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Reactions with Radioactive Ion Beams
NUCLEAR PHYSICS A ELSEVIER
Nuclear Physics A654 (1999) 235c-251c www.elsevier.nl/locate/npe'
Reactions with Radioactive Ion Beams Isao Tanihata RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan 1.
INTRODUCTION
Structures of nuclei far from the stability line are being studied through reactions with radioactive ion beams. Since the first measurement of interaction cross sections ( - l b of cross section) large amount of development has been made. In recent years, reaction studies have been extended to the reactions such as fragmentation cross sections, electromagnetic dissociations, Coulomb excitations, elastic scattering, inelastic scattering, (p, n) reactions, quasi-free nucleon-nucleon collisions, transfer reactions, and fusion reactions (down to sub-mb cross sections). Using these reactions with various unstable nuclei, new aspects of nuclear structure have been identified. These new structures have been observed due to the new variables that can now be studied in wide range of values; the isospin and the separation energy of a nucleus. In stable nuclei, first of all, the ratio of N and Z are restricted in between 1 to 1.5. As well the separation energy (Es) of a nucleon, either a proton or a neutron, is almost always 6 to 8 MeV. Because of the stability and these boundaries, (i) the observed central density is same for all stable nuclei (P0- 0.15 fm -3) and thus the radius of stable nucleus is proportional to A 1/3, and (ii) protons and neutrons are homogeneously mixed and no decoupling of proton and neutron distributions was observed. In unstable nuclei, on the other hand, the N/Z can be varied from 0.6 to 4. Also the Es can be varied from 40 MeV to 0 MeV. Because o f these variation, the decoupling of a proton and a neutron distributions has been observed as neutron halos and neutron skins.
Fig. 1 Difference of the potential in stable and unstable nuclei.
These differences are illustrated in Fig. 1. The upper figure is for a stable nucleus and the lower is for a neutron rich nucleus. The left-hand side of the y-axis in each figure shows the potential for proton and the righthand side shows that for neutrons. In stable nuclei the potential for protons and neutrons are same except that the protons see shallower potential due to the Coulomb interactions. The separation energies of a proton and a neutron are almost the same. All the properties of the density distributions
0375-9474/99/$ see front matter © 1999 Elsevier Science B.V. All rights reserved.
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listed above are due to these conditions. As a number of excess neutron increases, the proton potential become deeper due to the attractive p-n interactions. Therefore the separation energy of a proton become large. On the other hand the separation energy of a neutron become smaller and is near zero at the drip line. It is this difference of the separation energy (or Fermi energy from the bottom) that makes neutron skins. When a separation energy of neutron is smaller than 1 MeV, the neutron density shows a long tail called as neutron halo that extend several times further than the usual density tail. This is a new type of quantum tunneling effect in a nuclear bound state. Proton halos are not as pronounced as neutron halo but are formed in some proton drip line nuclei. The decoupling of nuclear density distributions have opened many new structure problems: new excitation modes such as the soft modes, borrowmean binding, and development of new cluster systems, if name a few. In this paper, I show several highlights of these studies. In the following section nuclear radii and density distributions are discussed. Then, in sec. 3, recent developments on studies of halo nuclei and soft-dipole excitation are presented. The possible relation between neutron skin and the equation-of-state of asymmetric nuclear matter is presented in sec.4. The magic numbers disappear in light neutron-rich nuclei. Several different mechanisms that change the shell structures are discussed in Sec. 5. In the last section the necessary developments for basic understanding of nuclear structure are listed.
2.
RADII AND DENSITY DISTRIBUTIONS OF UNSTABLE NUCLEI
Nuclear radii and density distributions of stable nuclei were determined by electron scattering (charge distribution), proton scattering (nucleon distribution), and other reactions. For unstable nuclei, however, different methods have been applied. They are isotope-shift measurements for charge radii and interaction-cross-section measurement for radii of nucleon distributions (matter radii). It became possible only after the development of radioactive-nuclear beams to determine matter radii of short-lived nuclei. Several different methods have been applied. They are measurements of interaction cross sections at beam energy around IA GeV and reaction cross sections below 100A MeV. Also nucleon(s) removal cross sections and momentum distributions of projectile fragments are used to obtain density distributions of halo nuclei. 2.1
Interaction Cross Sections and Matter radii
The interaction cross sections are measured systematically in light nuclei. Figure 2 shows the measured interaction cross sections for reaction at around 800A MeV with Carbon target. The interaction cross sections are shown for all p-shell nuclei and some of the sd-shell nuclei. On top of the smooth increase expected from the A 1/3 dependence, large increases of the cross sections are seen in all neutron-rich isotopes on or near the drip line. These are due to the formation of neutron halo in these nuclei. It has to be noted how large effects are seen due to neutron halos. A faster increase of the 2
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1400 -
A + 1 2 C reaction
A
1300-
f"
i i
m===~
~
-'.
[]
.t~ 1200-
4 1 - - He
<,_,1 °
~===~
- - o - Li
o 1100.
Be + B
m 1000" O
rj ~
~
900.
f RI=l.138Au3
800.
[]
C
O
N
-A-O --<>-- F ,:,
Ne
[]
Na
O
Mg
700-
00
5
10
15
20
25
30
35
A Fig. 2 Interaction cross sections of p and sd shell nuclei at the beam energy near 800A MeV. He: ref. 1, LI, Be: ref. 2, B: ref. 3-5, Ne a n d A=IT: ref. 6, A=20: ref. 7, Na: ref. 8, Mg:ref. 9, and others ref. 10.
cross sections in Na and Mg isotopes are reflection of neutron skin. The effective rms radius of nucleon distribution (Rmrms) is deduced from the interaction cross sections using an optical limit calculation of Glauber model. It is considered to be the simple and reasonably good model to connect a density distribution and an interaction cross section. Deduced effective rms radii are presented in Fig. 3. In the figure the radius of a ball is proportional to (Rmrms - 1,47 fm). The radius of 4He (=1.47 fm) is subtracted so that one can see the change of radius easier." In the figure, neutron halo nuclei are easy to be identified. In addition the most important, that can be seen in the figure, is the change of the radii among isobars. It shows the best evidence that the radius depends not only on the mass number A but also on the proton and the neutron numbers. It is not only due to the halo formation. The best case is seen in A=20 isobar where no halo nuclei are included. A brief analysis of 3
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isospin dependence was made under the Skyrme-Hartree-Fock model. '''7 An importance of density dependent interactions was pointed. However many new data have been accumulated and awaits for detailed analysis. The other important observation is an increase of radius when the proton numbers decrease along isotones. |
10i,uh
Z
~, A
oo o • o , ~ o O
- ~ ,deh.d~ An, , m l ~ l M F q m
qi~
~ o
OO~
.........
1 ~ou~~ /
• oOq ~
~o~o~ I
eo _ - - ' _ I,I
t~
......
o o D D
1_~
0.5
0 0
5
N
10
1
15
1.5
2 fm 20
Fig. 3 The effective rms radii of light nuclei are shown. The radius of the each ball in the chart is proportional to the (R%,, -1.47), where 1.47 is the radius of 4He. Stable nuclei are indicated by the darker ball. It is clearly seen that the nuclear radii depend on both N and Z.
2
2.2
i
Proton Radii
The radii of proton distributions (RPrms) had not been determined except for Na isotopes for nuclei discussed here. In Na isotopes the comparison of the RPrms and Rmrms has presented the first direct evidence
103 u
~
7 5 I
2
I
3
I
I
I
5
I I I
10
I
20
Z Fig.4 Charge-changing cross sections at high-energy. Circles show the cross sections of stable nuclei and square shows that of A - 2 0 isobars.
4
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of neutron skin. Recently charge-changing cross sections (C~c) of high-energy collision has been applied to study the proton distribution. It is directly connected to the proton density distribution in the single-scattering limit of the Glauber model. The multiple scattering effects and evaporation effects may increase the value of Oc but does not reduce it. Therefore, at high energy, a Oc is closely related to the radii of the proton distribution. In particular this statement is reasonable for proton-rich nuclei. In worst it shows the upper limit of RPrms for neutron rich nuclei. Recently, Cc'S of A=20 nuclei have been determined. Large changes of t~c'S are observed. It indicates that the distributions of protons and neutrons behave differently when the neutron-to-proton ratio changes. The charge changing cross sections of A=20 isobars are plotted against Z in Fig. 4 together with t~c'S of stable nuclei. Surprisingly Oc'S of A=20 lay on top of the t~c'S of stable nuclei. It suggests that the proton distribution is determined by Z and does not depend strongly on N. This is radically
Proton Halo Ne evidence •
m . . . .
-
Neutron Halo confirmed ~ evidence , predicted
l
Fig. 5 Candidatesof neutron halos and proton halos. different from the view we had until now and therefore has to be studied in more details.
