where \( \rho _ { 0 } = 0 . 1 7 \)\( \mathrm { f m ^ { - 3 } } \) is the empirical saturation density of symmetric nuclear matter. We have separated explicitly the kinetic contribution, \( K / A = 3 k _ { F } ^ { 2 } / 2 0 m \), from the potential terms. Coefficients of this parametrization are shown in II.

<table><tr><td rowspan="2"></td><td>a</td><td>b</td><td>α</td><td>β</td></tr><tr><td>( MeV )</td><td> ( MeV )</td><td></td><td></td></tr><tr><td>AV18</td><td>5.6520</td><td>−28.701</td><td>1.97</td><td>0.83</td></tr><tr><td>Paris</td><td>5.7215</td><td>−28.727</td><td>1.97</td><td>0.87</td></tr><tr><td>N3LO2N</td><td>98.155</td><td>−122.14</td><td>1.13</td><td>1.03</td></tr><tr><td>\( \mathbf { \delta } \) 3 \( _ { \cdot } \)\( \mathbf { ) } _ { \mathbf { \Phi } ) } \) +N2LO3N</td><td>17.767</td><td>−36.815</td><td>1.50</td><td>0.90</td></tr></table>

TABLE II. Fit coefficients for the energy per neutron, \( B / A \), following Eq. (22).

# IV. SUMMARY AND CONCLUSION

Within the BHF approach for pure neutron matter at zero temperature, we have in-vestigated di–neutron structures with emphasis placed on the low–density regime. We have calculated self–consistent sp potentials at Fermi momenta up to 2−3 \( \mathrm { f m ^ { - 1 } } \) using the continu-ous choice, restricting the system to a normal (nonsuperfluid) state. We have used AV18 and Paris internucleon potential, in addition to chiral \( \mathrm { N 3 L O } _ { 2 N } \) 2NF as well as \( \mathrm { N 3 L O } _ { 2 N } \mathrm { + N 2 L O } _ { 3 N } \) 3NF. Explicit account for di–neutron bound states is made in the \( { } ^ { 1 } \mathrm { S } _ { 0 } \) channel for the eval-uation of the mass operator during self–consistent searches of the sp potential.

The resulting sp solutions from each of the potentials considered in this work are in fair agreement with those found elsewhere [27, 33, 47–49]. The major conclusion of our work is that di–neutron bound states appear in the BHF approach in the \( { } ^ { 1 } \mathrm { S } _ { 0 } \) channel independently of the Hamiltonian that is used to model neutron interactions. In terms of the Fermi momentum, di–neutrons appear in the regime \( 0 . 0 6 \lesssim k _ { F } \lesssim 1 . 0 5 \)\( \mathrm { f m } ^ { - 1 } \) and are loosely bound, by less than 700 keV. The density dependence of their binding energy is very close for all interactions, which indicates a dominance of many–body correlations in di–neutron formation. In particular, because they appear at low densities, di–neutrons do not seem to be affected by 3NF. More indicative, these bound states form at densities where neutron effective masses become larger than the bare mass. Furthermore, the size of these bound states can get as high as ∼ 100 fm. In contrast to isospin–symmetric nuclear

matter, solutions for the sp spectra do not exhibit coexisting phases [12], mainly due to the fact that \( \mathrm { ^ { 3 } S D _ { 1 } } \) channel is fully suppressed in pure neutron matter. A recent study[50] addressing neutronic and symmetric nuclear matter, considering modern realistic NN interactions, confirms the robustness of theses findings.

The study of nuclear matter, even on its simplest nonrelativistic form, is an exceedingly difficult problem involving various scenarios in density, isospin asymmetry and temperature. On top of that, the emergence of superfluidity, superconductivity and clusterization multiply the physical scenarios under which matter can evolve when confined. The study we have presented is just a first step towards ab initio clusterization studies, going beyond traditional calculations in this context which are based on a variety of phenomenological approximations. In turn, these calculations can provide guidance on clustering in isospin–rich systems.

We can foresee a variety of extension of this work, both at the phenomenological and at the more theoretical level. Within this very same framework, we would like to study the melting of di–neutrons as temperature effects switch on. The extension to isospin asymmetric systems is of relevance for neutron–star matter, but also in the context of nuclear structure and the isospin dependence of clustering correlations. The competition between pairing and bound states in neutron matter is relevant for BEC–BCS studies, and the BHF approach is perfectly suited to provide quantitative guidance on this subject. Finally, it would be interesting to use other many–body techniques to establish firmly the existence of di–neutron bound states in isospin–rich nuclear systems.

# ACKNOWLEDGMENTS

H.F.A. acknowledges partial funding from FONDECYT under grant No 1120396. F.I. thanks funding from CONICYT under contract No. 221320081. This work was supported in part by STFC through Grants ST/I005528/1, ST/J000051/1 and ST/L005816/1. Partial support comes from “NewCompStar”, COST Action MP1304. F.I. thanks the hospitality of colleagues of the University of Surrey, UK, where part of this work took place.

[1] F. Kobayashi and Y. Kanada-En’yo, Phys. Rev. C 88, 034321 (2013).

[2] A. Spyrou, Z. Kohley, T. Baumann, D. Bazin, B. A. Brown, G. Christian, P. A. DeYoung, J. E. Finck, N. Frank, E. Lunderberg, S. Mosby, W. A. Peters, A. Schiller, J. K. Smith, J. Snyder, M. J. Strongman, M. Thoennessen, and A. Volya, Phys. Rev. Lett. 108., 102501 (2012)