Proton emission – new results and future prospects

Proton emission is the radioactive decay mode that is expected to determine the limit of observable proton-rich nuclei for most elements. Considerable progress has been made in the study of proton-emitting nuclei since the first observation of direct proton emission nearly 50 years ago. This has led to improvements in our understanding of this decay process and provided invaluable nuclear structure data far from the valley of beta stability. The rapid fall in half-lives with increasing neutron deficiency when proton emission dominates makes it likely that for some elements, the lightest isotopes whose ground states can be observed in conventional experiments have already been reached. The enhanced stability against proton emission of the recently discovered high-lying isomer in Ta raises the possibility that proton emission from multiparticle isomers could be observed in nuclei beyond the expected boundaries of the nuclear landscape.


Introduction
Isomers are a widespread feature across the chart of nuclides and their study can provide an important testing ground for a range of nuclear theories [1].The existence of isomeric states is also an important consideration in the study of nuclei beyond the proton drip line and is inextricably linked to the question of the limits of observable nuclei.The first experimentally observed case of direct proton emission was from a high-spin isomer in 53 Co [2,3].In this unique case, the proton emitter's ground state is bound to proton emission, but the excitation energy of the protonunbound isomer is sufficient to overcome the retarding effect of the centrifugal barrier and results in a proton-decay branching ratio of ∼1.5 %.Subsequent studies of proton emission have primarily focused on low-lying states in nuclei beyond the proton drip line.As these studies reach the limits of nuclei that are accessible using recoil separators, attention may again switch to proton emission from highlying isomeric states, in nuclei far beyond the proton drip line.

Proton emission from low-lying states
The discovery of the first cases of proton emission from nuclear ground states [4,5] followed a decade after the 53 Co results and many further proton emitters have been discovered since [6].Approximately half of the presently known cases of direct one-proton emission have been found in the region beyond the proton drip line that is bounded by the N = 82 and Z = 82 shell closures.In total, 21 cases of direct proton emission in this region have been reported to date.One reason for this rich sample a e-mail: rdp@ns.ph.liv.ac.uk is that either the proton-decaying states can be populated through alpha decays or the daughter nuclides are alpha emitters.This makes searches for proton-decay peaks with low numbers of counts very sensitive, because the alpha decays have characteristic energies that can be cleanly selected for correlation analyses and they tend to have fairly short half-lives, which result in relatively low levels of background from false correlations.
The structure of nuclei in this region is governed at low excitation energies by valence neutrons in the νf 7/2 and νh 9/2 orbitals and protons in the πs 1/2 , πd 3/2 and πh 11/2 orbitals.In odd-Z nuclides, two states are generally at low excitation energies that can decay by proton, alpha or beta emission (see figure 1a).In odd-A nuclei, the states usually have either an unpaired s 1/2 or h 11/2 proton, while in odd-odd nuclei either a d 3/2 or h 11/2 proton is coupled with an f 7/2 neutron to form the low-lying states.According to the Nordheim rules [7,8], the lowest-energy state formed by coupling a d 3/2 proton with an f 7/2 neutron would have spin and parity 2 − , while the lowest-energy state when coupling an h 11/2 proton with an f 7/2 neutron would be 9 + .The energy differences between the states have been found to be ≤300 keV (see figure 1b), so direct gamma decays from the isomeric state to the ground state in both odd-A and odd-odd nuclides would be very slow owing to the large spin difference.Consequently charged particle emission generally dominates from the low-lying isomeric states and approximately half of the known cases of proton emission in this region are from these isomers, with the remainder being from ground states.
This pattern of two low-lying states is generally borne out, as can be seen in figure 1a, except for a few of the most exotic nuclei where only the πh 11/2 state has been observed.This is thought to be because the low-spin ground states are too short-lived to survive the flight time through a recoil separator [12-15, 17, 18].The only other exception is the case of 160 Re, for which proton and alphaparticle emission have only been observed from the d 3/2 ground state [19][20][21].In this nuclide a 2.8 microsecond gamma-decaying isomer was identified [20] and subsequent in-beam gamma-ray spectroscopy measurements suggested that the isomer was based on a πh 11/2 orbital [22].The discovery of the alpha-decay branch from the πh 11/2 state in 164 Ir established the excitation energy of the corresponding state in 160 Re, which was interpreted as being the isomeric state [15].It seems that in 160 Re the multiplets of states formed by coupling the odd neutron and proton are so arranged as to allow a gamma-ray decay path that has a much shorter half-life than either proton or alpha emission from the πh 11/2 isomeric state [20].Measurements of proton-decay energies can be used to deduce Q p values that can be compared with predictions of atomic mass models.The systematics of Q p values determined from proton-decay measurements on elements from Tm to Tl are shown in figure 2. For Ta, Re, Ir, Au and Tl proton emitters, the prevalence of extensive alpha-decay chains above N = 82 allows Q p values to be determined indirectly for states that do not themselves have a known proton-decay branch.This is in contrast to the protonemitting Tm and Lu nuclides whose Q p values cannot be used in this way to deduce values for other nuclides.The smooth behaviour of the Q p values as a function of neutron number allows local extrapolations of the trends to be made, which can be used to predict the decay properties of as yet unobserved states [33].This makes it possible to identify good candidates for new proton emitter searches and to evaluate whether the limits of observable nuclei using conventional recoil separator techniques may have been reached.

