5.63 and 5.80 MeV levels of Ne20; de-excitation branching

j

1.E~4

I v

Nuclear Physics $5 (1964) 145--154; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

5.63 AND 5.80 MeV LEVELS OF NeS°; DE-EXCITATION BRANCHING E. ALMQVIST and J. A. K U E H N E R Chalk River Nuclear Laboratories, Chiffk River, Ontario, Canada Received 27 January 1964 Abstract: The ratio/'y/_P for the 5.63 and 5.80 MeV levels of Ne ~° has been determined to be 0.077

(4-0.008) and < 3 x 10-4, respectively, by using the C1e(C12, u)Ne 20 reaction and determining the fraction of the events in which the alpha-particle and the Ne 20 recoil are present in coincidence at the kinematically correct angles. In both cases these results in themselves are shown to imply radiative E 1 transition (5.63--~ 1.63 and 5.80--, 0, respectively) probabilities ,~ 5 × 10-5 Weisskopf units. When taken together with the life-time for the 5.63 MeV level measured by Evans et aL values o f / ' ( E l ) ~ 5 × 10-6 a n d / ' ~ ~ 6 Yoof the single-particle estimate are obtained for this state. I E

N U C L E A R REACTIONS CI~(C 12, ~')Ne ~°* --~ NeS°+7,, C19(C ts, ac')Neme* ~ O t S + ~ '', Ec12 = 16--22 MeV; measured l(Ne~°)/l(u'), u-spectrum. Ne e° deduced levels, Fy/_P.

]

I

1. Introduction The spins and parities of the 5.63 and 5.80 MeV levels of Ne 2° have been determined by Kuehner 1) to be 3- and 1-, respectively. The present paper which reports some additional work undertaken as part of a general programme of study of Ne 2° levels z) deals with measurements of the ratio of the de-excitation width for gamma radiation relative to the total de-excitation width for these two levels. In the case of the 5.63 MeV level the total width which has been determined recently by Evans et al. 3), can be combined with the results reported here to obtain the corresponding alpha-particle width. For the 5.80 MeV state an upper limit to the radiative width is deduced from the results presented. These radiative widths are of particular interest in astrophysical calculations involving alpha-particle capture by 016 at the high temperatures obtained in super-nova explosions as well as in comparisons with the values of widths computed using nuclear models for the structure of Ne 2°. The experimental method makes use of the fact that the momentum of the recoiling nucleus formed in a nuclear reaction suffers very little change due to gamma-ray emission while in flight, whereas a relatively large momentum change occurs following alpha-particle emission. The measurements, therefore, consist of determining the fraction of the events in which the alpha particle and the corresponding Ne z° recoil satisfy the required kinematic criteria; this fraction can be identified directly with the fraction Fv/F. A recoil-coincidence technique similar to that used by Eccles and Bodansky ~) was used to identify the events in which the recoil suffered little momentum change. The technique is particularly suited to heavy-ion reaction studies because the large centre-of-mass momenta that are associated with heavy 145

146

E. ALMQVIST AND J. A. KUEHNER

projectiles lead to large recoil momenta which in turn makes detection and identification of the heavy recoil-nucleus relatively easy as compared with the much less energetic recoils produced in light particle reactions. The technique is capable of putting a limit on F~/F equal to a few parts in 10". A brief report of some of this work was given at the Rutherford Jubilee Conference 5). 2. Experimental Arrangement

The carbon beam from the Chalk River tandem accelerator was used to.bombard ~, l0/,g/cm 2 self-supporting carbon foils to produce the reactions C t 2 + c t2 --, ~,+Ne20* /~ Ne2°+y "20Xd+~ ''"

(1)

