Inelastic electron scattering reveals a concentration of resonant E3 strength at (13.3 ±  0.2) MeV 
in 51Ni and (12.8 ±  0.2) MeV in 60Ni. The energy agrees closely with the 52 A- 1/ ' MeV predicted by Hamamoto for the isovector (1 hwl E3 mode on the basis of the Bohr-Mottelson self-consistent shell model, but the strength, (13 ± 1)% and (8 ± 2)% of the energy weighted sum rule, respectively, is a factor of 5 too large. This result weakens recent arguments in favor of a monopole assignment for the 53 A-i/ 3  MeV resonance found by (e,e'l in heavy nuclei.National Science FoundationNaval Postgraduate School Foundatio

Beachy, J.S.

Buskirk, F.R.

Kowalick, S.J.

Pitthan, R.

Calhoun, Institutional Archive of the Naval Postgraduate School

Calhoun: The NPS Institutional ArchiveFaculty and Researcher Publications Faculty and Researcher Publications Collection1977Resonant octupole strength at 13 MeVin(58)Ni and (60)Ni and the character of the53A(-1/3) state in heavy nucleiPitthan, R.Monterey, California. Naval Postgraduate SchoolR. Pitthan, J. S. Beachy, F. R. Buskirk and S. J. Kowalick, "Resonant OctupoleStrength at 13 MeV in 58 Ni and 60 Ni and the Character of the 53 A-l/3 state inHeavy Nuclei"http://hdl.handle.net/10945/51920Resonant Octupole Strength at 13 MeV in 58Ni and 60Ni and the Character of the 53A-l/J State in Heavy Nuclei R.Pitthan, J.S. Beachy, F.R. Buskirk, and S.J. Kowalick Department of Physics and Chemistry *Research supported in part by the National Science Foundation and the Naval Postgraduate School Research Foundation. • ABSTRACT Inelastic electron scattering reveals a concentration of resonant E3 strength at (13.3 ± 0.2) MeV in 51 Ni and (12.B ± 0.2) MeV in 60 Ni. The energy agrees closely with the 52 A-,/, MeV predicted by Hamamoto for the isovector (1 hw) E3 mode on the basis of the Bohr-Mottelson self-consistent shell model, but the strength, (13 ± 1)% and (8 ± 2)% of the energy weighted sum rule, respectively, is a factor of 5 too large. This result weakens recent arguments in favor of a monopole assignment for the 53 A-i/ 3 MeV resonance found by (e,e') in heavy nuclei. -1-A distinct resonant excitation at 13 MeV in 51 Ni, 60 Ni and 6 ~Ni has first been reported by Gulkarov et al. 1 , who searched for the surface quadrupole oscillations coupled to the volume dipole oscillations, predicted by the collective dynamic model. 2 The structure found was explained in the framework of this model. After the discovery that a giant quadrupole resonance existed as a genuine property of the nuclear continuum, a re-evaluation of the data in Born Approximation identified the 13 MeV resonance in all three isotopes as E2. 3 Later experiments which find structure at this energy [-(50-53) A- 1 / 3 MeV] in nuclei with 56 ~A~ 60 are contradictory to this result and contradictory to each other. Torizuka, et al.~ finds two E2 (or EO) states with a rather small width (<0.6 MeV) at 13.2 MeV and 14.0 MeV in 51 Ni, which exhaust 7.4 ± 0.7 and 4.8 ± 0.7% of the isosca-lar energy weighted quadrupole sum rule [(E2, ~T = O) EWSR]. Similarly, polarized proton measurements favor E2 (or EO), while ruling out E3. 5 Inelastic 3 He scattering on ~ 1 Ti, 56 Fe, 59 Co and 60Ni by Arvieux, et al. 6 finds consistently a peak with width r z 1.2 MeV at 51 A-i/ 3 MeV (13 MeV in 60 Ni) for which an E2 assignment was the most probable, but an E4 could not be ruled out. However, in 155 MeV proton scattering 7 and 250 MeV electron scattering1 on 56 Fe a peak around 13.5 MeV has (tentatively) been assigned E3. The report on inelastic scattering of deuterons 9 finally, while not giving an assignment, shows that the angular behavior -2-of the cross section of a state at 13 MeV is different from the E2 (6T = O) giant resonance at 16 MeV. While the existence of a resonance 13 MeV up in the con-tinuum with a width of only (1-2) MeV is exciting enough, even more importance comes to this state at 51 A- 1 / 3 from the observation in (e,e') of a state at the same energy (in A- 1 / 3 ) in many nuclei between 139 <A< 2oa 1 o-is which, con-sistent in