The drip line: nuclei on the edge of stability

20 November 2007

Dave Morrisey describes the challenges of neutron-rich isotopes.

What combinations of neutrons and protons can form a bound nucleus? The long-elusive answer continues to stimulate nuclear physicists. Even now, decades after most of the basic properties of stable nuclei have been discovered, a fundamental theory of the nuclear force is still lacking, and theoretical predictions of the limits of nuclear stability are unreliable. So, the task of finding these limits falls to experimentalists – who continue to find surprises among super-heavy isotopes of elements immediately beyond oxygen.

At the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University we recently discovered several new neutron-rich isotopes: 44Si, 40Mg, 42Al and 43Al (Tarasov et al. 2007 and Baumann et al. 2007;). These are at the neutron drip line – the limit in the number of neutrons that can bind to a given number of protons. The result confirms that these exotic neutron-rich nuclei gain stability from an unpaired proton, which narrows the normal gaps between shells and provides the opportunity to bind many more neutrons (Thoennessen 2004). This feature was firmly established in 2002 by the significant difference between the heaviest isotopes of oxygen (24O16) and fluorine (31F22). However, our observation of such ostensibly strange behaviour is still novel, since in stable nuclei, the attractive pairing interaction generally enhances the stability of “even–even” isotopes with even numbers of protons and neutrons.


The recent experiment at NSCL clearly identified three events of 40Mg in addition to many events of the isotopes previously observed, namely 31F, 34Ne, 37Na and 44Si (figure 1). It also confirmed that 30F, 33Ne and 36Na are unbound as there were no events; the lack of events corresponding to 39Mg indicates that it too is unbound. Furthermore, the 23 events of 42Al establish its discovery. The data also contain one event consistent with 43Al. Owing to the attractive neutron pairing interaction, the firm observation of the odd–odd isotope 42Al29 supports the existence of 43Al30 and lends credibility to the interpretation of the single event as evidence for the existence of this nucleus.


The discovery of the even–even isotope 40Mg28 is consistent with the predictions of two leading theoretical models, as well as with the experimentally confirmed staggered pattern of the drip line in this region (figure 2). It is interesting to note that if this experiment had not observed 40Mg, the drip line might have been considered to have been determined up to magnesium. However, with the observation of 40Mg, the question remains open as to whether 31F, 37Ne, 40Na and 40Mg are in fact the last bound isotopes of fluorine, neon, sodium and magnesium, respectively.

More important than the observation of the even–even 40Mg is the discovery of the odd–odd 42Al, which two leading theoretical models predicted to be unbound. The latest observation breaks the pattern of staggering at the drip line, somewhat akin to the situation at fluorine. In fact, it now appears possible that heavier nuclei up to 47Al may also be bound.

For many decades, the point at which the binding energy for a proton or a neutron goes to zero has been a clear-cut benchmark for models of the atomic nucleus. The drip line is the demarcation line between the last bound isotope and its unbound neighbour and each chemical element has a lightest (proton drip line) and a heaviest (neutron drip line) nucleus.

The proton drip line is relatively well established for most of the elements because the Coulomb repulsion among protons has a dramatic destabilizing effect on nuclei with significantly fewer neutrons than protons. On the other hand, the neutron-binding energy only gradually approaches zero as the neutron number increases. Subtle quantum-mechanical effects such as neutron pairing and energy-level bunching end up determining the stability of the heaviest isotope of each element. The weak binding of the most neutron-rich nuclei leads to the phenomena of neutron “skins” and “halos”, which give these nuclei some unusual properties.

The only method available at present to produce nuclei at, or near, the neutron drip line is through the fragmentation of stable nuclei followed by the separation and identification of the products in less than a microsecond (Thoennessen 2004). The fragmentation reactions produce a statistical distribution of products with a large range of excitation energies. The excitation energy is dissipated by particle emission through strong decay (primarily neutrons and protons) and then by electromagnetic decay before the fragments reach the detectors. The Coulomb force also favours the emission of neutrons, suppressing the production of the most neutron-rich products.

Current knowledge of the neutron drip line is limited to only the lightest nuclei. The portion of the chart of nuclides in figure 2 shows the known geography of the drip line and the variation in the predictions from two widely respected theoretical models. Researchers first observed the heaviest bound oxygen isotope, 24O, in 1970. However, it was much later before experiments showed that the nuclei 25O through 28O are unbound with respect to prompt neutron emission. Only in 1997 did nuclear physicists consider the drip line for oxygen to be established. Subsequently, the isotopes 31F, 34Ne and 37Na have been observed. Although no experiment has established that 33F, 36Ne, and 39Na are unbound, these heavier isotopes probably do lie beyond the neutron drip line. These earlier experiments also failed to observe the even–even nucleus 40Mg, and researchers even speculated that 40Mg might be unbound.

On the theoretical side, the finite-range droplet model (FRDM) uses a semi-classical description of the macroscopic contributions to the nuclear binding energy, which is augmented with microscopic corrections arising from local single-particle shell structure and the pairing of nucleons (Möller et al. 1995) – this gives the solid black line in figure 2. Another theoretical framework, the fully microscopic Hartree–Fock–Bogoliubov model (HFB-8), is a state-of-the-art quantum-mechanical calculation that puts the nucleons into a mean-field with a Skyrme interaction with pairing (Samyn et al. 2004). This is the dashed green line in figure 2. Although in many cases both models correctly predict the location of the neutron drip line, they cannot account for the detailed interplay of valence protons and neutrons, even among the oxygen and fluorine isotopes. The discrepancies between the models is still more apparent in the magnesium to silicon region.

The recent observations at NSCL required high primary beam intensity, high collection efficiency, high efficiency for identification and – perhaps most importantly – a high degree of purification, as the sought-after rare isotopes are produced infrequently, in approximately 1 in 1015 reactions. Currently, the worldwide nuclear science community is anticipating several new facilities, including the Facility for Antiproton and Ion Research in Germany, the Radioisotope Beam Factory in Japan and the Facility for Rare-Isotope Beams in the US. The facilities are needed for many reasons, including advancing the study of rare isotopes and investigating the limits of existence of atomic nuclei.

The result from NSCL is one among many that hints at scientific surprises associated with the ongoing pursuit of exotic, neutron-rich nuclei. A thorough and nuanced understanding of the nuclear force may remain beyond the collective understanding of nuclear science, but the drip line beyond oxygen – even if further out than previously expected – continues to beckon.

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