- Email: [email protected]
Nuclear structure studies with RI beams and cooler rings
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 532 (2004) 79–85
Nuclear structure studies with RI beams and cooler rings Isao Tanihata* RIKEN, RI Beam Science Laboratory, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan Available online 25 June 2004
Abstract Selected topics in present days nuclear structure physics studied by reactions of RI beams are presented. They are change in nuclear radii, single particle orbitals, and shapes. Dynamical changes are shown for nuclei far from the stability line in particular in p-sd shell. Among the future reaction study, a thick target method for a storage ring is presented. A possibility to obtain the highest luminosity for an internal target experiment is proposed. r 2004 Published by Elsevier B.V. Keywords: RI Beams; Neutron skin; Neutron halo; Magic numbers; Storage ring
1. Introduction
2. Nuclear radii and density distribution
Development of RI beams provided new views in nuclear structure physics. Several new structures such as neutron skins, neutron halos, and covalent-bond-type molecular structures have been discovered through reaction studies with RI beams [1]. One of the main changes is the great expansion of the region of structure studies that is now expanded to the proton and neutron drip line for nuclei up to oxygen. Before RI beams, neutron drip line was reached only up to Li and no reaction studies were made for unstable nuclei. It is this great expansion of studies that brought new insight into nuclear physics.
From studies of stable nuclei, three ‘‘basic properties’’ of nuclear density had been established:
*Fax: +81-48-46-21-554. E-mail address: [email protected] (I. Tanihata). 0168-9002/$ - see front matter r 2004 Published by Elsevier B.V. doi:10.1016/j.nima.2004.06.032
1. Half-density radius of the matter distribution is expressed as r0 A1=3 ; where r0 is the radius constant. 2. Protons and neutrons are homogeneously mixed in the nucleus, namely rp ðrÞprn ðrÞ: 3. Surface thickness is constant.
For determination of radii of unstable nuclei, isotope-shift measurements had been a unique technology. However, due to the technical limitations, such measurements have been made only for a limited number of elements. Moreover, these measurements provide only the charge radii or the proton radii of a nucleus. Almost no studies had
ARTICLE IN PRESS I. Tanihata / Nuclear Instruments and Methods in Physics Research A 532 (2004) 79–85
been made for the matter density distribution of unstable nuclei until the RI beam method was invented. The production and use of RI beams, which has been started in the mid-1980s [2,3], broke this restriction and enabled the study of matter radii and matter density distributions of unstable nuclei extending up to the proton and neutron drip lines. From studies of matter distributions of unstable nuclei, it was found that the three ‘‘basic properties’’ shown above is valid only for stable nuclei and do not hold for unstable nuclei. This fact is easily seen in the two-dimensional display of nuclear root-mean square radii in nuclear chart as shown in Fig. 1. These rms radii of nucleondistributions have been determined by the measurements of interaction cross-sections using highenergy (B800A MeV) RI beams[4, 5]. The observed differences of the radii between isobars clearly show the break of ‘‘basic property 1’’. A faster increase of Na isotopes radii is the reflection of neutron skin, which will be discussed below, and indicates the breaking of ‘‘basic property 2’’. The sudden large increase of the radii near the neutron drip line are the reflection of neutron halo and show the break of ‘‘basic property 3’’. 2.1. Neutron skin The first suggestion of a thick neutron skin was reported by Tanihata et al. [6]. They suggested extremely thick neutron skin of about 0.8 fm in 8 He. Recent proton elastic scattering studies of 6 He and 8He by Egelhof et al. [7] show more 15
Proton Drip line
Z
10
Neutron Drip line
5
(Rmrms - 1.47 ) fm
detailed density distributions and confirmed the neutron skin. The first direct comparison between neutron and proton radii over a wide range of neutron numbers was made in Na isotopes. Suzuki et al. [8] extracted the rms radii of proton and neutron distributions by combining the isotope shift and interaction cross-section data. Fig. 2 shows the results. The proton rms radii or2p >1=2 and the neutron rms radii or2n >1=2 are plotted as a function of the neutron number of Na isotope. In contrast to the slow change of or2p >1=2 ; neutron radius or2n >1=2 increases monotonically as neutron number increases. The thickness of the neutron skin DRð¼ or2n >1=2 or2p >1=2 Þ increase up to 0.4 fm in the most neutron-rich Na isotope studied here. This value of neutron skin is much larger than a possible skin (0.12 fm) observed in the most neutron-rich stable isotope 48Ca. Recent suggestive data are obtained by systematic measurements of charge-changing cross-sections (scc) of B to F isotopes [9]. As shown in the Fig. 3 the charge-changing cross-section does not increase when neutron number increases for a particular element. Instead, an increase is observed when proton number increases. At high energies, scc is directly related to charge distribution through the Glauber model analysis. A scc may be larger than the estimation of Glauber model 3.5 Root-mean-squareRadiu [fm]
80
Neutron Proton
3.0
2.5 8
0.5 1
1.5
2
0
5
10
15
20
N
Fig. 1. Root-mean square matter radii of light nuclei.
