Can Modern Nuclear Hamiltonians Tolerate a Bound Tetraneutron?

I show that it does not seem possible to change modern nuclear Hamiltonians to bind a tetraneutron without destroying many other successful predictions of those Hamiltonians. This means that, should a recent experimental claim of a bound tetraneutron be confirmed, our understanding of nuclear forces will have to be significantly changed. I also point out some errors in previous theoretical studies of this problem.

Figure 1

Energies of ${}^{4}n$ in external wells versus the well-depth parameter $V_0$.

Figure 2

${}^{1}S_0$ phase shifts from AV18 and modifications to it. The lines show the $pp$, $pn$, and $nn$ phase shifts for the unmodified AV18 while the symbols show the modified results.

Figure 3

Energies of nuclei and neutron clusters computed with the AV18/IL2 Hamiltonian with modified $NN$ potentials (${}^{1}S_0\mathrm{\text{−}}2\pi$ and ${}^{1}S_0$-AV1′) and with no modification (AV18), compared with experimental values for known nuclei.

Figure 4

Energies of nuclei and neutron clusters computed with modified $NNN$ and $NNNN$ potentials.