Study of electromagnetic transition strengths in 81Rb

Nuclear Physics A376 (1982) 367-378 C) North-Holland Publishing Company

STUDY OF ELECTROMAGNETIC TRANSITION STRENGTHS IN 8'Rb I J . PANQUEVA, H . P . HELLMEISTER, L . LOHMANN, K . P . LIEB and F . J . BERGMEISTER II. Physikalisches Institut der Universität Göttingen, .3400 Göttingen, Fed. Rep . Germany and P . VON BRENTANO and R. RICHTER Institut jiir Kernphysik der Universität zu Köln, 5000 Köln 41, Fed. Rep . Germany Received 12 August 1981 Abstract : High-spin states in " Rb were excited in the fusion-evaporation reaction "Cu("F, p2n)" Rb . Their lifetimes were determined by means of the recoil distance and Doppler-shift attenuation techniques . Deduced B(E2) and B(MI) transition strengths are discussed in the framework of the asymmetric rotor-plus-particle model . E

NUCLEAR REACTIONS "Cu(' "F, p2n)" Rb, E = 50, 55, 58 MeV : measured E. ., recoil distance, DSA lineshapes . "' Rb levels deduced T, . z , B(i.). Enriched target .

1. Introduction High-spin states in e t Rb have been extensively studied by Friederichs et al. ' ) with the reactions "Br(a, 2n) and "Zn( ' 60, p2n). By means of the Doppler shift techniques, the same group measured the lifetimes of the q+, 41 + and Al' states, populated in the reaction 65 Cu(' 9F, p2n)"Rb [ref.')] . The positive-parity yrast states have been successfully explained by Toki and Faessler') in terms of the triaxial rotor-plus-particle model with a variable moment of inertia (VMI). In the framework of this approach a fairly pure Coriolis decoupled I + band is constructed by intruding a g t single-particle state. This leads to energy spacings very similar to that of the ground-state band of the adjacent even core 'oKr. The interpretation of the positiveparity states in terms of this model is supported by the measured E2 strength of the -Y -" I + transition') which is that predicted with deformation parameters taken from the core Z). The main objections to this picture are the measured -~-'+ -. -V+ and + 41 + -+ ~Y- transition probabilities within the yrast band whose published experimental values exceed the theoretical ones by a factor of three and more Z). Therefore, one motivation for remeasuring the lifetimeslof'the'l~+ and 'y + states using both the t Supported by the Deutsches Bundesministerium für Forschung und Technologie . 367

36 8

J. Panqueva et al. / e `Rb

Doppler shift attenuation and the recoil distance methods was this serious discrepancy. The negative-parity yrast states, on the other hand, show a pronounced staggering in energy'), similar to that observed in "Kr, "Br and 83 Rb, for example 4-6). This staggering has been attributed to alternating admixtures of the 2p j, If, and 2p } orbits in the wave functions of states which differ by one unit of angular momentum 7). It is therefore to be expected that the stretched in-band M 1 transitions, which exhibit the single-particle features, may be considerably changed with respect to simple Nilsson bands. Lifetime measurements, in connection with the already known branching and mixing ratios of these transitions ' ), should provide a sensitive test for understanding these negative-parity states . In addition, the E2 strengths once more determine collective properties such as the quadrupole deformation of the core .

