- Email: [email protected]
Light exotic systems at relativistic velocities
Nuclear Physics A 834 (2010) 394c–399c www.elsevier.com/locate/nuclphysa
Light exotic systems at relativistic velocities H. Simona , a
GSI Helmholtzzentrum f¨ ur Schwerionenforschung GmbH, Planckstr. 1, D-64291 Darmstadt, Germany In this paper the results of a series of experiments, carried out at the GSI accelerator facilities in Darmstadt at the Aladin-LAND reaction setup are presented. Light nuclei at relativistic velocities, impinging on a carbon and a liquid hydrogen reaction target break up and all fragments are detected in coincidence. The observed correlations are used to draw conclusions on the underlying structure of the bound exotic projectiles as well as to explore continuum structures. 1. INTRODUCTION Light nuclei far from stability [1,2] provide a fertile testing ground for nuclear structure models and the underlying forces. A series of experiments [3] has been performed in order to study extremely neutron rich nuclei at and beyond the driplines, where the neutron separation energy vanishes, by using breakup reactions. Beams with large neutron excess were produced in flight at several 100 MeV/nucleus and directed to a versatile reaction setup (Figure 1). As demonstrated e.g. by Hansen and Tostevin [4] the relativistic kinematics allows describing the reaction process cleanly, and the internal motion of the valence nuclei is slow compared to the interaction time. It is expected from systematics [5,6] since the 1960s, that shell model level ordering is altered approaching the driplines. From theoretical side the effect of intruder states from different shells or, in general, the dissappearance of magic numbers, can be partially explained with a smaller derivative of the mean field potential at the diffuse surface [7] and thus a reduced spin-orbit interaction. Complementary, the interaction of proton-neutron spin-orbit partners has been studied [8] where the occupation of the different orbits can also be related to modified magic numbers. One may aim to study these effects for light exotic nuclei both experimentally – the intensity of secondary beams is highest and allows for precision studies – as well as theoretically, as for systems even ab-initio calculations ([9] and references therein) are feasible. Another interesting aspect is the vicinity of the continuum to the valence orbits in loosely bound systems, which can be explicitly treated in the Berggren basis [10] (e.g. for 11 Li [11]) in continuum shell model approaches. The neutron-rich side of the nuclear landscape exhibits a particular structure: pairing interaction makes isotopes with an even number of neutrons bound whereas the ones located inbetween are unbound. This is experimentally observed up to the Mg isotopes [12] and requires to treat them as three body systems as the one-neutron breakup channel, that is commonly and originally [13] used to study their properties is just part of a 0375-9474/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysa.2010.01.048
395c
H. Simon / Nuclear Physics A 834 (2010) 394c–399c TOF Wall
WDC2 LAND
WDC1
Target 4
11
e, 6,8 H
1 Li,
→ Be VETO2
→
ALADIN
+
WPC2
WPC3
m 25
VETO1 WPC1
SCI
← Figure 1. Reaction Setup: A mixed beam of several isotopes with the same magnetic rigidity and large emittance induced by the production process is identified event-by-event in an incoming tracking system before impinging on a target. Subsequently breakup fragments are produced and are measured using a magnetic spectrometer setup in conjunction with the highly efficient neutron time-of-flight detector (LAND).
