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Neutron Halo - Recent Experimental Progress at RIBF
Takashi Nakamura
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DOI: 10.22661/AAPPSBL.2019.29.5.19

Neutron Halo - Recent Experimental Progress at RIBF

TAKASHI NAKAMURA
DEPARTMENT OF PHYSICS, TOKYO INSTITUTE OF TECHNOLOGYA

ABSTRACT

A neutron halo in light neutron-rich nuclei along the neutron drip line has characteristic features due to its low-density neutron distribution extending beyond the normal nuclear size. The advent of the new-generation rare isotope beam facility, RIBF at RIKEN, has allowed neutron-halo nuclei in new regions of the nuclear chart to be explored. For nuclei in the island-of-inversion region (neutron-rich Ne, Na, Mg isotopes with the neutron number N~20) in the nuclear chart, where the conventional magic number N=20 does not persist, breakup reaction experiments on 29,31Ne and 37Mg have shown that these have a new type of halo structure, called a deformation driven p-wave halo. For lighter two-neutron halo nuclei, dineutron correlations corresponding to a spatially-compact neutron pair, have been investigated by quasi-free scattering (scattering of a nucleon inside the nucleus by a relativistic proton) and Coulomb breakup (breakup of a beam particle induced by a pulsed Coulomb field when it passes by a heavy target with relativistic velocity). Recent progress in the experimental research of neutron halo at RIBF is reviewed and discussed.

INTRODUCTION

A neutron halo is extended neutron matter involving one or two valence neutrons surrounding a core with saturated nuclear density, as illustrated for the most traditional halo nucleus 11Li in Fig.1 [1, 2]. In contrast to the common image of an atomic nucleus as being composed of saturated protons and neutrons, a neutron halo has extremely low-density compared to the saturated nuclear density and extends to nearly double the core radius. Before the first operation of RIBF (RI-beam factory) at RIKEN in 2007, the known neutron halo nuclei were limited to 6He, 11Li, 11,14Be,17,19B, and 15,19C. The duality of the core and halo, and the extended neutron distribution lead to the following characteristic reaction properties: 1) large interaction cross section, 2) narrow momentum distribution of the core fragment, and 3) soft E1 excitation (strong electric dipole response at low excitation energies) [3, 4, 5]. Halo nuclei are categorized into 1) two-neutron halo nuclei composed of a core and two halo neutrons, for example, 6He,11Li,14Be,17B, and 2) one-neutron halo nuclei composed of a core and a single-neutron halo, for example, 11Be, and 15,19C. A Halo is formed due primarily to weakly bound neutron(s) with 1n (2n) separation energy Sn (S2n) < ~1 MeV and quantum tunneling. The other important factor is the low angular momentum, l=0 or 1, of the halo neutron such that it is free from the effect of a centrifugal barrier that would hinder tunneling.

 

Fig. 1: Schematic view of the two-neutron halo nucleus 11Li that has a dual structure composed of the 9Li core surrounded by a neutron halo involving two neutrons. The radius of the 11Li halo is close to that of 208Pb.

 

Fig. 2: Halo nuclei, and their candidates are indicated in the nuclear chart. Before the commissioning of RIBF, halo nuclei had been known only up to 19C.

In spite of tremendous experimental and theoretical efforts, it is difficult to predict which nucleus has a halo structure. Indeed, one cannot easily predict the location of halo nuclei in the nuclear chart for heavier nuclei. Even if a halo nucleus is identified, it is still difficult to extract its halo wave function quantitatively. For instance, the interplay between the halo and shell evolution (variation of single-particle levels or shells according to the neutron number and the resultant change of magic numbers) has not been well understood. We need to clarify under what conditions the last neutrons are in an orbital with low angular momentum. Note that some halo nuclei appear where the conventional shell order does not allow a low-l orbital for the valence neutron. We note that shell-gap reduction or shell inversion may happen as in 11Li. Such difficulty can be attributed to the fact that experimentally the neutron drip line has been reached only up to neon isotopes (Z=10, See. Fig.2) [6], and the beam yield of very neutron-rich nuclei near the drip line is very limited [5].

