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Spectroscopy of neutron halo nucleus 11Be via the 11B (d, 2He) reaction at 70 MeV
Physics Letters B (1993) 7-12 North-Holland
PHYSICS LETTERS B
Spectroscopy of neutron halo nucleus via the liB(d, 2He) reaction at 70 MeV H. Sakai a, H. Okamura a, S. Ishida a, H. Okuno a, N. Fukunishi ~, H. Sagawa ~, A. Okihana b, Y. Nagai c, K. Takeda c, T. Toriyama ~'~ and A. Yoshida c,2 a Department of Physics, University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113, Japan b Department of Physics, Kyoto University of Education, Fukakusa, Fushimi-ku, Kyoto 612, Japan c Department of Applied Physics, Tokyo Institute of Technology, Ohokayama, Meguro, Tokyo 152, Japan Received 5 August 1992; revised manuscript received 11 January 1993
Differential cross sections and vector and tensor analyzing powers for the ttB(d, 2He)~lBe reaction at 70 MeV have been measured and Gamow-Teiler and spinflip dipole transitions are identified. Observed mean excitation energy and strength for the spinflip dipole transition in which possible neutron halo effect manifests itselfare consistent with the shell model prediction which takes the neutron halo into account.
Since the suggestion o f a neutron halo [ 1 ] in extremely neutron rich nuclei such as ~~Li, ~1Be and 14Be through interaction cross section measurements, a lot o f experimental and theoretical studies have been devoted to clarifying the p h e n o m e n o n . The narrow mom e n t u m distribution observed in the fragmentation process is interpreted to arise due to a neutron halo as a result o f the small separation energy [ 2 ]. These studies on the ground-state property indicate that the neutron density d i s t r i b u t i o n has a long tail extending outside the core o f the nucleus [ 3]. It is very interesting to study the structure o f excited states o f a halo nucleus. However, such a study is h a m p e r e d by the experimental difficulty to excite those neutron rich nuclei. K o b a y a s h i et al. [4 ] have tried to measure the pion double-charge-exchange ( D C X ) reaction ~ B ( ~ t - , z~+)11Li to reach excited states o f the 11Li nucleus. In this letter we report our a p p r o a c h by the I~B(d, ZHe) reaction to p r o d u c e the neutron halo nucleus I IBe which is the easiest nucleus to access. 2He indicates a p r o t o n - p r o t o n system coupled to the singlet S-state (1So). The (d, 2He) rei Present address: Musashi Institute of Technology, 1-28-1 Tamatsutsumi, Setagaya, Tokyo 158, Japan. 2 Present address: RIKEN, 2-1 Hirosawa, Wako, Saitama 35101, Japan.
action has an excellent spin-isospin selectivity [5,6]. It excites exclusively s p i n - i s o s p i n f l i p transitions e.g. G a m o w - T e l l e r ( G T ) type transitions ( A S = l , AL = 0), spinflip dipole ( S F D ) transitions ( A S = 1, AL = 1 ), etc. Note that the s p i n - p a r i t y J~ assignments for I IBe have been m a d e for only a few excited states [ 7 ]. The ground state is known to have an a n o m a l o u s J~ o f ½+ instead o f ½- which is very unexpected by naive shell model predictions. Recently Liu and Fortune studied the low-lying states in 11Be by the 9Be(t, p ) reaction with a 15 MeV triton b e a m [ 8 ]. So far the spectroscopic studies are limited by the low energy reactions or by the fl decay. The effect due to a neutron halo is expected to appear mainly in the dipole transition. Firstly, because o f the small binding energy o f the halo neutron the mean excitation energy o f the dipole state becomes smaller than that without a halo. Actually the neutron separation energy o f 11Be is only 0.5 MeV. Secondly, the dipole transition strength will be enhanced. The dipole transition is induced by the operator r[ Yta]Jt+l with J = 0 , 1, and 2. Therefore the matrix elements involving a halo, in general, have better overlap at large radius owing to the larger root m e a n square radius o f the halo neutron c o m p a r e d to that o f the core. On the contrary, almost no effect is
0370-2693/93/$ 06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.
