application/xmlProbing the 8He ground state via the 8He([formula omitted])6He reactionN. KeeleyF. SkazaV. LapouxN. AlamanosF. AugerD. BeaumelE. BechevaY. BlumenfeldF. DelaunayA. DrouartA. GillibertL. GiotK.W. KemperL. NalpasA. PakouE.C. PollaccoR. RaabeP. Roussel-ChomazK. RusekJ.-A. ScarpaciJ.-L. SidaS. StepantsovR. WolskiDirect reactionsSpectroscopyCRC calculations8HePhysics Letters B 646 (2007) 222-226. doi:10.1016/j.physletb.2007.01.035journalPhysics Letters BCopyright © 2007 Elsevier B.V. All rights reserved.Elsevier B.V.0370-26936465-622 March 20072007-03-22222-22622222610.1016/j.physletb.2007.01.035http://dx.doi.org/10.1016/j.physletb.2007.01.035doi:10.1016/j.physletb.2007.01.035http://vtw.elsevier.com/data/voc/oa/OpenAccessStatus#Full2014-01-01T00:14:32ZSCOAP3 - Sponsoring Consortium for Open Access Publishing in Particle Physicshttp://vtw.elsevier.com/data/voc/oa/SponsorType#FundingBodyhttp://creativecommons.org/licenses/by/3.0/

Journals

S300.2

PLB23719S0370-2693(07)00140-210.1016/j.physletb.2007.01.035Elsevier B.V.Experiments

Fig. 1

Schematic of the coupling scheme used in the CRC calculations.

Fig. 2

CRC calculation at 15.7 A MeV compared to the 8He(p,d)7He [16,17] and 8He(p,t)6He data. The dashed curves denote the result of a calculation where C2S(8He/6He0+) = C2S(8He/6He2+) = 1.0.

Fig. 3

CRC calculation at 61.3 A MeV compared to the 8He(p,t)6He data of Korsheninnikov et al. [15]. The dashed curves denote the result of a calculation where C2S(8He/6He0+) = C2S(8He/6He2+) = 1.0.

Table 1

t+He6 potential parameters. The real parts are of volume Woods–Saxon form at both energies while the imaginary parts are of surface and volume Woods–Saxon form at 15.7 and 61.3 A MeV, respectively

EnergyVrVaVWrWaWVSOrSOaSO15.7 A MeV81.21.340.79010.01.140.8811.151.050.38461.3 A MeV87.51.150.63221.71.460.8301.151.050.384Table 2

Spectroscopic amplitudes (SA) obtained from the CRC analysis

NucleusConfigurationnljSA8Hen2+He0+62S01.0a8Hen2+He2+61D20.12a8Hen+He3/2−61p3/21.7a7Hen+He0+61p3/2−0.728 [29]7Hen+He2+61p3/2−1.327 [30]

This work.

Probing the 8He ground state via the 8He(p,t)6He reaction

Keeley

⁎

nkeeley@cea.fr

Skaza

Lapoux

Alamanos

Auger

Beaumel

Becheva

Blumenfeld

Delaunay

Drouart

Gillibert

Giot

K.W.

Kemper

Nalpas

Pakou

E.C.

Pollacco

Raabe

Roussel-Chomaz

Rusek

J.-A.

Scarpaci

J.-L.

Sida

Stepantsov

Wolski

aCEA-Saclay DSM/DAPNIA/SPhN, F-91191 Gif-sur-Yvette, FrancebInstitut de Physique Nucléaire, IN2P3-CNRS, F-91406 Orsay, FrancecGANIL, Bld. Henri Becquerel, BP 5027, F-14021 Caen Cedex, FrancedDepartment of Physics, Florida State University, Tallahassee, FL 32306-4350, USAeDepartment of Physics, University of Ioannina, 45110 Ioannina, GreecefDepartment of Nuclear Reactions, The Andrzej Sołtan Institute for Nuclear Studies, ul. Hoża 69, PL-00681 Warsaw, PolandgFlerov Laboratory of Nuclear Reactions, JINR, Dubna, RU-141980, RussiahThe Henryk Niewodniczański Institute of Nuclear Physics, PL-31342 Kraków, Poland⁎Corresponding author.1

Present address: IKS, University of Leuven, B-3001 Leuven, Belgium.

Present address: CEA/DIF/DPTA/SPN, B.P. 12, F-91680 Bruyères-le-Châtel, France.