sequential decay path. Due to this intrinsic structure, three body models [14] can be very successfully applied [15,16] and give in particular access to experimentally observable intrinsic correlations. The appearance of this strong clustering is further supported by recent predictions based on FMD [17,18] and AMD [19] calculations. This paper addresses secondary beams of 6,8 He, 11 Li and 14 Be dissociating into typically 2 or 3 fragments which interact in the exit channel of the reaction, and occasionally form even more asymmetric nuclear systems like e.g. 5 H. The next chapter will deal with experimental methods. In the following ones selected findings in the outskirt of the nuclear landscape will be presented and discussed together with the underlying structure of the bound exotic projectiles leading to their formation. 2. PRODUCTION AND REACTION SETUP The accelerator facilities at the GSI Helmholtzzentrum f¨ ur Schwerionenforschung, Darmstadt, Germany were used to provide intense primary 18 O beams with an intensity of a about 1010 particles/s in several experiments. These beams impinged on a 4 g/cm2 natural Be production target. Mixed secondary beams, produced by nuclear fragmentation, were selected by pure magnetic rigidity constraints within the fragment separator (FRS) consisting of four dipole stages. Subsequently they were directed towards the ALADINLAND [20] reaction setup that was installed in the experimental area Cave-B. Different experiments were carried out using natural Carbon (1.2 g/cm2 ) and liquid Hydrogen (350 mg/cm2 ) targets. These low-Z materials ensure mainly nuclear interactions in the breakup reactions and their thickness corresponds to a ∼ 1% reaction probability in order to avoid multiple reactions in the target. Typical intensities for a particular secondary
396c
H. Simon / Nuclear Physics A 834 (2010) 394c–399c
beam species in the presented experiments carried out in the years 1995 and 2001 were 10-500 particles/s with a speed corresponding to 60 80% of the velocity of light. Kinematically complete experiments require a measurement of the momenta of all particles involved in the reactions. At present the moved and enhanced setup called R3 B/CaveC comprises in addition a large gamma and recoil proton detection array, being present as first prototypes only when gathering the data discussed in this paper. In Figure 1 the dimensions and principle of the experiment is depicted. Two active slit systems (VETO 1&2) serve to constrain the emittance of the fragment beams, a scintillator (SCI) and two position sensitive detectors (WPC 1&2) are used to define the incoming beam-particle vector and charge via the measured energy loss. The scattering angle for charged particles behind the target is measured using another position sensitive detector (WPC3). The charged particles are bent away from the original beam direction to analyse them separately from neutrons going straight through the large gap of the ALADIN magnet before being detected in the position sensitive large-area neutron-detector (LAND) with high efficiency (about 85% for a single neutron). The two position sensitive detectors behind the magnet (WDC 1&2) together with the fragment Time-of-Flight detector (TOF Wall) allow to identify the outgoing fragent. The time-of-flight is measured between the SCI start detector and TOF Wall and LAND. Multi neutron-events can be separated using a tracking routine finding primary hits out of the two to three interactions of the neutrons in the detector material. The response has been measured separately in a tagged deuteron break-up experiment and is used in simulation calculations for corrections. The forward focusing of the relativistic reaction products enables thus covering practically the full solid angle with high detection efficiency. 3. REACTION MECHANISM AND GROUND STATE PROPERTIES The occurance of nuclear haloes results from quantum-mechanical tunneling of loosely bound valence nucleons into the classical forbidden region and leading to a large spatial extend of these systems. Charged fragment (and neutron) momentum distributions are often used in exploratory studies, e.g. in separator experiments where longitudinal momentum distributions are measured with high precision (see e.g. [21]), in order to relate the spacial extend of halo nuclei to a narrow momentum distribution. The method is hampered for Borromean systems where the one-neutron removal-channels leads to an unbound system. One of the best studied cases is the nucleus 11 Li. A surprising finding for the final state consisting of one neutron and a charged 9 Li fragment is that regardless whether it’s reached via one-proton removal from 11 Be or just one-neutron removal from 11 Li the neutron momentum distribution is completely governed by the 9 Li–n final-state interaction [22] as the measured width in both cases is the same. This means, that even after removing a deeply bound proton from the projectile, the survival criteria for this particular final state restrict the amount of transferred momentum to the intermediate unbound system. By determining the missing momentum spectrum [23] it’s possible to reconstruct the original momentum of the removed halo neutron in a two-neutron halo like 11 Li. The intermediate 10 Li can subsequently be characterized [24] with invariant mass continuum spectroscopy. Of particular interest are the intrinsic correlations in the two-neutron haloes. They can be explored by studying angular correlations [23,25] in
H. Simon / Nuclear Physics A 834 (2010) 394c–399c
397c
Figure 2. Comparison of 7 He relative energy spectra obtained with a Carbon (open symbols) and liquid Hydrogen (full symbols) target.
