Nuclear Physics Division

Light neutron rich nuclei are a unique testing ground to study the properties of dilute nuclear matter. Phenomena like the appearance of a halo of neutrons surrounding a more compact core of protons and neutrons have been predicted and observed for the first time for ¹¹Li in 1985. Since then, many efforts to characterize the geometrical arrangement of the neutrons forming this halo have been made, but no consensus has been reached yet. This is due to the technological and methodological difficulties of such a task, like the elusive nature of those unstable nuclei.

¹¹Li, like ¹⁴Be and ¹⁷B, belongs to a special category of nuclei called Borromean, since they are formed by three sub-systems and become unbound when one of them is removed, like the Borromean rings on the coat of arms of the Italian House of Borromeo.

For example, if one neutron is removed from ¹¹Li, the remaining ¹⁰Li system is unbound and decay instantaneously in a neutron and ⁹Li, which is usually referred to as the “core”. To schematize, we can imagine those neutrons to assume one of the three configurations depicted in Fig. 2, that for intuitive reasons the practitioners call “uncorrelated”, “cigar-like” and “dineutron”, respectively.

A joint team lead by IRFU and RIKEN Nishina Center has proposed to tackle this question with an innovative method that consists in suddenly removing one of the two neutrons, causing the disaggregation of the system, and detecting all the particles issued from this process.

Three systems were studied simultaneously: ¹¹Li, ¹⁴Be and ¹⁷B. Several experiments, non-homogeneous in terms of methods and results, were already performed for ¹¹Li and signaled a preference for the dineutron configuration. In contrast, very few or no information was available for ¹⁴Be and ¹⁷B. One of the difficulty lies in the fact that they are unstable nuclei, thus the only way to realize the measurement is to produce them in a particle accelerator and send them on a target.  In our case, we used the 15-cm long MINOS liquid hydrogen target.

The reason why this was not attempted before is that measuring a 4-fold coincidence among the knocked out proton, removed neutron, decay neutron and fragment (see Fig. 3) requires a complex detection system and a very high luminosity1, that for unstable beams could be achieved only thanks to the performances of the RIBF radioactive beams factory and the MINOS concept, combining a thick liquid hydrogen target with a vertex tracker to preserve the vertex2 information necessary to reconstruct the momenta of the measured particles.

Using the measured momenta we built a map of the neutrons in the momentum space, that can be mathematically related to their configuration in the more familiar coordinate space. More exactly, we measured the opening angle between the momentum of the removed neutron and the momentum of the remaining neutron+core system as the observable sensitive to the configuration of the two neutrons. This quantity has been plotted as a function of the missing momentum, i.e. the intrinsic momentum of the removed neutron that is “missing” in the remaining fragment nucleus. It is experimentally verified that the neutrons of the halo at have typically smaller missing momentum with respect to the average one of the protons and neutrons in the nucleus. Therefore, to look at them we should focus on the left part of Fig. 4, where a prominent deviation from 90° (value corresponding to uncorrelated configurations) is observed. We interpret this deviation as due to the appearance of a dineutron-like correlation at the surface, which is more pronounced for ¹¹Li but still present in ¹⁴Be and ¹⁷B.

To theoretically backup our interpretation we collaborated with reaction theorists from the University of Sevilla, who have developed an approach able to calculate the observables of interest starting from a simplified but realistic enough description of the nuclei of interest based on a so-called “three body model”. The model was already validated for ¹¹Li in a previous paper. We further benchmarked it against several observables issued from our experiment for the case of ¹⁴Be, namely ¹²Be-n relative energy, ¹²Be transverse momentum, and eventually the opening angle distribution. The comparison is shown in Fig. 5 for the opening angle and is satisfactory…with the only slight exception of ¹⁴Be. We interpret this discrepancy as due to the fact that the three-body model is lacking some ingredients needed to describe this specific nucleus.

This overall satisfactory validation of the three-body model authorizes us to use it to calculate the probability density distribution for the three nuclei of interest. This distribution as a function of the neutron-neutron distance and the core-neutron distance, looks like in Fig. 6: dineutron-like correlation peaks toward small values of neutron-neutron distance, while cigar-like correlation extends towards larger values of this parameter. We can see that in all cases, but particularly for ¹¹Li, dineutron-like configuration dominates, in agreement with the experimental observation reported in Fig. 4.

This result represents a major step forward, as despite the major experimental difficulties of detecting simultaneously four particles at the same time, we managed to extract an experimental observable able to constrain the dineutron correlation in a clear way. In the future, we would like to extend our analysis to other nuclei and confirm that the dineutron correlation is a universal feature of Borromean nuclei as this first study suggests.