Magnetic-moment and lifetime measurements of Coulomb-excited levels in 79Br

Nuclear Physics A578 (1994) 300-316

NUCLEAR PHYSICS A

Magnetic-moment and lifetime measurements 79 of Coulomb-excited levels in Br K.4j. Speidel a, G. Jakob b, J. Cub c, S. Kremeyer a, H. Busch a, if. Crrabowy a, J. Gerber d, J. Rikovska e,% K. Heyde 9 a

Inssti%t, fair StrnWen- und Kernphysik, Univ. Bonn, Nussallee 14-16, W-53115 Bonn, Germany

'b Physik-Dept. Zecßn. Univ. München, James-Franck-Str., W-85748 Garching, Germany ` Gesellschaft Schwerionenforschung, Postfach 110552, W-64220Darmstadt, Germany Centpe de Recherches Nucléaires, F-67037 Strasbourg, France 4 Dept. of Physics Univ. of Oxford Oxford, OX13PU, UK f Dept. of Chemistry, Univ. ofMaryland College Park, MD 20742, USA I LOoratoiiiim roar 1le®retzsche Fysica, Vakgroep Subatomaire en Stralingsfysica, Universiteit Gent, Proeftuinstraat 86, B-9000 Gent, Belgium Received 12 April 1994 Ast

ct

e g-%cton of the 217, 523 and 761 keV levels in 79Br have been measured using Cou cnib excitation of 79Br beams are the transient field technique with Gd as ferromagnetic host, Lifetimes of several state:. have been determined using the Doppler-shift attet%Uatioil method . Mixing ratios of y-u aasiYions were deduced from measured angular carriQlatiotts. The data are discussed in the framework of the weak particle-core coupling and the petifcle-axial-rotor coupling models.

Keyvorcis. (NUCLEAR REACTIONS 28Si(79Br, 79Br'); E = 214 MeV; measured y(O,H) in p41a4imd rid, (particle) y-coin, Coulomb excitation, DSA; 79Br levels deduced g, T1/2, 8; Mul'tilayered targets; Models comparison

1. Irotroduction

Properties of nuclear states in 79,81 Br have been previously studied in Coulombexcilatiort experiments (1--3] in which beside energies and spins also lifetimes, trarfsition probabilities, multipole mixing and branching ratios were determined. The guclear structure of the two stable isotopes at low excitation energies has been generally discussed in the framework where the odd proton moving in the 2p3/2 0315 ,9474/94/$07,00 ©1994 Elsevier Science B.V. All rights reserved SSDit 0375 -94740000219-V

K-H.

Speidel et al. /Nucear Physics AS78 (1994) 300-316

301

shell is coupled to a nearly spherical core using either weak [1,2,4-6] or intermediate [7,8] coupling schemes. The deformed-shell model including configuration mixing has been used by Sahu and Pandya [9] to describe the structure of collective bands in "-81Br nuclei. Scholz and Malik [10; took into consideration experimental evidence for static deformation in odd-A nuclei in the element region of 31 < Z < 37 by coupling the odd particle to a deformed core. Recently, in a systematic study, the first measurements of the magnetic moments of ground and isomeric states of unstable neutron-deficient Br isotopes in the mass region between A = 72 and 77 have been made using the low-temperature nuclear orientation technique [11]. These data provide strong evidence for non-zero ground-state deformation which is explained rather well by the particleaxial-rotor coupling calculations. In this work it was emphasized that the Br nuclei lie in the transition region between weakly deformed structures observed for As and Se nuclei and the more deformed nuclei of Kr and Rb. On the basis of measured ground-state magnetic dipole moments and_electric quadrupole data a smooth change in prolate deformation from the [301]i to the Nilsson configurations was found when going from 81 Br to 'SBr [11]. The [3121 1 low-lying states of 73 Br and '1Br were described in terms of shape coexistence between a less deformed oblate ground state and a more deformed prolate yrast band. Thus a prolate-to-oblate ground-state shape transition between Br and 73Br has been suggested . Experimental data presented in this paper include for the first time g-factors of excited states . This provides an extended basis for a more detailed study of the structure of excited states in 79 Br. Taking into _account that the measured spin and parity of the ground state of 79 Br is j7r = 3 and the energies of its low-lying states are comparable with the excitation energy of the first 2+ state of the neighbouring even-mass 78Se nucleus, a weak-coupling picture where the odd proton in the 2p3/2 shell model is coupled to the even-even neighbour appears as a likely description . The assumption of the proton nature of the ground state of '9B is strongly supported by the measured g-factor [12] of g = 1.404266(3),

