Beta decay to continuum states : the case of 11 Be

Beta decay in exotic nuclei can lead to multi-particle final states. This contribution discusses briefly what decay mechanisms may enter in such decays and presents, on behalf of the IS541 collaboration at ISOLDE/CERN, preliminary data from a search for the beta-delayed proton decay of the halo nucleus 11Be. 1 Beta-particle decay mechanism The Q-values for beta-decays increase as one moves towards the driplines and eventually become larger than the particle separation energies in the daughter nuclei. This allows population of final states containing, apart from the beta particle and the associated (anti)neutrino, one or more particles (protons, neutrons or heavier particles) in continuum states and a recoiling final nucleus. Such processes allow many different physics questions to be probed experimentally — see [1, 2] for recent reviews — and are normally referred to as beta-delayed particle emission. However, this name suggests a two-step process: the beta decay feeding resonance states in the daughter nucleus that subsequently decay by particle emission. The other possible decay mechanism, beta decays feeding the continuum states directly, deserves consideration as well. Some indication for decays going directly into the continuum exist for halo nuclei, see [3–5] and references therein for details on the halo structure. The two-neutron halo nuclei 6He and 11Li appear both to have beta-delayed deuteron emission taking place directly into the continuum [1, 6]. For 11Li this process has a branching ratio of the order of 10−4, the low value mainly being due to the small energy window, whereas cancellation effects reduces the branching ratio for 6He down to the 10−6 level. The simple-minded model of the decays is that one of the two halo neutrons beta-decay into a proton and combines with the other one to form a deuteron. A complicating factor in the theoretical description of these two decays is therefore the “two neutron to deuteron” overlap that is sensitive to the correlations between the two neutrons. This is an interesting physics problem, but if the focus is on investigating the decay mechanism a much cleaner case would be the beta-delayed proton decay of a single-neutron halo nucleus. 2 The 11Be(βp) decay The most favourable case is 11Be(βp). Estimates of the branching ratio indicates that this will be a very rare process [7] due to the low energy available, see table 1; the branching ratio will in most ae-mail: kvr@phys.au.dk DOI: 10.1051/ C © Owned by the authors, published by EDP Sciences, 2014 , / 02090 (2014) 201 66 epjconf EPJ Web of Conferences 46602090 This is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/20146602090 Table 1. Energies [8] for 11Be beta-delayed particle decays x p n α t Sx(B) (keV) 11228.6 ± 0.4 11454.12 ± 0.16 8664.1 ± 0.4 11223.6 ± 0.4 Qβx (keV) 280.7 ± 0.3 55.2 ± 0.5 2845.1 ± 0.2 285.7 ± 0.2 Figure 1. Sketch of the collection station at ISOLDE. The 11Be beam is led through several collimators and collected in a Cu foil. Further shielding limits the count rate in the Ge detector that monitors the collection rate estimates be a few times 10−8. Looking for protons of kinetic energy a few hundred keV with this relative intensity is challenging, so the two attempts we have made have instead aimed at detecting the remaining nucleus, 10Be, that exists only in very small quantities on earth. The two following sections present the results obtained so far. 2.1 The IS374 experiment Both experiments have made use of the ISOLDE facility at CERN and its high-resolution separator that is crucial in order to limit the amount of contaminants in the samples. The IS374 experiment made sample collections in 2001 and the amount of remaining 10Be in the samples were determined in an accelerator mass spectromery (AMS) experiment in Uppsala in 2008, details of the experimental procedures can be found in a recent paper [7]. No conclusive evidence for the decay were found. The amount of 10Be in the sample was compatible with zero within the uncertainty and converted into a branching ratio of (2.5± 2.5) · 10−6, significantly above the published theoretical expectations, the most detailed of which [9] gave 3.0 · 10−8. 2.2 The IS541 experiment The IS541 experiment [10] made sample collections in December 2012, a schematic diagram is given in figure 1. The evaluation is still ongoing, so only preliminary results can be presented at this stage. The normalization was obtained from a Ge-detector that recorded the γ spectrum from the decay of 11Be during collection, see figure 2. The main line seen is at 2124 keV, correcting its intensity for detection efficiency and absorption gives a deduced amount of collected 11Be in the first sample slightly above 1012. Two other samples were taken: at the mass position of 11Li (0.02 mass units heavier than 11Be) and, for one second only, at the 10Be mass position. EPJ Web of Conferences


Beta-particle decay mechanism
The Q-values for beta-decays increase as one moves towards the driplines and eventually become larger than the particle separation energies in the daughter nuclei.This allows population of final states containing, apart from the beta particle and the associated (anti)neutrino, one or more particles (protons, neutrons or heavier particles) in continuum states and a recoiling final nucleus.Such processes allow many different physics questions to be probed experimentally -see [1,2] for recent reviews -and are normally referred to as beta-delayed particle emission.However, this name suggests a two-step process: the beta decay feeding resonance states in the daughter nucleus that subsequently decay by particle emission.The other possible decay mechanism, beta decays feeding the continuum states directly, deserves consideration as well.
Some indication for decays going directly into the continuum exist for halo nuclei, see [3][4][5] and references therein for details on the halo structure.The two-neutron halo nuclei 6 He and 11 Li appear both to have beta-delayed deuteron emission taking place directly into the continuum [1,6].For 11 Li this process has a branching ratio of the order of 10 −4 , the low value mainly being due to the small energy window, whereas cancellation effects reduces the branching ratio for 6 He down to the 10 −6 level.The simple-minded model of the decays is that one of the two halo neutrons beta-decay into a proton and combines with the other one to form a deuteron.A complicating factor in the theoretical description of these two decays is therefore the "two neutron to deuteron" overlap that is sensitive to the correlations between the two neutrons.This is an interesting physics problem, but if the focus is on investigating the decay mechanism a much cleaner case would be the beta-delayed proton decay of a single-neutron halo nucleus.

