Heavy-ion one-neutron transfer reactions involving 13C

Nuclear Physics A241 (1975) 159-169;

@ North-Holland Publishing Co., Amsterdam

Not to be reproduced by photoprint or microfilm without written permission from the publisher

HEAVY-ION

ONENEUTRON

TRANSFER

REACTIONS

INVOLVING

13C

(II). Electromagnetic lifetimes H. P. SEILER, R. KULESSA, P. M. COCKBURN and P. MARMIER Laborfiir Kernphysik, ETH, Ziirich, Switzerland and P. H. BARKER Physics Department, University of Auckland, Auckland, New Zealand Received 16 September 1974 Abstract: Heavy-ion one-neutron transfer reactions have been used to populate levels in ‘rB, r4C, lSN and 20F. The electromagnetic lifetimes of these levels have been measured using a form of the Doppler shift attenuation method.

E

NUCLEAR REACTIONS 9Be(13C, I%), 1oB(13C, 12C), %(“‘N, 15N), 13C(19F. “OF), E=9-19 MeV; measured E,,DSA. ‘lB, r4C, 15N, 2oFlevels deducedT&

1. Introduction In a previous publication ‘), studies of the spectroscopic factors of states involved in heavy-ion one-neutron transfer reactions have been reported. In these measurements, the yield of y-rays from excited states of the final nuclei was used to derive the total cross section for the reaction of interest, and this in turn provided information on the spectroscopic factors. The electromagnetic lifetimes of these same states may be determined by a variant of the Doppler shift attenuation method (DSAM). Heavy-ion reactions are very suitable for the DSAM because of the high velocity which is generally imparted to the recoiling nucleus. When this nucleus decays in flight, the energy of an emitted y-ray, as observed by a detector at rest, will differ from the value it would have if the nucleus were stationary in the laboratory. If, in addition, the nucleus is recoiling within a material substance, and hence slowing down, the y-ray spectrum will have a shape which is characteristic of, among other things, the lifetime of the emitting state and the slowing down procedure of the nucleus. In this paper we report on the measurement of the lifetimes of excited states of some light nuclei from “B to ‘OF. The technique employed was basically to compare the energy distribution of y-rays viewed by a Ge(Li) detector at 0” to the incident beam direction in the two cases of the emitting nuclei recoiling into (a) vacuum and (b) a stopping material. This comparison enables the extraction of the lifetime of the decay159

H. P. SEILER

160

et al.

ing nuclear state to be made as long as the ionic slowing down process is reasonably understood. A subsidiary series of experiments to measure the ranges of 13C and 19F ions in nickel and tantalum is described in the appendix. These were performed to augment existing data on the passage of ions through the backing materials which were used in the lifetime determinations. 2. Method The states whose lifetimes were measured are indicated in table 1. All were produced as final states following heavy-ion one-neutron transfer reactions involving 13C as either target or beam. The particular reaction for each case is also shown in the table. The thin targets required for the experimental procedure outlined above were, for the 13C, self-supporting foils of thickness about 30 pg/cm’, while the l”B and 9Be targets, 20-30 pg/cm’, were obtained by evaporation on to the back of thin carbon foils. For the backed targets, layers of the appropriate material were evaporated to a thickness of 20-30 pg/cm2 on to either tantalum or nickel sheet, 0.2 mm thick. The enrichment of the 13C and “B targets was 90 %. TABLE 1

Investigated states Reaction

lOB(l3C,

12C)‘lB:

%e(13C,

l*C*)*Be

13C(‘*N,

13N4)‘2C

13C(19F, zoF*)‘ZC

Beam energy

Excited state

(MeV)

WV)

13 9

15

“B(6.74) 14C(6.09) 14C(6.73) 14C(6.89) lSN(7.15) 15N(7.30)

“B(6.74 14C(6.09 ‘%(6.73 14C(6.89 ‘“N(7.15 -N(5.27 1 5N(7.30

17, 19

ZOF(0.66)

ZOF(0.66 -h 0)

Gamma transition (MeV) + + + + + + +

0) 0) 0) 6.09) 5.27) 0) 0)

