Energy dependence of isospin mixing in the decay of 64Zn

I.E.7: 2.L]

Nuclear Physics A248 (1975) 441~150; (~) North-HollandPublishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

ENERGY DEPENDENCE OF ISOSPIN MIXING IN THE DECAY OF 64Zn C. R. LUX and N. T. PORILE

Department of Chemistry, Purdue University, Lafayette, Indiana 47907, USA * Received 24 March 1975 (Revised 20 May 1975) Abstract: The 64Zn compound nucleus was formed at energies of 17.6-23.5 MeV in the reactions 63Cu + p and 6°Ni + ~ and energy spectra of the emitted protons and ~-particles were recorded. The extent of isospin mixing between the T> and T< states of the compound nucleus was determined by comparison of the quantity a(p, p')a(a, ~')/a(p, ~)a(~, p) with theory. The mixing fraction decreases from 0.8 to 0.4 over the above energy interval. The mixing matrix element shows a corresponding decrease from 0.34 to 0.07 keV. NUCLEAR REACTIONS 63Cu(p,p'), (p,~), E = 10.0 16.0 MeV; 6°Ni(~,~'), (e,p), E = 14.6-20.9 MeV; measured differential cross sections at 9 0 - 1 5 0 . °4Zn levels deduced isospin mixing fraction and mixing matrix element as function of energy.

1. Introduction The investigation ofisospin mixing between the T> and T< states of highly excited compound nuclei has been a subject of recent interest 1 - 5). We have recently reported on the energy dependence ofisospin mixing in 6 9 G a between 17 and 22 MeV [ref. 4)]. It was found that the isospin mixing fraction, kt, increased with energy from about 0.03 to 0.3. This result was somewhat surprising since general considerations suggest that the mixing fraction should decrease in the above energy range. Such a behavior would be expected 6, ~) in view of the fact that the lifetime of the compound nucleus decreases with increasing energy so that less time is available for mixing to occur. A recent more detailed analysis of the mixing process s, 9) indicates that the observed behavior is consistent with a decreasing isospin mixing matrix element over the above energy range. In view of the fact that the energy dependence of isospin mixing has to date been determined for only a single nucleus it is impossible to assess the generality of the observed behavior. We present here a study of isospin mixing in 64Zn between 17.6 and 23.5 MeV. The results will be compared with those previously obtained for 69Ga [ref. 4)].

Work supported by the US Atomic Energy Commission. 441

442

C . R . L U X A N D N. T. PORILE

2. Experimental T h e 6 4 Z n compound nucleus was formed by bombardment of 63Cu by protons and of 6°Ni by 4He ions. Its decay was studied by measurement of the energy spectra of the emitted protons and a-particles. The experiments were performed with beams from the Purdue tandem Van de Graaff. The experimental procedure has been describedin detail elsewhere 1°' 11). Briefly, the emitted charged particles were detected by a counter telescope consisting of two surface-barrier detectors. Particle identification was based on the power-law method 12). Energy spectra were recorded at 20 ° intervals between 90 ° and 150 ° to the beam. Background was negligibly small in all cases. The beam intensity was determined by digitizing the current collected in a Faraday cup attached to the beam line and was also monitored by a detector located at a fixed angle to the beam. Targets were self-supporting metallic foils having an isotopic purity in excess of 99~o*. The targets were ~ 0.9 mg/cm 2 thick and had good uniformity, as determined by energy loss measurements performed with an 241Am a-source. Experiments were performed with 10-16 MeV protons and 14.6-20.9 MeV 4He ions as summarized in table 1. The energies of the 4He ions were chosen to yield the same compound nucleus TABLE 1

Experimental cross sections for tabulated energies Bombarding Excitation Farget

Projectile

energy

energy

Exit channel

(MeV)

(MeV) 17.6

p

19.0

p :~ p c~ p

20.5

p

63Cu

p

10.0

6°Ni

o~

14.60

63Cu

p

11.5

6°Ni

~

16.17

63Cu

p

13.0

6°Ni

0~

17.74

63Cu

p

14.5

6°Ni

:~

19.31

63Cu

p

16.0

6°Ni

c~

20.88

p 22.0

23.5

* Obtained from Oak Ridge National Laboratory.

p c~ p ct p p ct

c.m. energy interval

Integrated cross section

(P,P')cN cross section

(MeV)

(mb)

(mb)

2.0-5.2 5.5 8.5 2.0 5.2 5.5 8.5 2.0- 6.6 5.7-10.2 2.0- 6.6 5.%10.2 2.0 8.0 6.0-10.7 2.0 8.0 6.O-10.7 3.5 9.5 6.5 13.0 3.5 9.5 6.5 13.0 4.5-11.0 8.0-13.0 4.5 11.0 8.0 13.0

