Lifetimes of the first four excited states of 32S

1 l.E.4

1

Nuclear Physics

A160 (1971) 25-32;

Not to be reproduced

LIFETIMES

by photoprint

OF THE FIRST

G. T. GARVEY D. A. HUTCHEON, Nuclear

@

North-Holland

or microfilm without

FOUR

Publishing

written permission

EXCITED

STATES

Co.,

Amsterdam

from the publisher

OF 32S

t, K W. JONES tt, L. E. CARLSON, A. G. ROBERTSON and D. F. H. START

Physcis Laboratory, Received

Oxford

University,

14 September

Oxford,

U.K.

1970

Abstract: The mean lifetimes of the first four excited states of % were obtained using the attenuated Doppler shift method and the reaction 3zS(cr, cr’)“*S. The results are t, = 0.23&0.06, 1.05& 0.30, 0.048 *0.013 and 0.18 *0.04 ps for the levels at excitation energies 2230, 3777, 4278 and 4458 keV respectively. Deduced E2 transition rates are compared with the predictions of collective and shell-model descriptions of these levels.

E

1. Introduction In a previous paper ‘) we have compared B(E2) values for the decay of states in 32S at 2.33 MeV (J” = 2:), 3.78 MeV (0:) and 4.46 MeV (4:) with predictions of two simple collective models. It was concluded that these B(E2) values were consistent with predictions of both a simple vibrational model and the inverted coexistence model “). The present paper gives results of a measurement of B(E2) values for the decay of the state at 4.28 MeV (2:). Thz lifetime of this state, as well as those of the 2:, 0: and 4: states, were measured by the Doppler shift attenuation method (DSAM). The results are discussed in terms of the inverted coexistence picture, the vibrational model with and without mixing of one- and two-phonon states and the shell model. 2. Experimental

procedure

The low-lying states of 32S and their y-ray decay modes are shown in fig. 1. The levels were populated by the 32S(a, a’) reaction and cc-particles scattered through 172 + 2” were detected by an annular 1 kSZ * cm silicon surface barrier counter whose bias was adjusted so that pulses due to protons from the (a, p) reaction fell below the alpha peaks of interest. Gamma rays in coincidence with the backscattered Mparticles were detected at angles of 39” and 148” to the beam direction by a 50 cm3 Ge(Li) counter whose resolution was 7 keV at 2.6 MeV. The true and chancet A. P. Sloan Foundation Fellow 1967-1969, on leave from Princeton University, Jersey, USA. tt On leave from Brookhaven National Laboratory, Upton, New York, USA. 25

Princeton,

New

26

G. T. GARVEY

et d

coincidence spectra were stored along with a singles spectrum in a on-line PDP-7 computer. The singles spectrum, decreased in count rate by requiring (change) coincidence with a pulser, contained peaks from “*Th, ‘*Y and 6oCo or 22Na sources and served to monitor baseline or gain changes of the system. The target was natural CdS, approximately 350 fig/cm2 thick, evaporated on a 3 mg/cm2 thick gold backing. These thicknesses were confirmed by measuring the widths of the peaks due to elastic scattering from gold and cadmium nuclei. Following a survey of a-particle yields over a range of bombarding energies, we chose 14.50 MeV as the bombarding energy during coIlection of y-ray spectra from the 2: and 2: states and 14.39 MeV for the study of the 2:, 0: and 4: states.

84

16

100

2+

Y

i

.

2230

too

o+

J”

‘I

v

?s

Fig. 1. The energies, spins and y-ray decay modes of the first four excited states of 32S.

3. Data analysis Mean lifetimes, r, were obtained from a dete~ination of F(z), the observed shifts in peak centroid as a fraction of the full Doppler shift calculated from reaction kinematics. Finite size of the Si and Ge(Li) detectors produced negligible effects for the geometry used in this experiment. The expressions of Lindhard, Scharff and Schiott “) (LSS) were used in calculating both the electronic and the nuclear stopping powers of the recoiling sulphur ions in the target and backing. It is usual procedure to take into account the Z-dependent fluctuations of experimental stopping power relative to the values of LSS theory 4, “) by writing the total stopping

“S

27

EXCXTED STATES

The multiplying parameter f, is obtained by comparing the LSS values with experimental ones. When experimental stopping powers are not available, effective charge theory “) may be used to calculate the stopping power of the desired ion from that measured for stopping of another ion in the same medium. Data for 3%I1ions stopping in gold lead to fe = 1.25 [ref. 6)], while the data for 32P ions in gold give fc= 0.8 [ref. 7)]. Due to this rapid variation in the mass region of interest, we decided to use f,= 1.0 and assign an error of +O.lS. The effects due to large-angle scattering from nuclei were calculated following the method of Blaugrund “). TABLE

