The $^{8}$He and $^{10}$He spectra studied in the $(t$,$p)$ reaction

The low-lying spectra of $^8$He and $^{10}$He nuclei were studied in the $^3$H($^6$He,$p$)$^8$He and $^3$H($^8$He,$p$)$^{10}$He transfer reactions. The $0^+$ ground state (g.s.) of $^8$He and excited states, $2^+$ at $3.6-3.9$ MeV and $(1^+)$ at $5.3-5.5$ MeV, were populated with cross sections of 200, 100-250, and 90-125 $\mu$b/sr, respectively. Some evidence for $^8$He state at about 7.5 MeV is obtained. We discuss a possible nature of the near-threshold anomaly above 2.14 MeV in $^8$He and relate it to the population of a $1^-$ continuum (soft dipole excitation) with peak value at about 3 MeV. The lowest energy group of events in the $^{10}$He spectrum was observed at $\sim 3$ MeV with a cross section of $\sim 140$ $\mu$b/sr. We argue that this result is possibly consistent with the previously reported observation of $^{10}$He, in that case providing a new g.s. position for $^{10}$He at about 3 MeV.


Introduction
To study drip-line nuclei with large neutron excess one should either transfer neutrons or remove protons or make multi-nucleon charge-exchange. Twoneutron transfer from tritium provides here important opportunities connected with the simplicity of reaction mechanism and simplicity of recoil particle (proton) registration. This class of reactions remains practically not exploited in the radioactive beam research. Availability of the unique cryogenic tritium target [1] in the Flerov Laboratory of Nuclear Reactions (JINR, Dubna) makes possible systematic studies of these reactions. The effectiveness of such an approach in the investigation of exotic nuclei was demonstrated in the recent studies of the 5 H system [2,3].
Although 10 He has been discovered more than a decade ago [4], very limited information on this system is available. The ground state properties were found in the 2 H( 11 Li, 10 He)X reaction as E10 He = 1.2(3), Γ < 1.2 MeV [4], and in the 10 Be( 14 C, 14 O) 10 He reaction as E10 He = 1.07 (7), Γ = 0.3(2) MeV [5]. Here and below EA He denotes the energy relative to the lowest breakup threshold for the A = {6, 8, 10} systems, while E denotes the excitation energy.
The 10 He g.s. was theoretically predicted [6] to be a narrow three-body 8 He+n+n resonance with E10 He ∼ 0.7 − 0.9 MeV, Γ ∼ 0.1 − 0.3 MeV and the valence neutrons populating mainly the [p 1/2 ] 2 configuration. A widely discussed shell inversion phenomenon in the N = 7 nuclei became the source of new interest to 10 He. Possible existence of a virtual state in 9 He was demonstrated in Ref. [7] and an upper limit a < −10 fm was established for the scattering length. Following this finding, the existence of a narrow near-threshold 0 + state in 10 He (E10 He = 0.05, Γ = 0.21 MeV) with a structure [s 1/2 ] 2 was predicted in Ref. [8] in addition to the [p 1/2 ] 2 0 + state. It was suggested in [8] that the ground state of 10 He had not been observed so far and the resonance at ∼ 1.2 MeV is actually the first excited state. The low-lying spectrum of 9 He was revised in the recent experiment [9] resulting in a higher, than in the previous studies, position of the p 1/2 state (experiment [9] provided unique spin-parity identification for the 9 He states below 5 MeV). The presence of the s 1/2 contribution is evident in the data [9], but the exact nature of this contribution (virtual state or nonresonant s-wave continuum) was not clarified and only a lower limit a > −20 fm was set in this work. This work triggered further theoretical research: problems with the interpretation of the 10 He spectrum and controversy between the 9 He and 10 He data were demonstrated in Ref. [10].
This intriguing situation inspired us to revisit the 10 He issue. The study of the 3 H( 8 He,p) 10 He reaction was accompanied by the study of the 3 H( 6 He,p) 8 He reaction providing a reference case of the relatively well investigated 8 He system.

