First observation of 20B and 21B

TL;DR

This paper reports the first observation of the neutron-rich isotopes 20B and 21B, identifying their resonant states and decay modes, and confirming their masses align with recent atomic-mass extrapolations.

Contribution

First experimental observation of 20B and 21B isotopes, including their resonance states and decay channels, expanding knowledge of neutron-rich boron isotopes.

Findings

Observed 20B and 21B as resonances.

Identified decay channels involving neutrons.

Masses agree with atomic-mass extrapolations.

Abstract

The most neutron-rich boron isotopes 20B and 21B have been observed for the first time following proton removal from 22N and 22C at energies around 230 MeV/nucleon. Both nuclei were found to exist as resonances which were detected through their decay into 19B and one or two neutrons. Two-proton removal from 22N populated a prominent resonance-like structure in 20B at around 2.5 MeV above the one-neutron decay threshold, which is interpreted as arising from the closely spaced 1-,2- ground-state doublet predicted by the shell model. In the case of proton removal from 22C, the 19B plus one- and two-neutron channels were consistent with the population of a resonance in 21B 2.47+-0.19 MeV above the two-neutron decay threshold, which is found to exhibit direct two-neutron decay. The ground-state mass excesses determined for 20,21B are found to be in agreement with mass surface extrapolations derived within the latest atomic-mass evaluations.

Tables

Table 1. Table 1: SM predictions for the spectroscopic factors for the decay of 20 B levels (Fig.  4 ) to the 19 B ground state.

$E$ (MeV)	$J^{\pi }$	${\ell }_n$	$C^{2}S$
3.13	$2_1^{-}$	0	0.21
		2	0.16
3.19	$1_1^{-}$	0	0.09
		2	0.52
3.55	$4_1^{-}$	2	0.30
3.93	$1_2^{-}$	0	0.07
		2	0.17
4.93	$2_2^{-}$	2	0.05
5.88	$3_1^{-}$	2	0.10
5.96	$0_1^{-}$	2	0.43
6.46	$3_2^{-}$	2	0.70

Table 2. Table 2: Experimental mass excesses (MeV) of the heaviest boron isotopes (present work and Ref.  Gaud12 ) compared to the most recent atomic-mass evaluations AME16 ; AME12 .

Isotope	AME12 AME12	AME16 AME16	Experiment
19B	58.78$\pm$0.40	59.77$\pm$0.53	59.77$\pm$0.35
20B	67.13$\pm$0.70	68.45$\pm$0.80	69.40$\pm$0.38
21B	75.72$\pm$0.90	77.33$\pm$0.90	78.38$\pm$0.40

Full text

Introduction.— The advent of dedicated radioactive-beam facilities has provided for a rather complete mapping of the nuclear landscape up to mass number $\sim 30$ Nakamura . As such it is now well established that the text-book shell structure of the nucleus, that translates into an enhanced stability for systems with “magic” numbers of protons ($Z$) and/or neutrons ($N$) of 2, 8, 20… is modified as the limits of particle stability, or driplines, are approached (see, for example, Ref. Dripline ). Significantly, these changes in shell structure, which have been attributed to a number of different mechanisms, including most recently and intriguingly the effects of three-body forces Otsuka10 , influence the location of the dripline itself.

In the naive shell-model picture, neutron numbers between 8 and 20 correspond to the filling of the $sd$-shell neutron single-particle orbitals ($\nu 0d_{5/2}$, $\nu 1s_{1/2}$, $\nu 0d_{3/2}$). Approaching the neutron dripline, the energies of these orbitals evolve, leading for example to the disappearance of the $N=20$ magic number for $Z=10$–12 (the so-called “Island of Inversion” IoI ) and to the appearance of new shell closures at $N=14$ and 16 in the oxygen isotopes Stan04 ; Hoffman ; BAB-WAR . In this respect, the most neutron-rich boron isotopes, which lie below doubly-magic 22,24O and straddle the neutron dripline, are of considerable interest (Fig. 1, inset) and, significantly, are now coming within the range of sophisticated ab initio models abnit and approaches that treat explicitly the continuum GSM . More generally, the boron isotopic chain exhibits a number of exotic structures: from the proton halo of 8B Boron8 , through the unbound threshold states of 16,18B JL ; Spyrou10 , to the two-neutron halo of 17B and the two/four neutron halo/skin of 19B Suzuki99 .