The 11 Be(βp) decay
The most favourable case is 11 Be(βp).Estimates of the branching ratio indicates that this will be a very rare process [7]   estimates be a few times 10 −8 .Looking for protons of kinetic energy a few hundred keV with this relative intensity is challenging, so the two attempts we have made have instead aimed at detecting the remaining nucleus, 10 Be, that exists only in very small quantities on earth.The two following sections present the results obtained so far.

The IS374 experiment
Both experiments have made use of the ISOLDE facility at CERN and its high-resolution separator that is crucial in order to limit the amount of contaminants in the samples.The IS374 experiment made sample collections in 2001 and the amount of remaining 10 Be in the samples were determined in an accelerator mass spectromery (AMS) experiment in Uppsala in 2008, details of the experimental procedures can be found in a recent paper [7].
No conclusive evidence for the decay were found.The amount of 10 Be in the sample was compatible with zero within the uncertainty and converted into a branching ratio of (2.5 ± 2.5) • 10 −6 , significantly above the published theoretical expectations, the most detailed of which [9] gave 3.0 • 10 −8 .

The IS541 experiment
The IS541 experiment [10] made sample collections in December 2012, a schematic diagram is given in figure 1.The evaluation is still ongoing, so only preliminary results can be presented at this stage.
The normalization was obtained from a Ge-detector that recorded the γ spectrum from the decay of 11 Be during collection, see figure 2. The main line seen is at 2124 keV, correcting its intensity for detection efficiency and absorption gives a deduced amount of collected 11 Be in the first sample slightly above 10 12 .Two other samples were taken: at the mass position of 11 Li (0.02 mass units heavier than 11 Be) and, for one second only, at the 10 Be mass position.The AMS was this time performed at the Vera facility in Vienna.Details of the procedure will be reported later, they resulted in a significant improvement of the sensitivity to the number of 10 Be atoms, measured relative to a known number of added 9 Be atoms.The deduced amount of atoms in the 10 Be sample agreed with the estimation from the implantation The number for the 11 Li sample was below 10 5 and consistent with the lack of observed γ-rays from the decay of 11 Li.The number for the 11 Be sample was just above 10 7 .
Contaminations in our sample could arise due to the tail of the main 10 Be peak or due to the tail of 11 Li, whose decay also produces 10 Be.Both possibilities are ruled out by the low recorded number of atoms for the 11 Li sample.The ISOLDE mass separator profile was followed down to the 10 −5 level that occured at a mass difference of 0.05 mass units.In principle the molecule 10 Be 1 H would appear on the 11 Be position, but this molecule is unlikely to be formed in the target and to survive through the laser ion source.The result gives therefore a strong indication for the 11 Be(βp) decay with a branching ratio in the range (5-10) •10 −6 .

Discussion and outlook
The experimentally found branching ratio is surprisingly large, but actually consistent with the outcome of the first experiment.As a first step, the intensity can be converted into a beta-strength via the standard relation A Gamow-Teller beta-strength B GT below 3 (the free neutron value, the Fermi-strength is expected to concentrate in the isobaric analogue state) is consistent with decays that take place with a centre-of-mass energy for the outgoing proton below 200 keV, above 200 keV the f-factor is too small.The definition of beta-strength is actually depending on what theoretical framework is used to extract it; however, this will not contribute significantly to the uncertainty here so the above simple relation can be used safely.
Since the most recent [9] theoretical prediction for a direct decay mechanism lies more than two orders of magnitude below the experimental value we shall look here mainly for an explanation of the decay intensity in terms of a sequential model.The latest compilation [11] lists three levels in the appropriate excitation energy range in 11 B with excitation energy (keV), spin-parity and width (keV): 11272 ± 14, 9/2 + , 110 ± 20; 11450 ± 17, unknown, 93 ± 17; 11600 ± 20, 5/2 + , 180 ± 20.Due to the Coulomb barrier the penetrabilities are low even for s-wave protons, see figure 3, and the 9/2 + and 5/2 + levels are therefore not expected to contribute to the decay since they would correspond to g-and d-waves.The 11.45 MeV level may contribute if its spin-parity is 1/2 + , but it is known to mainly decay via α-particle emission.Decays through this level would therefore only contribute to the proton channel with probability Γ p /Γ tot and one has to go to the limit of current error bars in order to make this level fit.Let us consider whether a new level in 11 B could describe the decay.The requirements of a large B GT and a penetrability that does not quench the decay too much may be fulfilled simultaneously if the proton wave-function of the level extends into the p+ 10 Be channel.This is a situation that has been considered theoretically earlier by Barker [12], but it would clearly be valuable to have a more thorough investigation of resonant structures in the p+ 10 Be continuum.
If our final analysis and future experiments confirm the present indications for a βp branching ratio much above the predicted value there will clearly be a need for clarification of our theoretical understanding of the process.

2 Figure 1 .
Figure 1.Sketch of the collection station at ISOLDE.The 11 Be beam is led through several collimators and collected in a Cu foil.Further shielding limits the count rate in the Ge detector that monitors the collection rate

Figure 2 .
Figure 2. The main lines in the γ spectrum recorded during the collection are the 2124 keV line from the decay of 11 Be and the 511 keV line from positron annihilation

Figure 3 .
Figure 3.The upper part of the figure shows the Coulomb potential in the p+ 10 Be system.The lower part shows the penetrability for s-wave protons of centre-of-mass energy 100 keV and 200 keV.The line marks the channel radius calculated as 1.4 fm •(1 + 10 1/3 )

Table 1 .
[8] to the low energy available, see table1; the branching ratio will in most Energies[8]for11Be beta-delayed particle decays