A double-focussing magnetic spectrometer mounted at 60° to the beam selected the primary alpha-particle group (co') corresponding to the particular state of Ne 2° being studied. The energy spread of these alpha particles which results from the centre-of-mass motion is large; the value of dE~dO in the laboratory system is 0.170 MeV per degree for the conditions in question or a total spread of 0.68 MeV over the acceptance aperture of the spectrometer. However, as has been illustrated previously 6) the Chalk River spectrometer provides compensation for this effect 7) so that the resolving power is limited entirely by other considerations of which the most important is target thickness. The spectrum in fig. 1 shows the alpha-particle groups corresponding to the 5.63 and 5.80 MeV states of Ne 2° to be clearly separated by the spectrometer. Clearly a solid state detector cannot achieve this separation in this case except either by stopping down the angular definition to the point where the counting efficiency becomes very low or by some very special arrangement e.g. a position sensitive counter combined with suitable electronic dE~dO compensation. It was for this reason the spectrometer was used as the detector of the primary alpha particles ~'. The remaining reaction products Ne 2°, O t6 and od' were detected in a solid state detector using conventional electronic circuitry. Coincidences within a resolving time 2z equal to 80 ns were required between ~' and the other reaction products. The coincidence spectra were displayed on the Chalk River two-dimensional pulseheight analyser and some of these are illustrated in the course of the discussion that follows. The bombarding energy was chosen in each case to give good yield of the state being examined e.g. 21.9 MeV is shown in fig, 1 to favour the 5.80 MeV state over the 5.63 MeV state. The angle for detection of ~' of 60° was chosen to correspond to a large angle of emission (~ 24°) of the corresponding Ne 2° recoil nucleus. Note that a "large" angle in this context means close to the maximum possible ( ~ 25°) for Ne 2° recoils. The positioning of the recoil counter at a large angle is desirable in order to keep to a low value the intense counting rate arising from elastic scattering which has strong forward peaking. It also happens to correspond to a recoil energy ( ~ 10 MeV) that makes the Ne 2° easy to detect in a solid state counter.

LEVELS

IN

147

Ne t°

The detector system efficiency was calibrated by observing coincidences between

the alpha-particles feeding the 4.25 and the 4.97 MeV states and the corresponding I

!

i

C'Z+C '2 ~Ne2°~ He* I J 5.80

I00

o u

/ 30.1

30.2

30.3

,/i /I

'

' 1 30.5

30.6

30.4

i

t

30.7

30.8

MHz

Fig. l. Spectrometer runs over the alpha-particle groups corresponding to the 5.80 and 5.63 MeV levels in N e a t T h e v a r i o u s s y m b o l s indicate r u n s m a d e at v a r i o u s times. T h e b o m b a r d i n g energy was 21.9 MeV. T h e a r r o w indicates the spectrometer field setting used in the m e a s u r e m e n t o n t h e 5.80 M e V state. 1

25.6"

/

100% 0

80%

x

o,

~ ~

2

40%

20"/.

/ 2°

4"

25.6"

F l,/1

6" 8" 10" 2" 4" 6* DEGREE SCALE (ARBITRARY ZERO}

Fig. 2. T h e ratio o f Ne2°-recoil c o u n t i n g rate (coincidences) to alpha-particle c o u n t i n g rate in t h e spectrometer as a f u n c t i o n o f recoil c o u n t e r position. T h e curve o n the left was obtained with a large aperture o n the recoil counter; that o n the right with the actual aperture that was used. T h e vertical position h a d been o p t i m i z e d p r i o r to these runs. recoiling N e 2° nuclei. In both these cases the residual nuclei are k n o w n to de-excite 100~o by gamma-ray emission so that every ~' has a coincident recoil N e 2° asso-

148

E. ALMQVIST AND . l . A .

KUEHNER

elated with it. The fact that a g a m m a ray may be emitted from the Ne 2° in flight does not change the recoil m o m e n t u m (or energy) appreciably; the m a x i m u m possible effectsfor the cases of interest are angular deflections of +AO < 0.5 ° and energy spreads _+ AE < 0.2 MeV. For every ~' that enters the magnetic spectrometer there is, therefore, a Ne 2° recoil emitted in a direction and with an energy which are both completely defined by the reaction kinematics to lie within narrow limits set by the above spreads plus those associated with the finite angular aperture of the spectrometer. I f the recoil counter is arranged to encompass these limits then the coincidence counting rate between ~' and the Ne 2° recoils must equal 100% of the ~' counting

" 016 ~ Ne2°

(MAGNETIC) Fig. 3. Illustration of directions in which the various associated particles may be emitted when the direction of 0r'is fixed by the spectrometer. The Ole-recoilsand ~'-particles can be emitted in directions that lie within the cones defined by the reaction kinematics. The Nc2°-recoil direction is almost uniquely defined as is discussed in the text. rate except for small effects caused by nuclear scattering in the target. The results illustrated on the left side of fig. 2 were taken with a recoil counter aperture somewhat larger than the estimated limiting values and show that indeed very near to 100 % coincidence efficiency cart be achieved using a solid state detector to count Ne z° recoils. A few percent loss appears to occur, probably largely due to small angle scattering in the target, but this has not been investigated in detail. In actual practice it turned out to be advantageous to somewhat reduce the recoil detector aperture for reasons to be given below. The calibrations for the apertures that were used are shown on the right side of fig. 2 to yield a coincidence efficiency of 75 %. The fact that the efficiency calibration is carried out with states of slightly different energies from those being studied can be shown to have negligible effect provided that the recoil counter is positioned to correspond to the appropriate recoil angle in each case; these positions can b e accurately computed and set relative to the calibration angles of fig. 2 once the latter positions have been determined. I f occasionally the recoiling Ne 2° breaks up while still in flight into O t6 and an alpha particle as is suggested in eq. (1) above, then clearly all the Ne 2° recoils that are detected in coincidence with ~' are associated with the gamma-ray de-excitation branch. Here breakup "in flight" implies a lifetime, • < 1 ns for the recoil coincidence method as described to be applicable. With this proviso the ratio Fr/F is directly