This Letter reports on the first observation of the neutron-unbound nuclei 20B and 21B Ozawa2003 , populated through high-energy proton removal and reconstructed using invariant-mass spectroscopy. These measurements, at the limits of present capabilities, provide for the first experimental mass determinations for both isotopes. In addition, evidence is presented showing that 21B decays by direct two-neutron emission. Finally, a comparison with the predictions of shell-model calculations is discussed and provisional spin-parity assignments provided for the levels observed.

Experiment.— The experiment was performed at the Radioactive Isotope Beam Factory (RIBF) of the RIKEN Nishina Center, as part of an experimental campaign investigating the structure of light neutron-rich nuclei beyond the dripline (see, for example, Refs. Kondo16 ; Togano16 ). Secondary beams of 22N and 22C were produced by fragmentation of a 345 MeV/nucleon 48Ca primary beam incident on a 20 mm thick beryllium target, and were separated using the BigRIPS fragment separator Kubo03 . The different isotopes present in the secondary beams were identified via the measurement of their energy loss, time of flight and magnetic rigidity, and transported to the object point of the SAMURAI spectrometer Koba13 , where a 1.8 g/cm2 carbon reaction target was located. The beam particles were tracked onto the target using two drift chambers. The energies at target mid-point and average intensities of the 22N and 22C beams were, respectively, 225 and 233 MeV/nucleon, and 6600 and 6 pps.

The beam-velocity reaction products were detected in the forward direction using the SAMURAI setup including the NEBULA neutron array Kondo15 , placed some 11 m downstream of the target. The SAMURAI superconducting dipole magnet Sato-SAMURAI , with a central field of 3 T, provided for the momentum analysis of the charged fragments. The dipole gap was kept under vacuum using a chamber equipped with thin exit windows Shimizu so as to reduce to a minimum the amount of material encountered by both the fragments and neutrons. Drift chambers at the entrance and exit of the magnet allowed the determination of their trajectories and magnetic rigidity Koba13 . This information, combined with the energy loss and time of flight measured using a 16-element plastic hodoscope, provided for the identification of the projectile-like fragments. The neutron momenta were derived from the time of flight, with respect to a thin plastic start detector positioned just upstream of the target, and the hit position measured with the 120 plastic scintillator modules (12$\times$12$\times$180 cm3) of the NEBULA array.

Results.— The relative energy ($E_{\rm{rel}}$) of the unbound boron isotopes was reconstructed from the momenta of the 19B fragment and neutron(s) as the invariant mass of the 19B+$xn$ system minus the masses of the constituents. It should be noted that 19B, owing to its extremely weakly-bound character (two-neutron separation energy of $0.14\pm 0.39$ MeV Gaud12 ), has no bound excited states and thus $E_{\rm{rel}}$ reflects directly the energy above the decay threshold. The spectra reconstructed using 19B+$n$ events from reactions induced by the 22N and 22C beams are shown in Fig. 1, and exhibit significant differences. In particular, while two-proton removal from 22N populates a clear resonance-like structure around 2–3 MeV, proton removal from 22C leads to a very broad distribution confined to energies below $\sim 2.5$ MeV.

None of these features can be attributed to the response function of the setup, as it varies smoothly with $E_{\rm{rel}}$ (see, for example, Fig. 1 of Ref. Kondo16 ). In order to deduce the character of any resonances in 20,21B, the spectra were described using single-level R-matrix line-shapes BW which were used as the input for a complete simulation of the setup (including the secondary-beam characteristics, the reaction, and the detector resolutions and acceptances) together with a non-resonant component. The resolution (fwhm) in the reconstructed $E_{\rm{rel}}$ was dominated by the NEBULA hit position determination and timing resolution, and varied as $\sim 0.4\sqrt{E_{\rm{rel}}}$ MeV.

