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Quadrupole deformation of 12Be studied by proton inelastic scattering
18 May 2000
Physics Letters B 481 Ž2000. 7–13
Quadrupole deformation of 12 Be studied by proton inelastic scattering H. Iwasaki a , T. Motobayashi b, H. Akiyoshi c , Y. Ando b, N. Fukuda a , H. Fujiwara b, Zs. Fulop ¨ ¨ c,1, K.I. Hahn c,2 , Y. Higurashi b, M. Hirai a, I. Hisanaga b, c N. Iwasa , T. Kijima b, T. Minemura b, T. Nakamura a , M. Notani c , S. Ozawa b, H. Sakurai c , S. Shimoura b, S. Takeuchi b, T. Teranishi c , Y. Yanagisawa b, M. Ishihara a,c a Department of Physics, UniÕersity of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan Department of Physics, Rikkyo UniÕersity, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501, Japan The Institute of Physical and Chemical Research (RIKEN), 2-1 Hirosawa, Wako, Saitama 351-0198, Japan b
c
Received 4 January 2000; received in revised form 25 March 2000; accepted 30 March 2000 Editor: J.P. Schiffer
Abstract 10,12 Be has been studied in inverse Inelastic proton scattering exciting the 2q 1 states in the neutron-rich beryllium isotopes q kinematics. From a coupled-channel analysis, the deformation lengths for the 2 1 states in 10 Be and 12 Be were determined to be 1.80 " 0.25 fm and 2.00 " 0.23 fm respectively, indicating that a tendency towards strong quadrupole deformation is preserved for these nuclei and that the singly-closed shell structure does not prevail in 12 Be. A quantitative analysis based on shell model calculations supports this picture. q 2000 Elsevier Science B.V. All rights reserved.
PACS: 21.10.Re; 25.40.Ep; 25.60.-t; 27.20.q n
Recent development of good quality radioactive beams has opened broad access to nuclei far from the stability line, thus revealing exotic nuclear properties. Evidence has been accumulating for the assumption that several neutron-rich nuclei, such as 11 Li and 11 Be, are strongly influenced by the
1
On leave from ATOMKI, Debrecen, Hungary. Present address: Department of Science Education, Ewha Woman’s University, Seoul 120-750, Korea. 2
low-lying intruder orbital and the N s 8 shell closure does not always persist in these nuclei w1–5x. Neighboring on these nuclei, 12 Be attracts great interest, since such intruder configuration mixing, which has been suggested in earlier works w3–5x, may enhance quadrupole deformability, as shown in the N s 20 nucleus 32 Mg w6–8x. For the case of 10 Be, the B Ž E2. value of the 2q 0q 1 g .s. transition has been measured to be 10.4 " 1.2 e 2 fm4 w9x. This value corresponds to 8.1 Weisskopf units ŽW.u.., implying fairly strong dynamic deformation. The behavior of q the 0q g .s. –2 1 level spacing among the beryllium iso-
0370-2693r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 0 - 2 6 9 3 Ž 0 0 . 0 0 4 2 8 - 7
™
8
H. Iwasaki et al.r Physics Letters B 481 (2000) 7–13
topes Ž 8 Be: 3.04 MeV, 10 Be: 3.37 MeV, 12 Be: 2.10 MeV w10,11x. suggests that the promotion of quadrupole deformation may occur also in the N s 8 nucleus 12 Be. The aim of this work is to study such deformability of the neutron-rich beryllium isotopes 10,12 Be in terms of the 2q 1 excitation in inelastic proton scattering. This work is the first attempt to measure the transition strength from the 0q g .s. state to 12 the 2q state in Be. The present measurement on 1 10 Be, along with the earlier studies w12–14x, provides a reference to interpret the results on 12 Be. Inelastic proton scattering at an intermediate energy makes a sensitive probe of the nuclear structure, especially for nuclei far from stability. As seen in recent experiments on neutron-rich nuclei, significant isovector contributions to the 2q 1 excitation were disclosed w15–17x, since the inelastic proton scattering is more sensitive to neutrons than to protons in a nucleus w18,19x. It also provides useful information for a test of shell model predictions as demonstrated in the Žp,p’. experiment on 56 Ni w20x. In these experiments with inverse kinematics, recoil protons were detected. In the present study, the angle-integrated inelastic cross sections for the 2q 1 states were obtained by detecting de-excitation g rays in coincidence with scattered 10,12 Be isotopes. The strong point of the method is a good excitation-energy resolution in the g-ray measurement. This is essential for resolving two excited states in 12 Be Žat 2.10 MeV and 2.70 MeV w11x., while measurements by the missing mass method or the recoil proton method may not provide enough resolution. Another attractive aspect of the present g-ray method is the feasibility of using a thick target and hence of exploiting a high experimental yield. The use of the inverse reaction is also an advantage for high-efficiency measurements, since the entire angular range of inelastic scattering can easily be covered. The experiment was performed at the RIKEN Accelerator Research Facility. Secondary beams of 10 Be and 12 Be were produced and separated by the RIKEN Projectile Fragment Separator ŽRIPS. w21x using a 100 MeVru 18 O primary beam incident on a 1.11 grcm2 9 Be target. The momentum and angular spreads of the secondary beams were limited to "1% and "1.7 degrees, respectively, through the use of a slit at the momentum dispersive focal plane and a collimator set just upstream of the secondary