1

Lifetimes of the first four excited states in 3zS This experiment

Jn” 2+1

&NW 2230+2

Other

F(r)

r(ps)

0.585&0.013 “)

0.23 kO.06

0.588+0.012 “)

Adopted value for t(ps)

0.29 ho.06 “)

0.27 f0.04

0.30 kO.08 d, 0.26 kO.08 “)

0:

3777-+2

0.202~0.016 “)

1.05 $0.30

10f0.3 * -0.2

2+ 2

4278 &2

0.92 &O.Ol b)

0.~8~0.013

0*029~~*002 ‘)

0.52:$;

0.84 10.30

I)

‘) 0.040~0.012

0.079 h) 0 035+0,003 b . -0.008 1

0.050~0.013 ‘) 4”1

4458f3

0.488&0.014 “)

0.18 ztO.04

0.18 rto.04

“) E, = 14.39 MeV. “) Ea = 14.50 MeV. “) Average of resonance fluorescence measurements II). 3 Ref. 9). ‘) Ref. lo). ‘) Ref. 13). *) Ref. IQ). h, Reported in ref. 14).

Because the stopping powers for sulphur ions in the CdS target and gold backing are different, the F(7) curve calculated for an ion produced in a reaction at the front of the target is different from that for an ion produced at the back. The computer program for calculating F(z) divided the target into eight equal sections and for each slice calculated an F(7) curve, assuming the reaction took place in the centre of that slice. The eight F(z) curves were averaged with equal weights, that is, the cross section for the reaction was assumed to be uniform over the energy thickness of the target (about 65 keV for 14.5 MeV a-particles and a 350 pg/cm2 CdS target). The possibility of a resonance occurring at either the front or the back of the target leads to an uncertainty in r which is approximately 20 y0 at z = 0.1 ps and 15 % at 1.0 ps. This uncertainty has been added in quadrature with other errors in ~termining the lifetimes.

28

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.?t d.

Excited state energies listed in table 1 were obtained by combining energies corresponding to peak centroids at 8, = 39” and BY= 148”, taking into account the cos BY dependence of the observed Doppler shift. 4. Results The attenuated Doppler shift of the 2.23 MeV level was measured in runs at both bombarding energies, 14.39 and 14.50 MeV. The two F(z) values are in good agreement with one another and lead to a lifetime z = 0.23 + 0.06 ps. The photopeak of the

60

I

1

1

690

900

CHANNEL

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NUMBER

I

910

Fig. 2. They-ray pulse-height spectrum for decay of the 2.23 MeV state. The calculated centroid for a y-ray showing no Doppler shift is indicated as Z.S., that for a fully-shifted gamma ray as F.S. The lineshape was calculated for a mean lifetime of 0.23 ps.

2.23 MeV y-ray observed at a detector angle of 148” and in coincidence with back-

scattered a-particles populating the 2.23 MeV level is shown in fig. 2. The lineshape shown was generated by the same computer program that produced the F(z) curves. The detector response, represented by a Gaussion function of 7.1 keV FWHM, was folded into this shape to produce the shape shown in fig. 2. No allowance was made for broadening due to large-angle nuclear scattering of recoil ions. The observed lineshape is consistent with a value r = 0.23 ps which is the result of a centroid shift analysis. Other Doppler shift measurements have been made in the alpha capture work of Graue and Lieb ‘) and the proton capture measurement by Thibaud et al. ’ “1. An average of bremsstrahlung resonance fluorescence measurements “) gives z = 0.29 + 0.06 ps. In assigning a lifetime to this level, we have not included the results of inelastic electron scattering I’). These are Helm’s value z = 0.16+0.02 ps and

32SEXCITED STATES

29

z = 0.36f0.04 ps of Lombard et al. The difference appears to be due mainly to the rejection by Lombard et al. of points measured at low momentum transfer. Background becomes large for low momentum transfer; on the other hand, only for small momentum transfer can the liietime be extracted in a model-independent manner. The lifetime of the 0: level at 3.78 MeV was found to be 1.05t0.30 ps, in good agreement with the results of Ollerhead et al. 13)and in fair agreement with those of Piluso et al. 14). Our result for the lifetime of the 2; level, 0.048 + 0.013 ps, is in excellent agreement with results of Thibaud et al. lo ), but is well over a standard deviation greater than that of Piluso et al. 14). In relating the lifetime of this state to the transition strength B(E2; 2; + 2;) we have used the branching and mixing ratios for the 2: + 2: transition given recently by Sargent et al. l”) (B.R. = 16 f 1 % and 6 = -32, with limits of ISI > 6). These differ appreciably from the earlier results (B.R. = 11+2 % _-1,4) of Poletti and Grace 15)_ It is possible to obtain a branching and 6 = -1.4f0.4 ratio from our Doppler shift runs provided a correction is made for angular correlation effects. The correction factor depends upon the value of the mixing ratio, and the limits set by Sargent et al. 16) lead to a branching ratio 10+5 %, while taking 6 = 1.4ty.2 the result is 15 +4 %. Piluso et al. 14) indicate a branching ratio of 14 y0 but do not indicate errors for this result. The difference in energy of the 4: --f 2: and 2: + 0: transitions was less than the resolution of the Ge(Li) detector, so that only the combined attenuation could be measured. This can be calculated in terms of F(r) and z for the 4: and 2: levels and the ratio, R, of the intensity of the 2: + 0: transition to that of the 4: -+ 2: transition at the angle of observation. The relationship is

