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QUADRUPOLE MIXED-SYMMETRY STATES IN 56Fe
J. Takamatsu, T. Nakagawa, A. Terakama, A. Narita, T. Tohei, M. Fujiwara, S. Morinobu, I. Katayama, H. Ikegami, K. Katori, et al.
To cite this version:
J. Takamatsu, T. Nakagawa, A. Terakama, A. Narita, T. Tohei, et al.. QUADRUPOLE MIXED- SYMMETRY STATES IN 56Fe. Journal de Physique Colloques, 1990, 51 (C6), pp.C6-423-C6-426.
�10.1051/jphyscol:1990643�. �jpa-00230910�
COLLOQUE DE PHYSIQUE
Colloque C6, suppl6ment au n022, Tome 51, 15 novembre 1990
QUADRUPOLE MIXED-SYMMETRY STATES IN 5 6 ~ e
J. TAKAMATSU, T. NAKAGAWA( A. TERAKAWA, A. NARITA, T. TOHEI,
M. FUJIWARA*
,
S. MORINOBU , I. KATAYAMA* , H. IKEGAMI*,
K. KATORI* * ,s . I. HAYAKAWA* * * , Y. FUJITA* * " * , M. TOSAKI' * * * " and S. H A T O R I * * * * * * Fepartment of Physics, Tohoku University, Sendai 980, Japan
Research Center for Nuclear Physics, Osaka University, Osaka 567, :?pan
Department of Physics, Osaka University, Osaka 567, Japan
* * * ~ s h i k a g a Institute of Technology, Ashikaga, Tochigi 326, Japan
* * * *
College of General Education, Osaka University, Toyonaka, Osaka 560, Japan
* * * * * Laboratory of Applied Physics, Kyoto Prefectural University, Kyoto
606, Japan
* * * f * *
Department of Physics, Kyoto University, Kyoto 606, Japan (presented by M. Fujiwara)
Re'sumk
Nous avons cherchi., par diffusion i n e l a s t i q u e de
2
e t $ 56 e t 65 MeV, des& t a t s de symetrie mixte quadrupolaire 24 du 5 6 ~ e . Les d i s t r i b u t i o n s angulaires de section e f f i c a c e e t pouvoir d analyse ont B t B comparees B des c a l c u l s DWBA macroscopique et microscopique. Nous discutons, t a n t d'un point de vue theorique qu'expkrimentale de l a p o s s i b i l i t e d'assignation 2; pour l e s
& t a t s 2 ; . 2; e t 2: du 5 6 ~ e .
Abstract - Quadrupole mixed-symmetry 2& states in 56Fe have been searched for by means of inelastic deuteron and polarized proton scattering experiments at 56 MeV and 65 MeV. The measured angular distributions of cross sections and analyzing powers were compared with macroscopic and microscopic DWBA calculations. The 2$, 2; and 2: states in 56Fe are discussed as the candidates of the 2& state from experimental and theoretical points of view.
1 - INTRODUCTION
Recently new nuclear collective excitations corresponding to out-of-phase motion of neutrons against protons have received much attention. They are often called "scissors states" or "mixed- symmetry states", and considered to have an isovector character /I/. In deformed even nuclei, mixed-symmetry states with J T = l + have been observed over a wide mass range (46Ti, 48Ti, 15'Gd, 164DY, 232Th, 2 3 8 ~ , etc.) using the inelastic scattering of electrons, gammas and protons. In non-deformed nuclei, on the other hand, quadrupole ( ~ " = 2 & ) mixed symmetry states are predicted to exist at low excitation energy with an intense excitation strength /2/. Candidates for the ~ " = 2 & levels are reported in the N=84 isotones and in Sm, Pd /3,4,5/.
