Direct observation of proton emission in 11Be

TL;DR

This paper reports the first direct measurement of proton emission from $^{11}$Be's $eta^- ext{p}^+$ decay, revealing a much larger branching ratio than predicted, explained by a resonance in $^{11}$B.

Contribution

It provides the first direct observation and measurement of $eta^- ext{p}^+$ decay in $^{11}$Be using a novel detector, challenging existing theoretical models.

Findings

Measured $eta^- ext{p}^+$ branching ratio is significantly larger than predicted.

Detected a narrow resonance in $^{11}$B above the proton separation energy.

First direct measurement of this decay mode in $^{11}$Be.

Abstract

The elusive $\beta^-\text{p}^+$ decay was observed in $^{11}$Be by directly measuring the emitted protons and their energy distribution for the first time with the prototype Active Target Time Projection Chamber (pAT-TPC) in an experiment performed at ISAC-TRIUMF. The measured $\beta^-\text{p}^+$ branching ratio is orders of magnitude larger than any previous theoretical model predicted. This can be explained by the presence of a narrow resonance in $^{11}$B above the proton separation energy.

Equations

$$\begin{array}{rl}\rho (E)& =(2\pi \hslash {)}^3\delta (\text{P}+\text{p}+{\text{p}}_e+{\text{p}}_{\nu })\\ & \times \delta (\Delta -E-{ϵ}_e-{ϵ}_{\nu })\frac{d^{3}P{d}^{3}p{d}^3{p}_e{d}^3{p}_{\nu }}{(2\pi \hslash {)}^{12}},\end{array}$$

$$\begin{array}{rl}dw(E)& =\frac{2\pi }{\hslash }{G}^2|\mathcal{M}{|}^2\frac{p_{\nu }^{2}d{o}_{\nu }{p}_e^{2}d{o}_e{p}^{2}d{o}_p}{(2\pi \hslash {)}^9}\\ & \times d{p}_{e}d{p}_{\nu }\frac{dp}{dE}dE\delta (X-{ϵ}_e-{ϵ}_{\nu }),\end{array}$$

$$dw(E)=\frac{1}{4{\pi }^5}\frac{m^5{c}^4}{{\hslash }^{10}}{G}^2|\mathcal{M}{|}^2{f}_0(x)p^{2}dp,$$

$$\begin{array}{rl}{f}_0(x)& =\frac{1}{5}\left(\frac{1}{6}{x}^4-\frac{3}{4}{x}^2-\frac{2}{3}\right)\\ & \times \sqrt{x^2-1}+\frac{1}{4}x\text{ln}\left(x+\sqrt{x^2-1}\right).\end{array}$$

$${\tau }^{-1}=\frac{\sqrt{2}}{4{\pi }^5}\frac{M^{3/2}{m}^{13/2}{c}^7}{{\hslash }^{10}}{G}^2{\int }_0^{\Omega }dϵ\sqrt{ϵ}{f}_0(x)|\mathcal{M}{|}^2.$$

Full text

11Be, 11B, $\beta$-delayed particle emission, $\beta^{-}\text{p}^{+}$, proton emission, halo nucleus

††preprint: APS/123-QED

It would seem, a priori, that $\beta^{-}$-decay and proton emission are incompatible processes in a neutron-rich nucleus. The $\beta^{-}$ decay moves isotopes north-west in the nuclear chart, towards the valley of stability and more bound systems, while the proton emission takes it south, becoming a less stable system. This process, called $\beta^{-}$-delayed proton emission ($\beta^{-}\text{p}^{+}$), is energetically forbidden in all but some nuclei for which their neutron separation energy is S${}_{n}<782$ keV Baye and Tursunov (2011). Only a handful of $A\leq 31$ nuclei that fulfil this condition have been observed, of which the most promising candidate is 11Be $\rightarrow^{10}$Be + p${}^{+}+\beta^{-}$.

Nuclei approaching the nuclear drip lines have large Qβ values available and decay into nuclei with low particle binding energy. This opens an energy window where different $\beta$-delayed particle emission channels are allowed Borge (2013). 11Be, which is the last bound odd beryllium isotope, has several of them energetically available: $\beta\alpha$ (Qβα=2845.2(2) keV, $b_{\alpha}$=3.30(10)% Refsgaard et al. (2019)), $\beta$t (Q${}_{\beta\text{t}}$=285.7(2) keV, not observed), $\beta^{-}\text{p}^{+}$ (Q${}_{\beta\text{p}}$=280.7(3) keV, $b_{p}$=$8.3(9)\cdot 10^{-6}$, indirectly observed Riisager et al. (2014)) and $\beta$n (Q${}_{\beta\text{n}}$=55.1(5) keV, not observed).