all experiments, has been assigned to be either E2 or EO. (See, e.g., Ref. 16 for the difficulties in dis-criminating E2 and EO in (e,e').) Since the existence of a second giant quadrupole reson-ance in the continuum below the 63 A- 1 / 3 MeV mode seems unlikely 15 (but not impossible~ the 53 A- 1 / 3 MeV state is a serious candidate for the giant monopole (breathing mode) resonance. On the other hand, 52 A- 1 / 3 MeV is the energy predicted by Hamamoto 17 for the isovector E3 (1 -tw0 ) state, based on the Bohr-Mottelson self-consistent shell model. In ~eneral, the various continuum modes discovered since 1971 have exhibited a very smooth dependence on nuclear mass A, and resonances at the same energy (again in A-i/ 3 MeV) in different nuclei have been found to be of the same multi-polarity. We thought it therefore of the utmost importance to investigate the 53 A-i/ 3 MeV mode in nuclei with A < 139. However, a first experiment on 19Y surprisingly did not show any resonant cross section around 53 A- 1 / 3 MeV which would be compatible to the strength found in heavy nuclei. 11 • -3-The measurements reported here were undertaken with 102 MeV electrons from the 120 MeV Electron Linear Acceler-ator of the Naval Postgraduate School. Experimental set-up and evaluation procedures have been described recently. 18 Since the state in question is a weak resonance close to the GDR and GQR (6T = Q~ great care was taken to select the correct line shape and its momentum transfer dependence. 1 ' Self-supporting targets of 51 Ni and 60Ni, with mass densities between 45 and 135 mg/cm 2 , isotopically enriched to 99% of the respective isotope were used at scattering angles of 45°, 60°, 75°, 90° and 105°. A typical spectrum is shown in Figure 1. While at low (q s 0.6 fm- 1 ) momen-tum transfer the radiation tail is the dominant part of the cross section, contributing 90% or more to it, this is no longer the case at higher momentum transfer. The structure of the spectra itself turned out to be more complex than those for any previous (e,e') experiment in heavier nuclei. Numerous resonances of El, Ml, E2, E3 and E4 character were found between 6 and 45 MeV which will be reported elsewhere in a comprehensive article. Here, due to its special importance for the monopole question, and with that the problem of nuclear compressibility, we will concentrate on the (51-53) A- 1 / 3 MeV resonance. Figure 1 thus shows only the disentangling into the resonant cross sections for the resonances found at 13.3 and 16.3 MeV in 51 Ni. The momen-tum transfer dependence for resonances at this energy in both isotopes is shown in Figure 2, which compares the • • -4-experimental values to DWBA calculations on the basis of the Goldhaber-Teller model. These calculations have been discussed in more detail in Ref. 18 which also contains the definitions of the sum rules and single particle units used. Figure 2 shows that E3 is the preferred assignment for the 13 MeV resonances in both nuclei, while the 16 MeV states follow an E2 momentum transfer dependence. The quantita-tive details like excitation energy, width and strength, are accummulated in Table 1. We are reasonably sure of the assignment. Electro-ex-citation of giant resonant states has given very reliable results since the initial discovery of modes other than the dipole state. Table l shows that the E3 states do not only exhaust a sizeable fraction of the sum rule, they are also quite strong in single particle units. Generally, one has found that collective transitions are described very well with the Goldhaber-Teller or Tassie model, where the trans-ition charge density is simply the derivative of the ground state charge density. For an E2 state the rms radius for the excited state would have to be approximately 30% smaller than that of the ground state in order to mimic the momentum transfer behavior of an E3. There are several problems to solve. First, one has to explain the different assignment for this resonance in medium-heavy contrasted to heavy nuclei. Secondly, the different assignments for the