8He–6He: a comparative study of nuclear fragmentation reactions

Nuclear Physics A 679 (2001) 462–480 www.elsevier.nl/locate/npe

8

He–6He: a comparative study of nuclear fragmentation reactions

K. Markenroth a , M. Meister a,b , B. Eberlein c,1 , D. Aleksandrov d , T. Aumann c,e , L. Axelsson a , T. Baumann e,2 , M.J.G. Borge f , L.V. Chulkov d , W. Dostal c , Th.W. Elze g , H. Emling e , H. Geissel e , A. Grünschloß g , M. Hellström e,3 , J. Holeczek e , B. Jonson a,∗ , J.V. Kratz c , R. Kulessa h , A. Leistenschneider g , I. Mukha b,d , G. Münzenberg e , F. Nickel e , T. Nilsson i , G. Nyman a , M. Pfützner e , V. Pribora d , A. Richter b , K. Riisager j , C. Scheidenberger e , G. Schrieder b , H. Simon b,i , J. Stroth e,g , O. Tengblad f , M.V. Zhukov a a Experimentell Fysik, Chalmers Tekniska Högskola and Göteborgs Universitet, S-412 96 Göteborg, Sweden b Institut für Kernphysik, Technische Universität, D-64289 Darmstadt, Germany c Institut für Kernchemie, Johannes-Gutenberg-Universität, D-55099 Mainz, Germany d Kurchatov Institute, RU-123182 Moscow, Russia e Gesellschaft für Schwerionenforschung (GSI), Planckstr. 1, D-64291 Darmstadt, Germany f Instituto Estructura de la Materia, CSIC, E-28006 Madrid, Spain g Institut für Kernphysik, Johann-Wolfgang-Goethe-Universität, D-60486 Frankfurt, Germany h Instytut Fizyki, Uniwersytet Jagiello´nski, PL-30-059 Kraków, Poland i EP-Division, CERN, CH-1211 Genève 23, Schweitz j Institut for Fysik og Astronomi, Aarhus Universitet, DK-8000 Aarhus C, Denmark

Received 14 July 2000; accepted 7 August 2000

Abstract Dissociation of 227 MeV/u 8 He in a carbon target has been studied in kinematically complete experiments. The data include the relative energy spectrum, angular distributions in the neutron knock-out channel (6 He + n) as well as diffractive dissociation and inelastic scattering into the (6 He + 2n) channel. The data are compared with corresponding results from the well-known halo nucleus 6 He. In both cases it is found that neutron knock-out is the dominating reaction channel. The relative energy spectrum (6 He + n) shows a structure, which is interpreted as being due to the I π = 3/2− resonance in the 7 He ground state with about equal contribution from its I π = 1/2− spin–orbit partner. ∗ Corresponding author.

E-mail address: [email protected] (B. Jonson). 1 Part of the Doctoral Thesis of B. Eberlein. 2 Present address: NSCL, Michigan State University, East Lansing, MI 48824-1321, USA. 3 Present address: Lund University, Department of Physics, PO Box 118, S-22100 Lund, Sweden.

0375-9474/01/$ – see front matter  2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 5 - 9 4 7 4 ( 0 0 ) 0 0 3 7 2 - 9

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The 7 He resonance shows a spin alignment similar to that observed in 5 He, but with a smaller anisotropy indicating that the structure of the 8 He ground state is more complicated than that of 6 He. The data in the (6 He + 2n) channel were used to identify resonances in the excitation energy spectrum of 8 He. If the spectrum is interpreted as two overlapping resonances, the spin-parity assignment for these is found to be 2+ and 1− , respectively.  2001 Elsevier Science B.V. All rights reserved. PACS: 27.20.+n; 24.70.+s; 25.06.-t

