- Email: [email protected]
Spinflip Dipole Giant Resonances in neutron rich light nuclei and neutron halo effects
NUCLEAR PHYSICS A
Nuclear Physics A569 (1994) 277c-286~ North-Holland, Amsterdam
Spinflip
Dipole
Neutron
Halo
Giant
Resonances
in Neutron
Rich
Light
Nuclei
and
Effects
H. Sakai”, S. Ishida’
and H. Okamuraa
aDepartment of Physics, University of Tokyo Hongo 7-3-1, Bunkyo-ku, Tokyo 113, Japan Gamow-Teller and spinflip dipole transitions in *‘Be and ‘Li are studied by means of the (d,‘He) reaction at 70 MeV. Differential cross sections and vector- and tensor-analyzing powers have been measured. A possible halo effect is investigated in llBe. The observed mean excitation energy and strength for the spinflip dipole transition in which a possible neutron halo effect appears are consistent with the shell model prediction which takes the neutron halo into account. 1. INTRODUCTION Recently the study of neutron rich nuclei attracted much interest. One of the reason for this is probably due to the suggestion of a neutron halo[l] in extremely neutron rich nuclei such as llLi, “Be and 14Be. Since then, a lot of experimental and theoretical studies have been made to clarify the neutron halo phenomenon. The spectroscopic study of neutron rich nuclei is interesting. However such a spectroscopic study is rather difficult because of a lack of the experimental means. In the beginning of the study (‘IF-, y) or inverse (y, r+) reactions [2] h ave been used and recently the charge-exchange (n,p) or even double-charge-exchange (a-, rt) reaction[3] are employed. However these reactions are secondary-beam experiments and therefore, to some extent, suffer from low beam intensity or poor energy resolution. We report here our approach to produce the neutron rich nucleus “Be and ‘Li with reaction the (d,2He). “Be is the easiest halo nucleus to access and ‘Li is considered to be the core nucleus of *lBe. Part of the llBe result has been reported in ref. [4]. We denote a proton-proton system coupled to the singlet S-state [‘So] as a 2He. The charge-exchange (d,‘He) reaction has an excellent spin-isospin selectivity[5, 61. It excites exclusively spin-isospinflip transitions e.g. Gamow-Teller (GT) type transitions (AS=l, AL=O), spinflip dipole (SFD) transitions (AS=l, AL=l) etc. The effect due to a neutron halo is expected to appear mainly in the dipole transition. Firstly, because of the small binding energy of the halo neutron the mean excitation energy of the dipole state becomes smaller than that without a halo. Actually the neutron separation energy of ‘lBe is only 0.5 MeV. Secondly, the dipole transition strength will be enhanced. The dipole transition is induced by the operator TIY1alJttl with J = 0, 1, and 2. Therefore the matrix elements involving a halo, in general, have a better overlap at large radii because of the larger root mean square radius of the halo neutron compared to that of the core. On the contrary, almost no effect is expected on the GT transition since the transition takes place within the same shell orbit and the operator has no radial part. Elsevier Science B.V. SSDZ 0375-9474(94)00029-M
278~
H. Sakai et al. I Spinflip dipole giant resonances in neutron rich light nuclei
2. EXPERIMENTS
AND
DATA
REDUCTION
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/cm2 was prepared by evaporating isotopically enriched (> 95%) 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 ‘Be target was a metallic foil with a thickness of 2.0 mg/cm2. The 2He particles were detected with two sets of multi~ounter arrays. They were designed to have an optimum detection efficiency for two protons with small relative energy (2He). Each array consisted of four sets of AE - E Si counter telescopes. In this configuration six different p - p pair coincidences become available in each array and the detection efficiency of ‘He particles increases accordingly. Each telescope has a solid angle of 6.7 msr. The final energy resolution of the 2He in terms of full width at half maximum was typically 600 keV. The experimental 2He cross sections quoted in this work were obtained after integrating observed triple differential cross sections over the detector solid angles and the relative two proton energy up to 1 MeV according to the prescription of Ref.[5, 71. Further details of the experimental procedures are described elsewhere Figure 1 shows the energy spectra of the cross section at Bta6= 35” for the “B and ‘Be targets. The result of i2C is also shown since it will be used as a spectroscopic reference in the later analysis. The dotted curves indicated in the figure are the possible contributions of the threebody phase space whose height is adjusted to reproduce a shape of the highly excited continuum region. Figure 2 shows the energy spectra after subtracting the three-body phase space contribution. General features are : discrete states in the low excitation energy most probably due to the GT transition and a broad bump in the high excitation energy probably due to the SFD tr~sition. Angular distributions (20” < @lab < 70”) for the cross sections (da,/&) an d vector- and tensor-analyzing powers (A, and Ayy) are displayed in Fig. 3.