Nickel region (EO, E2, E3 and E4) discussed earlier have to be explained. Concerning the -5-latter, one makes the astonishing discovery that none of the references quoted in the beginning makes a definite statement, nearly all assignments are called tentative. Critical analysis of the data also shows that the statisti-cal uncertainties are quite large 6 ' 7 , that the assignment rests mainly on two low points in the spectrum at the high-est momentum transfer•, or that other problems have been encountered (see, e.g., remark in Ref. 4 of Ref. 9). Although the excitation energy agrees closely with the 52 A- 1 / 3 MeV predicted by Hamamoto, 17 this state cannot be isovector due to its appearance in (d,d') spectra, 9 and its strength is a factor of 5 too large . We conclude that in medium-heavy nuclei the E3 strength is even more fragmented than anticipated. This leaves us with the first problem, to decide whether the 53 A- 1 / 3 MeV state is EO or E2. Analysis of the pub-lished data 10 - 15 • 18 shows that the strength is approximately proportional to the ground state isospin, i.e., the neutron excess. This property is difficult to explain if one does not want to assume the resonance to be an isovector E2 oscillation of the excess neutrons. 20 This assumption would explain why hadron scattering does not show this resonance, because isovector excitations are suppressed by a factor of ten compared to isoscalar ones. 15 Both macroscopic and microscopic calculations have predicted isovector E2 strength at the excitation energy of the isoscalar reson-ance. 21 If this state is the monopole (breathing mode) :a p " " .... ID -7-"' -6- Ill N ID N "' state, no inunediate reason is obvious why it should be pro- 0 0 0 0 0 0 0 0 portional to the neutron excess. -;;, +I +I +I +1 I>: M CX) CX) N In summary, electro-excitation of the giant resonance :> M .... 0 .... Q) ~ 0 0 0 0 region in 58 Ni and 50 Ni shows a relatively strong part of M M the E3 strength at 13 MeV. The results make a decision be- 'tl s::: -< ... '1 ... '1 53 A-t/J Ill "' 0 0 0 0 tween EO and E2 for a resonance at MeV in heavy i; M N M M ID .... M nuclei even more difficult, since it weakens our recent .µ -< "' CX) "' N "' ~ .,; I 5 .... "' .... argument in favor of a monopole assignment. UI l:Q Q) ~ u s::: "' "' s::: .µ 0 N .... N M Q) UI 0 0 0 0 Q) :> Ill I>: Q) ,.I( e +1 +I +I +I M Q) 0 M "' "' "' " ,.I( 0 ..... ~ ~ Ill p. .... .... ::I ,.; .µ u 0 I/) 'tl :> .... s::: Q) 0 Ill ~ M "' M M .... Q) Q) ' ~ 0 UI N •.-1 M M 0 oz I "' ID "' ID .a OP ~ .µ ::I'" M >< Q) 'tl'tl l'l M "'s::: "' ::I ft! 0 0 'tl .µ"" II Q) s::;Z UI ., .. N N N N E-< ::I ·.-t"' :> 0 0 <l l? s::: 0 0 ui~ Q) .µID Q)•.-1 e +I +I +I +I -< •.-1 ID .a ~ S:::O\ .µ M M CX) N ::IN >. >< .,; ..; MN l'l M ID I>: Q) 0 Q) M M M M I/) MI' .... > 3: u .... •.-1 l'l •.-IM UI .µ ' .µ .µ u M • M GI -< "'"'I ::I p. -< M N M N ~ p. .c 01 01 l'l l'l l'l l'l l'l Q) Q) l:Q Q) "' I>: M M .µ C'>IU s:::i:i >< •.-1 M 01 l'l 01 ~ ::I Q) Q) ·.-1 •.-1 II Q) u M M z z .a ::I .0 u 0 I>: E-<Z "' ::I -;;, :a E-< z • .. A -a-Figure 1. Spectrum of 120 MeV electrons scattered inelastically from 51 Ni at 105°. The spectrum shows very pronounced the trans-ition from the sharp bound states to the broad continuum states. Note that the zero is not suppressedi the giant reson-ance cross section is a sizeable fraction of the total cross sec-tion, i.e., with inclusion of the radiative and experimental background. The cross section has not been corrected for the constant magnetic dispersion 50 51Ni(o.