Experimental setup
Experiments were performed using a 34 MeV/amu primary beam of 11 B delivered by the JINR U-400M cyclotron. The secondary beams of 6 He and 8 He nuclei were produced by the separator ACCULINNA [11] and focused in a 20 mm spot on the target cell. For safety reasons, the main target cell, filled with 900 mPa tritium gas and cooled down to 28 K, was inserted into an evacuated protective box. Thus, the target had twin entrance and exit windows sealed with 12.7 µm stainless steel foils. For 4 mm distance between the inner entrance and exit windows the thickness of the tritium target was 2.0 × 10 20 cm −2 . Typical beam intensities incident on the target were ∼ 4 × 10 4 s −1 for the 6 He and ∼ 6 × 10 3 s −1 for the 8 He projectile nuclei. The admixtures of other particles in the beams were no more than 7% and the beam diagnostics completely eliminated them.
Experimental setup and kinematical diagram for the 3 H( 6 He,p) 8 He and 3 H( 8 He,p) 10 He reactions are shown in Fig. 1. For the small centre-of-mass system (cms) angles, where the maximal cross section is expected, the protons fly in backward direction in the lab system. The residuals ( 10 He and 8 He) and their decay products ( 8 He and 6 He) are moving in a relatively narrow angular cone in forward direction. Protons escaping back from the target hit a telescope consisting of one 300 µm and one 1 mm thick annular Si detectors. The active areas of these detectors had the outer and inner diameters of 82 mm and 32 mm, respectively. The proton telescope was installed 100 mm upstream of the target and covered an angular range of 171 • − 159 • in lab system. The first detector was segmented in 16 rings on one side and 16 sectors on the other side and the second, 1 mm detector was not segmented. A veto detector was installed upstream of the proton telescope to alert to the signals generated by the beam halo.
Zero angle telescope for the 6 He and 8 He detection was installed on the beam axis at a distance of 36.5 cm in the case of the 6 He beam and at 28.8 cm in the experiment with the 8 He beam. The telescope included six squared (60 × 60 mm) 1 mm thick detectors. The first two detectors of the telescope were segmented in 16 strips each in vertical and horizontal directions. All other detectors in the telescope were segmented in 4 strips in the 8 He run and in 16 strips in the 6 He run.
A set of beam detectors was installed upstream of the veto detector (not shown in Fig. 1). Two 0.5 mm plastic scintillators placed on a 8 m base provided the particle identification and projectile energy measurement. The overall time resolution was 0.5 ns. Beam tracking, giving a 1.5 mm resolution for the target hit position, was made by two multiwire chambers installed 26 and 80 cm upstream of the target.
Particle identification in the proton telescope was not imperative because, due to kinematical constraints, nothing but protons could be emitted in the backward direction in these reactions. The main background source were protons originating from the interactions of beam nuclei with the target windows. Test irradiations done with empty target showed that this background was almost completely eliminated when p-8 He or/and p-6 He coincidences were considered. In the case of the 3 H( 6 He,p) 8 He reaction the detection of the p-8 He coincidence events granted a selection for the reaction channel populating the 8 He g.s. For the decays of 10 He and excited 8 He nuclei the respective p-8 He and p-6 He coincidence information was used to clean the missing mass spectra and reconstruct the charged fragment energy in the cms of 10 He or 8 He.
Array of 48 detector modules of the neutron time-of-flight spectrometer DE-MON [12] was installed in the forward direction at a distance of 3.1 m from the target. In more rare events where triple p-6 He-n coincidences were detected the complete reaction kinematics was reconstructed.  Missing mass spectra of 8 He from the 3 H( 6 He,p) 8 He reaction are presented in Fig. 2. The peak corresponding to the 8 He g.s. is well seen in the p-8 He coincidence data. The tail visible in Fig. 2 (a) on the right side of the g.s. peak was caused by the pile-ups in the second (non-segmented) detector. Protons emitted from the target with energy ∼ 8.5 MeV correspond to the g.s. peak of 8 He. They passed through the 300 µm Si detector and were stopped in the second (1 mm) detector of the proton telescope. The background signals arose here from the beam halo particles [count rate of (2 − 3) × 10 3 s −1 ]. The veto detector allowed taking away these events in the data analysis but the energy resolution of the second detector was deteriorated. Operation conditions were much better for the segmented 300 µm detector. The count rate per any of its sectors was at least 10 times lower. Consequently, the background signals did not cause the resolution deterioration when the p-6 He coincidences were detected. In that case protons with energy < 7.5 MeV were emitted from the target and practically all of them were stopped in the 300 µm detector. Therefore, for the 8 He excited states the stated 450 keV resolution is valid.