target. The beam spot was defined by the collimator within a radius of 15 mm. The intensity of the secondary 10 Be Ž 12 Be. beam was about 3 = 10 4 Ž2 = 10 4 . counts per second. The particle identification of the incident beam was carried out event-byevent by using the time-of-flight ŽTOF. information obtained with two 1 mm thick plastic scintillators ŽPL’s. placed 5.3 m apart along the beam line. The light-output signals of the PL’s were incorporated in the particle identification. The purity of 10 Be Ž 12 Be. in the beam was around 95 Ž96. %. The incident angle of the beam was monitored by two parallel plate avalanche counters. The angular spread of the 10 Be Ž 12 Be. beam was 0.76 Ž0.54. degrees in r.m.s. for the horizontal direction and 0.97 Ž0.61. degrees in r.m.s. for the vertical direction. The secondary 10 Be Ž 12 Be. beam bombarded a 90.2 mgrcm2 thick ŽCH 2 . n target, with its energy in the middle of the target being 59.2 Ž53.8. MeVru. The 10 Be Ž 12 Be. scattering on 12 C was separately measured using a 89.8 mgrcm2 thick 12 C target. The contribution from 12 C in the ŽCH 2 . n target was found to be about a half of the total yield, and it was subtracted to deduce the result for the proton scattering. The amount of the other background was evaluated to be negligible from the measurement where the target was removed. The outgoing particles were detected by a plastic scintillator hodoscope located 5.0 m downstream of the secondary target. The hodoscope was mounted in a vacuum chamber, and consisted of thirteen 5 mm thick D E- and sixteen 60 mm thick E- plastic scintillators. The D E and E counters were set perpendicular to each other, dividing the hodoscope into 13 = 16 segments. The width of the D E counters was 40 mm or 100 mm, while the E counters were 30 mm or 75 mm wide. The narrower counters were placed in the central part of the hodoscope to improve the balance of the counting rate among the individual scintillators. The particle identification of the scattered particles was performed by the standard TOF-D E and TOF-E methods. The position information was determined by the segmentation of the hodoscope and was used to determine the scattering angle. The hodoscope with a large active area of 1 = 1 m2 accepted most of the inelastically scattered 10 Be Ž 12 Be. particles, whose scattering angle is kinematically limited within 5.6 Ž4.7. degrees when the
H. Iwasaki et al.r Physics Letters B 481 (2000) 7–13
incoming beam has no angular spread. The acceptance of the hodoscope was estimated by a Monte Carlo simulation, which took into account the finite size and angular spread of the incident beam, the multiple scattering in the secondary target Ž0.1 degrees in r.m.s.., and the detector geometry including gaps between the plastic bars. The efficiency was mainly determined by the acceptance. The average efficiency relevant to the angle-integrated cross section was found to be 83 " 4 Ž80 " 4. % for the 10 Be Ž 12 Be. scattering. De-excitation g rays were detected by an array of 55 NaI ŽTl. scintillators surrounding the target from 67 to 148 degrees with respect to the beam axis. Each scintillator crystal had a rectangular-prism shape with a size of 6 = 6 = 12 cm3 coupled with a 5.1 cm f photomultiplier tube. The energy resolution was typically 7.0% ŽFWHM. for 1275-keV g ray as measured with a 22 Na standard source. The total photo-peak efficiencies were calculated by means of the GEANT simulation code w22x to be 4.6% and
9
7.1%, respectively, for 3.37-MeV and 2.10-MeV g rays emitted from 10 Be and 12 Be in flight. The systematic error of the efficiency calculation was estimated to be 10% from the comparison with the measurement using standard 22 Na, 60 Co, and 137Cs sources. Fig. 1 Žleft. shows energy spectra of g rays measured in coincidence with inelastically scattered 10 Be Žtop. and 12 Be Žbottom., for which Doppler shifts are corrected. In each spectrum, the yields of g rays due to the 10 Be Ž 12 Be. q 12 C scattering and the accidental coincidence were subtracted. The photopeaks corresponding to the 2q 0q 1 g .s. transitions are clearly seen at 3.37 MeV and 2.10 MeV, respectively, for 10 Be and 12 Be. The photo-peak yields were obtained by fitting the g-ray spectra with the simulated ones shown by solid curves in Fig. 1 Žcenter.. The code GEANT was used for the simulation. The g – g coincidence events were also analysed. The right panels of Fig. 1 show the g-ray 0q spectra in coincidence with the 2q 1 g .s. transitions.
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Fig. 1. Left panels show g-ray energy spectra obtained in coincidence with inelastically scattered 10 Be Žtop. and 12 Be Žbottom., for which Doppler shifts are corrected. Center panels show the comparison between experimental and simulated spectra. The error bars in the spectra are statistical in origin and the solid curves represent simulated spectra including Compton scattering events Ždotted curves. and small 10 continuous background Ždot-dashed lines.. Right panels show g-ray spectra observed in coincidence with the 2q 0q Be 1 g .s. photo-peaks in Žtop. and 12 Be Žbottom..
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H. Iwasaki et al.r Physics Letters B 481 (2000) 7–13
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Table 1 Experimental angle-integrated cross sections for inelastic scatter10,12 ing exciting the 2q Be. The deduced b 2 and d 1 states in values are also listed. The symbols A and B denote the optical potential sets used in the analysis
s Žmb.
Optical b 2 potential
r 0 Žfm. R Žfm. d Žfm.
10
Be 17.6Ž3.2. A B
0.593Ž56. 1.48 0.692Ž65. 1.15
3.19 2.47
1.89Ž18. 1.71Ž16.
12
Be 27.0Ž4.0. A B
0.614Ž47. 1.48 0.725Ž54. 1.15
3.39 2.64
2.08Ž16. 1.91Ž14.
