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

Nuclear Physics A 700 (2002) 3–16 www.elsevier.com/locate/npe

8

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

M. Meister a,b , K. Markenroth a , D. Aleksandrov c , T. Aumann d , T. Baumann d,1 , M.J.G. Borge e , L.V. Chulkov c,d , D. Cortina-Gil f,d , B. Eberlein g , Th.W. Elze h , H. Emling d , H. Geissel d , M. Hellström d , B. Jonson a,∗ , J.V. Kratz g , R. Kulessa i , A. Leistenschneider h , I. Mukha b , G. Münzenberg d , F. Nickel d , T. Nilsson j , G. Nyman a , M. Pfützner d , V. Pribora c , A. Richter b , K. Riisager k , C. Scheidenberger d , G. Schrieder b , H. Simon b , O. Tengblad e , 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 Kurchatov Institute, RU-123182 Moscow, Russia d Gesellschaft für Schwerionenforschung (GSI), Planckstrasse 1, D-64291 Darmstadt, Germany e Instituto Estructura de la Materia, CSIC, E-28006 Madrid, Spain f Universidad de Santiago de Compostela, 15706 Santiago de Compostela, Spain g Institut für Kernchemie, Johannes-Gutenberg-Universität, D-55099 Mainz, Germany h Institut für Kernphysik, Johann-Wolfgang-Goethe-Universität, D-60486 Frankfurt, Germany i Instytut Fizyki, Uniwersytet Jagiello´nski, PL-30-059 Kraków, Poland j EP-Division, CERN, CH-1211 Genève 23, Schweitz k Institut for Fysik og Astronomi, Aarhus Universitet, DK-8000 Aarhus C, Denmark

Received 18 June 2001; revised 13 September 2001; accepted 19 September 2001

Abstract Dissociation of a 227 MeV/u 8 He beam in a lead target has been studied in a kinematically complete experiment. The results are compared with similar data from the well-known halo nucleus 6 He. Coulomb–nuclear interference in the inelastic channel gives evidence for a I π = 1− resonance in 8 He at Ex = 4.15 MeV. The deduced B(E1) value of 0.38 ± 0.07 e2 fm2 indicates a uniform distribution of the four neutrons around the α-particle core.  2002 Elsevier Science B.V. All rights reserved. PACS: 27.20.+n; 24.70.+ Keywords: N UCLEAR REACTIONS Pb(8 He, xn6 He), E = 227 MeV/nucleon; Pb(6 He, xnα), E = 240 MeV/nucleon; Measured σ , σ (θ ), σ (E). 8 He deduced resonance energy, B(E1)

* Corresponding author.

E-mail address: [email protected] (B. Jonson). 1 Present address: NSCL, Michigan State University, East Lansing, MI 48824-1321, USA.

0375-9474/02/$ – see front matter  2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 5 - 9 4 7 4 ( 0 1 ) 0 1 3 0 5 - 7

4

M. Meister et al. / Nuclear Physics A 700 (2002) 3–16

1. Introduction Over the past decade, a large number of experiments and theoretical investigations have been devoted to drip line nuclei of the lightest elements. Nuclei showing halo structures and neighboring unbound systems were in the focus [1–3]. Here we present the second of two consecutive papers on 8 He where we compare experimental results with existing data [4,5] for the well-known halo nucleus 6 He. Since 6 He has a relatively simple structure [6], it can be considered as a benchmark nucleus when comparing with nuclei close-by. Similarities and differences in the data help to elucidate the 8 He structure. In a first paper [7] devoted to a comparative study of 8 He and 6 He in nuclear fragmentation reactions, the experimental data on one neutron knock-out and diffractive dissociation of 8 He in a carbon target at 227 MeV/u were presented with the main conclusions: • The interaction cross section for 8 He together with the measured neutron removal channels show evidence for breakup into α + 4n, interpreted as a signature of the five-body character of 8 He. • The cross section for the one-neutron knock-out channel shows evidence for configurations with neutrons in the 0p1/2 shell as well as a core excited configuration, 6 He* + 2n, in the 8 He ground state. • The 7 He fragment was observed in the 3/2− ground state, together with an approximately equal contribution from its first excited state, I π = 1/2− (see also Ref. [8]). • The angular distribution of the 7 He decay products relative to the 7 He momentum vector shows an anisotropy amounting to about half of the value observed for 5 He, again indicating a more complicated structure for 8 He as compared to that of 6 He. • The excitation-energy spectrum 6 He + n + n reveals a broad distribution peaked at around 3.6 MeV interpreted as an overlap of a relatively narrow 2+ state at 2.9 MeV and a broad peak from a higher excited state at 4.15 MeV. • The differential cross section as a function of the center-of-mass angle gives an indication that the state at 4.15 MeV could have spin–parity I π = 1− . The probability to excite this state was found to be surprisingly large. The reactions with the lead target, discussed here, are expected to be characterized mainly by electromagnetic breakup in the virtual-photon field of the target [4]. The comparison of nuclear and electromagnetic interactions eliminates effects caused by the reaction mechanism and allows to extract structural information. As mentioned above, one interesting observation from the carbon target was the identification of a low-energy 1− resonance. If interpreted correctly, it would resemble a similar result for 11 Li from reactions with hadronic probes [9–11], which was interpreted as an indication of a resonance associated with a soft dipole resonance [12]. If this resonance is easily excited by a nuclear interaction it would be expected to be a dominant mode in a Coulomb excitation process. However, some controversial results on the excitation of the 11 Li dipole state in a Coulomb field have been obtained [13–15]. Therefore one of the key points in this paper is to investigate the Coulomb excitation of this 1− state in 8 He.