There are two peaks apparent in the 8 He excitation spectrum. We assign 2 + to the 8 He resonance at excitation energy E ≈ 3.6 MeV. The 2 + resonance with energy 3.57±0.12 MeV and width Γ=0.5±0.35 MeV was for the first time unambiguously, and with that good precision, obtained in Ref. [13]. Later on, this resonance was reported in a number of papers with energies close to 3.6 MeV and widths Γ ≈ 0.5 − 0.8 MeV (see, e.g., [14,15,and Refs. therein]). We assume that the E ≈ 5.4 MeV peak seen in Fig. 2 is the 1 + resonance of 8 He. The ground for this assumption comes from various theoretical results (e.g. [16,17,18]) stably predicting that in the 8 He excitation spectrum the next state after the 2 + should be the 1 + state. We note that evidence for the peak at E ∼ 5 − 6 MeV was found in Ref. [13]. The 8 He excited state at 5.4 MeV was recently reported also in Ref. [15]. A rapid rise of the 8 He spectrum at the 6 He+n+n decay threshold is seen in Fig. 2. This rise cannot be explained by the left "wing" of the 2 + resonance. The peculiar threshold behaviour is discussed in Section 6. We note also that the spectra in Fig. 2 show some evidence for a 8 He state at E≈7.5 MeV.
In the 3 H( 6 He,p) 8 He reaction the population cross section for the 8 He g.s., averaged in a range of 4 • − 10 • of the reaction cms, is found to be ∼ 200 µb/sr. The observed threshold anomaly makes the cross section derivation for the excited states of 8 He more complicated (and model dependent). The cross sections for the excited states are further discussed in Sections 5 and 6. background conditions. The missing mass spectrum in Fig. 3 (b) was obtained projecting the events confined in the 10 He locus.
Not a single event was detected in the 10 He spectrum below 2.5 MeV. This imposes a stringent (one count corresponds to 14 µb/sr) limit on the population cross section in the expected 10 He ground state region at about 1.2 MeV [4]. The lowest energy feature in the 10 He spectrum is a group of 10 events in between 2.5 and 5.5 MeV [see Fig. 3]. This ∼ 3 MeV group is well isolated from the rest of the spectrum and has a typical resonant cross section (∼ 140 µb/sr averaged for cms angles 3.5 • − 9.5 • ), see estimates in Section 5. Also, this group has a distinct feature: the energy distribution of the 8 He fragments obtained in the 10 He cms appears to be different from that in the rest of events in the 10 He spectrum. One can see in Fig. 3 (a) that within this group the E( 8 He) energies are around the maximal possible value. This means that the relative energy of the decay neutrons for such events tends to zero. This could be evidence for some strong specific momentum correlations or/and strong n-n final state interaction in this part of the 10 He spectrum. We think that the ∼ 3 MeV group of events represents a resonant state for 10 He; the possible nature of this state is discussed in Section 7.

Cross section estimates
Both the 8 He and 10 He states were populated in our experiments by the same "dineutron" transfer in the same kinematical conditions and, presumably, by the same direct reaction mechanism. This fact makes it very probable that spectroscopic information can be extracted from the cross sections in a straightforward way. For theoretical estimates of the spectroscopic factors we used somewhat extended phenomenological Cluster Oscillator Shell Model Approximation (COSMA) of Ref. [19]. Within this model the g.s. wave functions (WF) Ψ J of the 6,8,10 He isotopes can be written as The schematic notation [l n j ] J denotes the Slater determinant of n neutrons occupying l j orbital projected on the total spin J and normalized. The αparticle is considered to be an inert core and it is omitted in the notation. In the original paper [19] only the α 8 configuration in Eq. (1) was considered.