The shape of the non-resonant continuum was deduced for each reaction channel by mixing the measured 19B-$n$ pairs following the procedure described in Ref. MIX . Importantly, the uncorrelated distribution so obtained does not require any a priori parameterizations and incorporates explicitly the effects of the experimental response function. As such, it may be compared directly with the measured distribution in order to identify features arising from the decay of unbound states Giacomo . As may be seen in Figs. 2 and 3, the non-resonant distributions for the 19B+$n$ events from the 22N and 22C beams clearly cannot account for the prominent structures in either case.

Turning first to the results for two-proton removal from 22N, the inset of Fig. 2 displays the correlation function obtained as the ratio of the data and the uncorrelated non-resonant distribution MIX . Importantly, in addition to displaying more clearly the presence of a peak at about 5 MeV, the region below 1 MeV shows no resonant signal. In terms of resonances in 20B, only decays to the 19B ground state by $\ell=2$ neutron emission are expected to be observable 111Decay by $\ell=0$ neutron emission for all but threshold states will result in extremely broad structures.. In particular, the single-particle width for a $d$-wave resonance at 2.5 MeV is, assuming a standard Woods-Saxon potential, $\sim 1.3$ MeV. A fit in terms of a single prominent resonance at about 2.5 MeV and a weaker high-lying one (plus the non-resonant continuum) provides for a good description of the spectrum, with the energy and width of the former $E_{r}=2.44\pm 0.09$ MeV and $\Gamma=1.2\pm 0.4$ MeV Supp-url . Such a width suggests that the spectroscopic factor for the decay to the 19B ground state is large. Simple considerations, however, suggest that the lowest-lying levels of 20B will be a $1^{-},2^{-}$ doublet arising from the coupling of a $0p_{3/2}$ proton with a $1s_{1/2}$ neutron, and that the strong peak observed here may well result from the population of both states. This point, and the related fit shown in Fig. 2, is addressed in the discussion below in the light of shell-model calculations.

In the case of single-proton removal from 22C (Fig. 3), the 19B+$n$ channel does not exhibit any clear peaks arising from resonances in 20B, but rather a “plateau-like” distribution, modulated by the experimental response function, reminiscent of the direct phase-space decay of a three-body resonance Supp-url , in this case 21B. Despite the reduced two-neutron detection efficiency, the relative energy spectrum of 19B+$2n$ events, after applying cross-talk rejection conditions crosstalk , could be reconstructed as shown in the inset of Fig. 3. It displays clearly resonance-like strength in the region around 2.5 MeV. Using a simple Breit-Wigner line-shape with an energy-dependent width, the best fit was for a 21B resonance at $E_{r}=2.4\pm 0.4$ MeV with $\Gamma<3$ MeV. While the very limited statistics precluded the construction of the event-mixed three-body non-resonant continuum, the influence of such a distribution is expected to be less than the quoted uncertainties.

Having established that the reactions induced by the 22C beam populate a resonance-like structure in 21B, a more precise energy and width may be derived from the higher statistics two-body (19B+$n$) data set, as was the case in the study of 26O Kondo16 ; GSI-26O . The 19B+$n$ spectrum was fitted with a combination of the uncorrelated distribution derived from event mixing and simulated events arising from the decay of a resonance in 21B. The latter was assumed to occur by three-body phase space into 19B+$n$+$n$, and $E_{\rm{rel}}$ was reconstructed between the fragment and the neutron with the shortest time of flight (the procedure employed in the treatment of the data). The energy and width of the 21B resonance are sensitive to the location and slope, respectively, of the higher-energy edge of the 19B+$n$ distribution Supp-url .

The best fit, shown in Fig. 3, is for a resonance in 21B with $E_{r}=2.47\pm 0.19$ MeV and $\Gamma<0.6$ MeV. The errors include a systematic uncertainty derived from other direct-decay modes, in which the $n$-$n$ interaction modifies the three-body phase space Supp-url following the formalism of Ref. Dalitz . Given the very good description of the 19B+$n$ events from the 22C beam, any contribution from sequential decay through (and/or direct population of) 20B must be small ($\sim 10$%) Supp-url . This is consistent with the resonances found here in 20B being at similar energy or higher than in 21B, providing little or no opportunity for sequential decay to occur. As such, 21B may be considered a new case of direct two-neutron decay.