2. Experimental procedure and results The high-spin states in "Rb were populated by means of the reaction 65 Cu(' 9F, p2n)8 'Rb at beam energies of 50, 55 and 58 MeV. The 50-100 nA fluorine beam was provided by the HVEC FN tandem accelerator at the University of K61n. The Doppler shift attenuation (DSA) as well as the recoil distance Doppler shift (RDDS) methods were applied, since the lifetimes were expected to be in the range between 0.1 and 10 ps [ref. z)] . Both techniques have been described in detail in several previous papers 8). Due to the high recoil velocities of v/c - 0.014, a well-defined Doppler broadening and a clear separation of the shifted and unshifted peaks could be achieved in the RDDS measurements . For up to three Ge(Li) detectors positioned at different angles with respect to the beam axis, y-ray spectra between 100-1500 keV and of 4096 channels were accumulated simultaneously. The energy resolution was 1 .8-2 .5 keV at 1 .33 MeV (6°Co); the detector efficiency varied between 10 % and 15 %. In the RDDS measurements, 61Cu targets of 93-99 % enrichment, evaporated onto 1 .0 jum thin 300 Ug/cml stretched Au layers, were mounted in the plunger device, described previously 8). The flight distances D of the recoiling nuclei between the target and the movable 20 pm thick Ta stopper foil were measured on-line with a magnetic transducer and, for distances less than about 100 jtm, continuously monitored by the capacitance method 9). Varying D in random order between zero (equivalent to electrical contact) and 1000 ym, the mechanical distance setting with a micrometer screw was accurate to within 0.5 ,um (_" 0.1 ps). Also the thermal drift over a typical 60 min run was less than 0.5 ym. Before and after the measurements, the flatness and the surface structure of the targets were checked carefully under an optical microscope with depth resolution of 1 pm. The Ge(Li) detectors were positioned at 0 = 0°,

J. Panqueva et al. / "Rb

369

30°, 40°, 55° and 115° with respect to the beam axis. In this way, small contaminant lines interfering with Doppler-shifted peaks could be detected . By analyzing the intensity of the Doppler-shifted and unshifted peaks and normalizing both to the intensity of the radiation emitted after Coulomb excitation in the Au layer or the Ta stopper, up to six independent lifetime measurements were made simultaneously for each state. The decay functions R(D) were analyzed with the program CRONOS 1°) . The effect of hyperfine deorientation during recoil in vacuum as well as the kinematical spread of the recoil nuclei were neglected for reasons discussed previously $, "). Since all lifetimes i.e. decay lengths, were found to be small, no solid angle correction was necessary. Doppler-shifted lineshapes were measured at 0 = 0° to the beam direction and at 50 and 58 MeV beam energy . Additional spectra were recorded at 0 = 90°. From the lineshapes of transitions from long-lived states which are not Doppler broadened the intrinsic detector response function was obtained. The targets consisted of 400,ug/cm2 and 300 Ug/CM2 65 Cu, evaporated onto Ta and Pb backings, respectively . The fit of the experimental lineshapes was carried out by means of GNOMON 1z) . The influence of the kinematical spread of the recoiling nuclei on the shape of the y-ray peaks was considered, as explained in an earlier paper "3). A gaussian energy distribution with a FWHM of 25 % of the average recoil velocity was used in the evaluation . The angular spread, estimated to be dB = 6°, was neglected, as was the finite solid angle of the Ge(Li) detector . According to Warburton et al. 14), the stopping power function was represented as : -mdv/dt = k, v/vo+ko (v/vo) -1 . For the calculation of the nuclear part k, Bohr's ansatz 15) and a parametrisation of Kalbitzerand Oetzmann 16) were used ; but no significant difference was found. When Bohr's formula was used, the angular straggling of the ions due to atomic collisions was treated in Blaugrund's approximation 1') . The electronic component ke [ref. ' 8)] has been estimated with the LSS theory : k e = 1 .2 kLss. The justification for this procedure and especially for the factorfe = 1 .2 is given by the good agreement of the DSA and RDDS results for the 1 .58 MeV -Y-+ state. In both methods, the continuum feeding time, which is typically rF < 0.1 ps in this mass region 19), was neglected because it is considerably shorter than all measured mean lives. To account correctly for the delayed feeding from the many discrete states with comparable lifetimes, great care was taken to determine the relative intensities and effective decay constants of all known feeder states . The effective lifetime of each feeder transition is defined by fitting a single time constant on the decay curve (RDDS) or Doppler-shifted lineshape (DSA) of the feeder transition ; in the case of rotational bands with decreasing lifetimes for increasing spin, this procedure usually reflects the feeding pattern with an overall accuracy of a few percent. The branching ratios and relative feeder intensities were taken from the 0 = 90° spectra, after corrections made for the energy-dependent efficiency of the Ge(Li) detectors determined from 15'Eu and 226 Ra sources z o) and the anisotropies of the angular distributions 1) .