12
16
20
N
0 25
Fig. 2. Neutron and proton radii of Na isotopes. Neutron radii increase faster than that of protons and indicate the formation of neutron skin.
ARTICLE IN PRESS I. Tanihata / Nuclear Instruments and Methods in Physics Research A 532 (2004) 79–85
Fig. 3. Charge-changing cross-sections with C target. The curve in the figure shows the A1=3 dependence of radii that is followed well for stable nuclei.
due to possible proton emission at the ablation stage of the reaction. Therefore, scc provides an upper limit of the charge radius. A combination of sI and scc ; therefore, allows us to deduce the minimum estimation of the neutron skin thickness. Interaction cross-sections increase monotonically when neutron number increases for all elements. Therefore, the constancy of scc for isotopes in Fig. 3 indicates the development of neutron skin in all elements shown there. In Na isotope data (see Fig. 2), slightly larger radii of proton distribution are seen for most neutron deficient isotopes. It, therefore, suggests the proton skin of about 0.1–0.2 fm in these nuclei. The radii of proton and neutron distributions are same only for stable isotope 23Na.
81
strongly contributes to form two-neutron halo [11, 12]. It is essentially due of the small centrifugal barrier for those neutrons. In fact, these analyses showed that the rms radii of those neutron distributions diverge when the neutron separation energy goes to 0. Instead, the rms radius of wave function with angular momentum larger than or equal to 2 (or KX2) remains to finite value in the same limit. The density distributions of halo nuclei have been determined by several methods. The best method is the high-energy proton scatterings. In addition to the density distribution of He isotopes discussed before, the density distribution of 11Li has been determined by the proton elastic scattering at 800 MeV [7] as shown in Fig. 4. Long tail of the density distribution is clearly seen. This density distribution is consistent with the density distribution deduced from the interaction cross-sections by the method shown below. The density distributions of other neutron halo nuclei have not yet been determined by the elastic scattering. Instead, careful analyses of interactionand reaction-cross-sections using density model have been used to determine density distributions [4,5]. The analysis is made by changing the nucleon-nucleon cross-section or by changing target density distribution. From those studies, density distributions have been determined and long tails in the density distributions were confirmed [13–15].
2.2. Neutron halo A low-density tail of neutron distribution (neutron halo) has been discovered from an abrupt increase of interaction cross-section and a narrow momentum distribution of a neutron (or neutrons) in such a nucleus. The apparent reason of formation of neutron halo is the weak binding of the neutron. From analysis of the two-body halo wave function, Riisager et al. [10] found that s- and pwaves contribute to form single-neutron halo in most drastic way. Similarly, from three-body analysis, it was found that K ¼ 0; 1 waves most
Fig. 4. Density distribution of 11Li. Black curves are density determined by proton scattering and the blue region shows the density determined by sI :
ARTICLE IN PRESS 82
I. Tanihata / Nuclear Instruments and Methods in Physics Research A 532 (2004) 79–85
Fig. 5. Density distribution of neutron-rich nuclei determine from interaction cross-section measurements. Clear halo tails are seen in 15,19 C, 22N, and 23O.
Another method for determining density distributions assumes the relation between the asymptotic tail of the density distribution and the neutron separation energy to be the single particle nature. In this model, a halo nucleus is assumed to have a (core+neutron) structure and the last neutron has a single-particle wave function in a Woods–Saxon potential. Density distributions of many light neutron-rich nuclei have been determined and significant long tails of the neutron distribution have been observed from He to C isotopes (Fig. 5). Proton halos are also searched by the interaction and reaction cross-sections. Possible evidences of long tails have been shown in 8B, 17Ne, 23Al [16,17] However, the data are not sufficient to discuss the density distribution yet. Recent interests in halo nuclei go beyond the matter distribution and are now focused on understanding the spectroscopic information of halo states.