Discussion.— In the following the present results are discussed in the light of shell-model calculations (SM), that were undertaken SM in the full $psd$ model space (that is, comprising the $0p_{3/2}$, $0p_{1/2}$, $0d_{5/2}$, $1s_{1/2}$ and $0d_{3/2}$ single-particle orbits) for protons and neutrons using the monopole-based universal interaction YSOX Yuan12 , which successfully reproduces the location of the neutron dripline for carbon and oxygen. The spurious center-of-mass contributions were removed using the Lawson prescription. Configurations corresponding to up to five particle-hole excitations ($5\hbar\omega$) were included in the many-body space, but only small differences in the energies were observed with the $3\hbar\omega$ approximation used to design the interaction.

As alluded to above, the low-lying spectrum of 20B ($N=15$) should exhibit a series of states arising from the coupling of the odd valence neutron with a proton hole in the $0p_{3/2}$ orbit. While the calculation of two-proton removal reaction cross-sections is complex and beyond the scope of this work, the observation that single-proton removal from 22N (which exhibits a strong $1s_{1/2}$ valence neutron configuration) populates almost exclusively the $1/2^{+}$ ground state of 21C Sylvain suggests that removal of a second proton should favor population of a $1^{-},2^{-}$ doublet, one member of which would be expected to be the 20B ground state. Indeed, as seen in Fig. 4, the SM predicts these to be the lowest-lying levels with a very small separation. In addition, both states are predicted to exhibit $d$-wave neutron decay branches (Table 1), and the corresponding decay widths will thus be much less than the single-particle value of $\sim$1.3 MeV noted earlier.

In the light of these considerations, the 19B+$n$ relative energy spectrum was fitted assuming the structure at around 2.5 MeV to be composed of two closely spaced narrower $d$-wave resonances. As shown in Fig. 2, the inclusion of such a doublet, in addition to the high-lying resonance and the non-resonant continuum, allows the spectrum to be very well reproduced 222Statistically, the improvement in the goodness of the fit compared to assuming a single resonance Supp-url is not significant, from $\chi^{2}/{\rm{ndf}}=0.45$ to 0.33.. The best fit parameters for the three resonances were: $E_{r}=1.56\pm 0.15$, $2.50\pm 0.09$, and $4.86\pm 0.25$ MeV; and $\Gamma<0.5$, $0.9\pm 0.3$, and $<0.5$ MeV. A comparison with the shell-model calculations is shown in Fig. 4, whereby the energy with respect to the first particle-emission threshold is plotted. Given that the total binding energies are $\sim 60$ MeV, the energies of the predicted ground states and lowest-lying levels observed here are in reasonable accord.

In terms of excited states of 20B, taking into account the underbinding of the SM calculations ($\sim 1.5$ MeV), one may speculate that the weaker peak observed at 4.86 MeV ($E_{x}=3.30\pm 0.29$ MeV) could correspond to the $0_{1}^{-}$ and/or $3_{2}^{-}$ levels (Fig. 4), which are predicted to exhibit significant spectroscopic strength for neutron decay to 19B ground state (Table 1). It is interesting to note that the very weakly-bound character of 19B means that all the 20B levels observed here are energetically permitted to decay via $3n$ emission to 17B.

Turning to 21B ($N=16$), the SM predicts a $3/2^{-}$ ground state formed by the $0p_{3/2}$ proton hole and expected to be the only state populated with any observable strength following proton removal from 22C. Preliminary estimates made using the Gamow Shell Model GSM suggest a 21B ground state (unbound by about 1.7 MeV) with a width of $\Gamma\sim 130$ keV Nicolas , consistent with our upper limit of 600 keV.

In terms of the $N=16$ shell closure, the SM predicts a rather high-lying first excited state ($1/2^{-}$) in 21B, although with an excitation energy $E_{x}=3.6$ MeV lower than found experimentally in 24O (4.7 MeV Hoffman ; Tshoo12 ) and 23N (4.1 MeV 333The observation of Ref. Jones17 combined with the most recent evaluation of the single-neutron separation energy, $S_{n}=3.12\pm 0.47$ MeV AME16 .), and than predicted by these calculations in 22C (5.0 MeV). Given that the SM predicts the first excited state of 21B to have a strength some ten times less than the ground state in proton removal from 22C, its non-observation here is not surprising.