The model looks very schematic. However, it lists all the possible p-shell configurations, representing the dominant part of the WF. Particularly, for the 6 He g.s. coefficients α 6 , β 6 can be inferred from the three-cluster model calculations [20] α 6 = 0.926 , α 2 6 = 0.86 , β 6 = 0.226 , β 2 6 = 0.05 , exhausting 91% of the WF normalization (the corresponding 79% of K = 2, L = 0 and 12% of K = 2, L = 1 components are considered). The simplified 6 He WF can also be used with only p 3/2 configuration (α 6 = 1, β 6 = 0) to test the sensitivity to the 6 He structure. Assuming the 8 He WF (1) is normalized, we end up with only one unknown parameter β 8 in the model.
The cluster overlaps for the 8,10 He WFs within this model are: Using spin algebra and Talmi coefficients, the overlaps of the shell model configurations with the "dineutron" nn being in the s-wave motion relative to the core are obtained as Dineutron here is the the two neutrons with angular momentum and total spin equal to zero represented by minimal oscillator. The spectroscopic weight For the reactions studied in this work a reasonable estimate of the cross section ratio σ 10 /σ 8 for the 10 He and 8 He g.s. population is the ratio of the dineutron spectroscopic factors. They are found as The spectroscopic information obtained in the model is illustrated by Fig. 4. In the region β 8 > 0 the cross section ratio is changing dramatically [Fig. 4 (c)]. However, this region is presumably unphysical. In this region the weight of the dineutron configuration in 8,10 He is minimal [ Fig. 4 (b)] and the weight of the 6 He g.s. configuration in 8 He is minimal as well [ Fig. 4 (a)]. These configura-tions are expected to be maximized by the variational procedure as they are energetically highly preferable. Simple heuristic considerations show that the β 8 coefficient should be confined by condition β 8 < 0 [to maximize attractive (ls) interaction] and −0.5 < sign(β 8 )β 2 8 < −0.3 [to maximize pairing].
(1) For a reasonable weight of coefficient β 8 (for example, −0.5 < sign(β 8 )β 2 8 < 0) the population of the [s 2 1/2 ] state in 10 He is expected to be larger than the [p 2 1/2 ] state. A discrepancy can be seen in Ref. [21] between the experimentally obtained S 2n 8 = 1.3(1) and theoretical "shell model" value given as 1/6 (see Table 1 in [21]). The values obtained in our model vary between 0.8 and 1.1 (depending on the β 8 value) in a good agreement with the experiment of Ref. [21].

Possible nature of the threshold state in 8 He
In the missing mass spectrum of 8 He (see Fig. 2) attention is attracted by a steep rise ensuing straight from the three-body 6 He+n+n threshold. The lowest known resonant state of 8 He is 2 + at E = 3.57 MeV [13], Γ = 0.5 − 0.7 MeV. It decays sequentially via the 7 He ground state resonance (3/2 − at E7 He = 0.445 MeV, Γ = 0.15 MeV) by a p-wave neutron emission. This guarantees negligible population of the continuum below ∼ 0.6 MeV where decay takes place in a "three-body regime", σ ∼ E 4 8 He . Above that energy, population probability transfers to the "two-body p-wave regime", σ ∼ E 3/2 8 He . Consequently, the low-energy tail of the 2 + state can not be responsible for the near threshold events.
The only plausible source of the low-energy events, we have found, is the population of the E1 (means 1 − ) continuum. Theoretical studies of such continuum populated in reactions [22,23,24] show that the profile of the 1 − cross section typically well resembles the profile of the electromagnetic strength function dB E1 /dE. Such functions for spatially extended halo systems could provide very low-energy peak -the so called soft dipole mode -even without the formation of any 1 − resonant state.
We estimate the E1 strength function for the 8 He→ 6 He+2n dissociation using the model developed in [25]. For the WF with outgoing asymptotic generated by the dipole operatorD, acting on the g.s. WF Ψ g.s. , the E1 strength function is found as Vectors X and Y are Jacobi coordinates for the 6 He-n and ( 6 He-n)-n subsystems, respectively. Estimating the dipole strength for the light p-shell nuclei we can well take into account only the [p 2 ] → [sp] transitions and neglect the nn interactions and s-wave interaction between the core and neutron (unless the latter is not strongly attractive). In this approximation the three-body Green's function (GF) has a simple analytical form He is a free motion GF in the Y subsystem, and the GF in the X subsystem corresponds to the p-wave continuum with the 7 He g.s. 3/2 − resonance at E7 He = 0.445 MeV.
