Quantum calculation of vortices in the inner crust of neutron stars

Physical Review C - Nuclear Physics

Volumn 75, Issue 1, 2007, Pages

  Avogadro, P ^a,b   Barranco, F ^c   Broglia, R A ^a,b,d   Vigezzi, E ^b  

^a UNIVERSITY OF MILAN   (Italy)

^b INFN SEZIONE DI MILANO   (Italy)

^c UNIVERSIDAD DE SEVILLA   (Spain)

^d UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33846379913     PISSN: 05562813     EISSN: 1089490X     Source Type: Journal    
DOI: 10.1103/PhysRevC.75.012805     Document Type: Article

References (25)

1. The Structure and Evolution of Neutron Stars, edited by, D. Pines, R. Tamagaki, and, S. Tsuruta, (Addison-Wesley, New York, 1992).
2. B. Link, R. I. Epstein, and G. Baym, Astrophys. J. ASJOAB 0004-637X 10.1086/172202 403, 285 (1993);
3. M. B. Larson and B. Link, Mon. Not. R. Astron. Soc. MNRAA4 0035-8711 10.1046/j.1365-8711.2002.05439.x 333, 613 (2001);
4. B. Link and C. Cutler, Mon. Not. R. Astron. Soc. MNRAA4 0035-8711 10.1046/j.1365-8711.2002.05726.x 336, 211 (2002);
5. M. Hirasawa and N. Shibazaki, Astrophys. J. ASJOAB 0004-637X 10.1086/323884 563, 267 (2001);
6. P. B. Jones, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.792 79, 792 (1997);
7. P. B. Jones, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81. 4560 81, 4560 (1998);
8. P. B. Jones, Mon. Not. R. Astron. Soc. 257, 501 (1992);
9. P. B. Jones, Mon. Not. R. Astron. Soc. 1365-8711 10.1046/j.1365-8711. 1998.01464.x 296, 217 (1998).
10. B. Link, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.101101 91, 101101 (2003).
11. R. I. Epstein and G. Baym, Astrophys. J. ASJOAB 0004-637X 10.1086/166325 328, 680 (1988).
12. F. V. De Blasio and Ø. Elgaroy, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.1815 82, 1815 (1999);
13. Ø. Elgaroy and F. V. De Blasio, Astron. Astrophys. AAEJAF 0004-6361 10.1051/0004-6361:20010160 370, 939 (2001).
14. P. M. Pizzochero, L. Viverit, and R. A. Broglia, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.3347 79, 3347 (1997);
15. P. Donati and P. M. Pizzochero, Nucl. Phys. NUPABL 0375-9474 10.1016/j.nuclphysa.2004.07.002 A742, 363 (2004).
16. A. Fabrocini, S. Fantoni, A. Yu. Illarionov, and K. E. Schmidt, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.192501 95, 192501 (2005).
17. P. G. De Gennes, Superconductivity of Metals and Alloys (Addison-Wesley, New York, 1999).
18. D. Vautherin and D. M. Brink, Phys. Rev. C PRVCAN 0556-2813 10.1103/PhysRevC.5.626 5, 626 (1972).
19. E. Garrido, P. Sarriguren, E. Moya de Guerra, and P. Schuck, Phys. Rev. C PRVCAN 0556-2813 10.1103/PhysRevC.60.064312 60, 064312 (1999).
20. J. W. Negele and D. Vautherin, Nucl. Phys. NUPABL 0375-9474 10.1016/0375-9474(73)90349-7 A207, 298 (1973).
21. Y. Yu and A. Bulgac, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.161101 90, 161101 (2003). We have checked that we reproduce the results found in this reference if we scale the strength of our pairing interaction to have the same asymptotic value of the pairing gap (cf. also Ref. [5]).
22. The spin orbit interaction will not significantly change the phase space density relevant for vortex formation, because it shifts the partners of the ν=1 Cooper pairs by about the same amount.
23. The energy cost to create a vortex depends linearly on the height of the cylindrical box used for the calculation and shows a logarithmic divergence with respect to the radius of the box. We have verified that our results obey this geometrical scaling. Such dependences, however, disappear when we consider the pinning energy. We have verified that the value of the pinning energy, although obtained from the subtraction of large numbers, is remarkably stable with respect to changes in the box size for sufficiently large boxes. We have evaluated the error associated with the finite mesh size used in integrating these equations (Δρ=Δz=0.25 fm), and we estimate that the absolute value of the error associated with this quantity is less than 2 MeV.
24. M. A. Alpar, Astrophys. J. ASJOAB 0004-637X 10.1086/168063 346, 823 (1989).
25. The energy Eflow is obtained integrating the associated kinetic energy density (1/2)Φ2/n, where Φ is the vortex flow, Φ=/ mαVα2(ρ,z)(lα-ν). The condensation energy Econd is obtained by integrating the density -(3/8)n(ρ,z)Δ2(ρ,z)/[EF- V(ρ,z)].