Isospin-forbidden particle decays in light nuclei

Nuclear Physics ?,273 (1976) 477-492; (~) North-Holland Publishino Co., Amsterdam

Not to be reproduced by photoprint or microfilmwithout written permissionfrom the publisher

ISOSPIN-FORBIDDEN PARTICLE DECAYS IN LIGHT NUCLEI 011). Decay widths of the lowest T -- a2 level of 21Ne A. B. McDONALD AECL, Chalk River Nuclear Laboratories H. B. MAK, H. C. EVANS and G. T. EWAN Queen's University, Kingston and H. B. TRAUTVETI'ER * University of Toronto, Toronto, Canada Received 19 May 1976

Abstract: The lowest T = ½ level of 2tNe has been observed as an isospin-forbidden resonance in the tTO(~, n)2°Ne(l.63 MeV) reaction at an incident energy of 1862.2+2.6 keV, corresponding to an excitation energy of 8856.7 + 2.2 keV in 2~Ne. Total and partial decay widths were determined as follows: T = 2.8 + 0.5 keV; F,(O.O)/T < 0.3 ; F~Fn(1.63)/T = 0.42 + 0.16 eV. No resonant structure was observed for the second T = ½level in 21Ne and upper limits of 0.4 eV and 1.0 eV were determined for F~F.(O.O)/F and T,F.(l.63)/F, respectively. All available information on partial widths for isospin-forbidden nucleon decay of T = ½ levels from mass-9 to mass-41 have been compiled. Trends observable in these data are discussed. I

NUCLEAR REACTIONS 170(~, n), tTO(a, ny), E = 1.4-2.3 MeV; measured n, ~, yields. 21Ne, deduced T = { levels, F, F,, F.. Enriched target.

1. Introduction T h e lowest t w o T = ~ levels in 21Ne a r e u n b o u n d to i s o s p i n - f o r b i d d e n d e c a y b y o r n e u t r o n e m i s s i o n as s h o w n in fig. 1.The e x c i t a t i o n energies, spins a n d p a r i t i e s o f these levels h a v e been a c c u r a t e l y m e a s u r e d t, 2) by the isospin a l l o w e d 22Ne(3He, • )21Ne, 22Ne(d, t ) 2 t N e a n d 23Na(p, 3He)21Ne reactions. T h e b r a n c h i n g r a t i o s for n u c l e o n d e c a y to the g r o u n d state a n d first excited state o f 2°Ne a r e k n o w n 3) for t h e s e c o n d T -- ½ level in 21Ne a n d s i m i l a r i n f o r m a t i o n exists for b o t h a n a l o g o u s levels in 2 t N a [refs. 3 , , ) ] . T h e l o w e s t t w o T = ½ levels in 21Na have been o b s e r v e d as i s o s p i n - f o r b i d d e n r e s o n a n c e s in the 2°Ne(p, p ) 2 ° N e a n d 2°Ne(p, y ) 2 t N e reac-

, Present address: Universitat Mfinster, Miinster, W. Germany. 477

478

A . B . M c D O N A L D et al.

12o7 1.75

1.10 (I/2-,3,'2-)

J

I

~ ,0.,o

......

II0.60

I

19.9&

{V2;~[2-~]

I

2' F MANY T : 1/2 LEVELS

MANY t' : 1/2

2,Mg 6..56

17F+(~

LEVELS

=._.L~ =Ne+l: ).35 ~).OZ

~x/2÷ 3,,z~

2~Ne

0.34 I o.o

~,~ ~,7,1

2~Na

Fig. 1. Diagram o f A = 21, T = ~ levels.

tions 5,6) and total or partial widths were obtained for both levels. The present paper describes the observation of the lowest T = ] level of 21Ne as a isospinforbidden resonance in the 170(~, n)2°Ne reaction and the determination of its total and partial decay widths. A similar search for the second T = ~ level was unsuccessful and yielded only an upper limit for F~F./F. This information permits a comparison of analogous nucleon decay widths and a discussion of the T = ½ isospin impurities in the levels. The final section of the paper contains a discussion of the available information on isospin mixing in T = levels in light nuclei and the trends in this information as a function of mass number. 2. Experhnent The measurements were mainly performed with the 4 MV KN Van de Graaf accelerator at Queen's University. Some preliminary measurements were made with the 2.5 MV KN Van de Graaf accelerator at McMaster University, Hamilton, Ontario. Neutrons from the 170(~t, no) reaction and y-rays from the t70(~t, nl) reaction were observed at a number of angles for an incident energy range from 1.38 to 2.30 MeV. The ?-rays were detected in a 12.7 cm diameter by 15.2 cm long NaI(Tl) detector and in two 40 cm a Ge(Li) detectors. Neutrons were detected in a 5 cm diameter by 6.4 cm long INE213 liquid scintillator. Neutron-? pulse shape discrimination was employed as described in the previous paper 7) (II) of this series. Fig. 2 shows the observed excitation function in this energy region and indicates