The results of the model calculations, including the 6 He test, are shown in Fig.  5. The estimated 6 He strength function giving peak at about 1.1 MeV is in a reasonable agreement with the complete three-body calculations [22] giving peak at about 1.3 MeV. It can be seen that the strength function profile in 6 He is sensitive to two main aspects of the dynamics.  strength function peak shifting to higher energy if we artificially overbound the 6 He g.s. WF to E b = 2.5 MeV instead of 0.9 MeV decreasing its radial extent. When we turn from 6 He to 8 He these dynamical trends work in the opposite directions and largely compensate each other (the 8 He g.s. is more "compact" than the 6 He g.s., but the 7 He g.s. resonance is lower than the 5 He g.s. resonance). As a result we find the strength function peak position in 8 He to be somewhat lower than respective position in 6 He. This indicates that in 8 He, where the 2 + state is significantly higher than in 6 He, the lowest-energy feature in the continuum could be the 1 − excitation.
The behaviour of the cross section with the estimated E1 component taken into account is shown in Fig. 6. The 2 + state profile is given here by the standard R-matrix expression for the p-wave decay via the 7 He g.s. providing the widths Γ = 0.56−0.82 MeV for excitation energies E = 3.6−3.9 MeV (the reduced width is taken as Wigner limit). Without E1 contribution the data are in agreement with the standard position (E ≈ 3.6 MeV) of the 2 + state, but the near threshold behaviour of the cross section can not be reproduced. The 2 + population cross section in this case can be estimated as ∼ 250 µb/sr. The addition of the 1 − contribution allows to reproduce the low-energy part of the spectrum much better. In that case we can allow up to 60% feeding to the 1 − continuum. Then we get ∼ 100 µb/sr for the 2 + population and have to shift to about E ≈ 3.9 MeV the position of this state.
The proposed significant contribution of the 1 − cross section is not absolutely unexpected and never seen phenomenon. For example, the experimental spectrum from paper [26] is shown in the inset to Fig. 6. Inspected around the 6 He+n+n threshold "on a large scale" it shows the same presence of the lowenergy intensity which can not be attributed to the tail of the 2 + state. Strong population of the E1 continuum in 8 He by nuclear processes has been demonstrated in a comparison made for the nuclear and Coulomb dissociation data [27,28]. However, in the interpretation of the data presented in [27,28] the idea was accepted that the E1 cross section in 8 He should peak at higher energy than in 6 He (maximum at about E8 He ≈ 2 MeV above the threshold). This idea is based on the argument (ii) discussed above (smaller size of 8 He compared to 6 He); actual situation appears to be more complicated. As a result the authors of [27,28] have had to position the 2 + state below the E1 peak. Consequently, they had to ascribe to it a very low excitation energy 2.9 MeV (compared to about 3.6 MeV in the other recent works). The assumption of the very low-energy soft E1 peak in 8 He would probably allow to explain in a more natural way the data from [27,28]. Also, there exists a large uncertainty in the definition of the "standard" position of the 2 + state in 8 He (2.7 − 3.6 MeV, see Ref. [14]). We think that a significant component of the disagreement among different experimental works could be connected with the possibility that the 2 + state is typically observed in a mixture with the 1 − contribution. Correlation measurements could clarify this situation.

Interpretation of the 10 He spectrum
There is an evident discrepancy between the group of events at about 3 MeV observed in this experiment and the recognized position of 10 He g.s. at about 1.2 MeV. A possible explanation is that an excited state of 10 He was observed in our work and the ground state was not populated for some reason. We, however, find a different explanation preferable.