The experimental procedure was tist used to observe the y-ray transition at 90” to the incident beam direction with a Ge(Li) detector 10 cm away from the target. This enabled the centroid of the unshifted y-ray peak to be established. The detector was then rotated to the 0” position and a spectrum taken of the y-rays emitted from the thin target. Finally, with the detector in the same position and the beam energy unchanged, a third spectrum was taken of the y-rays emitted from the nuclei slowing down in a backing. Normally this ha1 part was performed for both tantalum and nickel backings for each y-transition. The choice of bombarding energy for each reaction was generally governed by the

161

1% (II)

ratio of the neutron transfer to compound nucleus reaction cross sections. As the latter rises steeply in the neighbourhood of the Coulomb barrier and its products contribute greatly to the y-ray background, incident energies were generally as low as was compatible with a reasonable yield of the desired y-ray. A source of error in these measurements could arise from a wandering in the gain of the Ge(Li) detector amplification system or in the analogue-to-digital converter. Accordingly, y-rays from radioactive sources were counted simultaneously with each run, and the results of that run discarded if the system had altered sufficiently to introduce any additional uncertainty into the final lifetime analysis. 3. Analysis A photon of energy Ey , observed at an angle 6 to the direction of movement of the emitting nucleus, has energy E, = E,(l + (v/ c ) cos 6). If the detector is at 0”, as in the present case, then 8 is the angle between the recoiling nucleus and the beam axis. Hence the shape of a y-ray line from a nucleus recoiling into vacuum, fv(Ev), represents the angular distribution of the reaction producing that nucleus. The shape of a line from a nucleus recoiling into a backing, f,(E,), contains in addition the effect of slowing down in the medium. Hence the stopped line may be calculated from the vacuum line as f;(~,)

=

IrnJi(E,) [-&em’/‘+ 6(EB- E,)e-“‘1 -a,

dEv ,

B

in which e-‘I’ describes the time distribution of excited nuclei with lifetime r and may be written as a function of E, and EB. The second term in brackets represents the contribution from those nuclei which are completely stopped before they decay. All the reactions shown in table 1 lead to recoil speeds of less than 6 uo, where 00 = c/137. In this region, Warburton et al. “) have shown that the rate of energy loss of a moving ion in materials may be parametrised as -

2 = k,

(~)-1+k.(-f-)1-k3(~)3,

where the first term represents the effects of ‘nuclear’ stopping, and the second and third those of ‘electronic’ stopping. Using this expression, emt” may be calculated explicitly, e -t/r =

C

’

(3)

where a, b and a depend only on the k-coefficients, on v. and on the ionic mass. Although theoretical estimates for k, and ‘k, do exS2* 3), values for the three parameters are best extracted from experimental range and stopping power data.’ All the parameters used in the present analysis have been obtained independently of the

162

H. P. SEILER et al. TABLE2 Parameters used in the lifetime analysis Nickel

llB 1% ‘5N 20F “) Ref. 4).

k,

k.

0.05 0.15 0.18 0.23

0.96 1.29 1.30 1.90

b, Ref. 5).

Tantalum k3 0.016 0.022 0.022 0.033

‘) Ref. 6).

“) ‘) ‘) ‘) *) Ref. ‘).

k,

k.

k3

0.20 0.38 0.40 0.52

0.40 0.54 0.65 0.75

0.006 b, 0.007 ‘) 0.007 d) 0 ‘)

‘) See appendix.

