Effect of polarization on superfluidity in low density neutron matter

Clark, J. W.; Källman, Carl-G.; Yang, C.-H.; Chakkalakal, Dennis A.

doi:10.1016/0370-2693(76)90580-3

Cited by 69 publications

(46 citation statements)

References 7 publications

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“…This first task places great demands on even the most advanced tools of manybody theory. For 1 S 0 pairing, there exists a "first generation" of results on this facet of the problem, obtained by several different approaches (Landau Fermi-liquid theory [32], the method of correlated basis functions [41,55], the polarization-potential approach [47,56] and diagrammatic perturbation theory [66]). However, little progress has been made on this aspect of 3 P 2 -3 F 2 pairing, and the issue of modifications of the associated input pairing interaction and single-particle energies due to short-and long-range correlations inside the nuclear medium remains open.…”

Section: Introductionmentioning

confidence: 99%

Triplet pairing in neutron matter

Khodel¹,

Khodel²,

Clark³

2001

Nuclear Physics A

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The separation method developed earlier by us [Nucl. Phys. A598 390 (1996)] to calculate and analyze solutions of the BCS gap equation for 1 S 0 pairing is extended and applied to 3 P 2 -3 F 2 pairing in pure neutron matter. The pairing matrix elements are written as a separable part plus a remainder that vanishes when either momentum variable is on the Fermi surface. This decomposition effects a separation of the problem of determining the dependence of the gap components in a spin-angle representation on the magnitude of the momentum (described by a set of functions independent of magnetic quantum number) from the problem of determining the dependence of the gap on angle or magnetic projection. The former problem is solved through a set of nonsingular, quasilinear integral equations, providing inputs for solution of the latter problem through a coupled system of algebraic equations for a set of numerical coefficients. An incisive criterion is given for finding the upper critical density for closure of the triplet gap. The separation method and its development for triplet pairing exploit the existence of a small parameter, given by a gap-amplitude measure divided by the Fermi energy. The revised BCS equations admit analysis revealing universal properties of the full set of solutions for 3 P 2 pairing in the absence of tensor coupling, referring especially to the energy degeneracy and energetic order of these solutions. The angle-average approximation introduced by Baldo et al. is illuminated in terms of the separation-transformed BCS problem and the small parameter expansion. Numerical calculations of 3 P 2 pairing parameters and gap functions, with and without coupling to the 3 F 2 state, are carried out for pairing matrix elements supplied by (vacuum) two-neutron interactions that fit nucleon-nucleon scattering data. It is emphasized that ab initio evaluation of the in-medium particle-particle interaction and associated single-particle energies will be required if a reliable quantitative description of nucleonic superfluids is to be achieved.

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Section: Introductionmentioning

confidence: 99%

Triplet pairing in neutron matter

Khodel¹,

Khodel²,

Clark³

2001

Nuclear Physics A

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“…The gap appears at densities of order n 0 or lower, where m * n is well determined and the pairing interaction in vacuum for the 1 S 0 channel is accurately known. Simple arguments (Pines 1971) show that medium polarization, the dominant medium effect on V , should induce a reduction of the 1 S 0 gap (Clark et al 1976) from its value without medium polarization. Much effort has been dedicated to take into account medium polarization at various levels of approximation.…”

Section: Pairingmentioning

confidence: 99%

Minimal Cooling of Neutron Stars: A New Paradigm

Page¹,

Lattimer²,

Prakash³

et al. 2004

ASTROPHYS J SUPPL S

555

736

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A new classification of neutron star cooling scenarios, involving either "minimal" cooling or "enhanced" cooling is proposed. The minimal cooling scenario replaces and extends the so-called standard cooling scenario to include neutrino emission from the Cooper pair breaking and formation process. This emission dominates that due to the modified Urca process for temperatures close to the critical temperature for superfluid pairing. Minimal cooling is distinguished from enhanced cooling by the absence of neutrino emission from any direct Urca process, due either to nucleons or to exotica such as hyperons, Bose condensates or deconfined quarks. Within the minimal cooling scenario, theoretical cooling models can be considered to be a four parameter family involving the equation of state (including various compositional possibilities) of dense matter, superfluid properties of dense matter, the composition of the neutron star envelope, and the mass of the neutron star. The consequences of minimal cooling are explored through extensive variations of these parameters. The results are compared with the inferred properties of thermally-emitting neutron stars in order to ascertain if enhanced cooling occurs in any of them.All stars for which thermal emissions have been clearly detected are at least marginally consistent with the lack of enhanced cooling, given the combined uncertainties in ages and temperatures or luminosities. The two pulsars PSR 0833-45 (Vela) and PSR 1706-44 would require enhanced cooling in case their ages and/or temperatures are on the lower side of their estimated values whereas the four stars PSR 0656+14, PSR 1055-52, Geminga, and RX J0720.4-3125 may require some source of internal heating in case their age and/or luminosity are on the upper side of their estimated values. The new upper limits on the thermal luminosity of PSR J0205+6449 (in the supernova remnant 3C58) and RX J0007.0+7302 (in CTA 1) are indicative of the occurrence of some enhanced neutrino emission beyond the minimal scenario.

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“…Based on Landau parameters and some microscopic efforts 8,66,67,68 , density fluctuations produce a modest enhancement of the pairing gap, whereas the spindensity channel generates a dominant suppression. Without introducing explicit spin-dependent correlations into the basis functions of the CBF treatment, their perturbative treatment within the CBF framework would be required.…”

Section: Summary and Prospectsmentioning

confidence: 99%

$$^1S_0$$ 1 S 0 Pairing in Neutron Matter

Fan

Clark

2017

J Low Temp Phys

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We report calculations of the superfluid pairing gap in neutron matter for the 1 S 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 (CBF), the required matrix elements in the correlated basis being evaluated by Fermi hypernetted-chain techniques. Different implementations of the Fermi-Hypernetted Chain Euler-Lagrange method (FHNC-EL) 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 1 S 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 (Phys. Rev. A 92, 023640 (2015)).

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Effect of polarization on superfluidity in low density neutron matter

Cited by 69 publications

References 7 publications

Triplet pairing in neutron matter

Triplet pairing in neutron matter

Minimal Cooling of Neutron Stars: A New Paradigm

$$^1S_0$$ 1 S 0 Pairing in Neutron Matter

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