1. Introduction The stability of the A = 8 isobar chain terminates on the neutron-rich side with 8 He. This nucleus has the largest N/Z ratio for any particle-stable nuclear system. The two heaviest bound He isotopes, 6,8 He, have attracted much attention in recent years. The reason is that they belong to the group of light dripline nuclei where the nuclear halo structure was first observed [1–3]. The lighter isotope 6 He is characterized as a Borromean two-neutron halo system [4] and has been studied in a large number of different experiments. Its structure is well understood and the ground state is to more than 90% a pure (0p3/2)2 state [5]. The relatively simple structure of 6 He makes it a bench-mark nucleus which can be used for comparative studies of nuclei close-by. The separation energy of the neutron pair in the 0p3/2 shell, forming the halo in 6 He, amounts to 973 keV while 2.139 MeV is needed to remove a neutron pair in 8 He. The neutron pairing energy in 8 He ( = 3.03 MeV) is one of the largest known and it is 275 keV larger than that of 6 He. A careful analysis of the measured cross sections for different breakup channels of 6 He and 8 He [7] suggests that the 8 He structure is best described as a five-body system (α + 4n) rather than as a two-neutron halo (6 He + 2n). Further experimental evidence for an α-neutron structure has been obtained in beta-decay experiments [8] where the beta-delayed triton branch mainly originates from a 9.3 MeV resonance in 8 Li, and has a GT transition probability of BGT = 5.18 corresponding to almost half of the GT sum rule. This result indicates that the 8 He ground state has a large overlap with an (α + t + n) structure in 8 Li [9]. Zhukov et al. [10,11] have suggested a five-body cluster orbital shell-model approximation (based on the discussion in Ref. [12]) to describe the 8 He ground state wave function as (α + 4n). In this paper we shall present the recent results from breakup of 8 He at 227 MeV/u in a carbon target. From this kinematically complete experiment, the relative energy spectrum, angular distributions and cross sections have been deduced. Throughout the paper we shall compare the obtained results with the corresponding ones for the well-known halo nucleus 6 He. These results for 6 He are previously published but are here included in the figures to illuminate the resemblances and differences between the two nuclei.

2. Experimental method The radioactive beams of 6,8 He were produced in an 8 g/cm2 Be production target by fragmentation of a primary 18 O (340 MeV/u) beam from the heavy-ion synchrotron SIS at

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Fig. 1. Overall resolution σEd with regard to the decay energy Ed for 7 He into neutron plus 6 He, and 8 He into two neutrons plus 6 He, respectively. The two curves are obtained from Monte Carlo event-simulation calculations applying known detector responses.

GSI, and were subsequently separated in the fragment separator FRS by magnetic analysis. The secondary beams had energies of 240 MeV/u and 227 MeV/u for 6 He and 8 He, respectively. The beam was then directed towards a carbon target (thickness 1.87 g/cm2 for 6 He and 1.3 g/cm2 for 8 He) placed directly in front of a large-gap dipole magnetic spectrometer. The neutrons, recorded in coincidence with alpha particles or 6 He, were detected in the large area neutron detector, LAND. The experimental setup was described in detail in Refs. [13,14]. Figure 1 shows the overall resolution with regard to decay energies for the studied 8 He reaction channels as obtained from Monte Carlo simulations. It deteriorates from about 100 keV at very low decay energy to about 500 keV at a decay energy of 3 MeV.

3. Nuclear reactions The momentum distributions of fragments emerging from fragmentation reactions are characterized by comparatively sharp peaks. The position of the peak is close to the primary beam velocity and its standard deviation (σ ) varies with the type of fragment. The acceptance of the experimental setup used in this experiment confines the region where events may be registered to about ±3σ in transverse direction around the fragmentation peak. We can divide our data into three different classes of specific events: – Detection of two neutrons in coincidence with the charged fragment (6 He in 8 He fragmentation and an α-particle in the 6 He case) corresponds to a quasi-sequential

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Table 1 Interaction cross sections (σi ) and cross sections for inelastic scattering (σin ), one-neutron knock-out (σ−1n ), and two-neutron knock-out (σ−2n ) for helium isotopes in a carbon target. The σi have been obtained by scaling data obtained at 790 MeV/u [6,7] to the energy of the present experiment. The last two columns represent the sum (Σ ) of all measured neutron removal channels and the difference (∆) between σi for 6,8 He and 4 He, respectively Projectile

σi (mb)

σin (mb)

σ−1n (mb)

σ−2n (mb)

Σ (mb)

∆ (mb)

4 He

457 ± 5 656 ± 5 749 ± 6

30 ± 5 32 ± 5

127 ± 14 129 ± 15

33 ± 23 29 ± 23

190 ± 27 190 ± 27

199 ± 7 292 ± 8

6 He 8 He

process — excitation of 8 He (6 He) as a single system to the continuum followed by its decay. The reaction mechanism might be either diffractive dissociation or inelastic scattering to separate resonance states. We refer to these types of reactions as the inelastic scattering channel with cross section σin . – Detection of only one neutron means that the second one has either been absorbed or has got a large momentum transfer and been deflected strongly. Such a reaction corresponds to the one-neutron knock-out or one-neutron stripping mechanism. In the following we refer to this channel as the neutron knock-out channel, σ−1n . – Reactions where only the charged fragment in the vicinity of the fragmentation peak is detected is referred to as the two-neutron knock-out channel, σ−2n . The measured cross sections for 4 He, 6 He and 8 He in a carbon target are presented in Table 1 where the interaction cross sections (σi ) are based on measurements at 790 MeV/u [6,7] and scaled to the energy of the present experiment. The scaling was done in Glauber calculations taking the energy dependence of the nucleon–nucleon cross sections into account. The resulting σi values at 227 MeV/u are found to be about 10% smaller than those at 790 MeV/u. The sum of all measured neutron-removal channels for 6 He (Σ in Table 1) is, within the experimental uncertainties, equal to the difference between the 6 He and 4 He interaction cross sections (∆ in Table 1). This was already realized in the 790 MeV/u experiment [7] and reflects that the 6 He structure can be described as an α + 2n system [15]. For 8 He the sum of the cross sections in all neutron removal channels is 292 mb. In our measurements, we were not able to study the (α + 4n) channel from 8 He and, as can be deduced from Table 1, there is about 102 mb of the interaction cross section in this channel. The data that we shall describe in the following are for the one neutron knock-out and inelastic scattering channels only. 3.1. One-neutron knock-out channels 3.1.1. Fragment momentum distributions In the sudden approximation, the momentum transfer to the (A − 1) system in the oneneutron knock-out reaction is neglected. The high-beam momentum justifies the use of this