Another interesting question is whether the two neutrons can be more strongly correlated in the halo than in normal nuclei. Migdal has predicted dineutron as two spatially-correlated neutrons that behave like a bound pair and appear on the surface of a nucleus [7]. Recently, theoretical efforts have been devoted to this issue in terms of possible dineutron in low-density nuclear matter, such as neutron halo and neutron skin [8, 9]. However, dineutron has not been directly confirmed except for some hints indicated in 11Li [10]. The question of whether multi-neutron halo beyond 2n halo can exist is not clarified yet.

The new-generation RI-beam facility RIBF at RIKEN has offered new opportunities for a wide range of experiments involving halo nuclei. Here, the recent progress in experimental studies of halo nuclei is reported, based on the experiments carried out mainly at RIBF. New halo nuclei, 22C, 29,31Ne, and 37Mg have been confirmed through the experiments at RIBF. In the following sections, after briefly describing the key spectrometers for the experiments on halo nuclei at RIBF, experiments involving new halo nuclei 22C, 29,31Ne, and 37Mg are described. Then I mention briefly the recent experiments on the quasi-free scattering on light halo nuclei.

ZDS and SAMURAI - Key Spectrometers at RIBF

At RIBF, two key spectrometers for exploring the drip line have been constructed: the ZeroDegree Spectrometer (ZDS) [11] and the Superconducting Analyzer for Multi-particles from RAdio Isotope Beam (SAMURAI) [12, 13, 14, 15]. Schematic layouts of ZDS and SAMURAI are shown in Fig.3 and Fig.4, respectively.

 

Fig. 3: The layout of ZDS is shown, together with the last two stages of the cyclotron accelerators, IRC, SRC, and the in-flight RI beam separator, BigRIPS at RIBF. As an example, the setup used for the inclusive nuclear and Coulomb breakup of 29Ne [16], 31Ne [17, 18], and 37Mg [19] is schematically shown. BigRIPS is used for separation and particle identification (PID) of the RI beam, while ZDS is used for the PID of the projectile-like fragments.

ZDS, which has been in operation since the beginning of RIBF in 2007, is a two-bend achromatic spectrometer to collect and momentum-analyze the charged particles near the projectile velocity at zero degrees. The momentum resolution P/ΔP is ~1000-6000, depending on the mode [11]. One of the main purposes is an unambiguous particle identification of the projectile-like reaction products with high resolution and medium acceptance. For halo nuclei, ZDS offers a powerful spectroscopic tool for investigating reaction cross sections, and 1n-removal reactions, as such a measurement requires primarily particle identification of incoming and outgoing charged particles. In the latter experiment, one can also obtain the momentum distribution of the projectile-like fragments. As an instance, the setup for the 1n removal of 29,31Ne and 37Mg is shown schematically in Fig. 3. In this case, the de-excitation γ-ray was also measured in coincidence by the NaI(Tl) scintillation detector array called DALI2.

 

Fig. 4: The layout of SAMURAI, which consists of a large-gap superconducting dipole magnet, SBT (beam scintillator), BDC (beam MWDC, not shown here), FDC1, FDC2 (MWDCs for charged fragments), HODF (hodoscope for charged fragments), NEBULA (neutron detector array), and DALI2 (γ-ray detector array). As an example, the setup for the Coulomb breakup of 22C is shown.