For the case of 10 Be, the g decay from the excited y w state at 5.96 MeV Ž2q 10x. is clearly recog2 or 11 nized, while no other peaks are significant. The contribution of the observed cascade decay through the 2q 1 state is deduced to be 14 " 6% of the 2 1 12 0q Be, any cascade g .s. photo-peak yield. As for transitions can hardly be seen including that from the second excited state at 2.70 MeV. Hence only the 1 s upper limit of 7% is taken for the cascade contribution. The cross section of inelastic proton scattering 10 Be obtained from the photo-peak to the 2q 1 state of yield is 17.6 " 3.2 mb, after correction for the cascade feeding. The quoted error includes the ambiguities in the photo-peak yield Ž9%., the hodoscope efficiency Ž5%., the g-ray detection efficiency Ž10%., and the cascade contribution from the second excited state Ž6%.. Similarly, the cross section for 12 Be is determined to be 27.0 " 4.0 mb. To extract the deformation parameter, we performed a coupled-channel calculation, using the ECIS79 code w23x in the framework of the standard symmetric rotational model. We used two different optical potentials, the potential A taken from Ref. w24x where elastic proton scattering of 12 Be at 55 MeVru is analysed, and the potential B obtained from the global phenomenological parameter set CH89 proposed in Ref. w25x. For the potential B, we used the normalization factor of the real potential l Õ s 0.9, which was determined from elastic proton scattering of 10 Be at 59 MeVru w26x. The nuclear deformation parameter b 2 was extracted from the experimental angle-integrated cross section by searching the best fit value with the ECIS calculation. In the calculation, the b 2 value was taken to be
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the same for the real and imaginary potentials. The best fit value of b 2 for the real potential did not strongly depend on this assumption. For instance, it did not change by more than 3%, when the b 2 value for the imaginary potential was varied to be 10% larger Žor smaller.. The extracted b 2 values are summarized in Table 1 together with the deformation lengths d s b 2 R s b 2 r 0 A1r3 calculated with the radius R of the real potential Žfor r 0 , see Table 1.. The extracted b 2 values differ by f 15% for the two optical potentials, whereas the difference is reduced if the deformation lengths are compared as usually the case for the analysis of inelastic scattering w27x. To further test the validity of the optical potential, we plot, in Fig. 2, the experimental differential cross sections of the inelastically scattered 10 Be Žtop. and 12 Be Žbottom.. The angular distributions are affected by the experimental angular resolutions, which amounted for the 10 Be Ž 12 Be. scattering to 0.84
Fig. 2. Observed differential cross sections for inelastic scattering 10 exciting the 2q Be Žtop. and 12 Be Žbottom.. The 1 states in experimental data points are represented by open circles with error bars. The solid Ždashed. curves represent calculated differential cross sections with the optical potential set A ŽB., where the experimental angular resolutions are taken into account Žsee text..
H. Iwasaki et al.r Physics Letters B 481 (2000) 7–13
Ž0.64. degrees in r.m.s. for the horizontal direction and 1.0 Ž0.67. degrees in r.m.s. for the vertical direction. The resolutions were rather deteriorated by the angular spread of the incident beam and the uncertainty of the position information of the hodoscope. For comparison, theoretical angular distributions calculated by the ECIS code are shown for the potential A ŽB. by solid Ždashed. curves. In this calculation, we folded the experimental angular resolutions, resulting in smeared angular distributions. Both of the potential sets reproduce the experimental data equally well, while small discrepancies remain at forward angles near 08. Thus, the preference was hardly determined between the two optical potentials by just using the present angular distributions. By taking an average of the results obtained for the two potentials, the deformation lengths d s 1.80 " 0.25 fm for 10 Be and d s 2.00 " 0.23 fm for 12 Be are adopted in the present work. The quoted errors contain the theoretical ambiguity as well as the experimental uncertainties, where the former is obtained as the difference between the results for the two potentials. Note that the value of 1.80 " 0.25 fm for 10 Be is consistent with the previous results of 1.84–1.99 fm deduced from several works on inelastic proton scattering at Ep s 12.0–16.0 MeV w14x. The deformation length is known for another isotope 9 Be, where the results of 1.61–2.13 fm were obtained from a scattering w28–30x. Comparison of these deformation lengths indicates that the neutronrich beryllium isotopes have a general trend towards large quadrupole deformation. Remarkably, there is little evidence of the N s 8 shell closure. The fading effect of the N s 8 shell closure can be demonstrated in a more quantitative way by comparison with theoretical predictions. In order to eval-
11
uate deformation lengths, we used the Bernstein’s prescription w18,19x,
dprobe s
4p bp M p q bn Mn 3eR
bp Z q bn N
.
Ž 1.
In this formula, the deformation length dprobe is expressed by the combination of the proton and neutron multipole matrix elements M p and Mn . The parameters bp and bn represent the interaction strengths of the probe particle with protons and neutrons in a nucleus. The values of bp and bn are characteristic of the probe particle. For example, the values of bp s 0.3 and bn s 0.7 are taken for the proton inelastic scattering to deduce the deformation length d w15x, while the values of bp s 1 and bn s 0 should be used for the electromagnetic deformation length d em . The nuclear radius R is taken as the standard value of 1.2 A1r3 fm. The matrix elements M p and Mn were obtained by performing shell model calculations in the p–sd model space based on the PSDMK effective interaction w31,32x. In order to study the N s 8 shell quenching schematically, two different values of De 2 s1r 2 s 0.0 MeV and De 2 s1r 2 s y3.41 MeV were tested, where De 2 s1r2 denotes the amount of lowering of the single-particle energy for the 2s 1r2 orbital. The setting of De 2 s1r 2 s 0.0 MeV corresponds to the normal shell gap and hence may lead to a closed-shell structure in 12 Be. On the other hand, the lowering of the 2s 1r2 orbital by 3.41 MeV as taken in Ref. w5x allows for the deterioration of the shell closure. The calculation involved excitations of one or two valence particles to the sd shell. We used effective charges of e p s 1.3e and e n s 0.5e, which are the same as those adopted in the sd-shell model w33x.
Table 2 Comparison between experimental deformation lengths and calculated ones. The Ž MnrM p .rŽ NrZ . ratios are also listed Žsee text. 10
12
Be
Be
d em Žfm.
d Žfm.
Ž Mn rM p .rŽ NrZ .
Effective interaction
exp. cal. cal.
2.92Ž17. 2.89 2.89
1.80Ž25. 2.04 2.04
0.51Ž12. 0.62 0.62
PSDMKŽ De 2 s1r2 s 0.0 MeV. PSDMKŽ De 2 s s y3.41 MeV.
exp. cal. cal.
– 2.43 2.79
2.00Ž23. 0.89 1.98
– 0.23 0.65
PSDMKŽ De 2 s1r2 s 0.0 MeV. PSDMKŽ De 2 s s y3.41 MeV.
