β delayed emission of a proton by a one-neutron halo nucleus
Introduction
Some neutron-rich halo nuclei can emit a proton. This process is possible if the neutron separation energy is very small. Indeed, when a sufficiently weakly bound halo neutron β decays, the produced proton can be emitted, possibly together with neutrons. Processes where this proton is bound with one or two neutrons have been observed in the β delayed deuteron and triton decays of 6He and 11Li [1], [2], [3], [4], [5], [6], [7], [8]. Recently we have calculated the branching ratio of an even rarer process where the proton remains unbound but is accompanied by a free neutron [9]. This decay is uniquely possible for 11Li, among nuclei with known separation energies. The study has been performed in a three-body model with a simplified description of the continuum. An even simpler process is however possible.
A one-neutron halo nucleus can be viewed as a normal nucleus, the core, to which a neutron is bound in an orbital with a large radius. The β decay of the bound halo neutron may occur, releasing the proton, under the condition of energy conservation where is the neutron separation energy of the decaying nucleus and , and are the neutron, proton and electron masses, respectively. Among one-neutron halo nuclei for which is known with sufficient precision, this decay is allowed at least for 11Be and 19C, and probably for 31Ne. It should be observable if the branching ratio is large enough. This decay mode of 11Be has been considered by Horoi and Zelevinsky but their results do not seem to have been published [10]. Here we study this rare decay mode within a two-body potential model. The initial halo nucleus is treated as a core + neutron bound state. The final states lie in the core + proton continuum. How rare is this decay is the main question raised in the present exploratory study.
Section snippets
Decay probability for β delayed proton emission
The β decay of the halo neutron releases the resulting proton from the core. The distribution of decay probability per time unit as a function of the energy of the relative motion of the two particles is given by [9] where is the dimensionless β-decay constant and is the ratio of the axial-vector to vector coupling constants. The Fermi integral depends on the kinetic energy available for the electron and
Results and discussion
Before making explicit calculations, we have to specify the choice of potentials. The Fermi strength (5) is proportional to the square of the overlap integral (7) between the initial and final radial wave functions. In order to have a realistic overlap, it is useful to have a correct node structure for these wave functions. Indeed, the presence of nodes leads to an integrand that changes sign one or several times and thus to a reduction of the overlap at small distances. Spectroscopic factors
Conclusion
As a summary, we have evaluated the order of magnitude of the decay probability per second for the β delayed proton emission by one-neutron halo nuclei. The best candidate for observing such a decay is 11Be in spite of the fact that its separation energy is not very small. The probability of this delayed decay is smaller than for the neutron-and-proton delayed decay of 11Li [9] by an order of magnitude. Because of a longer lifetime, the branching ratio is larger by two orders of magnitude. The
Acknowledgements
This Letter presents research results of BriX (Belgian Research Initiative on eXotic nuclei), the Interuniversity Attraction Pole Programme P6/23 initiated by the Belgian-state Federal Services for Scientific, Technical and Cultural Affairs (FSTC). E.M.T. thanks the IAP Programme for supporting his stay.
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