[s].
3. ANALYSIS
AND
DISCUSSION
We will employ the spectroscopic amplitudes of the Cohen-Kurath (CK)[S] and MillenerKurath(MK)[lO] wave functions in a theoretical description and at the same time use the results of the 12C(d,2He)12B 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 lp-shell orbits, and also by the MN 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 *‘B via 12C(a,p)[ll], or to 12N via 12C(p, 72)[12] is well reproduced by the CK wave functions. As for the SFD transitions, Gaarde et al.[I3] h ave shown that the experimental spectrum of the “C(p, n)12N reaction agrees well with the strength distribution calculated with the MK wave functions, and more recently Brady et al. have shown the same for the i2C(n,p) reaction[ll].
400
t . %(d.%) 400 :
200
200 -
=C(d.'He) 8,=3V
0
600
ff,,=35'
0
*Be(d,%e) B,,,=~!Y
600
400
400
200
200
0
0 -40
-30
Q-Value
-20
-10
[MeV]
Figure 1. Energy spectra for the (d,2He) reaction at 70 MeV and 8ia* = 35” on i2C (top), “B (middle) and ‘Be (bottom). The dashed line indicates the three-body phase space contribution,
-40
-30
Q-Value
-20
-10
[MeV]
Figure 2. Same as fig. 1 but the threebdo y phase space contribution is subtracted.
3.1. ~‘B(~,‘~e)l’Be In the spectrum of the 11B(d,2He)11Be 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 to draw a definitive conclusion. In order to assign the GT and SFD transitions we will empIoy an empirical approach to deduce the angular 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 l+ GT transition(AS=l,AL=O)and of the transition to the state at E,=4.5 MeV which is mostly due to the 2- SFD (AS=l,AL=l) states, observed in the 12C(d,2He)12B reaction[5]. A, and A,, on these l+ and 2- states have been investigated at 70 MeV and reported by Motobay~hi et aI.fl4, IS]. We note that it is difficult to determine the final state spin Jf
280~
H. Sakai et al. I Spinjlip dipole giant resonances in neutron rich light nuclei
0.0 -0.5 20
40
60
60
6c, [degree]
IizY 4.5
‘*
+
20
40
60
60
ecM [degree]
20
40 4~
60
60
[degree]
Figure 3. Cross sections and vector- and tensor-analyzing powers for the 11B(d,2He)“Be reaction (upper) and for the 12C( d ,‘He)l’B reaction (lower). Solid and dashed curves represent AL=0 and 1 transitions, respectively. See text for detail.
value in the present odd mass target because of non-zero initial spin J” value. The solid and dashed curves in Fig.3 represent the shapes of experimental AL=0 and AL=1 transitions. They are drawn by tracing data points of the 12C(d,2He)12B reaction in the figure. It should be noted that the shape of the angular distribution for the peak at E,=4.5 MeV which represents a 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 AL=1 transitions. As for the transitions to the low lying states (E, =0.3, 2.7 and 3.8 MeV) the angular distributions for du/dR are very similar with those of the ground state transition in the 12C(d,2He)12B reaction, indicating the GT-type transitions with AL=O. The CK model predicts strong GT states at E,=O.O, 2.0 and 4.1 MeV with J”=:-, z- and i-, respectively. Therefore the observed peaks most probably correspond to these GT states.
H. Sakzi et al. I ~pi~ip dipole giant reso~nces
in neutron rich
tight nuclei
281c
Note that the state at E, =0.3 MeV is known to be Jr=+-[lS]. The angular distribution of the cross section for the broad bump observed at around E,=lO 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 ~~/~~ are also similar to those of the transition to the SFD state at Ez=4.5 MeV in the ‘2C(d,2He)*2B reaction, suggesting a AL=1 transition. Th ese facts strongly indicate that this bump at E,=lO 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 A, and A,, data. General trends observed in the ‘2C(&2He)12B reaction such as large negative values at around 40” for the AL=0 transition or very small A,, value for the AL=1 transition are also seen in the ‘*B(d,2He)11Be reaction. 3.2. gBe(d,2He)gLi The general features of the present gBe(d,2He)gLi spectrum at &,=35” resemble the ‘Be(n,p)‘Li spectrum measured at E,=198 MeV and at 8,=1.8”[17] despite of a large difference of momentum transfer: two narrow peaks at low excitation energy and one broad peak in the high excitation energy. The narrow peaks are much more strongly populated by the (d,ZHe) reaction than by the (n,p) reaction.