1r2
1r2
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H. Iwasaki et al.r Physics Letters B 481 (2000) 7–13
In Table 2, the experimental values of d are compared with the calculated results. The calculation with the normal shell gap Ž De 2 s1r 2 s 0.0 MeV. yielded the negligible sd-admixture in the ground state wave function for both 10 Be Ž; 5%. and 12 Be Ž; 15%., preserving a feature of neutron shell closure at N s 8. This calculation reproduces well the experimental d value for 10 Be. However it considerably underestimates the value for 12 Be. This discrepancy for 12 Be can hardly be explained by the possible theoretical uncertainty of 20%, which may arise from the incident energy dependence of bp and bn values w18,19x andror the ambiguity in the effective charges w33x. Instead, the discrepancy is primarily attributed to the small value of Mn , which is a consequence of small sd-admixture as mentioned above. In contrast, the calculation with the narrow shell gap Ž De 2 s1r 2 s y3.41 MeV. resolves such a conflict for 12 Be, showing a good agreement with the experimental result. In this case, a large sd-admixture Ž; 45%. is obtained for the ground state of 12 Be. Such a large sd-admixture is a signature of broken closed-shell structure, and is in line with the result of a recent work w5x, which demanded sd-admixture of about 65% to account for the b transition rate of 12 Be. Table 2 also shows the results of d em . In the case of 10 Be, the experimental d em value is available from the observed B Ž E2. value w9x. The results of the shell model calculations are consistent with this value for either choice of De 2 s1r 2 . The shell model calculations for 12 Be have also yielded fairly large values of d em corresponding to B Ž E2. values of 5.0–6.6 W.u. It is worth noting that the results of d em for the two different De 2 s1r 2 are rather close to each other while those of d differ considerably. This enhanced sensitivity to De 2 s1r 2 of d is a reflection of the fact that the influence of neutron excitations is more significant in d than in d em . The contribution of neutrons to quadrupole deformation can be better expressed by the double ratio Ž MnrM p .rŽ NrZ .. If the neutron singly closed-shell structure prevails, this ratio tends to be 0. On the other hand, the ratio of unity is expected, if a nucleus is considered to be a homogeneous neutron-proton fluid w18,19x. Indeed the 9 Be nucleus, which is located in the middle of the shell, exhibits the ratio of 0.94 w30x. Such trends may be preserved even when
other effects such as that due to core polarization are taken into account, and a rapid decrease of the ratio is expected as the nucleus approaches the neutron shell closure w34x. For the case of 10 Be, the ratio of 0.51 " 0.12 is extracted from the experimental d em and d values on the basis of Eq. Ž1.. The calculated results are in fair agreement with this ratio, irrespective of the choice of De 2 s1r 2 . In contrast, the calculated results for 12 Be considerably differ for the different values of De 2 s1r 2 . A suppressed value of 0.23 is obtained for De 2 s1r 2 s 0.0 MeV, as expected for the case of the shell closure. On the other hand, a large value of 0.65 is obtained when the narrow shell gap is employed. This value is as large as that obtained for 10 Be, which is consistent with a significant neutron contribution for the 2q 1 excitation. As shown before, the small shell gap is strongly favored to account for the large d experimentally observed. The present analysis on Ž MnrM p .rŽ NrZ . indicates that the neutron contribution as enhanced by the broken shell closure is indeed essential to give rise to the large d of 12 Be. In summary, we have studied inelastic proton scattering on 10,12 Be in inverse kinematics. Fairly large deformation lengths were obtained for both 10 Be and 12 Be, indicating that the N s 8 nucleus 12 Be can hardly be treated as a singly closed-shell nucleus. This picture of the broken shell closure, which is consistent with the accumulating evidence for the 2 s1r2 intruder orbital, is supported by the shell model calculations of deformation lengths. Acknowledgements We would like to thank the RIKEN Ring Cyclotron staff members for their operation during the experiment. We are grateful to Professor A. Gelberg for careful reading of the manuscript. The present work is supported in part by the Ministry of Education, Science, Sports and Culture by Grant-In-Aid for Scientific Research under the program number ŽB. 08454069. References w1x I. Talmi, I. Unna, Phys. Rev. Lett. 4 Ž1960. 469. w2x N. Aoi et al., Nucl. Phys. A 616 Ž1997. 181c. w3x F.C. Barker, J. Phys. G 2 Ž1976. L45.
H. Iwasaki et al.r Physics Letters B 481 (2000) 7–13 w4x D.E. Alburger et al., Phys. Rev. C 17 Ž1978. 1525. w5x T. Suzuki, T. Otsuka, Phys. Rev. C 56 Ž1997. 847. w6x C. Detraz et al., Phys. Rev. C 19 Ž1979. 164; D. ´ Guillemaud-Mueller et al., Nucl. Phys. A 426 Ž1984. 37. w7x T. Motobayashi et al., Phys. Lett. B 346 Ž1995. 9. w8x N. Fukunishi, T. Otsuka, T. Sebe, Phys. Lett. B 296 Ž1992. 279. w9x S. Raman et al., At. Data Nucl. Data Tables 36 Ž1987. 1. w10x F. Ajzenberg-Selove, Nucl. Phys. A 490 Ž1988. 1. w11x F. Ajzenberg-Selove, Nucl. Phys. A 506 Ž1990. 1. w12x E.K. Warburton et al., Phys. Rev. 148 Ž1966. 1072. w13x T.R. Fisher et al., Phys. Rev. 176 Ž1968. 1130. w14x D.L. Auton, Nucl. Phys. A 157 Ž1970. 305. w15x J.H. Kelley et al., Phys. Rev. C 56 Ž1997. R1206. w16x J.K. Jewell et al., Phys. Lett. B 454 Ž1999. 181. w17x F. Marechal et al., Phys. Rev. C 60 Ž1999. 034615. ´ w18x A.M. Bernstein, V.R. Brown, V.A. Madsen, Phys. Lett. B 103 Ž1981. 255. w19x A.M. Bernstein, V.R. Brown, V.A. Madsen, Comments Nucl. Part. Phys. 11 Ž1983. 203.
