- Email: [email protected]
Scientific opportunities with in-flight separated beams
Nuclear Physics A 701 (2002) 422c–428c www.elsevier.com/locate/npe
Scientific opportunities with in-flight separated beams ✩ Bradley M. Sherrill National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI, USA
Abstract This article provides an overview of the use of fast (> 50 MeV/u) beams of radioactive ions for nuclear structure studies. 2002 Elsevier Science B.V. All rights reserved.
1. Introduction Nuclei near the limits of particle stability are among the most interesting to study. These nuclei, due to their unusual ratios of neutrons to protons, may provide the most stringent tests of the isospin dependence of out nuclear models. The drip lines are also where the cases of halo and extreme skin nuclei will be found [1–3]. This paper makes a very broad outline of the experiments possible using fast (> 50 MeV/u) radioactive beams produced via in-flight separation. It is based on the recent summary of fast beam experiments [4]. As described in that document, the key to experiments with nuclei at the extremes will be to develop sensitive experiments that can work with few atoms. Considerable progress in this regard has already been made at fragmentation facilities, such at GSI, GANIL, RIKEN and the NSCL. Fig. 1 illustrates the expected radioactive ion (rare isotope) beam intensities based of projectile fragmentation and a 18% momentum acceptance fragment separator. The production target is adjusted to fill the separator momentum acceptance and the primary beam is optimized for each fragment. The production cross sections are taken from the EPAX2 parameterization [5]. The figure is not intended to be correct in all details and reality may be very different depending on the production cross sections very far from stability. It is also important to note, that ISOL type production can in principle produce, ✩
This work was supported by the National Science Foundation. E-mail address: [email protected] (B.M. Sherrill).
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 6 2 1 - 9
B.M. Sherrill / Nuclear Physics A 701 (2002) 422c–428c
423c
Fig. 1. Intensities for in-flight separated secondary beams produced by projectile fragmentation from a 100 kW 400 MeV/u primary beam as described in the text.
in the production target, something like 10–100 times these value. The region of known nuclei is outlined with the solid line and the approximate path of the rp-process and the r-process are indicated by grey lines. The exciting prospect is that there appears to be the possibility to produce a significant number of r-process nuclei. The rp-process nuclei are produced in relatively large quantities. Further, it appears possible to reach the drip line for nuclei as heavy as 120 Zr. However, as is clear in the figure, these nuclei are produced at very low yields. In the worst cases at a level of only 1 atom/week.
2. Basic nuclear properties One of the most basic properties of a nucleus is whether or not it is particle stable. Fast beams provide an easy measure of particle stability as at sufficiently high energy the ion can be identified and its Z determined by energy loss and its A by flight time through a system. In this way many studies of the locations of the drip lines have been made. Recently along the proton drip line 48 Ni [6] and 100 Sn [7,8] have been discovered. The neutron drip line has only been determined for the lightest nuclei with Z up to 8. Recent studies have determined that 25 N, 26 O and 28 O are neutron unbound [9]. It is fascinating that the very neutron rich nuclei 31 Ne and 31 F were observed. It remains a puzzle why the stability line ends at 24 O, yet with one more proton increases all the way to 31 F. Masses can be measured by time-of-flight techniques, TOF, with only 1000 s of atoms. The flight time is measured over a long distance and the momentum is accurately determined. For a review of techniques in atomic mass measurement, see reference [10]. Related, exciting new results have come from the use of the use of the experimental storage ring, ESR, at GSI as a time of flight spectrometer [11]. Two different types of experiments have been performed. In one set of experiments exotic ions were injected into the ESR and
424c
B.M. Sherrill / Nuclear Physics A 701 (2002) 422c–428c
cooled. The power spectrum was measured for the circulating ions in an electronic pickup system and Fourier analyzed. The other technique employed used the ESR operated in an isochronous mode. This allows shorter lived nuclei (less than 1 s) to be measured since ion cooling, which can take up to 1 s, is not necessary. A variety of information has been extracted from decay studies of nuclei. Half-lives can be compared to global models to constrain model parameters [12]. Precision measurements can be used to determine fundamental constants [13]. Most decay studies involve high efficiency β detection used in connection with coincident charged particle or gamma-ray detectors. Particularly in the case where the β-decay energy window is large, detailed structure information can be obtained on the daughter nucleus. For example, 11 Li, has been studied in great detail and a variety of β-delayed decay modes have been observed [14,15]. Moments for lighter exotic nuclei have been determined primarily from the use of polarized beams and β-NMR techniques. Results for nuclei in the p-shell such as boron, carbon, nitrogen and oxygen have been published using polarized beams obtained from projectile fragmentation at RIKEN and the NSCL [16,17]. An alternative method to measure nuclear moments is the level mixing technique [18]. This technique has been used for a variety of states with lifetimes in the 50 ns to a few second range.