6
103
I
I
I
I
i
I
f
i
1
I
I
i
t
~e(d,'He)'~ I& = 70 MeV
lo2
8
0.5 0.0
0.5 - id&i 0.0
6 $1
0.0
TO.5 A?J -0.5
A
0.0 -0.5
1o-3 ' g ' ' ' t ' 20 40 60 80 GM
f_dw-el
20
40 GM
60 [degree]
80
, I / t t I I 20 40 60 80 %M
[degree]
Figure 4. Cross sections and vector- and tensor-analyzing powers of the low lying states (E, =O.O, and 2.7 MeVf for the gBe(~,2He)QL. I reaction. The solid curve represents the shape of the AL=0 transition. It is obtained by tracing data points of the ‘2C(d,2He)‘2B reaction in fig. 3. See text for detail.
Two narrow peaks at low excitation energies are identified as transitions to the ground state with J”= $- and to E,=2.7 MeV state with ($-)[16]. Thus transitions to these
282~
H. Sakai et al. I Spinflip dipole giant resonances in
states can be considered as due to a standard GT type because of the spin-parity relations, 3- + i- and $- --+ ($-). Figure 4 shows the angular distributions (do/&, A,, A,,) of these transitions. The solid curve represents the shape of experimental AL=0 transition. It is clear that the observed angular distributions are very different from the AL=0 shape expected for the GT-transition. This fact strongly suggests that the AL=2 transition dominates over the AL=0 transition. Note that the AL=2 transition is induced by the tensor interaction V& while the GT-transition is induced by the central interaction V,,. The dominance of the AL=2 transition may also explain why these two peaks are so weakly populated in the (n,p) reaction even at 1.8” where the GT-transition should dominates. The broad peak at E, 118 MeV most probably corresponds to the SFD-transitions although the angular distribution of the bump is unfortunately not yet available.
4.
COMPARISON TRON HALO
WITH
SHELL
MODEL
PREDICTIONS
WITH
NEU-
The shell model calculations with a neutron halo have been performed by Hoshino et a1.[18]. They showed that the effect of the neutron halo appears in the isovector SFD transition as follows : The mean excitation energy B 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 “C data as a reference. In the following we will show an analysis by using the data at ora* = 35” as a typical example where we expect moderate yields from the SFD transition and less contributions from the GT or higher AL transitions. z of the SFD transitions with (without) halo is indicated by the solid (dashed) arrow in Fig. 5. It is clear that the observed broad bump at around E, =lO MeV is much closer to the shell model prediction with a halo. As for the strength we analyze our results in terms of an unit cross section 8. It is most frequently used in the study of Gamow-Teller transitions and usually defined as wh ere the cross section is extrapolated to the momentum 6oT = e(q = O)IB(GT), 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 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 13C [14] and “C targets. 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 [lo] neutron halo for the SFD-transitions. The unit cross section at 35” is defined as 6, = %/B(o) where o is either GT or SFD. The &.GTvalues for llB, “C and 13C are obtained as 20.2, 17.9 and 18.7 pb/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. The exception is the ‘Be target which gives a huge &.GTvalue of 109 pb/sr. This large &.GT value can be attributed to the dominance of the AL=2 transition as mentioned in
H. Sakai et al. I Spiqflip dipole giant resonances in neutron rich light nuclei
283~
800
600
400
200
0 -40
-35
-30
-25
-20
-15
-10
Q-Value [MeV] Figure 5. Energy spectrum for the ‘1B(d,2He)“Be reaction. The solid curve is the result of a peak fitting analysis. The solid and dashed arrows indicate the position of mean excitation energies estimated with or without the neutron halo.
the previous section. Another reason might lie in the smallness of B(GT) value. Actually the CK model prediction is only B(GT)=0.037 and it is almost two orders of magnitude weaker than other GT-transitions (see table 1). Note that the experimentally deduced B(GT) value from the ‘Li P-decay measurement[l6] is 0.019. As for the SFD transitions, the &.SFD values of *rB are 1.42 or 1.98 &‘sr depending on calculations with or without halo, respectively. These values should be compared to that of 1.55 pb/sr of 12C. 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 du/dQ for the SFD transitjon depends on the assumption for the magnitudes of background due to the three-body phase space and for the contribution from the strengths other than the SFD transition. However, both ‘*B and 12C data are analyzed in a consistent manner, the relative uncertainty in du/dO is estimated to be rather small (< 20%). The 8s~~ values of ‘Be is unusual. It is only a half of i2C. 5.