3. Change of magic numbers From the spectroscopic studies of short lived nuclei, dynamic changes of the order of single particle orbitals are seen. Fig. 6 shows the comparison of normal ordering of single-particle
Fig. 6. Regions of dominance of S1=2 and d5=2 neutron orbitals in ground states.
orbitals and observed region of orbitals in ground states. It is clearly seen that the order of single particle orbitals are different from ‘‘normal’’ one and changing rapidly. It is seen that s1=2 orbitals always dominate near the neutron drip line. As a consequence of such changes in nuclear orbitals, it is naturally expected that the nuclear shell gaps would be modified in neutron- and proton-rich regions. The nucleon magic numbers can be identified from empirical systematics related to nuclear binding, such as, one-nucleon separation energy and beta-decay Q-values along the same isospin chain. The systematics of excitation energies (Ex ð2þ )) and B(E2) values of the even–even isotopes for neutron- and proton-rich nuclei also provides a good confirmation of magicity. Furthermore, the spectroscopy of nuclei,
ARTICLE IN PRESS I. Tanihata / Nuclear Instruments and Methods in Physics Research A 532 (2004) 79–85
show the presence of intruder orbitals that signifies the breakdown of a shell closure. The disappearance of the N ¼ 8 shell closure appeared as the first evidence in the discovery of the neutron halo in 11Li [3]. It showed the strong influence of the 2s1=2 orbital in the supposedly p1=2 closed shell. The extension of this breakdown continues to the Be isotopes, which can be observed clearly by the decrease in excitation energy of the 2þ state from 10Be to 12Be associated with quadrupole collectivity and furthermore confirmed by the presence of a low-lying 1 state [18]. In addition to the anomaly of binding energy in Na isotopes, a large quadrupole collectivity observed for 32Mg confirmed breakdown of N ¼ 20 shell closure [19]. Studies of beta delayed neutron emission probabilities of 44S [20] suggests the weakening of N ¼ 28 shell closure in regions below 48Ca. In contrast to the disappearance of magic numbers, recent studies of neutron separation energies and radii of C, N, O isotopes by Ozawa et al., have shown an appearance of a new magic number N ¼ 16 [21]. Further re-confirmation of this was found from an extensive study of other relevant quantities by Kanungo et al. [22], which also shows new regions of shell closures at N ¼ 6; 30; 32 in neutron-rich nuclei. Interestingly Z ¼ 16 also shows a magic number behavior in neutron-rich regions. Extending the same study to the proton-rich part of the nuclear chart they find new shell gaps originating at proton number Z ¼ 16; and N ¼ 6; 16 which are similar to the neutron-rich side. This suggests a kind of mirror symmetry for the new shell gaps at either sides of the stability line. The N ¼ 16 magic number was understood to originate due to a lowering of the 2s1=2 orbital in regions of small separation energy [21]. The reason for N ¼ 30 and Z ¼ 16 magicity in neutron rich nuclei is yet to be understood. Fig. 7 summarizes the changes of shell closures for light nuclei [22]. Although for lighter nuclei, conventional doubly magic nuclei like 10He, 28O are unbound. It is interesting to note that the existence of doubly magic 78Ni, 100,132Sn may show the persistence N ¼ 50; 82 shell closure there. The
83
Fig. 7. Summary of change of magic numbers for light nuclei.
changes in shell closures in this area are important subjects of investigation as they are intricately related to the understanding of the r-process nucleosynthesis.
4. Change of nuclear shapes So far we discussed the change of nuclear structure based on the shell orbitals. However, experiments and theories suggest much more radical change in nuclear shape. For example, covalent type molecular binding states have been observed in 12Be. 12Be has special character due to the halo structure of 6He. The excited states just above two He states (4He+8He, 6He+6He) are known to decay into He isotopes instead of decaying into Be isotopes that have much more decay energy. Further studies showed that they are states in which neutrons are orbiting around the two 4He cores. It is possible because the separation energy of such neutrons is very small (o1 MeV) compared with the separation energy of a neutron from the 4He core (20 MeV). Also the neutron orbitals are mainly p3/2 and thus four neutrons can be in the orbital forming covalent bond. This observation also presents us the importance of cluster formation of various types in neutron-rich nuclei. Cluster formation may be copious in low-density neutron cloud such as neutron skins and halos.