M. Meister et al. / Nuclear Physics A 700 (2002) 3–16

5

2. Experimental method The experiments on 227 MeV/u 8 He and 240 MeV/u 6 He were carried out at the ALADIN–LAND setup at GSI. Detailed descriptions of the experiment have been given earlier [4,5] and we only summarize the main features. The radioactive beams were produced in fragmentation reactions of 18 O (340 MeV/u) from the heavy-ion synchrotron, SIS, impinging on a 8 g/cm2 Be production target. The beam was then selected by magnetic analysis in the fragment separator, FRS, and directed towards a reaction target placed directly in front of the large-gap dipole magnetic spectrometer (ALADIN). In this experiment Pb targets of thickness 0.387 g/cm2 and 0.87 g/cm2 were used for 8 He and 6 He, respectively. The selected events for the 8 He breakup were coincidences between 6 He and neutrons, detected in the large area neutron detector, LAND, while α–neutron coincidences were selected for 6 He.

3. Reaction mechanisms and cross sections In the present experiment, the breakup channels of 8 He into 6 He + n or 6 He + 2n were investigated. Due to the limited acceptance the α + 4n channel was outside the range of the present setup. The selection of events for the fragmentation channels was made as in the previous paper [7]: • Inelastic scattering, σin : events with two neutrons detected in coincidence with a 6 He fragment. The reaction mechanism might be either diffractive dissociation or inelastic scattering to separate resonance states. • Neutron knock-out, σ−1n : events with one neutron detected in coincidence with the charged fragment. Such a reaction corresponds to a one-neutron knock-out or oneneutron stripping mechanism. • Two-neutron knock-out, σ−2n : events where only the charged fragment is detected. The measured cross sections for these three channels are given in Table 1 for the Pb and C targets. The second column (σiN ) is the nuclear part of the interaction cross sections, based on measurements at 790 MeV/u with a carbon target [16] and scaled to a lead target and to the energy of the present experiment. The scaling was done on the basis of Glauber calculations [17] using the experimentally determined matter density distribution for 12 C [18] and 208 Pb [19]. The results for the carbon target were taken from Ref. [7]. Let us first compare the 6 He data for C and Pb targets. For nuclear fragmentation of the halo nucleus 6 He the following relation [20,21] between the different reaction channels is fulfilled:

  N N + σ−2n = σiN 6 He − σiN 4 He , (1) σinN + σ−1n i.e. the difference between the interaction cross section for the halo nucleus and its core (∆ in Table 1) equals the summed cross sections for the fragmentation channels. First, note that the ratio R = ∆(208Pb)/∆(12 C) is very close to the the ratio between the nuclear radii for the two targets, which reflects the surface nature of the nuclear fragmentation process.

6

M. Meister et al. / Nuclear Physics A 700 (2002) 3–16

Table 1 Cross sections for fragmentation of 6 He at 240 MeV/nucleon and 8 He at 227 MeV/nucleon in Pb and C targets Proj. (target) σiN (mb) 4 He (Pb) 6 He (Pb) 8 He (Pb) 4 He (C) 6 He (C) 8 He (C)

2440 2939 3137 457 ± 5 656 ± 5 749 ± 6

σin (mb)

σ−1n (mb)

σ−2n (mb)

Σ (mb)

650 ± 110 293 ± 49

320 ± 90 328 ± 90

180 ± 100 ∼ 36

1150 ± 90 657 ± 49

30 ± 5 32 ± 5

127 ± 14 129 ± 15

33 ± 23 29 ± 23

190 ± 27 190 ± 27

∆ (mb)

499 697 199 ± 7 292 ± 8

σiN is the total interaction cross section (see text), Σ = σin + σ−1n + σ−2n and ∆ = σiN (6,8 He) − σiN (4 He).