370

J . Panqueva et al. / "Rb

50 0 DISTANCE

10 20 [jtm]

30

40

50

60

7

Fig. la. Recoil distance R(D) functions of the unshifted and Doppler-shifted component of the 875 keV * -. + transition in e' Rb. The insert shows a DSA fit to the line shape of this transition taken with a tantalum backing.

10 z

w z 103

Fig. Ib. R(D) functions of the 612 keV }- -. j - and the 760 keV I - -+ }- transitions between negativeparity yrast states.

s J. Panqueoa et al . / `Rb

371

TABLE I

Summary of lifetime measurements in e 1 Rb Transition E~ (keV) 709

I,

/`

loam energy Angle 9' (MeV)

-Y +

Î`

55

E, (eV) 623

875

+

8.7(5)

30 40 0 55 0

1 .3(2) 1 .2(1) 1 .1(2) 1 .4(2)

DSA:

0.31(4)

1 .25(10)

DSA :

1 .5(2) 1.2(2) 1.2(2) 1.2(l) 1 .25(20)

58

0

DSA:

0.6(2)

DSA:

0.16

0.6(2) d)

4-

55

0 55

340(140) 260(140)

+

55

v*

58,50

1024

-~L*

154

154

1-

613

459 613

17 71 -

}}-

55 55

0 55

5.0(6)

760

-

}-

55 55

30 40 0

1.6(3) 2.3(4) 2.2(3)

55 55 55

0 40 0

1.5(9)

55 55

30 40 55

4.7(4) 5.((4) 4.0(4)

55

30

2.0(4)

1740

2577

503 804

826

838

(

-

-

-)

-

(I~ )

adopted

9.0(3) 10 .5(9) 8.1(3) 7.7(5)

2608

1417

previous `)

8.6(2) 8.9(2) 8.7(2) 8.4(3)

55

914

FP ')

SP `)

lifer (ps)

30 40 0 55

55

1584

Mean

(I~ )

30

8.7(4)

300(140)

5.5(5)

5.3(5)

2.2(3)

2.1(3)

5.3(5)

1.6(2)

1 .4(2) 1 .4(2)

5.4(4)

1 .5(2)

4.8(5)

2.0(4) d)

`) SP denotes unshifted peak. ") FP denotes Doppler-shifted (flight) peak. °) Ref. 2). d) Effective value not corrected for feeding.

Some decay functions and the line shape of the 875 keV -y-+ -a Y+ transition are displayed in fig. 1 . The results are given in table 1 . The good agreement of the individual lifetime values for the 1 .58 MeV 4+ yrast state supports strongly the new value of T = 1.25 f 0.10 ps in contrast to the old value of 2 = 0.31 ps. [ref. 2)] . A rough evaluation of the 154 keV I - -" I - transition yielded an estimate of T (154) = 300 f 140 ps.

J. Panquena er al. / e' Rb

372

3. Discussion 3 .1 . THE POSITIVE-PARITY STATES

The properties of the positive-parity levels of S'Rb have been very satisfactorily interpreted by Toki and Faessler s) with the asymmetric rotor-plus-particle model (AROVMI) 2'). The assumption of triaxiality turned out to be very important in order to reproduce the nonfavoured states as well as two additional, presumed I = !?+ and 'I + states . In its simplest approach, the model couples one 1 g3 proton to an asymmetric (y-deformed) rotor with variable moment of inertia via the quadrupole interaction. The strong Coriolis force leads to a decoupled band of states with the spin sequence I = j = 1, j+2, j+4, . . ., and with energy spacings very similar to those of the ground-state band of the adjacent even-even core . In the actual more realistic version, the odd quasiparticle is allowed to occupy two single-particle shells, e.g. lg t and 2d ß . Due to spin flip, the contributions of other possible admixtures are small as has been pointed out in ref. 3 ) . We repeated the AROVMI calculations with a slightly different choice of parameters . Again, the values of the deformation parameters were taken from the even core. The quadrupole deformation ß = 0.27 is evaluated from the 21 -+ 0, E2 transition strength and the asymmetry parameter y = 26° isextracted from the energy ratio E2+IE2~ of the first and second excited 2+ states, according to the Davydov model. The VMI parameters 0 o lh 2 = 5.33 MeV - ' and C = 0.021 MeV' are fixed to the experimental level scheme of e°Kr. The energy gap of d = 1 .83 MeV is calculated from the odd-even mass difference . The Fermi energy AF and the difference ofthe spherical gt and d,t single-particle energies labelled ED are estimated from the Nilsson scheme, but both parameters are then slightly varied in the fit so that the low-spin states are reproduced . The result of the fit is displayedin fig. 2. Also shown is a fit with the interacting boson fermion model (IBFM) by Iachello and Scholten 22), taken from ref. 23). Both models provide about equally good fits . From the experimentally deduced B(E2) values in e' Rb which are summarized in table 2, and the s °Kr B(E2, 2 -+ 0) value, one calculates the ratios : R, - B(E2,12+ -+ 1 +)/B(E2, 2+ -" 0 + ) = 1 .37(8), (3) R Z - B(E2,

