ЯДЕРНАЯ ФИЗИКА, 2014, том 77, № 9, с. 1204-1216
ЭЛЕМЕНТАРНЫЕ ЧАСТИЦЫ И ПОЛЯ
CONVENTIONAL BCS, UNCONVENTIONAL BCS, AND NON-BCS HIDDEN DINEUTRON PHASES IN NEUTRON MATTER
© 2014 V. A. Khodel1)'2), J. W. Clark2)'3), V. R. Shaginyan4), M. V. Zverev^'5)*
Received September 3, 2013; in final form, January 8, 2014
The nature of pairing correlations in neutron matter is re-examined. Working within the conventional approximation in which the nn pairing interaction is provided by a realistic bare nn potential fitted to scattering data, it is demonstrated that the standard BCS theory fails in regions of neutron number density, where the pairing constant A, depending crucially on density, has a non-BCS negative sign. We are led to propose a non-BCS scenario for pairing phenomena in neutron matter that involves the formation of a hidden dineutron state. In low-density neutron matter, where the pairing constant has the standard BCS sign, two phases organized by pairing correlations are possible and compete energetically: a conventional BCS phase and a dineutron phase. In dense neutron matter, where A changes sign, only the dineutron phase survives and exists until the critical density for termination of pairing correlations is reached at approximately twice the neutron density in heavy atomic nuclei.
DOI: 10.7868/S004400271408011X
PREAMBLE
This contribution is dedicated with deep respect and admiration to Spartak Timofeevich Belyaev on the occasion of his 90th birthday. Three generations of physicists across the globe have taken inspiration from his prodigious achievements in theoretical nuclear physics and quantum many-body theory, as well as his wise and visionary leadership in the development and sustenance of world-renowned scientific institutions. Recognized by awards of the 2004 Feenberg Memorial Medal and the 2012 Pomeranchuk Prize as one of the founding fathers of modern many-body theory based on field-theoretic methods, he introduced the concept of anomalous propagators [1] that runs through all of current theoretical physics and is central to a microscopic understanding of pairing phenomena in nuclear and condensed matter systems. The impact of the profound advances he made in the theory of nuclear superfluidity during his 1957—1958 "wonder year" at the Bohr Institute and later in Novosibirsk, changed the course of nuclear
''National Research Centre "Kurchatov Institute", Moscow, Russia.
2) McDonnell Center for the Space Sciences and Department of Physics, Washington University, USA.
3)Centro de Ciencias Matematicas, University of Madeira, Funchal, Portugal.
4)Petersburg Nuclear Physics Institute, NRC "Kurchatov Institute", Gatchina, Russia.
5) Moscow Institute of Physics and Technology (State University), Dolgoprudny, Russia.
E-mail: mzverev@nm.ru
theory, giving rise to the "standard nuclear paradigm" in which BCS pairing correlations assume pivotal roles [2, 3]. S. T. has taught us [4] that "There is still a vast field of unsolved problems stimulating the progress of theoretical nuclear physics." Our contribution to this issue is offered very much in the same spirit, as we seek to establish that the study of pairing correlations remains a source of surprising and intriguing revelations about the microworld.
1. INTRODUCTION
Shortly after Bardeen, Cooper, and Schrieffer (BCS) introduced a theory of superconductivity in 1957, A.B. Migdal raised the possibility that the matter inside neutron stars may be superfluid. Since that time, hundreds of papers have been published to elucidate the properties of neutron matter and other nuclear systems implied by nucleonic pairing, within the framework of BCS theory [5]. In the generic zero-temperature Lifshitz phase diagram of a homogeneous 3D Fermi system subject to pairing correlations, the conventional BCS phase lies in the weak-coupling domain of small positive pairing constant A. Specifically, this dimensionless coupling parameter is defined by A = -VFN(0), where VF = = V(pF,pF) is the diagonal matrix element of the pairing interaction and N(0) = pFM*/n2 is the density of single-particle states, both evaluated at the Fermi surface. (The Fermi momentum is given by pF = (3n2p)1/3 in terms of the particle density p,
while M* stands for the effective mass.) The occurrence of the BCS phase in this domain is attributed to the enhancement of pairing correlations stemming from the logarithmic divergence of the propagator of a pair of opposite-spin quasiparticles as their total momentum P approaches zero. This enhancement leads to the formation of a condensate of Cooper pairs with P = 0, which entails violation of global U(1) phase rotation symmetry, and is responsible for the superfluidity of the BCS phase. A crucial feature of this phenomenon is the presence of a gap A(p) in the spectrum E(p) of single-particle excitations. In the relevant region of the Lifshitz phase diagram, the value of the BCS gap A0 = A(p = pF,T = 0) and critical temperature Tc, above which the BCS gap closes and BCS superfluidity is terminated, turn out to be exponentially small:
Ao = Qd e-2/X, Tc = 0.57Ao,
(1)
where QD is the BCS cutoff factor.