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Fig. 2. Transverse momentum distribution in one dimension of 5 He (upper panel) and 7 He fragments (lower panel) after neutron knock-out in a carbon target of 240 MeV/u 6 He and 227 MeV/u 8 He. The dotted line for 5 He shows the prediction in the transparent limit of the Serber model based on a 6 He wave function obtained in three-body microscopical calculations [17], and for 7 He, the predictions of the transparent limit of the Serber model based on the 8 He wave function from a five-body cluster-orbital shell-model approximation [18]. The solid lines are the results of calculations using the asymptotic single-neutron wave function with a cylindrical cut with radius Rcut = 3.1 fm and Rcut = 2.5 fm, for 6 He and 8 He, respectively (see text).

assumption which leads to the resulting momentum transferred to the fragment (pf ) being equal to the momentum of the stripped neutron in the projectile but with opposite direction (pn = −pf ) in the projectile rest frame. The momentum distribution of the fragment is thus mainly determined by the internal momentum distribution of the removed neutron in the projectile, which in turn is determined by the projectile ground-state wave function. We did not observe any essential difference between the momentum distributions in transverse and longitudinal directions. Figure 2a shows the 5 He transverse momentum distribution obtained from the sum of α and neutron momenta, while Fig. 2b shows the same type of data for 7 He constructed from the measured 6 He − n events. The full widths at half maximum are Γ (5 He) = 128 ± 3 MeV/c and Γ (7 He) = 156 ± 5 MeV/c. The corresponding momentum distributions were first calculated in the transparent limit of the Serber model [16]. The results from these calculations are shown as dotted lines in Fig. 2. For the neutrons in 6 He, the wave function was taken from a microscopic three-body

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calculation [17] giving Γ = 170 MeV/c. The discrepancy between this number and the experimental one is due to the fact that the calculation does not take the peripheral nature of the process into account since the Fourier transform of the entire wavefunction has been used. If the Fourier transform of the remaining part of the wavefunction is employed instead, the distribution of the fragments will be more narrow. For the 8 He case, the wave function was taken from the five-body cluster-orbital shell-model approximation [10,18] resulting in Γ = 233 MeV/c. The 8 He wave function was obtained using oscillator wave functions. The asymptote of this function does not correspond to the realistic case with zero potential at infinity and, thus, the function cannot be used in the models where mainly the asymptotic behavior of the function determines the momentum distributions. Again, we get a prediction which is much broader than the experimental one, and we can use similar arguments as above to explain the difference in momentum widths. We have also performed calculations in the opaque Serber model (full drawn curves in Fig. 2) using first spherical Hankel functions for the asymptotic part of the valence neutron wavefunction following the prescriptions given in Ref. [19]. The model satisfactorily reproduces the momentum distributions of the fragments in the fragmentation of heavy ions at relativistic energies on light targets. Instead of taking a Fourier transform of the full wave function, the Fourier transform of a cutoff portion of it was used [20,21]. The requirement of fragment survival was imitated by a cut in the wave function. The distortion from the target was taken into account by a cylindrical shape (with radius Rcut ) of the cuts — the knocked-out neutron should not occupy the space close to the trajectory of the fragment. The momentum distributions were computed by numerical integration. The calculated momentum distributions in longitudinal and transverse directions are very similar, as is also observed experimentally. The experimental momentum distributions were then fitted by varying the Rcut parameter and the best fits were obtained with Rcut = 3.1 fm and 2.5 fm for 6 He and 8 He, respectively. Starting from these values, we make a simple estimate of the neutron knock-out cross section using the following expression: σ−1n = σT hniP (Rcut ),

