google Scholar 

  50. B.L. Friman, E. Krotscheck, Phys. Rev. Lett. 49, 1705 (1982)

    Article  ADS  Google Scholar 

  51. E. Krotscheck, J. Springer, J. Low Temp. Phys. 132(5/6), 281 (2003)

    Article  ADS  Google Scholar 

  52. P. Noziéres, S. Schmitt-Rink, J. Low Temp. Phys. 59, 195 (1985)

    Article  ADS  Google Scholar 

  53. L. Yuan, Three-body pairing interaction effect on superfluidity with applications to neutron star matter. Ph.D. thesis Washington University, 2011

  54. Ø. Elgarøy, M. Hjorth-Jensen, Phys. Rev. C 57, 1174 (1998)

    Article  ADS  Google Scholar 

  55. L.G. Cao, U. Lombardo, P. Schuck, Phys. Rev. C 74, 064301 (2006)

    Article  ADS  Google Scholar 

  56. H.J. Schulze, A. Polls, A. Ramos, Phys. Rev. C 63, 044310 (2001)

    Article  ADS  Google Scholar 

  57. S.S. Zhang, L.G. Cao, U. Lombardo, P. Schuck, Phys. Rev. C 93, 044329 (2016)

    Article  ADS  Google Scholar 

  58. S. Gandolfi, A. Illarionov, F. Pederiva, K.E. Schmidt, S. Fantoni, Phys. Rev. C 80, 045802 (2009)

    Article  ADS  Google Scholar 

  59. A. Gezerlis, J. Carlson, Phys. Rev. C 77, 032801 (2008)

    Article  ADS  Google Scholar 

  60. A. Gezerlis, J. Carlson, Phys. Rev. C 81, 025803 (2010)

    Article  ADS  Google Scholar 

  61. J. Margueron, H. Sagawa, K. Hagino, Phys. Rev. C 76, 064316 (2007)

    Article  ADS  Google Scholar 

  62. F. Isaule, H.F. Arellano, A. Rios, Phys. Rev. C 94, 034004 (2016)

  63. M. Stein, A. Sedrakian, X.G. Huang, J.W. Clark, Phys. Rev. C 90, 065804 (2014)

  64. V.A. Khodel, J.W. Clark, V.R. Shaginyan, M.V. Zverev, Phys. Atomic Nucl. 77, 1145 (2014)

    Article  ADS  Google Scholar 

  65. M. Randeria, E. Taylor, Ann. Rev. Condens. Matter Phys. 5(1), 209 (2014). http://dx.doi.org/10.1146/annurev-conmatphys-031113-133829

  66. M. Stein, A. Sedrakian, X.G. Huang, J.W. Clark, Phys. Rev. C 93, 015802 (2016)

  67. A.D. Jackson, E. Krotscheck, D. Meltzer, R.A. Smith, Nucl. Phys. A 386, 125 (1982)

    Article  ADS  Google Scholar 

  68. J.M.C. Chen, J.W. Clark, E. Krotscheck, R.A. Smith, Nucl. Phys. A 451, 509 (1986)

    Article  ADS  Google Scholar 

  69. J.W. Clark, C.G. Källman, C.H. Yang, D.A. Chakkalakal, Phys. Lett. B 61(4), 331 (1976)

    Article  ADS  Google Scholar 

  70. J. Wambach, T. Ainsworth, D. Pines, Nucl. Phys. A 555, 128 (1993)

    Article  ADS  Google Scholar 

  71. H.J. Schulze, J. Cugnon, A. Lejeune, M. Baldo, U. Lombardo, Phys. Lett. B 375, 1–8 (1996)

    Article  ADS  Google Scholar 

  72. S. Fantoni, S. Rosati, Nuovo Cimento 43A, 413 (1977)

    ADS  Google Scholar 

  73. R.B. Wiringa, V.R. Pandharipande, Nucl. Phys. A 299, 1 (1978)

    Article  ADS  Google Scholar 

  74. V.R. Pandharipande, R.B. Wiringa, Rev. Mod. Phys. 51(4), 821 (1979)

    Article  ADS  Google Scholar 

  75. E. Krotscheck, Nucl. Phys. A 482, 617 (1988)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported, in part, by the College of Arts and Sciences, University at Buffalo SUNY, and the Austrian Science Fund Project I602 (to EK). JWC acknowledges support from the McDonnell Center for the Space Sciences and expresses gratitude to the University of Madeira and its branch of Centro de Investigação em Matemática e Aplicações (CIMA) for gracious hospitality during periods of extended residence.

Author information

Authors and Affiliations

  1. Department of Physics, University at Buffalo SUNY, Buffalo, NY, 14260, USA

    H.-H. Fan & E. Krotscheck

  2. Institut für Theoretische Physik, Johannes Kepler Universität, 4040, Linz, Austria

    H.-H. Fan & E. Krotscheck

  3. Department of Physics and McDonnell Center for the Space Sciences, Washington University, St. Louis, MO, 63130, USA

    J. W. Clark

  4. Centro de Investigação em Matemática e Aplicações, University of Madeira, 9020-105, Funchal, Madeira, Portugal

    J. W. Clark

Authors
  1. H.-H. Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. Krotscheck
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. W. Clark
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. Krotscheck.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fan, HH., Krotscheck, E. & Clark, J.W. \(^1S_0\) Pairing in Neutron Matter. J Low Temp Phys 189, 470–494 (2017). https://doi.org/10.1007/s10909-017-1813-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10909-017-1813-z

Keywords

Search

Navigation