SAMURAI, commissioned in 2012, is a versatile spectrometer with much wider acceptance. In contrast to ZDS, it has a single superconducting dipole magnet with a large gap. In Fig. 4, the experimental setup for the Coulomb breakup of 22C is shown schematically, where the incoming 22C projectile, the outgoing 20C fragment, and the two neutrons were measured in coincidence. One important aspect of SAMURAI is that it is ideally suited for kinematically complete measurements of the breakup reactions (e.g. Coulomb breakup). Other direct reactions, such as (p,n)-type charge exchange reactions [20] and (p,pn) [21] and (p,2p) quasi-free scattering in inverse kinematics, have also been studied. In this case, one can apply not only invariant mass spectroscopy that measures the momentum vectors for all the outgoing particles but also missing mass spectroscopy that measures the recoil particles from the target. In invariant mass spectroscopy, momenta of all the outgoing particles are measured to reconstruct the invariant mass of the intermediate excited state, while in missing mass spectroscopy coincidence measurements of the momenta of the beam and the recoil particles determine the excitation energy (mass) of the unmeasured residue. Such detailed spectroscopy experiments have become feasible owing to the large momentum and angular acceptance and rather good momentum resolutions (P/ΔP~1000) of SAMURAI [12]. The latter is important in identifying the charged particles. With SAMURAI, one can identify nuclei even in the mass region of 132Sn, as was realized for the measurement of the 132Sn(p,n) reaction [20].

22C - New 2n halo nucleus and possible magic nucleus

22C is the most neutron-rich bound carbon isotope at the neutron drip line, as shown in Fig.2. As the two neutron separation energy is very small (S2n = -0.14(46) MeV) [22], and the conventional shell model predicts the dominance of the 2s1/2 configuration, 22C has been a candidate for the prominent two-neutron halo nucleus. As the next s-wave two-neutron halo with 3s1/2 would be out of reach with the current and near-future RIB facilities, 22C may be the last accessible s-wave 2n halo nucleus, probably for the next ten years. This nucleus is also important in terms of shell evolution as a candidate for the N=16 new magic nucleus as 24O with N=16 is now an established doubly magic nucleus.

The first sign of the halo property of 22C was obtained by Tanaka et al. [23], where the enhanced reaction cross section of 22C with a proton target at 40 MeV/u was observed at RIPS (main RI-beam facility at RIKEN before the completion of RIBF). The rms radius of 22C evaluated there was 5.4(9) fm. This value was then revised to 3.44(8) fm by the high-statistics reaction cross section measurement of 22C on C target at 235 MeV/u at SAMURAI [24]. This rms radius is still significantly larger than 20C, indicating the halo nature of 22C. We should note that this reaction cross section was obtained as a by-product of the breakup experiment shown in Fig. 4, demonstrating the power of the large-acceptance spectrometer, SAMURAI.

At ZDS, the momentum distribution of 20C following the breakup of 22C on a carbon target was measured [25]. There, the narrow momentum distribution (about 73 MeV/c in FWHM) was observed as an indication of the 2n halo nucleus.

Coulomb breakup of 22C was measured at SAMURAI with the setup shown in Fig. 4. Currently, the analysis of this experimental data is in progress, as well as that for the 21C unbound states observed in the 1n removal channel in the reaction with the carbon target. The two-body constituent 21C in the 22C nucleus provides the key to understanding the shell structure of 22C. Note that 22C is a nucleus made of the three-body 20C+n+n, called Borromean, where any of the two-body constituents (20C+n, n+n) are unbound and the three-body system (20C+n+n) is bound. One of the crucial questions is whether the dineutron correlation exists in 22C, and if so, how it appears. The dineutron correlation is considered to be the result of the mixed shell configuration of two neutrons in orbitals with different parities [3, 9]. As the shell configuration of 22C should be very different from that of 11Li, such investigations shed lights on the interplay between the dineutron correlation and the shell structure. We have Coulomb breakup data on 19B as well, which is also under analysis. This may clarify the halo property of 19B, and the possible mixture of s- and d-wave neutrons in this nucleus.

29,31Ne, 37Mg - Deformation driven p-wave halo

The island of inversion is a group of neutron-rich nuclei, which was originally addressed for Z=10-12 (Ne, Na, Mg), and N=20-22 in the nuclear chart [26], as schematically shown in Fig.2. The nuclei in the island are characterized by the loss of N=20 magicity and strong prolate deformation of the ground state. Such a property is attributed to the fact that the energy level of the 2p-2h intruder configuration lies lower than that of the normal configuration. How broad the island is extended in the nuclear chart is one of the key questions. Here I show 29Ne [16], 37Mg [19] are within the island of inversion, in addition to the firm confirmation of that for 31Ne [17, 18]. The interplay between the halo phenomena and the shell evolution is expected to provide new insights in neutron-rich nuclei near the drip line. It is found that the deformation-driven p-wave halo is such a case.

