nuclear physics Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter. Nuclear physics should not be confused with atomic physics, which studies t ...

, an

atomic nucleus The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment. After the discovery of the neutron ...

is called a halo nucleus or is said to have a nuclear halo when it has a core nucleus surrounded by a "halo" of orbiting protons or neutrons, which makes the radius of the nucleus appreciably larger than that predicted by the

liquid drop model In nuclear physics, the semi-empirical mass formula (SEMF) (sometimes also called the Weizsäcker formula, Bethe–Weizsäcker formula, or Bethe–Weizsäcker mass formula to distinguish it from the Bethe–Weizsäcker process) is used to approxi ...

. Halo nuclei form at the extreme edges of the

table of nuclides A table or chart of nuclides is a two-dimensional Cartesian coordinate system, graph of isotopes of the elements, in which one axis represents the number of neutrons (symbol ''N'') and the other represents the number of protons (atomic number, sy ...

— the

neutron drip line The nuclear drip line is the boundary beyond which atomic nuclei decay by the emission of a proton or neutron. An arbitrary combination of protons and neutrons does not necessarily yield a stable nucleus. One can think of moving up and/or to ...

and proton drip line — and have short half-lives, measured in milliseconds. These nuclei are studied shortly after their formation in an

ion beam An ion beam is a type of charged particle beam consisting of ions. Ion beams have many uses in electronics manufacturing (principally ion implantation) and other industries. A variety of ion beam sources exists, some derived from the mercu ...

. Typically, an atomic nucleus is a tightly bound group of protons and neutrons. However, in some nuclides, there is an overabundance of one species of nucleon. In some of these cases, a nuclear core and a halo will form. Often, this property may be detected in scattering experiments, which show the nucleus to be much larger than the otherwise expected value. Normally, the cross-section (corresponding to the classical radius) of the nucleus is proportional to the cube root of its mass, as would be the case for a sphere of constant density. Specifically, for a nucleus of

mass number The mass number (symbol ''A'', from the German word ''Atomgewicht'' tomic weight, also called atomic mass number or nucleon number, is the total number of protons and neutrons (together known as nucleons) in an atomic nucleus. It is approxima ...

''A'', the radius ''r'' is (approximately) :

r = r_\circ A^,

where

r_\circ

is 1.2 fm. One example of a halo nucleus is ¹¹ Li, which has a half-life of 8.6 ms. It contains a core of 3 protons and 6 neutrons, and a halo of two independent and loosely bound neutrons. It decays into ¹¹ Be by the emission of an antineutrino and an electron. Its mass radius of 3.16 fm is close to that of ³² S or, even more impressively, of ²⁰⁸ Pb, both much heavier nuclei. Experimental confirmation of nuclear halos is recent and ongoing. Additional candidates are suspected. Several nuclides including ⁹B, ¹³N, and ¹⁵N are calculated to have a halo in the

excited state In quantum mechanics, an excited state of a system (such as an atom, molecule or nucleus) is any quantum state of the system that has a higher energy than the ground state (that is, more energy than the absolute minimum). Excitation refers to ...

but not in the

ground state The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. ...

List of known nuclides with nuclear halo

Nuclei that have a neutron halo include ¹¹ Be and ¹⁹ C. A two-neutron halo is exhibited by ⁶ He, ¹¹ Li, ¹⁷ B, ¹⁹ B and ²² C. Two-neutron halo nuclei break into three fragments and are called Borromean because of this behavior, analogously to how all three of the

Borromean rings In mathematics, the Borromean rings are three simple closed curves in three-dimensional space that are topologically linked and cannot be separated from each other, but that break apart into two unknotted and unlinked loops when any one of the t ...

are linked together but no two share a link. For example, the two-neutron halo nucleus ⁶He (which can be taken as a three-body system consisting of an alpha particle and two neutrons) is bound, but neither ⁵He nor the

dineutron Neutronium (sometimes shortened to neutrium, also referred to as neutrite) is a hypothetical substance composed purely of neutrons. The word was coined by scientist Andreas von Antropoff in 1926 (before the 1932 discovery of the neutron) for the ...

is. ⁸ He and ¹⁴ Be both exhibit a four-neutron halo. Nuclei that have a proton halo include ⁸ B and ²⁶ P. A two-proton halo is exhibited by ¹⁷ Ne and ²⁷ S. Proton halos are expected to be rarer and more unstable than neutron halos because of the repulsive forces of the excess proton(s).

List of known nuclides with nuclear halo

See also

References

Further reading