I I I I YIELD OF 1.63 MeV 7''s 2000

FROM Or

I

I

I

21Ne (T =3/z)

I0000

1 7 0 ( a , n l ) ZONe

= 50*

I

) ~b 5000

I000 ZINe(T=3/2)

.J LIJ >-

I

0 YIELD OF NEUTRONS FROM I 7 0 ( a , n o ) Z ° N e

800

I

I

4000

"

2JNe (T= 3/2)

Oa = 120" J

2000

(

400

-/2I

2.1

I

2.2

I

2.3

ALPHA ENERGY ( M e V ) Fig. 2. Excitation functions for the ~70(~t, no) and t To(or, n l) reactions. The arrows indicate the expected locations of the lowest two T = ½ levels of 2tNe.

200ttrO(f~Q,n I ) Z°Ne (I-63)

IOC -,1~.~ w Z Z

"J

~

I. ZINe~ 170(a,nol ZONe ".L_.

z u

"" IOC (/) lZ::) 0 U

I00

,

. I.

~ m O ( a , n

I O0

) ZiNe

.L 200

CHANNEL

1 300

I 400

Fig. 3. Neutron spectra obtained with the NE213 liquid scintillator with pulse shape discrimination. (a) Spectrum obtained at an incident energy o f E, = 1.850 MeV, with a target containing ~ 96 % of W t 7 0 3 and ~ 4 )~, o f WtaOa. (b) Spectrum obtained at E, = 1.837 MeV with the same target as (a). (c) Spectrum obtained at E, = 1.850 MeV with a target containing > 90 % w I a o 3 .

480

A.B. McDONALD et

al.

the expected locations of the lowest two T = ~ levels as determined by Hensley 1) from the 22Ne(3He, ~) reaction. The lowest T = ~ level is expected to occur at an incident energy of 1.862+ 0.005 MeV [ref. ~)], which is very near the 8 keV wide resonance observable at E~ = 1.841 MeV. An additional complication arises from a strong resonance in the sO(~, n) reaction which occurs between these two resonances. The targets used were enriched to 96.2~o in 170, but a small yield was still observable from the (0t, no) reaction on the residual t aO. However, the Q-value for this reaction (Q = - 0 . 6 9 8 MeV) was sufficiently different from the 170(~, no) reaction (Q = +0.588 MeV) that neutrons from the latter were readily distinguishable, as illustrated in fig. 3. The neutrons from l so(~, no) interfered only with the observation o f neutrons from the 170(~, nt)2°Ne(1.63) reaction. This reaction was therefore studied by observing the 1.63 MeV v-rays emitted by the first excited state of 2°Ne. The targets consisted of about 0.5 #g/cm 2 of WO 3 evaporated on 0.5 mm thick gold backings which were directly water cooled. With this arrangement, beams o f 15 #A of 2 MeV or-particles could be routinely used with little target deterioration. The yield was observed to decrease linearly with bombardment at a rate of about 4 % per hour. Overall energy resolution remained constant and was checked at regular intervals by measuring the excitation function of the strong narrow resonance at E~ = 1.783 MeV which had an observed full width at half maximum ( F W H M ) of 2.3 keV. Data were collected with a PDP-9 computer which automatically recorded spectra on tape and produced excitation function spectra for specified windows. The operator was required to change the incident beam energy for each step and start the accumulation period. The calibration constant o f the analyzing magnet was determined from the observation o f resonances 8) in the I*N(~, y) reaction at incident energies of E~ = 1611+2 keV and 2347+1.0 keV which correspond to energy levels in tSF at excitation energies of 5669 + 2 keV and 6241.2 + 1.0 keV respectively. Fig. 4 shows the observed yield of 1.63 MeV y-rays in the region o f excitation energy in 21Ne near the expected position of the T = { level. A resonance is clearly observed at an incident energy of 1862.2 + 2.6 keV, which corresponds to an excitation energy o f 8856.7 + 2.2 keV, in excellent agreement with the excitation energy of the lowest T = { level (8856+ 5 keV) determined by the 22Ne(3He, ~t) reaction 1). A search was also made for y-decay of the 8839 and 8857 keV levels in long runs on each resonance, using the Ge(Li) detectors in a close geometry. No decays were observable, owing to the neutron induced background in the detectors. However, this search served as further confirmation that the 8839 keV level is not the T = level. Assuming that F~
T = ½ L E V E L O F 2tNe I