which is as usual smaller than the Schmidt value (g = 2.53). The particle-core coupling model, in its most simple form, prescribes the coupling of the odd proton to the 2i core state to form a quartet of negative-parity states with spins of i, 2, i and 2. The states m Br at 306, 523, 606 and 761 keV possess these spins and have been considered as the prime candidates for this excited multiplet due to their strong Coulomb excitation (see Fig. 1). The further justification of these states as members of a single multiplet is their spin-weighted energy average of 613 keV which is in excellent agreement with the 2, core energy in 78Se of 614 keV generally considered as a salient feature of the weak-coupling picture . Another signature of the model in its simplest version (extreme weak-coupling limit) refers to the B(E2) values of the multiplet transitions to the ground state which ought to be the same and equal to the B(E2, 2 1 -+ 0,') of the even-even neighbour.

302

K-H. Speidelet al. /Nuclear Physics A578 (1994) 300-316 Ex [keV]

J; (7rT2)

1

954

(1R ,31r (3i1-XT 7/2i

832 793 761

(3fra)

606

Sil2

523

(3/T3)

397

(1i2' ) 3x12 V271

306 261 217

31T,

0

35Br44

Fig. 1. Low-level scheme of 79Br from Coulomb excitation. The ground state and the excited states assigned as members of a multiplet from particle-core coupling are marked by thick lines.

Moreover, M1 transitions from the multiplet states to the ground state should be strictly forbidden ; any MI admixtures to the E2 transitions can therefore only result from configuration mixing . Experimentally these simple prescriptions of the model are in general not rigorously fulfilled. An alternative approach is based on the assumption of strong coupling of the odd proton to a deformed 78Se core. Possible evidence of a sizable static deformation has been predicted in a number of papers (see e.g. Refs . [11,13]). This model yields a number of low-lying deformed states (mainly originating from the spherical 2p3/2 and 1f7/2 orbitals) and the collective bands built on top of these intrinsic excitations . Although strongly _mixed (see Section 3.2.2), one can distinguish two structures, one _based on the i ground state with excited states at 217 keV (? _) and 761 keV ( i ), and another based on the i state at 261 keV including the 2 level at 523 keV. The ground-state band_ has been observed in in-beam spectroscopy by Schwengner et al. [14]. The 2 state at 306 keV is probably another bandhead ([3211-1- ) originating from the spherical 1f7/2 orbital mainly, and the associated structure is strongly perturbed_ by Coriolis interaction. In this scheme it is much harder to understand the two i states at 397 and 606 keV. As discussed