The last two columns in Table 1, Σ and ∆, should thus according to Eq. (1) be equal. For the Pb target, however, we observe an excess of 651 mb. This number is very close to σin and shows the dominance of Coulomb dissociation in this channel. The Coulomb dissociation cross section may also be obtained from the difference between σin for the lead target (650 ± 110 mb in Table 1) and σin for the carbon target scaled with R, which gives a similar result of about 575 mb. A similar analysis of the 8 He data may be done but the contribution from channels with 4 He fragments (σα ), which were not detected in this experiment, makes the situation more complicated. Here, we may also use a relation similar to Eq. (1), which is based on theoretical [20] and experimental work [21]:

  N N σinN + σ−1n + σ−2n + σαN = σiN 8 He − σiN 4 He . (2) The difference between σin for the lead target (293 ± 49 mb in Table 1) and σin for the carbon target scaled with R shows that the Coulomb dissociation cross section is about 217 mb, thus significantly lower than in the 6 He case. The Coulomb dissociation cross section of 8 He can also be obtained from the difference between Σ and ∆ in Table 1. One finds, however, that the sum of the cross sections with 6 He in the exit channel is smaller than the expected nuclear contribution (∆ in Table 1). This discrepancy may be attributed to the σα channel, which in Ref. [7] was found to be 102 mb for the C target. If this number is scaled with R we get Σ = 920 mb for the Pb target and a Coulomb dissociation cross section of 223 mb, which is in perfect agreement with the value given above. The one-neutron removal cross sections, σ−1n , for 6 He and 8 He are very close to each other. Furthermore, the σ−1n cross sections for the Pb target are almost identical to the C results scaled with R on the basis of Glauber calculations. This shows that the Coulomb contribution is negligible in the one-neutron knock-out channel for 6 He as well as for 8 He. Calculations for the inelastic scattering (σin ) in an eikonal DWBA model, as used in our previous paper [7], result in nearly the same ratio of σin for different targets as was obtained from Glauber type of calculations. This scaling factor is close to the ratio of the

M. Meister et al. / Nuclear Physics A 700 (2002) 3–16

7

nuclear radii for the two targets. Note that several different selections of the scaling factor can be found in the literature. While some of them assume that the nuclear contribution is roughly proportional to the sum of projectile and target radii [22,23], others demand a significantly larger nuclear contribution for heavy targets [24,25]. In the next section it will be shown that DWBA calculations give an independent estimate on electromagnetic dissociation cross sections with values close to those given in this section.

4. Inelastic excitations This chapter will be devoted to a discussion of inelastic excitations of the projectiles into continuum states. These channels were obtained by selecting events where two neutrons are registered in coincidence with the residual charged fragment. All the measured distributions have been corrected for efficiency which includes effects due to the neutron tracking routine and the restricted acceptance of the experimental set-up. For a detailed discussion, see Refs. [4,26]. 4.1. Angular distributions The sum of the three momenta, p n1 + p n2 + p4 He (pn1 + p n2 + p 6 He ), represents the total momentum p 6 He (p8 He ) of the 6 He (8 He) system. The differential cross section as a function of the angle between the direction of the incoming beam and the center of mass of the outgoing system in the projectile–target CM system (ϑcm ) is shown in the upper part of Fig. 1 for the entire excitation-energy interval covered in our experiment (0–7 MeV) for 6 He. The corresponding differential cross section for 8 He is shown in the lower part of the figure. The distributions were analyzed in the eikonal DWBA model [27], which was also employed in the analysis of the corresponding data with a C target [7]. The calculated distributions are obtained under the assumption that the projectile (p) is excited in the Coulomb field of the target (t) to an excitation energy Ex while the target remains in its ground state. The direction of the projectile is along the z-axis with impact parameter b. In first-order perturbation theory the Coulomb inelastic-scattering amplitude is then [28]      ∞ Zt ki kf B(Eλ) µ Ex λ Ex b iχ(b )

Gλµ Jµ (qb )Kµ b db, (3) fC (θ )λµ = i e γβ hγβ h¯ ¯ 0

 where q is the transferred momentum, b = b0 + b02 + b2 with b0 = 2Zp Zt e2 /(h¯ β), and Gλµ (1/β) are the Winther–Alder relativistic functions [29]. The total eikonal phase is 1 χ(b) = − h¯ β

∞

opt

UN (b, z) dz + χC (b) with χC (b) = −∞

2Zp Zt e2 ln(kb). h¯ β

(4)

The high-energy tρρ approximation for the hadronic part of the optical potential, U (r), was used

8

M. Meister et al. / Nuclear Physics A 700 (2002) 3–16

Fig. 1. Differential cross sections for inelastic scattering of 240 MeV/u 6 He and 227 MeV/u 8 He in a lead target as a function of the center-of-mass scattering angle. The experimental data for 6 He are shown in the upper part of the figure and are compared to calculations in distorted-wave Born approximation (DWBA). The lines correspond to electric dipole (l = 1 Coulomb excitation without nuclear contributions. The dashed line shows the results of DWBA calculations and the solid line is corrected for resolution and finite acceptance. The data for 8 He are shown in the lower part of the figure. The dotted line displays the DWBA calculations for electric dipole (l = 1 Coulomb excitation giving a cross section of 160 ± 25 mb resulting in B(E1) = 0.38 ± 0.07 e2 fm2 . The dashed line shows the results of DWBA calculations with both nuclear and Coulomb contributions to the fragmentation and the solid one is corrected for resolution and acceptance.

h¯ 2 opt UN (r) = −2π fNN (0◦ ) m

∞

ρt (r )ρp (r − r ) dr,

(5)

−∞

where fNN (0◦ ) is the forward scattering nucleon–nucleon amplitude obtained from the optical theorem 2π(h¯ 2 /m)fNN (0◦ ) = 1/2h¯ σNN (αNN + i), where σNN is the nucleon– nucleon cross section and αNN the ratio of the real to the imaginary parts of the NN-