159_+ 9 24+ 1 183+ 6 31± 2 247 _+ 14 48+ 1 271 +17 64_+ 4 328± 13 54± 1 339_+11 75_+ 4 318±14 70+ 2 338±29 103± 5 284± 9 63_+ 2 302± 15 95_+ 4

152_+ 9

236 ± 14

308±13

299_+14

255± 9

ISOSPIN MIXING

443

excitation energies as the corresponding protons. Small adjustments were made for the slight difference in the energy lost by protons and aHe ions traversing the targets ~~). 3. Results

The data were processed with a number of codes to yield energy spectra and angular distributions in the c.m. system and to remove lines due to light-element impurities ~4). Fig. 1 shows a typical set of energy spectra: protons and c~-particles emitted at 150° in the decay of 64Zn excited to 20.5 MeV. All the spectra feature broad evaporation peaks followed by discrete lines at the higher energies. In addition, the proton spectra show a subsidiary peak below 2 MeV due to the emission of protons following low-energy neutron emission (~). This peak grows in importance with increasing bombarding energy. A similar feature appears in the ~-spectra at the highest bombarding energies. i01

I0 ~

6°Ni (c~,c~') .

,o°-

./

,

I0 °

,:. .~..

~/

i0-~'_

'.: . . . .

:

/ !

' ~.~::

,

i-:':

:

I0'

i o•

> i0 -2 i

I(5~

I

I

I

I

,

I

,

~t'. .¢.,~r

, o°

,

,

,

,

~ ",~.~

I0 -3

--

I0

..,f:

.k'5,2,.

"%"..:! "

16' • ..

.

"~:/i.~-:' 7.

"~Sk, '

' .:

I0 o

:

162

•

6

I

'~:;~:~

;..,..

I(J:4

,

63~ , ,~ ~utp,p)

63Cu(p,~)

8

I0

12

14

16

0

2

i

r

i

i

4

6

8

I0

iO-I

i

12

-2

14I0

Channel Energy (MeV) Fig. 1. Energy spectra (c.m.) of p r o t o n s and c~-particles emitted at 150' (lab) in the decay of the 64Zn c o m p o u n d nucleus at an excitation energy of 20.5 MeV.

444

c . R . LUX AND N. T. PORILE

T h e a n g u l a r d i s t r i b u t i o n s o f the e m i t t e d particles are s h o w n in fig. 2. T h e energy intervals to which the d i s t r i b u t i o n s a p p l y c o r r e s p o n d to the e v a p o r a t i o n p e a k s a n d are s u m m a r i z e d in t a b l e 1. A t the higher energies the t o w - e n e r g y limit o f the intervals is set sufficiently high to exclude the ~ o r ~ c o n t r i b u t i o n . T h e i n d i c a t e d uncertainties are a m e a s u r e o f the relative e r r o r s a n d are p r i m a r i l y d u e to those arising f r o m r e m o v a l o f i m p u r i t y lines a n d to differences between F a r a d a y c u p a n d m o n i t o r d e t e c t o r values for the b e a m intensity. T h e curves t h r o u g h the p o i n t s a re l e a s t - s q u a r e s fits o f the f o r m d(~/d~2 = a + b cos z 0. T h e b/a a n i s o t r o p y coefficients for the (p, p'),

Alphas

Protons 17.6

I//~

2.1

_" - ÷ ' I.

IO

1.5 I

I

I

I

I

|

19.0

.~./-

21

5.2

8'5

19

17 f

15 i

i

i

_ [//

AI

I

i

i

20.5 ,

E

I

27 24

%

/"

22 ,

I

6.1 /

I

I

- 4.7

I

I

I

I

22.0

/ J r " 8.2

T_

-

1 ~ ~~/1

2,

-5.4

-----"

7.2

/~"

"'-t-"~/

18

s.a 5.2

_~.~,~.~-. !

I

I

25.5 .

/ - t~ f

7.5

/

22

.~ ~ ~

~z" /

20

5.5

IS le

~ 9b,'Ol~Ol~,O

4.5 9'o

'

'

'

3.5

ecm Fig. 2. Angular distributions of protons and :(-particles emitted in the decay of 64Zn at the indicated excitation energies. Closed points and solid lines data and fitted curves for proton reactions; open points and dashed lines - data and fitted curves for 4He reactions.