K-H. Speidel et al. /Nuclear Physics A578(1994) 300-316

later (Section 3.2.2) at least one of them remains unaccounted for in the present model. This likely results from the fact that all calculated excited states are regarded as having the same deformation as the ground state. The particle-rotor calculations are restricted to the calculation of nuclear properties at a single deformation, so all eflects resulting from shape coexistence are lacking at present. The present work focusses mainly on magnetic moments of low-lying states in 79 Br which, except for the ground state, were completely lacking. In addition, lifetimes of most states have been remeasured or newly determined with high precision, allowing determination of B(E2) values of the most prominent transitions using E2/M1 mixing ratios deduced from angular-correlation measurements. As the lifetimes are in the ps range, magnetic moments can be measured best by employing the transient magnetic fields (TF) which arise when the ions penetrate ferromagnetic layers with high velocities [15]. In the present measurements, ferromagnetic Gd was used in which the TF strengths are generally larger by a factor of 1.4 compared to Fe at equal ion velocities . Another advantage of Gd over Fe is its smaller stopping power which allows the use of thicker Gd layers for a given energy loss of the ions resulting in longer interaction times with the TF and larger precession effects. These favourable properties, utilized in many earlie;measurements, were essential for the present experiments. 2. Experimental procedure and data analysis Low-lying states in 79Br (Fig. 1) were Coulomb excited up to an excitation energy of = 1 MeV by scattering a 79 Br beam of 214 MeV in energy and = 3 pnA intensity from a Si target. The ion beams were provided by the Munich tandem accelerator. Targets consisted of 0.85 mg/cm 2 thick natural abundance Si which was evaporated on a 4.4 mg/cm2 thick Gd layer backed by a 1.0 mg/cm2 Ta foil followed by a 1.35 mg/cm2 thick Al layer. The composition and sequence of the various target layers were chosen for the following reason : Si was used for Coulomb excitation and Gd for spin precession ; the Ta foil served aas substrate for the preparation of the Gd layer which was vacuum deposited on the substrate at a temperature of 800 K to obtain good ferromagnetic properties [16]; finally the Al layer was used for good thermal conductivity during beam borubardment . For magnetization of the target it was cooled to liquid-nitrogen temperature. An external field of 0.03 T was applied which was found to be sufficient for magnetic saturation. The y-rays emitted from Coulomb-excited levels in 79 Br were measured with four intrinsic Ge detectors of 30% efficiency and 9 x 9 cm2 BaF2 scintillators in coincidence with forward-scattered Si ions registered in a Si detector at 0° to the beam direction . The beam particles were stopped in an Al foil of 4 mg/cm2 thickness placed between target and detector which was thin enough to let the Si ions pass through to the Si detector. The corresponding Coulomb-excited Br ions were moving with a mean velocity of 2.5 0 (vo = ,3,c) through the Gd layer and

K-N. Speidel et al. INuclear PhysicsA578 (1994) 300-316

304 40

v 217

79

Br

10

400

200

600

800

EY[1ceV]

Fig. 2. y-coincidence spectrum from a Ge detector placed at 0° to the beam direction. All prominent lines are marked.

were stopped in the adjacent backings . A Ge detector of 45% efficiency at 0° was used to measure the lineshape of Doppler-shifted and -broadened y-lines for determining the lifetimes of the excited states . Fig. 2 shows a coincident y-spectrum from this detector. Particle-y angular correlations have been measured for several transitions . As seen in Fig. 3 most of these correlations exhibit very small anisotropies which are a consequence of the spins involved and the E2/M1 mixing ratios of the y-transitions. From a fit to the data using the angular correlation function W(O,) =1 +A'PP2(cos O,y ) +A 4 PP4(cos O. y ), we obtained the correlation coefficient values listed in Table 1 . Precession angles were derived from measured double ratios B of coincident counting rates with fields applied perpendicular to the y-detection plane alternately in the "up" and "down" direction. These are given by [17] _

FR - 1 tiW

+1

1 dW -

-1

W dOy

where (1/W )dW/dO,y is the logarithmic derivative ("slope S") of the angular correlation function which was determined for each angular correlation at angles O.y = ± 50° of the detectors with optimum sensitivity to the precessions (see Table 1). The precession angles can be further expressed as =g

AN h

BTF teff

where g is the g-factor of the nuclear stale and BTF the effective TF acting at the nucleus for a time reff . The latter were calculated for the well-determined reaction kinematics using the nuclear lifetime r and stopping powers [18] to determine the

K-H. Speidel et al. /Nuclear Physics A578 (1994) 300-316

305

Angle t) y

Fig. 3. Measured y-angular correlations of various transitions in to the data.