7
Volume 302, number l
PHYSICS LETTERS B
expected on the GT transition since the transition takes place within the same shell orbit and the operator has no radial part. It is the aim of the present study to ascertain these characteristic features experimentally. We will employ the spectroscopic amplitudes of the Cohen-Kurath (CK) [9] and Millener-Kurath (MK) [10] wave functions in the theoretical description and at the same time use the results of the IEC(d, 2He)IEB reaction as an experimental reference in the following analysis. It is known that the low-momentum transfer properties of various states in the p-shell are reasonably well described by the CK wave function which consists of all possible configurations of 1p-shell orbits, and also by the MK wave function which is the extension of the CK model to include excitations into the sd-shell. The mass 12 system is such a well studied case. For example the ground state GT transition to IEB via ~2C(n, p) [ 11 ], o r tO 12N via IEC(p, r/) [12] is well reproduced by the CK wave functions. As for the SFD transitions, Gaarde et al. [ 13 ] have shown that the experimental spectrum by the 12C(p, ?/)12N reaction agrees well with the strength distribution calculated with the MK wave functions, and more recently Brady et al. have shown the same by the IEC(n, p ) reaction [ 11 ]. The present experiment was carried out by using a vector and tensor polarized deuteron beam of 70 MeV with a typical polarization of 75% provided by the AVF cyclotron at the Research Center for Nuclear Physics, Osaka University. The ~B target with a thickness of about 0.5 mg/cm 2 was prepared by evaporating isotopically enriched ( > 9 5 % ) material onto a mylar film. The background due to the mylar film was subtracted by using the measured spectrum of a separate run for the mylar film. The 2He particles were detected with two sets of multicounter arrays. They were designed to have an optimum detection efficiency of two protons with small relative energy (2He). Each array consisted of four sets of AE-E Si counter telescopes. Owing to this configuration six different p - p pair coincidences become available in each array and the detection efficiency of 2He particles increases accordingly. Each telescope has a solid angle of 6.7 msr. The final energy resolution of the 2He in full width at half maximum was about 600 keV. The experimental 2He cross sections quoted in this work were obtained after integrating the observed
18 March 1993
triple differential cross sections over the detector solid angles and the relative two-proton energy up to l MeV according to the prescription by refs. [ 5,14 ]. Further details of the experimental procedures are described elsewhere [ 15 ]. The upper panel of fig. 1 shows the typical energy spectrum of the cross section at 0tab=35 ° for the lIB (d, 2He)~Be reaction. Three prominent discrete peaks in the low excited region and a broad bump at an excitation energy around 10 MeV with a width of about 7 MeV are clearly observed. The ground state seems to be not strongly populated, although our energy resolution prevents us from drawing a definitive conclusion. To extract the cross sections, the spectra are fitted with peaks of gaussian shape of three narrow and one wide widths (dotted curves) together with the continuum (dashed curve) due to the threebody phase space (PS) as indicated in fig. 1. The solid curve is the result of fitting. Angular distributions (20 ° < 0lab< 70 ° ) for the cross sections (da/d.Q) and vector and tensor analyzing powers (Ay and Ayy) are displayed in fig. 2. In order to assign the GT and SFD transitions we will employ an empirical approach to deduce the an-
800
nB(d 2He)nBe
,,E l
~~
~>~:
ooo
400 :m
c~ o
,d
200
1 ---
0 600
rn
O
0"u'b=35°
,zC(d,ZHe) lz B
400
~
i~
ft+~
Ed=70MeV
2OO 0 -40
-30
-20
-10
Q - V a l u e [MeV] Fig. I. Energy spectrum for the HB(d, 2He)l~Be (upper panel) reaction at 70 MeV and O~b=35 °. The solid curve is the result of a peak fitting analysis. The solid and dashed arrows indicate the positions of mean excitation energies estimated with or without the neutron halo. For comparisonpurposes the energy spectrum for the 12C(d, 2He)12B (lower panel) reaction at 70 MeV and O~ab=35 ° is also shown. See text for detail.
Volume 302, number 1
PHYSICS LETTERS B
1
I
I
1
0.5
I
" ~ EU [. ov]
0.0
"
1
~
I
I
I
0.3-
0.5 0.0 -0.5
2.7
0.5 0.0 -0.5
~
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2.7 I_
Ex[MeVi
)
~C
0.0 i0 -z
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i0 -4
~
=
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,
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I ! !I ° I ~'#t"
-0.5 0.5
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°°t
-0.5 0.0
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(XlO -t
I
-0.5 I
I~
40 60 80 0ca [ d e g r e e ]
0.5 0.0 -0.5
-0.5
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18 March 1993
20
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Ayy 0.5 0.0 -0.5 I I l l l l ~
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60 80 8cu [ d e g r e e ]
[ 1 1 1 1 1
20
40 60 80 0cM [ d e g r e e ]
Fig. 2. Cross sections and vector and tensor analyzing powers of the low-lying states (Ex=0.3, 2.7 and 3.8 MeV) and of the bump at Ex = 10 MeV for the HB (d, 2He)~lBe reaction and those of the ground state AL = 0 transition (GT type) and of the state at Ex = 4.5 MeV, AL = 1 transition ( SFD type ) for the ~2C( d, 2He) ]2B reaction. Solid and dashed curves represent AL = 0 and 1 transitions, respectively. They are obtained by tracing data points of the ~2C(d, 2He ) t2B reaction in the figure. See text for detail. around
gular momentum transfer (AL) by comparing the observed angular distributions with those of known transitions characteristic to the transferred angular momentum. For this purpose we use experimental results of the ground state 1+ GT transition (AS= l, AL = 0) and of the transition to the state at Ex = 4.5 MeV which is mostly due to the 2 - SFD (AS= l, A L = 1 ) states, observed in the t2C(d, 2He)12B react i o n [ 5 ]. Ay and Ayy on these 1+ and 2 - states have been investigated at 70 MeV and reported by Motobayashi et al. [ 16,17 ]. We note that it is difficult to determine the final state spin ,/f value in the present odd mass target because of non-zero initial spin j i value. Measurements for the 12C(d, 2He)IEB reaction were made separately under the same experimental condition and a typical energy spectrum at 0~,b= 35 ° is shown in the bottom panel of fig. 1. Angular distributions of dcr/dQ and Ay and Ayy are also