I

I

YIELD

21Ne (8.839)

FROM

I OF

481 I

~,ll

1.63MeV

170(a,nl)

s

2°Ne

2000

I000

o~ 5 0 C I-

~/2 ) >_ 2 0 0

or


I00

50 Q .J hi ~"

20

I0 )

I

1825

I

1

1845 ALPHA

1

I

1865

I

I

188

ENERGY

Fig. 4. Yield of 1.63 MeV y-rays from the tYO(~, nl)2°Ne(1.63) reaction at the indicated angles. The solid curves are fits to the data of the sum of two Breit-Wigner resonance line shapes without interference.

level. The lower partial width in the incident ~t-channel for the 8857 keV, T = level resulted in the expected y-decays being obscured by background. The solid curves through the data in fig. 4 are the sum of two Breit-Wigner resonance curves with no interference between them, with widths, resonance energies and relative amplitudes adjusted to fit the data. The quality of the fits implies that the assumption of no interference is correct. The fitted Breit-Wigner shape for the 8839 keV level was therefore subtracted as background under the observed T = ½ resonance as shown in fig. 5. The data shown in fig. 5a were accumulated with the NaI(T1) detector to obtain good statistical accuracy. The assumed background is shown as a solid curve in fig. 5a and the resultant resonance shape is shown as solid points in fig. 5b. The solid curve through the data in fig. 5b is a Breit-Wigner resonance with F = 4.2 keV. The open circles in fig. 5b are data for the no yield at the E= = 1783 keV resonance obtained immediately afterwards with the same target and beam conditions. The

482

A . B . M c D O N A L D et al. I

I

I

I

I

I

I

i

I

f

a

IO0(X)

5000 YIELD OF 1.63 MeV 7 ' s FROM I r O ( a , n l ) 2°Ne

(~ I-Z 0 (J

0

i

i

i

i

i

i

i

i

BACKGROUND SUBTRACTED

i

i

b

2000

1000

!

0

18~4

J

1860 ALPHA

i

'lD'lo 1866

I

J 1872

ENERGY

Fig. 5. (a) Yield of 1.63 MeV y-rays obtained with the NaI detector in the region of the T = ~ resonance. The solid curve is the tail of the Breit-Wigner line skape fitted to the broader resonance at E, = 1837 keV. (b) The solid circles are the experimental data shown in (a) after subtraction of the tail of the nearby resonance. The solid curve through the data is a Breit-Wigner resonance line shape with F = 4.2 keV. The open circles are data for the n o yield at the 1783 keV resonance, illustrating the combined beam-target energy dispersion.

asymmetric appearance of this resonance implies that its width, 2 keV, is dominated by target thickness and energy straggling. The target thickness was estimated to be about 1 keV by comparing the total yield for this resonance with that obtained for a thicker target for which the observed width ( ~ 20 keV) was dominated by energy loss in the target. The energy straggling theory of Vavilov 9) as reported by Seltzer and Berger 1o) predicts a FWHM of 1.24 keV and so the additional width is probably from target inhomogeneity. The procedure used to extract the width of the T = ½ resonance was to unfold the observed shape for the E~ = 1783 keV resonance from the observed shape of the T = ~ resonance. The result is 3.5+0.6 keV which corresponds to Fro t = 2.8_+0.5 in the c.m. system. No resonance was observed in the no yield for the T = ½ resonance or for the stronger resonance at E~ = 1841 keV. Fig. 6 compares the data for the 170(0t, no) reaction with the observed resonances in the 170(0t ' n 1) reaction. Assuming that the

T = ½ L E V E L O F 21Ne I

I

I

I

483 I

I

a 0.2

YIELD OF 1.63MeV FROM

O.I

7's

I'to(a,n I)20Ne

0 7 =0"

0.05

"C ..Q

0.02

E 0.01 x

b

I

"10

I

I

h Q

o°= 0"

,_

,I/, } o o o o ooooocooo °°~°°°°°°o

-

oooo I

1825

-- 2 5 *

x I/a .