Editor: V. Metag

Abstract

The weakly-bound 8He nucleus exhibits a neutron halo or thick neutron skin and is generally considered to have an α+4n structure in its ground state, with the four valence neutrons each occupying 1p3/2 states outside the α core. The 8He(p,t)6He reaction is a sensitive probe of the ground state structure of 8He, and we present a consistent analysis of new and existing data for this reaction at incident energies of 15.7 and 61.3A MeV, respectively. Our results are incompatible with the usual assumption of a pure (1p3/2)4 structure and suggest that other configurations such as (1p3/2)2(1p1/2)2 may be present with significant probability in the ground state wave function of 8He.

PACS

24.50.+g21.10.Jx24.10.Eq

Keywords

Direct reactionsSpectroscopyCRC calculations8He

The 8He nucleus has the largest neutron to proton ratio of any known particle-stable nucleus, and as such is an excellent test case for nuclear structure models at extreme values of isospin. In addition, 8He exhibits a neutron halo or thick neutron skin [1,2]. The 8He ground state is generally considered to have an α+4n structure, the possibility of a He6+2n structure being a priori ruled out on the grounds that the weak binding energy of 6He makes it an unsuitable core, see e.g. [3]. More concrete evidence against a 6He core is provided by the small dipole strength obtained in a 8He dissociation experiment [3] and the failure to satisfy the Glauber model expression: σ−2n(He8)=σI(He8)−σI(He6)[2] where σI is the interaction cross section and σ−2n the two-neutron removal cross section, expected to hold if 6He and 8He are both 2n halo nuclei. On the contrary, the relation: σ−2n(He8)+σ−4n(He8)=σI(He8)−σI(He4), which should hold if 8He has a 4n halo structure, is rather well fulfilled by the experimental cross sections [2].Various models of 8He based on the α+4n picture have been proposed, e.g. the microscopic multicluster model [4,5], the cluster orbital shell model with continuum discretization [6], and the cluster orbital shell model approximation (COSMA) [7]. A He8=α+n2+n2 three-cluster model has also been proposed [8]. The COSMA model [7] restricts the four valence neutrons to the 1p3/2 sub-shell, quoting the more accurate calculations of [6] as justification. The microscopic multicluster model gives good agreement with the experimental 6He transverse momentum distribution for two neutron removal from 8He [9], as does the COSMA model [7]. The COSMA model also describes the neutron longitudinal and transverse momentum distributions in coincidence with the 6He fragment for 8He dissociation by Al [3], and the combined 2n and 4n removal cross sections for 8He + Si for a range of energies [10]. The main 6He production mechanism in high energy 8He dissociation experiments appears to be sequential decay via the ground state of 7He, which decays exclusively into He6+n[3,11].The apparent success of the COSMA model suggests that the dominant configuration in the 8He ground state is indeed an α particle core surrounded by four valence neutrons filling the 1p3/2 sub-shell, equivalent to assuming pure jj coupling. However, the one-neutron knock out cross section for 227 MeV/u 8He on C is overpredicted by a factor of more than 2 under this assumption [11]. The spectroscopic factor for 6He knockout deduced from quasi-free scattering of 671 MeV/u 8He by a proton target is also not in agreement with the hypothesis of a closed 1p3/2 sub-shell [12].Translationally invariant shell model (TISM) calculations suggest that the 8He(p,t)6He reaction is a sensitive probe of the 8He ground state configuration [13]. In particular, the ratio of the 6He 01+ to 6He 21+ contributions depends quite strongly on the assumed structure of the 8He ground state. A DWBA analysis of 8He(p,t)6He data at 61.3A MeV[15] found a ratio of He0+8=He0+6+2n to He0+8=He2+6+2n spectroscopic factors of about unity, in agreement with the prediction of the COSMA model and the hypothesis of a closed 1p3/2 sub-shell. However, one-step [13] and two-step DWBA [14] analyses of similar data at 26A MeV found that they could not be described using spectroscopic factors calculated using the TISM and consistent with a (1p3/2)4 configuration for the 8He ground state. We present an analysis of new and existing 8He(p,t)6He data that yields spectroscopic factors (C2S) in good agreement with those obtained from quasi-free scattering [12] and consistent with little or no 6He 21+ contribution to the 8He ground state.Data for the 8He(p,t)6He reaction were obtained during an experiment carried out to study the structure of 8He by measuring the reactions induced by a 15.7A MeV8He beam from the GANIL SPIRAL facility incident on a proton-rich polypropylene (CH2)n target. The 8He(p,p), (p,p′), (p,d) and (p,t) reactions were all measured in the same experiment by detecting the protons, deuterons and tritons in coincidence with the He fragments. Identification of the light particles and reconstruction of their trajectories and energies enabled the yields for each of the reactions: (p,p), (p,p′), (p,d) and (p,t) to be obtained. The experimental conditions and data reduction procedure for the extraction of the (p,p) and (p,d) cross sections are described in [16,17]. The (p,t) cross sections were obtained using the same data reduction procedure, tritons being selected in lieu of protons or deuterons. The absolute normalisation was obtained as explained in [16,17]:

•the number of incident particles was measured by two beam tracking devices providing the beam trajectory, particle by particle;

•the detection efficiency was checked through an auxiliary measurement of the p+C13 elastic scattering in inverse kinematics, employing an 11.3A MeV13C beam. It was in excellent agreement with published results obtained in direct kinematics with an 11.5 MeV proton beam incident on a 13C target [18].

The normalisation of the 8He(p,t) data has a total uncertainty of 15%. Sources of systematic error are as discussed for the 8He(p,d)7He data [16,17].The new 8He(p,t)6He data, together with the existing measurement at 61.3A MeV[15] were analysed by detailed coupled reaction channels (CRC) calculations. The aim was to obtain a good description of both data sets with the same set of spectroscopic amplitudes. All calculations were performed with the code FRESCO [19]. The following ingredients are required: scattering potentials for p+He8, d+He7 and t+He6 at appropriate energies; binding potentials for p+n, n+d, n2+p, n+He7, n+He6 and n2+He6; and spectroscopic amplitudes for the 8He0+/7He3/2−, 7He3/2−/6He0+, 7He3/2−/6He2+, 8He0+/6He0+ and 8He0+/6He2+ overlaps. It is the 8He0+/6He0+ and 8He0+/6He2+ spectroscopic amplitudes that we wish to determine from our analysis; the other ingredients may be fixed from other sources except for the t+He6 scattering potentials, for which we make physically reasonable assumptions.Entrance channel potentials were calculated using the JLM prescription [20], as in a previous study of the 8He(p,d)7He reaction [16]. The real and imaginary normalisation factors for the JLM potentials, λV and λW, respectively, were treated as parameters, adjusted to obtain the best descriptions of the elastic scattering data by the CRC calculations. As there are no elastic scattering data available at 61.3A MeV the result of an optical model calculation using the JLM potential with real and imaginary parts both renormalised by factors of 0.8, found to give a satisfactory description of existing He8+p elastic scattering data over the incident energy range 25–72A MeV, was used as a substitute. The best fit λV, λW values obtained from the CRC calculations at 15.7 and 61.3A MeV were 1.02, 0.22 and 0.90, 0.70, respectively.Direct transfer of the two neutrons as a dineutron-like cluster, two-step transfer via the 8He(p,d)7He reaction and coupling between the 6He 01+ and 21+ states were included. Excitation of the 8He 21+ state was omitted as this coupling is weak. Fig. 1

gives a schematic of the coupling scheme. The 8He(p,d)7He couplings were as described in Skaza et al. [16], and included deuteron breakup couplings using the CDCC formalism. The deuteron breakup space was extended to an excitation energy of 44 MeV for the calculations at 61.3A MeV due to the greater available energy (tests confirmed that additional continuum bins made a negligible difference). Unlike in Skaza et al. [16] the Koning and Delaroche global nucleon potential [21] used to construct the d+He7 potentials at 15.7A MeV was tuned to obtain optimum agreement with the 8He(p,d)7He data at angles greater than 50° by multiplying the imaginary part by a factor of 2. As there are no 8He(p,d)7He data available at 61.3A MeV the Koning and Delaroche parameters calculated at the appropriate energy were used unchanged.