M. Meister et al. / Nuclear Physics A 700 (2002) 3–16

9

scattering amplitude. The σNN and αNN values given in [30] for 200 MeV/nucleon were used in the calculations. The matter-density distribution for 208 Pb was taken from high-energy proton-scattering data [19]. The harmonic-oscillator parameterization for 6,8 He, taken from Ref. [21], were used for the nuclear density of the projectile. This potential was checked by a comparison with experimental data on 12 C + 208 Pb elastic scattering at an energy close to the one in the present experiment [31]. A calculation for 6 He scattering assuming a dipole excitation mode is shown as the dashed line in the upper part of Fig. 1. The calculations were performed for E ∗ = 3.6 MeV, the mean excitation energy of the experimental distribution [4] in the energy range 0–10 MeV. The solid line represents the same calculation where experimental resolution and effects due to the finite acceptance are taken into account [5]. The calculation shown in Fig. 1, which assumes pure electromagnetic dissociation, reproduces the shape of the angular distribution well. The normalization to the experimental cross section at small angles gives σin = 600 mb and the corresponding strength B(E1) is equal to 1.4 ± 0.2 e2 fm2 . This value is in good agreement with the earlier result obtained from an integration of the experimental strength function [4] B(E1) = 1.2 ± 0.2 e2 fm2 . The calculated distribution obtained with the same procedure for 8 He, shown as a dotted line in the lower part of Fig. 1, is much steeper than the experimental distribution. One may, therefore, assume that the large-angle part has a significant contribution of nuclear origin, since this was not included in the calculation. An estimate of the Coulomb part may be obtained by normalizing the calculated distribution to the experimental one at small angles (5–10 mrad). This results in a cross section for Coulomb disintegration of 160 ± 25 mb, which is close to the two estimates given in Section 3, and a B(E1) strength of 0.38 ± 0.07 e2 fm2 . The calculations were done for the resonance energy of the adopted 1− state [7]. Note, that increasing the resonance energy by 1 MeV results in an increased B(E1) by about 20%. A recent measurement by Iwata et al. [23] performed with a beam energy of 24 MeV/u, however, resulted in a B(E1) value that is more than four times smaller. The broad resonance observed at Ex = 4.15 MeV in the 6 He + 2n relative energy spectrum with a carbon target (see Fig. 5 in Ref. [7]) was assigned to have I π = 1− . Since Coulomb excitation from the ground state would result in a final state with the same spin–parity one would expect interference between Coulomb and nuclear dipole transitions amplitudes to this state. To check this, the nuclear amplitudes were calculated using the DWBA approach [27], also described in Ref. [7], where the nuclear part of the optical-model potential is given by Eq. (5). The deformation parameter used in the calculation of nuclear disintegration in the Pb target (δ1N = 2.6 ± 0.3 fm) was determined from the analysis of the experimental data obtained with the C target [7]. The Coulomb and nuclear amplitudes were then added coherently: dσ /dΩ = kf /ki |fC (θ ) + fN (θ )eiφ |2 . The best fit to the data, with B(E1) fixed to 0.38 e2 fm2 , was obtained with φ = π/2. However, with B(E1) as a free parameter, a slightly better fit might be obtained resulting in a different B(E1), but this is within the error bars.

10

M. Meister et al. / Nuclear Physics A 700 (2002) 3–16

The result is shown in the lower part of Fig. 1 as a dashed line. The solid line, corrected for resolution and finite acceptance, provides a reasonable fit to the data. It is important to note, that neither Coulomb nor nuclear excitations separately can reproduce the experimental data. Moreover, the interference results in a shift of the oscillations towards the positions of the experimental distribution, which also can be seen as an evidence for the Coulomb–nuclear interference. These calculations also show that one cannot unambiguously subdivide σin into nuclear and Coulomb parts. We may thus conclude that the observation of Coulomb–nuclear interference provides further support for the I π = 1− resonance reported in Ref. [7]. The deformation length (δ1C ) which governs the Coulomb dissociation can be obtained from 3 NZ 2 2 e δ1 . B(E1) = 2π A 

(6)