the sequential breakup process. The measured correlation angle can be directly applied to explain e.g. laser spectroscopy charge radius measurements [26] for 9 Li and 11 Li by deducing the associated centre-of-mass motion of the charged 9 Li core. Taking further into account the new mass measurements [27,28] using a Penning trap and the MISTRAL mass spectrometer together with the new experimental quadrupole moment [29], a phenomenological wave function [15] for 11 Li could be determined. The 7 He continuum states populated from 8 He using a Carbon target [30] reveiled an interesting structure above the well known ground state that was interpreted as evidence for a new low-lying resonance state. As this state could be seen in a simple single particle picture as spin-orbit partner of the ground state this finding triggered a lot of experimental activities with contradictory results. A new measurement [31] using a liquid Hydrogen target is compared to the previous result in Figure 2. The resonance energies (Er =0.351(9)/0.387(2) MeV; C/H2 ) and widths (Γ=0.189(30)/0.190(6) MeV) for the ground-state agree well within their experimental uncertainties. However, the obtained spectroscopic factor 0.61(3) for the 6 He 0+ +n configuration rules out the simple p3/2 state interpretation for 7 He. The excited state at 1.02 MeV (Γ=0.5(2) MeV) is solely seen in the complex carbon target and attributed to a multi-step rescattering process. 4. CONTINUUM STRUCTURES AND THREE BODY CORRELATIONS Proton removal from exotic projectiles allows to cross the dripline and populate even more extreme states in the continuum. The reactions 11 Li→8 He+2n, 8 He+n+X and 14 Be→11 Li+2n, 11 Li+n+X [32] have been investigated. For the heavy He isotopes agreement to already existing data using a similar reaction at RIKEN [33] was obtained. The 10 He ground-state has been theoretically predicted [34] to be similar to the one of 11 Li. Furthermore, the low energy in 10 He is stronly interlinked [16] with the strength of the interaction in the 9 He system. We obtain a scattering length of about -3 fm in the 9 He relative energy spectrum in accordance with the given constraints in reference [16]. To check the similarity to the 11 Li ground-state the 3-body correlations in the system have been investigated. Using Jacobi coordinates i.e. relative momentum vectors it can be shown that only two variables: the fractional relative energy (ε = E12 /E123 ) in one of the
398c
H. Simon / Nuclear Physics A 834 (2010) 394c–399c
Figure 3. Measured relative energy spectra for the heaviest Li isotopes.
two body subsystems and the angle between the momentum vectors (ϑ) fully describes the relative motion of the three particles and can be related to the measured double differential cross section as shown in Eq. (1). W(ε, ϑ) ∝
† d2 σ ∝ Cα Cα Yα† (ε, ϑ)Yα (ε, ϑ) dεdϑ α,α
(1)
The measured cross sections can in turn be related to an expansion into hyperspherical harmonic functions Y with complex coefficients C depending on a set of quantum numbers α. Such, the phenomenological 11 Li-wave function obtained in the previous section could be directly compared to the measured spectra, and a strong modification of the original correlations in the 11 Li projectile by final state interaction in 10 He can be seen. Starting from 14 Be the heaviest Li isotopes could be produced and studied for the first time [32]. The 10,12 Li spectra (see Figure 3) can be described following the prescription in [35] where the neutron separation energy is a free parameter in the fit and used to check the validity of the reaction model. In both cases the correct separation energies for 11 Li,14 Be are obtained and the 12 Li spectrum can be fited with a single s-wave with a scattering length of -13.7(1.6) fm. For 13 Li the spectrum is described using a parametrisation [36] to describe the initial 11 Li+2n phase space in 14 Be. An enhancement is seen at low energies e.g. an resonance energy of 1.47(31) MeV and consequently interpreted as evidence for its existance. In summary a rich harvest of information for several bound and unbound light nuclear systems has been presented. In the near future we’ll run an experimental campaign using (p,2p), (p,pn) reactions in our improved setup R3 B/Cave-C, providing more detailed information on the reaction mechanism as the recoil protons from a hydrogen compound target and gamma radiation will be detected. In the further future we expect the possibility to explore heavier systems with the advent of very intense beams in the FAIR facility. 5. ACKNOWLEDGEMENTS This work results from collaborative efforts. I’d like to thank my colleagues: ´ Y. Aksyutina, T. Aumann, H. Alvarez-Pol, T. LeBleis, E. Benjamim, J. Benlliure, M.J.G. Borge, M. Caama˜ no, E. Casarejos, L.V. Chulkov, D. Cortina-Gil, K. Epinger, Th.W. Elze, H. Emling,
H. Simon / Nuclear Physics A 834 (2010) 394c–399c
399c
C. Forss´en, H. Geissel, R. Gernh¨auser, A. Gr¨ unschloß, M. Hellstr¨om, J. Holeczek, K.L. Jones, H. Johansson, B. Jonson, J.V. Kratz, R. Kr¨ ucken, R. Kulessa, C. Langer, M. Lantz, Y. Leifels, A. Lindahl, K. Mahata, M. Meister, P. Maierbeck, K. Markenroth, G. M¨ unzenberg, T. Nilsson, C. Nociforo, G. Nyman, R. Palit, M. Pantea, S. Paschalis, D. P´erez, M. Pf¨ utzner, V. Pribora, A. Prochazka, R. Reifarth, A. Richter, K. Riisager, C. Rodr´ıguez, C. Scheidenberger, G. Schrieder, J. Stroth, K. S¨ ummerer, O. Tengblad, H. Weick, and M.V. Zhukov.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36.