(1)

where σT is total cross section for free neutron–target interaction [23], P (Rcut ) is the probability to find a p3/2 neutron in the projectile outside the cylindrical cut, Rcut , and hni is the mean number of neutrons in the p3/2 -shell. In a shell model the hni values depend on the coupling scheme and lie between the jj and LS coupling limits. For 6 He, the accepted value is hni = 2. For 8 He, we have used hni = 4, a choice assuming jj coupling. Note, that LS coupling results in hni = 1.3 for 6 He and 2.5 for 8 He [24]. The Rcut values were taken from the fit to the corresponding momentum distributions (see above). P (Rcut ) was obtained by integration of the squared single-neutron wave function |ψ(r)|2 . The ψ(r) functions were calculated by solving the Schrödinger equation with Gaussianshaped potentials. The radial parameter of the potential was fixed by the known r.m.s. radii of 6 He and 8 He (2.48 fm for 6 He and 2.52 fm for the 8 He [26]) while the potential depths were chosen to reproduce the known one-neutron separation energies (1.86 MeV for 6 He and 2.58 for the 8 He). The results of the calculations as given in Table 2 are in

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Table 2 Calculated and experimental one-neutron knock-out cross sections, including parameters relevant in the calculations (σT is taken from [23]) exp

Projectile

σT (mb)

Rcut (fm)

P (Rcut ) (fm)

hni

calc (mb) σ−1n

σ−1n (mb)

6 He

278 ± 6 280 ± 6

3.1 2.5

0.202 0.282

2 4

111 316

127 ± 14 129 ± 15

8 He

satisfactory agreement with the experimental σ−1n value for 6 He. However, the calculations for 8 He gave a σ−1n value which is significantly larger than that measured in the neutron knock-out channel. The best agreement between the model and experiment is obtained with hni smaller than 2, which is below the lower limit expected from the LS coupling. The most plausible explanation for a small hni is a significant component of 6 He∗ + 2n in the 8 He ground state wavefunction but contributions from higher shells would also reduce the value. 3.1.2. Relative energy spectra The distribution of relative energy between the charged fragment and the neutron, obtained from invariant mass spectra, is calculated from the measured relative momentum, pfn , with Efn =

mf + mn 2 p 2mf mn fn

(2)

and shown for 5,7 He in Fig. 3. The 5 He data in the upper part of the figure are well described in a model assuming sequential fragmentation of 6 He [13,22] through the 5 He(3/2− ) resonance. The estimated small contribution from the broad 5 He(1/2− ) resonance [5] is not shown in the spectrum. The solid line displays the result of a Monte Carlo calculation employing the instrumental resolution and known resonance parameters of 5 He. The relative energy spectrum of the (6 He − n) system is shown in the lower part of Fig. 3. A fit using a pure p3/2 resonance at an energy Er = 0.44 MeV and a width Γ = 0.16 MeV [27] resulted in the distribution shown by a dashed line. It describes the maximum of the spectrum well but decays too fast towards higher energies. This tail is most likely due to contributions from higher shells. In earlier work an excited state in 7 He was observed at an energy of about 3.2 MeV above the n + 6 He threshold [28–30]. This state was first associated with a neutron in the p1/2 -orbital around 6 He in the ground state [29]. It has, however, been shown that the observed resonance mainly decays into 3n + 4 He [30]. Based on this the resonance was interpreted as a neutron in p1/2 -state coupled to the first excited 2+ -state in 6 He. The position of the 7 He(1/2− ) resonance with a neutron in p1/2 state coupled to the 6 He(g.s.) might then expected at about 2 MeV below this resonance. A good fit to the data is obtained if we assume an additional contribution coming from a resonance with resonance energy of 1.2 ± 0.2 MeV and resonance width 1 ± 0.2 MeV. The width of this resonance is close to the single particle limit for a neutron in the l = 1

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Fig. 3. The upper panel displays the relative energy spectrum of the α − n system after breakup of 240 MeV/u 6 He. Experimental data are shown as open circles. The solid line results from a Monte Carlo calculation in a sequential-fragmentation model [13]. In this calculation, a p-wave resonance with I π = 3/2− (Er = 0.77 MeV, Γ (ε) = 0.64 MeV and εr = 0.96 MeV [25]) was assumed. The lower panel shows the spectrum of the 6 He − n system after breakup of 227 MeV/u 8 He. The data points are plotted as open circles. The solid line is the result of a Monte Carlo calculation in the sequential-fragmentation model under the assumption of contributions from two p-wave resonances with I π = 3/2− at Er = 0.44 MeV (Γ = 0.16 MeV), and I π = 1/2− at Er = 1.2 ± 0.2 MeV (Γ = 1.0 ± 0.2 MeV). The dashed and the dotted lines display separate contributions of the two resonances.

orbital [31]. We therefore interpret it as due the the p1/2 -state. This I π = 1/2− resonance contributes to 40 ± 5% to the one-neutron knock-out channel. The present data on the 7 He momentum distribution and its relative energy spectrum implies that the 0p1/2 -shell plays an important role in the 8 He ground state. We note that earlier calculations [18,32,33] assumed that the effect of p1/2 -shell can be neglected in the 6−8 He isotopes. However, one may expect that the neutron knock-out from 8 He has a large probability of going to the 6 He(2+ ) + n channel even when the neutron is stripped from the 0p3/2 -shell as indicated by the 102 mb excess of the interaction cross section discussed above.