3. Direct reactions with fast beams Direct reactions have been used over the past 30 years to provide a wealth of information on the structure of nuclei. For stable isotopes, it is possible to produce a targets that can be bombarded by light ions. However, no such targets are available for most exotic nuclei due to their short half-lives. Exotic nuclei studies can, however, be done in inverse kinematics, where the role of target and beam are interchanged. For example, proton elastic of 11 Li has been studied at GSI and RIKEN by bombarding hydrogen targets by a 11 Li beam [19]. This data has been compared to various models of 11 Li in order to determine its structure [20]. Proton inelastic scattering with radioactive beams in inverse kinematics was first performed at GSI [21] for 56 Ni and has since been used routinely at various laboratories [22–25]. Exotic beams with energies between 30 MeV/nucleon and 100 MeV/nucleon are scattered off proton targets (which are 1–3 mg/cm2 thick) and protons with energies between 1 and 20 MeV are detected in segmented silicon detectors at laboratory angles close to 90 degrees. In general, with a large solid angle silicon detector array it is possible to perform inelastic scattering experiments with beam rates of as little as 500 particles/s. The equivalent of inverse kinematic pickup reactions, (p, d), has been used at GANIL to study the structure of 11 Be [26]. It was found that the 11 Be ground state is predominately s-wave with a small d-wave admixture. These results are very similar to the results that have been obtained via the knock out reactions described below. One of the first experiments with RNBs was the determination of the total interaction cross sections for neutron rich nuclei at LBL [3]. This technique continues to play an important role. Total reaction cross sections are also a useful observable for studying the changes in structure across a series of isotopes. Normally the interaction cross sections would be expected to scale with A1/3 . If, however, there are changes in structure, such as the development of a neutron skin, this rule will be violated. The measured interaction
B.M. Sherrill / Nuclear Physics A 701 (2002) 422c–428c
425c
cross sections can be compared to calculations and information on the skin or halo structure extracted. One of the best example is the study of neutron skins in sodium [27]. Another tool for studying the detailed structure of nuclei has been the use of knock out reactions. Electron-induced (e, e p) reactions have been used to study deeply bound states in nuclei and have found high momentum components in the wave functions and an interesting apparent lack of the full expected spectroscopic factors. These experiments are performed by measuring scattered electrons and protons and reconstructing the “missing momentum” for the recoil nuclei. This class of experiment can be applied to radioactive beams. In this case, the target is taken as a light nucleus. The “missing momentum” is directly determined by measuring the recoil momentum of the core. The final states of the core are determined by coincident γ -ray detection. Recently, experimental and theoretical work has demonstrated the power of singlenucleon knock out reactions [28–30]. The shape of the recoil distribution can be used to assign the l-value of the removed nucleon. Higher l-value removal has intrinsically larger momentum widths due to the stronger localization of the wave-function for high-l orbits. Spectroscopic factors can be assigned based on the partial cross sections to the excited states of the core compared to the cross sections expected for removal of a nucleon from a given orbit. The results can be compared with spectroscopic factors obtained in various nuclear models, such as large basis shell-model calculations. For example, in the case of 11 Li Simon et al. [28] were able to show the wave function is an almost equal mixture of s- and p-waves. Fig. 2 illustrates the technique with data from Navin et al. [31] for the reaction 9 Be(12 Be, 11 Be*)X leading to the well-known ground state and excited levels with spin and parity 1/2+ and 1/2− . The theoretical curve represents an eikonal calculation (solid line assuming l = 1 and a dashed line for l = 0 stripping) assuming various l-values for the removed nucleon. While the simple assumptions of the eikonal model may be questioned, more refined theories. The data are in excellent agreement with the expected momentum distributions and clearly demonstrate the l-value sensitivity of the technique. The experimental spectroscopic factors are compared to theory in Table 1. The models WBT and WBT2 are based on p–sd shell models. In the WBT2 interaction the parameters have been adjusted to reproduce 11 Be properties. The three body model is from Ref. [32]. A very interesting feature, besides the clear break down of the p-shell, is the prediction that significant spectroscopic strength lies in the d-wave state. This states could not be seen in this experiment since it is particle unbound. The same technique has been used to determine the structure of 11 Be by the reaction 9 Be(11 Be, 10 Be*)X and a comparison of measured and predicted cross sections [30]. These Table 1 Summary of spectroscopic factors measured for 12 Be from the knock out reaction described in the text jπ 1/2+ 1/2− 5/2+