+ -. zE)/B(E2, i~ + -+ +) = 1 .29(13),

R3 - B(E2, ~+ -+ ~+ )/B(E2, 4 + -> 2+) = 1 .38(16).

(4) (5)

They are in good agreement with the respective theoretical values of Rl = 1 .4, R 2 = 1 .25 and R3 = 1 .1 computed with an effective proton charge of e, = 1 .5e. This good agreement is also displayed in fig. 2, where the experimental transition strengths are compared with the predictions of the AROVMI model. The previous 2 ) discrepancy for the 121' -+ -V + and ~-+ -+ 17 + strengths has been removed, and experiment and theory are in accordance now. Also inserted into fig. 2 are the

J.

Ex ( Mev) 2 .5

Panqueua et al. / s' Rb

373

6'

115/21

17,2'

(1112'

10

1112'

4'

i

9/2' 0

Fig . 2 . Energies and B(E2) values of the positive-parity yrast states in s'Rb compared with the predictions of the asymmetric rotor-plus-particle model (AROVMI) and the interacting boson fermion model (IBFM) . For details see the text .

predictions of the IBFM 23), which gives a similarly good fit. In this connection it should be mentioned that there is no indication of a boson cut-off as has been observed by Panqueva et al. 2°) in the neightbouring nucleus '9Rb, but more precise 2 B(E2) values of stretched transitions in s' Rb TABLE

Ey (keV) 613 760 804 826 838 623 875 1024

I;'

If'

11 -

4-

(S,- ) (

-)

_1~ +

+ ~}+

}-

1-

1+

+ +

Branching ratio (%)

B(E2) (e' - fm`) exp

30(3) 67(2) 88(5) 96(2) 100

555±s °o 1080-1éó 1430 _+ 1;°0 425±48 g90+25ó

100 100 100

989(55) 1270(100) 1210±ióó

AROVMI-1 AROVMI-2 509 866 1037 1251 1464

243 699 830 1070 1352 1056 1317 1529

37 4

J. Panqueva et al. / e' Rb

values of the ~L + -. Y+ and higher-spin E2 strengths are required before any conclusion on this point can be drawn. Like in '9 Rb both approaches underline that the gt proton acts as a Coriolis coupled spectator without polarizing the deformed "Kr core . 3.2 . THE NEGATIVE-PARITY STATES