ARTICLE IN PRESS 84
I. Tanihata / Nuclear Instruments and Methods in Physics Research A 532 (2004) 79–85
5. Storage ring for internal target experiment As presented in several examples above, reaction studies carry essential importance for obtaining new information. A storage and cooler ring provides many additional opportunities in usage of RI beams. In particular, high-resolution studies and mass measurements are promising research possibility among others. Among those, proton elastic scattering would be the most important. Proton scatterings in the storage ring will provides the information of detail of the density distribution and equation-of-states (EOS) of asymmetric nuclear matter. The EOS of asymmetric nuclear matter is extremely important for understanding several astrophysical environments such as neutron star and supernovae but has not been studied from experimental data. Another extremely important use is to eliminate isomers in the RI beams. After the RI beam separator, the ground state and isomers in a nucleus may be mixed. Because a separation time in fragment separator is short (o100 ns), isomers with life time longer than that are also transmitted. If isomer is mixed in the beam it is impossible to identify a reaction from the ground state and that from an isomer. Only the possible method to get out of this problem is to wait the decay of isomers. A storage ring provides this possibility. Special requirement of the storage ring for RI beam is as follows: 1. Faster cooling time down to 1 ms range is desirable. However, this cooling is not for cooling the beam to very small momentum spread but to cool beam just enough to keep it in the ring for the lifetime of the beam nuclide. 2. We would like to use as thick target as possible to obtain high luminosity. 3. Sometime the intensity of RI is extremely small and thus an injection process may not put any nucleus in the ring. A quick method to detect whether expected nuclei are in or not helps faster accumulation of data. Simulations and R&D are going on to optimize the luminosity of storage ring for internal target studies. One of the interesting possibilities is the
use of a very thick target such as a foil of 1 mm that correspond to B1019 atoms/cm2. In particular, this is necessary for study of nuclei far from the stability line because they are very weak in intensity. However, their lifetime is short (o10 s) so that it is not necessary to keep the beam long in the storage ring. Let us see the back of the envelope estimation whether it is possible to operate under such a condition. Suppose just one particle is in the ring, the available luminosity is 1024 cm2 if one can use 1019 atoms/cm2 thick target. In this case, a stored nucleus reacts with target nucleus with an average rate higher than 1/s. Therefore, it is necessary to keep the beam only for seconds. The energy loss of the particle per turn for this target is 0.2Z2 keV and the necessary acceleration voltage per turn is only 0.2Z kV and is easily available. The emittance growth of the beam can be compensated by the acceleration of the beam after the deceleration. However, this compensation works only for emittance but not for energy spread. Unfortunately, the energy loss of the heavy ions in few hundred MeV per nucleon is smaller for higher-energy. Therefore the beam energy become broader as the number of turn increases. However, it may not be necessary to cool it if beam is kept in the ring until decay or react. The rarer RI-beam has usually of shorter half-life. Their half-lives are a few seconds or even shorter. Therefore, there would be no basic problem for applying this method.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
I. Tanihata, Nucl. Phys. A 693 (2001) 1. I. Tanihata, Hyperfine Intactions 21 (1985) 251. I. Tanihata, et al., Phys. Lett. B 160 (1985) 380. A. Ozawa, et al., Nucl. Phys. A 691 (2001) 599. A. Ozawa, T. Suzuki, I. Tanihata, Nucl. Phys. A 693 (2001) 32. I. Tanihata, et al., Phys. Lett. B 289 (1992) 261. P. Egelhof, et al., Eur. Phys. J. A 15 (2002) 27. T. Suzuki, et al., Phys. Rev. Lett. 75 (1995) 3241. L.V. Chulkov, et al., Nucl. Phys. A 674 (2000) 330. . K. Riisager, A.S. Jensen, P. Moller, Nucl. Phys. A 548 (3) (1992) 393. D.V. Fedorov, A.S. Jensen, K. Riisager, Phys. Rev. C 1994 (1) (1994) 201.
ARTICLE IN PRESS I. Tanihata / Nuclear Instruments and Methods in Physics Research A 532 (2004) 79–85 [12] D.V. Fedorov, A.S. Jensen, K. Riisager, Phys. Rev. C 50 (5) (1994) 2372. [13] M. Fukuda, et al., Phys. Lett. B 268 (1991) 339. [14] I. Tanihata, et al., Phys. Lett. B 287 (1992) 307. [15] T. Zheng, et al., Nucl. Phys. A 709 (2002) 103. [16] A. Ozawa, et al., Phys. Lett. B 334 (1994) 18. [17] X.Z. Cai, et al., Phys. Rev. C 65 (2002) 024610.
[18] [19] [20] [21] [22]
85
H. Iwasaki, et al., Eur. Phys. J. 13 (2002) 55. T. Motobayashi, et al., Phys. Lett. B. 346 (1995) 9. O. Sorlin, et al., Phys. Rev. C 47 (1993) 2941. A. Ozawa, et al., Phys. Rev. Lett. 84 (2000) 5493. R. Kanungo, I. Tanihata, A. Ozawa, Phys. Lett. B 528 (2002) 58.