This low neutron binding energy allows for the counterintuitive $\beta^{-}\text{p}^{+}$ decay to happen. In nuclei like 11Be, called halo nuclei, the last neutron is so weakly bound that it orbits far from an inert core Tanihata (1996); Al-Khalili (2004); Tanihata et al. (2013). The $\beta^{-}\text{p}^{+}$ decay mechanism has been modeled as a decay of the halo neutron into a proton that is either in a high-energy resonant state above its separation energy or directly in the continuum, free to be emitted Riisager (2014). This is similar to the $\beta$-delayed deuterium emission in the two-neutron halo nucleus 11Li. When one of the neutrons decays into a proton, it binds to the other forming a deuteron coupled to the continuum Raabe et al. (2008).

Riisager and collaborators performed experiments at ISOLDE to indirectly observe the 11Be $\rightarrow^{10}$Be decay Borge et al. (2013); Riisager et al. (2014); Riisager (2017). They implanted 11Be (T1/2=13.8 s) in a catcher. Using accelerated mass spectroscopy, they measured the amount of 10Be (T${}_{1/2}=1.5\cdot 10^{6}$ years) in the samples, obtaining $b_{p}=8.3(9)\cdot 10^{-6}$. Theoretical predictions using the 11B nuclear structure suggest that the $\beta^{-}\text{p}^{+}$ branch should have been orders of magnitude lower than observed Baye and Tursunov (2011); Borge et al. (2013); Riisager (2014).

There are two possible explanations for this discrepancy. The $\beta^{-}\text{p}^{+}$ decay could populate some unobserved resonance in 11B, changing the available phase space and enhancing the decay, or there could be additional, unaccounted for decay channels contributing to the total 11Be $\rightarrow^{10}$Be decay. Recently, it was suggested in Refs. Fornal and Grinstein (2018); Pfützner and Riisager (2018) that the halo neutron in 11Be is so weakly bound that it could decay into a particle of the dark sector, thus creating a 10Be nucleus and an undetectable dark particle. The experiment in Ref. Riisager et al. (2014) measured the total branching ratio of the 11Be $\rightarrow^{10}$Be decay, not the individual branching of the $\beta^{-}\text{p}^{+}$ and other hypothetical dark decay channels. The implications of this alternative dark decay in 11Be will be discussed at length in the other publication reporting results of this experiment Olaizola et al. (2019).

The aim of our experiment was to directly measure the $\beta^{-}\text{p}^{+}$ decay in 11Be and unambiguously assign a branching ratio to that specific decay channel. By directly observing the emitted protons and measuring their energy distribution, important information can be extracted about 11B nuclear structure and the $\beta^{-}\text{p}^{+}$ decay mechanism.

In order to efficiently detect and identify every particle emitted in the $\beta$-decay of 11Be, specially protons of $\sim 200$ keV of energy Riisager et al. (2014); Riisager (2014), the experiment was performed with the prototype Active Target Time Projection Chamber (pAT-TPC) Suzuki et al. (2012). This device allows for efficient and high-resolution measurement of very low energy particles. The pAT-TPC consists of a cylindrical gaseous volume of 50 cm length with 12 cm radius with a detection plane composed of a dual micropattern gas detector (Micromegas Giomataris et al. (1996) coupled to a Multi-layer Thick Gas Electron Multiplier Cortesi et al. (2017)). An electric field is applied along the beam axis between the cathode end and the detection plane. Ionization electrons released when a charged particle is crossing the gaseous volume are drifted to the segmented pad plane. There they are multiplied and collected in the Micromegas readout pads. The drift time and the energy loss rate are recorded by each pad individually. With this information and the centroids of the pads, the characteristic energy loss curve of each particle and their tracks can be reconstructed. Each particle track was analyzed independently using a sophisticated clustering algorithm Dalitz et al. (2019). Further information about the pAT-TPC can be found in Refs. Suzuki et al. (2012); Bradt et al. (2017); Ayyad, Y. et al. (2018).

