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Title: Relativistic description of BCS–BEC crossover in nuclear matter

Author(s): Bao Yuan Sun, Hiroshi Toki, and Jie Meng

Source: Physics Letters B
Volume: 683  Issue: 2-3  Page: 134-139 Published: 18 January 2010

Keyword(s): Pairing correlation; Nuclear matter; Relativistic pairing theory; Bare nucleon–nucleon interaction; Di-neutron spatial correlation; BCS–BEC crossover
KeyWords Plus: MEAN-FIELD THEORY; NEUTRON DRIP-LINE; STATE PROPERTIES; HALO; LI-11; SUPERCONDUCTIVITY; SUPERFLUIDITY; HE-6; PAIR

History: Received 15 April 2009; revised 30 September 2009; accepted 11 November 2009; Available online 9 December 2009

DOI: 10.1016/j.physletb.2009.11.065

Abstract: We study theoretically the di-neutron spatial correlations and the crossover from superfluidity of neutron Cooper pairs in the ¹S₀ pairing channel to Bose-Einstein condensation (BEC) of di-neutron pairs for both symmetric and neutron matter in the microscopic relativistic pairing theory. We take the bare nucleon-nucleon interaction Bonn-B in the particle-particle channel and the effective interaction PK1 of the relativistic mean-field approach in the particle-hole channel. It is found that the spatial structure of neutron Cooper pair wave function evolves continuously from BCS-type to BEC-type as density decreases. We see a strong concentration of the probability density revealed for the neutron pairs in the fairly small relative distance around 1.5 fm and the neutron Fermi momentum k_Fn is an element of [0.6, 1.0] fm^-1. However, from the effective chemical potential and the quasiparticle excitation spectrum, there is no evidence for the appearance of a true BEC state of neutron pairs at any density. The most BEC-like state may appear at k_Fn – 0.2 fm^-1 by examining the density correlation function. From the coherence length and the probability distribution of neutron Cooper pairs as well as the ratio between the neutron pairing gap and the kinetic energy at the Fermi surface, some features of the BCS-BEC crossover are seen in the density regions, 0.05 fm^-1 < k_Fn < 0.7 (0.75) fm^-1, for the symmetric nuclear (pure neutron) matter.

Figure: A two-dimensional plot for the probability density r²|Ψ_pair(r)|² of the neutron Cooper pairs as a function of the neutron Fermi momentum k_Fn and the relative distance r between the pair partners in symmetric nuclear matter.

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Title: Deformation Effect on the Center-of-Mass Correction Energy in Nuclei Ranging from Oxygen to Calcium

Author(s): ZHAO Peng-Wei (赵鹏巍), SUN Bao-Yuan (孙保元), and MENG Jie (孟杰)

Source: Chinese Physics Letters
Volume: 26  Issue: 11  Page: 112102 Published: November 2009

KeyWords Plus: GROUND-STATE PROPERTIES; MEAN-FIELD-THEORY; FINITE NUCLEI

History: Received 15 June 2009

DOI: 10.1088/0256-307X/26/11/112102

Abstract: The microscopic c. m. correction energies for nuclei ranging from oxygen to calcium are systematically calculated by both spherical and axially deformed relativistic mean-field (RMF) models with the effective interaction PK1. The microscopic c. m. correction energies strongly depend on the isospin as well as deformation and deviate from the phenomenological ones. The deformation effect is discussed in detail by comparing the deformed with the spherical RMF calculation. It is found that the direct and exchange terms of the c. m. correction energies are strongly correlated with the density distribution of nuclei and are suppressed in the deformed case.

Figure: Microscopic c.m. correction energies (solid lines) of nuclei ranging from Oxygen to Calcium in the spherical (a) and axially deformed (b) RMF calculations with the effective interaction PK1, in comparison with two phenomenological results (dashed lines). The solid lines from the left to the right respectively correspond to the isotopic chains from oxygen to calcium.

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Title: PAIRING PROPERTIES OF SYMMETRIC NUCLEAR MATTER IN RELATIVISTIC MEAN FIELD THEORY

Author(s): J. Li, B. Y. Sun, and J. Meng

Source: International Journal of Modern Physics E (IJMPE)
Volume: 17  Issue: 8  Page: 1441-1452  Published: September 2008

Keyword(s): Pairing correction; relativistic Hartree–Bogoliubov theory; symmetric nuclear matter; effective pairing interaction
KeyWords Plus: HARTREE-BOGOLIUBOV THEORY; GROUND-STATE PROPERTIES; NEUTRON DRIP-LINE; PSEUDOSPIN SYMMETRY; EXOTIC NUCLEI; SUPERFLUIDITY; HALO

History: Received 4 June 2008

DOI: 10.1142/S0218301308010519

Abstract: The properties of pairing correlations in symmetric nuclear matter are studied in the relativistic mean field (RMF) theory with the effective interaction, PK1. Considering the well-known problem that the pairing gap at the Fermi surface calculated with RMF effective interactions is three times larger than that with the Gogny force, an effective factor in the particle–particle channel is introduced. For the RMF calculation with PK1, an effective factor of 0.76 gives a maximum pairing gap of 3.2 MeV at a Fermi momentum of 0.9 fm^-1, which is consistent with the result with the Gogny force. Read more…