BCS theory reigned for several decades as the most successful theory in condensed-matter physics, both fundamentally and quantitatively. However, its limitations became apparent after the discovery of a family of high-temperature superconductors in the late 1980's. Failure of the theory was conclusively established with the revelation of the so-called pseudogap phase in experimental studies of putatively normal phases of high-Tc superconductors by means of angular-resolved-photoemission spectroscopy (ARPES). In such a phase, there still exists a gap in the single-particle spectrum, even though the superconductivity is already terminated [6, 7]. BCS theory, a bedrock of our understanding of the phenomena of superfluidity and superconditivity in which termination of these phenomena and closure of the energy gap are inseparable, is manifestly inappropriate when we attempt to describe the pseudogap phase.
A plethora of scenarios have been offered in explanation of such challenging behavior of high-Tc superconductors. Their discussion is well beyond the scope of the present article, in which we choose to highlight a scenario associated with the original model of in-medium pairing correlations explored by Shafroth, Butler, and Blatt [8—10] in the years leading up to the breakthrough made by BCS. This scenario envisions the formation of bound pairs in real three-dimensional space [10—17]. Such a process becomes feasible in the strong-coupling limit when the pair radius turns out to be smaller than the mean interparticle distance, while the pair binding energy E, playing the role of a gap in the spectrum of single-particle excitations, exceeds the Fermi energy eF = = PF/2M.
It follows that the pairing phase thus envisioned should involve the phenomenon of Bose—Einstein (BE) condensation. The most fully developed treatment of this phenomenon in solid-state physics, known as the theory of bipolaronic superconductivity, is the pioneering work of the late Alexandrov and his coauthors [11, 15, 18]. To honor his contribution, we call this phase of matter the Shafroth—Butler— Blatt—Alexandrov (SBBA) phase. The scenario of bipolaronic superconductivity is based on the polaron concept as set forth by Landau in 1933 [19, 20]. Conventional polarons, having spin 1/2, result from interactions between electrons and optical phonons, their mass Mp appearing to be much larger than the electron mass M [18, 21]. It is the mass Mp that enters the criterion for creation of a bound state of two polarons, the so-called bipolaron, and this criterion is met even if the attraction between polarons is moderate. In the description of superconductivity as a BE condensation of bound electron pairs, an idea already advanced by London in 1938, the interplay between bound pairs and the continuum of two-particle states is treated theoretically within the concept of quasichemical equilibrium, in analogy to thermodynamics of ordinary chemical reactions as presented in textbooks.
As T increases, the density of the superfluid Bose— Einstein condensate of real-space pairs declines and eventually vanishes, terminating superfluidity. The critical temperature TcBE for destruction of bipolaronic superconductivity is not exponentially small as in Eq. (1), instead showing qualitative agreement with the behavior observed in high-Tc superconductors. Since SBBA theory attributes the property of superfluidity to the bosonic system of bound pairs, there should be no jump of the specific heat C(T) at T = = TcBE, in contrast to this distinctive signature of BCS pairing at the associated critical temperature. Furthermore, it is easily verified that in SBBA theory the density of unbound fermions is proportional to e-E(T)/T. Hence, their contribution can be safely ignored when E(Tc) » Tc, and the ARPES data then give evidence for the persistence of the gap A(T) a: a E(T) in the spectrum of single-particle excitations above Tc.
The crisis faced by the BCS description in dealing with strongly correlated electron systems of solids, happening after 50 years of serenity, calls equally for a reassessment of the theory of nuclear pairing correlations, since nuclear systems, including atomic nuclei and neutron matter, are also composed of strongly correlated fermions.
In neutron matter, there exists a potential nuclear analog of the bipolaron, the in-medium dineutron. Like the bipolaron, the dineutron is non-existent
in vacuum. However, analogously to the bipolaron situation, the presence of the background medium might promote the formation of bound dineutron pairs. Highly relevant to this possibility is a distinctive feature of neutron—neutron scattering, namely a narrow resonance lying at the tiny energy of 0.067 MeV, which implies that neutrons attract each other much more effectively by intrinsic nucl
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