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The spectroscopic factors for the different configurations in 8 He, as deduced from the experimental partial cross sections in one-neutron knock-out channels, are: 45% (102 mb) for 6 He∗ + 2n(p3/2, p1/2 ), 33% (76 mb) for 6 He + 2n(p3/2) 22% (51 mb) for

and

6 He + 2n(p 1/2 ).

We thus observe the strongest contribution from the 6 He∗ + 2n configuration. This is in line with the assumption made for the model using a pure jj coupling presented in [10,11]. 3.1.3. Spin alignment The distributions of the directions of the relative momentum pfn on the polar angle ϑ are shown in Fig. 4 (the angle ϑ is defined as the angle between the fragment momentum, p5,7 He , and relative momentum p4,6 He−n ). A large spin alignment is observed for 5 He and the data are described by introducing an anisotropy of the decay products relative to the 5 He momentum. The correlation function [34] was found to have the form W (ϑαn ) ∼ 1 + 1.50(3) cos2 (ϑαn ).

(3)

The 7 He case displayed in the lower part of Fig. 4 shows a similar symmetric distribution but with a smaller anisotropy term W (ϑ6 He−n ) ∼ 1 + 0.7(1) cos2 (ϑ6 He−n ).

(4)

The complicated structure of 8 He gives significant contributions to the 3n + α channels even in a sudden one-neutron knock-out reaction. The four channels:

8 He → 6 He + n(3/2− ) − n, 8 He → 6 He + n(1/2− ) − n,

8 He → 6 He∗ + n(3/2−) − n, and 8 He → 6 He∗ + n(1/2− ) − n, strongly compete. Since they are not orthogonal, a coupling of them may result in a suppression of anisotropy of the measured angular distribution. This result is a challenge for more detailed theoretical investigations. 3.2. Inelastic scattering channels We now turn to the inelastic excitations of the projectiles into continuum states by selecting events where two neutrons are registered in coincidence with the residual charged fragment. Up to an excitation energy of about 4 MeV, the two neutrons fall within the acceptance of the LAND detector. Towards higher energies, the efficiency falls gradually [14], and the data have been corrected accordingly. 3.2.1. Excitation energy spectra The excitation energy spectrum as determined from the measured momenta of α and neutrons after inelastic excitation of 240 MeV/u 6 He is shown in the upper part of Fig. 5. The most striking feature is the sharp peak at an excitation energy corresponding to the known 2+ state in 6 He at 1.797 MeV (Γ = 0.113 MeV). The broad

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Fig. 4. Upper part: Angular distribution of the pαn vector vs. polar angles (ϑαn ) in a coordinate system with the z-axis parallel to the direction of the p5 He momentum. The solid line is the result of a Monte Carlo calculation with an anisotropy of the 5 He decay products described by a correlation function W (ϑαn ) = 1 + 1.5(3) cos2 (ϑαn ). The lower part shows the angular distribution of the p7 He−n vector vs. polar angles (ϑ6 He−n ) in a coordinate system with the z-axis parallel to the direction of the p7 He momentum. The solid line is the result of a Monte Carlo calculation with an anisotropy of the 7 He decay products described by a correlation function W (ϑ6 He−n ) = 1 + 0.7(1) cos2 (ϑ6 He−n ).

distribution towards higher energies is due to nonresonant electric dipole and quadrupole excitations [14,35]. The present experimental knowledge about excited states below 5 MeV in 8 He is summarized in Table 3. From these data one might conclude that 8 He has two resonances below 5 MeV, one in the energy interval from 2.6 MeV to 3.6 MeV and the other between 4.0 MeV and 4.6 MeV. The low-energy resonance has been interpreted as the

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Fig. 5. Upper part: excitation energy spectrum reconstructed from measured momenta of the two neutrons and the α-particle after dissociation of 240 MeV/u 6 He in a carbon target. The energy Ecnn denotes the energy above the two-neutron separation threshold. Data points are shown as open circles with error bars. The solid line represents a Monte Carlo simulation assuming a 2+ state in 6 He at an excitation energy of 1.797 MeV (Γ = 0.113 MeV). The lower part shows the excitation energy spectrum reconstructed from measured momenta of the two neutrons and 6 He after dissociation of 227 MeV/u 8 He in a carbon target. Data points are shown as open circles with error bars. The solid line represents a Monte Carlo simulation assuming a 2+ resonance at an excitation energy of 2.9 ± 0.2 MeV (Γ = 0.3 ± 0.3 MeV) and a resonance at 4.15 ± 0.20 MeV (Γ = 1.6 ± 0.2 MeV). The dashed and the dotted lines display separate contributions of the two resonances.

first excited 2+ state, which is supported by the measured differential cross section for inelastic scattering on a hydrogen target [36]. The nature of the resonance around 4 MeV is not known.