ISOSPIN MIXING

445

(p, ~), and (~, p) reactions are quite small, ~ 0q).l, indicating that the angular distributions are essentially isotropic over the measured angular intervals. The b/a value for the (~, ~') reaction is ~ 0.4. Previous studies in this mass and energy range have shown that the angular distributions are distinctly forward peaked. This feature arises from direct or precompound mechanisms and plays no role in the evaluation of evaporation cross sections. We have accordingly confined our measurements to backward angles. Evaporation cross sections for the reactions of interest corresponding to the listed energy intervals were obtained by integration over energy and angle. In performing the integration over angle we used the weighting factors obtained from the leastsquares fits and assumed symmetry about 90 °. The results are summarized in table 1, where the quoted uncertainties include the standard deviations in the least-squares fits as well as estimated uncertainties in target thickness (3 %) and detector geometry (2 ~,;). It is well known 2' lO. 11) that at low energies the (p, p') reaction, alone among the reactions of present interest, includes a small contribution from a precompound process even if only those spectra leading to a symmetric angular distribution are used in the evaluation of the cross sections. This contribution must be subtracted from the (p, p') cross sections before the isospin mixing fractions can be extracted from the data. The precompound contribution was determined by comparison of the nuclear temperature characterizing the (p, p') spectrum with that obtained from a calculated precompound spectrum 15) as well as with that expected for evaporation, as given by the mean temperature extracted from the (p, ~), (~, p), and (~, ~') spectra. This procedure has been described in detail elsewhere 3). The precompound contribution to the 63Cu(p, p') reaction increases slowly with energy and varies between 4 and 10%. The compound nuclear (p, p') cross sections are tabulated in the last column of table 1. 4. Discussion

In order to extract the isospin mixing fractions from the data the experimental compound nuclear cross sections are first recast in the form Rexp = a(P, p')cr(~, ~')/a(p, ~)a(~, p). In the absence of isospin conservation this quantity would be unity if tlae angular momentum distributions in the p and c~ entrance channels were the same. This condition is merely a restatement of the Bohr independence hypothesis. Since this requirement is not met a correction for angular momentum differences is applied by evaluating a quantity denoted by Rca~c, which is made up of the same combination of cross sections as Rexp except that these are now calculated by means of the spindependent statistical theory. The calculation is performed for the particular distributions of entrance channel spins of interest as obtained from an optical model calcula-

446

C . R . LUX AND N. T. PORILE

tion. The procedure has been described in detail elsewhere 10). The ratio of Rexp to Rcalc is designated G. The limiting values of G are unity, which is obtained if the T> and T< states of the compound nucleus are completely mixed prior to decay, and G. . . . which is the value if there is no mixing. Gma x is given by the expression Gma x = l

+a(p, p')>/a(p, p')<,

(1)

where the relevant (p, p') cross sections are those for reactions proceeding via the T> or T< states of the compound nucleus. These quantities are calculated by means of the spin- and isospin-dependent statistical theory 10). If partial mixing occurs the experimental G-value will lie between these limits. As before 5, 9),we consider the possibility of both downward mixing of T> intoT and denote the corresponding mixing fractions as /~ a n d # t, respectively. It has been shown t h a t / ~ <
(2)

where T o is the isospin of the target nuclide in the proton-induced reactions. The results of this analysis are summarized in table 2. The values of Rexp are somewhat larger than unity at all energies. The quoted uncertainties are based only on the random errors in the cross sections since the systematic errors cancel out. TABLE 2 Energy dependence of isospin mixing fractions and mixing matrix elements in the decay of 64Zn Excitation energy

('MeV) 17.6 19.0 20.5 22.0 23.5

Rexp 1.08+_0.08 1.16+_0.10 1.26+-0.07 1.30+-0.10 1.28 +_0.07

Rcalc

G

0.93+_0.05 1.16_+0.10 0.89+_0.04 1.30+_0.13 0.89+-0.04 1.40+_0.10 0.90+_0.04 1.45+_0.13 0.91 +_0.05 1.41+_0.10

Gmax

Ay

1.73 1.82 1.84 1.76 1.78

0.75+--0.15 0.59+-0.16 0.47+_0.12 0.37+_0.17 0.43+_0.13

kl~/',u

0.053 0.048 0.046 0.052 0.051

,u

0.79+0.16 0.62+_0.17 0.49+_0.12 0.39+_0.18 0.45+_0.14

IHcl (eV)

340_+120 187+_ 42 99+_ 16 84+_ 21 71+_ 13

The values of R~al~ are slightly lower than unity reflecting the angular momentum difference between the entrance channels. The 5 ~o uncertainty in these values is a measure of the effect of reasonable variations in the various parameters in the calculation. The parameters having the greatest effect on the calculated cross sections are the level density parameter, a, and pairing energy, 6, of the residual nuclei formed by either neutron, proton, or alpha emission from the compound nucleus. These parameters were adjusted to yield the best overall agreement between the calculated and experimental differential cross sections for the (p, ~), (~, p), and (~, c() reactions. A typical example of the quality of the fit is shown in fig. 3. The

ISOSPIN MIXING

447 30

105

=8.0 ~p =0.40

84 63

=9.5

e°Ni((l'~' )

24

=9.0

Sa

42 ~>

an=i.o61A

=5-01I 1

12

21

6

a)

.~ 0 E b~ "~]'~ 120

:..