3. NUCLEAR HALOS Neutron halos have been observed in many nuclei near or on the drip line. A neutron halo has been identified by two different types of observation; an enhancement
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of the interaction- (or reaction-) cross section and a narrow momentum distribution of the last neutrons. A formation of a halo is due to combined effects of the weak binding of last nucleon(s) and the mixing of a low angular momentum orbital, in particular 2s orbital in the presented region. Figure 5 shows the halo nuclei on a nuclear chart. Neutron halos are found in almost all isotopes. It indicates that single-particle orbitals are modified to form halo even for unfavorable places where 2s-orbital is not in order or not even close in ordinal shell structure. Examples are seen in 1 l L i , l 1,14Be and 19C. The basic 1400 I I I I 1I 1200 mechanism of these changes of orbitals is not 1000 well understood. Instead several different ~' a~ 800 mechanisms are considered. These are 600 discussed in sec. 5 in combination with the 400 change of magic numbers. 200 0
3.1 New Neutron Halo Nucleus 19C, 250
I
I
I
1200
I
I
1
Recently a new neutron halo has been E I100 w • I identified in 19C. The separation energy of 6" 1000 1 9 C is - 2 4 0 keV. The m o m e n t u m I distribution of 18 C fragments is observed to i I I I I 900 be very narrow. '3 It gives quite a contrast 130 with 17C that shows a broad momentum distribution of a fragment 16C. Recently I10 interaction cross sections is measured for 19C 90 + 12C reaction as well as for reactions of 70 I other C isotopes. Figure 6 shows the single50 ]B neutron s e p a r a t i o n e n e r g i e s ( S n ) , the I I I I I 30 16 17 18 19 20 21 14 15 interaction cross sections (~I), and the widths A (G/l) of the P// distribution of the one neutron Fr ~ 1/2+ 3/2 + (1/2+,3/2 +) removed fragment. Also the spin-parity J~ of 15C, 17C, and 19C are shown. A change of Fig. 6 Neutron separation energies, interaction cross sections with C target, and the width the t~I (thus the radius) is slow up to A=14, parallel momentum distribution of onethe closure of p-shell. (see Fig. 2) The neutron removal cross sections. interaction cross section increases slightly faster at A>I4. It indicates that neutrons are filled into the sd-shell here. The increase o f c I is larger from A=15 to 16 than that forA=17 to 18. It is considered to be due to a difference of the filling orbital; Sl/2 for the former and d5/2 for the later. It is seen definitely in the spin-parity of these nuclei. The cross section is enhanced at 19C apart from the systematic trend and then comes back in 20C. It therefore shows that the strong s 1/2 contributions exist in the ground state of 19C. These complicated change of orbitals are also seen in the o//. The width of 17C is much wider than those of 15C and
!
19C.
Let us see the density and the momentum distributions of 19C in more detail using a 18C core +neutron model. First the density distribution of 18C are determined 6
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assuming the Harmonic-Oscillator distribution. Then one neutron is added to form 19C. Since the spin-parity of 19C is not known we assumed several different configurations of neutron. They are 0+X2Sl/2, 2+X2Sl/2, 0+xld5/2, and 2+xld5/2 . The density distributions for these configurations are shown in Fig. 7a. They give quite a different density distributions, 0+X2Sl/2 configuration gives largest halo tail and d-wave shows shorter tail. None of the configuration provides the observed a I ; 0+X2Sl/2 configuration gives a larger cross section and the other configurations give smaller cross sections. The solid curve in the figure shows the mixed configuration of 2s1/2 and ld5/2 and provides the best fit to the observed value of ~I- The P// distribution of 18C .
.
.
.
I
.
.
.
.
I
.
.
.
(a) density distribution
.
(b) p//dist, of 18C from 19C
O+X2Sl/2 ~10-2
2+x2sl/2
g
d-wave
O+xld5/2 2+xld5/2
.~ 10-4
=~ 10-6
0 .
0
.
.
.
I
.
.
.
.
5
I
10 r (fm)
.
.
.
s-wave
0
.
O
15 -100
-50
0 50 PII (MeV/c)
100
Fig. 7 The density distribution of 19C and the momentumdistribution of 18C fragment. depend also strongly on the orbital as shown in Fig. 7b. The d-wave shows wide distribution (dotted curve) and the s-wave gives very narrow distribution. The momentum distribution of the mixed configuration is also shown by the solid curve in the figure. A reasonable fit is obtained. '4 Therefore, 19C has a developed neutron halo and thus indicates strong mixing of s- and d-waves. This situation is similar to B isotopes where a large increase of radius are observed in 17B. It is also observed recently that the radius of 19B is also extremely large.'" Boron isotopes has the neutron drip line at N=14 (19B) and thus is consistent with the closure of d5/2 orbital. However the large radii indicates again the strong mixing of s-wave. These observations suggest the importance of the interaction between a loosely bound orbital and the continuum. Low angular momentum orbitals are then favored to gain the binding energy because of the larger overlap to the continuum. Recently, Ozawa et al. ~2 also determined interaction cross sections of oxygen isotopes of A up to 24. The nucleus 240 is considered to be the drip-line nucleus because no heavier isotopes has been observed even in the most recent low-crosssection measurements using 48Ca beam?' Although the neutron separation energies of 2 3 0 (Sn=***) and 2 4 0 (S2n=***) are still pretty large, no more neutron-rich isotope does not seem bound. The interaction cross section increases very much from 2 2 0 to
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230, and same increase rate holds also from 2 3 0 to 240. Under the normal order of the shells these two nuclei occupy 2s orbitals as valence neutrons. It seems, therefore, natural to see large increases of radii. These nuclei may be extremely important for study of loosely bound nuclei or halo system. So far no pair of nuclei next each other show halos. No even-neutron halo nucleus had its single-neutron halo partner. The partner was always unbound. Because s-wave plays an important role for the halo, the resonance state could not be observed. Both of 2 3 0 and 2 4 0 are bound so that the paring and other two-neutron correlations in a halo might be studied in detail. Except for N isotopes, where no measurements have been reported yet, all isotopes of Z<8 elements show halo formation in neutron rich nuclei. For elements with Z>8, neutron orbitals goes into I f and 2p shell. Therefore the mechanism of the halo formation may be different. It is thus interesting future question to study neutron halos in these elements. 3.2
Proton Halo
In contrast with the neutron halos, proton halos appear in less pronounced way. It is due to the Coulomb barrier. The first candidates was 8B. The one-proton separation energy of 8B is only 140 keV. Firstly the width of the P//distribution of 7Be fragment was observed to be very narrow. Then the reaction cross section was measured at low energy and found to be larger than the systematics obtained by Kox in the stable nuclei. '6 Therefore it was considered that 8B has a proton halo of which amplitude is almost 10 times larger than 80
~ k q ) 0 of halo proton
6°1from°'/1; no,,
10-1
~ .
from p//
\-.j
0 e.-,
lo-3
+
2°1
from o I /
o~ 0
5
10
15
r (fm)
20
25 -300
-200
- 100
0
100
200
300
P// of7Be (MeV/c)
Fig. 8 The wave function of the valence proton in 8B and the momentum distribution of 7Be fragments from 8B. Two wave functions of the proton obtained one from the of interaction cross sections and the other from the longitudinal momentum distribution of 7Be fragment differ very much as shown in the right graph. However the wave function shown by the thick solid curve reproduces both interaction cross section and the momentum distribution if the distortion effect of the neutron removal is taken into account.
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the ones expected from a potential model. On the other hand, the oI'S at high-energy ( 800A MeV) shows no enhancement. The value of c I is same with that of mirror nuclei, 8Li. Since 8Li is bound stronger, no large halo is expected. The separation energy and the 6I are consistently explained by a potential model assuming the 7Be core + 1p3/2 shell proton. Some amount of extended tail exists, one may call it as a halo but it is not very well pronounced, but is much smaller in amplitude than expected from the P//data. The reason of this discrepancy has been understood as due to the reaction mechanism. Originally, the P// distribution was compared with the direct Fourier transformation of the wave function. In reality, however, 7Be is destroyed if a collision occurs at small impact parameter. Therefore, this part of the wave function of the last proton does not contribute to the spectrum. This effect is called as the distortion effect and can be formulated as; 17
2 d a = Sdrt ---~_ f~00(rt,z)e",pzz f dbD(b, rt)
dp//
(i)
where ¢p,, is the wave function of the halo neutron and D(b, r,) is the distortion factor. Figure 8 show the results of the calculations with and without distortion D(b, rt). With the distortion, the P// distribution can be reproduced with the same wave function that explains the ~I. The enhancement of the reaction cross section at low energies is still not explained with this wave function. However same amount of enhancement from Kox formula is observed even for stable nuclei. I consider this is due to other effects most likely due to the poor accuracy of Glauber model or complication of the reaction mechanism at low incident energies. In conclusion, the set of data is understood consistently without introducing an enhanced halo. The interaction cross sections of a pair of mirror nuclei are equal within the experimental errors for all pairs except for 17Ne-17N pair. It is well understood by a potential model. Even for a proton-rich partner with an extremely small separation energy, the Coulomb barrier effectively makes the wave function similar to that of the neutron in the mirror partner. This is why the 8B halo is small in spite of the small separation energy. As the only exception, 17Ne shows a much larger ~I than 17N. It suggests that the ground state of 17Ne may have strong mixing of 2Sl/2 wave and thus shows a sizable proton halo. Measurements of the mirror beta decay (I 7Ne -> 17F and 17N -> 170) also show a large asymmetry that is consistent with a mixing of 2Sl/2 wave in 17Ne ground state. 18,19 No t9//distribution of Ne fragments has been measured yet. It is desirable to have such a data to understand the proton halo in 17Ne.