•') E,: 102MeY e.105• 1 EXCITAllON ENEllGY (M•V) of the spectrometer. For graphical purposes, the number of points shown (measured were 10/MeV) has been reduced by a factor of 2 below 10 MeV, and by a factor of 4 above. The decomposition of the spectrum into the resonant cross sec-tions for the E3 state at 13.3 and the E2 state at 16.2 MeV are shown, a giant E3 state in the bound state region at 7 MeV, the Ml giant states at 10 MeV and the isovector E3 and E2 resonances at 27 and 32 MeV, respectively, are also apparent. The statistical error is of the size of the circles representing the data. -9-Figure 2. Comparison of the experimental resonant cross section at 13 and 16 MeV in 58 Ni and '"Ni with DWBA cal-culations for E2 and E3 transitions using the hydrodynamical model. The open circles (0) represent the experimental results for the resonances around 13 MeV, the closed circles C•l for the 16 MeV resonance. It is evident that the former are better described by an E3 assignment, while the latter follow the E2 DWBA curve. The closed triangle (Tl with arrow indicates an upper limit for the 16.3 MeV resonance in 58 Ni, while the closed triangle (!) indicates that the cross section for the 16.2 MeV resonance in 60 Ni was held constant to the value extrapolated from lower momentum transfer. 15 10 58Ni /('·-~'~, 5 J/ \ I I I " 2 I E2 / ,'/f/ '/ i i .i 0.5 I 2 i I I ~t-t /{ '• I T \ l \ I \ I E2 ,,. -·- . // /// I I i i I 0.3 0.4 0.5 0.6 0.7 (0.8 1) moment1.m tran$fer fm--10-REFERENCES 1. I.S. Gulkarov, N.G. Afanasev, V.M. Khvastunov, N.G. Shevchenko, V.D. Afanasev, G.A. Savitskii, and A.A. Khomich, Sov. J. Nucl. Phys. !• 274 (1969) (Yad. Fiz. !• 478 (1969)). 2. D. Drechsel, J.B. Seaborn, and w. Greiner, Phys. Rev. ~. 983 (1967). 3. I.S. Gulkarov, Sov. J. Nucl. Phys. 18, 267 (1974) (Yad. Fiz. 18, 519 (1973)); Sov. J. Nucl.-Phys. 20, 9 (1975) (Yad. Fiz. 20, 17 (1974)). -4. Y. _Torizuka, Y. Kojima, T. Saito, K. Itch, and A. Nakada, Res. Rep. Lab. Nucl. Science, Tohoku University §, 165 (1973). 5. D.C. Kocher, F.E. Bertrand, E.E. Gross, R.S. Lord, and E. Newman, Phys. Rev. Letters 31, 1070 (1973). 6. J. Arvieux, M. Buenerd, A.J. Cole, P. de Saintignon, G. Perrin and D.J. Horen, Nucl. Phys. A247, 238 (1975). 7. N. Marty, M. Morlet, A. Willis, v. Comparat, R. Frascaria, Nucl. Phys. A238, 93 (1975). 8. Y. Torizuka, Y. Kojima, T. Saito, K. Itch, A. Nakada, s. Mitsunobu, M. Nagao, K. Hosoyama, s. Fukuda and H. Miura, in "Proc. of the Int'l. Conf. on Photonuclear Reactions and Applications," Asilomar, 1973, edited by B. L. Berman (Lawrence Livermore Laboratory, Univ. of California, Livermore, 1973). 9. C.C. Chang, F.E. Bertrand, and D.C. Kocher, Phys. Rev. Letters l!• 221 (1975). 10. R. Pitthan, z. Physik ~· 283 (1973). 11. A. Schwierczinski, Ph.D. Thesis, Darmstadt 1976 (unpublished). 12. G.L. Moore, F.R. Buskirk, E.B. Dally, J.N. Dyer, X.K. Maruyama and R. Pitthan, z. Naturforsch. 3la, 668 (1976). -13. R.S. Hicks, I. P. Auer, J.C. Bergstrom and H.S. Caplan, Nucl. Phys. A278, 261 (1977). 14. R. Pitthan, F.R. Buskirk, E.B. Dally, J.N. Dyer and X.K. Maruyama, Phys. Rev. Letters 33, 849 (1974); Phys. Rev. Letters 34, 848 (1975); Proc.-Ynt'l. Conf. on Nuclear Structure and-Spectroscopy, Amsterdam 1974, edited by H.P. Blok and A.E.L. Dieperink (North-Holland, Amsterdam, 1974) Vol. 2, p. 306 • .. -11-15. R. Pitthan and F.R. Buskirk, Phys. Rev. Cl6, September 1977. 16. P. Strehl, z. Physik 234, 416 (1970). 17. I. Hamamoto, in "Proc. of the Int'l. Conf. on Nuclear Structure Studies Using Electron Scattering and Photoreac-tion," Sendai, 1972; edited by K. Shoda and H. Ui (Suppl. Res. Rep. Lab. Nucl. Sci., Tohoku Univ., Vol. 5, 1972). 18. R. Pitthan, F.R. Buskirk, E.B. Dally, J.o . Shannon , and W.R. Smith, Phys. Rev. Cl6, September 1977. 19. E.F. Gordon and R. Pitthan, Nucl. Instr. Methods, in press. 20 . L.C. Biedenharn, M. Trivedi, M. Danos, Phys. Rev. Cll, 1482 (1975). 21. E.C. Halbert, J.B. McGrory, G.R. Satchler and F. Speth, Nucl. Physics A245, 189 (1975). DEPARTMENT QF THE NAVY Dept of Physics & CtfemistrY. Attn: .. ~j-~-~!.' ... ~-~-tt~~~--'--~-~~e 61 P~ · Naval Postgraduate School .Monterey .. Cal-it-ornia 93940 Ol'l'ICIAL BUSINESS PIENALTY F"Olt PRIVATE USE, UOO POSTAGE AND P"EES .. AID DE,.AltTMENT oir THE NAVY DoD 316 ~ u.a.MAIL 

Resonant octupole strength at 13 MeVin (58)Ni and (60)Ni and the character of the 53A(-1/3) state in heavy nuclei

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Resonant octupole strength at 13 MeVin (58)Ni and (60)Ni and the character of the 53A(-1/3) state in heavy nuclei

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