displayed in fig. 2 and they are generally consistent with previous results [ 16,17 ]. The solid and dashed curves in fig. 2 represent the shapes of experimental A L = 0 and A L = 1 transitions. They are drawn by tracing data points of the 12C(d, 2He) [2B reaction in the figure. It should be noted that the shape of the angular distribution for the peak at Ex=4.5 MeV which represents the AL = 1 transition is almost unchanged by including yields at higher excitations. This fact indicates that the yields in the higher excitation region are also mainly due to the A L = 1 transitions. Unfortunately we were unable to extract analyzing powers for the region beyond the 4.5 MeV peak due to an experimental problem except those at 0~,b= 35 ° (0CM = 42 ° ). If we calculate the analyzing powers including yields in the higher excitation region Ex = 230 MeV, the Ay and Aye values at 0~ab= 35 ° of the ~2C(d, 2He)t2B reaction become - 0 . 0 4 + 0 . 0 4 and
Volume 302, number I
PHYSICSLETTERSB
0.09 + 0.08, respectively. These values are in agreement within statistical errors with those of the 4.5 MeV peak alone of fig. 2. As for the transition to the low-lying states (Ex=0.3, 2.7 and 3.8 MeV) the angular distributions for da/dO are very similar to those of the ground state transition in the '2C(d, 2He)~2B reaction, indicating the GT type transitions with AL = 0. The CK model predicts strong GT states at Ex = 0.0, 2.0 and 4.1 MeV with J~=½-, 3 - and ~-, respectively. Therefore the observed peaks most probably correspond to these GT states. Note that the state at Ex = 0.3 MeV is known to be J~= ½- [ 7 ]. The angular distribution of the cross section for the broad bump observed at around Ex = 10 MeV has a flatter shape suggesting a larger AL transfer than those of the discrete transitions to the low-lying states. The angular distributions for da/dl2 are also similar to those of the transition to the SFD state at Ex=4.5 MeV in the ~2C(d, 2He)12B reaction, suggesting a AL = 1 transition. These facts strongly indicate that this bump at Ex= 10 MeV is mainly due to the spinflip dipole transition. The above AL assignments based on the angular distributions of cross sections are further supported by the Ay and Aye data. General trends observed in the ~2C(d, 2He)'2B reaction such as large negative values at around 40 ° for the AL = 0 transition or a very small Ayy value for the AL = 1 transition are also seen in the '~B (d, 2He)~Be reaction. The shell model calculations with a neutron halo have been performed by Hoshino et al. [ 18 ]. They showed that the effect of the neutron halo appears in the isovector SFD transition as follows: The mean excitation energy/~of SFD transitions is shifted down by about 2 MeV and the SFD transition strength B(SFD) is enhanced by about 40% compared with the calculations without the neutron halo. We examine these unique features quantitatively by using '2C data again as a reference. In the following we will show an analysis by using the data at 0tab= 35 ° as a typical example where we expect a moderate yield from the SFD transition and less contributions from the GT or higher AL transitions. However the arguments used here are general and in principle applicable to any angle without losing generality. E" of SFD transitions with (without) halo is indicated by the solid (dashed) arrow in fig. 1. It is clear 10
18 March 1993
that the observed broad bump at around Ex = 10 MeV is much closer to the shell model prediction with halo. As for the strength we analyze our results in terms of the unit cross section & It is most frequently used in the study of Gamow-Teller transitions and usually defined as t~Gx= (daGx/d.Q)(q=O)/B(GT), where the cross section is extrapolated to the momentum transfer q = 0 and corrected for the energy loss dependence [ 12 ]. Here we define the unit cross section at a scattering angle of 35 ° and we will not apply the correction due to the energy loss since it is estimated to be small [ 12 ] and the values of the energy loss of GT or SFD transitions are similar for both target nuclei. The cross sections at 35 ° for the GT transition (summed over three low-lying peaks) and the SFD bump are listed in table 1 together with those of the ~2C target. The shell model estimates after summing up strengths at appropriate excitation energy intervals listed in table 1 are also given; CK wave functions [ 9 ] for the GT transitions and MK wave functions with [ 18 ] or without [ 10 ] neutron halo for the SFD transitions. The unit cross section at 35 ° is defined as ~, = (da,~/dO)/B(a) where a is either GT or SFD. 6cT values for '~B and ~2C are obtained as 20.2 and 18.7 ~tb/sr, respectively. They are almost equal. Thus the proportionality relation seems to hold for the GT transitions. This fact also indicates that the GT state is not influenced by the presence of a neutron halo as is expected. As for the SFD transitions, the 6SVD values of ~B are 1.42 or 1.98 ~tb/sr depending on calculations with or without halo, respectively. These values should be compared to that of 1.55 ~tb/sr of ~2C. This result seems to support the shell model prediction of 40% enhancement of SFD transitions due to the neutron halo if the same kind of proportionality holds for the SFD transitions. We note that da/dI2 for the SFD transition depends on the assumption for the magnitude of the background due to the three-body phase space and for the contribution from the strengths other than the SFD transition. However, both liB and 12C data are analyzed in a consistent manner, the relative uncertainty in da/dg2 is estimated to be rather small ( < 20%). One might think that the shell model predictions on B ( G T ) or B(SFD) depend on the interactions and configurations of model space used in the calculations and consequently this leads to a fur-
Volume 302, number 1
PHYSICS LETTERS B
18 March 1993
Table 1 Cross sections for the (d, 2He) reaction on 12C and HB at 70 MeV and 35 °, GT and SFD strengths and unit cross sections. Relative uncertainties in dtr/dO for the GT transitions and those for the SFD transitions are estimated to be less than 5% and 20%, respectively, apart from the overall normalization. G T transition ( A L = O )
E~ (MeV)
Target
Ji
Jr
t2C
0+
1+
0.0
lib
~-
½(~ - )
0.3 2.7
(~ -)
3.8
SFD transition (AL= 1 ) Target Ji Jf
12C
0+
Ex (MeV)
de/dQ (~tb/sr)
) ~
B ( G T ) (fm 2) CK a)
17.6
0.98
17.9
14.8
0.73
20.2
dtr/d,Q (lab/sr)
#s~(p.b/sr)
B(SFD) (fm 2 ) MK b)
0)
2-30
48.3
31.0
")
2-23
34.7
17.5
1-
6GT (I-tb/s r) CK a)
M K + halo c)
MK b)
M K + halo c)
1.55
2HB
a) Ref. [9].