E
σexp
σsp
(MeV)
(mb)
(mb)
0 0.32 1.8
32.0 ± 4.7 17.5 ± 2.6 –
75.9 47.2 –
Sexp
∗ Sexp
0.42 ± 0.10 0.37 ± 0.10 –
0.53 ± 0.13 0.45 ± 0.12 –
Sth WBT
WBT2
3B
0.51 0.91 0.40
0.69 0.58 0.55
0.7 0.26 –
426c
B.M. Sherrill / Nuclear Physics A 701 (2002) 422c–428c
Fig. 2. Measured longitudinal momentum distributions in the laboratory frame for 11 Be residues in the ground state (a) and excited state (b) after one-neutron removal reactions of 12 Be. The solid (dashed) curves are calculations for l = 0, 1 neutron removal, normalized to the measured cross section. The errors shown are only statistical. The narrow line in (a) illustrates the line profile of the spectrograph for the incident 12 Be beam, rescaled for display purposes.
authors were able to show that the standard picture of 11 Be as a inert 10 Be core with a valence halo neutron is more or less correct. In particular, they found that the 11 Be groundstate wave function has a small but nonnegligible d5/2 contribution of around 15%. Some structure models had predicted admixtures closer to 50%, a result that would have brought into question the standard halo picture of weakly bound nuclei. An important feature of knock our reactions is that they can be performed with very weak beams of only a few ions per minute. This stems from the large knock out cross sections (several hundred mb), the use of thick targets (nearing 1 g/cm2 for beams of several hundred MeV/u), and high detection efficiency for the core fragment and deexcitation γ -rays. Hence, this technique can be applied to the nuclei farthest from stability that are only weakly produced, provided beam energies of more than 50 MeV/u are available. A variant on the knock out technique is Coulomb dissociation. In this case a photon is used to initiate the knock out. Coulomb dissociation cross sections can also be very large as the equivalent photon flux is intense for a fast ion passing a high-Z target. This technique has the added advantage that the photon flux and the photon–nucleus interaction are well
B.M. Sherrill / Nuclear Physics A 701 (2002) 422c–428c
427c
known. The total removal cross section can be compared to theoretical cross sections and provides a clear indication of the ground-state structure of the dissociated ion. This technique has been applied to several cases, including 11 Be [33], and the heavy carbon isotopes [34,35]. As an illustration of the power of this method, the Coulomb breakup of 19 C [34] was clearly able to show that the ground state of 19 C is + and the binding energy is in the range of 600 keV. All of these experiments were performed with beam intensities of only ions/s. Other direct reactions have also been used. Proton inelastic scattering was used to study the excited structure of 11 Li [36]. Evidence was seen for a low-lying dipole state. This technique involves detection of fragments from the decay of a state and reconstruction of the invariant mass. This type of invariant mass spectroscopy has also been applied to 10 Li [37]. Charge exchange reactions with (t, 3 He) have been used to study the excited structure of 6 He. This experiment again showed, as in the 11 Li case, a lower-lying 1− strength, in this case, at around 5 MeV excitation energy [38].
4. Summary Estimates of the availability of rare isotopes based on production cross sections for projectile fragmentation indicate that a wide variety of new nuclei will become accessible when new facilities such as the Radioactive Ion Beam Factory at RIKEN is completed, the Rare Isotope Accelerator is approved and constructed in the United States. Further GSI will continue to push the boundaries of known nuclei as their primary beam intensities increase. Estimates based on EPAX2 and an ambitious fragment separator acceptance indicate that it may be possible to reach the neutron drip line up to around 120 Zr. Exciting possibilities such as this should continue to stimulate the development of techniques to work with low intensity secondary beams. Fast beams will be critical for these developments as they provide an efficient method for experimentation with weak beams.
