Short lifetimes in 29Si-29P for the test of shell-model wave functions

Nuclear Physics A517 (1990) 176-192 North-Holland

SHORT LIFETIMES

IN 29Si-29P FOR THE TEST OF SHELL-MODEL WAVE FUNCTIONS

P. TIKKANEN,

J. KEINONEN

and

A. KURONEN

Accelerator Laboratory, University of Helsinki, Hiimeentie 100, SF-00550 Helsinki, Finland

A.Z. Institute of N&ear

KISS,

E. KOLTAY

and

E. PINTYE’

Research of the Hungarian Academy of Sciences, P.O. Box 51, H-4001 Debrecen, Hungary B.H. WILDENTHAL

Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA

Received 22 March 1990 (Revised 16 May 1990)

. and 29P have been measured using the Abstract: Mean lifetimes of levels in the mirror nuclei 29SI Doppler-shift-attenuation (DSA) method and the reactions ‘5N(‘60, np)%i and %i(p, y)*‘P. The lifetime values or limits were determined for 14 bound levels in *%i below the excitation energy of 9 MeV and for 4 levels in 29P below the excitation energy of 4.1 MeV. The lifetimes of 5 levels in %i are reported for the first time. In order to provide effective stopping of recoils, the targets were prepared by implanting 15N and %i into Ta backings. The Monte Carlo method and experimental stopping power were used in the DSA analysis. The experimental transition strengths are compared with recent shell model calculations. E

NUCLEAR REACTIONS ‘5N(‘60, np), E = 17, 20, 22 MeV; ‘sSi(p, y). E = 1.38, 1.65, 2.08, 2.29 MeV; measured DSA. %i, *9P levels deduced T,,, Implanted, enriched “N,‘sSi targets.

1. Introduction The present work is a continuation to our systematic study of the short lifetimes in the sd-shell nuclei ‘-‘). R ecent work on large-basis multi-shell wave functions for the sd-shell nuclei 6-8) h as revealed the necessity of such reliable and consistent lifetime data for the Ml and E2 transition strengths. Previous to this experiment, several studies ‘) have been reported in the literature on the lifetime values in the mirror nuclei 29Si and 29P, the most extensive ones in 29Si being based on the reaction 26Mg((u, n)29Si and in 29P on the reaction 28Si(p, -Y)~~P. Most of the previously existing information on lifetimes is based on ’ Present address: 0375-9474/90/$03.50

Department

of Radiation

@ 1990 - Elsevier

Therapy,

Science

University

Publishers

Medical

School,

B.V. (North-Holland)

Debrecen,

Hungary.

P. Tikkanen et al. / Short lifetimes

Doppler-shift

attenuation

(DSA)

ated targets with slow stopping and because the slowing-down

studies ‘). However,

177

because

a variety

of evapor-

powers were used in these studies of short lifetimes theory lo) was used in many instances without

sufficient experimental confirmation, the reported values have large uncertainties and many mutual inconsistencies. This paper describes lifetime measurements in the mirror nuclei 29Si-29P using the improved DSA method as developed in the Helsinki University accelerator laboratory ie5) through the heavy-ion reaction 15N(‘60, pn)29Si and the reaction 28Si(p, -Y)~~P. The effective stopping power is obtained by using implanted 15N and **Si targets in Ta. In comparison with the previous lifetime measurements this is an essential advantage in the determination of short nuclear lifetimes with the DSA method. Additional differences are the use of the experimentally known stopping power, the computer simulation of y-ray lineshapes with a Monte Carlo method and the consistent use of the same technique in the DSA analysis of the heavy-ion reaction 1sN(‘60,n)29Si and the 28Si(p, y)*‘P reaction data; the recoil atoms are produced at velocities where the electronic or nuclear stopping power, respectively, is dominant. With this technique the lifetime values of the excited states in the mirror nuclei 29Si-29P could be determined to an accuracy which is sufficient to permit extraction of Ml and E2 transition strengths for a meaningful comparison with theoretical values.

2. Experimental

arrangements

In the 15N(i60, pn)29Si reaction studies, 17-22 MeV I60 beams of about 200 particle nA were supplied by the 5 MV tandem accelerator EGP-IO-II of the Helsinki University accelerator laboratory. The beam spots were 2 x 2 mm2 on the target. In the 28Si(p, y)29P reaction studies the 5 MV of Nuclear Research in Debrecen and the Helsinki University accelerator laboratory of about 25 kA. The beams were collimated

Van de Graaff accelerator of the Institute 2.5 MV Van de Graaff accelerator of the supplied 1.38 to 2.29 MeV proton beams to form a spot of 3 x 3 mm2 on the target.