Already in 1964, McCullen et al. /6/ pointed out that several 3"=lt ,2+,3+,...,7+ states with scissors-mode properties are predicted in f7/2 shell nuclei. Thus, the next interesting subject is the investigation of the 2+
states in fp shell nuclei where the quadrupole mixed-symmetry states are theoretically expected at around 3 MeV of excitation energy. Indeed, Eid et al. /7/ suggested on the base of the y-decay data that the 2]ti strength in 56Fe was shared almost equally between the 2.658-MeV 2: and 2.960- MeV 2; levels, and an (e,e') experiment supported this suggestion /8/. In the (e,e') experiment, it was found that the 28 and 2; levels were excited with a similar strength and that the obtained E2 form factors for the two states were consistent with the assumption of equally shared mixed-symmetry states. However, there seems to be a controversial result from inelastic scattering of a-particles exciting only isoscalar levels /9/; the 2 t level in 56Fe is found to be strongly excited with an strength comparable with that of the 2; level.
Independent measurements for the 2 f , 2$ and 2:- . levels in 5 6 ~ e are, therefore, needed to give more insight on the mixed-symmetry 2& states. An extensive set of hadron scattering data permits one to examine the validity of the wave functiohs obtained from the experiments with electromagnetic probes on one hand, and to examine the reaction mechanism associated with hadron scattering on the other hand. It should be noted that longitudinal form factors of 2+ states in electron scattering only serve for giving proton transition
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990643
C6-424 COLLOQUE DE PHYSIQUE
densities, while cross sections and analyzing powers in hadron scattering bear on both neutron and proton transition densities. We note that a comparison between proton and deuteron scattering results is known to be quite effective in identifying a 2+ level as a mixed symmetry state /5/. In addition, detailed microscopic shell model calculations for fp shell nuclei are now available. The result of these calculations allows us to make a detailed comparison of hadron scattering data with the results of (e,e') and y-decay data from various standpoints.
2
-
EXPERIMENTS and RESULTSInelastic scattering experiments of 65-MeV polarized protons and 56-MeV deuterons were performed at the Research Center for Nuclear Physics (RCNP), Osaka University. The target used was a self-supporting 56Fe foil with a thickness of 1.05 mg/cm2 (99.9% enrichment). The scattered protons and deuterons were
0
&
0 a
.C
5
0 400 800 1200 1600 2000? g.
Z b
s 5 6 ~ e ( d , d ' ) co ~n el,),. = 2 5 O
v
F!+ 3
0 400 800 1200 1600 2000
Excitation Energy (Channels)
Fig.1. Energy spectra of inelastic proton (a) and deuteron (b) scattering from 56Fe.
Fig.2. Cross sections and analyzing powers for protons and deuterons scattered from the 2+ levels in 56Fe. The solid curves are DWBA predictions in the harmonic vibrational model.
analyzed with the spectrograph RAIDEN. The experimental set-up is described in detail elsewhere /lo/. Fig.
1 shows two spectra from inelastic proton and deuteron scattering experiments. The energy resolution was -30 keV (FWHM). Six 2+ peaks are evidently identified in the two spectra below the excitation energy 4 MeV. No reliable cross section has been obtained for the 3.748-MeV 22 state due to the small excitation strength and the presence of the 3.756-MeV 6+ state.
Angular distributions of cross section and analyzing power for the 0.847-MeV 2?, 2.658-MeV 2 f , and 2.960-MeV 2; levels are shown in Fig. 2 together with the DWBA predictions using a code ECIS79. In both the (p,p') and (d,d7) reactions, the excitation strength of the 2f level is much larger than that of the 23+ level, and the angular distributions da/dR for the 2; level are completely different from those for other 2+ levels.