lifetime determinations, and they are shown in table 2. No data could be found for IIB and “N in tantalum. However, data for these ions in gold are available and were used to infer the values for tantalum. The error introduced by this procedure was negligibly small. Using eqs. (1) and (2), the shape of the stopped y-ray line may be calculated from the shape of the vacuum line, with the y-ray lifetime as the only free parameter. The value of z for which the calculated line agrees best with the measured stopped line is then the lifetime of the nuclear state. These considerations are only valid when the detector energy resolution is negligibly small. In practice this was not the case, and so the detector resolution function, assumed to be a Gaussian, was folded out of the measured vacuum line to give an ‘ideal’ vacuum line. This was then operated on using eqs. (1) and (2) to give an ‘ideal stopped line, and the resolution folded back in, to give a line which was compared with the measured stopped line using the method of least squares. In fig. 1 is shown the analysis for the 0.66 MeV y-ray from the decay of the first excited state of ‘OF following the bombardment of 13C with 17 MeV ’ 2F ions. The top curve shows the best fit to the measured vacuum line, and the two lower curves the fits to the stopped lines in nickel and tantalum using a mean life z of 390 fs. An example with a shorter lifetime is the 6.89 MeV to 6.09 MeV transition, (z = 34 fs), in 14C following the ‘Be(13C, 14C* ) *Be reaction with 9 MeV 13C ions. This is shown in fig. 2. Complications can arise in the analysis if the energy level of interest is fed not only directly in the transfer reaction, but also by de-excitations from higher levels in the same nucleus. A limit to the latter process can be obtained from the intensities of the appropriate de-excitation y-rays in the y-ray spectra. In all but two of the present cases, no such y-rays were seen. The 6.09 MeV state of 14C was fed about 20 y. from the 6.89 MeV state. This gave an apparently slower component in the 6.09 MeV state decay, but had no influence on the fixing of an upper limit on its lifetime. The 0.66 MeV state in 20F was fed very weakly from the 2.04 MeV state, and the additional uncertainty thereby introduced into the analysis for the former is included in the quoted errors. Also included in the relatively larger quoted errors for the short lifetime cases are the effects on the thin target line shapes of the finite thicknesses of the thin targets (z 25 pg).

163

Vacuum

Vacuum 1

A,.+ ..::; .-

t_.

Z..

/

,

,

!

.,.*..‘+

i

Tantdum

E, keV1 Fig. 1. Analysis of the 0.66 MeV line from Z°F following the L3C(1gF, z°F*)‘zC reaction with 17 MeV lgF ions.

Fig. 2. Analysis of the 0.80 MeV line from 14C following the gBe(13C, 1*Cf)8Be reaction with 9 MeV 13C ions.

4. Results

Table 3 contains the results of the lifetime analyses for the nuclear states which were populated in the reactions shown in table 1. It can be seen that lifetimes obtained with nickel and with tantalum backings are generally in good agreement. As with most DSAM measurements lifetimes can only be extracted when they are of the same order as the slowing down time of the ions in the material. Outside this region upper or lower limits must be quoted. Other experimental results are also shown in table 3. The agreement is generally good and in most cases the precision has been improved. As can be seen from fig. 3, the analysis for the lifetime of the 7.15 MeV state of I ‘N is somewhat affected by the presence of another y-ray close by in the spectrum. However, this is reflected in the relatively large error bars, 33f 10 and 24+ IO fs.

*) Ref. 4). k, Ref. 16).

pickel tantalum mean other measurements shell model

b, Ref. *).

< 50 <50 < 50 < 3OOy

1“B(6.74)

d, Ref. g).

*) Ref. lo).

‘) Ref. Ii).

12000 ‘)

25OOf700 2400&700 2500~500 2900 “)

i 5N(5.27)

‘) Ref. lJ).

24 ‘)

19 x 104 ‘)

0.06 “)

“) Ref. 14).

3815 3415 36&4 < 3oOb)

> 5x104 > 5x104 > 5x104 9.7 x 104 d)

< 10 < 10 < 10 < 3OOb)

‘qL89)

14C(6.73)

“C(6.09)

TABLE3 Measured mean lives (fs)

b, Ref. l*).

< < < <

33510 24110 284: 8 10% 2s) llOf2Sh)

‘) Ref. 7).

50 50 JO 10 ‘1

1SN(7.30)

lsN(7.15)

j) Ref. IS).

2900 ‘)

390150 385f40 390&40 370f60 ‘1

20F(0.66)

B po zf-

3 cd a p

1% (11)

15N(7.15 -

.

527

T

165

MeV)

Vacuum

1

..