~-
b) Ref. [10].
24.4
1.98
1.42
¢)Ref. [18].
ther ambiguity of the analysis. Such an ambiguity is also small in terms o f the unit cross section 8 as long as the same interactions and the same configurations are used in the calculation o f both 12B and l~Be, since the variation of the summed strength within the wide excitation energy interval of the present case tends to be similar for both nuclei so that the relative ratio of is rather independent o f such variations. By knowing #SFD the yield of the ground state transition can be estimated as 0.075 lab/sr with B ( S F D ) =0.053 fm 2 [ 18]. This is only 0.97% of the nearly G T transition at Ex= 0.3 MeV, consequently it is too small to be seen in fig. 1. Finally we would like to remark on the distortedwave Born approximation ( D W B A ) approach. We have performed one-step DWBA calculations employing the code T W O F N R [ 19 ] according to the prescription o f ref. [ 16 ] with the same parameters. The transition form factors are taken from refs. [ 9,18 ]. We found that the shapes of the angular distributions o f da/dg2 depend, although not strongly, on the individual states and are not so stable as those
o f the nucleon scattering such as the (p, p ' ) or (p, n) reactions. This is primarily due to the inherent complexity of the reaction mechanism associated with the (d, 2He) reaction even though it has an excellent spin-isospin selectivity as a probe. We have neglected non-central interactions and exchange amplitudes as well as the deuteron D-state in the calculations although they certainly play important roles. As an example we examined, though preliminarily, the effect of a tensor interaction and found that the shape of the angular distribution for the GT transition could be well reproduced [20]. On the contrary it was needed to include the two-step processes in the DWBA calculations to get a similar quality fit if the central interactions were only employed as has been shown in refs. [ 16,17 ]. Note that if we perform the (n, p) reaction type calculation which assumes the proton in the deuteron as a spectator and ignores the internal freedom of the deuteron or 2He particle we can reproduce the data rather well. However even in such a simplified calculation it is known that the DWBA cross section 11
Volume 302, number 1
PHYSICS LETTERS B
changes up to 30% depending on the choice o f various parameters [ 11,21 ]. U n d e r these circumstances it is difficult to draw a definitive conclusion from the D W B A calculation alone. We hope the present d a t a might stimulate efforts to develop the full microscopic D W B A treatment to include these freedoms. In summary, we have successfully studied the structure o f the neutron halo nucleus 11Be by the I~B (d, 2He) reaction at 70 MeV. Three discrete peaks in the low excitation energy region and a b r o a d b u m p at a r o u n d 10 MeV excitation are clearly observed. They are identified to be due to G T a n d S F D transitions, respectively, by comparing the observed angular distributions with those of known G T and S F D transitions in the 12C(d, 2He) 12B reaction. This identification is supplemented by the vector and tensor analyzing power data. We have shown on the basis o f the empirical analyses that the G T transition receives almost no effect o f the neutron halo while the S F D transition does reflect the neutron halo as a 2 MeV shift down o f the mean excitation energy a n d also as an enhancement o f the transition strength, although a more definite conclusion awaits further detailed analyses o f the present data. Higher deuteron b e a m energies would be a great help in that ambiguities o f the reaction m e c h a n i s m would be reduced. An effort in this direction has been started at the R I K E N Ring Cyclotron facility and new experimental results are expected to be available in the near future. We thank K. M u t o for helpful discussions and also I. Sugai for preparing the 11B target. We are grateful
12
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to W. Bentz for reading the manuscript. This work is supported financially in part by the G r a n t - i n - A i d for Scientific Research No. 6342007 o f Ministry o f Education, Science and Culture o f Japan. This experim e n t was p e r f o r m e d at R C N P under Program N u m ber 29A13.
References [ 1] I. Tanihata et al., Phys. Rev. Lett. 55 (1985) 2676. [ 2 ] I. Tanihata et al., Phys. Lett. B 206 ( 1988 ) 592. [3] T. Kobayashi et al., Phys. Rev. Lett. 60 (1988) 2599; Nucl. Phys. A 538 (1992) 343c; M. Fukuda et al., Phys. Lett. B 268 ( 1991 ) 339. [4 ] T. Kobayashi et al., preprint RIKEN-AF-NP- 106. [ 5 ] D.P. Stahel et al., Phys. Rev. C 20 (1979) 1680. [ 6 ] K.B. Beard et al., Phys. Rev. C 26 (1982) 720. [7] F. Ajzenberg-Seloveet al., Nucl. Phys. A 481 (1990) 1. [8] G.-B. Liu and H.T. Fortune, Phys. Rev. C 42 (1990) 167. [9] S. Cohen and D. Kurath, Nucl. Phys. 73 (1965) 1. [ 10] D.J. Millener and D. Kurath, Nucl. Phys. A 255 ( 1975 ) 315. [ 11 ] F.P. Brady et al., Phys. Rev. C 43 ( 1991 ) 2284. [ 12] T.N. Taddeucci et al., Nucl. Phys. A 469 (1987) 125. [ 13 ] C. Gaarde et al., Nucl. Phys. A 422 (1984) 189. [ 14 ] T. Motobayashi et al., Nucl. Instrum. Methods A 271 (1988) 491. [15]H. Okamura, Ph.D. thesis, Kyoto University (1989), unpublished. [ 16 ] T. Motobayashi et al., Phys. Rev. C 34 (1986) 2365. [ 17 ] T. Motobayashi et al., J. Phys. G 14 ( 1988 ) L 137. [ 181 T. Hoshino, H. Sagawa and A. Arima, Nucl. Phys. A 523 (1991) 228. [19]M. Igarashi, Computer program TWOFNR (1977), unpublished. [20 ] H. Okamura et al., in preparation for publication. [ 21 ] H. Ohnuma et al., Nucl. Phys. A 467 ( 1987 ) 61.