The “N targets were prepared by implanting about a 20 pg/cm2 fluence of 100 keV 15Nt ions into 0.4mm thick Ta backings at the isotope separator of the Helsinki University accelerator laboratory. The “Si targets were prepared by implanting a 15 pg/cm* fluence of 60 keV “Sit ions into 0.4 mm thick Ta backings at the isotope separator. The y-radiation resulting from target bombardment was detected in measurements performed in Helsinki by a PGT 100 cm3 and 120 cm’, and Canberra 83.4 cm3 Ge(Li) detector and in measurements in Debrecen by a Harshaw 105 cm3 Ge(Li) detector with efficiencies of 21.8%, 28%, 18% and 22%, respectively. The energy resolutions of the detection systems were 2.0, 3.0, 1.9 and 3.0 keV at E, = 1.33 MeV, and 2.9, 4.1, 2.8 and 4.3 keV at E, = 2.6 MeV, respectively. The y-ray spectra were stored in a 4 K or 8 K memory with a dispersions of 0.53-2.0 keV/channel. The stability of

F’. Tikknnen

178

the spectrometer

was checked

The energy and source 11) placed

efficiency calibration in the target position.

et al. / Short lifetimes

with a *‘*Tl y-source of the

3. Measurements 3.1. THE 15N(160, pn)%

REACTION

and 40K laboratory

y-detectors

was done

background. with a “Co

and results

STUDY

The Doppler-shifted -y-rays were detected at the angles 0” and 135” relative to the beam direction. The detector was located 4.0-8.0 cm from the target and was shielded from low-energy y-rays and X-rays by 4 mm of lead. The corrections for solid-angle attenuation of the observed Doppler shifts and for the finite initial velocity distribution were determined from full-shifted y-rays of short-lived states. Figs. l-3 show portions of the y-ray spectra from the DSA measurements of the 2.43, 3.07, 4.08, 4.74 and 5.81 MeV states. 1

4ooc

l-

I

I

I

1

I

I

I

I

E, = 2.43 MeV ’ 5N(1 60,pn)2gSi E = 22. 1 MeV

I -

7=

26 fs

I-

I-

al-

I

2440

I

I

2460

2480

CHANNEL

I

2500

I

2 5: !O

NUMBER

Fig. 1. Portion of y-ray spectrum recorded in the DSA measurement of the 2.43 MeV *‘%i state (2.43 + 0 MeV transition). The dispersion is 1.00 keV/channel. The solid line is the Monte Carlo simulation of the y-ray lineshape at 0’; the fit is shown for the lifetime 26 fs. The adopted lifetime is ~(2.43) = 25.8 f 1.3 fs. The dashed line is the Monte Carlo simulation for the lifetime 0 fs and represents the initial velocity distribution of the *%i recoils.

179

P. Tikkanen et al. / Short lifetimes

E, =

7000

-

6000

-

5000

-

4 0

4000

-

% r

3000

-

2000

-

1000

-

15N(’

d

E = 22.1

MeV

z

7 = 47 fs

Z 3 g

o-

1 BO

1060

1040

CHANNEL

NUMBER

Fig. 2. As for fig. 1, but for the 3.07 MeV state (3.07 + 2.03 MeV transition). is for the lifetime 47 Ss; ~(3.07) = 47 * 3 fs.

The Monte Carlo simulation

The DSA analysis was performed by the computer simulation of y-ray lineshapes with a Monte Carlo method lm5). A summary of the results is given in table 1. Several y-ray peaks were included in the DSA analysis for each state when possible. The stopping power of Ta for Si was taken to be

(1) The uncorrected

nuclear

stopping

power was calculated

by the Monte Carlo method,

where the scattering angles of the recoiling ions were directly derived from the classical scattering integral ‘) and the interatomic interaction was described by the Thomas-Fermi potential. The relevant data for the description of the nuclear stopping of the recoiling low-velocity “Si (and 29P, see below) nuclei in Ta were taken from our earlier study ‘) in which the experimental correction parameter (0.67 f 0.05) for the nuclear stopping power was determined for **Si recoiling in Ta. The electronic stopping power was obtained by using the recent experimental values

P. Tikkanen et al. / Short lifetimes

180

5000

d g

4000

2 s

3000

p

2000

E = 22.1 MeV

5 8

1000

0 2750

2500

2550

2900

CHANNEL NUMBER Fig. 3. As for fig. 1, but for the 4.74 MeV (4.74-t 2.03 MeV and the 4.08 MeV (4.08 + 1.27 MeV) states. The Monte Carlo lifetimes of the states; ~(4.74) = 65 f 3 fs, ~(5.81) = 44 i 3 fs, sum of the three simulated

transition), the 5.81 MeV (5.81+3.07 MeV) simulations (dashed lines) are for the shown and ~(4.08) = 82 * 5 fs. The solid line is the lineshapes.