Acknowledgements This article is a much shorted version of the publication Scientific Opportunities with Fast Beams at RIA. The 12 Be experiment is the work of A. Navin et al. and the 6 He charge exchange experiment is the work of T. Nakamura et al.
References [1] [2] [3] [4] [5] [6] [7]
J. Dobaczewski, Phil. Trans. R. Proc. London A 356 (1998) 2007. P.G. Hansen, A.S. Jensen, B. Jonson, Annu. Rev. Nucl. Sci. 45 591. I. Tanihata, Prog. Part. Nucl. Phys. 35 (1995) 505. Scientific Opportunities with Fast Beams at RIA, http://www.nscl.msu.edu/research/ria/whitepaper.pdf. K. Sümmerer, B. Blank, submitted to Phys. Rev. C and GSI Preprint-99-37. B. Blank, Phys. Rev. Lett. 84 (2000) 1116. R. Schneider et al., Z. Phys. A 348 (1994) 241.
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[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] [37] [38]
B.M. Sherrill / Nuclear Physics A 701 (2002) 422c–428c
M. Lewitowicz, Phys. Lett. B 322 (1994) 20. H. Sakurai, Phys. Lett. B 448 (1999) 180. W. Mittig, A. Lepine-Szily, N.A. Orr, Annu. Rev. Nucl. Sci. 47 (1997) 27. H. Geissel, in: Sherrill, Morrissey, Davids (Eds.), ENAM98: Exotic Nuclei Atomic Masses, AIP Conf. Proc., Vol. 455, 1998, p. 11. J.C. Wang et al., Phys Lett. B 454 (1999) 1. C. Longour et al., Phys. Rev. Lett. 81 (1998) 3337. D.J. Morrissey et al., Nucl. Phys. A 627 (1997) 222. N. Aoi et al., Z. Phys. A 358 (1997) 253. K. Matsuta et al., Phys. Lett. B 459 (1999) 81. M. Huhta et al., Phys. Rev. C 57 (1998) R2790. G. Neyens, in: Sherrill, Morrissey, Davids (Eds.), ENAM98: Exotic Nuclei and Atomic Masses, AIP Conf. Proc., Vol. 455, 1998, p. 58. G.D. Alkhazov et al., Phys. Rev. Lett. 78 (1998) 2313. S. Karataglidis et al., Phys. Rev. C 61 (2000) 024319. G. Kraus et al., Phys. Rev. Lett. 73 (1994) 1773. J.H. Kelley et al., Phys. Rev. C 56 (1997) R1206. J.K. Jewell et al., Phys. Lett. B 454 (1999) 181. F. Marchal et al., Phys. Rev. C 60 (1999) 034615. L.A. Riley et al., Phys. Rev. Lett. 82 (1999) 4196. S. Fortier et al., Phys. Lett. B 461 (1999) 22. T. Suzuki et al., Phys. Rev. Lett. 75 (1995) 3241. H. Simon et al., Phys. Rev. Lett. 83 (1999) 496. A. Navin et al., Phys. Rev. Lett. 81 (1998) 5089. T. Aumann et al., Phys. Rev. Lett. 84 (2000) 35. A. Navin et al., Phys. Rev. Lett., submitted. F.M. Nunes et al., Nucl. Phys. A 609 (1996) 43. T. Nakamura et al., Phys. Lett. B 394 (1997) 11. T. Nakamura et al., Phys. Rev. Lett. 83 (1999) 1112. D. Ridikas et al., Nucl. Phys. A 628 (1998) 363. A.A. Korsheninnikov et al., Phys. Lett. B 326 (1994) 31. M. Thoennessen, Phys. Rev. C 59 (1999) 111. T. Nakamura et al., Phys. Lett. B 493 (2000) 209.
Scientific opportunities with in-flight separated beams ✩ Bradley M. Sherrill National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI, USA
Abstract This article provides an overview of the use of fast (> 50 MeV/u) beams of radioactive ions for nuclear structure studies. 2002 Elsevier Science B.V. All rights reserved.