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Table 3 Experimentally determined excited states in 8 He. Excitation energies E ∗ and resonance widths Γ are given in MeV Ref. [28] E∗

Γ

Ref. [37] E∗

2.8(4) 4.4(2)

1.8(2)

Γ

Ref. [38] E∗ 1.3 2.6(3) 4.0(3)

Ref. [39]

Γ

E∗

1.0(5) 0.5(3)

3.59(6) 4.54(15)

Ref. [40] Γ

E∗

Γ

0.5 0.70(25)

3.57(12)

0.50(35)

Here, we investigate our data for 8 He into the 6 He + 2n channel of which the excitation energy spectrum is shown in the lower part of Fig. 5. In this case, there is no broad tail towards higher energies. An explanation for this observation could be either a suppression of the high-energy strength due to a competition with the 8 He → α + 4n channel (Q = −3.111 MeV) or the presence of one broad or several overlapping resonances. The experimental distribution may, in principle, be treated as one single broad resonance. However, the statistical evidence of a narrow structure at low energy and the existing experimental information on 8 He levels which was discussed above, indicate that the most plausible explanation is the presence of two overlapping resonances. This interpretation is also supported by the following two observations: – the width of the observed structure is at least twice as large as expected for any p-states from single-particle limit and it can therefore hardly be due to one single 2+ state; – the cross section is about 30 mb (the same as for excitation of 6 He in the entire interval from 0 up to 10 MeV) which seems to be too large for the excitation of one single 2+ state. The cross-section value indicates that this state would exhaust a very large fraction of the sum-rule strength. The solid line in the figure correspond to a Monte Carlo calculation using two Breit– Wigner shaped resonances. The fit to the spectrum resulted in the position of the first resonance at 2.9 ± 0.2 MeV (Γ = 0.3 ± 0.3 MeV) and the second resonance at 4.15 ± 0.20 MeV (Γ = 1.6 ± 0.2 MeV). Note, that the parameters of the high energy resonance are in good agreement with those obtained in the stopped-pion-absorption experiment [28] and the resonance at 2.9 MeV is in good agreement with the results given in Refs. [37,38]. If the lowest excited state corresponds to a neutron in p1/2 -shell and a hole in p3/2 -shell one would expect two states, 2+ and 1+ , close to each other. This expectation comes from recent theoretical predictions using large-basis shell-model calculations which place the 2+ -state at E ∗ ≈ 5 MeV [41], and from quantum Monte Carlo calculations [42] which result in E ∗ = 2.3 MeV. The second excited state is in both calculations a 1+ state at an energy of about 2.5–3 MeV above the 2+ state. The characteristics of the known lowest excited states of the neighboring N = 6 nucleus 10 Be (two 2+ states at 3.37 and 5.96 MeV and a 1− state at 5.96 MeV) confirm the 2+ assignment of the low energy resonance but indicate that the second resonance might be either a second 2+ -state or a 1− state, or an

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overlap of both. The measured angular distribution of the excited 8 He may shed light on the momentum transferred in the reaction and, hence, on the quantum numbers of the unknown state. 3.2.2. Angular distributions in inelastic scattering The sum of momenta (pn1 + pn2 + p6 He ) represents the momentum (p8 He ) of the excited nucleus 8 He. The differential cross section as a function of ϑcm (the angle between the direction of the incoming beam and the center of mass of the outgoing system in the projectile-target CM system) is shown in the lower part of Fig. 6 for the entire excitationenergy interval covered in our experiment. The corresponding differential cross section for 6 He at the excitation energies above the narrow 2+ resonance is shown in the upper part of the figure. The angular distribution in the 6 He case has a peak at small scattering angles. In earlier work [14,35], two possible explanations for the origin of this peak were given: it can be assigned either to a monopole or an electric dipole (Coulomb) excitation. No firm assignment could, however, be made based on the 6 He data alone. Our approach to make a comparative study may solve this problem since 8 He does not have such a peak. The reason for the difference in differential cross section might be due to the different probability of excitation of the corresponding excitation mode. The cross section for electromagnetic dissociation of the projectile is very sensitive to its binding energy since the α-particle in 6 He is bound by 973 keV, while 2.139 MeV is needed to release 6 He from 8 He. The cross section for 8 He dissociation into 6 He + 2n is much smaller than that for 6 He dissociation into α + 2n. Thus, the assumption of the electromagnetic nature of this branch of excitations can explain the observed difference in angular distributions. The difference in Coulomb disintegration of the two nuclei will be discussed in detail in a paper following this [43]. For 6 He the peak was interpreted as due to the first excited 2+ state and thus with a transferred momentum λ = 2. The broad 8 He state at 4.15 MeV contributes to about 80% of the inelastic scattering channel and thus determines the main features of the experimental angular distribution. Does the cross section obtained for excitation of the narrow state at 2.9 MeV in 8 He suggest a quadrupole transition? Since the two states strongly overlap and the contribution from the narrow state is small, the differential cross section for excitation of this state cannot be directly obtained. However, a check based on the absolute value of the cross section can be done by comparing the experimentally and theoretically determined deformation lengths (δ2 ) for the lowest excited 2+ state. The sum-rule limit for quadrupole excitation is given by the following equation [48,49]: δ22 = λ(2λ + 1)