of Ta for 26Mg ions 2’) to calculate the stopping power for 29Si (and 29P, see below) ions in the framework of the semi-empirical model of Ziegler er al. 22). The uncertainty of the electronic stopping power was estimated to be *7%. We have recently studied the effect of implanted target atoms on the density of the backing material and lifetimes obtained by DSA ‘)_ The data incidate that at concentrations below about 20 at.% of light implants the possible density changes in Ta have an insignificant effect on the lifetime values. By the use of our earlier data on density changes in implanted Ta backings ‘*3) along with the fluences of 15N and 28Si, the implanted layers were assumed to have an insignificant effect on the density of Ta probed by /3 = 2.7% 29Si or 0.2% 29P recoils. In the deduction of the lifetime values the corrections for indirect feedings were obtained by analysing the population of the 29Si states at each energy of the oxygen beam. The y-ray decay schemes of the bound states in 29Si have been extensively studied in the literature ‘). A simulated lineshape was obtained as the sum of the shapes corresponding to the direct prompt and delayed population of the state. The sum was weighted by the experimental fractions of the populations. Uncertainties of the feeding lifetimes were those given in table 1 for adopted lifetimes. At the E(r60) = 16.6 MeV bombarding energy only the 2.43 MeV state was populated strongly enough for a meaningful DSA analysis. The dominant part of the population was due to the direct, prompt feeding. The (2.3 f 0.3)% delayed feeding

P. Tikkanen et al. / Short lifetimes

181

TABLE 1 Summary

of the lifetimes

in *%i obtained

in the present work, and comparison T(fs) previous

T(fS) adopted h,

2.43

3.07 3.62 4.08 4.74 4.90 5.25 5.29 5.65 5.81 6.11 6.19 6.78 8.761

16.6 19.6 22.1 19.6 22.1 19.6 22.1 19.6 22.1 19.6 22.1 19.6 22.1 19.6 22.1 19.6 22.1 19.6 22.1 19.6 22.1 19.6 22.1 19.6 22.1 22.1 22.1

26*2 25.2:;; 26.1” 3 4**Y 4712 3740*80 3790*90 79*5 83+5 64*2 6612 22+6 27+4 79+2 81*2 13+6 714 46*20 51*3 42zt5 46*4 29*7 32+6 2019 26*5 22*3 28+6

25.8+ 1.3

ref. ‘2) 26.6i

1.6

ref. ‘3)

ref. ‘4)

29111

1313

with previously values

ref. 15)

ref. ‘6)

24*14

23111

20::;

20*7

c74

1760*190

374Ok190

4200+500

4000+800

5800’3000 IS””

X2*5

4018

48*8

65*3

33*10

45*10

25*4

Cl0

101-3

914

Cl0


51*3

<20

40+15

44+3

2018

c20

3115

<20


25+4

i20

Cl5

22*3 2816

110

to the intensity

others 20*7’)

4200*500?

70*20

100120


“) Values have been corrected for delayed feedings. Error limits given include statistical due to the feeding transitions (see text). h, Values include also the uncertainty in the experimental stopping power. “) Ref. I’). d, Ref. “). ‘) Ref. *“).

(relative

20*7

4613

so* 10

ref. ‘7)

146

4713

SO*4

known values

of the decay y-rays)

uncertainties

and uncertainties

from the 5.29 MeV (r = 9 fs) state had

a negligible effect on the deduced lifetime value. At the E(160) = 19.6 MeV bombarding energy no feeding corrections were necessary for the 6.19, 6.11, 5.81, 5.65 and 5.29 MeV states. The feeding fractions and lifetimes

used in the DSA analysis

of the 3.62 MeV (J” =g-),

5.25 MeV (z-),

6.78 MeV (y-) and 8.76 MeV (y-) states of the K TT= $- rotational band are described in the following. Due to the small population of the 6.78 and 8.76 MeV states their lifetimes were extracted from the y-ray spectra measured at E(160) = 22.1 MeV. These lifetime values along with the y-ray intensities observed at E(160) = 19.6 MeV were used for the feeding corrections of the lower-lying levels. In the simulation of the 1631 keV (5.25+ 3.62 MeV) y-ray lineshape the delayed (3.6+0.2)% feeding through the cascade 8.76 MeV (J” = y-; T = 28 fs) -P 6.78 MeV (y-; 22 fs) + 5.25 MeV (s-), the (5.6*0.6)% and (14.2* l.O)% feedings from the y- and yP states, respectively, and the (76.6* 1.5)% direct prompt feeding, were taken into account. The

l? Tikkanen et al. / Short lifetimes

182

(1.7+0.2)%, (2.6*0.3)%and (6.6*0.5)%feedings through the cascades 8.76 MeV !yP; 28 fs) + 6.78 MeV (y-; 22 fs) + 5.25 MeV (z-; 79 fs) + 3.62 MeV (I-), y-+4--+ the (4.7+0.5)% and (35.5* l.O)% feedings from 2 and y- + f - -f i-, respectively, the y- and z- states, respectively, and the (48.3 f 1.5)% direct prompt feeding, were included

in the analysis

of the 1596 keV (3.62+2.03

MeV)

y-ray

lineshape.