The spin and parity of the ground state of s' Rb has been experimentally deduced by Ekstróm et al. zs) as Ix = j - . Friederichs et al. 1) found a quasirotational band built upon this level with the spin sequence I, I+ 1, . . . . which is strongly perturbed with respect to a simple Nilsson band . The authors attributed the observed energy staggering to the mixing of the close lying p,, f,, and p3 shells . No lifetimes have been published up to now. We performed AROVMI calculations also for the negative-parity band, using the same deformation and moment of inertia parameters as for the positive-parity states . Again the values of ED and 'F were optimized to the spectrum and varied in the limits given by the Nilsson estimation. Since the AROVMI computer code accommodates only two orbits, we performed two-shell calculations with either f.-p,. (AROVMI-1) or f p., (AROVMI-2) mixing . The third possibility p,:--p, can be ruled out, because the oscillator potential is filled up to the L2 = I orbital of the f., shell for the deformation ß n, 0.3 . The two fits to the level scheme are given in fig. 3 together with the experimental level scheme . The f,-p, interference gives slightly better results with an average deviation of 45 keV in comparison to 52 keV for the f,-p, admixture, although the attainable agreement is worse in the former combination. This result can be explained by a decrease of the ftp, interaction due to the opposite spin direction. From the amplitudes of the single-particle wave functions listed in table 3, one sees that in the AROVMI-1 approach the states up to - contain a 60-90 % - [301] - state. In the AROVMI-2 case, component, which decreases to 40 % for the the situation is less transparent. There the main contributions for the same states come from the 0 = J, K = J orbital of the pi shell (30-95 %) and the 12 = 1, K = j orbital of the p- shell (30-65 %).This makes the f.,-p, assumption less plausible, because jK-d2j = 2 demands a stronger dependence on the y-deformation which cannot be verified experimentally . E2 transitions. The K = I structure also is demonstrated by the E2 transition strengths. The theoretical predictions in fig. 2 and table 2 have been obtained with the same effective proton charge ep = 1 .5e as in the positive-parity band. Once more AROVMI-1 reproduces the experimental data slightly better than the AROVMI-2 calculation. Both two-shell mixtures underestimate the collectivity of the ~- level by 30-50 %. The exceptionally long lifetime of the -u- state and the possible decrease going to the .17 - state may indicate that these states contain large three-quasiparticle contributions, as has been discovered by Gast et al. e) in the neighbouring "Rb,and

J. Panqueua et al. / e' Rb

Ex (MeV)

B(E2) (e2 fm4 )

2 .5

81Rb

375

BIMI)

NEGATIVE PARITY STATES

(MWU)

AROVMI-1 (f5dp, 2 ) --- AROVMI-2 (k2- p3d AI =-1

AI =-2 2.0

p312

200

2000

100

1 1 .5

srr

1 .0

50

1500

- ttl

í i

ii

I I

i

1000 AROM-1

20 10

' AROV111-7

5 a5

500 2

0L

AROVMI-1

3r2 EXP

0

AROVMI-2

512

912

1312 1712

512

912

1312

1

Fig. 3 . Negative-parity yrast states in 8 'Rb . Left-hand side : Comparison of energies with AROVMI-1 05/2 - PI /2 mixing) and AROVMI-2 (173,2-Pan mixing) calculations . Right-hand side: Transition strengths of stretched E2 and M 1 transitions . The theoretical estimates of the d/ = -1 M 1 transition strengths refer to 13 312 and 17512 single-shell calculations and the two-shell calculations mentioned above.

TABLE

3

Single-particle energies E, and compositions of intrinsic AROVMI wave functions 12) for ~ = 26° in 2') terms of Nilsson basis states (; = (r)lji2) : ja) = j jrA-)t -a C ji UQ) : for details see ref. a

Ea (MeV)

Q=}

f512

f512 ß=-}

AROVMI-1

1 2 3 4

-4 .6 -0 .9 1 .8 5 .1

-0.87 0.02 -0.32 0.36

0.19 0.92 -0.29 0.15

0 .01 0 .12 0 .73 0 .67

AROVMI-2

1 2 3 4 5

-4 .5 -3 .3 -0 .8 2 .1 3 .5

0.33 0.80 -0.44 -0.15 -0.15

0.13 -0.52 -0.64 -0.54 -0.07

-0 .11 -0 .09 0 .04 0 .15 -0 .98

f512

Q=}

Pan

Q=-4

P312

Q=4

PI 12 ld =} -0 .45 0 .35 0 .53 0 .63

0 .25 -0 .20 -0 .48 0 .81 0 .09

-0 .89 0.18 -0 .40 0.07 0.08

37 6

J.

Panqueva et al.