LEVELS IN Ne20

149

given by the ratio of Ne 2° counts in the coincidence spectra to the corresponding number of ~' counts. The efficiency factor obtained from the calibration of fig. 2 must of course be included in the computation of the ratio. It turns out that when the direction of ~' is defined, all associated 016 nuclei have recoil directions that fall within a cone that lies with its axis along the corresponding NeZ°-recoil direction as is shown in fig. 3. Because of their greater velocity the associated break-up alpha particles 0(' are spread out over a cone which subtends an even larger angle about the same direction. A detector placed at the appropriate TABLE 1 Results o f kinematic computations for a b o m b a r d i n g energy o f 21.9 MeV and 0~' being observed at 60 ° with an angular aperture o f 4 ° E*

4.25

4.97

5.63

5.80

E(0c') E(Ne) 0(Ne)

12.35 9.91 25.6 ° 0.7 -1-0.3 °

11.60 9.95 24.7 ° 0.7 ±0.3 °

10.92 9.97 23.9 ° 0.7 -4-0.3 ° 10.55 5.76 8.6 ° 5.12 0.32 36.9 °

10.74 9.98 23.7 ° 0.7 +0.3 ° 10.80 5.98 9.5 ° 5.46 0.24 41 °

6.79

6.82 8.28 3.49 4.87 0

6.83 8.53 3.71 5.21 0

dO(d.E/d.O)(Ne) d0(Ne) £(0)max E(0)min

AO(O)max E(~')max E(o(')min A0(~')max After 325 /~g/em2 AI window E(Ne) E(0)max E(0)min E(0c")max E(0(')min

6.76

All energies are in MeV and angles in degrees in the laboratory system.

angle to see Ne 2° recoils in coincidence with a' will now also show 016 recoils and alpha particles in the coincidence spectrum. It is easy to see that the 016 and ~" particles will each appear with two values of energy corresponding to "forward" and "backward" emission along the Ne 2° recoil direction. These features are clearly apparent in the spectra of fig. 4. Table 1 which is discussed more fully below summarizes some of the kinematic effects for one set of runs. It is typical that one energy value for oc" is very low so that only a single group of alpha particles appear in the region of the spectrum that is displayed. The reason that it is advantageous to ,have the recoil counter subtend precisely the cone of Ne 2 0 recoils or in practice a somewhat smaller rather than a larger angle is that any excess solid angle increases the intensity of the 016 and the alpha-particle peaks relative to the Ne 2° peak. Since the intensity

150

E. A L M Q V I S T A N D J. A . K U E H N E R

of the latter peak is the quantity of interest it is important to reduce the intensity of unwanted groups in this region of the spectrum. A slight drop below 100 % in the coincidence efficiency is not serious and the exact value can be determined by calibration as was indicated earlier. The results of a set of kinematic computations are summarized in table 1. It is immediately apparent that the energy of the Ne 2° recoils are almost independent ii

Iot

/~

o O- 35.7

0

~

~x "(0

a"

tr 20 b-I

o

O3

o (..) Z

~

0 = 33.7*

o

A ]o~o0'+

,o

Z~-

o

_

j

,

,s

I0

0

RANDOM ELASTIC

o~

~ ° o

8=27"7°

O 's .

o o~

RANDOM

ELASTIC

U

-

"

20

Ne~°

O= 23-7 ° RECOIL

,o

1 I0

20

30

40

50

60

70

CHANNEL NUMBER Fig. 4. Recoil coincidence spectra observed at 16.6 MeV bombarding energy and with the spectrometer selecting alpha particles corresponding to the 5.63 MeV state. The lowest spectrum was taken with the counter at the optimum position for Ne=°-recoil detection; the Ne =o group is clearly seen. This group vanishes as the counter is moved away from the recoil direction. The 016 and ="-particle peaks remain as is discussed in the text.