The resulting value is δ1C = 0.9 ± 0.1 fm which is smaller than the corresponding value for the nuclear deformation length, δ1N = 2.6 ± 0.3 fm, obtained in Ref. [7]. A Coulomb field, being of long range, measures the nuclear transition densities as a whole with a slowly varying weight function, namely r λ Yλ,µ (ϑ, ϕ). The cross section for the electromagnetic dissociation is then proportional to the average squared shift between the center of the nuclear charge distribution and the center of the nuclear mass. On the other hand, the short-range hadronic interactions are more sensitive to the spatial distribution of individual nucleons, especially at the surface of the nucleus. A large spatial separation of a neutron from the rest of the nucleus combined with a small shift between charge and mass centers results in a suppressed Coulomb disintegration and an enhanced nuclear dipole transition. This explains the difference between the two obtained deformation lengths. As mentioned above, the dipole strength for electromagnetic dissociation is proportional to the squared mean distance between the center-of-mass of the core and the whole nucleus (rc . This fact was used in Ref. [4], where (rc = 1.12 ± 0.13 fm was obtained for 6 He (where the core is an α particle). Recently, the effective core radii in 6 He (rch = 1.88 ± 0.12 fm) and in 8 He (rch = 1.55 ± 0.15 fm) were evaluated in high-energy proton-scattering experiments [33]. If one √ 2 4 6 8 accepts He as the core for both He and He, then the equation (rc = rch − rα2 results in (rc = 1.14 ± 0.12 fm and (rc = 0.43 ± 0.54 fm for 6 He and 8 He, respectively. The value of (rc for 6 He is in a good agreement with an estimate made in Ref. [4]. The (rc value for 8 He together with the non-energy-weighted cluster sum rule [4] gives an upper limit for the dipole strength B(E1)
0.17 ± 0.44 e2 fm2 . The smaller B(E1) value for 8 He as compared with that for 6 He may be explained as due to a more uniform distribution of neutrons around the core. The value rch = 1.76 ± 0.03 fm derived from interaction cross sections [21] results in B(E1)
0.42 ± 0.14 e2 fm2 . A calculation in the framework of the five-body model for

M. Meister et al. / Nuclear Physics A 700 (2002) 3–16

11

given in Ref. [32] 2 gives B(E1)
0.72 e2 fm2 . Our experimental value B(E1) = 0.38 ± 0.07 e2 fm2 thus seems to exhaust the full dipole strength of the relative motion between the 4 He core and the valence neutrons. Note, that the cross section which was analyzed corresponds to data with 6 He in the exit channel. The nuclear fragmentation of 8 He shows that channels with 4 He fragments also give a large contribution. The experimental B(E1) value indicates that the electromagnetic dissociation of 8 He into 4 He fragments is not significant. The final conclusion on the importance of the α + 4n channel can, however, only be made when the channel with 4 He fragments is experimentally available. Up to now we did not use any assumption on the shape of the strength distribution. The energy-weighted cluster sum rule gives access to the energy dependence of the strength. The 6 He data showed that the energy-weighted cluster sum rule is fully exhausted for E ∗
10 MeV [4]. Under the assumption that the 8 He dipole strength function is described by a Breit–Wigner shape with the adopted parameters of the 1− resonance results in an energyweighted strength of 1.85 ± 0.35 e2 fm2 MeV. This value corresponds to about 25% of the energy-weighted cluster sum rule and indicates that additional contributions must be expected at higher energies. Additional information can be obtained from an analysis of the measured excitationenergy spectra as discussed in the following section. 8 He

4.2. Excitation-energy spectra The spectrum of excitation energies above the three-body decay threshold Ecnn or, in other words, the distribution of the total kinetic energy in the three-body system f + n + n (here f is either 4 He or 6 He) was calculated from the relative momentum p 2nn between two neutrons and the relative momentum p f −nn between the center-of-mass of the two neutrons and a charged fragment Ecnn =

2mn + mf 2 1 2 p + p . mn nn 4mf mn f −nn

(7)

The distribution of Ecnn as determined from the measured momenta of the α particle and the two neutrons after fragmentation of 240 MeV/u 6 He in a Pb target is shown in the upper part of Fig. 2. The dashed line represents the contribution from nuclear excitation obtained from the C data and scaled to Pb. The broad distribution shown by the solid line is the result of a calculation based on the experimentally determined dipole strength function dB(E1)/dEx (Fig. 4 in Ref. [4]). The nuclear contribution is small and an overall agreement with the experimentally obtained distribution can be achieved by assuming pure electromagnetic dissociation. The spectrum of the excitation energies above the three-body threshold for 8 He disintegration in Pb into the 6 He + 2n channel (Q = −2.14 MeV) is shown in the lower part of Fig. 2. This case, as discussed above, is characterized by a significant contribution 2 The r values adopted by the authors of the respective publications were: 1.49 ± 0.01 fm [33], 1.63 ± 0.03 α [21] and 1.47 ± 0.01 fm [32].

12

M. Meister et al. / Nuclear Physics A 700 (2002) 3–16

Fig. 2. Top: excitation-energy spectrum above the three-body decay threshold reconstructed from measured momenta of the two neutrons and the α particle after dissociation of 240 MeV/u 6 He in a lead target. Data points are shown as open circles with error bars. The dashed line represents the estimated nuclear contribution to the measured cross section, while the solid line corresponds to electromagnetic dissociation calculated with the experimentally derived strength function [4]. Bottom: 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 lead target. Data points are shown as open circles with error bars. The dashed line represents the estimated nuclear contribution to the measured cross section, while the solid line corresponds to an electromagnetic dissociation, calculated with a Breit–Wigner distribution (E ∗ = 4.15 MeV, Γ = 1.6 MeV).