PHYSICS LETTERS B
Spectroscopy of neutron halo nucleus via the liB(d, 2He) reaction at 70 MeV H. Sakai a, H. Okamura a, S. Ishida a, H. Okuno a, N. Fukunishi ~, H. Sagawa ~, A. Okihana b, Y. Nagai c, K. Takeda c, T. Toriyama ~'~ and A. Yoshida c,2 a Department of Physics, University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113, Japan b Department of Physics, Kyoto University of Education, Fukakusa, Fushimi-ku, Kyoto 612, Japan c Department of Applied Physics, Tokyo Institute of Technology, Ohokayama, Meguro, Tokyo 152, Japan Received 5 August 1992; revised manuscript received 11 January 1993
Differential cross sections and vector and tensor analyzing powers for the ttB(d, 2He)~lBe reaction at 70 MeV have been measured and Gamow-Teiler and spinflip dipole transitions are identified. Observed mean excitation energy and strength for the spinflip dipole transition in which possible neutron halo effect manifests itselfare consistent with the shell model prediction which takes the neutron halo into account.
Since the suggestion o f a neutron halo [ 1 ] in extremely neutron rich nuclei such as ~~Li, ~1Be and 14Be through interaction cross section measurements, a lot o f experimental and theoretical studies have been devoted to clarifying the p h e n o m e n o n . The narrow mom e n t u m distribution observed in the fragmentation process is interpreted to arise due to a neutron halo as a result o f the small separation energy [ 2 ]. These studies on the ground-state property indicate that the neutron density d i s t r i b u t i o n has a long tail extending outside the core o f the nucleus [ 3]. It is very interesting to study the structure o f excited states o f a halo nucleus. However, such a study is h a m p e r e d by the experimental difficulty to excite those neutron rich nuclei. K o b a y a s h i et al. [4 ] have tried to measure the pion double-charge-exchange ( D C X ) reaction ~ B ( ~ t - , z~+)11Li to reach excited states o f the 11Li nucleus. In this letter we report our a p p r o a c h by the I~B(d, ZHe) reaction to p r o d u c e the neutron halo nucleus I IBe which is the easiest nucleus to access. 2He indicates a p r o t o n - p r o t o n system coupled to the singlet S-state (1So). The (d, 2He) rei Present address: Musashi Institute of Technology, 1-28-1 Tamatsutsumi, Setagaya, Tokyo 158, Japan. 2 Present address: RIKEN, 2-1 Hirosawa, Wako, Saitama 35101, Japan.
action has an excellent spin-isospin selectivity [5,6]. It excites exclusively s p i n - i s o s p i n f l i p transitions e.g. G a m o w - T e l l e r ( G T ) type transitions ( A S = l , AL = 0), spinflip dipole ( S F D ) transitions ( A S = 1, AL = 1 ), etc. Note that the s p i n - p a r i t y J~ assignments for I IBe have been m a d e for only a few excited states [ 7 ]. The ground state is known to have an a n o m a l o u s J~ o f ½+ instead o f ½- which is very unexpected by naive shell model predictions. Recently Liu and Fortune studied the low-lying states in 11Be by the 9Be(t, p ) reaction with a 15 MeV triton b e a m [ 8 ]. So far the spectroscopic studies are limited by the low energy reactions or by the fl decay. The effect due to a neutron halo is expected to appear mainly in the dipole transition. Firstly, because o f the small binding energy o f the halo neutron the mean excitation energy o f the dipole state becomes smaller than that without a halo. Actually the neutron separation energy o f 11Be is only 0.5 MeV. Secondly, the dipole transition strength will be enhanced. The dipole transition is induced by the operator r[ Yta]Jt+l with J = 0 , 1, and 2. Therefore the matrix elements involving a halo, in general, have better overlap at large radius owing to the larger root m e a n square radius o f the halo neutron c o m p a r e d to that o f the core. On the contrary, almost no effect is
0370-2693/93/$ 06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.