Before the RIBF was commissioned, experiments on 31Ne and 37Mg were almost impossible: Identification of these isotopes [27] was made only with the limited intensity of about five and one counts per day for 31Ne and 37Mg, respectively. RIBF changed this situation drastically, as 48Ca beam at 345 MeV/u with strong intensity over 100 pμA, combined with the wide acceptance in-flight separator BigRIPS, offers intensities with 4-5 orders of magnitude larger. Even the first 31Ne/37Mg experiments at RIBF already provided about five counts per second (cps), and the recent record intensity of 31Ne reached about 50 cps.

 

Fig. 5: (a) One-neutron removal cross sections of Coulomb breakup on Pb for 31Ne decaying to the 30Ne ground state, and (b) that on C. The cross sections are compared with theories for the configuration of a 2p3/2 neutron on the 30Ne ground state with C2S=1, which depends strongly on Sn. The Green area shows the Sn value from the direct mass measurement [22]. Comparison of each theory to the experimental data provides the allowed region in C2S vs. Sn as shown in (c).

As one of the earlier experiments at RIBF, using the setup shown in Fig. 3, inclusive Coulomb and nuclear breakup of 31Ne was investigated at about 230 MeV/u, where 'inclusive' means that the one-neutron removal cross section as well as the γ-ray from the 30Ne core fragment were only measured without neutron coincidence. From this experiment, one can extract the one-neutron removal cross sections for decay directly to the 30Ne ground state, both for C and Pb targets. The Coulomb breakup part of the one-neutron removal cross section on Pb was then deduced. One issue in extracting the structure information was the large uncertainty of the mass (Sn = -0.06±0.39 MeV [22]), since the one-neutron removal cross section in these reactions strongly depends on Sn.

The sensitivity to the halo amplitude is, on the other hand, quite distinctive between the nuclear- and Coulomb breakup, thereby providing a useful spectroscopic tool. Figure 5 compares the one neutron removal cross section for direct decay into 30Ne for Coulomb breakup (a) and that for the breakup by the C target (b), with the theoretical calculations (Coulomb breakup: direct breakup model, Nuclear breakup: eikonal calculation). The theoretical calculations are performed for the unit single-particle cross sections for the configuration of a p-wave valence neutron coupled to the 30Ne ground state, and shown as a function of Sn, demonstrating the different sensitivities. We showed in Ref. [18] that only this configuration can explain the data. As shown in Fig.5(c), this comparison is then used to evaluate the spectroscopic factor for this configuration, and MeV [18]. The value C2S represents the overlap probability between the initial state (31Ne) and the single-particle state (a neutron in 2p3/2) coupled to the core nucleus (30Ne ground state). Currently, the Sn value obtained here is more accurate than the one from the direct mass measurement [22] and is included in the most recent standard mass evaluation, AME2016 [28].

This result shows that the spin-parity of 31Ne is 3/2-, with significant contribution of the valence neutron in 2p3/2 orbital coupled to the 30Ne ground state. Interestingly, such a ground state is out of the scope of the naïve shell model picture of 1f7/2 dominance and 7/2- spin-parity for a N=21 nucleus. This result thus provides clear evidence that 31Ne is in the island of inversion. Furthermore, such small separation energy and the significant p-wave (low-l) valence neutron favor the halo picture. The existence of the halo was independently confirmed by the enhancement of the reaction cross section measured at BigRIPS at RIBF [29].

