DOUBLE QUADRUPOLE EXCITATION IN 112Cd VIA ([MATH], d') AND ([MATH], p')

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DOUBLE QUADRUPOLE EXCITATION IN 112Cd VIA ([MATH], d’) AND ([MATH], p’)

R. Hertenberger, G. Eckle, F. Eckle, G. Graw, D. Hofer, H. Kader, P.

Schiemenz, N. Fujiwara, K. Hosono, M. Kondo, et al.

To cite this version:

R. Hertenberger, G. Eckle, F. Eckle, G. Graw, D. Hofer, et al.. DOUBLE QUADRUPOLE EXCI-

TATION IN 112Cd VIA ([MATH], d’) AND ([MATH], p’). Journal de Physique Colloques, 1990, 51

(C6), pp.C6-427-C6-430. �10.1051/jphyscol:1990644�. �jpa-00230911�

DOUBLE QUADRUPOLE EXCITATION IN Cd VIA

(3,

^{d ) AND}

( 6 .

^p ' ⁾

R. HERTENBERGER, G. and F. ECKLE, G. GRAW, D. HOFER, H. KADER, P. SCHIEMENZ, N. FUJIWARA*, K. HOSONO* . M. KONDO*, M. MATSUOKA*,

T. NORO*, T. SAITO* , S. KATO*, OKAMOTO'*, S. MATSUKI* * , C. H A T E G A N * " ~ , N. BLASI* * * * , ^S. MICHELETTI* * * * and R. de LEO'****

g e k t i o n P h y s i k , U n i v e r s i t y o f Munich, 0 - 8 0 4 6 G a r c h i n g , F.R.G.

RCNP, O s a k a U n i v e r s i t y , I b a r a k i , o s a k a 5 6 7 , J a p a n

* * D e p a r t m e n t of P h y s i c s , K y o t o U n i v e r s i t y , K y o t o , J a p a n

* * * I n s t i t u t o f A t o m i c P h y s i c s , B u c a r e s t , Romania

* * * *

SIN d i F i s i c a N u c l e a r e , I - 2 0 1 3 3 Milano, I t a l y

* * * * *

SIN d i F i s i c a N u c l e a r e , I - 7 0 1 2 6 B a r i , I t a l y

112Cd has been investigated in several unpolarized experiments.l)2)3) It is known as vibrational like nucleus and the IBA model works nicely for the low lying states. For questions concerning the high excitation region as well as for reasons of precision additional polarized high resolution experiments

-

20 Mev(d,dl) and 65 MeV($,pi) -were performed by us.

As a first result a similar description of the low lying states, especially the two phonon states &+, Z2+ and 41+, within the second order vibrational model is given for both experiments. Transition moments coincide within 5%. A comparison with electromagnetic B(E2) and B(E3) values yields deviations less then 15%. In the vibrational model calculations the same parametrization was used for the diagonal and transition potential, determined in a simultaneous fit on ground state, 2!+ and 3,-. Using this potential &+ and 41* show mainly two phonon character, but the two phonon model fails in the case of the 22+ state. It seems t o be mixed with a higher lying 2+ state.

Part of the excitation spectra for 112Cd

above: 20 Mev(2,dif down: 65

The 2 phonon multiplett is indicated by 12>.

0,-.17

--

kin 3012>+cos 3011>

Coupling scheme as used in the coupled channel analysis (ECIS).

First order transitions are indicated by single arrow, second order by double arrow.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990644

COLLOQUE DE PHYSIQUE

Low energetic deuterons are a good probe t o study multiphonon excitations, as multistep excitation is enhanced a t 20 ~ e ~ ( 3 , d ' ) . Using the Q3D inagnetic spectrograph in combination with our focal plane detector with modular cathode readout we achieve a relative resolution of 2.5

.

10-4. Nearly all levela up t o an Ex of 4 MeV are well separated and the assignment of excitation energies is possible within f 1 KeV (Fig.1). From these precise d a t a multipole moments M(EX) are extracted (in 1. order) and compared with available B(EX) values.