2π h¯ 2 . 3AmE ∗

(5)

The 6 He data on a carbon target result in δ2 = 1.7 ± 0.3 fm for excitation of the first 2+ state [14]. This corresponds to about 2.5–5% of the sum rule. The deformation parameter δ2 = 1.0 ± 0.3 for 0+ → 2+ transition in 8 He was determined from experimental data in

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Fig. 6. Differential cross sections for inelastic scattering in a carbon target of 240 MeV/u 6 He and 227 MeV/u 8 He as a function of the center-of-mass angle. The experimental data for 6 He in the excitation energy interval 2.5–4.5 MeV (see Fig. 5) are compared to calculations in a distorted-wave Born approximation (DWBA). The lines correspond to electric dipole λ = 1 (dotted line) and quadrupole λ = 2 (dashed line) transitions. The solid line represents the sum of these two contributions. The data for 8 He cover the full excitation energy interval (Fig. 5). The dotted line corresponds to a nuclear dipole transition, λ = 1, and the dashed curve represents a DWBA calculation with λ = 2. All theoretical distributions are corrected for the experimental resolution in the experiment.

Ref. [36]. The cross section estimated in the present experiment for inelastic scattering to the 2.9 MeV state is equal to 7 ± 2 mb. Derived from the value of the cross section δ2 = 1.5 ± 0.5 fm is in a reasonable agreement with those based on the data of Ref. [36] and corresponds to 3–10% of the sum rule. Thus the present experimental data for excitation of the 2+ state in 8 He do not contradict to the earlier experiment with 8 He. Moreover, comparison between 6 He and 8 He shows that general features of the excitation of the 2+ state are common for the two nuclei.

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We shall now proceed to the analysis of the 8 He angular distribution, based on the eikonal Born approximation (DWBA) [44]. The same kind of analysis was earlier used to describe the 6 He data [13]. The determination of the transferred angular momentum is based on the fact that positions of the maxima and minima in the angular distribution are determined by the nuclear density distributions in the projectile and the target. The nuclear inelastic-scattering amplitude for multipolarities λ > 0 in the eikonal Born approximation of the deformed potential model is given by: s Z∞ µδ M i (λ − µ)! 0 λ N Jµ (qb0) eiχ(b ) =(b)b db, fλµ (θ ) = √ 2 (λ + µ)! 4π h¯ 0

Z∞ =(b) = −∞





opt

dUN z (b, z) eiql z dz, Pλµ √ dr b 2 + z2

(6)

where M = mp mt /mp + mt is the projectile-target reduced mass, δλ is the deformation length, Pλµ (x) is the Legendre polynomial, Jµ (qb0)qis the Bessel function, q = √ 2Z Z e2 2 ki kf sin(θ/2) is the transferred momentum, b0 = b0 + b02 + b2 with b0 = h¯pβkti and b as impact parameter, ql = ki − kf cos θ is the change in longitudinal component of the momentum. The total eikonal phase is determined by: 1 χ(b) = − h¯ β

Z∞

opt

UN (b, z) dz + χC (b), −∞

χC (b) =

2Zp Zt e2 ln(ki b). h¯ β

(7) opt

The high-energy tρρ approximation for the nuclear part of the optical potential, UN (r), was used: Z∞ h¯ 2 opt ◦ ρt (r0 )ρp (r − r0 ) dr, (8) UN (r) = −2π fNN (0 ) m −∞