1900

. .‘1

2ooo

Fig. 3. Analysis of the 1.88 MeV line from lsN following the 13C(14N, ‘sN*)lzC 15 MeV 14N ions.

reaction

with

The results of shell model calculations are also quoted in those cases for which they have been made. States in the nucleus 14C have been treated by Alburger et al. 14) as two nucleons in (Ip,, 2s, Id,) built on an inert (l~)~(lp+)’ core. Their results are in good agreement with experimental values. Shukla and Brown Is) have considered the 5.27 MeV state of r5N by adding lp-2h, 2p-3h and 3p-4h configurations on to a deformed I60 core. This led to a r of 12 ps which is not unsatisfactory when compared with the present experimental value of 2.5 +0.5 ps. For the 0.66 MeV state of 20F Arima ef al. 16) calculated a r of 2900 fs using an I60 core with the other four nucleons in the (2s-ld,) shell. This is in disagreement with the present value of 390+40 fs, and also with that of Holtebekk et al. 13), 376&-60 fs. Appendix

The types of experiments which provide stopping information most suitable for application in the DSAM are probably those which measure the projected range of a

X66

H. P. SEILER et

al.

heavy-ion beam in a backing, since from such data one can derive parameters appropriate to ion velocities which extend down to zero. This means that the effect of both ‘electronic’ and ,‘nuclear’ collisions is being observed. Phihips et al. 6*‘) have measured the projected ranges of “N ions in Ni, Ag and Au in the energy range O-5 MeV. We have used essentially the same method for t3C and ’ ‘F ions in the metals nickel and tantalum, in the hope of discovering a systematic variation of the stopping behaviour with respect to the atomic number of the moving ion. The energy loss parameters of other ions in these metals could then be obtained by interpolation or extrapolation. The 13C(p, y)t4N reaction has a resonance for 9.2 MeV y-rays at E, = 1.748 MeV, which is 0.08 keV wide and has a$ = 14.8 MeV [ref. I’)]. The “F(p, a~)‘~0 reaction has a resonance for 6-7 MeV y-rays at E, = 1.375 MeV, which is 11 keV wide and has CT= 300 mb [ref. “‘)]. Clean discs of nickel or tantalum were bombarded with either 13C or 19F beams from the tandem accelerator of the ETH, Zurich, at energies corresponding to ion velocities of up to 5u,,(u, = c/137). The area of the TABLE4 Measured projected ranges r3C in Ni

r3C in Ta (M:V)

2 3 4 6 8 10

1.010.3 1.4hO.4 1.7rto.3 2.2kO.4 2.7&0.3 3.350.3

~mg~rnz)

2 3 4 6 8 IO 12

1.9hO.2 2.5*0.2 2.9*0.2 4.2AO.4 5.4*0.4 6.2 AO.2 7.210.4

lgF in Ni E R (MeV) (m~cmz) 3 4 6 8 10 12

r9F in Ta E

R

(MeV)

(mg/cm’)

1.1 hO.3 1.3kO.3 1.7*0.3 2.0f0.3 2.4&0.3 2.8&0.3

3 4 6 7 8 9 10

1.9*0.3 2.3kO.3 3.2ztO.3 3.3hO.3 3.8&0.3 4.010.3 4.4io.3

TABLE5 Coefficients from range data “)

k, (mtdcm*) Nickel 1% tsN ‘9F Tantalum raC 13NinAu r5NinTa ‘9F

0.15

0.18 0.23

0.38 0.185 0.52

k, (mg/cm*)

k3 (ms/cm*)

1.29 (1.15) “) 1.25 (1.40) 1.90 (1.73)

0.022 (0.018) (0.022) 0.033 (0.023)

0.54 (0.54) 0.61 (0.60) (0.65) 0.75 (0.78)

0.007 (0.007) (0.008) (0.008) (0.006)

“) Probable errors OR k,, k3 and k, are on the average approximately 10 %. b, The values in brackets are derived from the dE/dx compilation of ref. l*).

‘“C (If)

167

beam was restricted by a 0.5 cm diameter collimator placed immediately in front of the disc and light element deposition on the surface of the metal was minimised by using a cool-trap at liquid nitrogen temperature. Bombardment was normally continued until about lOl6 ions had come to rest in the metal. The collimator was then changed for one of 0.3 cm diameter, aad the stopped ions were used as tax-get for I

R

frngkm2~

‘I

I

I

-I

13C in Ni

3

2

I

v/v* Fig. 4a,

VJ% Fig. 46. Fig. 4. Computed fits to the range data of table 4 with coefficients of table 5.