79

Br. The curves are least-squares fits

Table 1 Measured angular-correlation coefficients and derived slope values at the detection angles ®,y = ± 50° for the precessions . The deduced mixing ratios are compared with earlier data [191 Aexp Aexp 8 J; -I, Jf ISI E., (keV) 2 4 217 306 523 544 606 761

21

21

(i )-~ 31

22

21

21

21

(24 )- 21 zt

21

present

earlier

-0.001(2)

0.087(17)

0.08(3)

0.088(30)

0.029(15)

-0.013(15)

-

-

0.13(2)

0.036(4)

-0.021(14)

0.055(6)

0.26(3)

0.21(5)

0 .059(2)

0.127(29)

0.074(1)

> 100

0.19(6)

-0.018(42)

0.051(53)

-

-

0.30(3)

0.493(8)

00

00

-0.053(12)

0.352(7)

-0.067(10)

3Qfi

K-.91 Speidel et al. /Nuclear PhysicsA578 (1994) 300-.316

Tobt 7 Wasared lifetimes and deduced values of B(E2) and B(M1) in Weisskopf units (B W) compared to ezaclier data 1191 Ey T (PS) B(E2) B(M1) I; (10'3 W.u.) a (W.U.) a (keV) (keV') present earlier

~23 6 7161 7161 710 793

2r

217

za ( io

523

2.76(8)

606

2.70)

238

2.1503)

21

544

2.17(5)

761 793

306

1

zr

(_3

~,

2^)

68(5) 6.10)

7407) 1202 .5) 1.9(6)

8(6)

45(1)

4102)

179(2)

21(5)

2.90)

10(2)

2.160)

1.70)

250)

302)

-

22(1) b

-

8(1) b

954 1.6(1) (zz ) Pt,,(2) -- Z0,13 (eZfrh4), BW(MI)=1.79 wN" 8%t%Ai4X Aare Iv2 . 9'54

680) 320)

t11cS4 entrance (ti) and exit (t2) times of the ions in the Gd layer (see Table 1): T exp ---

t'

- exp _ t2

the onpulax correlations have in general very small anisotropies, the precession angles depend strongly on the magnitude and accuracy of the specific slope values (set Uble 1), This circumstance was a great challenge in the experiment and

p>`Qbably one reason why these measurements were not done before . bar the determination of the g-factors from the measured precessions (Table 2) the lifetimes had to be known to sufficient accuracy . Since this information was g~:Aeiaily lacking we measured simultaneously the lifetimes of most excited levels rmay3Ag the Doppler-shift attenuation method . This was achieved by analyzing the tricasnred Doppler-broadened lineshapes of the -y-transitions observed with a ire detector, After background and random subtraction the experimental lineShapes were fitted applying stopping powers to Monte Carlo simulations including the Secdind-order Doppler effect as well as the finite size and energy resolution of the Gc detector. e lifetime of the 761 keV level (Fig. 4), which was not accurately known, was obtaiAed from the analysis of three different y-rays emitted from this level (Fig. 1): the Z38,544 and the 761 keV -y-lines (see also Figs. 2, 4 and 5). As seen from Table Z tbl~Y agree very well within error. 'Tbo, error on the lifetime of the 217 keV level was significantly reduced. The tiFetine of the 306 keV state was found to be substantially sl;o;rtPr than previously reported .

K-H. Speidel et al. /Nuclear Physks A578 (1994) 300-316

307

Er = 761 keV T = 2.16(5) ps

M

0 y 0

U

760

780

800

E,i,[keV] Fig. 4. Observed and calculated lineshapes of the 761 keV y-transition. The curve sho-a is a best fit to the data which includes the stopped component ef the 793 keV transition (see Fig. i~

T

20

. Er = 523 keV

15 Ô

ti = ?'36(8) ps E,t= 544 keV ti = 2.17(5) Ps

10

0

a 0 U

520

540

560

E,r[keV]

Fig. 5. Observed and calculated lineshapes of the 523 and 544 keV -y-transitions . The t..ro curves shown are separate best fits to the data which have been drawn together .