The 11Be isotopes were produced by a 480-MeV proton beam (9.8 $\mu$A of intensity) delivered by the TRIUMF main cyclotron Bylinskii and Craddock (2014) impinging on a uranium carbide (UCx) target. The TRIUMF Resonant Ionization Laser Ion Source Lassen et al. (2006) selectively ionized Be isotopes to a $1^{+}$ state. After separation of $A/q$=11, particles were further stripped to a $q$=$2^{+}$ state and re-accelerated to $\sim 390$ A keV. The beam intensity was attenuated to $\sim 10^{5}$ particles per second to reduce deadtime. The experiment was run in a cycled mode: ions were implanted for 1 s, the charge carriers produced during the implantation were evacuated for 0.5 s and finally 7 s were used to observe 11Be decay. The beam energy was selected to stop the 11Be at the center of the pAT-TPC. The ions were expected to neutralize and undergo minimal Brownian motion. However, most of the 11Be drifted to the cathode where they decayed. The response of the pAT-TPC to low-energy protons was determined by injecting protons in the detector. A molecular OH+ beam was extracted from the Off-Line Ion Source and accelerated before impacting a thin foil to break up the molecule. The p+ was then further accelerated to 220 keV/A. Protons entered the TPC gas volume with $E=198$ keV, as inferred from energy loss parameterizations. The energy resolution of the detector, which amounts to about 15 keV (FWHM) was obtained by integrating the energy loss curve for each proton event to determine the total deposited charge.

The detector was filled with 60 torr of 4He+CO2 (90-10$\%$) gas mixture to stop 200 keV protons within $\sim 10$ cm. Due to the extremely low branching ratio expected for the $\beta^{-}\text{p}^{+}$ channel, two different triggers, low- and high-level, were used to separate regions of interest in the energy spectrum: 20-300 keV and 300-1500 keV, respectively. The latter was downscaled by a factor of 64 to reduce the triggers of the $\beta\alpha$ decay.

Figure 1 shows the total energy spectrum of charged particles emitted following the 11Be $\beta$-decay. The vertical dashed line indicates the separation between trigger windows. One of the products of the decay into 7Li + 4He and 7Li* + 4He, coming from the cathode of the detector, was identified on an event-by-event basis. In addition, decays in the gas, in which both products were detected simultaneously, ($\sim 10\%$ of the total) were also measured (1200 keV).

The identification of protons in the region of interest, which is dominated by 7Li*, was performed using the characteristic energy loss distribution. An analytical energy loss curve fit to experimental proton and 7Li energy loss curves was used to perform a $\chi^{2}$-test for every particle track. These reference curves determined experimentally are shown in Fig. 2 for a $\beta^{-}\text{p}^{+}$ decay (upper panel) and a 7Li*+4He decay (lower panel) event. In these events, both the proton and 7Li* are emitted from the cathode of the detector. The experimental energy loss curves of each event (square for protons and dots for 7Li*) were compared to both reference curves using an objective function containing the amplitude (energy loss) per unit time (time bucket). Since the reference curves were determined at a fixed angle and energy, they were shaped and re-normalized to take into account the energy-range of the particle, its angle of emission and the starting time bucket of the event. In each step of the algorithm, the objective function is evaluated, selecting the curve that minimizes the $\chi^{2}$.

The results of the minimization process, in terms of $\chi^{2}$, have also been validated by scrutiny. The $\beta^{-}\text{p}^{+}$ decay candidates, 391 in total, were inspected and found to be similar to the one shown in the upper panel of Fig. 2.

Background and misidentification of events in the energy spectrum were evaluated by analyzing the distribution as a function of $\chi^{2}$ value (not normalized), as shown in Fig. 3. Below a $\chi^{2}$ value of 200 111This value was chosen based on a correlation matrix showing the $\chi^{2}$ obtained comparing both reference curves., the energy spectrum (solid dots in the lower panel) exhibits a clear peak that is in excellent agreement with a Breit-Wigner distribution with two contributions: protons emitted from the cathode with 178(20) keV, and 10$\%$ of decays in gas with 196 keV (178 keV plus 18 keV from the 10Be recoil), respectively, both with a width of 12(5) keV. The proton penetrability as a function of the energy was also taken into account. The sharp energy distribution clearly indicates that the $\beta^{-}\text{p}^{+}$ decay from 11Be proceeds through an unobserved resonance in 11B. Based on the Qβ and the proton plus recoil energies (the electron screening term is negligible for Be), the resonance is predicted at an energy of 11425(20) keV. From the proton energy distribution, and taking into account the detector energy resolution, the width of the resonance is $\Gamma=12(5)$ keV. The branching ratio for the $\beta^{-}\text{p}^{+}$channel was obtained relative to the well known $\beta\alpha$ one, $b_{\alpha}$=3.30(10)% Refsgaard et al. (2019). The result is $1.3(3)\cdot 10^{-5}$, in agreement with the previous indirect measurement Riisager et al. (2014). The measured branching ratio and resonance energy yields a very small log(ft)=4.8(4), which suggests a strongly allowed $\beta$ decay. From the $\beta$ decay selection rule of the J${}^{\pi}=1/2^{+}$ 11Be gs.s, we can assume $\Delta J=0,1$ and no change in parity, therefore we propose J${}^{\pi}=(1/2,3/2^{+})$ for the newly found resonance.