This picture can be interpreted in terms of the Nilsson model (single-particle levels as a function of the quadrupole deformation parameter (β) calculated for a deformed mean-field potential) for a weakly bound neutron. For the 21st neutron, in the spherical limit (β=0), 1f7/2 and 2p3/2 levels are unbound and degenerate. Then the Jahn-Teller effect, deformation due to degeneracy of two configurations, occurs and the ground state becomes barely bound and strongly deformed. When the neutron separation energy is smaller, the p-wave neutron component is relatively more significant than the f-wave one since halo formation is favored to reduce the kinetic energy [30]. In this respect, the halo is formed due to the deformation with the enhanced p-wave component. Hence, 31Ne provides the first confirmed case of deformation-driven p-wave halo. The large-scale shell model (shell model with large model space) shows large quadrupole transition probabilities (large B(E2) values) for the transition between the low-lying states, supporting the case for large deformation.

 

Fig. 6: Large-scale shell model calculation (SDPF-M) shows the occupancy of 2p-2h (red squares) is largest around N=19-23, and is becoming smaller towards N=28. At 37Mg, this occupation is still significant and thus within the island of inversion. The figure is adopted from Ref. [19].

Using the same technique of combining inclusive Coulomb and nuclear breakup, we could find that the ground states of 37Mg and 29Ne are of negative parity, having the dominant configuration of 2p3/2, with strong deformation [16, 19]. Accordingly, we confirmed that 29Ne and 37Mg are also deformed-driven p-wave halo nuclei. Large rms radii for 29Ne and 37Mg indicated by the reaction cross section measurements confirmed their halo structure [29, 31]. 37Mg represents currently the heaviest neutron halo nucleus confirmed. Figure 6 illustrates the occupations of normal 0p-0h (black dots) and intruder 2p-2h (red squares) configurations according to the neutron number for magnesium isotopes. A similar study is shown for 29Ne in Ref.[16]. These studies show that 29Ne is at the lower-mass edge of the island of inversion, and 37Mg is near the higher-mass edge of the island. Recently, systematic studies of in-beam γ-ray spectroscopy observed the first 2+ and 4+ energies for the neutron-rich Mg isotopes [32, 33], and found that the deformation persists up to 40Mg. This picture somewhat contradicts the calculation that the 2p-2h dominance is diminished towards 40Mg in Fig.6. So not only the 2p-2h mechanism for N=20 but another mechanism such as the melting of the N=28 shell gap may play a role for the persistence of this strong deformation for a wider range of neutron-rich nuclei. Caurier, Nowacki, and Poves called this big island of deformation [34]. Note that even for 31Ne and 37Mg, the degeneracy of 2p3/2 and 1f7/2 (loss of N=28 gap) was observed, which indeed provided an important factor for p-wave halo formation.

Dineutron in Halo Nuclei?

Dineutron, as a spatially correlated pair, has not been directly observed so far. At RIBF, two approaches are in progress to search for dineutron. One method is Coulomb breakup of two-neutron halo nuclei, where the extracted low-lying E1 (electric dipole) strength as soft E1 excitation can be related to the geometrical two-neutron correlation as applied to 11Li [10]. At SAMURAI, the Coulomb breakup experiments were performed for 19B, 22C, and the analysis is in progress.

 

Fig. 7: Schematic concept of the quasi-free scattering of 11Li(p,pn) is shown in the rest frame of 11Li. The initial knockout process is used to determine the momentum of the first neutron inside 11Li, while the momentum of the second neutron determines the residual core-n state.

The other approach is quasi-free (p,pn) scattering on two-neutron halo nuclei in inverse kinematics. Figure 7 shows a schematic concept of this method applied for 11Li. The initial scattering of the proton with a neutron in the halo probes the momentum content of this neutron in the rest frame of the nucleus. Combined with the information of the second neutron relative to the 9Li core, one can obtain the opening angle between the two neutrons. Accordingly, one can study the nn correlation as a function of the 10Li state or the momentum of the neutron, which can provide a measure of how close to the surface the valence neutron is located. This method is based on theoretical considerations by Kikuchi [35]. At SAMURAI at RIBF, this method was applied to 11Li, 14Be, and 17B [21, 36]. The preliminary analysis showed already some hint of dineutron in the surface of 11Li [36].