There are two important problems, pointed by theoreticians, in the interpretation of the 10 He spectrum. (i) Possible existence of a near-threshold 0 + state with the [s 2 1/2 ] structure, due to the shell inversion phenomenon [8]. In this case we would have two 0 + states in the low-energy continuum of 10 He, nearby each other. The [s 2 1/2 ] state is predicted in [10] to have very specific properties (tentatively assigned as "three-body virtual state") and it distorts strongly the higher-lying spectrum associated with the [p 2 1/2 ] 0 + state. At first blush it is not impossible that the [s 2 1/2 ] 0 + state is not populated in our experiment. (ii) Reaction mechanism issue was pointed in Ref. [10]. The most clear observation of the 10 He g.s. was made so far in the experiment with the 11 Li beam [4]. It was shown in [10] that, in contrast to the typical transfer reactions, the experiments with the 11 Li beam can provide very specific signal for the [p 2 1/2 ] 0 + state: in the 11 Li case the spectrum is shifted downwards due to the abnormal size of the halo component of the 11 Li WF.
Let us consider the second issue first. The measured missing mass spectrum of 10 He is shown in Fig. 7 in comparison with the experimental data [4] and calculations [10] taking into account the reaction mechanisms in both cases. It is clear that the calculations are somewhat overbound (∼ 0.5 − 0.7 MeV), but otherwise consistent with the data in both cases. It has also been shown in Sec. 5 that the absolute cross section value for the 3 MeV group of events is quantitatively consistent with the population of a p-wave state. We can conclude here that it is very probable that the 1.2 MeV peak observed in Ref. [4] and the 3 MeV peak in our work represent the same state. It should be emphasized that the calculated peak energy for the (t,p) reaction cross section is consistent with the resonance properties inferred from the S-matrix in [10]: the eigenphase for 3 → 3 scattering is passing π/2 at about the peak energy. Therefore, the peak energy observed in the transfer reaction could provide a better access to the 10 He properties. Now we return to the first issue. Is it possible that the theoretically predicted in [8] low-lying 0 + state with the [s 2 1/2 ] structure exists, but it is not populated in our reaction? It was shown in [10] Fig. 8 (a) for different interactions in the 8 He-n s-wave channel (the positive values of scattering length indicated for two curves in Fig. 8 (a) imply that repulsive interaction takes place in the s-wave state). In Ref.
[10] the cases of a < −5 fm in 9 He correspond to the formation of extremely sharp near threshold 0 + 10 He states. Otherwise, there is only the [p 2 1/2 ] state at ∼ 2.4 in the 10 He continuum. It can be seen in Fig. 8 (b) that only scattering lengths a ≥ −5 fm (and hence no [s 2 1/2 ] state) are qualitatively consistent with our data. Thus the data favour the situation of the [p 2 1/2 ] ground state of 10 He. In this way our data also indirectly lead to contradiction with the 8 He-n scattering length limit a < −10 fm claimed in Ref. [7].
The interpretation proposed above is very nonorthodox and is based, at the moment, on the limited statistics data. However, alternatively we face a problem to explain why the "real" ground state was not observed in our experiment despite the very low cross section limit achieved (σ 10 < 14 µb/sr) and the estimates of Section 5 indicating large population probability for possible [s 2 1/2 ] state.

Conclusion.
In this work we studied the 8 He and 10 He spectra in the same (t, p) transfer reaction. This allowed us, when interpreting the data, to be free in our speculations of the reaction mechanism peculiarities. We think that our results are not in contradiction with the previous works done on these nuclei in the sense of the data, however, making various theoretical estimates we arrived at different conclusions on several issues.  [4], if one takes into account the peculiar reaction mechanism for the 11 Li beam used in [4]. If this interpretation is valid, a new ground state energy of about 3 MeV should be established for 10 He since the peak position obtained in the transfer reaction corresponds to the S-matrix pole position, while for reactions with 11 Li there is a strong difference. (4) The absence of the near-threshold state in 10 He, predicted to have a [s 2 1/2 ] structure [8] imposes, according to calculations [10], a stringent limit a > −5 fm on the 8 He-n scattering length. This is in contradiction with the existence of a virtual state in 9 He, declared to have a < −10 fm in Ref. [7].
Further measurements of a similar style are desirable. This would allow to reveal the potential of correlation measurements for such complicated systems and to resolve the interesting problems outlined in this work.