(0◦ )

is the forward scattering nucleon–nucleon amplitude obtained by the where fNN optical theorem 1 h¯ 2 fNN (0◦ ) = h¯ σNN (αNN + i), m 2 σNN is the nucleon–nucleon cross section and αNN is the ratio of the real and the imaginary parts of the NN-scattering amplitude. The positions of oscillations do not depend neither on σNN nor on αNN , but both these values influence the absolute values of the cross sections. The σNN and αNN values given in [45] for 200 MeV/nucleon were used in our calculations. The matter-density distribution for 12 C was taken from electron scattering data [46]. The harmonic-oscillator parameterization for 6,8 He, taken from Ref. [7], were used for the nuclear density of the projectile. The results of the calculations for the quadrupole transitions in 6 He and 8 He are shown in Fig. 6 as dashed lines. The predicted peak position is close to the experimental one in both spectra. The 8 He experimental data, however, clearly shows a shift of the peak towards 2π

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smaller angles. The experimental distribution agrees with a calculation assuming a λ = 1 excitation. The best fit to the experimental data was obtained with a deformation length δ1 = 2.6 ± 0.3 fm as shown by the dotted line in the lower part of Fig. 6. Note, that we did not use any free parameter to adjust the position of the peak. This observation leads to the conclusion, that, in contrast to the fragmentation of 6 He, where a quadrupole transition dominates, the dipole mode is the strongest one in the excitation of 8 He. The inelastic scattering, which is described by a one-body operator, will only connect states with wave functions ψA and ψA∗ that have one or more components which differ only in the state of one of the nucleons. Suppose that a nucleon makes a transition between orbitals whose quantum numbers are (l1 = 1, j1 = 3/2) → (l1 = 0, j1 = 1/2). The main configuration of J π = 1− state then corresponds to a hole in the 0p3/2 -shell and a neutron in the 1s1/2 -shell. Thus, due to its position above the 6 He + 2n threshold and a neutron in the s-shell, the state is characterized by extremely large effective spatial size and the corresponding resonance should have a large width of about 10 MeV [47]. The width of the adopted 1− state in 8 He (Fig. 5) is only 1.6 MeV indicating either a collective nature of the state or a mixture with a d-wave. The dipole state is expected to be strongly excited in an electromagnetic interaction. This was observed in the 8 He fragmentation on a lead target [43] which supports our 1− assignment to the resonance at 4.2 MeV.

4. Summary Experimental data on neutron knock-out and diffractive dissociation of 8 He in a carbon target at 227 MeV/u have been discussed in comparison to corresponding data for 6 He. The main conclusions for 8 He are: – The difference of the 8 He and 4 He interaction cross sections of 292 mb exceeds the sum σin + σ−1n + σ−2n by about 100 mb. This excess is due to the breakup into α + 4n and is likely a sign of the five-body character of 8 He. – The momentum distribution of the 7 He fragments in the one-neutron knock-out channel was fitted by varying the Rcut parameter and, in a simple approach, with the number of neutrons in the 0p3/2 -shell assumed to be hni = 4. The cross section σ−1n then appears to be overestimated showing that the ground-state structure of 8 He is more complicated. Configurations with neutrons in the 0p1/2 -shell and 6 He∗ + 2n are expected. – The relative energy spectrum of 7 He (6 He + n) shows a structure that cannot simply be described as sequential decay through the 3/2− ground-state resonance of 7 He. A better description may be obtained assuming an about equal contribution from its 1/2− spin–orbit partner. – The angular distribution of the 7 He momentum vector shows an anisotropy amounting to only about half of that in the 6 He case, which again indicates a more complicated structure of 8 He.

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– The differential cross section as a function of center-of-mass scattering angle in the inelastic channel 6 He + n + n shows a peak at about 30 mrad. This is interpreted as predominant nuclear dipole excitation with a very large cross section. – The corresponding excitation energy spectrum shows a broad distribution up to about 3.5 MeV. This may be interpreted either as a single broad 1− resonance, or a relatively narrow 2+ state and a broader higher-lying excited 1− state. The comparison between the data for 6 He and 8 He has thus shown that the structure of the latter is very complex and supports its description as a five-body system. To fully uncover the nature of this intricate system more precise data are required. In particular, a detection system capable of registering all the fragments in the five-body channel (α +4n) needs to be implemented.

Acknowledgements This work was supported by the BMBF under Contracts 06 DA 820, 06 OF 474 and 06 MZ 864 and by GSI via Hochschulzusammenarbeitsvereinbarungen under Contracts DA RICK, OF ELZ, MZ KRK and partly supported by the Polish Committee of Scientific Research under KBN grant No. 2 PO3B 14418, EC under contract ERBCHGE-CT920003, CICYT under contract AEN92-0788-C02-02 (MJGB) and WTZ under contract RUS 674-98. One of us (B.J.) acknowledges the support through an Alexander von Humboldt Research Award. The authors acknowledge fruitful discussions with Horst Lenske, Sergei Fayans and Leonid Grigorenko.

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