Elsevier

Physics Letters B

Volume 606, Issues 1–2, 20 January 2005, Pages 43-51
Physics Letters B

Nodal lines in the cranked HFB overlap kernels

https://doi.org/10.1016/j.physletb.2004.10.063Get rights and content

Abstract

Norm overlap kernels of the cranked Hartree–Fock–Bogoliubov states are studied in the context of angular momentum projection. In particular, the geometrical distribution of nodal lines, i.e., one-dimensional structures where the overlap kernels possess null value, is investigated in the three-dimensional space defined by the Euler angles. It is important to know the distribution of these nodal lines when one attempts to determine the phase of norm overlap kernels.

Section snippets

Acknowledgments

We greatly thank Professor N. Onishi for giving us good insights through discussions in order to tackle the present problem. M.O. is grateful for discussions with Professors H. Flocard and P.-H. Heenen. Careful reading of the manuscript by Prof. P. Walker is acknowledged. Financial support from the Japanese Society for the Promotion of Sciences (JSPS) and an EPSRC advanced research fellowship GR/R75557/01 are appreciated by M.O. Parts of the numerical calculations were performed at the Centre

References (21)

  • S. Islam et al.

    Nucl. Phys. A

    (1979)
  • I. Hamamoto

    Nucl. Phys. A

    (1976)
  • M. Oi et al.

    Phys. Lett. B

    (1998)
  • N. Onishi et al.

    Nucl. Phys.

    (1966)
  • N. Onishi et al.

    Prog. Theor. Phys.

    (1980)
  • K. Hara et al.

    Nucl. Phys. A

    (1982)
  • M. Baranger et al.

    Nucl. Phys.

    (1965)
    K. Kumar et al.

    Nucl. Phys. A

    (1968)
  • T. Horibata et al.

    Nucl. Phys. A

    (1996)
  • P. Möller et al.

    At. Data Nucl. Data Tables

    (1995)
  • M. Bender et al.

    Rev. Mod. Phys.

    (2003)
There are more references available in the full text version of this article.

Cited by (23)

  • Why does the sign problem occur in evaluating the overlap of HFB wave functions?

    2018, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
  • Matrix elements of one-body and two-body operators between arbitrary HFB multi-quasiparticle states

    2014, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
    Citation Excerpt :

    The Onishi formula [4,5] is the first expression of the overlap between two different HFB vacua, but the sign of the overlap is not determined. Many works have been done to overcome this sign problem [6–14]. In Ref. [14], Robledo made the final solution and proposed a new formula using the Pfaffian rather than the determinant.

  • A convenient implementation of the overlap between arbitrary Hartree-Fock-Bogoliubov vacua for projection

    2014, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
    Citation Excerpt :

    Unfortunately, the Onishi formula leaves the sign of the overlap undefined due to the square root of a determinant. Several efforts have been made to overcome this sign problem [11–16]. In 2009, Robledo proposed a different overlap formula with the Pfaffian rather than the determinant [17].

  • A new formulation to calculate general HFB matrix elements through the Pfaffian

    2012, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
    Citation Excerpt :

    However, in an attempt to go beyond the mean-field description, especially in the case of three-dimensional angular momentum projection, there has been a difficulty originating from the long-standing problem in the phase determination of norm-overlap kernels through the Onishi formula [4]. This problem has been thoroughly investigated by many authors, for instance, in Refs. [4–8]. Many of them relied upon the analytic continuity approach for the phase determination, which can be carried out with the Onishi formula [4].

  • Norm-overlap formula for Hartree-Fock-Bogoliubov states with odd number parity

    2012, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
    Citation Excerpt :

    Such a case was seen in the cranked HFB wave functions, and it was discovered that the so-called “nodal lines” (a collection of zeros of the overlap) are the source of the problem [4]. A method to overcome this problem was presented in Ref. [4], and an improvement to the method was recently found by the present authors [5]. With this method based on the Onishi formula, the sign problem was solved.

View all citing articles on Scopus
View full text