B. Jonson, Phys. Rep. 389 (2004) 1. A.S. Jensen, K. Riisager, D.V. Fedorov, E. Garrido, Rev. Mod. Phys. 76 (2004) 215. T. Aumann, Eur. Phys. Journ. A26 (2005) 441. P.G. Hansen, J. Tostevin, Annu. Rev. Nucl. Part. Sci. 53 (2003) 219. I. Talmi, I. Unna, Phys. Rev. Lett. 4 (1960) 469. P.G. Hansen, Nucl. Phys. A682 (2001) 310c. J. Dobaczewski et al., Phys. Rev. C53 (1996) 2809. T. Otsuka et al., Phys. Rev. Lett. 87 (2001) 082502. D.J. Dean, Nucl. Phys. A805 (2008) 145c. T. Bergren, Nucl. Phys. A109 (1968) 265. R. Id Betan et al., Phys. Lett. B584 (2004) 48. T. Baumann et al., Nature 449 (2007) 1022. P.G. Hansen, B. Jonson, Europhys. Lett. 4 (1987) 409. M.V. Zhukov et al., Phys. Rep. 231 (1993) 151. N.B. Shulgina et al., Nucl. Phys. A825 (2009) 175. L. Grigorenko et al., Phys. Rev. C77 (2008) 034611. T. Neff, H. Feldmeier, R. Roth, Nucl. Phys. A752 (2005) 321. T. Neff, H. Feldmeier, Eur. Phys. J. Spec. Top. 156, (2008) 69. Y. Kanada-En’yo and H. Horiuchi, Prog. Theor. Phys. Suppl. 142 (2001) 205. Th. Blaich et al., Nucl. Instum. Meth. A314 (1992) 136. E. Sauvan et al., Phys. Rev. C69 (2004) 044603. M. Zinser et al., Phys. Rev. Lett. 75 (1995) 1719. H. Simon et al., Phys. Rev. Lett. 83 (1999) 496. H. Simon et al., Nucl. Phys. A791 (2007) 267. L.V. Chulkov et al., Phys. Rev. Lett. 79 (1997) 201. R. Sanchez et al., Phys. Rev. Lett. 96 (2006) 033002. M. Smith et al., Phys. Rev. Lett. 101 (2008) 202501. C. Gaulard et al., Nucl. Phys, A826 (2009) 1. R. Neugart et al., Phys. Rev. Lett. 101 (2008) 132502. M. Meister et al., Phys. Rev. Lett. 88 (2002) 102501. Yu. Aksyutina et al., Phys. Lett. B679 (2009) 191. Yu. Aksyutina et al., Phys. Lett. B666 (2008) 430. A. Korsheninnikov et al., Phys. Lett. B326 (1994) 31. S. Aoyama, Phys. Rev. Lett. 89 (2002) 052501. G.F. Bertsch, K. Hencken, H. Esbensen, Phys. Rev. C57 (1998) 1366. C. Forss´en, B. Jonson, M.V. Zhukov, Nucl. Phys. A673 (2000) 143.