1. Introduction Nuclei near the limits of particle stability are among the most interesting to study. These nuclei, due to their unusual ratios of neutrons to protons, may provide the most stringent tests of the isospin dependence of out nuclear models. The drip lines are also where the cases of halo and extreme skin nuclei will be found [1–3]. This paper makes a very broad outline of the experiments possible using fast (> 50 MeV/u) radioactive beams produced via in-flight separation. It is based on the recent summary of fast beam experiments [4]. As described in that document, the key to experiments with nuclei at the extremes will be to develop sensitive experiments that can work with few atoms. Considerable progress in this regard has already been made at fragmentation facilities, such at GSI, GANIL, RIKEN and the NSCL. Fig. 1 illustrates the expected radioactive ion (rare isotope) beam intensities based of projectile fragmentation and a 18% momentum acceptance fragment separator. The production target is adjusted to fill the separator momentum acceptance and the primary beam is optimized for each fragment. The production cross sections are taken from the EPAX2 parameterization [5]. The figure is not intended to be correct in all details and reality may be very different depending on the production cross sections very far from stability. It is also important to note, that ISOL type production can in principle produce, ✩
This work was supported by the National Science Foundation. E-mail address: [email protected] (B.M. Sherrill).
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 6 2 1 - 9
B.M. Sherrill / Nuclear Physics A 701 (2002) 422c–428c
423c
Fig. 1. Intensities for in-flight separated secondary beams produced by projectile fragmentation from a 100 kW 400 MeV/u primary beam as described in the text.
in the production target, something like 10–100 times these value. The region of known nuclei is outlined with the solid line and the approximate path of the rp-process and the r-process are indicated by grey lines. The exciting prospect is that there appears to be the possibility to produce a significant number of r-process nuclei. The rp-process nuclei are produced in relatively large quantities. Further, it appears possible to reach the drip line for nuclei as heavy as 120 Zr. However, as is clear in the figure, these nuclei are produced at very low yields. In the worst cases at a level of only 1 atom/week.
2. Basic nuclear properties One of the most basic properties of a nucleus is whether or not it is particle stable. Fast beams provide an easy measure of particle stability as at sufficiently high energy the ion can be identified and its Z determined by energy loss and its A by flight time through a system. In this way many studies of the locations of the drip lines have been made. Recently along the proton drip line 48 Ni [6] and 100 Sn [7,8] have been discovered. The neutron drip line has only been determined for the lightest nuclei with Z up to 8. Recent studies have determined that 25 N, 26 O and 28 O are neutron unbound [9]. It is fascinating that the very neutron rich nuclei 31 Ne and 31 F were observed. It remains a puzzle why the stability line ends at 24 O, yet with one more proton increases all the way to 31 F. Masses can be measured by time-of-flight techniques, TOF, with only 1000 s of atoms. The flight time is measured over a long distance and the momentum is accurately determined. For a review of techniques in atomic mass measurement, see reference [10]. Related, exciting new results have come from the use of the use of the experimental storage ring, ESR, at GSI as a time of flight spectrometer [11]. Two different types of experiments have been performed. In one set of experiments exotic ions were injected into the ESR and
424c
B.M. Sherrill / Nuclear Physics A 701 (2002) 422c–428c
cooled. The power spectrum was measured for the circulating ions in an electronic pickup system and Fourier analyzed. The other technique employed used the ESR operated in an isochronous mode. This allows shorter lived nuclei (less than 1 s) to be measured since ion cooling, which can take up to 1 s, is not necessary. A variety of information has been extracted from decay studies of nuclei. Half-lives can be compared to global models to constrain model parameters [12]. Precision measurements can be used to determine fundamental constants [13]. Most decay studies involve high efficiency β detection used in connection with coincident charged particle or gamma-ray detectors. Particularly in the case where the β-decay energy window is large, detailed structure information can be obtained on the daughter nucleus. For example, 11 Li, has been studied in great detail and a variety of β-delayed decay modes have been observed [14,15]. Moments for lighter exotic nuclei have been determined primarily from the use of polarized beams and β-NMR techniques. Results for nuclei in the p-shell such as boron, carbon, nitrogen and oxygen have been published using polarized beams obtained from projectile fragmentation at RIKEN and the NSCL [16,17]. An alternative method to measure nuclear moments is the level mixing technique [18]. This technique has been used for a variety of states with lifetimes in the 50 ns to a few second range.