7
Volume 302, number l
PHYSICS LETTERS B
expected on the GT transition since the transition takes place within the same shell orbit and the operator has no radial part. It is the aim of the present study to ascertain these characteristic features experimentally. We will employ the spectroscopic amplitudes of the Cohen-Kurath (CK) [9] and Millener-Kurath (MK) [10] wave functions in the theoretical description and at the same time use the results of the IEC(d, 2He)IEB reaction as an experimental reference in the following analysis. It is known that the low-momentum transfer properties of various states in the p-shell are reasonably well described by the CK wave function which consists of all possible configurations of 1p-shell orbits, and also by the MK wave function which is the extension of the CK model to include excitations into the sd-shell. The mass 12 system is such a well studied case. For example the ground state GT transition to IEB via ~2C(n, p) [ 11 ], o r tO 12N via IEC(p, r/) [12] is well reproduced by the CK wave functions. As for the SFD transitions, Gaarde et al. [ 13 ] have shown that the experimental spectrum by the 12C(p, ?/)12N reaction agrees well with the strength distribution calculated with the MK wave functions, and more recently Brady et al. have shown the same by the IEC(n, p ) reaction [ 11 ]. The present experiment was carried out by using a vector and tensor polarized deuteron beam of 70 MeV with a typical polarization of 75% provided by the AVF cyclotron at the Research Center for Nuclear Physics, Osaka University. The ~B target with a thickness of about 0.5 mg/cm 2 was prepared by evaporating isotopically enriched ( > 9 5 % ) material onto a mylar film. The background due to the mylar film was subtracted by using the measured spectrum of a separate run for the mylar film. The 2He particles were detected with two sets of multicounter arrays. They were designed to have an optimum detection efficiency of two protons with small relative energy (2He). Each array consisted of four sets of AE-E Si counter telescopes. Owing to this configuration six different p - p pair coincidences become available in each array and the detection efficiency of 2He particles increases accordingly. Each telescope has a solid angle of 6.7 msr. The final energy resolution of the 2He in full width at half maximum was about 600 keV. The experimental 2He cross sections quoted in this work were obtained after integrating the observed
18 March 1993
triple differential cross sections over the detector solid angles and the relative two-proton energy up to l MeV according to the prescription by refs. [ 5,14 ]. Further details of the experimental procedures are described elsewhere [ 15 ]. The upper panel of fig. 1 shows the typical energy spectrum of the cross section at 0tab=35 ° for the lIB (d, 2He)~Be reaction. Three prominent discrete peaks in the low excited region and a broad bump at an excitation energy around 10 MeV with a width of about 7 MeV are clearly observed. The ground state seems to be not strongly populated, although our energy resolution prevents us from drawing a definitive conclusion. To extract the cross sections, the spectra are fitted with peaks of gaussian shape of three narrow and one wide widths (dotted curves) together with the continuum (dashed curve) due to the threebody phase space (PS) as indicated in fig. 1. The solid curve is the result of fitting. Angular distributions (20 ° < 0lab< 70 ° ) for the cross sections (da/d.Q) and vector and tensor analyzing powers (Ay and Ayy) are displayed in fig. 2. In order to assign the GT and SFD transitions we will employ an empirical approach to deduce the an-
800
nB(d 2He)nBe
,,E l
~~
~>~:
ooo
400 :m
c~ o
,d
200
1 ---
0 600
rn
O
0"u'b=35°
,zC(d,ZHe) lz B
400
~
i~
ft+~
Ed=70MeV
2OO 0 -40
-30
-20
-10
Q - V a l u e [MeV] Fig. I. Energy spectrum for the HB(d, 2He)l~Be (upper panel) reaction at 70 MeV and O~b=35 °. The solid curve is the result of a peak fitting analysis. The solid and dashed arrows indicate the positions of mean excitation energies estimated with or without the neutron halo. For comparisonpurposes the energy spectrum for the 12C(d, 2He)12B (lower panel) reaction at 70 MeV and O~ab=35 ° is also shown. See text for detail.
Volume 302, number 1
PHYSICS LETTERS B
1
I
I
1
0.5
I
" ~ EU [. ov]
0.0
"
1
~
I
I
I
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2.7
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2.7 I_
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-0.5
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18 March 1993
20
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60 80 8cu [ d e g r e e ]
[ 1 1 1 1 1
20
40 60 80 0cM [ d e g r e e ]
Fig. 2. Cross sections and vector and tensor analyzing powers of the low-lying states (Ex=0.3, 2.7 and 3.8 MeV) and of the bump at Ex = 10 MeV for the HB (d, 2He)~lBe reaction and those of the ground state AL = 0 transition (GT type) and of the state at Ex = 4.5 MeV, AL = 1 transition ( SFD type ) for the ~2C( d, 2He) ]2B reaction. Solid and dashed curves represent AL = 0 and 1 transitions, respectively. They are obtained by tracing data points of the ~2C(d, 2He ) t2B reaction in the figure. See text for detail. around
gular momentum transfer (AL) by comparing the observed angular distributions with those of known transitions characteristic to the transferred angular momentum. For this purpose we use experimental results of the ground state 1+ GT transition (AS= l, AL = 0) and of the transition to the state at Ex = 4.5 MeV which is mostly due to the 2 - SFD (AS= l, A L = 1 ) states, observed in the t2C(d, 2He)12B react i o n [ 5 ]. Ay and Ayy on these 1+ and 2 - states have been investigated at 70 MeV and reported by Motobayashi et al. [ 16,17 ]. We note that it is difficult to determine the final state spin ,/f value in the present odd mass target because of non-zero initial spin j i value. Measurements for the 12C(d, 2He)IEB reaction were made separately under the same experimental condition and a typical energy spectrum at 0~,b= 35 ° is shown in the bottom panel of fig. 1. Angular distributions of dcr/dQ and Ay and Ayy are also