Light exotic systems at relativistic velocities H. Simona , a
GSI Helmholtzzentrum f¨ ur Schwerionenforschung GmbH, Planckstr. 1, D-64291 Darmstadt, Germany In this paper the results of a series of experiments, carried out at the GSI accelerator facilities in Darmstadt at the Aladin-LAND reaction setup are presented. Light nuclei at relativistic velocities, impinging on a carbon and a liquid hydrogen reaction target break up and all fragments are detected in coincidence. The observed correlations are used to draw conclusions on the underlying structure of the bound exotic projectiles as well as to explore continuum structures. 1. INTRODUCTION Light nuclei far from stability [1,2] provide a fertile testing ground for nuclear structure models and the underlying forces. A series of experiments [3] has been performed in order to study extremely neutron rich nuclei at and beyond the driplines, where the neutron separation energy vanishes, by using breakup reactions. Beams with large neutron excess were produced in flight at several 100 MeV/nucleus and directed to a versatile reaction setup (Figure 1). As demonstrated e.g. by Hansen and Tostevin [4] the relativistic kinematics allows describing the reaction process cleanly, and the internal motion of the valence nuclei is slow compared to the interaction time. It is expected from systematics [5,6] since the 1960s, that shell model level ordering is altered approaching the driplines. From theoretical side the effect of intruder states from different shells or, in general, the dissappearance of magic numbers, can be partially explained with a smaller derivative of the mean field potential at the diffuse surface [7] and thus a reduced spin-orbit interaction. Complementary, the interaction of proton-neutron spin-orbit partners has been studied [8] where the occupation of the different orbits can also be related to modified magic numbers. One may aim to study these effects for light exotic nuclei both experimentally – the intensity of secondary beams is highest and allows for precision studies – as well as theoretically, as for systems even ab-initio calculations ([9] and references therein) are feasible. Another interesting aspect is the vicinity of the continuum to the valence orbits in loosely bound systems, which can be explicitly treated in the Berggren basis [10] (e.g. for 11 Li [11]) in continuum shell model approaches. The neutron-rich side of the nuclear landscape exhibits a particular structure: pairing interaction makes isotopes with an even number of neutrons bound whereas the ones located inbetween are unbound. This is experimentally observed up to the Mg isotopes [12] and requires to treat them as three body systems as the one-neutron breakup channel, that is commonly and originally [13] used to study their properties is just part of a 0375-9474/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysa.2010.01.048
395c
H. Simon / Nuclear Physics A 834 (2010) 394c–399c TOF Wall
WDC2 LAND
WDC1
Target 4
11
e, 6,8 H
1 Li,
→ Be VETO2
→
ALADIN
+
WPC2
WPC3
m 25
VETO1 WPC1
SCI
← Figure 1. Reaction Setup: A mixed beam of several isotopes with the same magnetic rigidity and large emittance induced by the production process is identified event-by-event in an incoming tracking system before impinging on a target. Subsequently breakup fragments are produced and are measured using a magnetic spectrometer setup in conjunction with the highly efficient neutron time-of-flight detector (LAND).