0.02 -

0.01

I

O0

~. ~ -

I

o,,, o,o,,,,,',oo,' ' ' 8n •

0,05

I'k~ ×x

° °

On -'72 ~

1 7 0 ( . , no ) ZONe I 1845

ALPHA

I

I 1865

I

I 1885

ENERGY

Fig. 6. (a) Yield of 1.63 MeV y-rays from tTO(~t, nt)2°Ne at 0~ = 0 °, indicating the locations of the observed resonances. (b) Yield of neutrons from the t 70(at ' no)2ONe reaction at the indicated lab angles.

amplitudes of the resonances in the (~(, no) and (~, nl) channels are proportional to F~F.o/F and F.F,,/F, and that F,o+F., ~ F, then it is possible to set a limit on F,o/F by comparing the (c(, no) and (c(, nl) excitation function as observed in the NE213 neutron detector. Relative detection efficiencies for n o and nl were obtained from the tabulation of Verbinskii et al. 1t) for similar detectors. In this way it was possible to set an upper limit of F,o/F < 0.3 for the T = ½ level and F.o/F < 0.3 for the 1841 keV resonance. Since the neutron yield from the E. = 1841 keV resonance was almost entirely from the (0{, n t) reaction, an absolute normalization for the v-ray and neutron excitation functions could be obtained from the values of O'tot for this level measured 12) by Bair and Haas (their fig. 4). Assuming that the resonance in the yield of 1.63 MeV y-rays is a Breit-Wigner resonance shape without interference (see figs. 4 and 5), and using the reaction formalism for an isolated resonance t 3) we obtain the result FJF., = 0.67 + 0.24 eV.

484

A.B. McDONALD -

1

•

I

•

2.0~-

"

et al.

"

...

I

--

I

21Ne ( 9 . 1 3 9 , T = 3 / 2 ) [ O••OOOO0

1.6:3 MeV 7 ' s 1.0

FROM

Itlll

I

I70(a,nl)z°Ne(I.63)

ee•

•

8}, = 5 0 ° ~-

I

* ! I

I

I

._~

(n 5.0

...........!

E 2.0

"o rro(a,nj)Z°Ne (I.65) I:> -o I.O e~ = 0 ° , 5.0~- • • ! I

•

•

2.0

i

~no

--I O* 2190

l

]

,

"" • O O o o o O •

I 2200

ALPHA

J

J

0•0• 0000000

!,r0 ( . , n o ) 2 O N e

1.0 ! 2180

e•ee••oo • • •

I 2210

I 2220

•

-T

ENERGY

Fig. 7, O b s e r v e d yields o f y-rays a n d n e u t r o n s f r o m the 170(~t ' no ) a n d 170(ct, n 1) reactions. The a r r o w a n d e r r o r b a r s h o w the e x p e c t e d l o c a t i o n o f the second T --- ~ level in 21Ne.

Since the penetrability for ~t-decay of the T = ~ level is ,~ 200 times smaller than the penetrability for n, decay we may assume F~ .~ F . . Then we may summarize the results as F,o < 1.0 keV, 1.3 < F., < 3.3 keV, 0.43 < F~o < 1.3 eV. A search was made for a resonance corresponding to the 9.139 MeV, T = ~ level but no resonance could be found in the yield of neutrons or 1.63 MeV ~,-rays, as shown in fig. 7. The sensitivity to a weak resonance is reduced in this case due to the large background from a broad T = ½ resonance, which is clearly shown in fig. 2. The energy resolution o f ~ 2.5 keV could have made a very narrow, destructively interfering resonance unobservable. However, on the assumption o f a Breit-Wigner shaped, constructively interfering resonance similar to all others observed in this energy region, it is possible to" set upper limits o f F~F,o/F< 0.4 eV and F=F,J F < 1.0 eV, which imply F~ < 0.9 eV and F~ < 3.0 eV, respectively when combined with the previously measured 3) values of F.o/F and F,JF.

T = ] L E V E L O F 21Ne

485

3. Discussion The isospin-forbidden particle decay properties of the lowest T = ~ levels of 21Ne and 2~Na are summarized in table 1. The information for 21Na comes from measurements of Fpo in the 2°Ne(p, p) reaction 5) and branching ratio measurements determined from fl-delayed proton emission 4). The decay properties of these levels

TABLE 1 Decay properties of T = ] levels in mass-21 2 iNe(8.857)(F,ot = 2.8 + 0.5) ~)

F.

final state

72 = r°/2p~)

(eV) a)

n + 2°Ne 0.0 (0 +) 1.63(2 + ) 4.25(4 +)

< 1000 +500 2800_1ooo bound

4.97(2 - ) Ct+170(0.0)

bound 0.87+0.44

< 1350 +350 2000_700

21 Na(8.970)(Fto t _- 0. 75+o.os -0.25) b)

Ratio 2 2 ~,./~'p

~zp = Fp/2e¢)

< 32.9 +3 17_ s

120+60

Fp (eV) b)

61+24o +8 120_,o

> 0.12

< 17

150_+~o° +28 420_140 < 3

714_+48 2*o < 1030

180 +12 60 < 145

final state p + 2°Ne 0.0 (0 +) 1.63(2 +) 4.25(4 +) 4.97(2 - ) ~t+JVF(0.0)

_

a) Present work. b) Refs. 4.5.30). c) Calculated for r = 1.4(11/3 + 201/3).