168

H. P. SEILER et al.

the (p, y) or (p, a~) reactions mentioned above. The y-rays were detected at 90” to the beam direction using a 30 cm3 volume germanium detector. In each case the yield curve was found to be broadened and shifted to a higher’ proton energy, Ep, the energy difference (E, -I$) corresponding to the .energy the protons lose in traversing the metal before reaching the embedded ions. Using the range tables for protons in metals given by Northcliffe 18), the energies (E,,-E,) were converted into the projected ranges which are shown in table 4. Although there is some uncertainty in the absolute values of the proton ranges which are tabulated in ref. 18), t h is is cancelled in the subtraction of the proton ranges corresponding to Ep and E,. It has been shown by Warburton et al. [see e.g. ref. “)I that a simple phenomenological description of the slowing down of heavy ions in matter is adequate for most DSAM studies. In this approach the stopping power is written as in eq. (2) where the k, term represents the effects of nuclear stopping, k,(o/o,J is the velocity proportionality of the electronic stopping predicted by Lindhard and Scharff “) and the cubic term is to take into account the turning over of the electronic stopping curve at higher velocities. The above expression may be easily integrated to give a closed expression for the projected range of an ion as a function of its initial velocity. Thus the results presented may be fitted to obtain values for k,, , k, and k, . Table 5 shows the coefficients obtained not only from 13C and ’ 9F in Ni and Ta but also from the results of Phillips et al. 6B ‘) for “N in Ni and Au. In the cases where the highest initial ion velocity was well below the limit of validity of the Lindhard-Scharff approach, i.e. below Zf, k, has been set to zero. The figures in brackets are the electronic stopping coeffi-

R (mg/cm2)

15N in Au

7

1

2

3

4

b

-

5

6

1

‘ho

Fig. 5. Computed fits to the range data of ref. ‘), for 15N ions in Au.

1% (II)

169

cients derived from the dE/dx compilations of Northcliffe et al. la). Probable errors on k,, k, and k, are on the average approximately 10 %. The computed fits to the projected range data of table 4 with the coefficients of table 5 are shown in fig. 4. From table 5 it can be seen that there is indeed a systematic variation of the stopping behaviour in a particular medium as the atomic number of the ion is changed, and that coefficients for light ions recoiling into nickel or tantalum could be obtained by interpolation or extrapolation, sufficiently accurately for use in DSAM measurements. The case of ’ 5N ions in gold seems to be an exception, and this is illustrated in fig. 5, where the experimental results of Phillips et al. ‘) are shown together with the coefficients from the present least squares fit. Also shown is the range curve calculated from the values of k, and k, which would be expected from the systematic behaviour of the other ions. As can be seen, this lies consistently about 0.25 mg/cm’ below the experimental points. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18)

H. P. Seiler et al., Nucl. Phys. 241 (1975) 159 A. E. Blaugrund, Nucl. Phys. 88 (1966) 501 J. Lindhard and M. Scharff, Phys. Rev. 124 (1961) 128 E. K. Warburton et al., Phys. Rev. 148 (1966) 1072 T. R. Fisher et al., Phys. Rev. 176 (1968) 1130 P. H. Barker and W. R. Phillips, Proc. Phys. Sot. 86 (1965) 379 W. R. Phillips and F. H. Read, Proc. Phys. Sot. 81 (1963) 1 E. K. Warburton ef al., Phys. Rev. 109 (1958) 1199 K. W. Allen et al., Can. J. Phys. 46 (1960) 1575 P. G. Bizzeti et al., Nucl. Phys. A104 (1967) 577 P. M. Cockburn et al., Bull. Am. Phys. Sot. 13 (1968) 1423 K. P. Lieb, Nucl. Phys. 85 (1966) 461 T. Holtebekk et al., Nucl. Phys. Al42 (1970) 251 D. E. Alburger et al., Phys. Rev. 148 (1966) 1050 A. P. Skukla and G. E. Brown, Nucl. Phys. All2 (1968) 296 A. Arima er al., Nucl. Phys. A170 (1971) 273 F. Ajzenburg-Selove and T. Lauritsen, Nucl. Phys. 11 (1959) 1 L. C. Northcliffe and R. F. Schilling, Nucl. Data. Tables A7 (1970) 233