3. Direct reactions with fast beams Direct reactions have been used over the past 30 years to provide a wealth of information on the structure of nuclei. For stable isotopes, it is possible to produce a targets that can be bombarded by light ions. However, no such targets are available for most exotic nuclei due to their short half-lives. Exotic nuclei studies can, however, be done in inverse kinematics, where the role of target and beam are interchanged. For example, proton elastic of 11 Li has been studied at GSI and RIKEN by bombarding hydrogen targets by a 11 Li beam [19]. This data has been compared to various models of 11 Li in order to determine its structure [20]. Proton inelastic scattering with radioactive beams in inverse kinematics was first performed at GSI [21] for 56 Ni and has since been used routinely at various laboratories [22–25]. Exotic beams with energies between 30 MeV/nucleon and 100 MeV/nucleon are scattered off proton targets (which are 1–3 mg/cm2 thick) and protons with energies between 1 and 20 MeV are detected in segmented silicon detectors at laboratory angles close to 90 degrees. In general, with a large solid angle silicon detector array it is possible to perform inelastic scattering experiments with beam rates of as little as 500 particles/s. The equivalent of inverse kinematic pickup reactions, (p, d), has been used at GANIL to study the structure of 11 Be [26]. It was found that the 11 Be ground state is predominately s-wave with a small d-wave admixture. These results are very similar to the results that have been obtained via the knock out reactions described below. One of the first experiments with RNBs was the determination of the total interaction cross sections for neutron rich nuclei at LBL [3]. This technique continues to play an important role. Total reaction cross sections are also a useful observable for studying the changes in structure across a series of isotopes. Normally the interaction cross sections would be expected to scale with A1/3 . If, however, there are changes in structure, such as the development of a neutron skin, this rule will be violated. The measured interaction
B.M. Sherrill / Nuclear Physics A 701 (2002) 422c–428c
425c
cross sections can be compared to calculations and information on the skin or halo structure extracted. One of the best example is the study of neutron skins in sodium [27]. Another tool for studying the detailed structure of nuclei has been the use of knock out reactions. Electron-induced (e, e p) reactions have been used to study deeply bound states in nuclei and have found high momentum components in the wave functions and an interesting apparent lack of the full expected spectroscopic factors. These experiments are performed by measuring scattered electrons and protons and reconstructing the “missing momentum” for the recoil nuclei. This class of experiment can be applied to radioactive beams. In this case, the target is taken as a light nucleus. The “missing momentum” is directly determined by measuring the recoil momentum of the core. The final states of the core are determined by coincident γ -ray detection. Recently, experimental and theoretical work has demonstrated the power of singlenucleon knock out reactions [28–30]. The shape of the recoil distribution can be used to assign the l-value of the removed nucleon. Higher l-value removal has intrinsically larger momentum widths due to the stronger localization of the wave-function for high-l orbits. Spectroscopic factors can be assigned based on the partial cross sections to the excited states of the core compared to the cross sections expected for removal of a nucleon from a given orbit. The results can be compared with spectroscopic factors obtained in various nuclear models, such as large basis shell-model calculations. For example, in the case of 11 Li Simon et al. [28] were able to show the wave function is an almost equal mixture of s- and p-waves. Fig. 2 illustrates the technique with data from Navin et al. [31] for the reaction 9 Be(12 Be, 11 Be*)X leading to the well-known ground state and excited levels with spin and parity 1/2+ and 1/2− . The theoretical curve represents an eikonal calculation (solid line assuming l = 1 and a dashed line for l = 0 stripping) assuming various l-values for the removed nucleon. While the simple assumptions of the eikonal model may be questioned, more refined theories. The data are in excellent agreement with the expected momentum distributions and clearly demonstrate the l-value sensitivity of the technique. The experimental spectroscopic factors are compared to theory in Table 1. The models WBT and WBT2 are based on p–sd shell models. In the WBT2 interaction the parameters have been adjusted to reproduce 11 Be properties. The three body model is from Ref. [32]. A very interesting feature, besides the clear break down of the p-shell, is the prediction that significant spectroscopic strength lies in the d-wave state. This states could not be seen in this experiment since it is particle unbound. The same technique has been used to determine the structure of 11 Be by the reaction 9 Be(11 Be, 10 Be*)X and a comparison of measured and predicted cross sections [30]. These Table 1 Summary of spectroscopic factors measured for 12 Be from the knock out reaction described in the text jπ 1/2+ 1/2− 5/2+
E
σexp
σsp
(MeV)
(mb)
(mb)
0 0.32 1.8
32.0 ± 4.7 17.5 ± 2.6 –
75.9 47.2 –
Sexp
∗ Sexp
0.42 ± 0.10 0.37 ± 0.10 –
0.53 ± 0.13 0.45 ± 0.12 –
Sth WBT
WBT2
3B
0.51 0.91 0.40
0.69 0.58 0.55
0.7 0.26 –
426c
B.M. Sherrill / Nuclear Physics A 701 (2002) 422c–428c
Fig. 2. Measured longitudinal momentum distributions in the laboratory frame for 11 Be residues in the ground state (a) and excited state (b) after one-neutron removal reactions of 12 Be. The solid (dashed) curves are calculations for l = 0, 1 neutron removal, normalized to the measured cross section. The errors shown are only statistical. The narrow line in (a) illustrates the line profile of the spectrograph for the incident 12 Be beam, rescaled for display purposes.
