Di-neutrons in neutron matter within a Brueckner-Hartree-Fock approach

We investigate the appearance of di-neutron bound states in pure neutron matter within the Brueckner-Hartree-Fock approach at zero temperature. We consider the Argonne $v_{18}$ and Paris bare interactions as well as chiral two- and three-nucleon forces. Self-consistent single-particle potentials are calculated by controlling explicitly singularities in the $g$ matrix associated with bound states. Di-neutrons are loosely bound, with binding energies below 1 MeV, but are unambiguously present for Fermi momenta below $1{\mathrm{fm}}^{-1}$ for all interactions. Within the same framework we are able to calculate and characterize di-neutron bound states, obtaining mean radii as high as $\sim 110$ fm. Implications of these findings are presented and discussed.

Figure 1

BHF self-consistent sp potentials for pure neutron matter as a functions of sp momentum $k$. Short-dashed, dash-dotted, dashed, and solid curves correspond to AV18, Paris, ${\mathrm{N}3\mathrm{LO}}_{2N}$, and ${\mathrm{N}3\mathrm{LO}}_{2N}+{\mathrm{N}2\mathrm{LO}}_{3N}$ bare potentials, respectively. Panels (a)–(d) present solutions for $k_F=1.0,1.4,1.6$, and $1.8{\mathrm{fm}}^{-1}$, respectively.

Figure 2

Effective-to-bare-mass ratio $m^{*}/m$ in pure neutron matter as a function of Fermi momentum, $k_F$. Panels (a)–(d) correspond to results for AV18, Paris, ${\mathrm{N}3\mathrm{LO}}_{2N}$, and ${\mathrm{N}3\mathrm{LO}}_{2N}+{\mathrm{N}2\mathrm{LO}}_{3N}$ bare potentials, respectively. Continuous curves represent fits based on Eq. (7).

Figure 3

Di-neutron binding energy in pure neutron matter as a function of Fermi momentum. Circles, asterisks, diamonds, and squares correspond to AV18, Paris, ${\mathrm{N}3\mathrm{LO}}_{2N}$, and ${\mathrm{N}3\mathrm{LO}}_{2N}+{\mathrm{N}2\mathrm{LO}}_{3N}$ bare potentials, respectively. Results correspond to pairs with zero total momentum.

Figure 4

Di-neutron binding energy, relative to the deuteron binding energy in vacuum, as a function of the pair momentum $K$ and $k_F$ in pure neutron matter. Results have been obtained with the ${\mathrm{N}3\mathrm{LO}}_{2N}+{\mathrm{N}2\mathrm{LO}}_{3N}$ interactions.

Figure 5

Radial probability density, $r^2{\left|\mathrm{\Psi }\left(r\right)\right|}^2$, for di-neutron bound states in pure neutron matter ($k_F=0.6{\mathrm{fm}}^{-1}$) as a function of the relative distance. Short-dashed, dash-dotted, dashed and solid curves correspond to AV18, Paris, ${\mathrm{N}3\mathrm{LO}}_{2N}$, and ${\mathrm{N}3\mathrm{LO}}_{2N}+{\mathrm{N}2\mathrm{LO}}_{3N}$ bare potentials, respectively. Gray-filled curve represents the deuteron ($S$ and $D$ waves) probability density in free space based on the AV18 bare potential.

Figure 6

Mean radius $\langle r\rangle$ for di-neutrons in pure neutron matter as a function of $k_F$. Circles, asterisks, diamonds, and squares correspond to AV18, Paris, ${\mathrm{N}3\mathrm{LO}}_{2N}$, and ${\mathrm{N}3\mathrm{LO}}_{2N}+{\mathrm{N}2\mathrm{LO}}_{3N}$ bare potentials, respectively.

Figure 7

(a) Di-neutron binding energy and (b) mean radii as a function of Fermi momentum $k_F$ for two choices of sp spectrum. Dashed curves with filled circles are obtained by considering the full spectrum, $e\left(k\right)=k^2/2m+U\left(k\right)$, whereas solid curves are obtained with the approximation $e\left(k\right)=k^2/2m^{*}$, with $m^{*}$ obtained from Eq. (6). Results are based on the AV18 bare interaction, but similar results are obtained with other interactions.

Figure 8

Radial probability density for di-neutrons in ${}^{1}S_0$ channel obtained from BHF equation (solid curves), Cooper-pair wave equation (long-dashed curves), and BCS anomalous density (short-dashed curves). Red-shaded curves in all frames represent the ${}^{3}S_1$-channel deuteron radial probability density in free space. Panels (a)–(c) correspond to solutions for $k_F=0.25$, 0.60, and 1.0 ${\mathrm{fm}}^{-1}$, respectively.

Figure 9

Binding energy per neutron for pure neutronic matter as a function of density. Short-dashed, dash-dotted, dashed, and solid curves correspond to AV18, Paris, ${\mathrm{N}3\mathrm{LO}}_{2N}$, and ${\mathrm{N}3\mathrm{LO}}_{2N}+{\mathrm{N}2\mathrm{LO}}_{3N}$ bare potentials, respectively.