The n+d and n2+p binding potentials were taken from [22] and [23], respectively. The n+He7 and n+He6 binding potentials used the “standard” parameters R=1.25×A1/3 fm, a=0.65 fm; the n2+He6 binding potential employed a radius of 2.5 fm, close to the measured matter radius of 8He, and a diffuseness of 0.7 fm. All potentials were of Woods–Saxon form with depths adjusted to give the correct binding energies. The 7He/6He0+ form factor was calculated within a bin of width 320 keV, the potential depth being adjusted to give a resonance at the correct position above the n+He6 threshold. Tests found that doubling the width of the bin did not affect the results.No t+He6 elastic scattering data are available, therefore we used 3He + 6Li optical potentials in lieu. At 61.3A MeV we used the 72 MeV type A potential of Bragin et al. [24], while at 15.7A MeV we used potential A of Basak et al. [25]. The 6He 01+→21+ coupling employed a collective model form factor and the isoscalar deformation length of [26], the potential parameters being adjusted to recover the no-coupling t+He6 elastic scattering. The adjusted parameters are given in Table 1

Spectroscopic amplitudes for the n+p overlaps were as in Skaza et al. [16]. The n+He7 spectroscopic amplitude was fixed by an analysis of the 8He(p,d) data at 15.7A MeV and is 12% smaller than the value given in Skaza et al. [16] due to a slight error (a parameter controlling the calculation of the non-local kernels was inadvertently left too large) which does not otherwise significantly affect the results presented there. The spectroscopic amplitudes for the d+n overlap were fixed by setting the dominant S-wave component to 90% of the pure d⊗n value following [27] and adjusting the small D-wave component to give the D2 value of [28]. The n+He0+6 spectroscopic amplitude was fixed by the spectroscopic factor obtained from the ratio of the measured decay width of the 7He ground state to the pure single particle width calculated in a potential well using standard parameters [29]. As there is no empirical means of fixing the spectroscopic amplitudes for the n+He2+6 overlap we assumed a 1p3/2 configuration with a spectroscopic amplitude taken from the variational Monte Carlo (VMC) shell model calculation of [30]. This calculation also gives a n+He0+6 spectroscopic factor identical to that obtained from the measured decay width. The n2+p spectroscopic amplitude was fixed at unity and the n2+He0+6 and n2+He2+6 spectroscopic amplitudes adjusted to obtain the best fit to the data.The calculations are compared with the transfer data in Figs. 2 and 3

and the best fit spectroscopic amplitudes are given in Table 2

. The agreement between the calculations and both data sets is good. We emphasise that the only differences between the calculations at the two incident energies are the scattering potentials and the size of the deuteron breakup space. The improved agreement between calculation and data at angles greater than 50° for the 8He(p,d)7He reaction at 15.7A MeV compared to Skaza et al. [16] is mainly due to tuning the Koning and Delaroche potential used to construct the d+He7 potentials, the two-step transfer process having little effect on this reaction channel. We emphasise that this tuning of the potential does not significantly affect the cross section at angles smaller than 50°, most important for determining the spectroscopic factor.