I

'

'I''"I

I

'

'I

....

I

a

I '' I'"'1 I ' ' PROTON DECAYS TO LOWEST 2+ LEVEL

PROTON DECAYS

TOGROUN SD TATEi ~

''"1

10-4

10-4

2

),'p2

T

I

Ye

tI tit

),2 w

10-5

10-5

t 10-e

10-6

I 2

, ,[J,,~l 5 lO

I I i I,,,,I 20 50 tOO A

I

2

, ~I=,,,I 5 10

I

20

,

,I,,,,I

50

I00

A

Fig. 8. R e d u c e d widths for p r o t o n decay of the lowest T = ] levels o f A = 4 N + 1 nuclei to (a) the g r o u n d state of A = 4 N nuclei a n d (b) the lowest 2 + level o f A = 4 N nuclei.

A.B. McDONALD et al.

486

are clearly very different, as has been previously observed for masses 13 and 17. The reduced width for decay to the 1.63 MeV, 2 + level is more than a factor of ten larger for the 21Ne level. The strong trend towards larger neutron decay widths is evident in figs. 8 to 10 which present the available information on isospin-forbidden decay widths as a function o f mass number. The information from which these figures were prepared is contained in table 2. In an attempt to put all of the isospin-forbidden decay widths in a suitable form for comparison, the observed widths have been converted to reduced widths 72 = /-,. . . . /2P where P is the Coulomb penetrability calculated for radius r c = 1.4(1 ~ + A ~) where A is the mass number o f the A = 4N nucleus to which the T = ~ levels decay by nucleon emission. These reduced widths are then divided by V2 w = h2/2ltR 2 to remove the approximate mass dependence of isospin allowed nucleon decay. As a test that this technique is effective in removing the effects of penetrability, similar calculations were performed for a series o f analogous T = ½ levels in mass 13 and 17. The resulting mirror reduced widths were found to agree within experimental errors. The use o f a different value o f r o, or of r = roA~ [as is used in refs. 14, 17, 30)] will produce some variation in relative values o f P, but the main effect will be a gradual change as a function of A. The ratio V2h2, which is plotted in figs. 8-11 depends on the isospin mixing of T = ½ levels into the T = ½ level through Coulomb or other charge dependent inter-

'

'

I ....

I

b

NEUTRON DECAYS/t

NEUTRON DECAYS TO GROUND STATE 10-4

10-4

-:"

r~

10-5

10-5

10"6

10-6 I

2

,

t I,,

5

,I

I

10

20 A

,

/

, I .... I

50

100

I

2

5

20

10

50

I00

A

Fig. 9. Reduced widths for neutron decay o f the lowest T = ½ levels o f A = 4 N + 1 nuclei to (a) the ground state of A = 4 N nuclei and (b) the lowest 2 + level o f A = 4 N nuclei.

T = ½ LEVEL O F 2tNe

....

I ....

I

'

I

487 I

PROTON DECAYS TO EXCITED STATES I 2-(p,f)

10-4 t 4+(d) )'pz

~3-(d)

~17.3-(d)

4*(d )

-(s) ~.(s) 10-5

t

O÷(p)

I

o.,o,

10-6

, , , , I ,i,,I I0

15

I

20

A

3O

I

40

I

50

Fig. 10. Reduced widths for proton decay of the lowest T = ½ levels o f A = 4 N + 1 nuclei to various excited states o f A = 4 N nuclei. The spins and parities o f the final state and the angular m o m e n t u m o f t h e emitted proton are indicated in each case.

actions and also on the probability for decay of these T = ½ levels by nucleon emission. It is worth noting, therefore, that trends observable in the present data are not indicative of the total isospin impurities in these T = ½ levels, but only of those impurities which have significant probabilities for decay to the particular final state observed. The fact that the data in figs. 8 and 9 show such regular trends as a function of mass suggests that the decay widths are not dominated by random admixtures of nearby T = ½ levels, but result from more global properties of the Coulomb or charge dependent nuclear interactions. Some features of the isospin mixing are immediately evident from the data. First, the very different trends for the neutron and proton decay widths suggest that isospin mixing in the A = 4N final nuclei is not the dominant reason for the trends. Such

488

A . B . M c D O N A L D et al. I

i

~

i

i

PROTON DECAYS TO GROUND STATE

/

o

10-4

ANTI-ANALOG /!~ ~ MIXING

/

~f2

I

~

"--.

