Two-proton decay

A search for the two-proton ground-state radioactivity has a long history, however, apart from the well-known three-body $(\alpha{}pp)$decay of ⁶Be, such decay mode has not yet been experimentally discovered. One hopes that simultaneous emission of two protons may give us invaluable information about the two-particle ground-state correlations in nuclei. Such an emission explores a different phase space than the standard two-particle transfer experiments which were used to study pairing correlations in nuclei. Indeed, in the emission process the two-protons may leave the nucleus in various final states, ranging from a quasi-bound diproton to anticorrelated protons emitted in opposite directions, while in transfer reactions they are absorbed from a given initial state.

The simultaneous two-proton emission, whenever it is energetically possible, i.e., only beyond the proton drip line, must compete with two other decay modes which are usually much more probable, namely, the one-proton emission and $\beta$ decay. Therefore, one has to look for nuclei in which one-proton decay is energetically impossible (which limits the selection to even-Z elements), and where the two-proton decay energy is sufficiently large. During the emission process, the two protons must tunnel through a wide Coulomb barrier, typically traversing the classically forbidden region of even up to about 100fm. Hence, the emission probability very strongly depends on the available Q_2p value. For small Q_2p values, $\beta$decay is more probable, while for the large ones the life time of the given nucleus is very short. Therefore, the window of opportunity to observe the two-proton decay is fairly small. Nevertheless, several candidate nuclei were already identified (¹⁹Mg, ⁴²Cr, ⁴⁵Fe, ^48,49Ni,...), and intense searches of this new decay mode are presently conducted, see e.g. Ref. [16].

Two-proton emissions from excited states was already observed in different configurations, such as the decays of analog states, e.g. from ³¹Cl (see Ref. [17] and references cited therein), or resonances, see Ref. [18] where the decay of ¹⁸Ne was studied. All these experiments encounter difficulties in extracting information about the decay process from observed data. Indeed, in order to differentiate between various two-proton decay scenarios one has to perform the full three-body calculations, where the two protons and the daughter nucleus are allowed to develop arbitrary correlations, and the full three-body wave function is obtained. The simple diproton emission can be calculated very easily within the WKB approximation (see Ref. [19] and references to earlier papers cited therein). However, the three-body calculations with Coulomb interaction are much more difficult, and have become available only very recently [20,21].

  

Figure 2: Left: Width and life time as functions of the ground-state energies of ¹⁹Mg and ⁴⁸Ni counted with respect to the two-proton decay threshold. Results of the three-body calculations (solid lines) are compared with those obtained within the diproton and two-proton approximations. From Ref. [20]. Right: Calculated life times of the ground-state (Q_p=1.19MeV) and isomer (Q_p=1.25MeV) proton emission from ¹⁴¹Ho. Different lines correspond to various Nilsson orbitals. Measured values indicate that the ground-state and isomer emission occurs from the 7/2^-[523] and 1/2⁺[411] Nilsson orbitals, respectively. From Ref. [22].

Such calculations reproduce the experimental width of the ⁶Be decay very well. Examples of results obtained for ¹⁹Mg and ⁴⁸Ni are shown in the left panel of Fig. 2 [20]. It can be seen that the widths based on the diproton hypothesis and those obtained by assuming a direct decay to continuum from the $\ell$=0 state are very similar. The later widths strongly depend on $\ell$, and are much smaller for values corresponding to relevant shell-model orbitals occupied at a given number of protons. Results obtained by the full three-body calculations are by about three orders of magnitude smaller than those obtained for the $\ell$=0 diproton emission. This shows that the final-state proton-proton interaction is not sufficient to maintain this pair of particles in a correlated state during the emission process. Since the full three-body wave function of the complete system is obtained, one can determine and compare with experiment not only the life time, but also all relevant correlation observables, e.g., the relative angles and energy correlations. This is crucial for the attempts to determine initial-state correlations from experiment. However, reliable conclusions about the proton-proton ground-state correlations can be obtained only from calculations that release the assumption of the inert core, and take the effects of core configuration mixing into account. In this sense, the method used in Refs. [20,21] is complementary to that developed in the SMEC model discussed in the previous section. The former one treats the two-body continuum exactly but assumes an inert core, while the latter one neglects two-body continuum but uses the full shell-model space for the core. Clearly, a combined approach is very much called for.