3.3 Soft E1 Mode of Excitation When the proton and the neutron distributions in a nucleus are decoupled, forming a skin or a halo, giant resonances would be modified. A many theoretical studies of such modifications of giant resonances have been made. Among them soft 9
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E1 mode of excitations are the most studied experimentally. The neutrons in a halo are well decoupled from the core that includes neutrons as well as protons. Under such a condition, a low-frequency oscillation between the core and the halo may occur. Ikeda predicted this oscillation, the soft E l - g i a n t resonance, right after the discovery of a neutron halo in 1 ILi.20 Several experiments have been carried out to identify this resonance by the electromagnetic dissociation of halo nuclei. Although the enhancement of the E1 strength is definitely observed at a low excitation energy (E*<2 MeV), it was not clear whether this strength is due to a resonance state or not. Recently a narrow resonance state has been observed in 11Li and found that it is connected by the E1 transition from the ground state. Therefore it present an clear evidence of a soft E 1 resonance. Let us see a short history on the E 1 mode of excitation. The first evidence of a low-energy E1 strength was reported by Kobayashi et al. 21 as an enhancement of the electromagnetic dissociation (EMD) cross sections. They showed that normalized EMD cross sections of neutron-rich nuclei are much larger than that of 12C, a well-bound nucleus. They also observed that this enhancement is larger when the separation energy of the last neutron(s) is small and concluded that this enhancement is consistent with 1.3 the soft El idea. The E l strength distribution of l l B e was m e a s u r e d as a I I ! 2.9 p(llLi,pllLi ) function o f the e x c i t a t i o n energy by Nakamura et al.22 They showed a concentration of the E1 strength around 1 MeV excitation energy. From the angular distribution, they also c o n f i r m e d that the E M D process is mainly through E1 transition. F r o m a simple continuum model, though, they 0 0 4 8 12 14 concluded that the E1 transition E* ( l l L i ) [ M e V ] is mainly a direct process, but not through a resonance. In Fig. 9 The excitation spectrum by an inelastic scattering of 1 IBe ' however, the first excited 1 ILi ' The spectrum of elastic scattering, to show the state (1/2-, Ex=0.320 MeV) is resolution of the system is shown by the dashed line. A clear peak is seen at excitation energy of 1.3 MeV. bound and carries a large E1 strength. Therefore, we do not expect an unbound resonance state with a large E1 strength. 30[
i1
[]
_ _
p(1 ILi,pgLi)
J /'48
Contrary, no bound excited state is known in 11Li. Therefore a resonance state may be expected in l lLi. Recently, both elastic and inelastic scattering of 1 ILi+p have been studied.23 In the experiments, elastic scattering and inelastic scattering were identified by the missing energy by detecting the recoil proton as well as by an 10
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identification of the forward-going fragment. For example, the elastic scattering is confirmed by detecting forward-going 11Li in coincidence with a scattered proton. The inelastic scattering is similarly confirmed by detecting 9Li or a fragment other than 11Li. Figure 9 shows the excitation spectrum of 1 1Li" Several excited states were seen. Among them, they clearly see the state at the excitation energy of 1.3 MeV. This state is consistent with the one observed by Kobayashi et al. by a double charge-exchange reaction of a pion, liB(g-, g+)llLi.24 A comparison of the excited states with those of 9Li indicates that this first excited state of 11 Li is due to the excitation of the halo. It takes about 2.7 MeV to excite the core, as can be seen from the states of 9Li.
1000
100
.1
.01 15 °
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Figure 10 shows the angular distribution of the elastic scattering and the inelastic OpC.m. scattering to the first excited state. A DWBA analysis of the data shows that only the L-1 Fig. 10 The angular distributions of proton elastic and inelastic scattering of I ! Li. The transition is consistent with the observed angular distribution of the inelastic scattering angular distribution. Therefore, it is a can be reproduced only by the L-1 transition, resonance that carries a large E1 strength. Recent coupled-channel analysis also shows that the angular distribution is consistent with a soft El giant resonance assumption.25 25 °
35 °
45 °
55 °
The El strength distribution of l lLi by EMD was measured at MSU and at RIKEN.26.27 Both of them showed a smooth distribution with a broad peak at low energy. Although a strong contribution from the direct process may be consistent with the data, they could not exclude the contribution from a resonance state. A recent data at GSI however shows a structure with a rather narrow peak at 1.2 MeV.2s This peak may indicate the contribution of the first excited state. If it is so, the first excited state is the awaited soft-E1-resonance state. However, the present statistics of the GSI data is not sufficient enough to be called a confirmed peak. Also, it is not clear how much contribution is from the direct transition to the continuum. Therefore, the relation between the 1.3 MeV first excited state observed in the inelastic scattering and the peak in EMD spectrum is yet not clear. It is important to improve the EMD data as well as theoretical calculations including both continuum and resonance. Recently, after the conference, a new experiment has been reported by M. G. Gomov et al. PRL 81 (1998) 432.29 They used I~C0t-, pd)"Li reaction and observed an excited state also at about 1 MeV excitation. It thus strongly supports the existence of a real excited state at 1.2 MeV. 11
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I. Tanihata/Nuclear Physics A654 (1999) 235c-251c NEUTRON SKINS AND EQUATION OF STATE OF ASYMMETRIC NUCLEAR MATTER.
The properties of the equation of state (EOS) of the symmetric nuclear matter, such as the saturation density and compressibility, have been studied by a systematic study of the density distribution of nuclei and by the giant resonance. The EOS was then extrapolated, for examples, to the neutron matter for a study of neutron star. However, no direct study of the EOS of asymmetric nuclear matter has been made so far.
10
">"
0
~D
Z~
~ -10
Radioactive nuclear beams enabled us to study radii of unstable nuclei over a wide range of the A / Z ratio. Studies of giant resonances in particular isoscaler E0 transitions are among the recent interests for studying EOS of asymmetric nuclear matter. Experiments are planned in several laboratories.
Recent systematic measurements of the interaction cross sections for the Na i s o t o p e t o g e t h e r with i s o t o p e - s h i f t 10 measurements provided neutron and proton radii separately.9 The growth of a neutron 0 skin in neutron-rich nuclei was observed > for the first time. Therefore, it has been demonstrated that the proton and neutron radii and the skin thickness can be studied -10 for unstable nuclei that have a wide range of A / Z . In addition, several planned facilities for the production of high-energy, -20 0.05 0.1 0.15 0.2 high-intensity radioactive nuclear beams are expected to provide an opportunity to P m [fm-3] determine the density distributions of Fig. I 1 The Equation of state (EOS) of unstable nuclei through proton and electron symmetric and asymmetric nuclear matter by scattering. It is therefore an appropriate two familiar models. question to ask which properties of nuclear densities reflect the difference in the EOS of asymmetric nuclear matter. -20
The properties of a nucleus near stable line are well described by many nuclear models. Among them are microscopic models using effective interactions, such as non-relativistic Hartree-Fock calculations and relativistic mean-field calculations. Within these frameworks, one uses several different parameter sets that are appropriate for a problem, or for a region in the nuclear chart. Figure 11 shows the EOS of nuclear matter obtained by two popular models: a Skyrme 12
1. Tanihata/Nuclear Physics A654 (1999) 235c-251c Hartree-Fock calculation with the SIII interaction (SKIII) and a relativistic mean-field calculation with the TM1 parameter set (RMF). These two models are commonly used and are known to describe reasonably well the properties of nuclei, such as the density distributions of stable nuclei and isotope shifts of unstable nuclei. However, as can be seen in F i g . l l , the EOS's of asymmetric nuclear matter show a distinct difference. While the saturation d e n s i t y in the S K I I I is almost independent of the proton to neutron ratio (Z/N), it shifts to a low density for a small 7__,/Nvalue in the RMF.
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0.2 0.16 ~ O. 12 I .E ~ 0.08 a . 0.04 0 0.16 ~I
0.12
These two models give a different ~ 0.08 density distribution for neutron-rich nuclei, as shown in Fig.12, as an a . 0.04 0.15 , 0 0
2
4
6
8
I0
r [fm]
0.05.