SURGERY
We have studied the structure of the neutron rich nuclei ‘Li and l*Be by means of the (d,‘He) reaction at 70 MeV. Common features observed in the spectra are : discrete peaks
284c
H. Sakai et al. I ~~in~ip dipole giant resomzn&esin tzeutron rich light nuclei
Table 1 Cross sections for the (d,‘He) reaction on 13C, i2C, l*B and ‘Be at 35”, GT and SFD strengths and unit cross sections. The value of 13C is taken from ref. [14]. GT
transition
Target J;
Jf
(AL=O) EE MeV
duJdC2 @b/u)
B(GT) CKl’l
13 c
12
g-
=c
0”
O--2-
2-30
48.3
31.0
=B
$-
f+_;’
5-23
34.7
17.5
‘Be
a-2
;+_;+
6-28
12.6
17.7
1.55 24.4
1.98
1.42
0.71
in the low excitation energy region and a broad bump at around 8-10 MeV excitation. In the ‘lBe spectrum three discrete peaks and a broad bump are identified to be due to GT and SFD transitions, respectively, by comparing the observed angular distributions with those of known GT and SFD transitions in the ‘2C(d,2He)‘2B reaction. This identification is supplemented by the vector- and tensor-analyzing power data. We have shown on the basis of the empirical analyses that the GT transition receives almost no effect of the neutron halo while the SFD transition does reflect the neutron halo as a 2 MeV shift down of the mean excitation energy and also as an enhancement of the transition strength. Two peaks in the gLi spectrum have a very different angular distribution pattern from AL=O. The transitions to these states seem to be governed by the tensor interaction which allows AL=2. Because of this the &,-JTvalue is about 5 times Iarger than others studied. On the contrary the r?s~n value is only half of that of r2C. In order to understand these
H. Sakai et al. f ~p~ip
dipole giant resonances in neutron rich light nuclei
285c
features we need an analysis in terms of the distorted wave Born approximation(DWBA). However such an approach is not yet successful presumably due to the inherent complexity of the reaction mechanism associated with the (d,‘He) reactio#]. For this reason we used an empirical approach here to analyze the data rather than a conventional DWBA approach. Higher deuteron beam energies would be a great help in reducing ambiguities of the reaction mechanism. Particularly an analyzing power measurement with a polarized deuteron beam is useful in determining the spin of the SFD states[l9]. We have started an effort in this direction at the RIKEN Ring Cyclotron facility and have constructed the polarized ion source[20]. N ew results will be available in the near future. We would like to acknowledge the assistance of H. Okuno, A. Okihana, Y. Nagai, K. Takeda, T. Toriyama and A. Yoshida with various aspects of data acquisition. We thank N. Fukunishi and H. Sagawa for their help in the theoretical calculations. This work is supported financially in part by the Grant-in-Aid for Scientific Research No.6342007 of Ministry of Education, Science and Culture of Japan. The present experiments were performed at RCNP under Program Numbers 29A13 and 30A03.
REFERENCES 1. I. Tanihata et al., Phys. Rev. Lett. 55 (1985) 2676. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.
For example, H.W. Baer, Proc. VII. Conf. on High-Energy Physics and Nuclear Structure, Zurich (19771, p.245. T. Kobayashi, Nucl. Phys. A553 (1993) 465~. H. Sakai et al., Phys. Lett. B302 (1993) 7. D.P. Stahel et al., Phys. Rev. C20 (1979) 1680. K.B. Beard et al., Phys. Rev. C26 (1982) 720. T. Motobay~hi et al., Nucl. In&r. Meth. A271 (1988) 491. H. Okamura, Ph.D. thesis, Kyoto University, 1989, unpublished. S. Cohen and D. Kurath, Nucl. Phys. 73 (1965) 1. D.J. Millener and D. Kurath, Nucl. Phys. A255 (1975) 315. F.P. Brady et al., Phys. Rev. C43 (1991) 2284. T. N. Taddeucci et al., Nucl. Phys. A469 (1987) 125. C. Gaarde et al., Nucl. Phys. A422 (1984) 189. T. Motobayashi et al., Phys. Rev. C34 (1986) 2365. T. Motobayashi et al., J. Phys. G: Nucl. Phys. 14 (1988) L137. F. Ajzenberg-Selove et al., Nucl. Phys. A481 (1990) 1. K.P. Jackson, in Spin Observables of Nuclear Probes edited by C.J.Horowitz, C.D.Goodman and G.E.Walker (Plenum, 1988), p. 139. T. Hoshino, H. Sagawa and A. Arima, Nucl. Phys. A523 (1991) 228. D.V. Bugg and CWilkin, Nucl. Phys. A467 (1987) 575. C. Wilkin and D.V. Bugg, Phys. Lett. 154B (1985) 243. H. Okamura et al., in Workshop on Polarized Ion Sources and Polarized Gas Targets edited by W. Haeberli and L.W. Anderson (AIP Conf. Proc. 1993), in press.