/

s' Rb

recently discussed for the case of e t Rb by Funke et al. 29) . Gast et al. 6) assigned an intrinsic [(f,, gt) core (& g ] configuration to the band starting with the second ~state at 2.31 MeV. The three-quasiparticle configuration proposed by Funke et al. 29) involves a broken g proton pair which may be responsible also for the backbending observed in the ground-state band of ' o Kr. Unfortunately, no further members of such (3qp) bands are known in BtRb at high angular momentum . MI transitions . The experimental M1 transition strengths determined from the measured branching ratios and lifetimes are of the order of B(M1) = 2-30 e Z . fMZ . They are compared in table 4 with the predictions of the asymmetric rotor-plusparticle model described above. In addition to the two-shell calculations we also performed ones in which the particle was restricted to move in either the p,, f, or p, shell. It is obvious that these latter calculations do not reproduce the experimental values . In particular, pure p t or f, configurations underestimate very strongly the B(M1, - -. -) and B(M1, z- -. -) values, whereas the predictions with a pure p, configuration are systematically too high (with the possible exception of the I - -. J - M1 strength). On the other hand, it is very clear that a considerable p,t component is required in order to reproduce 'the measurements . Turning now to the two-shell calculations we find that the theoretical values are still too low by a factor of about ten. On the other hand, the trend of the data with the spin is fairly well reproduced in AROVMI-1 (f,p,) . It would thus seem (although we are not able to prove this hypothesis now) that all three orbits are required in order to account for the size and spin dependence of these M1 transitions . TABLE 4 M1 transition strengths B(MI) for negative-rarity yrast states in e'Rb, experimental and AROVMI calculations

B(M 1) x

Transition 1"

lff

F,(keV)

a-

154 459 ") 301 ') 503 9) 323 5)

11-

d)

single shell

exp 5.7±1 :9 38 ±' 4 .0±ó :65 1 .6±0 .2 0.

7

26

') Triaxiality y = 26°; g =. 1.0 . AROVMI-1, g = 0.6 . `) AROVMI-2, g = 0.6 . E2/M1 mixing ratio ó = 0.14±0.03 [ref. °) ó = 0.30±0.06 [ref. ')]. 1) ó = 0.013±0 .002 [ref.')] . 5)~ Assumed ó = 0.

b)

d)

10° (e' -

fm') two shells

')

Pare

f5n

Pin

f5/2-PI/2 °)

f5n-Pan `)