Fig. 12 Densitydistributionof nucleicalculatedby Skyrme Hartree-Fockand RelativisticMean Field models.
example.29 This figure shows the density distribution of 2 0 8 p b and 2 6 6 p b for the SKIII [Fig. 12(a)] and for the RMF [Fig. Matter <1 12(b)]. The central part of the density ,E 0.1 distribution does not change in the SKIII, but decreases for 266pb in the RMF. It therefore Neutron suggests that the EOS is directly reflected by 0.05 the density distribution of unstable nuclei. It is however not clear whether it is due to the Proton SIII macroscopic effect or due to the microscopic 0effect from a model. 40 60 80 100 120 140 160 180 N Macroscopic calculations are also made Fig. 13 Resultsof the macroscopic calculation of central densitiesforSn isotopes. The matter densitydecreases as neutronnumber increases in the RMF-EOS, that reflect the decrease of the saturationdensity for a neutron rich matter.
using only the EOS's. The central density, the skin thickness, and the surface diffuseness were calculated using two different types of EOS obtained from SKill and RMF calculations.30 Figure 13 shows 13
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the results of calculations for the central density of Sn isotopes. For both of the EOS, the neutron density increases and the proton density decreases when neutrons are added to the nuclei. However, the nucleon density shows a different behavior. When the neutron number increases, the central density remains the same for the EOS obtained from SKIII ; on the other hand, it decreases for the EOS obtained from TM1. It therefore shows that the change in the saturation density in asymmetric nuclear matter is directly reflected to the density of the nucleus. The thickness of the neutron skin is also predicted to be different when these two EOS are used. A comparison to the Na isotope data was made in ref. 30. The errors in the experimental data are still too large to select out an EOS. Also, Na may not be large enough to select the gross property of the density distribution. Precise measurements of the density distribution of a heavier isotope chain is awaited. 5. C O U L O M B E X C I T A T I O N AND C H A N G E IN S H E L L S T R U C T U R E . Recent studies along N=8 and N=20 isotones show that these magic numbers disappears when the neutron-to-proton ratio is large. Relative position of the singleparticle orbitals l p l / 2 , ld5/2, and 2s1/2 changes gradually for N=7 and 9 isotones. An inversion of lpl/2 and 2Sl/2 orbitals is seen in 1lBe. In halo nuclei such as 11Li and 11Be ' a strong mixing of 2s1/2 w a v e is one of the important ingredient of formation of the long tail. The Coulomb excitation of neutron-rich nuclei is one of the most efficient method to see the deformation of a nucleus. The first measurement was made using beam of 32Mg.31 The E2 transition strength [B(E2)] between ground state of 32Mg and the first excited state shows an anomaly and represent a large deformation of this nucleus. It thus indicates an disappearance of the magic number N=20. Coulomb-excitation measurements are extended to other N=20 Reasons of disappearance of magic numbers nuclei and S isotopes as well as to some of N=28 1. Deformation nuclei. The magic number 2. Weak (or strong) binding N=20 seems broken below Stronger bindingfor smaller I orbital (Halo) Z=13. No clear evidence 3. Change ofls coupling of break has been seen in N=28 so far but a Separation of p and n distributions (skin) Change of diffuseness softening of the shell is suggested. 4. Change of shape of potential
Change of diffuseness Disappearance and Woods-Saxon --> Harmonic Oscillator c h a n g e of the m a g i c numbers are e x t r e m e l y Long density tail important for Reasonsof change in magic numbers. u n d e r s t a n d i n g n u c l e a r Fig. 14 structure and also for nucleosynthesis. In addition to the well known "deformation", several other causes of 14
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the shell modification can be considered. (see Fig. 14) Near the drip lines, an orbital of a low angular momentum comes down and helps a formation of halo. This is one of the reason of the disappearance of N=8 magic number. At the same time, a change of the order of orbitals occurs when a separation energy of a proton is large near the neutron drip line and similarly for a neutron near the proton drip line. The order of the orbitals we had been studied are the ones with separation energy only around 8 MeV. The change of orbitals due to the difference of separation energy occurs even if the potential shape is kept unchanged such as Woods-Saxon potential with a constant surface diffuseness. In addition formations of neutron (or proton) skins and neutron (or proton) halos indicate a change of the shape of the nuclear potential, in particular, the surface diffuseness and the difference of the radii between proton and neutron potentials. Mean field models predict that the formation of neutron skin makes the surface diffuseness larger. Therefore the order of orbitals changes towered to that of harmonic oscillator. A formation of halo also make an extremely longer tail and that brings the order of orbitals towered to that of Coulomb potential (mixed parity in a major shell). The change of los splitting also changes the order of orbitals. A separation of proton and neutron density distribution explicitly bring an effect due to the isovector part of los force. A change of the potential shape modify the overlap of the wave function and the derivative of the potential. Of course, the strength of the los coupling may change when N/Z is far from 1. Effects of these changes have not been systematically studied yet but this may be one of the most important direction of researches in radioactive beam facilities. 6.
SUMMARY.
Recent studies using radioactive nuclear beams are presented here from a global view point. A new view point of nuclear density distributions is discussed and the breaking of rules that governed the density distribution of stable nuclei are presented. The new neutron halo nuclei, the soft excitations of halo nuclei, a relation between neutron skin and the equation of state of asymmetric nuclear matter, and change of the magic numbers are discussed. These studies present us challenges for nuclear structure problems as shown below. 1.
What is the guiding principle to make the general potentials for protons and neutrons in a nucleus?
2.
Where and how the magic numbers change?
3.
How does one treat cluster, deformation, and single-particle orbital from one base?
4.
How does one treat the pairing near the threshold?
5.
Can we determine the EOS of an asymmetric nuclear matter?
Facilities of radioactive nuclear beams are increasing in all part of the word. 15
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Several major facilities such as NSCL at MSU, Spiral at GANIL, RI Beam factory in RIKEN, and TRIUMF are upgrading or constructing new facilities. Great advances in studies of nuclear structure are expected to come in near future.
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.
I. Tanihata et al., Phys. Letters B 160 (1985) 380. I. Tanihata et al., Phys. Rev. Letters 55 (1985) 2676. I. Tanihata et al., Phys. Letters B 206 (1988) 592. M. Obuti et al., Nucl. Phys. A 609 (1996) 74. A. Ozawa et al., Nucl. Phys. A 608 (1996) 63. A. Ozawa et al., Phys. Letters B 334 (1994) 18. L. Chulkov et al., Nucl. Phys. A 603 (1996) 219-237. T. Suzuki et al., Phys. Rev. Letters 75 (1995) 3241. T. Suzuki et al., Nucl. Phys. A 630 (1998) 661-677. A. Ozawa and T. Suzuki, private communications. Recently Alkalili et al. pointed out that the optical limit of the calculation may be under estimating the radii of halo nuclei. They proposed the(core+halo neutron) model for the interaction cross sections. In the figure, however, the results of optical limit calculations are shown. It is simply because the detailed analysis of these halo nuclei have not been sufficiently made. The detailed analysis of all halo nuclei are presently in progress. J. S AI-Khalili and J. A. Tostevin, Phys. Rev. Letters 21 (1996) 3903, J. S AI-Khalili, J. A. Tostevin, and I.-J. Thompson Phys. Rev. C 54(1996) 1843. I. Tanihata et al., Phys. Letters B 206 (1988) 475. D. Bazin et al., Phys. Rev. C 57 (1998) 2156. D. Bazin et al., Phys. Rev. Letters 74 (1995) 3569. Recently a new high-statistic data is published for 18C P// distribution. T. Baumann et al., Phys. Letters B 439 (1998) 256. It does not agree with the MSU data and shows wider momentum distribution as seen in the Fig. 6. Taking the error bars of each data points of the momentum distribution in the MSU data, the momentum distributions themselves does not contradict strongly with each other. However the fitting has to be made again to update. H. Sakurai et al., Phys. Letters B (1999) in press. S. Kox et al., Phys. Rev. C 35 (1987) 1678. Y. Ogawa, K. Yabana, and Y. Suzuki, Nud. Phys. A543 (1992) 722. M.J.G. Borge et al., Phys. Letters B 317 (1993) 25. Ozawa et al., J. Physics G: Nucl. Part. Phys. 24 (1998) 143. K. Ikeda, Nucl. Phys. A538 (1992) 355c. T. Kobayashi et al., Phys. Letters B 232 (1989) 51. T. Nakamura et al., Phys. Letters B 331 (1994) 296. C. -B. Moon et al., Phys. Letters, B 297 (1992) 39. A. A. Korsheninnikov al., Phys. Rev. C 53 (1996) R537. T. Kobayashi et al., Nucl. Phys. A538 (1992) 343c. A.A. Korsheninnikov et al., Physical Review Letters, 78 (1997) 2317. K. Ieki et al., Phys. Rev. Letters 70 (1993)730. S. Shimoura et al., Phys. Letters B 348 (1995) 29-34 Zinser et al., Nucl. Phys. A 619 (1997) 15. H. Emling, J. Phys. G.: Nucl. Part. Phys. 24 (1998) 1561. 16
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29. 30. 31.
Y. Sugawara private communication. K. Oyamatsu Nuclear Physics A 634 (1998) 3. T. Motobayashi et al., Phys. Letters B 346 (1995) 9.