displayed in fig. 2 and they are generally consistent with previous results [ 16,17 ]. The solid and dashed curves in fig. 2 represent the shapes of experimental A L = 0 and A L = 1 transitions. They are drawn by tracing data points of the 12C(d, 2He) [2B reaction in the figure. It should be noted that the shape of the angular distribution for the peak at Ex=4.5 MeV which represents the AL = 1 transition is almost unchanged by including yields at higher excitations. This fact indicates that the yields in the higher excitation region are also mainly due to the A L = 1 transitions. Unfortunately we were unable to extract analyzing powers for the region beyond the 4.5 MeV peak due to an experimental problem except those at 0~,b= 35 ° (0CM = 42 ° ). If we calculate the analyzing powers including yields in the higher excitation region Ex = 230 MeV, the Ay and Aye values at 0~ab= 35 ° of the ~2C(d, 2He)t2B reaction become - 0 . 0 4 + 0 . 0 4 and
Volume 302, number I
PHYSICSLETTERSB
0.09 + 0.08, respectively. These values are in agreement within statistical errors with those of the 4.5 MeV peak alone of fig. 2. As for the transition to the low-lying states (Ex=0.3, 2.7 and 3.8 MeV) the angular distributions for da/dO are very similar to those of the ground state transition in the '2C(d, 2He)~2B reaction, indicating the GT type transitions with AL = 0. The CK model predicts strong GT states at Ex = 0.0, 2.0 and 4.1 MeV with J~=½-, 3 - and ~-, respectively. Therefore the observed peaks most probably correspond to these GT states. Note that the state at Ex = 0.3 MeV is known to be J~= ½- [ 7 ]. The angular distribution of the cross section for the broad bump observed at around Ex = 10 MeV has a flatter shape suggesting a larger AL transfer than those of the discrete transitions to the low-lying states. The angular distributions for da/dl2 are also similar to those of the transition to the SFD state at Ex=4.5 MeV in the ~2C(d, 2He)12B reaction, suggesting a AL = 1 transition. These facts strongly indicate that this bump at Ex= 10 MeV is mainly due to the spinflip dipole transition. The above AL assignments based on the angular distributions of cross sections are further supported by the Ay and Aye data. General trends observed in the ~2C(d, 2He)'2B reaction such as large negative values at around 40 ° for the AL = 0 transition or a very small Ayy value for the AL = 1 transition are also seen in the '~B (d, 2He)~Be reaction. The shell model calculations with a neutron halo have been performed by Hoshino et al. [ 18 ]. They showed that the effect of the neutron halo appears in the isovector SFD transition as follows: The mean excitation energy/~of SFD transitions is shifted down by about 2 MeV and the SFD transition strength B(SFD) is enhanced by about 40% compared with the calculations without the neutron halo. We examine these unique features quantitatively by using '2C data again as a reference. In the following we will show an analysis by using the data at 0tab= 35 ° as a typical example where we expect a moderate yield from the SFD transition and less contributions from the GT or higher AL transitions. However the arguments used here are general and in principle applicable to any angle without losing generality. E" of SFD transitions with (without) halo is indicated by the solid (dashed) arrow in fig. 1. It is clear 10
18 March 1993
that the observed broad bump at around Ex = 10 MeV is much closer to the shell model prediction with halo. As for the strength we analyze our results in terms of the unit cross section & It is most frequently used in the study of Gamow-Teller transitions and usually defined as t~Gx= (daGx/d.Q)(q=O)/B(GT), where the cross section is extrapolated to the momentum transfer q = 0 and corrected for the energy loss dependence [ 12 ]. Here we define the unit cross section at a scattering angle of 35 ° and we will not apply the correction due to the energy loss since it is estimated to be small [ 12 ] and the values of the energy loss of GT or SFD transitions are similar for both target nuclei. The cross sections at 35 ° for the GT transition (summed over three low-lying peaks) and the SFD bump are listed in table 1 together with those of the ~2C target. The shell model estimates after summing up strengths at appropriate excitation energy intervals listed in table 1 are also given; CK wave functions [ 9 ] for the GT transitions and MK wave functions with [ 18 ] or without [ 10 ] neutron halo for the SFD transitions. The unit cross section at 35 ° is defined as ~, = (da,~/dO)/B(a) where a is either GT or SFD. 6cT values for '~B and ~2C are obtained as 20.2 and 18.7 ~tb/sr, respectively. They are almost equal. Thus the proportionality relation seems to hold for the GT transitions. This fact also indicates that the GT state is not influenced by the presence of a neutron halo as is expected. As for the SFD transitions, the 6SVD values of ~B are 1.42 or 1.98 ~tb/sr depending on calculations with or without halo, respectively. These values should be compared to that of 1.55 ~tb/sr of ~2C. This result seems to support the shell model prediction of 40% enhancement of SFD transitions due to the neutron halo if the same kind of proportionality holds for the SFD transitions. We note that da/dI2 for the SFD transition depends on the assumption for the magnitude of the background due to the three-body phase space and for the contribution from the strengths other than the SFD transition. However, both liB and 12C data are analyzed in a consistent manner, the relative uncertainty in da/dg2 is estimated to be rather small ( < 20%). One might think that the shell model predictions on B ( G T ) or B(SFD) depend on the interactions and configurations of model space used in the calculations and consequently this leads to a fur-
Volume 302, number 1
PHYSICS LETTERS B
18 March 1993
Table 1 Cross sections for the (d, 2He) reaction on 12C and HB at 70 MeV and 35 °, GT and SFD strengths and unit cross sections. Relative uncertainties in dtr/dO for the GT transitions and those for the SFD transitions are estimated to be less than 5% and 20%, respectively, apart from the overall normalization. G T transition ( A L = O )
E~ (MeV)
Target
Ji
Jr
t2C
0+
1+
0.0
lib
~-
½(~ - )
0.3 2.7
(~ -)
3.8
SFD transition (AL= 1 ) Target Ji Jf
12C
0+
Ex (MeV)
de/dQ (~tb/sr)
) ~
B ( G T ) (fm 2) CK a)
17.6
0.98
17.9
14.8
0.73
20.2
dtr/d,Q (lab/sr)
#s~(p.b/sr)
B(SFD) (fm 2 ) MK b)
0)
2-30
48.3
31.0
")
2-23
34.7
17.5
1-
6GT (I-tb/s r) CK a)
M K + halo c)
MK b)
M K + halo c)
1.55
2HB
a) Ref. [9].
~-
b) Ref. [10].