The

(6.5*0.5)% feeding from the 5.65 MeV (51 fs) state was taken into account in the analysis of the 4.74 MeV state. The DSA analysis of the 4.08 MeV state included the (19.0* l.O)% and (5.9*0.5)% feedings from the 5.65 MeV (51 fs) and 4.74 MeV (65 fs) states, respectively. The cascade 5.65 + 4.74+ 4.08 MeV corresponded to a fraction of 0.5% and was therefore excluded from the DSA analysis. In the DSA analysis of the 3.07 MeV (~=47 fs) state, the (4.6*0.5)% and (4.6*0.5)% feedings from the 5.65 MeV (51 fs) and 5.81 MeV (44 fs) states, respectively, were used. The (5.0*0.6)% feeding from the 3.62 MeV (3.76 ps) state produces mainly a stop peak which could be ignored in the DSA analysis. The (2.1+0.4)%, (13.2* 1.5)% and (3.7*0.5)% delayed feedings from the 5.29 MeV (9 fs), 5.81 MeV (44 fs) and 6.11 MeV (31 fs) states, respectively, were taken into account in the DSA analysis of the 2.43 MeV state. At the E(160) = 22.1 MeV bombarding energy the following feedings were included in the analysis of the states within the Km = g- band. (The (16.0 rt 1.2)% feeding from the 8.76 MeV (y-; 28 fs) state was used for the 6.78 MeV (y-) state. The (4.4*0.6)% feeding through the cascade ~-+~-+~-, the (6.8+0.8)% and (12.3* l.l)% feedings from the ?- and yP states, respectively, were taken into account in the analysis of the 4- state. The (2.9 * 0.5)%, (4.5 * 0.6)% and (8.1* 0.9)% feedings through the cascades y- + y- + z- --, g-, y- + pP + z- and y- + $- + $-, respectively, and the (50.6~1~1.5)% feeding from the ;- state were considered in the DSA analysis of the J” = z- band head at 3.62 MeV. The (5.2*0.6)% feeding from the 5.65 MeV state was taken into account for the 4.74 MeV state. The (17.5 f 1.5)% and (7.4* 0.8)% feedings from the 5.65 and 4.74 MeV states, respectively, were used for the 4.08 MeV state. The 0.4% feeding through the cascade 5.65 + 4.74 + 4.08 MeV was not included in the DSA analysis. The feeding corrections for the 3.07 MeV state were done in the same way as in the analysis of the E(160) = 19.6 MeV data. The feeding fractions from the 3.62, 5.65 and 5.81 MeV states were (4.110.5)%, (3.4+0.5)% and (5.6*0.6)%, respectively. The (2.3*0.3)%, (32.3*1.5)% and (4.5* 0.6)% feedings from the 5.29, 5.81 and 6.11 MeV states, respectively, were used for the 2.43 MeV state.

3.2. THE %i(p,

Y)*~P REACTION

STUDY

The DSA measurements were performed with the detector at angles 0” and 90” to the beam direction and target-detector distances of 4.5 and 7 cm. A shield of 3 mm lead was applied to reduce the intensity of low-energy y-rays and X-rays. The corrections for solid-angle attenuation of the observed Doppler shifts were

183

P. Tikkanen et al. / Short lifetimes

taken

into account

An accumulated

using primary charge

y-ray transitions

at the E, = 2082 keV resonance.

of 0.1 to 0.5 C was collected

for each y-spectrum.

The 29P nucleus has only three bound states (E, = 1.38, 1.95 and 2.42 MeV, ref. ‘)). They can be excited at eight *%i(p, Y)~~P resonances below E, = 2.88 MeV. In selecting

resonances

for the DSA measurements,

the y-decay

scheme and resonance

strengths from ref. “) were used. Only the E, = 1380, 1652, 2083 and 2285 keV resonances have y-ray yields high enough for DSA measurements with implanted targets. In order to ensure that the F(7) values were not affected by unknown feedings, the measurements were performed on more than one resonance, if sufficient population could be seen. The branching ratios of primary transitions were taken from ref. ‘). In the analysis of the y-ray spectra obtained in the DSA measurements, the branches and their intensities were observed to be in agreement with the literature data. The summary of the present DSA measurements is given in table 2. Figs. 4 and 5 show portions of the y-ray spectra from the DSA measurements of the 2.42 and 4.08 MeV states. The F(r) values shown in the table are averages from at least two sets of measurements. The DSA analysis of the experimental F(r) values was performed using Monte Carlo calculations im5). The stopping power of Ta for 29P was as described earlier, eq. (1). Corrections to the quoted F(T) values for indirect feedings were introduced where necessary. The corrections are explained in the following. At the E, =2.29 MeV bombarding energy the 3.11 MeV (T =33 f 15 fs, ref. “)) state, feeds the 1.95 MeV (r= 590 fs) and 1.38 MeV (244 fs) states with intensities TABLE 2 Summary

of the lifetimes

EX

EP

(MeV)

(keV)