For the 4 + 2 --f 0 cascade we have R = 1.0. Our result 22 = 0.23 ps and the corresponding value calculated for F(z2), combined with the calculated F(r4) curve, give F,*, as a function of r4. The curves for F(r4) and FToTare shown in fig. 3. Our measured value Ftot = 0.488 f0.014 leads to z4 = 0.180 +0.055 ps. The corresponding measurement in our earlier work I), reanalysed using z2 = 0.23 ps, gives z4 = 0.18+0.03 ps. Both measurements lead to z4 = 0.17 ps if we use z2 = 0.27 ps, the average of all lifetime measurements on the 2: level. The average lifetimes listed in table 1 were obtained using the weighting procedure of Skorka et ai. “). The error of 7 % quoted by Piluso et al. 14) for the lifetime of the 4.28 MeV (2;) level seems somewhat unrealistic, since this corresponds to an uncertainty of no more than 9 % on the stopping power. We feel that a more reasonable error on the latter is 20 y0 and have thus assigned an error of kO.0045 ps to their lifetime in calculating the weighted mean lifetime. No details of the analysis of the lifetime measurements are given in ref. 14).

30

0. T. I

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et ai.

I

I

I

0.6-

IO-r4

1OP

ld’2 -c4

lo-l1

hc)

Fig. 3. Attenuation factors calculated as a function of the lifetime of the 4r+ level. The quantity & is the attenuation of the 4L+ -+ 2r + transition alone, while FIot is that of unresolved 4,* + 2r+ and 2r+ + OX+ transitions assuming zz = 0.23 ps and F2 = 0.585.

5. Discussion In table 2 we present the reduced matrix elements, B(E2), calculated from the average lifetimes of table 1. They are also presented as fractions of B(E2; 2: -+ 0:) to simplify comparison with model predictions. The inverted coexistence model of Bar-Touv and Goswami “) assumes a spherical state 0: in addition to a rotational band Of, 2:, 4: . . . . The model allows mixing of the spherical and deformed 0’ states, the mixing parameter being chosen to reproTABLE2 Transition

B(E2) in (e* * fm4) 2; -+o: 0; + 2:

Calculated relative strengths

Experimental

55+ro I,&

relative B(E2)

inverted coexistence

simpte vibrational

vib~tion~ with mixing

shell model

1

1

1

1

1

2 *0+1.5 -0.8

2.55

2

2

0.61

2.15

2

2

1.3

4: -+2;

ss+= -15

15f0.6 . -0.5

2: +2:

85&26

1.6f0.5

2

1.4

0.34

22’-+0:

12&4

0.2?&08

0

0.14

0.31

=S

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duce the observed energies of the O:, 2:, 0: and 4: levels. This mixing permits transitions to occur between the deformed 2: state and the deformed components of both the 0: and 0: states. The predicted ratio B(E2; 0: -+ 2:)/B(E2; 2: + 0:) = 2.55 is in good agreement with the experimental ratio of 2.0?:::. However, the prediction B(E2; 4: + 2:)/B(E2; 2: -+ 0:) = 2.15 is at the upper limit of the observed ratio, 1.5’:::. Another model which has been considered in 32S is the vibrational model in which the 2: state is a one-phonon state, while the O:, 2: and 4: states are degenerate two-phonon states at twice the energy of the one-phonon state. The spectrum observed in 32S strongly resembles this form. The relative B(E2) values are also well predicted, with the exception of the 2: + 0: transition. There should be no transition from the two-phonon 2: state to the no-phonon 0: state, but this transition is seen. This shortcoming of the vibrational model may be removed by allowing mixing of the one- and two-phonon 2’ states. For a mixture 12:) = cX]n= 1; 2+>+/qn

= 2; 2+>,

12;) = /3]n = 1; 2+)-c+

= 2; 2f),

and making use of [1/(2J+ l)]](n = 1; 2+))E2]]n = 2; J+)12 = $(n IZ = 1; 2+)12 and a2+fi2 = 1, we have B(E2; 4: + 2:)