P

Tz w

I0"5~--

~

~-

x /~. / /

x/

~ ISO VECTOR MONOPOLE MIXING

id6

J

8

I

I

I

10

15

I

I

I

20

50

40

A Fig. 11. Calculations 2o) of isospin-forbidden proton widths of T = ~ levels due to T = ½ admixtures of anti-analogue (squares) and isovector monopole configurations (crosses). Filled circles are the experimental results as listed in table 2.

final state mixing would imply similar widths for analogous neutron and proton decays. As discussed in paper II, the difference in these widths implies isotensor matrix elements for the mixing of T = ½ levels into the T = ~ levels, which are of comparable size to the isovector matrix elements. The general trend of larger neutron widths suggests that the relative phase of the dominant isovector and isotensor matrix elements is the same in the region below mass-20, resulting in larger impurities in the Tz = ½, T = ½ levels. A simple mechanism produced by the Coulomb interaction which could produce larger impurities for T~ = ½ has been suggested by Adelberger et al. 32). Another indication of the presence of two-body (and hence isotensor) contributions to the isospin mixing matrix elements, is the observation that reduced widths for proton decay in mass 13 and 21 are dominated by decays to negative parity states in 12C and 2°Ne (see fig. 10). These decays must result from admixtures of T = ½ configurations from the next major shell [(sd)2(p)7(4He core) in 13N and (pf)2(sd)3(t60 core) in 2tNa]. If T = ~ configurations of this form were present in

T = ~ LEVEL OF 2*Ne

489

TABLE 2 NUCLEON DECAYS OF T=3/9 LEVELS NUCLEUS ENERGY(T=3/2),J g

F(keV)

FINAL S T A T E

FBRANCN(eV)

t

y2(eV)

V2 (x y~

10"6) REFERENCES

(MeV)

9Be

1~.390,

3/2"

0.329

± 0.067

B.(,.9, 09'+

n + ~Be(O.0) n

+ 13C

13N

15.109,

15.066,

3/2-

3/2-

5.8

~ 0.7

0.77 ~ 0.15

:B.(O.O~ ~:

1/2-

5.0 ± 1.0

17F

11.200,

i/2-

0.15 0.~3 + 0.22

21Ne

8.857,

~1. . . . . . . . . . .

25AI

7.901,

5/2 +

2.8 ~ 0.5

÷ .... + 00.25 .08

5/2 +

155 ± 50

33Ci

5.5q8,

1/2 +

110 ± 15

,7~

.........÷

90~20

+

. . . . . . .

/2 +

.....

0.~1,0.38 21.,,.23 8.0 t 1.5 1.3

, 0.7

21,,2,29

73 ± 21 388 ~ 05 70 ~ q9

23 121 22

± 7 ~ 20 i 15

2~,25

~,7

10.8

P + 12 12C(0"0) + C(~.~) + 12 C(7,6)

0++ 2 0+

132 ,i 37 i16 2q W1 IW 7~ 18 126 37

1 1 1

30 ~ ~ 26 ~ IW ± 5 109 ± 27 70 f 21

9.3 i 1.9 8.1 ± 1.7 w.w ~ 1.5 3k ± 8 22 ~ 7

~ 0 0 ~ 1200 ) 250 110

1 1 2

926 ~ 2W7 (257 ~ 113) (2100 ± 900)

338 ~ 80 (94 ± 40) (770 ± 3~0)

3-

i-

n + 180(0,0) ~ 150(0'0) (6.1) 3-

P + 160(0"0) 0+ + 180(,'.0) 0 +

40

1

+10 20 < 17

1 1

+ 30

+1.8 3.6 < 0.7

+ 25

3-

2

79

+ 150(6.9)

2+

100 + ~

1

53 + 31

+ 150(7.1)

1-

60 190 + lO0

0

72

n + 20Ne(0-O)

0÷

n + 20Ne(l.6)

2+

95 - 50

7.5

+ 160(6.i)

< 1000 + 500 2800 - 1000

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the T = ½ levels [which are predominantly (p)9(4He) and (sd)5( 160)] then one-body charge dependent interactions could be responsible for the mixing. It is more likely that the mixing results from two-body charge dependent matrix elements involving the main T = ~ configurations 15). The calculations of Walker and Schlobohm 16) for mass-17 indicate that two-body Coulomb matrix elements can be substantial even for admixtures of (fp)2(p)- 1(160) configurations. Admixtures of this type of configuration may be enhanced 15) because the T = ½ levels lie in a region of excitation energy containing many T = ½ levels of this type. The proton decays to the 0 ÷ ground states (fig. 8a) appear to exhibit an oscillation with a periodicity of 8 in mass number which is superimposed on a general increasing

490

A.B. McDONALD

et al.

