Neutron Dripline for Magnesium nuclei and hypernuclei

Hypernuclei containing lambda ($\Lambda)$-hyperons are of current interest in nuclear as well as astro-physics. The effect of addition of a $\Lambda $-hyperon on the neutron-dripline of a Magnesium nucleus is investigated in a microscopic framework using the Frankfurt chiral effective model. The chiral flavor-SU(3) yields a good fit to nuclei as well as reproduces 2-solar-mass neutron stars. In this model, we find that the neutron dripline is at $^{42}$Mg. If a $\Lambda $-hyperon is added, it opens up an additional degree of freedom, allowing for a wider energy distribution, and leads to a dripline at $^{51}_{\Lambda}$Mg. The general behavior of additional binding is expected in hyper-nuclei; however the size of the shift is quite striking. When the calculations are repeated with the SPL-40 and NL-3 parameter sets, the dripline nuclei without and with a $\Lambda $-hyperon are found to be $^{52}$Mg and $^{47}_{\Lambda}$Mg (for SPL-40) and $^{46}$Mg and $^{47}_{\Lambda}$Mg (for NL3), respectively. The last experimentally measured nucleus of the Mg isotope chain is $^{40}$Mg which, according to a macroscopic model, is the last bound neutron-rich Mg-isotope. The macroscopic and all three microscopic models well describe the measured $\Lambda $-separation energy of all $\Lambda -$hypernuclei. But, the results near the drip line are found to be very model dependent. Especially, while the SU(3) model suggests that the addition of a $\Lambda $-hyperon leads to an outward shift of the dripline by 8 neutrons, the SPL-40 model indicates an inward shift by rejecting 6 neutrons. Both results are remarkable and calls for experimental verification.