Nuclear Physics A569 (1994) 277c-286~ North-Holland, Amsterdam
Spinflip
Dipole
Neutron
Halo
Giant
Resonances
in Neutron
Rich
Light
Nuclei
and
Effects
H. Sakai”, S. Ishida’
and H. Okamuraa
aDepartment of Physics, University of Tokyo Hongo 7-3-1, Bunkyo-ku, Tokyo 113, Japan Gamow-Teller and spinflip dipole transitions in *‘Be and ‘Li are studied by means of the (d,‘He) reaction at 70 MeV. Differential cross sections and vector- and tensor-analyzing powers have been measured. A possible halo effect is investigated in llBe. The observed mean excitation energy and strength for the spinflip dipole transition in which a possible neutron halo effect appears are consistent with the shell model prediction which takes the neutron halo into account. 1. INTRODUCTION Recently the study of neutron rich nuclei attracted much interest. One of the reason for this is probably due to the suggestion of a neutron halo[l] in extremely neutron rich nuclei such as llLi, “Be and 14Be. Since then, a lot of experimental and theoretical studies have been made to clarify the neutron halo phenomenon. The spectroscopic study of neutron rich nuclei is interesting. However such a spectroscopic study is rather difficult because of a lack of the experimental means. In the beginning of the study (‘IF-, y) or inverse (y, r+) reactions [2] h ave been used and recently the charge-exchange (n,p) or even double-charge-exchange (a-, rt) reaction[3] are employed. However these reactions are secondary-beam experiments and therefore, to some extent, suffer from low beam intensity or poor energy resolution. We report here our approach to produce the neutron rich nucleus “Be and ‘Li with reaction the (d,2He). “Be is the easiest halo nucleus to access and ‘Li is considered to be the core nucleus of *lBe. Part of the llBe result has been reported in ref. [4]. We denote a proton-proton system coupled to the singlet S-state [‘So] as a 2He. The charge-exchange (d,‘He) reaction has an excellent spin-isospin selectivity[5, 61. It excites exclusively spin-isospinflip transitions e.g. Gamow-Teller (GT) type transitions (AS=l, AL=O), spinflip dipole (SFD) transitions (AS=l, AL=l) etc. The effect due to a neutron halo is expected to appear mainly in the dipole transition. Firstly, because of the small binding energy of the halo neutron the mean excitation energy of the dipole state becomes smaller than that without a halo. Actually the neutron separation energy of ‘lBe is only 0.5 MeV. Secondly, the dipole transition strength will be enhanced. The dipole transition is induced by the operator TIY1alJttl with J = 0, 1, and 2. Therefore the matrix elements involving a halo, in general, have a better overlap at large radii because of the larger root mean square radius of the halo neutron compared to that of the core. On the contrary, almost no effect is expected on the GT transition since the transition takes place within the same shell orbit and the operator has no radial part. Elsevier Science B.V. SSDZ 0375-9474(94)00029-M
278~
H. Sakai et al. I Spinflip dipole giant resonances in neutron rich light nuclei
2. EXPERIMENTS
AND
DATA
REDUCTION
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/cm2 was prepared by evaporating isotopically enriched (> 95%) 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 ‘Be target was a metallic foil with a thickness of 2.0 mg/cm2. The 2He particles were detected with two sets of multi~ounter arrays. They were designed to have an optimum detection efficiency for two protons with small relative energy (2He). Each array consisted of four sets of AE - E Si counter telescopes. In this configuration six different p - p pair coincidences become available in each array and the detection efficiency of ‘He particles increases accordingly. Each telescope has a solid angle of 6.7 msr. The final energy resolution of the 2He in terms of full width at half maximum was typically 600 keV. The experimental 2He cross sections quoted in this work were obtained after integrating observed triple differential cross sections over the detector solid angles and the relative two proton energy up to 1 MeV according to the prescription of Ref.[5, 71. Further details of the experimental procedures are described elsewhere Figure 1 shows the energy spectra of the cross section at Bta6= 35” for the “B and ‘Be targets. The result of i2C is also shown since it will be used as a spectroscopic reference in the later analysis. The dotted curves indicated in the figure are the possible contributions of the threebody phase space whose height is adjusted to reproduce a shape of the highly excited continuum region. Figure 2 shows the energy spectra after subtracting the three-body phase space contribution. General features are : discrete states in the low excitation energy most probably due to the GT transition and a broad bump in the high excitation energy probably due to the SFD tr~sition. Angular distributions (20” < @lab < 70”) for the cross sections (da,/&) an d vector- and tensor-analyzing powers (A, and Ayy) are displayed in Fig. 3.