trend approximately proportional to A 3.o. The two lines in fig. 8a correspond roughly with the extremal values o f the osicillation and are separated by a factor of 5. It has been suggested 14.30) that these oscillation are correlated with similar variations in the branching ratios for 0t-decay of T = 2 levels in A = 4N nuclei 18), perhaps through an enhancement in isospin mixing in the A = 8 N + 4 nuclei. Although such enhancements is isospin mixing might conceivably arise from some regularity in •-clustering, no strong odd-even effects have been observed in the binding energies between ~-clusters in this mass region and no such trends are evident in spectroscopic factors for ~-transfer 14, 30). The analogous neutron decay widths show a very different variation with mass. As stated above, this suggests that isospin impurities in the final states are not likely to be mainly responsible for the observed reduced widths. Also, the absence of oscillations in the reduced widths for proton decay to the lowest 2 + levels of the A = 4N nuclei (fig. 8b) suggests that there may not be a periodic variation in the total isospin mixing in the T = ~ levels. It is possible that the oscillation arises instead from a variation in the probability for the T = ½ admixtures to decay to the ground state of the A = 4N nuclei. For example, if the T = ½ admixtures have a two-particle, one-hole structure relative to the ground state o f the A = 4N nuclei, as do the T = ½ levels, then the oscillation could be due to variations in the 2p-2h strength in the A = 4N ground states. The isospin allowed decay widths for the T = ½ anti-analogues of the lowest T = ~) levels in 13N and 17F are significantly different [-13N(3.51 MeV)" Yp/YW 2 2 = 0.04; 17F(3.10MeV): 7p/TW 2 2 = 0.007] and suggest smaller 2p-2h components in the 160 ground state than in ~zc. If such effects are responsible for the oscillations, then one would expect somewhat larger and less variable reduced widths for decay to j r = 2+ excited states where 2p-2h configuration admixtures are expected to be larger. This is observed to be so f o r A =<24. The data presented for the neutron decays in fig. 9 cover a limited range o f masses because the T = { levels for A = 4 N + 1 are bound to neutron decays above mass-25. The available data exhibit a much stronger variation with mass than the proton decay data. (The straight lines drawn in figs. 9a and b vary a s .4 7"5 and A 4"9 respectively compared to A 3.0 for the proton decays.) There is an indication from a measurement 19) o f the isospin forbidden (d, p) reaction to the lowest T = ~ level of 4tCa 2 2 ,.~ that ~,/~w ~ 4 × 10-3, suggesting a slower increase in the neutron widths for higher masses. The mass dependence of most types of Coulomb mixing has been discussed by Trainor e t al. ~7) for proton decays to the ground state. Ignoring the variation with mass of the isospin allowed decay probabilities, they conclude that ~'~/~v is proportional to A N with N = 2.6 for isovector monopole mixing into the T = ] level or the T = 0 final states, or N ~ 4 for T = ½ anti-analogue state mixing into the T = ] level via the one-body Coulomb interaction. These mass dependences are borne

T = ½ LEVEL OF 21Ne

491

out by calculations by Lev and Auerbach 20) for the percentage of T = ½ impurity in the T = ½levels due to one-body Coulomb mixing of the anti-analogue configuration or the isovector monopole state. However, as illustrated in fig. 11, the calculated values of the reduced widths for proton decay increase more slowly than A 2 .6 because the probability for isospin-allowed proton emission from the T = ½ impurity decreases with increasing mass, particularly for the monopole state. Neither form of mixing gives a good description of the data. In addition, the same authors 20) calculate the isovector and isotensor components for the Coulomb mixing of the anti-analogue state and find the isotensor components to be less than one-tenth the isovector ones. This would imply similar isospin impurities in the TZ = _ ½, T = ~ levels, and similar widths for neutron and proton emission, which is clearly in conflict with the experimental results. A more comprehensive calculation is now needed that combines coherently all possible mixing contributions from the Coulomb interaction, including effects which are likely to produce significant isotensor admixtures. The latter could arise from mixing of more complicated configurations by the two-body interaction. The effects of charge dependence of the nucleon-nucleon interaction should also be calculated, since it is expected to have significant isotensor components. The data obtained to date have elucidated many qualitative features of isospin mixing and will impose strong constraints on more detailed calculations. The regular trends in the data suggest the domination of similar mechanisms throughout the mass region. A comparison with more comprehensive calculations should reveal those aspects of the Coulomb or charge dependent nuclear interactions responsible for these trends. The authors are pleased to thank E. G. Adelberger and K. A. Snover for helpful discussions and J. L. Gallant for technical assistance in the preparations of targets. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14)