All data are summarized in Table 2. Fig. 5 shows fits to the close-lying 523 and 544 keV y-lines . 3. Results and interpretation 3.1. Mixing ratios and reduced transition probabilities

From the measured angular correlations, E2/M1 mixing ratios of y-transitions were deduced . These data (see Table 1), which agree except for the 544 keV

308

It.-N. Speidel et al. /Nuclear Physics A578 (1994) 300-316

transition with earlier results [19], combined with the lifetimes of the nuclear states (neglecting the small total-conversion coefficients), yield reduced transition probabilities B(M1) and B(E2) which are given in single-particle Weisskopf units (W.u.) in Table 2. As seen from Table 2 the B(E2) values of transitions between the multiplet states and the ground state are considerably enhanced over the single-particle estimates and are reasonably comparable in magnitude with each other and with the B(E2, 2i --), Oi) = 34(1) W .u. of the even-even core partner 78Se [13]. The relatively small B(E2) value of the 606 keV state (a factor 3 smaller than the even-mass neighbour) very likely results from configuration mixing with the ground state. Configuration mixing is generally required to account for the non-zero M1 transitions between the multiplet stags and the ground state. However, as seen from Table 2, all M1 transitions are slow compared with the single-particle prediction. 3.2. Magnetic moments

To extract g-factor values from the measured precessions one needs the effective TF in the experimental ion conditions. As the TF is a priori not known and a calibration with a known g-factor was not feasible we have used the empirical linear parametrization as given by BTF = aZvlvo, where a is the strength parameter which was determined from many data [20] to be 12 T for the Fe host and 17 T for the Gd host (see also [211). This parametrization has been tested in several recent measurements [17,22] and was found to be a reliable description of TF at moderate ion velocities ûs long as heavy-ion-beam-induced attenuation effects can be excluded (see e.g. [23,24]). In the present case the Br ions have a rather low mean velocity in the Gd layer of 2.5vo. However, in the context of these attenuations the Br projectiles are heavy ions with a mean d E/dx of 16 MeV/pm in Gd. The stopping-power dependence of these perturbations [24] is sufficient to anticipate an attenuation of the TF strength leading to deviations from the calculated value (Eq. (5)) . However, at the low velocity of the Br ions the TF is associated mainly with 4s and 3s electrons, outer orbitals of the Br ions, where the attenuations are generally less pronoun,--ed. The orbital dependence of the attenuation mechanism has been studied in earlier specific measurements [25,. On the basis of these results the calculated value of the effective TF (Eq. (5)) at the mean velocity of 2.5vo, BTF = 1 .49(15) kT, has been used for the analysis of the precessions in determining the g-factors . The error accounts for an eventual small attenuation which was estimated from extrapolations of previous and new data [24,26].

K-H. Speidel et al. /Nuclear Physics AS78 (1994) 300-316

309

Table 3 Measured precesssion angles and deduced g-factors using calculated effective times . The g-factors deduced rely on the linear parametrization of the TF (see text) E, (keV)

J;

teff (PS)

VP (mrad)

g(J;) b

217

5 ?t 5?2

1.08(2)

3400)

0.4(1) a

0.840)

6309)

1.10)

0.78(1)

63(36)

1.1(7)

0.78(1)

29(3)

0.53(8)

523 544 761 a

?t

ii

Corrected for feeding from the 761 keV state via the 544 keV transition. The effective time quoted refers to the direct population of the level (see Fig. 1 and text). b Uncertainty of TF value is included.

In spite of the weakly anisotropy angular correlations associated with the E2/M1 mixed y-transitions we succeeded in measuring the magnetic moments of two short-lived levels at 217 and 523 keV both having spin and parity i . The 523 keV level is a member of the multiplet. In addition, the g-factor of the 761 keV state decaying by pure E2 to the ground state has been measured, the larger anisotropy of its angular correlation giving a more accurate result. The 544 keV transition from the same 761 keV level could also be used to obtain additional information on this g-factor, with less accuracy due to the poorer angular correlation (see Figs. 1, 2 and Table 3). The weighted mean of the two measurements yields g(761 keV) = 0.54(8) . All the values quoted in Table 3 were deduced from the measured precession angles applying Eq. (3). The g-factor value of the 217 keV level required a more ciaborate analysis as the measured precession (Table 3) had to be corrected for -mbstantial feeding mainly from the 761 keV level via the 544 keV transition. In contrast, the feeding of the 523 keV level was a negligible correction. In the presence of a feeding component, the measured angular correlation and double ratio R consist of two parts: one is related with the direct population of the 217 keV level and the other refers to the feeding or indirect population from the excited 761 keV level. For the latter both states with their specific g-factors contribute to the precession. If a is the fraction of the direct-feeding intensity in the 217 keV transition the angular correlation is given by (6) Wtot(19.y) = (1 - a)Wd(Oy) + aWina(ey)~ and if both precessions in question are small, R (see Eq. (2)) can be expressed as R = 1 + [(1-a)E a +aE;na ], where dWa/dOY Ea = 40a Wtot(Oy)