17
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Nuclear Physics A654 (1999) 235c-251c www.elsevier.nl/locate/npe'
Reactions with Radioactive Ion Beams Isao Tanihata RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan 1.
INTRODUCTION
Structures of nuclei far from the stability line are being studied through reactions with radioactive ion beams. Since the first measurement of interaction cross sections ( - l b of cross section) large amount of development has been made. In recent years, reaction studies have been extended to the reactions such as fragmentation cross sections, electromagnetic dissociations, Coulomb excitations, elastic scattering, inelastic scattering, (p, n) reactions, quasi-free nucleon-nucleon collisions, transfer reactions, and fusion reactions (down to sub-mb cross sections). Using these reactions with various unstable nuclei, new aspects of nuclear structure have been identified. These new structures have been observed due to the new variables that can now be studied in wide range of values; the isospin and the separation energy of a nucleus. In stable nuclei, first of all, the ratio of N and Z are restricted in between 1 to 1.5. As well the separation energy (Es) of a nucleon, either a proton or a neutron, is almost always 6 to 8 MeV. Because of the stability and these boundaries, (i) the observed central density is same for all stable nuclei (P0- 0.15 fm -3) and thus the radius of stable nucleus is proportional to A 1/3, and (ii) protons and neutrons are homogeneously mixed and no decoupling of proton and neutron distributions was observed. In unstable nuclei, on the other hand, the N/Z can be varied from 0.6 to 4. Also the Es can be varied from 40 MeV to 0 MeV. Because o f these variation, the decoupling of a proton and a neutron distributions has been observed as neutron halos and neutron skins.
Fig. 1 Difference of the potential in stable and unstable nuclei.
These differences are illustrated in Fig. 1. The upper figure is for a stable nucleus and the lower is for a neutron rich nucleus. The left-hand side of the y-axis in each figure shows the potential for proton and the righthand side shows that for neutrons. In stable nuclei the potential for protons and neutrons are same except that the protons see shallower potential due to the Coulomb interactions. The separation energies of a proton and a neutron are almost the same. All the properties of the density distributions
0375-9474/99/$ see front matter © 1999 Elsevier Science B.V. All rights reserved.
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listed above are due to these conditions. As a number of excess neutron increases, the proton potential become deeper due to the attractive p-n interactions. Therefore the separation energy of a proton become large. On the other hand the separation energy of a neutron become smaller and is near zero at the drip line. It is this difference of the separation energy (or Fermi energy from the bottom) that makes neutron skins. When a separation energy of neutron is smaller than 1 MeV, the neutron density shows a long tail called as neutron halo that extend several times further than the usual density tail. This is a new type of quantum tunneling effect in a nuclear bound state. Proton halos are not as pronounced as neutron halo but are formed in some proton drip line nuclei. The decoupling of nuclear density distributions have opened many new structure problems: new excitation modes such as the soft modes, borrowmean binding, and development of new cluster systems, if name a few. In this paper, I show several highlights of these studies. In the following section nuclear radii and density distributions are discussed. Then, in sec. 3, recent developments on studies of halo nuclei and soft-dipole excitation are presented. The possible relation between neutron skin and the equation-of-state of asymmetric nuclear matter is presented in sec.4. The magic numbers disappear in light neutron-rich nuclei. Several different mechanisms that change the shell structures are discussed in Sec. 5. In the last section the necessary developments for basic understanding of nuclear structure are listed.
2.
RADII AND DENSITY DISTRIBUTIONS OF UNSTABLE NUCLEI
Nuclear radii and density distributions of stable nuclei were determined by electron scattering (charge distribution), proton scattering (nucleon distribution), and other reactions. For unstable nuclei, however, different methods have been applied. They are isotope-shift measurements for charge radii and interaction-cross-section measurement for radii of nucleon distributions (matter radii). It became possible only after the development of radioactive-nuclear beams to determine matter radii of short-lived nuclei. Several different methods have been applied. They are measurements of interaction cross sections at beam energy around IA GeV and reaction cross sections below 100A MeV. Also nucleon(s) removal cross sections and momentum distributions of projectile fragments are used to obtain density distributions of halo nuclei. 2.1
Interaction Cross Sections and Matter radii
The interaction cross sections are measured systematically in light nuclei. Figure 2 shows the measured interaction cross sections for reaction at around 800A MeV with Carbon target. The interaction cross sections are shown for all p-shell nuclei and some of the sd-shell nuclei. On top of the smooth increase expected from the A 1/3 dependence, large increases of the cross sections are seen in all neutron-rich isotopes on or near the drip line. These are due to the formation of neutron halo in these nuclei. It has to be noted how large effects are seen due to neutron halos. A faster increase of the 2
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1400 -
A + 1 2 C reaction
A
1300-
f"
i i
m===~
~
-'.
[]
.t~ 1200-
4 1 - - He
<,_,1 °
~===~
- - o - Li
o 1100.
Be + B
m 1000" O
rj ~
~
900.
f RI=l.138Au3
800.
[]
C
O
N
-A-O --<>-- F ,:,
Ne
[]
Na
O
Mg
700-
00
5
10
15
20
25
30
35
A Fig. 2 Interaction cross sections of p and sd shell nuclei at the beam energy near 800A MeV. He: ref. 1, LI, Be: ref. 2, B: ref. 3-5, Ne a n d A=IT: ref. 6, A=20: ref. 7, Na: ref. 8, Mg:ref. 9, and others ref. 10.
cross sections in Na and Mg isotopes are reflection of neutron skin. The effective rms radius of nucleon distribution (Rmrms) is deduced from the interaction cross sections using an optical limit calculation of Glauber model. It is considered to be the simple and reasonably good model to connect a density distribution and an interaction cross section. Deduced effective rms radii are presented in Fig. 3. In the figure the radius of a ball is proportional to (Rmrms - 1,47 fm). The radius of 4He (=1.47 fm) is subtracted so that one can see the change of radius easier." In the figure, neutron halo nuclei are easy to be identified. In addition the most important, that can be seen in the figure, is the change of the radii among isobars. It shows the best evidence that the radius depends not only on the mass number A but also on the proton and the neutron numbers. It is not only due to the halo formation. The best case is seen in A=20 isobar where no halo nuclei are included. A brief analysis of 3
/. Tanihata/Nuclear Physics A654 (1999) 235c-251c
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isospin dependence was made under the Skyrme-Hartree-Fock model. '''7 An importance of density dependent interactions was pointed. However many new data have been accumulated and awaits for detailed analysis. The other important observation is an increase of radius when the proton numbers decrease along isotones. |
10i,uh
Z
~, A
oo o • o , ~ o O
- ~ ,deh.d~ An, , m l ~ l M F q m
qi~
~ o
OO~
.........
1 ~ou~~ /
• oOq ~
~o~o~ I
eo _ - - ' _ I,I
t~
......
o o D D
1_~
0.5
0 0
5
N
10
1
15
1.5
2 fm 20
Fig. 3 The effective rms radii of light nuclei are shown. The radius of the each ball in the chart is proportional to the (R%,, -1.47), where 1.47 is the radius of 4He. Stable nuclei are indicated by the darker ball. It is clearly seen that the nuclear radii depend on both N and Z.
2
2.2
i
Proton Radii
The radii of proton distributions (RPrms) had not been determined except for Na isotopes for nuclei discussed here. In Na isotopes the comparison of the RPrms and Rmrms has presented the first direct evidence
103 u
~
7 5 I
2
I
3
I
I
I
5
I I I
10
I
20
Z Fig.4 Charge-changing cross sections at high-energy. Circles show the cross sections of stable nuclei and square shows that of A - 2 0 isobars.
4
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of neutron skin. Recently charge-changing cross sections (C~c) of high-energy collision has been applied to study the proton distribution. It is directly connected to the proton density distribution in the single-scattering limit of the Glauber model. The multiple scattering effects and evaporation effects may increase the value of Oc but does not reduce it. Therefore, at high energy, a Oc is closely related to the radii of the proton distribution. In particular this statement is reasonable for proton-rich nuclei. In worst it shows the upper limit of RPrms for neutron rich nuclei. Recently, Cc'S of A=20 nuclei have been determined. Large changes of t~c'S are observed. It indicates that the distributions of protons and neutrons behave differently when the neutron-to-proton ratio changes. The charge changing cross sections of A=20 isobars are plotted against Z in Fig. 4 together with t~c'S of stable nuclei. Surprisingly Oc'S of A=20 lay on top of the t~c'S of stable nuclei. It suggests that the proton distribution is determined by Z and does not depend strongly on N. This is radically
Proton Halo Ne evidence •
m . . . .
-
Neutron Halo confirmed ~ evidence , predicted
l
Fig. 5 Candidatesof neutron halos and proton halos. different from the view we had until now and therefore has to be studied in more details.