[s].
3. ANALYSIS
AND
DISCUSSION
We will employ the spectroscopic amplitudes of the Cohen-Kurath (CK)[S] and MillenerKurath(MK)[lO] wave functions in a theoretical description and at the same time use the results of the 12C(d,2He)12B 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 lp-shell orbits, and also by the MN 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 *‘B via 12C(a,p)[ll], or to 12N via 12C(p, 72)[12] is well reproduced by the CK wave functions. As for the SFD transitions, Gaarde et al.[I3] h ave shown that the experimental spectrum of the “C(p, n)12N reaction agrees well with the strength distribution calculated with the MK wave functions, and more recently Brady et al. have shown the same for the i2C(n,p) reaction[ll].
400
t . %(d.%) 400 :
200
200 -
=C(d.'He) 8,=3V
0
600
ff,,=35'
0
*Be(d,%e) B,,,=~!Y
600
400
400
200
200
0
0 -40
-30
Q-Value
-20
-10
[MeV]
Figure 1. Energy spectra for the (d,2He) reaction at 70 MeV and 8ia* = 35” on i2C (top), “B (middle) and ‘Be (bottom). The dashed line indicates the three-body phase space contribution,
-40
-30
Q-Value
-20
-10
[MeV]
Figure 2. Same as fig. 1 but the threebdo y phase space contribution is subtracted.
3.1. ~‘B(~,‘~e)l’Be In the spectrum of the 11B(d,2He)11Be 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 to draw a definitive conclusion. In order to assign the GT and SFD transitions we will empIoy an empirical approach to deduce the angular 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 l+ GT transition(AS=l,AL=O)and of the transition to the state at E,=4.5 MeV which is mostly due to the 2- SFD (AS=l,AL=l) states, observed in the 12C(d,2He)12B reaction[5]. A, and A,, on these l+ and 2- states have been investigated at 70 MeV and reported by Motobay~hi et aI.fl4, IS]. We note that it is difficult to determine the final state spin Jf
280~
H. Sakai et al. I Spinjlip dipole giant resonances in neutron rich light nuclei
0.0 -0.5 20
40
60
60
6c, [degree]
IizY 4.5
‘*
+
20
40
60
60
ecM [degree]
20
40 4~
60
60
[degree]
Figure 3. Cross sections and vector- and tensor-analyzing powers for the 11B(d,2He)“Be reaction (upper) and for the 12C( d ,‘He)l’B reaction (lower). Solid and dashed curves represent AL=0 and 1 transitions, respectively. See text for detail.
value in the present odd mass target because of non-zero initial spin J” value. The solid and dashed curves in Fig.3 represent the shapes of experimental AL=0 and AL=1 transitions. They are drawn by tracing data points of the 12C(d,2He)12B reaction in the figure. It should be noted that the shape of the angular distribution for the peak at E,=4.5 MeV which represents a 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 AL=1 transitions. As for the transitions to the low lying states (E, =0.3, 2.7 and 3.8 MeV) the angular distributions for du/dR are very similar with those of the ground state transition in the 12C(d,2He)12B reaction, indicating the GT-type transitions with AL=O. The CK model predicts strong GT states at E,=O.O, 2.0 and 4.1 MeV with J”=:-, z- and i-, respectively. Therefore the observed peaks most probably correspond to these GT states.
H. Sakzi et al. I ~pi~ip dipole giant reso~nces
in neutron rich
tight nuclei
281c
Note that the state at E, =0.3 MeV is known to be Jr=+-[lS]. The angular distribution of the cross section for the broad bump observed at around E,=lO 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 ~~/~~ are also similar to those of the transition to the SFD state at Ez=4.5 MeV in the ‘2C(d,2He)*2B reaction, suggesting a AL=1 transition. Th ese facts strongly indicate that this bump at E,=lO 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 A, and A,, data. General trends observed in the ‘2C(&2He)12B reaction such as large negative values at around 40” for the AL=0 transition or very small A,, value for the AL=1 transition are also seen in the ‘*B(d,2He)11Be reaction. 3.2. gBe(d,2He)gLi The general features of the present gBe(d,2He)gLi spectrum at &,=35” resemble the ‘Be(n,p)‘Li spectrum measured at E,=198 MeV and at 8,=1.8”[17] despite of a large difference of momentum transfer: two narrow peaks at low excitation energy and one broad peak in the high excitation energy. The narrow peaks are much more strongly populated by the (d,ZHe) reaction than by the (n,p) reaction.
