Superfluid ground state of neutron matter and other strongly interacting many-fermion systems

Clark, John W.; Yang, C.-H.

doi:10.1007/bf02755910

Cited by 18 publications

(12 citation statements)

References 11 publications

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“…Conventional wisdom gives v J LL < 0 as a sufficient (but not necessary!) condition for a pairing instability in partial wave L. The indicated lower bound property is of course consistent with this statement, but we are able to provide a more incisive condition for the extent of the pairing instability in terms of the behavior of the characteristic determinant associated with the integral equation (20) (or alternatively, with the characteristic determinant of the integral equation (13) for the shape function χ(k) [80,117]). Concerning the dependence of k c on effective mass, it is seen in fig.…”

Section: (L·s)supporting

confidence: 76%

“…However, these terms are angleindependent and, like the scale term, contribute only to the diagonal part of the r.h.s. of (20). In fact, to within corrections of order ∼ d 2 F ln d F , the result for the D coefficients calculated from the angle-independent terms alone (i.e., dropping ln D 2 (n)), is the same as the result we obtain if we simply replace the quantity D 2 (k) in the energy denominator of the original equation by its angle average (7),…”

Section: Small-parameter Expansion and Angle-average Approximationsupporting

confidence: 65%

“…of eqs. (20) for the coefficients D JM LL ′ . We may carry out an integration by parts with respect to the variable ξ, to derive a principal term (within the angular integration) that goes like ln D 2 (k F , n) and a remainder that involves D 2 (k) only in the factor…”

Section: Small-parameter Expansion and Angle-average Approximationmentioning

confidence: 99%

“…of eq. (20) that are diagonal in the magnetic quantum number, i.e., only for M 1 = M. Since ∆ F is a small quantity, the contribution from the scale term ln ∆ 2 F greatly exceeds that from the angle-dependent part ln D 2 (n), which remains of order of 1 even in the limit ∆ F → 0. It is worth noting that the ∆-independent contributions coming from terms in ln(2|ξ|) are also of order of 1.…”

Section: Small-parameter Expansion and Angle-average Approximationmentioning

confidence: 99%

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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: (L·s)supporting

confidence: 76%

Section: Small-parameter Expansion and Angle-average Approximationsupporting

confidence: 65%

Section: Small-parameter Expansion and Angle-average Approximationmentioning

confidence: 99%

Section: Small-parameter Expansion and Angle-average Approximationmentioning

confidence: 99%

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Triplet pairing in neutron matter

Khodel¹,

Khodel²,

Clark³

2001

Nuclear Physics A

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“…This issue was naturally addressed by the introduction of Jastrow-Feenberg correlation factors 10,11,12 . Cluster-expansion techniques were applied to evaluate the required expectation values 13 .…”

mentioning

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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The correlated wave function approach to finite nuclear systems

Clark

The Many-Body Problem Jastrow Correlations Versus Brueckner Theory

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Superfluid ground state of neutron matter and other strongly interacting many-fermion systems

Cited by 18 publications

References 11 publications

Triplet pairing in neutron matter

Triplet pairing in neutron matter

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

The correlated wave function approach to finite nuclear systems

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