sequential decay path. Due to this intrinsic structure, three body models [14] can be very successfully applied [15,16] and give in particular access to experimentally observable intrinsic correlations. The appearance of this strong clustering is further supported by recent predictions based on FMD [17,18] and AMD [19] calculations. This paper addresses secondary beams of 6,8 He, 11 Li and 14 Be dissociating into typically 2 or 3 fragments which interact in the exit channel of the reaction, and occasionally form even more asymmetric nuclear systems like e.g. 5 H. The next chapter will deal with experimental methods. In the following ones selected findings in the outskirt of the nuclear landscape will be presented and discussed together with the underlying structure of the bound exotic projectiles leading to their formation. 2. PRODUCTION AND REACTION SETUP The accelerator facilities at the GSI Helmholtzzentrum f¨ ur Schwerionenforschung, Darmstadt, Germany were used to provide intense primary 18 O beams with an intensity of a about 1010 particles/s in several experiments. These beams impinged on a 4 g/cm2 natural Be production target. Mixed secondary beams, produced by nuclear fragmentation, were selected by pure magnetic rigidity constraints within the fragment separator (FRS) consisting of four dipole stages. Subsequently they were directed towards the ALADINLAND [20] reaction setup that was installed in the experimental area Cave-B. Different experiments were carried out using natural Carbon (1.2 g/cm2 ) and liquid Hydrogen (350 mg/cm2 ) targets. These low-Z materials ensure mainly nuclear interactions in the breakup reactions and their thickness corresponds to a ∼ 1% reaction probability in order to avoid multiple reactions in the target. Typical intensities for a particular secondary
396c
H. Simon / Nuclear Physics A 834 (2010) 394c–399c
beam species in the presented experiments carried out in the years 1995 and 2001 were 10-500 particles/s with a speed corresponding to 60 80% of the velocity of light. Kinematically complete experiments require a measurement of the momenta of all particles involved in the reactions. At present the moved and enhanced setup called R3 B/CaveC comprises in addition a large gamma and recoil proton detection array, being present as first prototypes only when gathering the data discussed in this paper. In Figure 1 the dimensions and principle of the experiment is depicted. Two active slit systems (VETO 1&2) serve to constrain the emittance of the fragment beams, a scintillator (SCI) and two position sensitive detectors (WPC 1&2) are used to define the incoming beam-particle vector and charge via the measured energy loss. The scattering angle for charged particles behind the target is measured using another position sensitive detector (WPC3). The charged particles are bent away from the original beam direction to analyse them separately from neutrons going straight through the large gap of the ALADIN magnet before being detected in the position sensitive large-area neutron-detector (LAND) with high efficiency (about 85% for a single neutron). The two position sensitive detectors behind the magnet (WDC 1&2) together with the fragment Time-of-Flight detector (TOF Wall) allow to identify the outgoing fragent. The time-of-flight is measured between the SCI start detector and TOF Wall and LAND. Multi neutron-events can be separated using a tracking routine finding primary hits out of the two to three interactions of the neutrons in the detector material. The response has been measured separately in a tagged deuteron break-up experiment and is used in simulation calculations for corrections. The forward focusing of the relativistic reaction products enables thus covering practically the full solid angle with high detection efficiency. 3. REACTION MECHANISM AND GROUND STATE PROPERTIES The occurance of nuclear haloes results from quantum-mechanical tunneling of loosely bound valence nucleons into the classical forbidden region and leading to a large spatial extend of these systems. Charged fragment (and neutron) momentum distributions are often used in exploratory studies, e.g. in separator experiments where longitudinal momentum distributions are measured with high precision (see e.g. [21]), in order to relate the spacial extend of halo nuclei to a narrow momentum distribution. The method is hampered for Borromean systems where the one-neutron removal-channels leads to an unbound system. One of the best studied cases is the nucleus 11 Li. A surprising finding for the final state consisting of one neutron and a charged 9 Li fragment is that regardless whether it’s reached via one-proton removal from 11 Be or just one-neutron removal from 11 Li the neutron momentum distribution is completely governed by the 9 Li–n final-state interaction [22] as the measured width in both cases is the same. This means, that even after removing a deeply bound proton from the projectile, the survival criteria for this particular final state restrict the amount of transferred momentum to the intermediate unbound system. By determining the missing momentum spectrum [23] it’s possible to reconstruct the original momentum of the removed halo neutron in a two-neutron halo like 11 Li. The intermediate 10 Li can subsequently be characterized [24] with invariant mass continuum spectroscopy. Of particular interest are the intrinsic correlations in the two-neutron haloes. They can be explored by studying angular correlations [23,25] in
H. Simon / Nuclear Physics A 834 (2010) 394c–399c
397c
Figure 2. Comparison of 7 He relative energy spectra obtained with a Carbon (open symbols) and liquid Hydrogen (full symbols) target.