(7)

(8)

K-H. Speidel et al. I Nuclear Physics A578

310

and Eind = 40;nd

with

and

(1994) 300-316

dW;nd/d0y

(9)

Wtot(®y)

AN

Od - g(217) h BTF teff

Oind =

MN

g(761)

+g(217)

t2

Jt i

(10) t exp - -- BTF(t) dt T1 1

[exp(- t ) - exp T 1 - T2 fi T1 T2

12

- t )IBTF(t) dt . T2

(11)

The dW/d®y values refer to the specific angular correlations where for the indirect population of the 217 keV level the 544 keV (i -> 2 ) corresponds to an unobserved transition. The values T1 and T 2 refer to the nuclear lifetimes of the feeding 761 keV and the 217 keV state, respectively. For BTF the linear parametrization (Eq. (5)) was used . As the angular correlations and slopes are well determined either from measurements or calculations, the only unknowns in these expressions are the fraction a and the g-factor of interest g(217) . From the y-spectra a feeding fraction a = 0.38 was estimated . Straightforward analysis yielded a g-factor value: g = 0.4(1). Since the slope values of the angular correlations in question and the g-factors of both the feeding state and the state of interest are very similar, this result is almost independent of a. For the interpretation of the experimental data two theoretical approaches have been considered: (i) the weak particle-core coupling model and (ii) the particleaxially-symmetrical-rotor model. 3.2.1. The particle-core coupling model The magnetic moment of a mixed state with a single-particle and a particle-core component which is described by a wave function of the form [27] Ij,mi= 1 - a2 Ij,mi+al2 ;®j' ;j,mi becomes, after some Racah algebra,

L(j) _ (1 -a2)w(j) +a2

(12)

1

[6+ j(j + 1) -j'(j' + 1 )]M-(2i ) ( 4(i + 1

1 e i '+1)+j(j+1) - 6]g(j') +2j'(j+1)[j (

(13)

For a pure core-coupled multiplet state 12'10 2p3/ : ; J, M>, the general expression . (Eq. (13)) reduces to the following result (ci = 1, j =j = J and j' = i) if one uses

K-H. Speidel et al. /Nuclear Physics A578 (1994) 300-316

the experimental (or "effective") values g(21) = 0.39(11) for the 78 Se co .- [13) and g (b = 1.464266(3) of the 79 Br ground state as the 2p3/2 proton state: J=2 :

J-

5:

2

g (22 - )

-

(59k2 ) = -

.!!-) ju ( 2 i ) +N,( 7 2

11 (2+) + 13 3 14~ 1 21~(21 5

2

3

+

1

) =0 .77 (±0.22),

3-

- sl~(21 ) + 5A( 21 ) = 0 .59, 3 2

J= 1 :

g ..

J-1 : 2

1 - - 2W( 2+ ) - 31~( 21) _ -0 .62 . 1 g(2 ) 2

Comparing these data with the measured values of the 761 keV (J W = 2 ) and the 523 keV (J 7r = i _) states there is marginal agreement due to the large error of the g-factor of the core state. , 'e have also considered admixed configurations . 2 state (E = 761 keV). Admixtures of a 1f7/2 proton component to the 12 +1 ® 2p3/2 ; 2 > multiplet state leads to the expression (see Eq. (12)) ) =a2 .0.82+(1-a2) .1 .42,

g(2

using gs = 0.7g free . This, however, can only make the discrepancy larger indicating that the J~ = 2 state is most probably a rather pure 12i ® 2p3/2 ; z > state bearing in mind that the 1f7/2 shell is mainly closed in ' 9Br. Other components like 12i ®1f5/2 ; 2 ), resulting into a g-factor of --

18tL(2 i)