Nuclear Instruments and Methods in Physics Research A 532 (2004) 79–85
Nuclear structure studies with RI beams and cooler rings Isao Tanihata* RIKEN, RI Beam Science Laboratory, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan Available online 25 June 2004
Abstract Selected topics in present days nuclear structure physics studied by reactions of RI beams are presented. They are change in nuclear radii, single particle orbitals, and shapes. Dynamical changes are shown for nuclei far from the stability line in particular in p-sd shell. Among the future reaction study, a thick target method for a storage ring is presented. A possibility to obtain the highest luminosity for an internal target experiment is proposed. r 2004 Published by Elsevier B.V. Keywords: RI Beams; Neutron skin; Neutron halo; Magic numbers; Storage ring
1. Introduction
2. Nuclear radii and density distribution
Development of RI beams provided new views in nuclear structure physics. Several new structures such as neutron skins, neutron halos, and covalent-bond-type molecular structures have been discovered through reaction studies with RI beams [1]. One of the main changes is the great expansion of the region of structure studies that is now expanded to the proton and neutron drip line for nuclei up to oxygen. Before RI beams, neutron drip line was reached only up to Li and no reaction studies were made for unstable nuclei. It is this great expansion of studies that brought new insight into nuclear physics.
From studies of stable nuclei, three ‘‘basic properties’’ of nuclear density had been established:
*Fax: +81-48-46-21-554. E-mail address: [email protected] (I. Tanihata). 0168-9002/$ - see front matter r 2004 Published by Elsevier B.V. doi:10.1016/j.nima.2004.06.032
1. Half-density radius of the matter distribution is expressed as r0 A1=3 ; where r0 is the radius constant. 2. Protons and neutrons are homogeneously mixed in the nucleus, namely rp ðrÞprn ðrÞ: 3. Surface thickness is constant.
For determination of radii of unstable nuclei, isotope-shift measurements had been a unique technology. However, due to the technical limitations, such measurements have been made only for a limited number of elements. Moreover, these measurements provide only the charge radii or the proton radii of a nucleus. Almost no studies had
ARTICLE IN PRESS I. Tanihata / Nuclear Instruments and Methods in Physics Research A 532 (2004) 79–85
been made for the matter density distribution of unstable nuclei until the RI beam method was invented. The production and use of RI beams, which has been started in the mid-1980s [2,3], broke this restriction and enabled the study of matter radii and matter density distributions of unstable nuclei extending up to the proton and neutron drip lines. From studies of matter distributions of unstable nuclei, it was found that the three ‘‘basic properties’’ shown above is valid only for stable nuclei and do not hold for unstable nuclei. This fact is easily seen in the two-dimensional display of nuclear root-mean square radii in nuclear chart as shown in Fig. 1. These rms radii of nucleondistributions have been determined by the measurements of interaction cross-sections using highenergy (B800A MeV) RI beams[4, 5]. The observed differences of the radii between isobars clearly show the break of ‘‘basic property 1’’. A faster increase of Na isotopes radii is the reflection of neutron skin, which will be discussed below, and indicates the breaking of ‘‘basic property 2’’. The sudden large increase of the radii near the neutron drip line are the reflection of neutron halo and show the break of ‘‘basic property 3’’. 2.1. Neutron skin The first suggestion of a thick neutron skin was reported by Tanihata et al. [6]. They suggested extremely thick neutron skin of about 0.8 fm in 8 He. Recent proton elastic scattering studies of 6 He and 8He by Egelhof et al. [7] show more 15
Proton Drip line
Z
10
Neutron Drip line
5
(Rmrms - 1.47 ) fm
detailed density distributions and confirmed the neutron skin. The first direct comparison between neutron and proton radii over a wide range of neutron numbers was made in Na isotopes. Suzuki et al. [8] extracted the rms radii of proton and neutron distributions by combining the isotope shift and interaction cross-section data. Fig. 2 shows the results. The proton rms radii or2p >1=2 and the neutron rms radii or2n >1=2 are plotted as a function of the neutron number of Na isotope. In contrast to the slow change of or2p >1=2 ; neutron radius or2n >1=2 increases monotonically as neutron number increases. The thickness of the neutron skin DRð¼ or2n >1=2 or2p >1=2 Þ increase up to 0.4 fm in the most neutron-rich Na isotope studied here. This value of neutron skin is much larger than a possible skin (0.12 fm) observed in the most neutron-rich stable isotope 48Ca. Recent suggestive data are obtained by systematic measurements of charge-changing cross-sections (scc) of B to F isotopes [9]. As shown in the Fig. 3 the charge-changing cross-section does not increase when neutron number increases for a particular element. Instead, an increase is observed when proton number increases. At high energies, scc is directly related to charge distribution through the Glauber model analysis. A scc may be larger than the estimation of Glauber model 3.5 Root-mean-squareRadiu [fm]
80
Neutron Proton
3.0
2.5 8
0.5 1
1.5
2
0
5
10
15
20
N
Fig. 1. Root-mean square matter radii of light nuclei.