19 30 18 38 21 48

0.1 0.0 0.3 0.0 0.2 0.0

0.7 0.0 0.7 0.0 0.6 0.0

0.3 0.3 0.7 0.4 0.9 0.5

16 0.2 1 .0 0.5 2.5 1 .7

J. Panqueva el al. / s' Rb

37 7

In conclusion, we have demonstrated that large a portion of the energies and electromagnetic transition strengths of high-spin states in e t Rb can be understood in terms of the asymmetric rotor model with one particle in a single shell (positiveparity states) or at least two shells (negative-parity states) acting as a spectator of the a °Kr core . A consistent picture for the yrast states of both parities has therefore been designed. In spite of the rather large quadrupole deformation of ß = 0.27, a well-developed rotational aligned g., proton band was observed with E2 transitions in agreement with the RAC model. This is in agreement with results obtained with ' 9Rb [ref. 2")] and seems to be a consequence of just this large deformation. When moving higher in mass number to "Rb it was recently found 2e) that a weak-coupling description works best ; on the other hand, when going to the odd As isotopes, a strong polarization of the core was deduced from the + -. + E2 strengths with respect to the corresponding Ge cores 27, 28 ). Although two-shell calculations for the negative-parity states are quite successful in explaining the energies and E2 strengths, they fail on the M 1 transition probabilities which are most crucial in determining the correct contributions of the p,, f, and p . single-particle wave functions. As the stretched E2 transition matrix elements are not very sensitive to the details of the single-particle orbit(s) considered, the negativeparity states may still be a helpful tool with which to establish the collective features of the core, but they lack the simplicity of the g-, intruder orbit. The authors are particularly grateful to Prof. A. Faessler and Dr. H. Toki for providing the AROVMI code, and Prof. A. Gelberg and U. Kaup for fruitful discussions. The help of Dr. J. Keinonen with part of the analysis is appreciated. References 1) H . G . Friederichs, A. Gelberg, B. Heits, K. O . Zell and P . von Brentano, Phys. Rev . C13 (1976) 2247 2) H . G . Friederichs, A . Gelberg, B . Heits, K . P. Lieb, M . Uhrmacher, K. O . Zell and P . Von Brentano, Phys . Rev . Lett. 34 (1975) 745 3) H . Toki and A . Faessler, Phys . Lett. 63B (1976) 121 4) E . Nolte and P . Vogt, Z. Phys . A275 (1975) 33 5) H. Schäfer, A. Dewald, A . Gelberg, U . Kaup, K . O. Zell and P. von Brentano, Z . Phys . A293 (1979) 85 6) W . Gast, K . Dey, A . Gelberg, U . Kaup, F . Paar, R. Richter, K. O. Zell and P . von Brentano, Phys. Rev . C22 (1980) 469 7) U. Kaup, diploma thesis, 1979, unpublished 8) M . Uhrmacher, thesis, University of K61n, 1973, unpublished ; K. P . Lieb, M. Uhrmacher, J . Dauk and A. M . Kleinfeld, Nucl . Phys. A223 (1974) 445 9) T. K . Alexander and S . Bell, Nucl . Instr . 81 (1970) 22 10) H. P . Hellmeister, diploma thesis, University of K61n, 1976, unpublished 11) R . Rascher, M . Uhrmacher and K . P. Lieb, Phys. Rev. C13 (1976) 1217 12) Ch . Keveloh and H. P . Hellmeister, University of Göttingen, 1980, unpublished 13) H. P. Hellmeister, J . Keinonen, K . P . Lieb, U . Kaup, R . Rascher, R . Ballini, J . Delaunay and H . Dumont, Nucl . Phys. A332 (1979) 241 14) E. K . Warburton, J. W. Olness and A. R . Poletti, Phys . Rev . 160 (1967) 938 15) N . Bohr, Mat . Fys. Medd . Dan . Vid . Selsk. 18, no . 8 (1948)

37 8

J.

Panqueva et al. / s'Rb

16) S. Kalbitzer and H. Oetzmann, Invited paper Int. Conf. on ion beam modifications of materials, Budapest, Hungary, 1978 17) A . E. Blaugrund, Nucl . Phys . 88 (1966) 501 18) V. Lindhard, M . Scharff and H . E . Schiott, Mat . Fys . Medd. Dan . Vid . Selsk. 33, no . 14 (1963) 19) H . P . Hellmeister, K . P . Lieb and W. Müller, Nucl. Phys . A307 (1978) 515 20) V. Zobel, J . Eberth, U . Eberth and E . Eube, Nucl. Instr . 141 (1977) 329 ; V. Zobel, thesis, University of K61n, 1976, unpublished 21) H . Toki and A . Faessler, Z . Phys. A276 (1976) 35 ; Nucl. Phys . A253 (1975) 231 22) F . Iachello and O . Scholten, Phys. Rev . Lett. 43 (1979) 679 23) U . Kaup, University of K61n, 1980, unpublished ; P. von Brentano, A . Gelberg and U . Kaup, Contribution to the Workshop on interacting Bose-Fermi systems in nuclei, Erice, Sicily, 1980 24) J . Panqueva, H . P. Hellmeister, F . J Bergmeister and K . P. Lieb, Phys. Lett. 9í8B (1981) 248 25) C . Ekstr6m, S . Ingelmann and G . Wassenberg, unpublished 26) L . Lühmann, diploma thesis, Göttingen, 1981, unpublished 27) H . P. Hellmeister, E. Schmidt, M . Uhrmacher, R . Rascher, K . P . Lieb and D . Pantelica, Phys . Rev . C17 (1978) 2113 28) B . Heits, H . G. Friederichs, A. Gelberg, K . P . Lieb, A . Perego, R . Rascher, K . O . Zell and P . von Brentano, Phys. Lett . 61B (1976) 33 29) L . Funke et al ., Nucl. Phys . A355 (1981) 228