of nuclear fragmentation, which is shown as a dashed line. The spectrum was interpreted in Ref. [7] as an overlap of a relatively narrow 2+ state at 2.9 MeV and a broad peak from an excited 1− state at 4.15 MeV. The possible influence of the α + 4n threshold (Q = −3.111 MeV) was discussed in [7]. The data presented here are, however, in support of the assignment of a 1− state. The cross section for the excitation of the 2+ state with a carbon target was found to be 7 ± 2 mb. One would expect that also in a lead target this state is excited mainly by

M. Meister et al. / Nuclear Physics A 700 (2002) 3–16

13

nuclear excitation, with a cross section of approximately 17 mb as estimated by scaling. Using the same reasoning, the broad resonance at 4.15 MeV will get a cross section of approximately 63 mb for nuclear excitation on a lead target. The dipole resonance has the largest probability to be excited by electromagnetic interactions, while the electromagnetic quadrupole transition is expected to be negligible [34]. We therefore performed a calculation for Coulomb dissociation assuming a Breit– Wigner shaped strength function (shown as the solid line in the lower part of Fig. 2) by using the resonance parameters obtained from the carbon-target measurements (Ex = 4.15 ± 0.2 MeV, Γ = 1.6 ± 0.2 MeV, Ref. [7], Fig. 5) multiplied with the corresponding virtual-photon spectra [35]. As shown in Fig. 2 an reasonable agreement is achieved with the experimental distribution. The mean excitation energy E ∗  determined from the experimental data in the range 0–10 MeV is equal to 5.5 ± 0.8 MeV, while E ∗  = 4.4 MeV expected for the Coulomb dissociation through the state at 4.15 MeV and the nuclear excitation of the two states in 8 He results in E ∗  = 4.8 MeV. The experimental data contain an excess cross section above E ∗ = 7 MeV (Ecnn = 5 MeV), where the contribution from the resonance excitation is expected to be small. The experimental energy-weighted strength function in the energy range E ∗ = 7–10 MeV gives about 2 e2 fm2 MeV, i.e. about the same value as obtained in Section 4.1 for the whole 1− resonance. The conclusion can thus be drawn that the electromagnetic dissociation of 8 He contains noticeable contributions from nonresonant break-up mechanism of 8 He.

5. Summary Experimental data on fragmentation of 8 He in a lead target at 227 MeV/u have been presented and were discussed in the light of corresponding data for 6 He. The main conclusions for 8 He are: • The one-neutron knock-out channel, dominating in the fragmentation on a light target, is still an important part of the fragmentation on a lead target. The electromagnetic contribution to this channel is negligible. • The Coulomb dissociation cross section for reactions with a lead target has been evaluated from the experimental data by three different methods. It is found that the cross section for the 8 He dissociation is a factor 3 smaller than that for 6 He. • Contrary to the case of 6 He, where the Coulomb interaction plays a dominant role, the 8 He inelastic scattering is governed by both nuclear and Coulomb interactions. The differential cross section as a function of center-of-mass angle shows a behavior which is explained as a Coulomb–nuclear interference effect supporting the assignment of I π = 1− for the resonance in 8 He at Ex = 4.15 MeV. • The B(E1) value obtained for 8 He to the channel 6 He + 2n is approximately a factor of 3–4 smaller than that of 6 He. The comparison between the B(E1) values for 6 He and 8 He gives evidence for a smaller effective core radius for 8 He as compared to the

14

M. Meister et al. / Nuclear Physics A 700 (2002) 3–16 6 He

radius. The smaller radius leads to the conclusion that 8 He is characterized by a more uniform distribution of the four neutrons around the α-particle core. • The B(E1) value obtained for 8 He almost exhausts the full non-energy-weighted cluster sum rule. However, the assumption of a Breit–Wigner resonance strength function results only in 25% of the energy-weighted cluster sum rule. Contributions at higher excitation energies are observed which presumably reflect the presence of a nonresonant fragmentation.

Acknowledgements This work was supported by the BMBF under Contracts 06 DA 820, 06 OF 112 and 06 MZ 864 and by GSI under Contracts DA RICK, OF ELZ, MZ KRK and partly supported by the Polish Committee of Scientific Research under Contract PBZ/PB03/113/09, EC under contract ERBCHGE-CT92-0003, CICYT under Contract AEN92-0788-C02-02 (MJGB), WTZ under Contract RUS 674-98 and RFBR under Contract 01-02-16685. One of us (B.J.) acknowledges the support through an Alexander von Humboldt Research Award.