Note that angular distribution patterns of cross sections for several 2+ levels at higher excitation energy are very similar to those of the 2f level. Fairly good fits in cross section have been obtained, except for the 2:
level, with the DWBA predictions in the harmonic vibrational model. The
p2
values deduced from the (p,p') data are found to be compatible with those from the (d,d') data (see Fig. 2). We notice, however, that in the whole angular range of the (p,p7) reaction, there are noticeable deviations between the data and the DWBA prediction in cross section and analyzing power in except fof the 2At level, indicating a necessity of detailed analyses. I t should be stressed that the analyzing power for 2+ states are very sensitive to probe the nuclear structure.3 - DISCUSSION
In order t o understand the character of the 2+ states, the microscopic DWBA analyses for the (p,p') reaction have been made with the DWBA83 code using two microscopic transition form factors, one from Hartung et al. /8/ and the other from the results of the full fp shell-model calculations by Nakada, Sebe and Otsuka /11/. By introducing the effective charge and g-factor, they have obtained the B(E2) and B(M1) values for the low-lying 2+ states consistent with the experimental data. Their calculations predict that the quadrupole mixed-symmetry component splits into the 2f and 2: states, not into the 2: state. This contradicts the (e,e') result. Since the effective charges in their shell model calculations are e:ff=1.4e and e ~ ~ ~ = 0 . 9 e , the DWBA calculations need to be normalized to the experimental cross sections by an enhancement factor of 5-6. The DWBA calculations included both the direct and the exchange processes. For each 2+ state, about 30 one- particle one-hole (lp-lh) transition amplitudes were required in the case of the full fp shell-model calculation.
Fig.3. Cross sections and analyzing powers for protons scattered from the 2:, 2 i , 23+, and 2; levels in 5 6 ~ e compared to the results of the microscopic DWBA calculations. The solid and dotted curves are the DWBA predictions with the wave functions obtained by the full fp shell model calculations and the (e,e7) results, respectively. Enhancement factors have been applied t o the calculated curves.
C6-426 COLLOQUE DE PHYSIQUE
Fig. 3 shows the (p,p7) data for the 2:-2: states, which are compared with the results of the microscopic DWBA calculation with the density dependent Paris-Hamburg (DD) interaction at 100 MeV 1121. Note that the results of the DWBA calculations using the DD interaction and the M3Y interaction are not largely different to each other in cross section and analyzing power. Remarkable agreements between the data and the results of the DWBA calculation in the shape of cross section have been obtained for the 2:, 2;, and 2: states when we employ the wave functions from the full fp shell-model calculations (see the solid lines in Fig.3). Enhancement factors needed are found to be fairly consistent with the theoretical expectation 5-6.
On the other hand, the DWBA calculations using the wave functions deduced from the (e,e') data only give poor fits with the data in cross section, and a wide range of enhancement factors ( 1 ~ 2 9 ) are necessary to fit the absolute magnitude of the cross sections for the 2f, 2?, 2: states. Although the experimental data of the cross sections and analyzing powers for the 2; and 2; states are different, the DWBA results calculated with the wave functions from the (e,e') data are completely similar.
Large disagreement in analyzing power between the data and the DWBA predictions is a challenging problem t o be solved. Taking into account the lack of explicit inclusion of the 2hw excitations (or the core excitation effect) in the shell model calculations, this could perhaps be due to the neglect of small admixtures of collective amplitudes of the 2hw excitations. In addition, we fail to reproduce the cross section pattern of the 2; state, which is theoretically inferred to have the components dominated by neutron excitations. It is, however, gratifying that each specific feature for the 2:-2: states in cross section patterns is qualitatively fairly well described with the results of the full fp shell model calculation.
4 - CONCLUSION
In conclusion, we present the hadron scattering data including analyzing powers. These data in conjunction with the (e,e') and y-decay data are useful for getting deeper insight on the mixed-symmetry 2& states in 56Fe. At present, the DWBA analyses based on our hadron experiments seem to be consistent with the results of Nakada, Otsuka and Sebe, denying the simple picture that the 2: state is a partner of the shared mixed- symmetry state. However, further investigation is necessary for getting the clear conclusion on the 2& states in 5 9 e . The measurement of the (e,e') form factors in the high momentum transfer region of q=1.2-2.0 fm-' is desirable, and much efforts should be devoted to reproduce the analyzing power data. Several candidates of the 2+ states are expected in other fp shell nuclei (54Cr, 58Fe and 58Ni, etc.). A systematic study of hadron scattering on these nuclei is now in progress. M.
5
-
ACKNOWLEDGMENTSWe thank Prof. T. Otsuka and Dr. H. Nakada for stimulating discussions and for providing the unpublished results of their shell model calculations. One of us (M.F) thanks Prof. M. Pignanelli for his encouraging interest in our work. Thanks are also due to the RCNP cyclotron crew for the operation of the cyclotron.
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