F(T) (%I

1.38

1380 1652 2083 2285 1380

15*7? 2116 23+6”) 21*2 815

1.95

2.42 4.08 “) “) ‘I “) ‘) ‘)

2285 2083 2285 1380

1113 s2*11 7115 71*7

in “P obtained

in the present work, and comparison

s(fs) (previous

T(fS) Cfs;“)

adopted

250*100 240180 235180 240+25’) 610’5”” 2(10

580”9”

e

13” 17*12 28+3 ‘) 2414’)

with the previously

h,

ref, 2~)

ref. 24)

ref. 25)

values) ‘)

ref. 26)

ref. 26) ‘)

244+32

240”’ d

200160

187’:;

240570

205140

590”90 110

390”901””

370+80

34O::F

450*90

465160

2814 13’2

others 210+60’.‘) 180130h) 2x5*80’)

320”‘0 I.8 II” 1 29Oi70’) 280*60’)

) 24*5

known values

15*4

70:::

25*12

33*11

13::

151-4

33*15

Only statistical uncertainty and uncertainty due to the feeding is shown. Values include also the uncertainty in the experimental stopping power. From *%(p, v) unless indicated otherwise. Value has not been corrected for feeding. In addition to the F(T) value lifetime value is based on the analysis of y-ray lineshape From *“Si(d, or). “) Ref. “). ‘) Ref. -). “) Ref. ‘*). ‘) Ref. 30).

P. Tikkanen et al. / Short lifetimes

184

I 5

=

I

2.42Me'J

28Si(p,y)2gP

0

I

41

1

I

I

CHANNEL

I

,

4620

4600

NUMBER

The dispersion Fig. 4. As for fig. 1, but for the 2.42 MeV *9P state (2.42+0 MeV transition). 0.528 keV/ch. The Monte Carlo simulation is for the lifetime 28 fs; ~(2.42) = 28 *4 fs.

is

of (4.5* l.O)% and (3.9& l.O)%, respectively. Due to the small feeding intensities and short feeding lifetime, the feeding correction had an insignificant effect on the deduced lifetime values of the 1.95 MeV and 1.38 MeV states. The 2.42 MeV (28 fs) state feeds the 1.95 MeV and 1.38 MeV states with the intensities of (2.8 f 0.4)% and (2.2 * 0.4)%, respectively. The feeding correction was also in these cases insignificant. Due to the (1.4* 0.3)% feeding from the 1.95 MeV state, the lifetime value of the 1.38 MeV level was corrected from 245 * 23 fs to 240 f 25 fs. The (2.0 f 0.3)% feeding from the 2.42 MeV (28 fs) state had a negligible effect on the lifetime value of the 1.38 MeV state. At the E,= 2.08 MeV bombarding energy the lifetime value of the 1.38 MeV level was corrected from 240* 80 fs to 235 * 80 fs due to the (12 f l)% feeding from the 2.42 MeV (28 fs) state. At the E, = 1.65 MeV bombarding energy no correction to the lifetime value of the 1.38 MeV state was necessary. No delayed feedings are known. The E,= 1.38 MeV bombarding energy corresponds to the resonance state at E, = 4.08 MeV (24+ 5 fs). The lifetime value 630* zz”,fs of the 1.95 MeV state was

I? Tikkanen et al. / Short lifetimes

185

Ex= 4.08MeV Ep = 1.38

MeV

I

0

1

5110

CHANNEL

I

5130

NUMBER

Fig. 5. As for fig. 1, but for the 4.08 MeV “P state (4.08+ 1.38 MeV transition). simulation is for the lifetime 24 fs; ~(4.08) = 2415 fs.

The Monte

Carlo

corrected to 610*:,0: fs due to the 100% primary transition. The 0.3% feeding from the 2.42 MeV state has a negligible effect on the lifetime value of the 1.95 MeV state. The lifetime value 320* 120 fs of the 1.38 MeV level was corrected to 2.50* 100 fs due to the (90* l)% and (9* 1)% feedings from the 4.08 MeV and 1.95 MeV states, respectively. The effect of the (1.1 f 0.2)% feeding from the 2.42 MeV (28 fs) state had a negligible effect on the deduced lifetime value of the 1.38 MeV state.

3.3 COMPARISON

OF THE

PRESENT

AND

PREVIOUS

RESULTS

The lifetimes of the lowest states in 29Si and 29P have been measured several times. The previous results along with our measurements are summarized in tables 1 and 2 and displayed in figs. 6-9 for the 2.43 and 3.07 MeV 29Si states and 1.38 and 1.95 MeV 29P states. In the figures the values of the weight of the measurements, on a logarithmic scale, are plotted as function of the lifetime values. The weight is assumed to be (AT)-~ where AT is the quoted uncertainty of the lifetime measurements. In those few cases where only a statistical error has been reported in the

P. Tikkanen et al. / Short lifetimes

186

loN

()_

-

N

I

d 1:

v-

zii 3

-2r I

E 020

60 LIFETIME

Fig. The due been

( fs

T

)