M(EA) =

; P -

d iag B(EI) =

&

I M ( E I ) I ~

T o distinguish between multistep excitation or changed form factors (second order direct transition)

-

^mixed

up in the (d,dt) experiment - t h e comparison with high energetic 65 MeV($,p')data is very helpful, as lstep excitation is dominating. In this experiment, performed by part of us at the Osaka spectrograph RAIDEN a similar relative resolution was achieved. Nevertheless many multipletts are no longer separated and the exact excitation energies of the (d,d1) measurement were used in the peak fit machinery to evaluate the ($,pl) data.

For the following it might be helpful t o define the meaning of f i s t and second order transitions. In the vibrational model the potential V(r,R) is expanded in a Taylor series around the mean value & of the surface vibration.

One yields, with

&

⁼ F(Qx,,)

with term 1 being the diagonal part and terms 2+3 the transition part of the potential. Term 2 describes first order transitions, is linear in the deformation

&

and of first derivative type form

transitions deal with term 3 being quadratic in

Fig.3 shows angular distributions for the low lying states in 112Cd, on the left side d

6

^and Ay for the d o '

65 MeV($,pl) and on the right side and i T l l for the 20 ~ e ~ ( b , d ' ) experiment. The data are arranged according t o the level scheme. The solid curves correspond to coupled channel vibrational model calculations performed in the full coupling scheme of fig.2. For both experiments the optical potential was fitted simultaneously on the ground state and the the two highest excited states, the 21+ and 31- states. The same parametrization was used for the diagonal and transition potential. The dashed curves are first order calculations (single arrows in fig.2) with the same optical model parametrization. For the 65 MeV data the

0.0 . . . .

lo' ,\! , i s t : : : i

m a m m

l*

10'

ir-.. \w

^eigstic

^Ii\jph

lo'

lbLm I o - - l * m m m

-

^{ID lm Ma}

Fig. 3: The low lying states in W d .

solid curve: second order vibrational model calculations in the coupling scheme of fig.2.

dashed: ^as solid, but first order calculations dotted: second order two phonon description of 22+

COLLOQUE DE PHYSIQUE

GS,21t and 31- show nearly identical results as the second order curves, but considerable deviations appear in the case of the 20 MeV data, equivalent t o enhanced contributions of multistep effects.

T o proof the vibrational behaviour of 112Cd, we tried to describe the states, known as two phonon states, in a second order vibrational model calculation using the coupling scheme of fig.2 for the Oz+ and 41, level and the fitted potential mentioned above. Such calculations result in qualitatively good agreement with the experimental d a t a for the 02+ and 41+ state (solid curves). First order calculations are not sufficient for both experiments, indicating the strong interference of the first order multistep (2lt H 2phonon state) and the second order direct excitation. Even for the high energetic data multistep plays here an important role. For the 20 MeV 02+ state the two phonon strength was reduced by 25%, for the 65 MeV 41t state it was increased by 15%.

The 22+ state cannot be described in the 2 phonon model (dotted curves). Strength and shape of the angular distributions are off. T o achieve the remarkable good solid curves it is necessary to take an additional first order direct transition into account. Its strength (8) is by a factor of 4 smaller than the respective 21+ value.

The wave function of the 22* becomes a mixture between 1 phonon and 2 phonon description, 21+

31-

$J= cos3011>

+

sin 3012>

65 MeV

P

M o w .I55 68(7) .13 391(39) 20 MeV

P

M(EA)

.17 72(7) .13 382(38)

whereby the strength of the 2 phonon contribution is reduced by 50% (=sin 30). This can be interpreted as mixing of the 22+ with a higher lying 2+ state, which might be an intruder state.1) A first order calculation is not sufficient visible from the dashed curve a t the 20 MeV data, again indicating the necessity of the second order direct transition.

M(EA) =

4 3 3

70(1) 4 )

337(27) ^{5 )}

Apart from the vibrational model analysis we are engaged in comparing transition moments with IBA predictions. Up t o now two preliminary statements can be made: The first four 3- states are nicely described in the f-d boson coupling frame of IBA 1 (f,fd,fd2 ...). But for the higher lying 2,+ states (n13) the IBA model fails completely. The structure of these seems t o be stronlgy influenced by mixing with other states as

observed for the 22+ state.

REFERENCES

Phys. Rev. C25 (1981) 3160 Phys. Lett. 162B (1985) 1 Nucl. Phys. A505 (1989) 109

At. Data and Nuc. Data Tab. 42 (1989) 92