w20x w21x w22x w23x w24x w25x w26x w27x w28x w29x w30x w31x
w32x w33x w34x
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G. Kraus et al., Phys. Rev. Lett. 73 Ž1994. 1773. T. Kubo et al., Nucl. Instrum. Methods B 70 Ž1992. 309. CERN Program library Long Writeup, W5013. J. Raynal, Coupled channel code ECIS79, unpublished. A.A. Korsheninnikov et al., Phys. Lett. B 343 Ž1995. 53. R.L. Varner et al., Phys. Rep. 201 Ž1991. 57. M.D. Cortina-Gil et al., Phys. Lett. B 401 Ž1997. 9. A. Bohr, B.R. Mottelson, Nuclear Structure, vol. 2, World Scientific, 1998. M.N. Harakeh et al., Nucl. Phys. A 344 Ž1980. 15. R.J. Peterson, Nucl. Phys. A 377 Ž1982. 41. S. Roy et al., Phys. Rev. C 52 Ž1995. 1524. OXBASH, The Oxford, Buenos-Aires, Michigan State, Shell Model Program, B.A. Brown, A. Etchegoyen, W.D.M. Rae, MSU Cyclotron Laboratory Report number 524 Ž1986.. D.J. Millener, D. Kurath, Nucl. Phys. A 255 Ž1975. 315. B.A. Brown, B.H. Wildenthal, Ann. Rev. Nucl. Part. Sci. 38 Ž1988. 29. V.A. Madsen, V.R. Brown, Phys. Rev. Lett. 52 Ž1984. 176.
Physics Letters B 481 Ž2000. 7–13
Quadrupole deformation of 12 Be studied by proton inelastic scattering H. Iwasaki a , T. Motobayashi b, H. Akiyoshi c , Y. Ando b, N. Fukuda a , H. Fujiwara b, Zs. Fulop ¨ ¨ c,1, K.I. Hahn c,2 , Y. Higurashi b, M. Hirai a, I. Hisanaga b, c N. Iwasa , T. Kijima b, T. Minemura b, T. Nakamura a , M. Notani c , S. Ozawa b, H. Sakurai c , S. Shimoura b, S. Takeuchi b, T. Teranishi c , Y. Yanagisawa b, M. Ishihara a,c a Department of Physics, UniÕersity of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan Department of Physics, Rikkyo UniÕersity, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501, Japan The Institute of Physical and Chemical Research (RIKEN), 2-1 Hirosawa, Wako, Saitama 351-0198, Japan b
c
Received 4 January 2000; received in revised form 25 March 2000; accepted 30 March 2000 Editor: J.P. Schiffer
Abstract 10,12 Be has been studied in inverse Inelastic proton scattering exciting the 2q 1 states in the neutron-rich beryllium isotopes q kinematics. From a coupled-channel analysis, the deformation lengths for the 2 1 states in 10 Be and 12 Be were determined to be 1.80 " 0.25 fm and 2.00 " 0.23 fm respectively, indicating that a tendency towards strong quadrupole deformation is preserved for these nuclei and that the singly-closed shell structure does not prevail in 12 Be. A quantitative analysis based on shell model calculations supports this picture. q 2000 Elsevier Science B.V. All rights reserved.
PACS: 21.10.Re; 25.40.Ep; 25.60.-t; 27.20.q n
Recent development of good quality radioactive beams has opened broad access to nuclei far from the stability line, thus revealing exotic nuclear properties. Evidence has been accumulating for the assumption that several neutron-rich nuclei, such as 11 Li and 11 Be, are strongly influenced by the
1
On leave from ATOMKI, Debrecen, Hungary. Present address: Department of Science Education, Ewha Woman’s University, Seoul 120-750, Korea. 2
low-lying intruder orbital and the N s 8 shell closure does not always persist in these nuclei w1–5x. Neighboring on these nuclei, 12 Be attracts great interest, since such intruder configuration mixing, which has been suggested in earlier works w3–5x, may enhance quadrupole deformability, as shown in the N s 20 nucleus 32 Mg w6–8x. For the case of 10 Be, the B Ž E2. value of the 2q 0q 1 g .s. transition has been measured to be 10.4 " 1.2 e 2 fm4 w9x. This value corresponds to 8.1 Weisskopf units ŽW.u.., implying fairly strong dynamic deformation. The behavior of q the 0q g .s. –2 1 level spacing among the beryllium iso-
0370-2693r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 0 - 2 6 9 3 Ž 0 0 . 0 0 4 2 8 - 7
™
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H. Iwasaki et al.r Physics Letters B 481 (2000) 7–13
topes Ž 8 Be: 3.04 MeV, 10 Be: 3.37 MeV, 12 Be: 2.10 MeV w10,11x. suggests that the promotion of quadrupole deformation may occur also in the N s 8 nucleus 12 Be. The aim of this work is to study such deformability of the neutron-rich beryllium isotopes 10,12 Be in terms of the 2q 1 excitation in inelastic proton scattering. This work is the first attempt to measure the transition strength from the 0q g .s. state to 12 the 2q state in Be. The present measurement on 1 10 Be, along with the earlier studies w12–14x, provides a reference to interpret the results on 12 Be. Inelastic proton scattering at an intermediate energy makes a sensitive probe of the nuclear structure, especially for nuclei far from stability. As seen in recent experiments on neutron-rich nuclei, significant isovector contributions to the 2q 1 excitation were disclosed w15–17x, since the inelastic proton scattering is more sensitive to neutrons than to protons in a nucleus w18,19x. It also provides useful information for a test of shell model predictions as demonstrated in the Žp,p’. experiment on 56 Ni w20x. In these experiments with inverse kinematics, recoil protons were detected. In the present study, the angle-integrated inelastic cross sections for the 2q 1 states were obtained by detecting de-excitation g rays in coincidence with scattered 10,12 Be isotopes. The strong point of the method is a good excitation-energy resolution in the g-ray measurement. This is essential for resolving two excited states in 12 Be Žat 2.10 MeV and 2.70 MeV w11x., while measurements by the missing mass method or the recoil proton method may not provide enough resolution. Another attractive aspect of the present g-ray method is the feasibility of using a thick target and hence of exploiting a high experimental yield. The use of the inverse reaction is also an advantage for high-efficiency measurements, since the entire angular range of inelastic scattering can easily be covered. The experiment was performed at the RIKEN Accelerator Research Facility. Secondary beams of 10 Be and 12 Be were produced and separated by the RIKEN Projectile Fragment Separator ŽRIPS. w21x using a 100 MeVru 18 O primary beam incident on a 1.11 grcm2 9 Be target. The momentum and angular spreads of the secondary beams were limited to "1% and "1.7 degrees, respectively, through the use of a slit at the momentum dispersive focal plane and a collimator set just upstream of the secondary