authors were able to show that the standard picture of 11 Be as a inert 10 Be core with a valence halo neutron is more or less correct. In particular, they found that the 11 Be groundstate wave function has a small but nonnegligible d5/2 contribution of around 15%. Some structure models had predicted admixtures closer to 50%, a result that would have brought into question the standard halo picture of weakly bound nuclei. An important feature of knock our reactions is that they can be performed with very weak beams of only a few ions per minute. This stems from the large knock out cross sections (several hundred mb), the use of thick targets (nearing 1 g/cm2 for beams of several hundred MeV/u), and high detection efficiency for the core fragment and deexcitation γ -rays. Hence, this technique can be applied to the nuclei farthest from stability that are only weakly produced, provided beam energies of more than 50 MeV/u are available. A variant on the knock out technique is Coulomb dissociation. In this case a photon is used to initiate the knock out. Coulomb dissociation cross sections can also be very large as the equivalent photon flux is intense for a fast ion passing a high-Z target. This technique has the added advantage that the photon flux and the photon–nucleus interaction are well
B.M. Sherrill / Nuclear Physics A 701 (2002) 422c–428c
427c
known. The total removal cross section can be compared to theoretical cross sections and provides a clear indication of the ground-state structure of the dissociated ion. This technique has been applied to several cases, including 11 Be [33], and the heavy carbon isotopes [34,35]. As an illustration of the power of this method, the Coulomb breakup of 19 C [34] was clearly able to show that the ground state of 19 C is + and the binding energy is in the range of 600 keV. All of these experiments were performed with beam intensities of only ions/s. Other direct reactions have also been used. Proton inelastic scattering was used to study the excited structure of 11 Li [36]. Evidence was seen for a low-lying dipole state. This technique involves detection of fragments from the decay of a state and reconstruction of the invariant mass. This type of invariant mass spectroscopy has also been applied to 10 Li [37]. Charge exchange reactions with (t, 3 He) have been used to study the excited structure of 6 He. This experiment again showed, as in the 11 Li case, a lower-lying 1− strength, in this case, at around 5 MeV excitation energy [38].
4. Summary Estimates of the availability of rare isotopes based on production cross sections for projectile fragmentation indicate that a wide variety of new nuclei will become accessible when new facilities such as the Radioactive Ion Beam Factory at RIKEN is completed, the Rare Isotope Accelerator is approved and constructed in the United States. Further GSI will continue to push the boundaries of known nuclei as their primary beam intensities increase. Estimates based on EPAX2 and an ambitious fragment separator acceptance indicate that it may be possible to reach the neutron drip line up to around 120 Zr. Exciting possibilities such as this should continue to stimulate the development of techniques to work with low intensity secondary beams. Fast beams will be critical for these developments as they provide an efficient method for experimentation with weak beams.
Acknowledgements This article is a much shorted version of the publication Scientific Opportunities with Fast Beams at RIA. The 12 Be experiment is the work of A. Navin et al. and the 6 He charge exchange experiment is the work of T. Nakamura et al.
References [1] [2] [3] [4] [5] [6] [7]
J. Dobaczewski, Phil. Trans. R. Proc. London A 356 (1998) 2007. P.G. Hansen, A.S. Jensen, B. Jonson, Annu. Rev. Nucl. Sci. 45 591. I. Tanihata, Prog. Part. Nucl. Phys. 35 (1995) 505. Scientific Opportunities with Fast Beams at RIA, http://www.nscl.msu.edu/research/ria/whitepaper.pdf. K. Sümmerer, B. Blank, submitted to Phys. Rev. C and GSI Preprint-99-37. B. Blank, Phys. Rev. Lett. 84 (2000) 1116. R. Schneider et al., Z. Phys. A 348 (1994) 241.
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