3. NUCLEAR HALOS Neutron halos have been observed in many nuclei near or on the drip line. A neutron halo has been identified by two different types of observation; an enhancement
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of the interaction- (or reaction-) cross section and a narrow momentum distribution of the last neutrons. A formation of a halo is due to combined effects of the weak binding of last nucleon(s) and the mixing of a low angular momentum orbital, in particular 2s orbital in the presented region. Figure 5 shows the halo nuclei on a nuclear chart. Neutron halos are found in almost all isotopes. It indicates that single-particle orbitals are modified to form halo even for unfavorable places where 2s-orbital is not in order or not even close in ordinal shell structure. Examples are seen in 1 l L i , l 1,14Be and 19C. The basic 1400 I I I I 1I 1200 mechanism of these changes of orbitals is not 1000 well understood. Instead several different ~' a~ 800 mechanisms are considered. These are 600 discussed in sec. 5 in combination with the 400 change of magic numbers. 200 0
3.1 New Neutron Halo Nucleus 19C, 250
I
I
I
1200
I
I
1
Recently a new neutron halo has been E I100 w • I identified in 19C. The separation energy of 6" 1000 1 9 C is - 2 4 0 keV. The m o m e n t u m I distribution of 18 C fragments is observed to i I I I I 900 be very narrow. '3 It gives quite a contrast 130 with 17C that shows a broad momentum distribution of a fragment 16C. Recently I10 interaction cross sections is measured for 19C 90 + 12C reaction as well as for reactions of 70 I other C isotopes. Figure 6 shows the single50 ]B neutron s e p a r a t i o n e n e r g i e s ( S n ) , the I I I I I 30 16 17 18 19 20 21 14 15 interaction cross sections (~I), and the widths A (G/l) of the P// distribution of the one neutron Fr ~ 1/2+ 3/2 + (1/2+,3/2 +) removed fragment. Also the spin-parity J~ of 15C, 17C, and 19C are shown. A change of Fig. 6 Neutron separation energies, interaction cross sections with C target, and the width the t~I (thus the radius) is slow up to A=14, parallel momentum distribution of onethe closure of p-shell. (see Fig. 2) The neutron removal cross sections. interaction cross section increases slightly faster at A>I4. It indicates that neutrons are filled into the sd-shell here. The increase o f c I is larger from A=15 to 16 than that forA=17 to 18. It is considered to be due to a difference of the filling orbital; Sl/2 for the former and d5/2 for the later. It is seen definitely in the spin-parity of these nuclei. The cross section is enhanced at 19C apart from the systematic trend and then comes back in 20C. It therefore shows that the strong s 1/2 contributions exist in the ground state of 19C. These complicated change of orbitals are also seen in the o//. The width of 17C is much wider than those of 15C and
!
19C.
Let us see the density and the momentum distributions of 19C in more detail using a 18C core +neutron model. First the density distribution of 18C are determined 6
1. Tanihata/Nuclear Physics A654 (1999) 235c-251c
241"c
assuming the Harmonic-Oscillator distribution. Then one neutron is added to form 19C. Since the spin-parity of 19C is not known we assumed several different configurations of neutron. They are 0+X2Sl/2, 2+X2Sl/2, 0+xld5/2, and 2+xld5/2 . The density distributions for these configurations are shown in Fig. 7a. They give quite a different density distributions, 0+X2Sl/2 configuration gives largest halo tail and d-wave shows shorter tail. None of the configuration provides the observed a I ; 0+X2Sl/2 configuration gives a larger cross section and the other configurations give smaller cross sections. The solid curve in the figure shows the mixed configuration of 2s1/2 and ld5/2 and provides the best fit to the observed value of ~I- The P// distribution of 18C .
.
.
.
I
.
.
.
.
I
.
.
.
(a) density distribution
.
(b) p//dist, of 18C from 19C
O+X2Sl/2 ~10-2
2+x2sl/2
g
d-wave
O+xld5/2 2+xld5/2
.~ 10-4
=~ 10-6
0 .
0
.
.
.
I
.
.
.
.
5
I
10 r (fm)
.
.
.
s-wave
0
.
O
15 -100
-50
0 50 PII (MeV/c)
100
Fig. 7 The density distribution of 19C and the momentumdistribution of 18C fragment. depend also strongly on the orbital as shown in Fig. 7b. The d-wave shows wide distribution (dotted curve) and the s-wave gives very narrow distribution. The momentum distribution of the mixed configuration is also shown by the solid curve in the figure. A reasonable fit is obtained. '4 Therefore, 19C has a developed neutron halo and thus indicates strong mixing of s- and d-waves. This situation is similar to B isotopes where a large increase of radius are observed in 17B. It is also observed recently that the radius of 19B is also extremely large.'" Boron isotopes has the neutron drip line at N=14 (19B) and thus is consistent with the closure of d5/2 orbital. However the large radii indicates again the strong mixing of s-wave. These observations suggest the importance of the interaction between a loosely bound orbital and the continuum. Low angular momentum orbitals are then favored to gain the binding energy because of the larger overlap to the continuum. Recently, Ozawa et al. ~2 also determined interaction cross sections of oxygen isotopes of A up to 24. The nucleus 240 is considered to be the drip-line nucleus because no heavier isotopes has been observed even in the most recent low-crosssection measurements using 48Ca beam?' Although the neutron separation energies of 2 3 0 (Sn=***) and 2 4 0 (S2n=***) are still pretty large, no more neutron-rich isotope does not seem bound. The interaction cross section increases very much from 2 2 0 to
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230, and same increase rate holds also from 2 3 0 to 240. Under the normal order of the shells these two nuclei occupy 2s orbitals as valence neutrons. It seems, therefore, natural to see large increases of radii. These nuclei may be extremely important for study of loosely bound nuclei or halo system. So far no pair of nuclei next each other show halos. No even-neutron halo nucleus had its single-neutron halo partner. The partner was always unbound. Because s-wave plays an important role for the halo, the resonance state could not be observed. Both of 2 3 0 and 2 4 0 are bound so that the paring and other two-neutron correlations in a halo might be studied in detail. Except for N isotopes, where no measurements have been reported yet, all isotopes of Z<8 elements show halo formation in neutron rich nuclei. For elements with Z>8, neutron orbitals goes into I f and 2p shell. Therefore the mechanism of the halo formation may be different. It is thus interesting future question to study neutron halos in these elements. 3.2
Proton Halo
In contrast with the neutron halos, proton halos appear in less pronounced way. It is due to the Coulomb barrier. The first candidates was 8B. The one-proton separation energy of 8B is only 140 keV. Firstly the width of the P//distribution of 7Be fragment was observed to be very narrow. Then the reaction cross section was measured at low energy and found to be larger than the systematics obtained by Kox in the stable nuclei. '6 Therefore it was considered that 8B has a proton halo of which amplitude is almost 10 times larger than 80
~ k q ) 0 of halo proton
6°1from°'/1; no,,
10-1
~ .
from p//
\-.j
0 e.-,
lo-3
+
2°1
from o I /
o~ 0
5
10
15
r (fm)
20
25 -300
-200
- 100
0
100
200
300
P// of7Be (MeV/c)
Fig. 8 The wave function of the valence proton in 8B and the momentum distribution of 7Be fragments from 8B. Two wave functions of the proton obtained one from the of interaction cross sections and the other from the longitudinal momentum distribution of 7Be fragment differ very much as shown in the right graph. However the wave function shown by the thick solid curve reproduces both interaction cross section and the momentum distribution if the distortion effect of the neutron removal is taken into account.
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the ones expected from a potential model. On the other hand, the oI'S at high-energy ( 800A MeV) shows no enhancement. The value of c I is same with that of mirror nuclei, 8Li. Since 8Li is bound stronger, no large halo is expected. The separation energy and the 6I are consistently explained by a potential model assuming the 7Be core + 1p3/2 shell proton. Some amount of extended tail exists, one may call it as a halo but it is not very well pronounced, but is much smaller in amplitude than expected from the P//data. The reason of this discrepancy has been understood as due to the reaction mechanism. Originally, the P// distribution was compared with the direct Fourier transformation of the wave function. In reality, however, 7Be is destroyed if a collision occurs at small impact parameter. Therefore, this part of the wave function of the last proton does not contribute to the spectrum. This effect is called as the distortion effect and can be formulated as; 17
2 d a = Sdrt ---~_ f~00(rt,z)e",pzz f dbD(b, rt)
dp//
(i)
where ¢p,, is the wave function of the halo neutron and D(b, r,) is the distortion factor. Figure 8 show the results of the calculations with and without distortion D(b, rt). With the distortion, the P// distribution can be reproduced with the same wave function that explains the ~I. The enhancement of the reaction cross section at low energies is still not explained with this wave function. However same amount of enhancement from Kox formula is observed even for stable nuclei. I consider this is due to other effects most likely due to the poor accuracy of Glauber model or complication of the reaction mechanism at low incident energies. In conclusion, the set of data is understood consistently without introducing an enhanced halo. The interaction cross sections of a pair of mirror nuclei are equal within the experimental errors for all pairs except for 17Ne-17N pair. It is well understood by a potential model. Even for a proton-rich partner with an extremely small separation energy, the Coulomb barrier effectively makes the wave function similar to that of the neutron in the mirror partner. This is why the 8B halo is small in spite of the small separation energy. As the only exception, 17Ne shows a much larger ~I than 17N. It suggests that the ground state of 17Ne may have strong mixing of 2Sl/2 wave and thus shows a sizable proton halo. Measurements of the mirror beta decay (I 7Ne -> 17F and 17N -> 170) also show a large asymmetry that is consistent with a mixing of 2Sl/2 wave in 17Ne ground state. 18,19 No t9//distribution of Ne fragments has been measured yet. It is desirable to have such a data to understand the proton halo in 17Ne.