12
16
20
N
0 25
Fig. 2. Neutron and proton radii of Na isotopes. Neutron radii increase faster than that of protons and indicate the formation of neutron skin.
ARTICLE IN PRESS I. Tanihata / Nuclear Instruments and Methods in Physics Research A 532 (2004) 79–85
Fig. 3. Charge-changing cross-sections with C target. The curve in the figure shows the A1=3 dependence of radii that is followed well for stable nuclei.
due to possible proton emission at the ablation stage of the reaction. Therefore, scc provides an upper limit of the charge radius. A combination of sI and scc ; therefore, allows us to deduce the minimum estimation of the neutron skin thickness. Interaction cross-sections increase monotonically when neutron number increases for all elements. Therefore, the constancy of scc for isotopes in Fig. 3 indicates the development of neutron skin in all elements shown there. In Na isotope data (see Fig. 2), slightly larger radii of proton distribution are seen for most neutron deficient isotopes. It, therefore, suggests the proton skin of about 0.1–0.2 fm in these nuclei. The radii of proton and neutron distributions are same only for stable isotope 23Na.
81
strongly contributes to form two-neutron halo [11, 12]. It is essentially due of the small centrifugal barrier for those neutrons. In fact, these analyses showed that the rms radii of those neutron distributions diverge when the neutron separation energy goes to 0. Instead, the rms radius of wave function with angular momentum larger than or equal to 2 (or KX2) remains to finite value in the same limit. The density distributions of halo nuclei have been determined by several methods. The best method is the high-energy proton scatterings. In addition to the density distribution of He isotopes discussed before, the density distribution of 11Li has been determined by the proton elastic scattering at 800 MeV [7] as shown in Fig. 4. Long tail of the density distribution is clearly seen. This density distribution is consistent with the density distribution deduced from the interaction cross-sections by the method shown below. The density distributions of other neutron halo nuclei have not yet been determined by the elastic scattering. Instead, careful analyses of interactionand reaction-cross-sections using density model have been used to determine density distributions [4,5]. The analysis is made by changing the nucleon-nucleon cross-section or by changing target density distribution. From those studies, density distributions have been determined and long tails in the density distributions were confirmed [13–15].
2.2. Neutron halo A low-density tail of neutron distribution (neutron halo) has been discovered from an abrupt increase of interaction cross-section and a narrow momentum distribution of a neutron (or neutrons) in such a nucleus. The apparent reason of formation of neutron halo is the weak binding of the neutron. From analysis of the two-body halo wave function, Riisager et al. [10] found that s- and pwaves contribute to form single-neutron halo in most drastic way. Similarly, from three-body analysis, it was found that K ¼ 0; 1 waves most
Fig. 4. Density distribution of 11Li. Black curves are density determined by proton scattering and the blue region shows the density determined by sI :
ARTICLE IN PRESS 82
I. Tanihata / Nuclear Instruments and Methods in Physics Research A 532 (2004) 79–85
Fig. 5. Density distribution of neutron-rich nuclei determine from interaction cross-section measurements. Clear halo tails are seen in 15,19 C, 22N, and 23O.
Another method for determining density distributions assumes the relation between the asymptotic tail of the density distribution and the neutron separation energy to be the single particle nature. In this model, a halo nucleus is assumed to have a (core+neutron) structure and the last neutron has a single-particle wave function in a Woods–Saxon potential. Density distributions of many light neutron-rich nuclei have been determined and significant long tails of the neutron distribution have been observed from He to C isotopes (Fig. 5). Proton halos are also searched by the interaction and reaction cross-sections. Possible evidences of long tails have been shown in 8B, 17Ne, 23Al [16,17] However, the data are not sufficient to discuss the density distribution yet. Recent interests in halo nuclei go beyond the matter distribution and are now focused on understanding the spectroscopic information of halo states.