Assuming that the lowest-lying levels observed here correspond to the ground states of 20,21B, the resonance energies, in combination with the 19B binding energy Gaud12 , may be used to determine the one- and two-neutron separation energies. These are plotted in Fig. 4, whereby the experimental results are compared with those derived from mass-surface extrapolations AME16 ; AME12 . The corresponding mass excesses are tabulated in Table 2. As can be seen, the mass-surface extrapolations from the 2012 mass evaluation overbind 19,20,21B by $\sim 1$–3 MeV. However, the more recent 2016 evaluation, which benefits from the 19B, 22C and 23N mass measurements Gaud12 , provides estimates for the mass excesses of 20,21B that are compatible with the present work. In this spirit, the present 20,21B masses will permit mass-surface extrapolations in this region to be made with improved precision and further from stability.

Conclusions.— In summary, using high-energy proton removal coupled with invariant-mass spectroscopy, the most neutron-rich boron isotopes to date have been observed for the first time. In the case of 20B a prominent resonance-like structure was observed at about 2.5 MeV above the one-neutron decay threshold that, guided by theoretical considerations, has been identified as the $1^{-},2^{-}$ ground-state doublet, with energies $E_{r}=1.56\pm 0.15$ and $2.50\pm 0.09$ MeV. A weaker higher-lying peak was also observed at $4.86\pm 0.25$ MeV ($E_{x}=3.30\pm 0.29$ MeV). The data acquired for 21B were consistent with the population of a resonance $2.47\pm 0.19$ MeV above the two-neutron emission threshold, assigned to be the expected $3/2^{-}$ ground state. These results allowed the first determinations to be made of the ground-state masses of 20,21B, which are in agreement with the extrapolations of the most recent atomic-mass evaluations. In addition, 21B was found to exhibit direct two-neutron decay.

The identification and first spectroscopy of 20,21B presented here opens the way to the exploration of structure and correlations beyond the dripline below 24O. In particular, improvements in secondary-beam intensities and neutron detection should permit $n$-$n$ correlations in the decay of 21B to be investigated Dalitz ; 16Be ; Comment-16Be and its first excited state to be located. This, coupled with work underway to investigate the excited states of 22C, including the all important $2_{1}^{+}$ level Jones17 ; N=16 ; CC-C22 , will provide direct insights into the $N=16$ shell closure beyond the neutron dripline as well as stringent tests of a new generation of ab initio and related theoretical models, including those incorporating explicitly the continuum.

Acknowledgment.— We wish to extend our thanks to the accelerator staff of the RIKEN Nishina Center for their efforts in delivering the intense 48Ca beam, and to C. Yuan for the matrix elements of the YSOX interaction. N.L.A., F.D., J.G., F.M.M. and N.A.O. acknowledge partial support from the Franco-Japanese LIA-International Associated Laboratory for Nuclear Structure Problems as well as the French ANR-14-CE33-0022-02 EXPAND. A.N. and J.G. would like to acknowledge the JSPS Invitation fellowship program for long-term research in Japan at the Tokyo Institute of Technology and RIKEN, respectively. S.L. acknowledges the support provided by the short-term research International Associate Program of RIKEN, as well as the Tokyo Institute of Technology for the Foreign Graduate Student Invitation Program. This work was also supported in part by JSPS KAKENHI Grant No. 24740154 and 16H02179, MEXT KAKENHI Grant No. 24105005 and 18H05404, the WCU (R32-2008-000-10155-0), the GPF (NRF-2011-0006492) programs of the NRF Korea, the HIC for FAIR, the CUSTIPEN (China-US Theory Institute for Physics with Exotic Nuclei) funded by the US Department of Energy, Office of Science under grant number DE-SC0009971, and the Office of Nuclear Physics under Awards No. DE-SC0013365 (MSU) and No. DE-SC0018083 (NUCLEI SciDAC-4 Collaboration).