D. C. l-lensley, Phys. Lett. 27B 0968) 644 G. W. Butler, J. Cemy, S. W. Cosper and R. L. McGrath, Phys. Rev. 155 (1968) 1096 J. M. Cameron, G. C. Neilson and T. C. Sharma, Phys. Lett. 36B (1971) 35 R. G. Sextro, R. A. Gough and J. Cerny, Phys. Rev. C8 0973) 258; R. G. Sextro, Ph.D. thesis, U. Calif. Berkeley (1973) unpublished A. B. McDonald, J. R. Patterson and H. Winkler, Nud. Phys. A37 0969) 545 R. C. Bearse, J. C. Legg, G. C. Morrison and R. E. Segel, Phys. Rev. CI (1970) 6()8 A. B. McDonald, T. K. Alexander and O. Hausser, Nu¢l. Phys. 273 (1976) 464 C. Rolls, A. M. Charlesworth and R. E. Azuma, Nucl. Phys. A199 (1973) 257 P. V. Vavilov, JETP (Soy. Phys.) 5 (1957) 749 S. Seltzer and M. Berger, Nucl. Sci. Series no. 39, National Acad. of Sci. Pub. no. 1133 (1963) 187 V. V. Verbinskii, W. R. Burrus, T. A. Love, W. Zobel and N. W. Hill, Nucl. Instr. 65 (1968) 8 J. K. Bair and F. X. Haas, Phys. Rev. C7 (1973) 1356 H. E. Gore, in Nuclear reactions, ed. P. M. Endt and M. Demeur (North-Holland, Amsterdam, 1959) p. 259 E. J. Ludwig, Bull. Am. Phys. Soc. 20 (1975) i187

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A.B. McDONALD et al.

15) E. G. Adelberger, Proc. Int. Conf. on nuclear structure and spectroscopy, Amsterdam, ed. H. P. Blok and A. E. L. Dieperink (Scholar's Press, Amsterdam, 1974) p. 641 16) G. E. Walker and D. Schlobohm, Nucl. Phys. AI40 (1970) 49 17) T. A. Trainor, T. B. Clegg and W. J. Thompson, Phys. Rev. Lett. 33 (1974) 229 18) R. L. McGrath, Nuclear isospin, ed. J. D. Anderson et al. (Academic Press, New York, 1969) p. 29 19) Kamal K. Seth, private communication 20) A. Lev and N. Auerbach, Nucl. Phys. A206 (1973) 563; N. Auerbach and A. Lev, Phys. Lett. 34B (1971) 13; Nucl. Phys. A180 (1972) 651 21) A. B. McDonald, T. K. Alexander, O. H~iusser, D. Disdier, E. G. Adelberger, H. B. Mak, A. P. Shukla and A. V. Nero, Nucl. Phys. 273 (1976) 451 22) J. C. Adloff, K. H. Souw and C. L. Cocke, Phys. Rev. C3 (1971) 1808; J. C. Adloff, W. K. Lin, K. A. Souw and P. Chevallier, Phys. Rev. C5 (1972) 664 23) J. C. Bergstrom, I. P. Auer, M. Ahmad, F. J. Kline, J. H. Hough, H. S. Caplan and J. L. Groh, Phys. Rev. C7 (1973) 2228 24) E. G. Adelberger, A. B. McDonald, C. L. Cocke, C. N. Davids, A. P. Shukla, H. B. Mak and D. Ashery, Phys. Rev. C'/(1973) 889 and references therein 25) E. G. Adelberger, M. D. Cooper, R. E. Marrs and K. A. Snover, Annual Report, Nuclear Physics Laboratory, U. of Wash. 1974, pp. 39, 117 26) F. Hinterberger, P. V. Rossen, H. G. Ehrlich, B. Schiiller, R. Jahn, J. Bisping and G. Welp, Nucl. Phys. A253 (1975) 125 27) J. C. Hardy and R. I. Verrall, Phys. Lett. 13 (1964) 149; J. C. Hardy, Nucl. Data Tables 11 (1972) 327 28) J. R. Patterson, H. Winkler and C. S. Zaidens, Phys. Rev. 163 (1967) 1051 29) J. C. Hardy, J. E. Esterl, R. G. Sextro and J. Cerny, Phys. Rev. C3 (1971) 700 30) P. Ikossi, Ph.D. thesis, U. North Carolina (1975) unpublished; P. G. Ikossi, W. J. Thompson, T. B. Clegg, W. W. Jacobs and E. J. Ludwig, to be published 31) D. R. Goosman and R. W. Kavanagh, Phys. Rev. 161 (1967) 1156 32) E. G. Adelberger, R. E. Marrs and K. A. Snover, to be published