References [1] [2] [3] [4]

P.G. Hansen, A.S. Jensen, B. Jonson, Annu. Rev. Nucl. Part. Sci. 45 (1995) 591. I. Tanihata, J. Phys. G 22 (1996) 157. B. Jonson, K. Riisager, Philos. Trans. R. Soc. London A 356 (1998) 2063. T. Aumann, D. Aleksandrov, L. Axelsson, T. Baumann, M.J.G. Borge, L.V. Chulkov, J. Cub, W. Dostal, B. Eberlein, Th.W. Elze, H. Emling, H. Geissel, V.Z. Goldberg, M. Golovkov, A. Grünschloß, M. Hellström, K. Hencken, J. Holeczek, R. Holzmann, B. Jonson, A.A. Korsheninnikov, J.V. Kratz, G. Kraus, R. Kulessa, Y. Leifels, A. Leistenschneider, T. Leth, I. Mukha, G. Münzenberg, F. Nickel, T. Nilsson, G. Nyman, B. Petersen, M. Pfützner, A. Richter, K. Riisager, C. Scheidenberger, G. Schrieder, W. Schwab, H. Simon, M.H. Smedberg, M. Steiner, J. Stroth, A. Surowiec, T. Suzuki, O. Tengblad, M.V. Zhukov, Phys. Rev. C 59 (1999) 1252. [5] D. Aleksandrov, T. Aumann, L. Axelsson, T. Baumann, M. Borge, L.V. Chulkov, J. Cub, W. Dostal, B. Eberlein, Th.W. Elze, H. Emling, H. Geissel, V.Z. Goldberg, M. Golovkov, A. Grünschloß, M. Hellström, J. Holeczek, R. Holzmann, B. Jonson, A.A. Korsheninnikov, J.V. Kratz, G. Kraus, R. Kulessa, Y. Leifels, A. Leistenschneider, T. Leth, I. Mukha, G. Münzenberg, F. Nickel, T. Nilsson, G. Nyman, B. Petersen, M. Pfützner, A. Richter, K. Riisager, C. Scheidenberger, G. Schrieder, W. Schwab, H. Simon, M.H. Smedberg, M. Steiner, J. Stroth, A. Surowiec, T. Suzuki, O. Tengblad, M.V. Zhukov, Nucl. Phys. A 633 (1998) 234. [6] M.V. Zhukov, B.V. Danilin, D.V. Fedorov, J.M. Bang, I.J. Thompson, J.S. Vaagen, Phys. Rep. 231 (1993) 151. [7] K. Markenroth, M. Meister, B. Eberlein, T. Aumann, L. Axelsson, T. Baumann, M. Borge, L.V. Chulkov, W. Dostal, Th.W. Elze, H. Emling, H. Geissel, A. Grünschloß, M. Hellström, J. Holeczek, B. Jonson, J.V. Kratz, R. Kulessa, A. Leistenschneider, I. Mukha, G. Münzenberg, F. Nickel, T. Nilsson, G. Nyman, M. Pfützner, V. Pribora, A. Richter, K. Riisager, C. Scheiden-

M. Meister et al. / Nuclear Physics A 700 (2002) 3–16

[8]

[9] [10]

[11] [12] [13] [14]

[15]

[16] [17] [18] [19] [20] [21] [22] [23]

[24] [25] [26]

[27]