6
103
I
I
I
I
i
I
f
i
1
I
I
i
t
~e(d,'He)'~ I& = 70 MeV
lo2
8
0.5 0.0
0.5 - id&i 0.0
6 $1
0.0
TO.5 A?J -0.5
A
0.0 -0.5
1o-3 ' g ' ' ' t ' 20 40 60 80 GM
f_dw-el
20
40 GM
60 [degree]
80
, I / t t I I 20 40 60 80 %M
[degree]
Figure 4. Cross sections and vector- and tensor-analyzing powers of the low lying states (E, =O.O, and 2.7 MeVf for the gBe(~,2He)QL. I reaction. The solid curve represents the shape of the AL=0 transition. It is obtained by tracing data points of the ‘2C(d,2He)‘2B reaction in fig. 3. See text for detail.
Two narrow peaks at low excitation energies are identified as transitions to the ground state with J”= $- and to E,=2.7 MeV state with ($-)[16]. Thus transitions to these
282~
H. Sakai et al. I Spinflip dipole giant resonances in
states can be considered as due to a standard GT type because of the spin-parity relations, 3- + i- and $- --+ ($-). Figure 4 shows the angular distributions (do/&, A,, A,,) of these transitions. The solid curve represents the shape of experimental AL=0 transition. It is clear that the observed angular distributions are very different from the AL=0 shape expected for the GT-transition. This fact strongly suggests that the AL=2 transition dominates over the AL=0 transition. Note that the AL=2 transition is induced by the tensor interaction V& while the GT-transition is induced by the central interaction V,,. The dominance of the AL=2 transition may also explain why these two peaks are so weakly populated in the (n,p) reaction even at 1.8” where the GT-transition should dominates. The broad peak at E, 118 MeV most probably corresponds to the SFD-transitions although the angular distribution of the bump is unfortunately not yet available.
4.
COMPARISON TRON HALO
WITH
SHELL
MODEL
PREDICTIONS
WITH
NEU-
The shell model calculations with a neutron halo have been performed by Hoshino et a1.[18]. They showed that the effect of the neutron halo appears in the isovector SFD transition as follows : The mean excitation energy B 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 “C data as a reference. In the following we will show an analysis by using the data at ora* = 35” as a typical example where we expect moderate yields from the SFD transition and less contributions from the GT or higher AL transitions. z of the SFD transitions with (without) halo is indicated by the solid (dashed) arrow in Fig. 5. It is clear that the observed broad bump at around E, =lO MeV is much closer to the shell model prediction with a halo. As for the strength we analyze our results in terms of an unit cross section 8. It is most frequently used in the study of Gamow-Teller transitions and usually defined as wh ere the cross section is extrapolated to the momentum 6oT = e(q = O)IB(GT), 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 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 13C [14] and “C targets. 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 [lo] neutron halo for the SFD-transitions. The unit cross section at 35” is defined as 6, = %/B(o) where o is either GT or SFD. The &.GTvalues for llB, “C and 13C are obtained as 20.2, 17.9 and 18.7 pb/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. The exception is the ‘Be target which gives a huge &.GTvalue of 109 pb/sr. This large &.GT value can be attributed to the dominance of the AL=2 transition as mentioned in
H. Sakai et al. I Spiqflip dipole giant resonances in neutron rich light nuclei
283~
800
600
400
200
0 -40
-35
-30
-25
-20
-15
-10
Q-Value [MeV] Figure 5. Energy spectrum for the ‘1B(d,2He)“Be reaction. The solid curve is the result of a peak fitting analysis. The solid and dashed arrows indicate the position of mean excitation energies estimated with or without the neutron halo.
the previous section. Another reason might lie in the smallness of B(GT) value. Actually the CK model prediction is only B(GT)=0.037 and it is almost two orders of magnitude weaker than other GT-transitions (see table 1). Note that the experimentally deduced B(GT) value from the ‘Li P-decay measurement[l6] is 0.019. As for the SFD transitions, the &.SFD values of *rB are 1.42 or 1.98 &‘sr depending on calculations with or without halo, respectively. These values should be compared to that of 1.55 pb/sr of 12C. 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 du/dQ for the SFD transitjon depends on the assumption for the magnitudes of background due to the three-body phase space and for the contribution from the strengths other than the SFD transition. However, both ‘*B and 12C data are analyzed in a consistent manner, the relative uncertainty in du/dO is estimated to be rather small (< 20%). The 8s~~ values of ‘Be is unusual. It is only a half of i2C. 5.