the sequential breakup process. The measured correlation angle can be directly applied to explain e.g. laser spectroscopy charge radius measurements [26] for 9 Li and 11 Li by deducing the associated centre-of-mass motion of the charged 9 Li core. Taking further into account the new mass measurements [27,28] using a Penning trap and the MISTRAL mass spectrometer together with the new experimental quadrupole moment [29], a phenomenological wave function [15] for 11 Li could be determined. The 7 He continuum states populated from 8 He using a Carbon target [30] reveiled an interesting structure above the well known ground state that was interpreted as evidence for a new low-lying resonance state. As this state could be seen in a simple single particle picture as spin-orbit partner of the ground state this finding triggered a lot of experimental activities with contradictory results. A new measurement [31] using a liquid Hydrogen target is compared to the previous result in Figure 2. The resonance energies (Er =0.351(9)/0.387(2) MeV; C/H2 ) and widths (Γ=0.189(30)/0.190(6) MeV) for the ground-state agree well within their experimental uncertainties. However, the obtained spectroscopic factor 0.61(3) for the 6 He 0+ +n configuration rules out the simple p3/2 state interpretation for 7 He. The excited state at 1.02 MeV (Γ=0.5(2) MeV) is solely seen in the complex carbon target and attributed to a multi-step rescattering process. 4. CONTINUUM STRUCTURES AND THREE BODY CORRELATIONS Proton removal from exotic projectiles allows to cross the dripline and populate even more extreme states in the continuum. The reactions 11 Li→8 He+2n, 8 He+n+X and 14 Be→11 Li+2n, 11 Li+n+X [32] have been investigated. For the heavy He isotopes agreement to already existing data using a similar reaction at RIKEN [33] was obtained. The 10 He ground-state has been theoretically predicted [34] to be similar to the one of 11 Li. Furthermore, the low energy in 10 He is stronly interlinked [16] with the strength of the interaction in the 9 He system. We obtain a scattering length of about -3 fm in the 9 He relative energy spectrum in accordance with the given constraints in reference [16]. To check the similarity to the 11 Li ground-state the 3-body correlations in the system have been investigated. Using Jacobi coordinates i.e. relative momentum vectors it can be shown that only two variables: the fractional relative energy (ε = E12 /E123 ) in one of the
398c
H. Simon / Nuclear Physics A 834 (2010) 394c–399c
Figure 3. Measured relative energy spectra for the heaviest Li isotopes.
two body subsystems and the angle between the momentum vectors (ϑ) fully describes the relative motion of the three particles and can be related to the measured double differential cross section as shown in Eq. (1). W(ε, ϑ) ∝
† d2 σ ∝ Cα Cα Yα† (ε, ϑ)Yα (ε, ϑ) dεdϑ α,α
(1)
The measured cross sections can in turn be related to an expansion into hyperspherical harmonic functions Y with complex coefficients C depending on a set of quantum numbers α. Such, the phenomenological 11 Li-wave function obtained in the previous section could be directly compared to the measured spectra, and a strong modification of the original correlations in the 11 Li projectile by final state interaction in 10 He can be seen. Starting from 14 Be the heaviest Li isotopes could be produced and studied for the first time [32]. The 10,12 Li spectra (see Figure 3) can be described following the prescription in [35] where the neutron separation energy is a free parameter in the fit and used to check the validity of the reaction model. In both cases the correct separation energies for 11 Li,14 Be are obtained and the 12 Li spectrum can be fited with a single s-wave with a scattering length of -13.7(1.6) fm. For 13 Li the spectrum is described using a parametrisation [36] to describe the initial 11 Li+2n phase space in 14 Be. An enhancement is seen at low energies e.g. an resonance energy of 1.47(31) MeV and consequently interpreted as evidence for its existance. In summary a rich harvest of information for several bound and unbound light nuclear systems has been presented. In the near future we’ll run an experimental campaign using (p,2p), (p,pn) reactions in our improved setup R3 B/Cave-C, providing more detailed information on the reaction mechanism as the recoil protons from a hydrogen compound target and gamma radiation will be detected. In the further future we expect the possibility to explore heavier systems with the advent of very intense beams in the FAIR facility. 5. ACKNOWLEDGEMENTS This work results from collaborative efforts. I’d like to thank my colleagues: ´ Y. Aksyutina, T. Aumann, H. Alvarez-Pol, T. LeBleis, E. Benjamim, J. Benlliure, M.J.G. Borge, M. Caama˜ no, E. Casarejos, L.V. Chulkov, D. Cortina-Gil, K. Epinger, Th.W. Elze, H. Emling,
H. Simon / Nuclear Physics A 834 (2010) 394c–399c
399c
C. Forss´en, H. Geissel, R. Gernh¨auser, A. Gr¨ unschloß, M. Hellstr¨om, J. Holeczek, K.L. Jones, H. Johansson, B. Jonson, J.V. Kratz, R. Kr¨ ucken, R. Kulessa, C. Langer, M. Lantz, Y. Leifels, A. Lindahl, K. Mahata, M. Meister, P. Maierbeck, K. Markenroth, G. M¨ unzenberg, T. Nilsson, C. Nociforo, G. Nyman, R. Palit, M. Pantea, S. Paschalis, D. P´erez, M. Pf¨ utzner, V. Pribora, A. Prochazka, R. Reifarth, A. Richter, K. Riisager, C. Rodr´ıguez, C. Scheidenberger, G. Schrieder, J. Stroth, K. S¨ ummerer, O. Tengblad, H. Weick, and M.V. Zhukov.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36.