*",

63Cu(p,P')

"

E

63Cu(p'a)

90

>~

12

6c 30

,: Z / , , '~%:',., 12 3 6 9 12 15 18 Channel Energy (MeV) Fig. 3. Comparison of experimental (points) and calculated (curves) energy spectra of particles emitted in the decay of 64Zn excited to 22.0 MeV. The level density parameters and pairing energies used in the spin-dependent statistical model calculation are tabulated in the insert. The residual nuclei to which these quantities apply are identified by the particle emitted in their formation. The calculated (p, p') spectrum includes the experimentally determined fractional isospin mixing. The experimental (p, p') spectrum includes the precompound contribution. 0

3

6

9

ratios o f Rexp to Rcalc yield the values o f G a n d these are seen to lie b e t w e e n unity a n d Gmax i n d i c a t i n g t h a t p a r t i a l isospin m i x i n g occurs at all energies. T h e values o f A# are o b t a i n e d b y m e a n s o f eq. (2). T h e q u o t e d u n c e r t a i n t i e s are b a s e d o n those in the G-values. T h e values o f p m a y be o b t a i n e d f r o m the corres p o n d i n g A# by m e a n s o f a n analysis 9) which leads to a f o r m u l a for the r a t i o of u p w a r d to d o w n w a r d m i x i n g fractions, #t/#. The analysis is b a s e d on the a p p l i c a t i o n o f g o l d e n rule no. 2 to the u p w a r d a n d d o w n w a r d m i x i n g processes. Since b o t h these processes involve the s a m e isospin m i x i n g m a t r i x element, [Hd, the g o l d e n rule can be w r i t t e n as

IHc] = [27~2~( U, J ) J

=

[_2z~Q>(u,J)J

'

(3)

w h e r e F+ a n d F T are the d o w n w a r d a n d u p w a r d m i x i n g widths, a n d the ~ are the

448

C.R. LUX AND N. T. PORILE

level densities of the T< or T> states. Since the mixing widths are related to the mixing fractions by relations of the form FI{u, J) = F~'(U, S)#/(1-#),

(4)

where F~" is the decay width of the T> states, one can in turn relate the mixing fractions to the decay widths to obtain the relation 9)

Vt/# = F((U, J)/2ToF2(U, J),

(5)

where F ( and F2 are, respectively the proton and the total decay widths of the T< states of the compound nucleus so that the ratio of mixing fractions can be evaluated by means of the spin-dependent statistical theory. Knowing both A# and #1'/# one can obtain the values of # and then those of the mixing matrix element by the relation

= F IHcl

r ; t v , s).

L4=To..e>(U,g)(1-#i

"

(6)

The values of #t/# are given in the seventh column of table 2. The results were obtained for the most probable spin of the compound nucleus. The ratios are ~ 0.05 at all energies reflecting the fact that the branching ratio for proton emission from the T< states of the 64Zn compound nucleus is ~ 0.25 in the energy range of interest. As a result, the values of # are only slightly larger than those of A#. The isospin mixing matrix elements are tabulated in the last column of table 2. The listed uncertainties are based exclusively on those in the corresponding #. The absolute uncertainty in IHc] must be substantially larger than indicated since the Fermi gas model level density expression is not that accurate. However, the quoted errors should give a fairly close indication of the relative uncertainty in the matrix elements. The energy dependence of the mixing fraction is displayed in the top panel of fig. 4. Our previous results for 696a [ref. 4)] are included for comparison. It is seen that the isospin mixing fractions of 64Zn and 696a do not display the same energy dependence since # increases with energy for 6968 whereas it shows the opposite behavior for 64Zn. The trend displayed by the 64Zn values is readily understood since it indicates that mixing competes less effectively with decay as the energy of the compound nucleus increases. Presumably this trend reflects the decreasing lifetime of the compound nucleus. The difference in the behavior of the #-values of 64Zn and 696a thus must reflect the relative behavior of the mixing and decay widths as a function of energy. While the decay process is well understood within the context of the statistical model, relatively little is known about mixing. The analysis outlined abeve permits the determination of the mixing matrix element and the results for 64Zn and 696a are shown in the bottom panel of fig. 4. It is interesting to note that both ]Hc[ values display essentially the same variation with energy despite the differing behavior of the corresponding mixing fractions. It turns out that the proton decay width of the