3. Change of magic numbers From the spectroscopic studies of short lived nuclei, dynamic changes of the order of single particle orbitals are seen. Fig. 6 shows the comparison of normal ordering of single-particle
Fig. 6. Regions of dominance of S1=2 and d5=2 neutron orbitals in ground states.
orbitals and observed region of orbitals in ground states. It is clearly seen that the order of single particle orbitals are different from ‘‘normal’’ one and changing rapidly. It is seen that s1=2 orbitals always dominate near the neutron drip line. As a consequence of such changes in nuclear orbitals, it is naturally expected that the nuclear shell gaps would be modified in neutron- and proton-rich regions. The nucleon magic numbers can be identified from empirical systematics related to nuclear binding, such as, one-nucleon separation energy and beta-decay Q-values along the same isospin chain. The systematics of excitation energies (Ex ð2þ )) and B(E2) values of the even–even isotopes for neutron- and proton-rich nuclei also provides a good confirmation of magicity. Furthermore, the spectroscopy of nuclei,
ARTICLE IN PRESS I. Tanihata / Nuclear Instruments and Methods in Physics Research A 532 (2004) 79–85
show the presence of intruder orbitals that signifies the breakdown of a shell closure. The disappearance of the N ¼ 8 shell closure appeared as the first evidence in the discovery of the neutron halo in 11Li [3]. It showed the strong influence of the 2s1=2 orbital in the supposedly p1=2 closed shell. The extension of this breakdown continues to the Be isotopes, which can be observed clearly by the decrease in excitation energy of the 2þ state from 10Be to 12Be associated with quadrupole collectivity and furthermore confirmed by the presence of a low-lying 1 state [18]. In addition to the anomaly of binding energy in Na isotopes, a large quadrupole collectivity observed for 32Mg confirmed breakdown of N ¼ 20 shell closure [19]. Studies of beta delayed neutron emission probabilities of 44S [20] suggests the weakening of N ¼ 28 shell closure in regions below 48Ca. In contrast to the disappearance of magic numbers, recent studies of neutron separation energies and radii of C, N, O isotopes by Ozawa et al., have shown an appearance of a new magic number N ¼ 16 [21]. Further re-confirmation of this was found from an extensive study of other relevant quantities by Kanungo et al. [22], which also shows new regions of shell closures at N ¼ 6; 30; 32 in neutron-rich nuclei. Interestingly Z ¼ 16 also shows a magic number behavior in neutron-rich regions. Extending the same study to the proton-rich part of the nuclear chart they find new shell gaps originating at proton number Z ¼ 16; and N ¼ 6; 16 which are similar to the neutron-rich side. This suggests a kind of mirror symmetry for the new shell gaps at either sides of the stability line. The N ¼ 16 magic number was understood to originate due to a lowering of the 2s1=2 orbital in regions of small separation energy [21]. The reason for N ¼ 30 and Z ¼ 16 magicity in neutron rich nuclei is yet to be understood. Fig. 7 summarizes the changes of shell closures for light nuclei [22]. Although for lighter nuclei, conventional doubly magic nuclei like 10He, 28O are unbound. It is interesting to note that the existence of doubly magic 78Ni, 100,132Sn may show the persistence N ¼ 50; 82 shell closure there. The
83
Fig. 7. Summary of change of magic numbers for light nuclei.
changes in shell closures in this area are important subjects of investigation as they are intricately related to the understanding of the r-process nucleosynthesis.
4. Change of nuclear shapes So far we discussed the change of nuclear structure based on the shell orbitals. However, experiments and theories suggest much more radical change in nuclear shape. For example, covalent type molecular binding states have been observed in 12Be. 12Be has special character due to the halo structure of 6He. The excited states just above two He states (4He+8He, 6He+6He) are known to decay into He isotopes instead of decaying into Be isotopes that have much more decay energy. Further studies showed that they are states in which neutrons are orbiting around the two 4He cores. It is possible because the separation energy of such neutrons is very small (o1 MeV) compared with the separation energy of a neutron from the 4He core (20 MeV). Also the neutron orbitals are mainly p3/2 and thus four neutrons can be in the orbital forming covalent bond. This observation also presents us the importance of cluster formation of various types in neutron-rich nuclei. Cluster formation may be copious in low-density neutron cloud such as neutron skins and halos.