+ 4s'A(1f5/2) i

might intervene which, in case of negative interference, could bring the value of the ure core-coupled state in the direction of the experimental value. 5states (Ex = 217 keV and Ex = 523 keV). For these levels mixing between the 1f5/ 2 proton configuration and the core-coupled 12i ® 2p3/2 ; ? ) configuration is expected . For the purely collective part one obtains g = 0.77 (see above), and for the pure ) 1f5/2 particle configuration g = 0.58 (gs = 0.7gfee) results. Then the g-factor of the mixed state becomes g(i ) =a2-0.77+(1-a2)-0 .58,

whereby the 523 keV is mainly the collective state and the 217 keV the single-particle state. The particular assignment of the states made agrees quite well with the measured B(E2) values.

K-H. Speidel et al. /Nuclear Physics A578 (1994) 300-316

312

Table 4 Absolute transition probabilities to the ground state calculated with different versions of the particlerotor coupling model for E2 = 0.23 (I[PTR-MO], II[VMI(S)], III[PTR-HEXI, see text). The experimental data are from the present work and [191 E; (keV) B(E2) (W.u.) B(M1) (10 -3 W.u.) !;ff

Exp. 261

;2

606

(i4 )

< 0.15

I

II

III

Exp.

0.95

2

0.35

1(1(2)

2

7

1 .3

1.3(1)

5

1

8(6)

16

6

12

45(1)

523

22

21(5)

44

53

48

68Q)

25(1)

23

23

15

11

II

III

121

94

105

33

33

23

32(1)

217 761

I

0.3 74

0.1 67

0 .1 76

3.2.2 Particle-axially-symmetrical--rotor calculations The model, its parameters and the calculation procedure have been described by Griffiths et al. [11]. Only an axially symmetrical shape of the core has been considered as no evidence for deviations from axial symmetry was found for odd-A Br isotopes. We present here results of several variations of the model [11] using the modified oscillator with constant (PTR-M(3) and variable moment of inertia (VMI (S)). As a new extension of the calculations, the effect of hexadecapole deformation (E4 = + 0.04) has been examined (l'TR-HEX). The calculations have been performed for quadrupole deformations E 2 in the range between 0.16 and 0.26, and the best value was found from the fit to the experimental magnetic dipole and electric quadrupole _moments_ of the _ground state . In the next step four excited states with J' = 1 z , i and i were calculated in the same range of deformation, and their properties w re compared to the experimental data. In this way we were able to identify calculated excited states that correspond to experimental levels and have E 2 values close or equal to that of the ground state. In Tables 4 and f., we show the results for E2 = 0.23, which gave the best overall fit to the experimental data. 11

Table 5 Comparison of the measured g-factors of levels in 79Br with the results from the particle-rotor calculations for E2 = 0.23 (see text and Table 4) E; (keV) J;r Exp. Calc. U 217

I

II

III

3 ?1

1.404

1.19

1.37

1 .13

5

0.4(1)

0.54

0.56

0.55

523

zl 5 ?2

1.1(3)

0.88

761

0.89

0.87

21

0.54(8)

0.66

0.75

0.88

K-H. Speidel et al. /Nuclear Physics A578 (1994) 300-316

3

313

ByiiuauuENER "IWA.- .riïunERNERSERESrEE ;

aa

Li11111111111111111111111111111iii1.11(111111111111111111111111111Er

£2 Fig. 6. Comparison of experimental results for the ground state as well as for the J' = 2 state at 761 dependence _Their on the keV with predictions from the particle-rotor coupling calculations (VMI (S)). quadrupole deformation is displayed (see text) . The calculations predict two J' = i states among which the J~ = 2 1 state gives better agreement with the experimental values (see text) . The different :-ymbols of the curves are the calculated values. The stars and open circles refer to the J' = 22 and 21 levels, respectively.

The experimental i level at 306 keV decays to the ground state via an E2/M1 transition with a rather strong E2 component (see Table 2). None of the calculated i levels has the B(E2) value bigger than 4 W.u. in the range of deformations considered. We thus conclude that this state cannot easily be understood in the present model space. ( i -) levels. The experimental results indicate four z - states below 700 keV of excitation, the lowest of them being the ground state (Fig. 1). We obtain a very good fit to _the ground-state moments for E2 = 0.23 (see Fig. 6). The second calculated 1 state can be associated with the 261 keV level as it decays to the (2) - level.