target. The beam spot was defined by the collimator within a radius of 15 mm. The intensity of the secondary 10 Be Ž 12 Be. beam was about 3 = 10 4 Ž2 = 10 4 . counts per second. The particle identification of the incident beam was carried out event-byevent by using the time-of-flight ŽTOF. information obtained with two 1 mm thick plastic scintillators ŽPL’s. placed 5.3 m apart along the beam line. The light-output signals of the PL’s were incorporated in the particle identification. The purity of 10 Be Ž 12 Be. in the beam was around 95 Ž96. %. The incident angle of the beam was monitored by two parallel plate avalanche counters. The angular spread of the 10 Be Ž 12 Be. beam was 0.76 Ž0.54. degrees in r.m.s. for the horizontal direction and 0.97 Ž0.61. degrees in r.m.s. for the vertical direction. The secondary 10 Be Ž 12 Be. beam bombarded a 90.2 mgrcm2 thick ŽCH 2 . n target, with its energy in the middle of the target being 59.2 Ž53.8. MeVru. The 10 Be Ž 12 Be. scattering on 12 C was separately measured using a 89.8 mgrcm2 thick 12 C target. The contribution from 12 C in the ŽCH 2 . n target was found to be about a half of the total yield, and it was subtracted to deduce the result for the proton scattering. The amount of the other background was evaluated to be negligible from the measurement where the target was removed. The outgoing particles were detected by a plastic scintillator hodoscope located 5.0 m downstream of the secondary target. The hodoscope was mounted in a vacuum chamber, and consisted of thirteen 5 mm thick D E- and sixteen 60 mm thick E- plastic scintillators. The D E and E counters were set perpendicular to each other, dividing the hodoscope into 13 = 16 segments. The width of the D E counters was 40 mm or 100 mm, while the E counters were 30 mm or 75 mm wide. The narrower counters were placed in the central part of the hodoscope to improve the balance of the counting rate among the individual scintillators. The particle identification of the scattered particles was performed by the standard TOF-D E and TOF-E methods. The position information was determined by the segmentation of the hodoscope and was used to determine the scattering angle. The hodoscope with a large active area of 1 = 1 m2 accepted most of the inelastically scattered 10 Be Ž 12 Be. particles, whose scattering angle is kinematically limited within 5.6 Ž4.7. degrees when the
H. Iwasaki et al.r Physics Letters B 481 (2000) 7–13
incoming beam has no angular spread. The acceptance of the hodoscope was estimated by a Monte Carlo simulation, which took into account the finite size and angular spread of the incident beam, the multiple scattering in the secondary target Ž0.1 degrees in r.m.s.., and the detector geometry including gaps between the plastic bars. The efficiency was mainly determined by the acceptance. The average efficiency relevant to the angle-integrated cross section was found to be 83 " 4 Ž80 " 4. % for the 10 Be Ž 12 Be. scattering. De-excitation g rays were detected by an array of 55 NaI ŽTl. scintillators surrounding the target from 67 to 148 degrees with respect to the beam axis. Each scintillator crystal had a rectangular-prism shape with a size of 6 = 6 = 12 cm3 coupled with a 5.1 cm f photomultiplier tube. The energy resolution was typically 7.0% ŽFWHM. for 1275-keV g ray as measured with a 22 Na standard source. The total photo-peak efficiencies were calculated by means of the GEANT simulation code w22x to be 4.6% and
9
7.1%, respectively, for 3.37-MeV and 2.10-MeV g rays emitted from 10 Be and 12 Be in flight. The systematic error of the efficiency calculation was estimated to be 10% from the comparison with the measurement using standard 22 Na, 60 Co, and 137Cs sources. Fig. 1 Žleft. shows energy spectra of g rays measured in coincidence with inelastically scattered 10 Be Žtop. and 12 Be Žbottom., for which Doppler shifts are corrected. In each spectrum, the yields of g rays due to the 10 Be Ž 12 Be. q 12 C scattering and the accidental coincidence were subtracted. The photopeaks corresponding to the 2q 0q 1 g .s. transitions are clearly seen at 3.37 MeV and 2.10 MeV, respectively, for 10 Be and 12 Be. The photo-peak yields were obtained by fitting the g-ray spectra with the simulated ones shown by solid curves in Fig. 1 Žcenter.. The code GEANT was used for the simulation. The g – g coincidence events were also analysed. The right panels of Fig. 1 show the g-ray 0q spectra in coincidence with the 2q 1 g .s. transitions.
™
™
Fig. 1. Left panels show g-ray energy spectra obtained in coincidence with inelastically scattered 10 Be Žtop. and 12 Be Žbottom., for which Doppler shifts are corrected. Center panels show the comparison between experimental and simulated spectra. The error bars in the spectra are statistical in origin and the solid curves represent simulated spectra including Compton scattering events Ždotted curves. and small 10 continuous background Ždot-dashed lines.. Right panels show g-ray spectra observed in coincidence with the 2q 0q Be 1 g .s. photo-peaks in Žtop. and 12 Be Žbottom..