ARTICLE IN PRESS 84
I. Tanihata / Nuclear Instruments and Methods in Physics Research A 532 (2004) 79–85
5. Storage ring for internal target experiment As presented in several examples above, reaction studies carry essential importance for obtaining new information. A storage and cooler ring provides many additional opportunities in usage of RI beams. In particular, high-resolution studies and mass measurements are promising research possibility among others. Among those, proton elastic scattering would be the most important. Proton scatterings in the storage ring will provides the information of detail of the density distribution and equation-of-states (EOS) of asymmetric nuclear matter. The EOS of asymmetric nuclear matter is extremely important for understanding several astrophysical environments such as neutron star and supernovae but has not been studied from experimental data. Another extremely important use is to eliminate isomers in the RI beams. After the RI beam separator, the ground state and isomers in a nucleus may be mixed. Because a separation time in fragment separator is short (o100 ns), isomers with life time longer than that are also transmitted. If isomer is mixed in the beam it is impossible to identify a reaction from the ground state and that from an isomer. Only the possible method to get out of this problem is to wait the decay of isomers. A storage ring provides this possibility. Special requirement of the storage ring for RI beam is as follows: 1. Faster cooling time down to 1 ms range is desirable. However, this cooling is not for cooling the beam to very small momentum spread but to cool beam just enough to keep it in the ring for the lifetime of the beam nuclide. 2. We would like to use as thick target as possible to obtain high luminosity. 3. Sometime the intensity of RI is extremely small and thus an injection process may not put any nucleus in the ring. A quick method to detect whether expected nuclei are in or not helps faster accumulation of data. Simulations and R&D are going on to optimize the luminosity of storage ring for internal target studies. One of the interesting possibilities is the
use of a very thick target such as a foil of 1 mm that correspond to B1019 atoms/cm2. In particular, this is necessary for study of nuclei far from the stability line because they are very weak in intensity. However, their lifetime is short (o10 s) so that it is not necessary to keep the beam long in the storage ring. Let us see the back of the envelope estimation whether it is possible to operate under such a condition. Suppose just one particle is in the ring, the available luminosity is 1024 cm2 if one can use 1019 atoms/cm2 thick target. In this case, a stored nucleus reacts with target nucleus with an average rate higher than 1/s. Therefore, it is necessary to keep the beam only for seconds. The energy loss of the particle per turn for this target is 0.2Z2 keV and the necessary acceleration voltage per turn is only 0.2Z kV and is easily available. The emittance growth of the beam can be compensated by the acceleration of the beam after the deceleration. However, this compensation works only for emittance but not for energy spread. Unfortunately, the energy loss of the heavy ions in few hundred MeV per nucleon is smaller for higher-energy. Therefore the beam energy become broader as the number of turn increases. However, it may not be necessary to cool it if beam is kept in the ring until decay or react. The rarer RI-beam has usually of shorter half-life. Their half-lives are a few seconds or even shorter. Therefore, there would be no basic problem for applying this method.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
I. Tanihata, Nucl. Phys. A 693 (2001) 1. I. Tanihata, Hyperfine Intactions 21 (1985) 251. I. Tanihata, et al., Phys. Lett. B 160 (1985) 380. A. Ozawa, et al., Nucl. Phys. A 691 (2001) 599. A. Ozawa, T. Suzuki, I. Tanihata, Nucl. Phys. A 693 (2001) 32. I. Tanihata, et al., Phys. Lett. B 289 (1992) 261. P. Egelhof, et al., Eur. Phys. J. A 15 (2002) 27. T. Suzuki, et al., Phys. Rev. Lett. 75 (1995) 3241. L.V. Chulkov, et al., Nucl. Phys. A 674 (2000) 330. . K. Riisager, A.S. Jensen, P. Moller, Nucl. Phys. A 548 (3) (1992) 393. D.V. Fedorov, A.S. Jensen, K. Riisager, Phys. Rev. C 1994 (1) (1994) 201.
ARTICLE IN PRESS I. Tanihata / Nuclear Instruments and Methods in Physics Research A 532 (2004) 79–85 [12] D.V. Fedorov, A.S. Jensen, K. Riisager, Phys. Rev. C 50 (5) (1994) 2372. [13] M. Fukuda, et al., Phys. Lett. B 268 (1991) 339. [14] I. Tanihata, et al., Phys. Lett. B 287 (1992) 307. [15] T. Zheng, et al., Nucl. Phys. A 709 (2002) 103. [16] A. Ozawa, et al., Phys. Lett. B 334 (1994) 18. [17] X.Z. Cai, et al., Phys. Rev. C 65 (2002) 024610.
[18] [19] [20] [21] [22]
85
H. Iwasaki, et al., Eur. Phys. J. 13 (2002) 55. T. Motobayashi, et al., Phys. Lett. B. 346 (1995) 9. O. Sorlin, et al., Phys. Rev. C 47 (1993) 2941. A. Ozawa, et al., Phys. Rev. Lett. 84 (2000) 5493. R. Kanungo, I. Tanihata, A. Ozawa, Phys. Lett. B 528 (2002) 58.