Proton emission from high-lying isomers
In addition to the low-lying isomeric states discussed in the previous section, higher-lying multiparticle isomers are also known in this region.For example, seniority 3 [πh 3  11/2 ]27/2 − isomers have been identified in the N = 82 isotones 149 Ho, 151 Tm and 153 Lu [34][35][36].The possibil-Heavy Ion Accelerator Symposium 2015 ity of proton emission from the corresponding isomer in 155 Ta to states in 154 Hf is discussed in ref. [18].The proton decay directly to the ground state of 154 Hf would be favoured by having the largest Q p value, but be hindered by the large centrifugal barrier associated with the spin difference between the initial and final states.Decays to excited, higher-spin states in 154 Hf would be less hindered because the centrifugal barrier would be lower, but the excitation energy would reduce the effective Q p value.In general, the balance between these competing effects will determine which proton-decay paths are most favoured in the decay of a given isomer.
Multiparticle isomers that decay by alpha emission have been established in N = 84 isotones [16,37,38].In even-even nuclei these isomers are interpreted as having a [νf 7/2 νh 9/2 ]8 + structure, while in the odd-Z isotones the πh 11/2 proton couples with this configuration to give an isomeric 25/2 − state.Both 155 Lu and 157 Ta are unbound to proton emission (see figure 2) and the probability of proton-decay branches to states in their respective daughter nuclides are analysed in ref. [39].In the case of 155 Lu, proton emission from the isomer would be faster than from lower-lying states, which are only just unbound, whereas for 157 Ta all proton-decay paths from the isomer have longer partial half-lives than low-lying states.
The alpha and gamma decays of an even more complicated isomeric state in 158 Ta have been reported recently [39,40].A possible structure for this isomer is [πh −3 11/2 νf 7/2 νh 9/2 νi 13/2 ]19 − , analogous to that proposed for an isomer in 152 Ho [41].This isomer in 158 Ta lies at an excitation energy of 2668 keV and although it is unbound to proton emission by 3261 keV, no proton-decay branch could be identified [39].Analysis of the predicted lifetimes for proton-decay paths to states in the daughter nuclide 157 Hf revealed that none of them would be sufficiently short to compete with the other decay branches.Indeed, in contrast to the case of 53 Co, the direct proton decay of the 19 − isomer to the 7/2 − ground state of 157 Hf would have a longer partial half-life than either of its lower-lying states.

Conclusions
Experimental studies of odd-Z nuclei have identified more than 30 proton-emitting nuclei, with examples known for most elements from iodine (Z = 53) to bismuth (Z=83).These studies have revealed how the half-lives of lowlying states generally decrease with increasing neutron deficiency, dropping more rapidly when proton or alpha emission dominates over beta decay.For some elements it appears likely that the lightest isotopes whose ground states can be observed in conventional recoil separator experiments have already been reached.
The enhanced stability against proton emission of the high-lying isomers in 157,158 Ta [39] raises the possibility that multiparticle isomers could provide observable states in nuclei whose low-lying states decay by proton emission too quickly to be studied with a recoil separator.Calculations suggest that multiparticle isomers in neutron-rich nuclei [42,43] and superheavy nuclei [44] may also have enhanced stability.Decays of long-lived isomers beyond the expected boundaries of the nuclear landscape are an intriguing prospect for future experiments.

Figure 1 .
Figure 1.(a) Chart indicating the observed low-lying isomers in odd-Z nuclei.The triangles indicate nuclei in which only the high-spin isomer has been observed, the squares indicate those in which both the high-spin and low-spin isomers have been observed and the circle indicates 160 Re, which is the only nuclide in this region where only the low-spin isomer has been observed.Nuclides to the left of the line are known proton emitters.(b) Energy differences between the πh 11/2 isomers and the low-spin (πs 1/2 or πd 3/2 ) isomers.The low-spin isomers represent the ground states of the nuclides shown, except for the Lu isotopes for which the πh 11/2 configuration forms the ground state.The open symbols denote odd-A nuclei, while odd-odd nuclei are indicated by the filled symbols.Data are taken from refs.[9-16].

Figure 2 .
Figure 2. Experimental proton-decay Q-values of odd-Z elements from Tm to Tl measured directly are shown by the filled circles.Values estimated by combining these values with αdecay measurements are indicated by the empty circles.(a) is for high-spin (πh 11/2 ) states in odd-Z, even-N nuclei, while (b) shows the corresponding values for odd-Z, odd-N nuclei.(c) and (d) show the values for low-spin (πs 1/2 or πd 3/2 ) states in odd-Z, even-N and odd-Z, odd-N nuclei, respectively.Data are taken from refs.[4, 5, 9-18, 21, 23-32].