™
H. Iwasaki et al.r Physics Letters B 481 (2000) 7–13
10
Table 1 Experimental angle-integrated cross sections for inelastic scatter10,12 ing exciting the 2q Be. The deduced b 2 and d 1 states in values are also listed. The symbols A and B denote the optical potential sets used in the analysis
s Žmb.
Optical b 2 potential
r 0 Žfm. R Žfm. d Žfm.
10
Be 17.6Ž3.2. A B
0.593Ž56. 1.48 0.692Ž65. 1.15
3.19 2.47
1.89Ž18. 1.71Ž16.
12
Be 27.0Ž4.0. A B
0.614Ž47. 1.48 0.725Ž54. 1.15
3.39 2.64
2.08Ž16. 1.91Ž14.
For the case of 10 Be, the g decay from the excited y w state at 5.96 MeV Ž2q 10x. is clearly recog2 or 11 nized, while no other peaks are significant. The contribution of the observed cascade decay through the 2q 1 state is deduced to be 14 " 6% of the 2 1 12 0q Be, any cascade g .s. photo-peak yield. As for transitions can hardly be seen including that from the second excited state at 2.70 MeV. Hence only the 1 s upper limit of 7% is taken for the cascade contribution. The cross section of inelastic proton scattering 10 Be obtained from the photo-peak to the 2q 1 state of yield is 17.6 " 3.2 mb, after correction for the cascade feeding. The quoted error includes the ambiguities in the photo-peak yield Ž9%., the hodoscope efficiency Ž5%., the g-ray detection efficiency Ž10%., and the cascade contribution from the second excited state Ž6%.. Similarly, the cross section for 12 Be is determined to be 27.0 " 4.0 mb. To extract the deformation parameter, we performed a coupled-channel calculation, using the ECIS79 code w23x in the framework of the standard symmetric rotational model. We used two different optical potentials, the potential A taken from Ref. w24x where elastic proton scattering of 12 Be at 55 MeVru is analysed, and the potential B obtained from the global phenomenological parameter set CH89 proposed in Ref. w25x. For the potential B, we used the normalization factor of the real potential l Õ s 0.9, which was determined from elastic proton scattering of 10 Be at 59 MeVru w26x. The nuclear deformation parameter b 2 was extracted from the experimental angle-integrated cross section by searching the best fit value with the ECIS calculation. In the calculation, the b 2 value was taken to be
™
the same for the real and imaginary potentials. The best fit value of b 2 for the real potential did not strongly depend on this assumption. For instance, it did not change by more than 3%, when the b 2 value for the imaginary potential was varied to be 10% larger Žor smaller.. The extracted b 2 values are summarized in Table 1 together with the deformation lengths d s b 2 R s b 2 r 0 A1r3 calculated with the radius R of the real potential Žfor r 0 , see Table 1.. The extracted b 2 values differ by f 15% for the two optical potentials, whereas the difference is reduced if the deformation lengths are compared as usually the case for the analysis of inelastic scattering w27x. To further test the validity of the optical potential, we plot, in Fig. 2, the experimental differential cross sections of the inelastically scattered 10 Be Žtop. and 12 Be Žbottom.. The angular distributions are affected by the experimental angular resolutions, which amounted for the 10 Be Ž 12 Be. scattering to 0.84
Fig. 2. Observed differential cross sections for inelastic scattering 10 exciting the 2q Be Žtop. and 12 Be Žbottom.. The 1 states in experimental data points are represented by open circles with error bars. The solid Ždashed. curves represent calculated differential cross sections with the optical potential set A ŽB., where the experimental angular resolutions are taken into account Žsee text..
H. Iwasaki et al.r Physics Letters B 481 (2000) 7–13
Ž0.64. degrees in r.m.s. for the horizontal direction and 1.0 Ž0.67. degrees in r.m.s. for the vertical direction. The resolutions were rather deteriorated by the angular spread of the incident beam and the uncertainty of the position information of the hodoscope. For comparison, theoretical angular distributions calculated by the ECIS code are shown for the potential A ŽB. by solid Ždashed. curves. In this calculation, we folded the experimental angular resolutions, resulting in smeared angular distributions. Both of the potential sets reproduce the experimental data equally well, while small discrepancies remain at forward angles near 08. Thus, the preference was hardly determined between the two optical potentials by just using the present angular distributions. By taking an average of the results obtained for the two potentials, the deformation lengths d s 1.80 " 0.25 fm for 10 Be and d s 2.00 " 0.23 fm for 12 Be are adopted in the present work. The quoted errors contain the theoretical ambiguity as well as the experimental uncertainties, where the former is obtained as the difference between the results for the two potentials. Note that the value of 1.80 " 0.25 fm for 10 Be is consistent with the previous results of 1.84–1.99 fm deduced from several works on inelastic proton scattering at Ep s 12.0–16.0 MeV w14x. The deformation length is known for another isotope 9 Be, where the results of 1.61–2.13 fm were obtained from a scattering w28–30x. Comparison of these deformation lengths indicates that the neutronrich beryllium isotopes have a general trend towards large quadrupole deformation. Remarkably, there is little evidence of the N s 8 shell closure. The fading effect of the N s 8 shell closure can be demonstrated in a more quantitative way by comparison with theoretical predictions. In order to eval-
11
uate deformation lengths, we used the Bernstein’s prescription w18,19x,
dprobe s
4p bp M p q bn Mn 3eR
bp Z q bn N
.
Ž 1.
