UPT (b, Z)dZ,. (2) with UPT the sum of the potentials simulating the interactions between the projectile constituents and the target. The eikonal model gives good ...
Breakup of halo nuclei within a Coulomb-corrected eikonal model P. Capel1,2 , D. Baye1,2 , P. Descouvemont2 and Y. Suzuki3
1 Physique
Quantique, C.P. 165/82, Nucl´eaire Th´eorique et Physique Math´ematique, C.P. 229, Universit´e Libre de Bruxelles, B 1050 Brussels, Belgium and 3 Department of Physics, Niigata University, Niigata 950-2181, Japan
2 Physique
Abstract The Coulomb-corrected eikonal (CCE) model provides a unique technique to investigate the breakup of three-body projectiles. In this paper, we present the CCE and compare its results to experiment for the breakup of 6 He at 240AMeV. Our results reopen the long-standing problem of the possible existence of a low-lying 1− resonance in 6 He spectrum. New experimental results are required to solve this problem.
The development of radioactive ion beams in the mid-80s led to the discovery of halo nuclei [1]. These light neutron-rich nuclei exhibit one of the most peculiar quantal structures. They present large matter radii in comparison with their isobars. This peculiarity results from the low separation energy of one or two neutrons of these nuclei: due to their low binding these valence neutrons tunnel far from the other nucleons. Halo nuclei are thus seen as two- or three-cluster systems: a core, which contains most of the nucleons, to which one or two neutrons are loosely bound. In addition, two-neutron halo nuclei also exhibit the Borromean property: while the three-body is bound, none of the two-body subsystems is. For example 6 He, consisting of an α and two neutrons, is bound, whereas neither 5 He nor dineutron is. This typical two-neutron halo nucleus has thus been the subject of many experimental and theoretical works.
1
Because of their short lifetime, halo nuclei must be studied by indirect spectroscopic techniques. Breakup reaction, in which the core-halo structure dissociates through interaction with a target, is one of these techniques. An accurate reaction model coupled to a realistic description of the projectile is thus needed to extract valuable information from measurements. Various such models have been developed for the breakup of one-neutron halo nuclei [2]: coupled-channel calculations with a discretised continuum (CDCC), time-dependent model and the more recent dynamical eikonal approximation (DEA) [3]. However these models remain very expensive in a computational point of view. They are therefore difficult to extend to three-body projectiles. In that respect the eikonal approximation [4] looks promising: it is simple in use, fast in implementation and easy to interpret. Indeed, within that approximation, the projectile wave function after collision is simply modified from the initial bound-state wave function Φ0 as Ψeik = eiχ(b) Φ0 ,
(1)
where the eikonal phase computed at impact parameter b reads 1 χ(b) = − hv ¯
Z
∞
UP T (b, Z)dZ,
(2)
−∞
with UP T the sum of the potentials simulating the interactions between the projectile constituents and the target. The eikonal model gives good results for nuclear-induced reactions. However it diverges for the Coulomb interaction. To solve that divergence problem, Margueron, Bonaccorso and Brink have proposed a Coulomb correction to the eikonal model [5]. This correction consists in replacing at first order the Coulomb part χC of the eikonal phase (2) by the first-order term of the perturbation theory χF O . It can be summarised as
eiχ = eiχN eiχC → eiχN eiχC − iχC + iχF O , where χN is the nuclear part of the eikonal phase. We have recently analysed this Coulomb-corrected eikonal model (CCE) by comparison to the DEA for the breakup of one-neutron halo nuclei [6]. This analysis has shown that most of the breakup observables are correctly reproduced within the CCE. Therefore, we have extended the CCE to the breakup of two-neutron halo nuclei [7] and compared our predictions with experimental data measured at GSI for 6 He impinging on lead at 240AMeV [8]. The structure of 6 He is modelled within the hyperspherical harmonics framework for both its bound and continuum states [7]. The α-n interaction
dσbu /dE (b/MeV)
0.5 Total J = 1− Exp. π
0.4 0.3 0.2 0.1 0
0
1
2 3 E (MeV)
4
5
Figure 1: Breakup cross section of 6 He on lead at 240AMeV as a function of the 4 He-n-n energy after dissociation. Total cross section (full line) and 1− contribution (dashed line). Experimental data are from Ref. [8]
is simulated by the potential of Kanada et al. [9], and the n-n interaction is described by the Minnesota potential [10]. These interactions do not reproduce the correct binding energy of 6 He, therefore we slightly adjust the n-n potential to fit the experimental value. The breakup cross section obtained with our model [7] is shown in Fig. 1 as a function of the total α-n-n relative energy after breakup (full line). It is composed of two peaks at low energy: a narrow one superimposed on a broad one. Above 2 MeV, the cross section decreases slowly. The narrow peak is due to the well known 2+ resonance of 6 He at 820 keV above the one-neutron separation threshold. The broad peak appears only in the 1− partial-wave contribution (dashed line) and is interpreted as resulting from a 1− resonance. This resonance has not (yet) been observed experimentally. In particular, the experimental data of Aumann et al. [8] do not exhibit such a peak. To understand the influence of the projectile description on that broad peak, we have repeated the calculation using different ways to adjust 6 He binding energy: instead of scaling the n-n interaction, we have fitted the α-n interaction or added a three-body force. In all cases a broad peak appears
in the 1− contribution to the breakup cross section. The shape and location of that peak barely change with the choice of the interaction [7]. Since other structure models also predict a 1− resonance at low energy in 6 He spectrum [11], we assume the broad peak observed in Fig. 1 not to be an artefact of the present model. The existence or nonexistence of a 1− broad resonance in the low-energy spectrum of 6 He is an interesting physical problem that should be clarified by future experiments. The present analysis shows that breakup reaction is an ideal technique to study this problem. Were the nonexistence of this resonance confirmed by new experiments, the description of the continuum of Borromean nuclei with existing model would be challenged.
References [1] P. G. Hansen, A. S. Jensen and B. Jonson, Annu. Rev. Nucl. Part. Sci 45, 591 (1995). [2] J. Al-Khalili and F. M. Nunes, J. Phys. G 29, R89 (2003). [3] D. Baye, P. Capel and G. Goldstein, Phys. Rev. Lett. 95, 082502 (2005). [4] R. J. Glauber, in Lecture in Theoretical Physics, edited by W. E. Brittin, L. G. Dunham, (Interscience, New York, 1959), Vol. 1, p. 315. [5] J. Margueron, A. Bonaccorso and D. M. Brink, Nucl. Phys. A720, 337 (2003). [6] P. Capel, D. Baye and Y. Suzuki, Phys. Rev. C 78, 054602 (2008). [7] D. Baye, P. Capel, P. Descouvemont and Y. Suzuki, Phys. Rev. C 79, 024607 (2009). [8] T. Aumann et al. Phys. Rev. C 59, 1252 (1999). [9] H. Kanada, T. Kaneko, S. Nagata and M. Nomoto, Prog. Theor. Phys. 61, 1327 (1979). [10] D. R. Thompson, M. Lemere and Y. C. Tang, Nucl. Phys. A286, 53 (1977). [11] B. V. Danilin, I. J. Thompson, J. S. Vaagen and M. V. Zhukov, Nucl. Phys. A632, 383 (1998).