6. A plot of the weights of lifetime measurements of the 2.43 MeV “Si state versus lifetime value. weight of a measurement is taken as (AT)-* where AT is the quoted uncertainty. If the uncertainty to the stopping power is not included in the original paper (see table 3), an uncertainty of 20% has added in quadrature for the comparison with other values. Two contours of r(adopted) *2(47) are also shown.

literature or where no information is available on the DSA analysis, an uncertainty of 20% has been added in quadrature for the comparison with the values from those measurements for which the uncertainty due to the stopping power is included. Note that in the cases where the literature data include such an uncertainty, the values obtained without experimental stopping data are still subject to a systematic error. The reference value in figs. 6-9 is the adopted value, and contours at *2(Ar)

t

l

amaentvalw

x

adapted valw

I\ ,++, I\

0

20 LIFETIME

40 T

60 ( fs )

80

Fig. 7. As for fig. 6, but for the 3.07 MeV *?G state. The adopted value is the weighted present value and the value of ref. “).

average

of the

187

P. Tikkanen et al. / Short lifetimes

200

100

300

LIFETIME

T

400

( fs )

Fig. 8. As for fig. 6, but for the 1.38 MeV “P state. For the inclusion of the uncertainty the previous DSA measurements see table 4.

in the results of

are centered at this value. The experimental conditions of the present and previous DSA measurements of 29Si and 29P are shown in tables 3 and 4, respectively. When comparing the results with previous low-velocity data, it is worth noting that systematically shorter lifetime values are obtained by the use of the large-angle scattering correction of Blaugrund 3’) than those obtained in the present realistic Monte Carlo simulations. The systematic error increases with increasing lifetime value. For the /? = 1% 29Si recoils in Ta, the attenuation factor F(r) = 5% results in the lifetime value of 3.5 ps according to Blaugrund’s approximation and in the value of 4.5 ps with the Monte Carlo simulation. The attenuation factor F(r) = 10% for

200

400

LIFETIME

T

600 800 ( fs )

Fig. 9. As for fig. 8, but for the 1.95 MeV 29P state. The present value is used as the adopted the calculation of the transition matrix elements.

value in

P. Tikkanen et al. / Short lifetimes

188

TABLE

3

Summary of DSA measurements for lifetimes of the ?Gi levels studied in the present work. If the stopping power from the LSS theory lo) with the large-angle scattering by Blaugrund 3’) have not been used in the DSA analysis, it is marked in the footnotes. Work

Reaction

present 17 )

‘5N(‘60, pn) Z8Si(d, p)

16 )

v/c (X) 2.4-2.8 0.30-0.71 0.53-0.64

Wp,

P’Y)

26Mg(a, n)

ZH(28Si, p)

0.3 0.6-0.8 0.69 - 0.94 0.7-1.1 4.7-5.1

Slowing-down

medium

Ta+ implanted “N evaporated Si (13 pg/cm*) + Au evaporated Si (160 kg/cm’) + C evaporated Si (90 kg/cm’) + C evaporated Si (140 pg/cm’) + Ni evaporated Si (75, 420,490 pg/cm’)+Cu evaporated Si (110 kg/ cm’) + Au *?Si02 (250 pg/cm’) 26Mg(10%)-Au(90%) alloy 26Mg (1 mg/cm2) + Au 26Mg (1 mg/cm’)+Au TiD (38 p,g/cm*) + Au TiD (190 pg/cm*) + Mg, Cu, Au

DSA analysis “) Y Y

“) Experimental stopping power, Monte Carlo simulation of the slowing-down. ‘) In addition to the statistical errors a 20% uncertainty in the stopping power was included in the reported values. ‘) 10% uncertainty of the stopping power was included in the reported values. d, Electronic stopping power was corrected with a factor f, = 0.92 obtained from experimental data for ‘?Si ions in carbon “). Nuclear stopping power was corrected by a factor off, = 2.0 for scattering from 26Mg and by f, = 1.0 for scattering from “‘Au. These values were obtained in the fitting of the experimental and calculated lineshape of the 2.03+0 MeV transition with three free parameters: r,(2.03 MeV), f,(Mg), and f,(Au). The uncertain knowledge of the stopping power was taken into account by combining an arbitrary 15% additional uncertainty with the statistical uncertainty. ‘) The errors quoted do not contain any estimate of the systematic uncertainty due to the uncertainties in the slowing-down theory. This uncertainty was estimated to be *25%. ‘) The stopping power was parametrized to reproduce experimental electronic energy loss values. The nuclear stopping power was described by 1.26K(u/u,)-‘, where values for K were obtained from Bohr’s estimate 33) of the nuclear stopping power at u = u0 = c/137. An uncertainty of 5% of the stopping power is included in the quoted error limits.