In this formula, the deformation length dprobe is expressed by the combination of the proton and neutron multipole matrix elements M p and Mn . The parameters bp and bn represent the interaction strengths of the probe particle with protons and neutrons in a nucleus. The values of bp and bn are characteristic of the probe particle. For example, the values of bp s 0.3 and bn s 0.7 are taken for the proton inelastic scattering to deduce the deformation length d w15x, while the values of bp s 1 and bn s 0 should be used for the electromagnetic deformation length d em . The nuclear radius R is taken as the standard value of 1.2 A1r3 fm. The matrix elements M p and Mn were obtained by performing shell model calculations in the p–sd model space based on the PSDMK effective interaction w31,32x. In order to study the N s 8 shell quenching schematically, two different values of De 2 s1r 2 s 0.0 MeV and De 2 s1r 2 s y3.41 MeV were tested, where De 2 s1r2 denotes the amount of lowering of the single-particle energy for the 2s 1r2 orbital. The setting of De 2 s1r 2 s 0.0 MeV corresponds to the normal shell gap and hence may lead to a closed-shell structure in 12 Be. On the other hand, the lowering of the 2s 1r2 orbital by 3.41 MeV as taken in Ref. w5x allows for the deterioration of the shell closure. The calculation involved excitations of one or two valence particles to the sd shell. We used effective charges of e p s 1.3e and e n s 0.5e, which are the same as those adopted in the sd-shell model w33x.
Table 2 Comparison between experimental deformation lengths and calculated ones. The Ž MnrM p .rŽ NrZ . ratios are also listed Žsee text. 10
12
Be
Be
d em Žfm.
d Žfm.
Ž Mn rM p .rŽ NrZ .
Effective interaction
exp. cal. cal.
2.92Ž17. 2.89 2.89
1.80Ž25. 2.04 2.04
0.51Ž12. 0.62 0.62
PSDMKŽ De 2 s1r2 s 0.0 MeV. PSDMKŽ De 2 s s y3.41 MeV.
exp. cal. cal.
– 2.43 2.79
2.00Ž23. 0.89 1.98
– 0.23 0.65
PSDMKŽ De 2 s1r2 s 0.0 MeV. PSDMKŽ De 2 s s y3.41 MeV.
1r2
1r2
12
H. Iwasaki et al.r Physics Letters B 481 (2000) 7–13
In Table 2, the experimental values of d are compared with the calculated results. The calculation with the normal shell gap Ž De 2 s1r 2 s 0.0 MeV. yielded the negligible sd-admixture in the ground state wave function for both 10 Be Ž; 5%. and 12 Be Ž; 15%., preserving a feature of neutron shell closure at N s 8. This calculation reproduces well the experimental d value for 10 Be. However it considerably underestimates the value for 12 Be. This discrepancy for 12 Be can hardly be explained by the possible theoretical uncertainty of 20%, which may arise from the incident energy dependence of bp and bn values w18,19x andror the ambiguity in the effective charges w33x. Instead, the discrepancy is primarily attributed to the small value of Mn , which is a consequence of small sd-admixture as mentioned above. In contrast, the calculation with the narrow shell gap Ž De 2 s1r 2 s y3.41 MeV. resolves such a conflict for 12 Be, showing a good agreement with the experimental result. In this case, a large sd-admixture Ž; 45%. is obtained for the ground state of 12 Be. Such a large sd-admixture is a signature of broken closed-shell structure, and is in line with the result of a recent work w5x, which demanded sd-admixture of about 65% to account for the b transition rate of 12 Be. Table 2 also shows the results of d em . In the case of 10 Be, the experimental d em value is available from the observed B Ž E2. value w9x. The results of the shell model calculations are consistent with this value for either choice of De 2 s1r 2 . The shell model calculations for 12 Be have also yielded fairly large values of d em corresponding to B Ž E2. values of 5.0–6.6 W.u. It is worth noting that the results of d em for the two different De 2 s1r 2 are rather close to each other while those of d differ considerably. This enhanced sensitivity to De 2 s1r 2 of d is a reflection of the fact that the influence of neutron excitations is more significant in d than in d em . The contribution of neutrons to quadrupole deformation can be better expressed by the double ratio Ž MnrM p .rŽ NrZ .. If the neutron singly closed-shell structure prevails, this ratio tends to be 0. On the other hand, the ratio of unity is expected, if a nucleus is considered to be a homogeneous neutron-proton fluid w18,19x. Indeed the 9 Be nucleus, which is located in the middle of the shell, exhibits the ratio of 0.94 w30x. Such trends may be preserved even when
other effects such as that due to core polarization are taken into account, and a rapid decrease of the ratio is expected as the nucleus approaches the neutron shell closure w34x. For the case of 10 Be, the ratio of 0.51 " 0.12 is extracted from the experimental d em and d values on the basis of Eq. Ž1.. The calculated results are in fair agreement with this ratio, irrespective of the choice of De 2 s1r 2 . In contrast, the calculated results for 12 Be considerably differ for the different values of De 2 s1r 2 . A suppressed value of 0.23 is obtained for De 2 s1r 2 s 0.0 MeV, as expected for the case of the shell closure. On the other hand, a large value of 0.65 is obtained when the narrow shell gap is employed. This value is as large as that obtained for 10 Be, which is consistent with a significant neutron contribution for the 2q 1 excitation. As shown before, the small shell gap is strongly favored to account for the large d experimentally observed. The present analysis on Ž MnrM p .rŽ NrZ . indicates that the neutron contribution as enhanced by the broken shell closure is indeed essential to give rise to the large d of 12 Be. In summary, we have studied inelastic proton scattering on 10,12 Be in inverse kinematics. Fairly large deformation lengths were obtained for both 10 Be and 12 Be, indicating that the N s 8 nucleus 12 Be can hardly be treated as a singly closed-shell nucleus. This picture of the broken shell closure, which is consistent with the accumulating evidence for the 2 s1r2 intruder orbital, is supported by the shell model calculations of deformation lengths. Acknowledgements We would like to thank the RIKEN Ring Cyclotron staff members for their operation during the experiment. We are grateful to Professor A. Gelberg for careful reading of the manuscript. The present work is supported in part by the Ministry of Education, Science, Sports and Culture by Grant-In-Aid for Scientific Research under the program number ŽB. 08454069. References w1x I. Talmi, I. Unna, Phys. Rev. Lett. 4 Ž1960. 469. w2x N. Aoi et al., Nucl. Phys. A 616 Ž1997. 181c. w3x F.C. Barker, J. Phys. G 2 Ž1976. L45.
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