3.3 Soft E1 Mode of Excitation When the proton and the neutron distributions in a nucleus are decoupled, forming a skin or a halo, giant resonances would be modified. A many theoretical studies of such modifications of giant resonances have been made. Among them soft 9
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E1 mode of excitations are the most studied experimentally. The neutrons in a halo are well decoupled from the core that includes neutrons as well as protons. Under such a condition, a low-frequency oscillation between the core and the halo may occur. Ikeda predicted this oscillation, the soft E l - g i a n t resonance, right after the discovery of a neutron halo in 1 ILi.20 Several experiments have been carried out to identify this resonance by the electromagnetic dissociation of halo nuclei. Although the enhancement of the E1 strength is definitely observed at a low excitation energy (E*<2 MeV), it was not clear whether this strength is due to a resonance state or not. Recently a narrow resonance state has been observed in 11Li and found that it is connected by the E1 transition from the ground state. Therefore it present an clear evidence of a soft E 1 resonance. Let us see a short history on the E 1 mode of excitation. The first evidence of a low-energy E1 strength was reported by Kobayashi et al. 21 as an enhancement of the electromagnetic dissociation (EMD) cross sections. They showed that normalized EMD cross sections of neutron-rich nuclei are much larger than that of 12C, a well-bound nucleus. They also observed that this enhancement is larger when the separation energy of the last neutron(s) is small and concluded that this enhancement is consistent with 1.3 the soft El idea. The E l strength distribution of l l B e was m e a s u r e d as a I I ! 2.9 p(llLi,pllLi ) function o f the e x c i t a t i o n energy by Nakamura et al.22 They showed a concentration of the E1 strength around 1 MeV excitation energy. From the angular distribution, they also c o n f i r m e d that the E M D process is mainly through E1 transition. F r o m a simple continuum model, though, they 0 0 4 8 12 14 concluded that the E1 transition E* ( l l L i ) [ M e V ] is mainly a direct process, but not through a resonance. In Fig. 9 The excitation spectrum by an inelastic scattering of 1 IBe ' however, the first excited 1 ILi ' The spectrum of elastic scattering, to show the state (1/2-, Ex=0.320 MeV) is resolution of the system is shown by the dashed line. A clear peak is seen at excitation energy of 1.3 MeV. bound and carries a large E1 strength. Therefore, we do not expect an unbound resonance state with a large E1 strength. 30[
i1
[]
_ _
p(1 ILi,pgLi)
J /'48
Contrary, no bound excited state is known in 11Li. Therefore a resonance state may be expected in l lLi. Recently, both elastic and inelastic scattering of 1 ILi+p have been studied.23 In the experiments, elastic scattering and inelastic scattering were identified by the missing energy by detecting the recoil proton as well as by an 10
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identification of the forward-going fragment. For example, the elastic scattering is confirmed by detecting forward-going 11Li in coincidence with a scattered proton. The inelastic scattering is similarly confirmed by detecting 9Li or a fragment other than 11Li. Figure 9 shows the excitation spectrum of 1 1Li" Several excited states were seen. Among them, they clearly see the state at the excitation energy of 1.3 MeV. This state is consistent with the one observed by Kobayashi et al. by a double charge-exchange reaction of a pion, liB(g-, g+)llLi.24 A comparison of the excited states with those of 9Li indicates that this first excited state of 11 Li is due to the excitation of the halo. It takes about 2.7 MeV to excite the core, as can be seen from the states of 9Li.
1000
100
.1
.01 15 °
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Figure 10 shows the angular distribution of the elastic scattering and the inelastic OpC.m. scattering to the first excited state. A DWBA analysis of the data shows that only the L-1 Fig. 10 The angular distributions of proton elastic and inelastic scattering of I ! Li. The transition is consistent with the observed angular distribution of the inelastic scattering angular distribution. Therefore, it is a can be reproduced only by the L-1 transition, resonance that carries a large E1 strength. Recent coupled-channel analysis also shows that the angular distribution is consistent with a soft El giant resonance assumption.25 25 °
35 °
45 °
55 °
The El strength distribution of l lLi by EMD was measured at MSU and at RIKEN.26.27 Both of them showed a smooth distribution with a broad peak at low energy. Although a strong contribution from the direct process may be consistent with the data, they could not exclude the contribution from a resonance state. A recent data at GSI however shows a structure with a rather narrow peak at 1.2 MeV.2s This peak may indicate the contribution of the first excited state. If it is so, the first excited state is the awaited soft-E1-resonance state. However, the present statistics of the GSI data is not sufficient enough to be called a confirmed peak. Also, it is not clear how much contribution is from the direct transition to the continuum. Therefore, the relation between the 1.3 MeV first excited state observed in the inelastic scattering and the peak in EMD spectrum is yet not clear. It is important to improve the EMD data as well as theoretical calculations including both continuum and resonance. Recently, after the conference, a new experiment has been reported by M. G. Gomov et al. PRL 81 (1998) 432.29 They used I~C0t-, pd)"Li reaction and observed an excited state also at about 1 MeV excitation. It thus strongly supports the existence of a real excited state at 1.2 MeV. 11
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I. Tanihata/Nuclear Physics A654 (1999) 235c-251c NEUTRON SKINS AND EQUATION OF STATE OF ASYMMETRIC NUCLEAR MATTER.
The properties of the equation of state (EOS) of the symmetric nuclear matter, such as the saturation density and compressibility, have been studied by a systematic study of the density distribution of nuclei and by the giant resonance. The EOS was then extrapolated, for examples, to the neutron matter for a study of neutron star. However, no direct study of the EOS of asymmetric nuclear matter has been made so far.
10
">"
0
~D
Z~
~ -10
Radioactive nuclear beams enabled us to study radii of unstable nuclei over a wide range of the A / Z ratio. Studies of giant resonances in particular isoscaler E0 transitions are among the recent interests for studying EOS of asymmetric nuclear matter. Experiments are planned in several laboratories.
Recent systematic measurements of the interaction cross sections for the Na i s o t o p e t o g e t h e r with i s o t o p e - s h i f t 10 measurements provided neutron and proton radii separately.9 The growth of a neutron 0 skin in neutron-rich nuclei was observed > for the first time. Therefore, it has been demonstrated that the proton and neutron radii and the skin thickness can be studied -10 for unstable nuclei that have a wide range of A / Z . In addition, several planned facilities for the production of high-energy, -20 0.05 0.1 0.15 0.2 high-intensity radioactive nuclear beams are expected to provide an opportunity to P m [fm-3] determine the density distributions of Fig. I 1 The Equation of state (EOS) of unstable nuclei through proton and electron symmetric and asymmetric nuclear matter by scattering. It is therefore an appropriate two familiar models. question to ask which properties of nuclear densities reflect the difference in the EOS of asymmetric nuclear matter. -20
The properties of a nucleus near stable line are well described by many nuclear models. Among them are microscopic models using effective interactions, such as non-relativistic Hartree-Fock calculations and relativistic mean-field calculations. Within these frameworks, one uses several different parameter sets that are appropriate for a problem, or for a region in the nuclear chart. Figure 11 shows the EOS of nuclear matter obtained by two popular models: a Skyrme 12
1. Tanihata/Nuclear Physics A654 (1999) 235c-251c Hartree-Fock calculation with the SIII interaction (SKIII) and a relativistic mean-field calculation with the TM1 parameter set (RMF). These two models are commonly used and are known to describe reasonably well the properties of nuclei, such as the density distributions of stable nuclei and isotope shifts of unstable nuclei. However, as can be seen in F i g . l l , the EOS's of asymmetric nuclear matter show a distinct difference. While the saturation d e n s i t y in the S K I I I is almost independent of the proton to neutron ratio (Z/N), it shifts to a low density for a small 7__,/Nvalue in the RMF.
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0.2 0.16 ~ O. 12 I .E ~ 0.08 a . 0.04 0 0.16 ~I
0.12
These two models give a different ~ 0.08 density distribution for neutron-rich nuclei, as shown in Fig.12, as an a . 0.04 0.15 , 0 0
2
4
6
8
I0
r [fm]
0.05.