B. Jonson, Phys. Rep. 389 (2004) 1. A.S. Jensen, K. Riisager, D.V. Fedorov, E. Garrido, Rev. Mod. Phys. 76 (2004) 215. T. Aumann, Eur. Phys. Journ. A26 (2005) 441. P.G. Hansen, J. Tostevin, Annu. Rev. Nucl. Part. Sci. 53 (2003) 219. I. Talmi, I. Unna, Phys. Rev. Lett. 4 (1960) 469. P.G. Hansen, Nucl. Phys. A682 (2001) 310c. J. Dobaczewski et al., Phys. Rev. C53 (1996) 2809. T. Otsuka et al., Phys. Rev. Lett. 87 (2001) 082502. D.J. Dean, Nucl. Phys. A805 (2008) 145c. T. Bergren, Nucl. Phys. A109 (1968) 265. R. Id Betan et al., Phys. Lett. B584 (2004) 48. T. Baumann et al., Nature 449 (2007) 1022. P.G. Hansen, B. Jonson, Europhys. Lett. 4 (1987) 409. M.V. Zhukov et al., Phys. Rep. 231 (1993) 151. N.B. Shulgina et al., Nucl. Phys. A825 (2009) 175. L. Grigorenko et al., Phys. Rev. C77 (2008) 034611. T. Neff, H. Feldmeier, R. Roth, Nucl. Phys. A752 (2005) 321. T. Neff, H. Feldmeier, Eur. Phys. J. Spec. Top. 156, (2008) 69. Y. Kanada-En’yo and H. Horiuchi, Prog. Theor. Phys. Suppl. 142 (2001) 205. Th. Blaich et al., Nucl. Instum. Meth. A314 (1992) 136. E. Sauvan et al., Phys. Rev. C69 (2004) 044603. M. Zinser et al., Phys. Rev. Lett. 75 (1995) 1719. H. Simon et al., Phys. Rev. Lett. 83 (1999) 496. H. Simon et al., Nucl. Phys. A791 (2007) 267. L.V. Chulkov et al., Phys. Rev. Lett. 79 (1997) 201. R. Sanchez et al., Phys. Rev. Lett. 96 (2006) 033002. M. Smith et al., Phys. Rev. Lett. 101 (2008) 202501. C. Gaulard et al., Nucl. Phys, A826 (2009) 1. R. Neugart et al., Phys. Rev. Lett. 101 (2008) 132502. M. Meister et al., Phys. Rev. Lett. 88 (2002) 102501. Yu. Aksyutina et al., Phys. Lett. B679 (2009) 191. Yu. Aksyutina et al., Phys. Lett. B666 (2008) 430. A. Korsheninnikov et al., Phys. Lett. B326 (1994) 31. S. Aoyama, Phys. Rev. Lett. 89 (2002) 052501. G.F. Bertsch, K. Hencken, H. Esbensen, Phys. Rev. C57 (1998) 1366. C. Forss´en, B. Jonson, M.V. Zhukov, Nucl. Phys. A673 (2000) 143.