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ground state via a predominantly M1 transition although the calculated B(M1) is much larger than the experimental value. Both 21 and _3 - levels are_ strongly mixed and contain almost equal amounts of the [312]2 and [301]; Nilsson configurztions . The third calculated i state_corresponds reasonably well to the 606 keV level. This exhausts the theoretical i states and thus we do not obtain a candidate that could be associated viith the 397 keV_ state (see Fig. 1). (?) levels. The two lowest-lying calculated 2 states have a very similar intrinsic structure as the 2 states and can be understood as collective excitations built on them. They can be associated with the experimental levels at 217 and 523 keV. From Tables 4 and _5 we observe a good reproduction of B(E2) values and of the g-factors for both i states. The calculated B(M 1) value of the i strongly underestimates the experimental value showing towards a more complicated structure in that specific wave function. It is generally known that g-factors are not very sensitive to deformations but B(M1) values can vary in an important way, even for rather modest changes in the wave_functions. levels. We calculated two 2 states close to the Fermi level which have a structure similar to the lower-lying i and 2 states and can therefore be interpreted as a collective excitation built on them. In particular, the 'lowest state can be associated with the 761 keV level (a member of the ground-state band) on the basis of the analysis shown in detail in Fig. 6. 4. Conclusions The present data on lifetimes and magnetic moments of low-lying states of 79Br oh:a!ned for the first time by Coulomb excitation and y-ray spectroscopy using the Doppler-shift attenuation and transient field techniques contribute to a better understanding of the nuclear structure . The experimental accuracy of the magnetic moments is, with the exception of the J' = i state at 761 keV, generally poor due to the inherent low anisotropic angular correlaticns of the y-transitions in question . This could only be improved by time-carisuming measurements and a more efficient detector set-up. Both the particle-core and the particle-axial-rotor coupling model calculations can account for the experimental g-factors . This does not come as a surprise since the particle-coupling mechanism induces effects in the nuclear wave functions that give rise to observable properties that are very similar to results obtained using a small but `static' deformation . The particular attractive properties of the weak--coupling model are its very simple structure allowing for closed, analytical expres iono ::f many nuclear properties (e.g. g-factors, see Eqs. (12), (13)) which in the present case seems to work quite well. The particle-rotor coupling model indicates very strong mixing between deformed states originating out of the 2p3/2 and 1f5/2 spherical orbitals. This result can be expected as experimentally all the `band' members are not connected by dominating E2 transitions but decay in a very fragmentated way. No evidence was

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found for the presence of a i state (originating from the 2p1/2 orbital, mainly) below 1 MeV for E2 = 0.23. This strengthens the argument that the 306 keV (i -) and the 606 keV (; -) states have deformations different from the ground state and may be seen as coexisting states. Despite a very good overall agreement between theory and experiment that has been presented in this paper, more sophisticated model calculations may be needed, in particular if data of higher precision are available, to account more accurately for a detailed nuclear structure of 79Br. Finally it is noted that the present measurements with Br beams gave again clear evidence for beam-induced attenus*tions of TF observed on the highvelocity and Coulomb-excited 28Si ions which could be measured simultaneously with the Br nuclei. These results are in excellent agreement with earlier observations and w*11 be presented in a forthcoming publication [261 . Acknowledgements The authors thank Dr . P. Maier-Komor for preparing the delicate multilayered targets and the operating staff of the tandem accelerator for providing excellent beam conditions . One of us (K.H.) is grateful to the NFWO and IIKW for financial support during the course of this study. J.R. wishes to thank the US DOE for financial support under contract No. DE-FG05-88ER40418. Support by the BMFT and the Deutsche Forschungsgemeinschaft is acknowledged . References [11 [2] [3] [41 [5] [6] [7] [8] [9] [10] [11] [12] [13] [141 [15] [16] [171 [18]

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