SURGERY
We have studied the structure of the neutron rich nuclei ‘Li and l*Be by means of the (d,‘He) reaction at 70 MeV. Common features observed in the spectra are : discrete peaks
284c
H. Sakai et al. I ~~in~ip dipole giant resomzn&esin tzeutron rich light nuclei
Table 1 Cross sections for the (d,‘He) reaction on 13C, i2C, l*B and ‘Be at 35”, GT and SFD strengths and unit cross sections. The value of 13C is taken from ref. [14]. GT
transition
Target J;
Jf
(AL=O) EE MeV
duJdC2 @b/u)
B(GT) CKl’l
13 c
12
g-
=c
0”
O--2-
2-30
48.3
31.0
=B
$-
f+_;’
5-23
34.7
17.5
‘Be
a-2
;+_;+
6-28
12.6
17.7
1.55 24.4
1.98
1.42
0.71
in the low excitation energy region and a broad bump at around 8-10 MeV excitation. In the ‘lBe spectrum three discrete peaks and a broad bump are identified to be due to GT and SFD transitions, respectively, by comparing the observed angular distributions with those of known GT and SFD transitions in the ‘2C(d,2He)‘2B reaction. This identification is supplemented by the vector- and tensor-analyzing power data. We have shown on the basis of the empirical analyses that the GT transition receives almost no effect of the neutron halo while the SFD transition does reflect the neutron halo as a 2 MeV shift down of the mean excitation energy and also as an enhancement of the transition strength. Two peaks in the gLi spectrum have a very different angular distribution pattern from AL=O. The transitions to these states seem to be governed by the tensor interaction which allows AL=2. Because of this the &,-JTvalue is about 5 times Iarger than others studied. On the contrary the r?s~n value is only half of that of r2C. In order to understand these
H. Sakai et al. f ~p~ip
dipole giant resonances in neutron rich light nuclei
285c
features we need an analysis in terms of the distorted wave Born approximation(DWBA). However such an approach is not yet successful presumably due to the inherent complexity of the reaction mechanism associated with the (d,‘He) reactio#]. For this reason we used an empirical approach here to analyze the data rather than a conventional DWBA approach. Higher deuteron beam energies would be a great help in reducing ambiguities of the reaction mechanism. Particularly an analyzing power measurement with a polarized deuteron beam is useful in determining the spin of the SFD states[l9]. We have started an effort in this direction at the RIKEN Ring Cyclotron facility and have constructed the polarized ion source[20]. N ew results will be available in the near future. We would like to acknowledge the assistance of H. Okuno, A. Okihana, Y. Nagai, K. Takeda, T. Toriyama and A. Yoshida with various aspects of data acquisition. We thank N. Fukunishi and H. Sagawa for their help in the theoretical calculations. This work is supported financially in part by the Grant-in-Aid for Scientific Research No.6342007 of Ministry of Education, Science and Culture of Japan. The present experiments were performed at RCNP under Program Numbers 29A13 and 30A03.
REFERENCES 1. I. Tanihata et al., Phys. Rev. Lett. 55 (1985) 2676. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.
For example, H.W. Baer, Proc. VII. Conf. on High-Energy Physics and Nuclear Structure, Zurich (19771, p.245. T. Kobayashi, Nucl. Phys. A553 (1993) 465~. H. Sakai et al., Phys. Lett. B302 (1993) 7. D.P. Stahel et al., Phys. Rev. C20 (1979) 1680. K.B. Beard et al., Phys. Rev. C26 (1982) 720. T. Motobay~hi et al., Nucl. In&r. Meth. A271 (1988) 491. H. Okamura, Ph.D. thesis, Kyoto University, 1989, unpublished. S. Cohen and D. Kurath, Nucl. Phys. 73 (1965) 1. D.J. Millener and D. Kurath, Nucl. Phys. A255 (1975) 315. F.P. Brady et al., Phys. Rev. C43 (1991) 2284. T. N. Taddeucci et al., Nucl. Phys. A469 (1987) 125. C. Gaarde et al., Nucl. Phys. A422 (1984) 189. T. Motobayashi et al., Phys. Rev. C34 (1986) 2365. T. Motobayashi et al., J. Phys. G: Nucl. Phys. 14 (1988) L137. F. Ajzenberg-Selove et al., Nucl. Phys. A481 (1990) 1. K.P. Jackson, in Spin Observables of Nuclear Probes edited by C.J.Horowitz, C.D.Goodman and G.E.Walker (Plenum, 1988), p. 139. T. Hoshino, H. Sagawa and A. Arima, Nucl. Phys. A523 (1991) 228. D.V. Bugg and CWilkin, Nucl. Phys. A467 (1987) 575. C. Wilkin and D.V. Bugg, Phys. Lett. 154B (1985) 243. H. Okamura et al., in Workshop on Polarized Ion Sources and Polarized Gas Targets edited by W. Haeberli and L.W. Anderson (AIP Conf. Proc. 1993), in press.