B(E2; 0; + 2:)

B(E2; 2: -+ 0:) = B(E2; 2: -i 0;) = u2

2 ’

B(E2; 2; + 0;)

B(E2; 2; 3 2:) = 2(2a2 - 1)” B(E2; 2: --+0:)

= 0; O+]]E2]]

’

l--a2 =-* B(E2; 2: + 0:) cz2

A choice of c1= 0.94 gives B(E2; 2; + 2:) = 1.4, B(E2; 2: + 0:)

B(E2; 2: --) 0:) __ = 0.14 B(E2; 2: --) 0:)

in agreement with experiment (table 2). Thus, mixing of the 2+ states can remove all discrepancies between the vibrational model and observed B(E2) values. On the other hand, mixing causes a shift from the unperturbed energies such that (for a = 0.94) E(2:)/E(2:) = 2.5 while the observed ratio is 1.9. In the last column of table 2 is a list of relative B(E2) values resulting from shellmodel calculations 18). Effective charges of 1.5 for protons and 0.5 for neutrons were used, and configurations were restricted to those with 12, 11 or 10 nucleons in the Id, shell and 4, 5 or 6 in the 2s+- Id, shells. The strength of the 2: -+ 0: transition is predicted to be 43.5 e2 * fm4 wh’ich is in good agreement with experiment, but the calculated strengths of the 0: -+ 2: and 2: -+ 2: transitions are too small. We conclude that the vibrational model gives a good description of the y-ray decay of the first four excited states in 32S A contrary conclusion was drawn by Thibaud et al. lo), who rejected the vibrationalmodel in favour of the Davydov-Filippovmodel.

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et a/.

These conclusion rests on using a ratio B(E2; 2; -+ 2:)/B(E2; 2: --f 0:) = 0.58 _tO.35, ours on a value 1.6_tO.5. Our higher value results from the use of new values for branching and multipole mixing ratio 16) of the 2: + 2: transition and slightly different values for the lifetimes of the 2: and 2: states. The inverted coexistence picture of the O:, 2:, 0: and 4: states is not ruled out by our results. However, the shell-model appears inappropriate, since reduced E2 strengths for the 0: 3 2: and 2: -+ 2: transitions are greatly underestimated. We wish to acknowledge the support of the US Atomic Energy Commission, the UK Science Research Council and the National Research Council of Canada. References 1) G. T. Garvey, K. W. Jones, L. E. Carlson, A. G. Robertson and D. F. H. Start, Phys. Lett. 2) 3) 4) 5) 6) 7) 8) 9) 10) 11)

12)

13) 14) 15) 16) 17) 18)

29B (1969) 108 J. Bar-Touv and A. Goswami, Phys. Lett. 28B (1969) 391 J. Lindhard, M. Scharff and H. E. Schi@tt, Mat. Fys. Medd. Dan. Vid. Selsk. 33 (1963) No.14. J. H. Ormrod and H. E. Duckworth, Can. J. Phys. 41 (1963) 1424 B. Fastrup, P. Hvelplund and C. Sautter, Mat. Fys. Medd. Dan. Vid. Selsk. 35 (1966) No. 10 W. Booth and 1. S. Grant, Nucl. Phys. 63 (1965) 481 T. Andersen and G. Sorensen, Can. J. Phys. 46 (1968) 483 A. E. Blaugrund, Nucl. Phys. 88 (1966) 501 H. Graue and K. P. Lieb, Nucl. Phys. Al27 (1969) 13 J. P. Thibaud, M. M. Aleonard, D. Castera, P. Hubert, F. Leccia and P. Mennrath, Nucl. Phys. Al35 (1969) 281 E. C. Booth and K. A. Wright, Nucl. Phys. 35 (1962) 472; E. C. Booth, B. Chassan and K. A. Wright, Nucl. Phys. 57 (1964) 403; D. L. Malaker, L. Schiller and W. C. Miller, Bult. Am. Phys. Sot. 9 (1964) 9 R. H. Helm, Phys. Rev. 104 (1956) 1466; R. Lombard, P. Kossanyi-Demay and G. R. Bishop, Nucl. Phys. 59 (1964) 398 R. Ollerhead, T. Alexander and 0. Hausser, Bull. Am. Phys. Sot. 13 (1968) 87 C. J. Piluso, G. C. Salzman and D. K. McDaniels, Phys. Rev. 181 (1969) 15.55 A. R. Poletti and M. A. Grace, Nucl. Phys. 78 (1966) 319 B. W. Sargent, J. R. Leslie and J. H. Montague, Contrib. to the Int. Conf. on properties of nuclear states, Montreal (1969) S. J. Skorka, J. Hertel and T. W. Retz-Schmidt, Nucl. Data 2A (1966) 347 H. Wildenthal, private communication