It is apparent from Table 2 that, unlike the prediction of the COSMA model [15], we find a 6He 21+ component of the 8He ground state that is much smaller than the 6He 01+ contribution. Nevertheless, our absolute spectroscopic amplitudes are consistent over two widely separated incident energies and we are able to describe the whole of the data—elastic scattering, one and two neutron pickup—at 15.7A MeV. For comparison, we give the results of calculations where the spectroscopic amplitudes for the 8He/6He0+ and 8He/6He2+ overlaps have both been set to unity as the dashed curves in Figs. 2 and 3. While the descriptions of transfer leading to the 6He 21+ state at 15.7A MeV are comparable, it is clear that the dashed curves do not at all describe the transfer leading to the 6He 01+ at either energy nor that to the 6He 21+ state at 61.3A MeV. However, these results may depend on the choice of t+He6 optical potentials, which are not known. We therefore carried out a series of tests to investigate the sensitivity of our results to these quantities.As the t+He6 elastic scattering has not so far been measured we were forced to use the nearest available optical potentials as a basis for our calculations. While the potentials given in Table 1 do give very good consistency over the two incident energies, alternative potentials are available in the literature for the same data [24,25,31]. Potentials that give equivalent t+He6 elastic scattering give similar results, regardless of potential “family” or whether the imaginary part is of surface or volume Woods–Saxon form. The effect of the choice of t+He6 potential on the consistency of the spectroscopic amplitudes over the two incident energies is less conclusive. The 8He/6He2+ spectroscopic amplitudes are reasonably consistent at both energies provided that the t+He6 potential for the calculation at 61.3A MeV is consistent with the elastic scattering predicted by the potential of Bragin et al. [24]. The same is true for the 8He/6He0+ spectroscopic amplitudes if one takes the forward angle region at 15.7A MeV where we unfortunately do not have data. Calculations at 61.3A MeV that use potentials consistent with the t+He6 elastic scattering given by the potentials of Burtebaev et al. [31] give spectroscopic amplitudes significantly larger than those obtained at 15.7A MeV for both 6He states. However, none of the potentials give results consistent with the COSMA prediction.Test DWBA calculations did find a reasonably consistent value for the ratio of 8He/6He0+ to 8He/6He2+ spectroscopic factors over the two data sets, although the value varied from 1.1 to 2.2 depending on the exit channel potentials used. However, the absolute values for the 8He/6He0+ and 8He/6He2+ spectroscopic factors extracted from the DWBA analyses showed a very large range and were not at all consistent between the two incident energies, suggesting that the DWBA, with its assumption of weak coupling and a single-step reaction mechanism, is inadequate here.To summarise, the consistency of our results over two widely spaced incident energies depends on the unknown t+He6 potential. While it is true that none of our CRC calculations are consistent with the COSMA prediction for the 8He/6He0+ to 8He/6He2+ spectroscopic factor ratio a question mark must remain over our results until realistic t+He6 potentials are available—this remark applies equally to DWBA analyses. This ambiguity could be removed by measurements of the appropriate elastic scattering in inverse kinematics; such measurements are in principle possible with a cryogenic tritium target. Obtaining data for transfer to the 6He 01+ state over a larger angular range—forward angles at 15.7A MeV to cover the first peak and at larger angles to define the second peak at 61.3A MeV—would also remove some of the uncertainty in the present analysis. One might also question the use of a calculated spectroscopic amplitude for the n+He2+6 overlap; this procedure will only be as reliable as the calculation. However, the standard shell model using the Cohen and Kurath wave functions [30], the VMC shell model [30] and the TISM [13] all give reasonably similar results for this value, as they do for the n+He0+6 overlap, these latter in good agreement with the value extracted from the measured total decay width. Test calculations found that taking a smaller value for the n+He2+6 spectroscopic amplitude will yield a larger n2+He2+6 spectroscopic amplitude; taking a value for the n+He2+6 spectroscopic factor half that of the n+He0+6 one gives a ratio of 8He/6He0+ to 8He/6He2+ spectroscopic factors of 7, still much larger than the COSMA prediction of about 1.In conclusion, we have obtained a consistent description of two data sets for the 8He(p,t)6He reaction at widely differing incident energies with 8He=6He0++2n and 8He=6He2++2n spectroscopic factors of 1.0 and 0.014, respectively. The value for the 8He/6He0+ overlap is in remarkably good agreement with that obtained from a recent quasi-free scattering experiment [12], 1.3±0.1. Our value for the 8He/7He3/2− spectroscopic factor, 2.9, is also in good agreement with the quasi-free scattering result, 3.3±0.3[12]. Our original CCBA analysis [17] of the 8He(p,d)7He data concluded that the 8He/7He3/2− spectroscopic factor obtained, 4.4±1.3, was consistent with a relatively pure (1p3/2)4 configuration for the 8He ground state, as assumed in the COSMA model. The final error bar, including all sources of uncertainty, was such that we were unable to draw a more definite conclusion. However, the current figure of 2.9—the reduction compared to the CCBA result is due to strong coupling effects taken into account by the CRC calculation—is significantly smaller than the sum-rule value and, combined with our results for the 8He(p,t)6He reaction, enables us to be more specific. Our results suggest that the 8He(p,t)6He reaction is a rather more sensitive probe of the 8He ground state than the 8He(p,d)7He neutron pickup, and that while the (1p3/2)4 configuration is probably the dominant component of the 8He ground state, there is a significant probability of finding the “valence” neutrons in other configurations such as (1p3/2)2(1p1/2)2, suggested in [12].This result should, perhaps, not be surprising; assuming the 8He ground state to consist of an α particle core plus four neutrons filling the 1p3/2 sub-shell is equivalent to assuming pure jj coupling. The intermediate coupling model of Cohen and Kurath [32] for the stable 1p-shell found that for the lighter nuclei, up to about A=9, the coupling was actually very close to pure LS coupling, gradually changing to jj coupling as the mass increased through the shell. Our results provide new constraints for modern structure calculations, e.g. the ab initio shell model, which aim to describe the structure of light exotic nuclei. It will be interesting to see whether such calculations confirm the picture of a significant (1p3/2)2(1p1/2)2 component, for example, in the 8He ground state.

Acknowledgements

N.K. gratefully acknowledges the receipt of a Marie Curie Intra-European Fellowship from the European Commission, contract No. MEIF-CT-2005-010158. K.W.K. acknowledges the support of the US National Science Foundation.

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