the /3 = 0.2% 29P recoils in Ta, corresponds to the lifetime values of 380 fs and 500 fs according to Blaugrund’s approximation and the Monte Carlo simulation, respectively. The previous lifetime values for the 3.62 MeV state obtained with low-velocity 29Si recoils (tables 1 and 3) are within the large statistical uncertainties not in disagreement with the present result. However, they are systematically longer than the values obtained for high-velocity ‘9Si recoils in this work and ref. 12). This can only be explained to be due to the stopping power values used. The reason behind the agreement between the present result and that of ref. 12) where a method simpler than Blaugrund’s approximation was utilized, is the fact that in the DSA measurements with high-velocity 29Si recoils the electronic stopping power is dominant and the y-ray lineshape is affected by the large angle scattering only in a short low-velocity region. The longer lifetime value of the 1.95 MeV state than obtained in all the

189

P. Tikkanen et al. / Short lifetimes TABLE

4

As for table 3, but for the 29P levels studied Work present 2x ) 29 ) ?3 ) 24

1 25 3” I 26 27i 26)

Reaction

“Si(p, Y)

*aSi(d, n)

Slowing-down

v/c (%)

0.19-0.24 Ta+implanted 0.21 0.19-0.21 0.19 0.19, 0.21 0.19-0.23 0.14-0.22 0.23, 0.24 0.78-0.84 0.36-0.45

in the present

Si evaporated evaporated evaporated evaporated evaporated evaporated evaporated evaporated

“Si

work

medium

DSA analysis

(15 pg/cm*)

“)

SiO (15, 110 kg/cm*) + Au Si and “SiO, (- 130 pg/cm’) Si (130 pg/cm2) + Au Si (220, 350 pg/cm’) + Au Si (50 kg/cm’) + Au ‘“Si (300 kg/cm’)+Ta Si (180, 440 +g/ cm’) + Ta *‘Si (50 pg/cm’) + Au

+ Ta

Y ‘) d, ‘? c

)

“) Experimental stopping power. Monte Carlo simulation of the slowing-down. ‘) The nuclear energy loss was approximated according to ref. 34) Same F(r) curve was used for both target materials. ‘) In addition to the statistical errors the errors quoted on the lifetimes include the estimated 20% uncertainty in the calculated stopping power. ‘) Nuclear stopping power approximated according to ref. j4).

29P recoils (tables 2 and 4), is most likely previous measurements for low-velocity due to the use of the Monte Carlo simulation. The systematic error in all the previous lifetime values due to Blaugrund’s approximation, is the reason behind the adoption of the present lifetime value of 620* 160 fs for the 1.95 MeV state in 29P. The adopted lifetime value of the 3.62 MeV state is 3750* 140 fs. In other cases the systematic error in previous results was assumed to be covered by the uncertainty due to the stopping power or large statistical uncertainties and all the known lifetime values were taken into account in the deductions of the adopted values for the calculations elements to be discussed in sect. 4.

of the Ml and E2 matrix

4. Discussion Absolute values of electromagnetic matrix elements for transitions between states of 29Si-29P are deduced from the lifetimes of the decaying states (as measured in the present experiment and combined with previous results as described above) and the branching and mixing ratios tabulated in ref. ‘). These experimental matrix element values are presented in table 5 in comparison with theoretical absolute values calculated from the full sd-shell wave functions of the universal sd-shell (USD) hamiltonian [ref. “)I. The USD wave functions have been shown to yield a generally good accounting for spectroscopic features of sd-shell staes when combined with the appropriate effective operators “). The E2 and M 1 operators used to calculate the matrix elements listed in table 5 have been obtained from analyses of a compilation 35) of electromagnetic data for states of A = 17-39 nuclei. In these analyses, the

P. Tikkanen et al. / Short lifetimes

190

TABLE 5 Experimental

4 (MeV)

6 (MeV)

and theoretical

2J,

2Jr

transition

matrix

elements

“) between

Mixing

Branching 1^, (7.)

~

T(fS)

positive-parity

states in *%*‘P IM(E2)l(e

/M(M~)I(PL,)~)

fm’)?

ratio S(E2/Ml)

exP

SM

0.508 f 0.009

0.34

Cf.p.

