The ground states of the nuclei <math><mmultiscripts><mrow><mi>Mg</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>40</mn></mrow></mmultiscripts></math> and <math><mmultiscripts><mrow><mi>Na</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>39</mn></mrow></mmultiscripts></math> are investigated using the hyperspherical formalism. Since they are located at the edge of the “big island of inversion”, we concentrate on whether we are likely to find two-neutron Borromean halos in these nuclei. A three-body model with effective n-n and <math><mmultiscripts><mrow><mi>Mg</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>38</mn></mrow></mmultiscripts><mo>+</mo><mi>n</mi></math> interactions is built for <math><mmultiscripts><mrow><mi>Mg</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>40</mn></mrow></mmultiscripts></math> based on the available data. We also give predictions for the low-lying spectrum of <math><mmultiscripts><mrow><mi>Na</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>38</mn></mrow></mmultiscripts><msup><mrow><mo>=</mo></mrow><mrow><mn>37</mn></mrow></msup><mrow><mi>Na</mi></mrow><mo>+</mo><mi>n</mi></math> and two-neutron separation energy of the <math><mmultiscripts><mrow><mi>Na</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>39</mn></mrow></mmultiscripts></math> nucleus. Depending on parameter choice, we report an increase in the matter radii in the range 0.1-0.5 fm relative to those of the core nuclei. The results suggest a two-neutron halo structure in <math><mmultiscripts><mrow><mi>Mg</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>40</mn></mrow></mmultiscripts></math> for a subset of parameters, reinforcing the prediction of a Borromean halo nucleus. The calculations indicate that a two-neutron halo is even more likely for <math><mmultiscripts><mrow><mi>Na</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>39</mn></mrow></mmultiscripts></math>. As expected, the halo is linked to the disappearance of the shell gap in these nuclei due to the inversion of the <math><mn>2</mn><msub><mrow><mi>p</mi></mrow><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msub></math> and <math><mn>1</mn><msub><mrow><mi>f</mi></mrow><mrow><mn>7</mn><mo>/</mo><mn>2</mn></mrow></msub></math> orbitals. We study the total cross section for scattering of these nuclei from a carbon target using a Glauber model and show that these provide a clear signal to assess the halo structure.

Poland

United Kingdom

India

Japan

Jagjit Singh

Spain

J. Casal

W. Horiuchi

N.R. Walet

W. Satuła

Prediction of two-neutron halos in the = 28 Isotones Mg and Na