It is noted that this method is also useful to observe the energy of the core-n system, which is crucial in understanding the three-body Borromean system of the two-neutron halo nuclei. Recently, using the 14Be(p,pn) reaction in inverse kinematics, Corsi et al. clarified the shell structure of the unbound 13Be nucleus, which had long been controversial [21].

Conclusions and Perspective

The key spectrometers, SAMURAI and ZDS, at RIBF have played significant roles in expanding the territory of halo nuclei in the neutron drip-line region of the nuclear chart. In this facility, the neutron halo structure was newly confirmed for 22C, 29Ne, 31Ne, and 37Mg. In particular, we note that the interplay between halo formation and shell evolution was found important in the neutron-drip line region of the island of inversion, as shown for 29,31Ne and 37Mg, where a deformation-driven p-wave halo is formed. Recently, the exclusive measurements of Coulomb and nuclear breakup of 31Ne were made at SAMURAI, whose analysis is in progress. Here 'exclusive' means that both 30Ne and the neutron from 31Ne are measured in coincidence to reconstruct the 31Ne excitation energy (invariant mass method). With this, one can extract the E1 strength as a function of the excitation energies, which would further pin-down the structure of 31Ne. Such information is important to assess quantitatively the deformation and the shell property of deformation-driven p-wave halo nuclei. The quest for heavy halo nuclei and dineutron continues. At SAMURAI, we plan to build new types of neutron detector, one for the high-resolution high-granularity, HIME, and the other is NEBULA-PLUS to enhance the neutron detection efficiency in particular for multiple neutrons. With that, we expect to explore further heavier and more neutron-rich nuclei.

On the other hand, simpler experiments such as measurements of reaction cross sections and inclusive Coulomb and nuclear breakup are also important to obtain the first clue about a halo. Such experiments are useful in particular for very neutron-rich nuclei where the beam intensities are extremely weak (< one particle per second).

The possibility of neutron halo and its relation to the shell evolution in 27,29,31F, 34Ne, 34,37Na 40Mg will be interesting topics in the coming years as these are candidates for the next halo nuclei (see Fig.2). We should note that the observation of halo states in nuclei such as 31Ne and 37Mg, where the naive shell model picture does not allow the valence neutron to have low angular momentum, implies that halo nuclei may tend to appear all along the neutron drip line.

Recently, at TRIUMF in CANADA, low-energy RI beams were used to observe the low-lying resonance of 11Li by inelastic scattering [37]. As soft E1 excitation in most halo nuclei showed a structure-less continuum [3, 4, 10], it would be interesting to understand the characteristic features of such low-lying resonances.

The quest for nuclei beyond the neutron drip line is continuing. Recently, we have observed the weakly unbound nucleus 26O [38], as well as heavy boron isotopes, 20,21B [39], beyond the neutron drip line. These unbound resonances can be candidates for dineutron structure.

Combined with the intense RI-beams, with unique spectrometers such as SAMURAI and ZDS, and expecting new detectors such as HIME and NEBULA-PLUS, one would explore nuclei along the neutron drip line, thereby clarifying the halo properties, related exotic phenomena, and underlying many-body mechanism in the near future. This is also important for understanding the underlying mechanism of nucleo-synthesis in the universe such as the r-process, and the structure of neutron stars.

Acknowledgement: I would like to thank the accelerator staff at RIBF and the BigRIPS team for their excellent development and operation of the beams to realize the great success of experiments mentioned here. I also thank all the collaborators of the experiments using ZDS and SAMURAI. The present work was supported in part by JSPS KAKENHI Grant No. 22340053, No. 16H02179, and by MEXT KAKENHI Grants No. 24105005 and No. 18H05404. I thank Y. Kubota for providing figure (Fig.7).

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Takashi Nakamura is Professor at the Department of Physics, School of Science, Tokyo Institute of Technology. He received D.Sci from the University of Tokyo in 1996. He worked at RIKEN, University of Tokyo, and Michigan State University before becoming an Associate Professor at Tokyo Institute of Technology in 2000. Since 2007, he has been is his current position. His research field is experimental nuclear physics.

 
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