Fig. 12 Densitydistributionof nucleicalculatedby Skyrme Hartree-Fockand RelativisticMean Field models.
example.29 This figure shows the density distribution of 2 0 8 p b and 2 6 6 p b for the SKIII [Fig. 12(a)] and for the RMF [Fig. Matter <1 12(b)]. The central part of the density ,E 0.1 distribution does not change in the SKIII, but decreases for 266pb in the RMF. It therefore Neutron suggests that the EOS is directly reflected by 0.05 the density distribution of unstable nuclei. It is however not clear whether it is due to the Proton SIII macroscopic effect or due to the microscopic 0effect from a model. 40 60 80 100 120 140 160 180 N Macroscopic calculations are also made Fig. 13 Resultsof the macroscopic calculation of central densitiesforSn isotopes. The matter densitydecreases as neutronnumber increases in the RMF-EOS, that reflect the decrease of the saturationdensity for a neutron rich matter.
using only the EOS's. The central density, the skin thickness, and the surface diffuseness were calculated using two different types of EOS obtained from SKill and RMF calculations.30 Figure 13 shows 13
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the results of calculations for the central density of Sn isotopes. For both of the EOS, the neutron density increases and the proton density decreases when neutrons are added to the nuclei. However, the nucleon density shows a different behavior. When the neutron number increases, the central density remains the same for the EOS obtained from SKIII ; on the other hand, it decreases for the EOS obtained from TM1. It therefore shows that the change in the saturation density in asymmetric nuclear matter is directly reflected to the density of the nucleus. The thickness of the neutron skin is also predicted to be different when these two EOS are used. A comparison to the Na isotope data was made in ref. 30. The errors in the experimental data are still too large to select out an EOS. Also, Na may not be large enough to select the gross property of the density distribution. Precise measurements of the density distribution of a heavier isotope chain is awaited. 5. C O U L O M B E X C I T A T I O N AND C H A N G E IN S H E L L S T R U C T U R E . Recent studies along N=8 and N=20 isotones show that these magic numbers disappears when the neutron-to-proton ratio is large. Relative position of the singleparticle orbitals l p l / 2 , ld5/2, and 2s1/2 changes gradually for N=7 and 9 isotones. An inversion of lpl/2 and 2Sl/2 orbitals is seen in 1lBe. In halo nuclei such as 11Li and 11Be ' a strong mixing of 2s1/2 w a v e is one of the important ingredient of formation of the long tail. The Coulomb excitation of neutron-rich nuclei is one of the most efficient method to see the deformation of a nucleus. The first measurement was made using beam of 32Mg.31 The E2 transition strength [B(E2)] between ground state of 32Mg and the first excited state shows an anomaly and represent a large deformation of this nucleus. It thus indicates an disappearance of the magic number N=20. Coulomb-excitation measurements are extended to other N=20 Reasons of disappearance of magic numbers nuclei and S isotopes as well as to some of N=28 1. Deformation nuclei. The magic number 2. Weak (or strong) binding N=20 seems broken below Stronger bindingfor smaller I orbital (Halo) Z=13. No clear evidence 3. Change ofls coupling of break has been seen in N=28 so far but a Separation of p and n distributions (skin) Change of diffuseness softening of the shell is suggested. 4. Change of shape of potential
Change of diffuseness Disappearance and Woods-Saxon --> Harmonic Oscillator c h a n g e of the m a g i c numbers are e x t r e m e l y Long density tail important for Reasonsof change in magic numbers. u n d e r s t a n d i n g n u c l e a r Fig. 14 structure and also for nucleosynthesis. In addition to the well known "deformation", several other causes of 14
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the shell modification can be considered. (see Fig. 14) Near the drip lines, an orbital of a low angular momentum comes down and helps a formation of halo. This is one of the reason of the disappearance of N=8 magic number. At the same time, a change of the order of orbitals occurs when a separation energy of a proton is large near the neutron drip line and similarly for a neutron near the proton drip line. The order of the orbitals we had been studied are the ones with separation energy only around 8 MeV. The change of orbitals due to the difference of separation energy occurs even if the potential shape is kept unchanged such as Woods-Saxon potential with a constant surface diffuseness. In addition formations of neutron (or proton) skins and neutron (or proton) halos indicate a change of the shape of the nuclear potential, in particular, the surface diffuseness and the difference of the radii between proton and neutron potentials. Mean field models predict that the formation of neutron skin makes the surface diffuseness larger. Therefore the order of orbitals changes towered to that of harmonic oscillator. A formation of halo also make an extremely longer tail and that brings the order of orbitals towered to that of Coulomb potential (mixed parity in a major shell). The change of los splitting also changes the order of orbitals. A separation of proton and neutron density distribution explicitly bring an effect due to the isovector part of los force. A change of the potential shape modify the overlap of the wave function and the derivative of the potential. Of course, the strength of the los coupling may change when N/Z is far from 1. Effects of these changes have not been systematically studied yet but this may be one of the most important direction of researches in radioactive beam facilities. 6.
SUMMARY.
Recent studies using radioactive nuclear beams are presented here from a global view point. A new view point of nuclear density distributions is discussed and the breaking of rules that governed the density distribution of stable nuclei are presented. The new neutron halo nuclei, the soft excitations of halo nuclei, a relation between neutron skin and the equation of state of asymmetric nuclear matter, and change of the magic numbers are discussed. These studies present us challenges for nuclear structure problems as shown below. 1.
What is the guiding principle to make the general potentials for protons and neutrons in a nucleus?
2.
Where and how the magic numbers change?
3.
How does one treat cluster, deformation, and single-particle orbital from one base?
4.
How does one treat the pairing near the threshold?
5.
Can we determine the EOS of an asymmetric nuclear matter?
Facilities of radioactive nuclear beams are increasing in all part of the word. 15
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Several major facilities such as NSCL at MSU, Spiral at GANIL, RI Beam factory in RIKEN, and TRIUMF are upgrading or constructing new facilities. Great advances in studies of nuclear structure are expected to come in near future.
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I. Tanihata et al., Phys. Letters B 160 (1985) 380. I. Tanihata et al., Phys. Rev. Letters 55 (1985) 2676. I. Tanihata et al., Phys. Letters B 206 (1988) 592. M. Obuti et al., Nucl. Phys. A 609 (1996) 74. A. Ozawa et al., Nucl. Phys. A 608 (1996) 63. A. Ozawa et al., Phys. Letters B 334 (1994) 18. L. Chulkov et al., Nucl. Phys. A 603 (1996) 219-237. T. Suzuki et al., Phys. Rev. Letters 75 (1995) 3241. T. Suzuki et al., Nucl. Phys. A 630 (1998) 661-677. A. Ozawa and T. Suzuki, private communications. Recently Alkalili et al. pointed out that the optical limit of the calculation may be under estimating the radii of halo nuclei. They proposed the(core+halo neutron) model for the interaction cross sections. In the figure, however, the results of optical limit calculations are shown. It is simply because the detailed analysis of these halo nuclei have not been sufficiently made. The detailed analysis of all halo nuclei are presently in progress. J. S AI-Khalili and J. A. Tostevin, Phys. Rev. Letters 21 (1996) 3903, J. S AI-Khalili, J. A. Tostevin, and I.-J. Thompson Phys. Rev. C 54(1996) 1843. I. Tanihata et al., Phys. Letters B 206 (1988) 475. D. Bazin et al., Phys. Rev. C 57 (1998) 2156. D. Bazin et al., Phys. Rev. Letters 74 (1995) 3569. Recently a new high-statistic data is published for 18C P// distribution. T. Baumann et al., Phys. Letters B 439 (1998) 256. It does not agree with the MSU data and shows wider momentum distribution as seen in the Fig. 6. Taking the error bars of each data points of the momentum distribution in the MSU data, the momentum distributions themselves does not contradict strongly with each other. However the fitting has to be made again to update. H. Sakurai et al., Phys. Letters B (1999) in press. S. Kox et al., Phys. Rev. C 35 (1987) 1678. Y. Ogawa, K. Yabana, and Y. Suzuki, Nud. Phys. A543 (1992) 722. M.J.G. Borge et al., Phys. Letters B 317 (1993) 25. Ozawa et al., J. Physics G: Nucl. Part. Phys. 24 (1998) 143. K. Ikeda, Nucl. Phys. A538 (1992) 355c. T. Kobayashi et al., Phys. Letters B 232 (1989) 51. T. Nakamura et al., Phys. Letters B 331 (1994) 296. C. -B. Moon et al., Phys. Letters, B 297 (1992) 39. A. A. Korsheninnikov al., Phys. Rev. C 53 (1996) R537. T. Kobayashi et al., Nucl. Phys. A538 (1992) 343c. A.A. Korsheninnikov et al., Physical Review Letters, 78 (1997) 2317. K. Ieki et al., Phys. Rev. Letters 70 (1993)730. S. Shimoura et al., Phys. Letters B 348 (1995) 29-34 Zinser et al., Nucl. Phys. A 619 (1997) 15. H. Emling, J. Phys. G.: Nucl. Part. Phys. 24 (1998) 1561. 16
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