15

berger, G. Schrieder, H. Simon, J. Stroth, O. Tengblad, M.V. Zhukov, Nucl. Phys. A 679 (2001) 462. M. Meister, K. Markenroth, T. Aumann, L. Axelsson, T. Baumann, M. Borge, L.V. Chulkov, W. Dostal, B. Eberlein, Th.W. Elze, H. Emling, H. Geissel, A. Grünschloß, M. Hellström, J. Holeczek, B. Jonson, J.V. Kratz, R. Kulessa, A. Leistenschneider, I. Mukha, G. Münzenberg, F. Nickel, T. Nilsson, G. Nyman, M. Pfützner, V. Pribora, A. Richter, K. Riisager, C. Scheidenberger, G. Schrieder, H. Simon, J. Stroth, O. Tengblad, M.V. Zhukov, Phys. Rev. Lett., submitted. T. Kobayashi, Nucl. Phys. A 553 (1993) 465c. A.A. Korsheninnikov, E.A. Kuzmin, E.Yu. Nikolsky, O.V. Bochkarev, S. Fukuda, S.A. Goncharov, S. Ito, T. Kobayashi, S. Momota, B.G. Novatsky, A.A. Ogloblin, A. Ozawa, V. Pribora, I. Tanihata, K. Yoshida, Phys. Rev. Lett. 78 (1997) 2317. M.G. Gornov, Yu. Gurov, S. Lapushkin, P. Morokhov, V. Pechkurov, T.K. Pedlar, K.K. Seth, J. Wise, D. Zhao, Phys. Rev. Lett. 81 (1998) 4325. R. Kanungo, C. Samanta, J. Phys. (London) G 24 (1998) 1611; R. Kanungo, I. Tanihata, C. Samanta, Prog. Theor. Phys. (Kyoto) 102 (1999) 1133. S. Shimoura, T. Nakamura, M. Ishihara, N. Inabe, T. Kobayashi, T. Kubo, R.H. Siemssen, I. Tanihata, Y. Watanabe, Phys. Lett. 348B (1995) 29. K. Ieki, A. Galonsky, D. Sackett, J.J. Kruse, W.G. Lynch, D.J. Morrisey, N.A. Orr, B.M. Sherrill, J.A. Winger, F. Deák, Á. Horváth, Á. Kiss, Z. Seres, J.J. Kolata, R.E. Warner, D.L. Humphrey, Phys. Rev. C 54 (1996) 1589. M. Zinser, F. Humbert, T. Nilsson, W. Schwab, H. Simon, T. Aumann, M.J.G. Borge, L.V. Chulkov, J. Cub, Th.W. Elze, H. Emling, H. Geissel, D. Guillemaud-Mueller, P.G. Hansen, R. Holzmann, H. Irnich, B. Jonson, J.V. Kratz, R. Kulessa, Y. Leifels, H. Lenske, A. Magel, A.C. Mueller, G. Münzenberg, F. Nickel, G. Nyman, A. Richter, K. Riisager, G. Schrieder, K. Stelzer, J. Stroth, A. Surowiec, O. Tengblad, E. Wajda, E. Zude, Nucl. Phys. A 619 (1997) 151. I. Tanihata, H. Hamagaki, O. Hashimoto, S. Nagamiya, Y. Shida, N. Yoshikawa, O. Yamakawa, K. Sugimoto, T. Kobayashi, D.E. Greiner, N. Takahashi, Y. Nojiri, Phys. Lett. 160B (1985) 380. P.J. Karol, Phys. Rev. C 11 (1975) 1203. H. de Vries, C.W. de Jager, C. de Vries, At. Data Nucl. Data Tables 36 (1987) 495. G.D. Alkhazov, S.L. Belostotsky, O.A. Domchenkov, Yu.V. Dotsenko, N.P. Kuropatkin, V.N. Nikulin, M.A. Shuvaev, A.A. Vorobyov, Nucl. Phys. A 381 (1982) 430. Y. Ogawa, K. Yabana, Y. Suzuki, Nucl. Phys. A 543 (1992) 722. I. Tanihata, D. Hirata, T. Kobayashi, S. Shimoura, K. Sugimoto, H. Toki, Phys. Lett. 289B (1992) 261. D.L. Olson, B.L. Berman, D.E. Greiner, H.H. Heckman, P.J. Lindstrom, H.J. Crawford, Phys. Rev. C 28 (1983) 1602. Y. Iwata, K. Ikei, A. Galonsky, J.J. Kruse, J. Wang, R.H. White-Stevens, E. Tryggestad, F. Deák, Á. Horváth, Á. Kiss, Z. Seres, J.J. Kolata, J. von Schwarzenberg, R.E. Warner, H. Schelin, Phys. Rev. C 62 (2000) 064311. C.H. Dasso, S.M. Lenzi, A. Vitturi, Phys. Rev. C 59 (1999) 539. S.N. Ershov, B.V. Danilin, J.S. Vaagen, Phys. Rev. C 62 041001(R). D. Aleksandrov, T. Aumann, L. Axelsson, T. Baumann, M.J.G. Borge, L.V. Chulkov, J. Cub, W. Dostal, B. Eberlein, Th.W. Elze, H. Emling, H. Geissel, V.Z. Goldberg, M. Golovkov, A. Grünschloss, M. Hellström, J. Holeczek, R. Holzmann, B. Jonson, J.V. Kratz, G. Kraus, K. Markenroth, M. Meister, I. Mukha, G. Münzenberg, F. Nickel, T. Nilsson, G. Nyman, B. Petersen, M. Pfützner, V. Pribora, A. Richter, K. Riisager, C. Scheidenberger, G. Schrieder, W. Schwab, H. Simon, M.H. Smedberg, M. Steiner, J. Stroth, A. Suroviec, O. Tengblad, M.V. Zhukov, Nucl. Phys. A 669 (2000) 51. C.A. Bertulani, H. Sagawa, Nucl. Phys. A 588 (1995) 667.

16

[28] [29] [30] [31] [32] [33]

[34] [35]

M. Meister et al. / Nuclear Physics A 700 (2002) 3–16

C.A. Bertulani, A.M. Nathan, Nucl. Phys. A 554 (1993) 158. A. Winther, K. Alder, Nucl. Phys. A 319 (1979) 518. M.S. Hussein, R.A. Rego, C.A. Bertulani, Phys. Rep. 201 (1991) 279. J.Y. Hostachy, M. Buenerd, J. Chauvin, D. Lebrun, Ph. Martin, J.C. Lugol, L. Papineau, P. Roussel, N. Alamanos, J. Arvieux, C. Cerruti, Nucl. Phys. A 490 (1988) 441. M.V. Zhukov, A.A. Korsheninnikov, M.H. Smedberg, Phys. Rev. C 50 (1994) R1. G.D. Alkhazov, M.N. Andronenko, A.V. Dobrovolsky, P. Egelhof, G.E. Gavrilov, H. Geissel, H. Irnich, A.V. Khanzadeev, G.A. Korolev, A.A. Lobodenko, G. Münzenberg, M. Mutterer, S.R. Neumaier, F. Nickel, W. Schwab, D.M. Seliverstov, T. Suzuki, J.P. Theobald, N.A. Timofeev, A.A. Vorobyov, V.I. Yatsura, Phys. Rev. Lett. 78 (1997) 2313. C.A. Bertulani, A. Sustich, Phys. Rev. C 46 (1992) 2340. C.A. Bertulani, G. Baur, M.S. Hussein, Nucl. Phys. A 526 (1991) 751.