ISOSPIN MIXING

449

o., .'~~ 0.6

F

0.4

0.2

/~L

0

i

i

I

.300

\ 20C

\ \

I e%l 10G

7

i~

,~, ~0 2'1 2'2 ~3 ~4 U (MeV)

Fig. 4. Energy dependence ofisospin mixing fraction (top panel) and mixing matrix element (bottom) in the decay of 64Zn (closed points) and 69Ga (open points). The lines show the trend of the data. The ]Ho] for 69Ga have been multiplied by a factor of 5.

T< states of 6 9 G a increases less rapidly with energy than that of 64Zn while the level density of the T> states increases more rapidly. The net effect of these factors makes up for the increase in/~ observed for 6 9 G a and leads to the same behavior of the matrix elements. The observed decrease in IHcl is consistent with the results obtained at low energies. Bloom 16) tabulated IH¢] values derived from//-decay studies. The values fluctuate widely from one nucleus to another but lie mostly in the 1-40 keV range. This variation is presumably due to the fact that at these low energies mixing takes place between discrete T> and T< levels whose overlap depends on the particular configurations involved. Much of this variation is damped out at higher energies since the mixing occurs between many overlapping levels g). The present ]Hcl values extrapolate into the keV region at low energies and so tie in rather well with the/3decay data. Although the uncertainties in ]Hcl are rather sizeable it does appear that the values begin to level off above ~ 20 MeV.

450

C.R. LUX AND N. T. PORILE

T h e e x t e n t o f i s o s p i n m i x i n g in 64Zn at a n e n e r g y o f 19.5 M eV has b e e n p r e v i o u s l y s t u d i e d b y Vaz, L u a n d H u i z e n g a 2 ) . T h e s e a u t h o r s o b t a i n e d Rex p v a l u e s f r o m the s a m e type o f e x p e r i m e n t as r e p o r t e d h e r e a n d e x t r a c t e d t h e # - v a l u e b y a s o m e w h a t s i m p l i f i e d f o r m o f the p r e s e n t l y u s e d analysis. T h e i r results are Rex v = 1.3 _+0.1 a n d # = 0.5_+0.1. W i t h i n t h e l i m i t s o f error, these v a l u e s are in g o o d a g r e e m e n t w i t h o u r results at 19.0 M e V . T h e a s s i s t a n c e o f J. C. P a c e r a n d J. R. W i l e y in c o l l e c t i n g t h e d a t a is g r a t e f u l l y acknowledged.

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16)

S. M. Grimes, J. D. Anderson, A. K. Kerman and C. Wong, Phys. Rev. C5 (1972) 85 L. C. Vaz, C. C. Lu and J. R. Huizenga, Phys. Rev. C5 (1972) 463 J. Wiley, J. C. Pacer, C. R. Lux and N. T. Porile, Nucl. Phys. A212 (1973) 1 N. T. Porile, J. C. Pacer, J. Wiley and C. R. Lux, Phys. Rev. C9 (1974) 2171 N. T. Porile, C. R. Lux, J. C. Pacer and J. Wiley, Nucl. Phys. A240 (1975) 77 D. H. Wilkinson, Phil. Mag. 1 (1956) 379 A. M. Lane and R. G. Thomas, Rev. Mod. Phys. 30 (1958) 257 S. M. Grimes, Phys. Rev. Cll (1975) 253 N. T. Porile and S. M. Grimes, Phys. Rev. C l l (1975) 1567 A. J. Kennedy, J. C. Pacer, A. Sprinzak, J. Wiley and N. T. Porile, Phys. Rev. C5 (1972) 500 A. Sprinzak, A. J. Kennedy, J. C. Pacer, J. Wiley and N. T. Porile, Nucl. Phys. A203 (1973) 280 F. S. Goulding, D. A. Landis, J. Cerny and R. H. Pehl, Nucl. Instr. 31 (1964) 1 C. F. Williamson, J. P. Boujot and J. Picard, Report CEA-R3042, Saclay, 1966, unpublished A. J. Kennedy, J. Pacer, A. Sprinzak, J. Wiley and N. T. Porile, Nucl. Instr. 101 (1972) 471 M. Blann and F. M. Lanzafame, Nucl. Phys. A142 (1970) 559 S. D. Bloom, in Isobaric spin in nuclear physics, ed. J. D. Fox and D. Robson (Academic Press, New York, 1966)p. 123