We evaluated the probability of the direct “democratic” decay (simultaneous emission of the proton and $\beta^{-}$) when there are four particles in the final state: electron (pe, $\epsilon_{e}$), electron antineutrino (pν, $\epsilon_{\nu}$), proton (p, E) and the final nucleus (P, E$\sim 0$). The release of kinetic energy is 11506-11228=278 keV so that for the electron $p_{e}R\sim(1/400)(R/\text{fm})$, i.e. always small even for halo nuclei with R $\sim 10$ fm (even smaller for the antineutrino). The density of final states for free particles can be estimated, with the normalization to the unit volume, as:

[TABLE]

The probability of the decay is:

[TABLE]

where X is the total energy of the electron and antineutrino including $m_{e}c^{2}$, and $\mathcal{M}$ is the dimensionless sum of the Fermi and Gamow-Teller nuclear matrix elements depending on the halo wave-function.

The integration can be performed exactly:

[TABLE]

where $x=X/mc^{2}$ and:

[TABLE]

The inverse lifetime follows as (M is the nucleon mass)

[TABLE]

For calculating the matrix element, we use the analytic form of the neutron halo wave-function Hussein et al. (1999) and the Coulomb proton wave-function in the field of the charge $Z=5$. The result for the half-life summing the Fermi and Gamow-Teller contributions is $\tau_{1/2}\sim 2.2\cdot 10^{10}$ s which corresponds to a branching ratio $6.3\cdot 10^{-10}$ for the democratic decay, in glaring contrast with the experimental result.

We also estimated the $\beta$-decay rate of 11Be into a proton-emitting resonance of 11B, using a simple model to compute the overlap $\mathcal{O}=\langle\phi_{n}|\phi_{p}\rangle$ between the halo neutron $\phi_{n}(2s_{1/2})$ in 11Be and the final single-proton resonance $\phi_{p}(2s_{1/2})$ of 11B, as well as the width $\Gamma_{p}$ of the resonance. Both states are calculated making use of Woods-Saxon potentials similar to those used in Riisager (2014), complemented with the Coulomb interaction in the proton case. Setting the resonance energy at the experimental value, the overlap and the width are found to be $\mathcal{O}=0.53$ and $\Gamma_{p}=44$ keV, respectively. Within this model, we can also give a rough estimate of the spectroscopic factor $S(^{11}\text{B})$ of the 11B resonance using the expression $\gamma_{p}=S(^{11}\text{B})\Gamma_{p}$, where $\gamma_{p}$ is the experimental proton emission width. We obtained $S(^{11}\text{B})\approx 0.34$, suggesting that the newly observed 11B resonance has a sizable single-proton content.

The corresponding partial lifetime $t^{p}_{1/2}$ can be estimated by integrating the Gamow-Teller strength over a Lorentzian distribution characterizing the energy spreading of the resonance, with the experimental centroid and width. We assume that the spectroscopic factor of the halo neutron of the 11Be ground state is $\approx 1$ Macchiavelli et al. (2018), and that the initial and final isospins are $T_{i}=3/2$ and $T_{f}=1/2$. This results in a pure Gamow-Teller transition, with $\langle F\rangle=0$ and $g_{A}^{2}\langle GT\rangle^{2}=0.15$. With the values of the overlap $\mathcal{O}$ and the spectroscopic fator $S(^{11}\text{B})$ estimated above, we obtain $t^{p}_{1/2}=1.7\times 10^{6}~{}\text{s}$, and $b_{p}=8.0\times 10^{-6}.$

In summary, we have performed the first direct observation of a $\beta^{-}\text{p}^{+}$ decay. This new result is in agreement with the previous indirect measurement Riisager et al. (2014). The use of the pAT-TPC also allowed for a precise measurement of the emitted proton energy, which in turn clarified that the decay proceeds sequentially though a narrow resonance [$E=11425(20)$ keV, $\Gamma=12(5)$ keV, J${}^{\pi}=(1/2,3/2^{+})$] in 11B. This resonance, unobserved yet, also explains why the branching ratio is orders of magnitude larger than previous theoretical models predicted. Calculations including this new result can reproduce the measured branching ratio. In contrast, when a democratic decay is considered, the result is orders of magnitude lower than observed.