SM

9.4*0.5

11.7

17.4io.3

19.1

%i 1.27

0

3

1

412115

2.03

0

5

1

435*

2.43

3.07

0

3

3

16.410.4

5

0.46*0.17

1.27

5

1.27 2.03

5 3

9

5

5.29

5.65

0

3.07

9

1.1510.12

1.06

3,5

2.43

-0.08

93.0*

1.0

7.01

1.0

11.0*

*a.02

0.46 f 0.04

0.46

cl.46

1.20

3

2.2 i 0.6

0.7

0.04 * 0.07

0.43 * 0.04

0.20

0.7*

1.05

7.211.8

1.3

8.8 * 2.0

1.0

41*2 cr1.16 -0.3OztO.06 2.0 * 0.2

25+3

1.12

1.27*0.12

1.20

0.10010.014

0.22

f 0.03

0.48 i 0.05

1.01

9.8 5.2

2215

20.5

23.8SO.9

24.4

<88 50*

10

6.3 + 0.7 10.2il.l

-0.06

4.1 30.0 5.2

0.6kO.5

1.0*0.2

4.0 20.3

1264

0.32

0.19 * 0.02

18.2

3.5*0.5 0.38 * 0.03

1.0

45*4 31+5

5.3 + 2.7

* 0.04

-0.05

3013

5

11.2 1.4

28.2kO.7

12*2 42+8

5

17.0*

15.7

17.7*o.s

68*5

47*2

5

3.07 2.03

5113

3

2.43 6.11

* 0.02

13.0*

9 7

918 <241

-0.04

7612

I

4.74 2.03

914

5

0.79 0.80

20*4

32*4

3

10.6

1.05

5

2.43

10.7*2.1

0.98 * 0.03

2.03

5


3.2

0.86

i 0.02

50*3

3

0.96 f 0.02

1.s*1.s

-0.26

3 7

* 0.08

0.68 * 0.02

0.33

so*4

1.27 1.27

-0.09

0.384iO.012

18*4

25*4

1

2.03

0.32 kO.07

32*5 65*3

7 5

4.08 5.81

8115

5

4.08 4.90

46*2

3

7

0.03 * 0.03

s3.1*0.4

1.27

2.03 4.74

26.0 * 1.0

2.03 2.03 4.08

1

*a.009

91.9zto.4 8.110.4

3

1.27

-0.197

100 15

1.3ztO.6

78*4

ea.29

C8.5

22*2

~0.18

15.9

6.9 12.0 10.1

=P 1.38

0

3

1

218117

1.95

0

5

1

620 f 160

1.38 2.42

3 3

0

1.38

7

“)

Except

b,

If the mixing

The

for lifetimes,

uncertainties

the values

are taken

ratios are not known, of the lifetimes

13.8 18.1 2.4

0.41

4.1*6.1

8413

-0.22

* 0.02

0.66 f 0.05

1.03

7.2 f 0.8

0.91 *a.10

0.84

(1.7

0.90

from

0.15*0.14

0.12*0.02

1.01*0.11

0.58

16*

14

8.1 16.0

<446

12.3

29*3

21.6

6.8*1.3

7.0

ref. 9).

the experimental

and branching

9.1*

0.49 f 0.07

52*3

5

1.95

1.1

16.0 f 2.0 * 0.06

44*3

24+5

3

0.43

-0.04

4+2

5

1.95

0.62*0.02

8.011.0 12*2

3

1.38 4.08

29~~4

1

0.17*0.02

100 92.Okl.O

ratios

matrix

elements

are not taken

into

are given account

as upper

limits for pure multipoles.

in the values

of the upper

limits.

one-body densities calculated from the USD wave functions are matched with the corresponding experimental matrix elements and the optimal corrections to the conventional free-nucleon parametrizations of the E2 and Ml operators are extracted by least squares fits. The E2 effective operator was determined 36) in the context of a model in which the neutrons and protons are assumed to carry orbital and state-independent effective charges. The single-particle wave functions are assumed to have harmonic oscillator

P. Tikkanen et al. / Short lifetimes

radial dependence

and a mass dependence

191

of the form hw = 45A-r’3 -25Am213. The

Ml effective operator was determined ‘) in the context of a model in which the orbital, spin (I = 2 and 1= 0 components treated independently) and tensor terms of the operator

were allowed

terms determined from the fit. The of the values rationale for using effective operators of this sort, “renormalizations” obtained by using the free-space values of the neutron and proton charges and moments, is the need to compensate for nuclear configurations and nucleonic states which are excluded from the model space in which the wave functions are generated. The correction values obtained empirically, as described above, are consistent with values obtained from theoretical studies 37). The data set 35) used for determining the E2 effective operator consisted of the 147 experimental matrix elements from sd-shell transitions which have uncertainties of *lo% or less. The effective charges extracted from the fit to these data were +0.389e for the isoscalar charge [h(&,+ se,)] and 0.089e for the isovector charge [$( 6e, - se,)]. The data set used for determining the M 1 effective operator consisted of matrix elements obtained from both magnetic moments and Ml transitions. Again, only values with uncertainties smaller than *lo% were included. The parametrization of the effective Ml operator and the resulting values for the renormalization are discussed in detail in ref. ‘). Theoretical values of Ml and E2 matrix elements for transitions in 2ySi-29P were then calculated with these effective operators and are listed in table 5. A very good agreement can be seen between the experimental and theoretical matrix elements. Only for the [;I: + [$I: (5.81+ 3.07 MeV) transition in “Si is the theoretical E2 matrix element considerably larger than the experimental one. This could be due to erroneous experimental mixing ratio for this transition, since the matrix elements for the other two branches are very well reproduced. This work was supported Science Foundation.

to have correction

by the Academy

of Finland

and the U.S. National

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