24.4
1.98
1.42
¢)Ref. [18].
ther ambiguity of the analysis. Such an ambiguity is also small in terms o f the unit cross section 8 as long as the same interactions and the same configurations are used in the calculation o f both 12B and l~Be, since the variation of the summed strength within the wide excitation energy interval of the present case tends to be similar for both nuclei so that the relative ratio of is rather independent o f such variations. By knowing #SFD the yield of the ground state transition can be estimated as 0.075 lab/sr with B ( S F D ) =0.053 fm 2 [ 18]. This is only 0.97% of the nearly G T transition at Ex= 0.3 MeV, consequently it is too small to be seen in fig. 1. Finally we would like to remark on the distortedwave Born approximation ( D W B A ) approach. We have performed one-step DWBA calculations employing the code T W O F N R [ 19 ] according to the prescription o f ref. [ 16 ] with the same parameters. The transition form factors are taken from refs. [ 9,18 ]. We found that the shapes of the angular distributions o f da/dg2 depend, although not strongly, on the individual states and are not so stable as those
o f the nucleon scattering such as the (p, p ' ) or (p, n) reactions. This is primarily due to the inherent complexity of the reaction mechanism associated with the (d, 2He) reaction even though it has an excellent spin-isospin selectivity as a probe. We have neglected non-central interactions and exchange amplitudes as well as the deuteron D-state in the calculations although they certainly play important roles. As an example we examined, though preliminarily, the effect of a tensor interaction and found that the shape of the angular distribution for the GT transition could be well reproduced [20]. On the contrary it was needed to include the two-step processes in the DWBA calculations to get a similar quality fit if the central interactions were only employed as has been shown in refs. [ 16,17 ]. Note that if we perform the (n, p) reaction type calculation which assumes the proton in the deuteron as a spectator and ignores the internal freedom of the deuteron or 2He particle we can reproduce the data rather well. However even in such a simplified calculation it is known that the DWBA cross section 11
Volume 302, number 1
PHYSICS LETTERS B
changes up to 30% depending on the choice o f various parameters [ 11,21 ]. U n d e r these circumstances it is difficult to draw a definitive conclusion from the D W B A calculation alone. We hope the present d a t a might stimulate efforts to develop the full microscopic D W B A treatment to include these freedoms. In summary, we have successfully studied the structure o f the neutron halo nucleus 11Be by the I~B (d, 2He) reaction at 70 MeV. Three discrete peaks in the low excitation energy region and a b r o a d b u m p at a r o u n d 10 MeV excitation are clearly observed. They are identified to be due to G T a n d S F D transitions, respectively, by comparing the observed angular distributions with those of known G T and S F D transitions in the 12C(d, 2He) 12B reaction. This identification is supplemented by the vector and tensor analyzing power data. We have shown on the basis o f the empirical analyses that the G T transition receives almost no effect o f the neutron halo while the S F D transition does reflect the neutron halo as a 2 MeV shift down o f the mean excitation energy a n d also as an enhancement o f the transition strength, although a more definite conclusion awaits further detailed analyses o f the present data. Higher deuteron b e a m energies would be a great help in that ambiguities o f the reaction m e c h a n i s m would be reduced. An effort in this direction has been started at the R I K E N Ring Cyclotron facility and new experimental results are expected to be available in the near future. We thank K. M u t o for helpful discussions and also I. Sugai for preparing the 11B target. We are grateful
12
18 March 1993
to W. Bentz for reading the manuscript. This work is supported financially in part by the G r a n t - i n - A i d for Scientific Research No. 6342007 o f Ministry o f Education, Science and Culture o f Japan. This experim e n t was p e r f o r m e d at R C N P under Program N u m ber 29A13.
References [ 1] I. Tanihata et al., Phys. Rev. Lett. 55 (1985) 2676. [ 2 ] I. Tanihata et al., Phys. Lett. B 206 ( 1988 ) 592. [3] T. Kobayashi et al., Phys. Rev. Lett. 60 (1988) 2599; Nucl. Phys. A 538 (1992) 343c; M. Fukuda et al., Phys. Lett. B 268 ( 1991 ) 339. [4 ] T. Kobayashi et al., preprint RIKEN-AF-NP- 106. [ 5 ] D.P. Stahel et al., Phys. Rev. C 20 (1979) 1680. [ 6 ] K.B. Beard et al., Phys. Rev. C 26 (1982) 720. [7] F. Ajzenberg-Seloveet al., Nucl. Phys. A 481 (1990) 1. [8] G.-B. Liu and H.T. Fortune, Phys. Rev. C 42 (1990) 167. [9] S. Cohen and D. Kurath, Nucl. Phys. 73 (1965) 1. [ 10] D.J. Millener and D. Kurath, Nucl. Phys. A 255 ( 1975 ) 315. [ 11 ] F.P. Brady et al., Phys. Rev. C 43 ( 1991 ) 2284. [ 12] T.N. Taddeucci et al., Nucl. Phys. A 469 (1987) 125. [ 13 ] C. Gaarde et al., Nucl. Phys. A 422 (1984) 189. [ 14 ] T. Motobayashi et al., Nucl. Instrum. Methods A 271 (1988) 491. [15]H. Okamura, Ph.D. thesis, Kyoto University (1989), unpublished. [ 16 ] T. Motobayashi et al., Phys. Rev. C 34 (1986) 2365. [ 17 ] T. Motobayashi et al., J. Phys. G 14 ( 1988 ) L 137. [ 181 T. Hoshino, H. Sagawa and A. Arima, Nucl. Phys. A 523 (1991) 228. [19]M. Igarashi, Computer program TWOFNR (1977), unpublished. [20 ] H. Okamura et al., in preparation for publication. [ 21 ] H. Ohnuma et al., Nucl. Phys. A 467 ( 1987 ) 61.