of the Ne 2° excitation energy - all four cases considered have recoil energies in the range 9.91-9.98 MeV. Thus a pulse-height calibration obtained for Ne 2° recoils f r o m any state is valid for the other states. On the other hand the energy broadening due to dE/dO effects is very large being 0.7 MeV in e a c h case which at first sight makes it difficult to resolve the slightly more energetic O 16 group from the Ne 2°recoil group. However, if a foil is inserted between the target and detector the resulting energy losses enhance the separation between the O x6 and the Ne 2° recoils. An absorber nominally equivalent to 325 #g/cm 2 of A1 was used in this experiment and the computed effects on the particle energies are given in the lower part of the table. In practice it was found that some solid state counters had sufficient dead

151

LEVELS IN Ne ~°

layer or "window" on the surface to make additional foil unnecessary. The optimum foil value was determined experimentally. The data shown in fig. 4 were taken with an Au-Si surface barrier detector which had a sui~ciently thick dead layer on the surface to obviate the need for an absorber. The spectra in fig. 5 on the other hand

300 250

C~oo Z O Iso

I00

50

I0

20

30

40

50

IO

20

30

40

50

60

70

SO

90

60

70

80

90

70

60

5 0 - -

l-- 40 z

0 U

30

20

Io -

0

CHANNEL

IO0

NUMBER

Fig. 5. Recoil coincidence spectra observed at 21.9 MeV bombarding energy and with the spectrometer selecting alpha particles corresponding to the 5.80 M e V state. The lower spectrum is at the correct angle for Ne s° recoils but very few counts appear at the expected pulse-height indicated by the arrow. The upper spectra show Ne ~ recoils from the 4.25 and 4.97 M e V states as discussed in the text.

were obtained with a counter that required an additional 300 pg/cm 2 A1 absorber in front of it in order to obtain good separation o f the 016 and Ne 2° peaks. 3. Results The results o f a number of runs on the 5.63 MeV state similar to that illustrated in fig. 4 are summarized in table 2. A spectrum obtained in a long run on the 5.80 MeV level is shown in fig. 5 and above it are two calibration spectra. The spectrum

152

E. ALMQVIffF AND J. A. KUEHNER

in the upper left part of the figure was measured immediately preceding the run on the 5.80 MeV level; the insert was done the previous day. Both these spectra show only the Ne 2° recoil peak. The lower spectrum on the other hand dearly shows O 16 TABLE 2 Summary of results with only statistical errors shown 5.63 MeV state Run number 1 2 3 4 5

Ne2°-recoil counts 119 127 95 86 130

~' counts ~) 1395 1700 1175 1667 1420 Mean

/'~/-P 0.085(:[:0.009) 0.075(4-0.008) 0.081(4-0.008) 0.052(d: 0.006) 0.090(4- 0.009) 0.077(4-0.004)

5.80 MeV state Run number 1

2 3 Sum

ct'

Ne2°-recoil counts

Estimated "tail"

Difference

6

5.0(:[: 1) 5.6(4-1.1) 10.8(4-3.8) 21.4(+4.1)

1.0(±2.6) --2.6(4-2.1) 0.2(~5) -- 1.4(4-6.1)

3 11 20

countsa) 4270 3750 9180 17200

Limit Correction for "tail" of 5.63 MeV state Difference

Fr/1-' × 104 2.3 (4-6) --6.9 (-4-6) 0.22(+5.4) --0.8 (4-3.5) b) < 2.7 1.5 <

a) These are observed counts × efficiency factor. b) This value was computed from the summed counts.

nuclei and alpha particles from the breakup of the 5.80 MeV state in Ne2°; very few counts appear at the pulse height indicated by the arrow which corresponds to the Ne2°-recoil energy. The Ne 2° intensity in this spectrum was estimated by a d d i n g the counts in six channels centered on the arrow and subtracting a background or "tail" from the more intense adjacent peaks. The main uncertainty in obtaining a limit on the Ne2°-recoil yield is in estimating the tail to be expected from the strong 016 peak immediately to the right of the Ne 2° position. It was found that the tail below the peaks depended somewhat on the total counting rate in the detectors. To illustrate this the left-hand calibration spectrum was done with a stronger beam than either the actual run or the inset spectrum; the former obviously has an excessive~ow-energy tail. Care was therefore taken to run with a low beam and to keep conditions the same for all runs including calibrations. Table 2 summarizes all the results obtained.

LEVELS IN Ne80

153

Another source of error that must be kept in mind is the possibility that some ~' particles associated with the state at 5.63 MeV enter the spectrometer counter when this is set to select the 5.80 MeV level. In this case some Ne 2° recoils from the 5.63 MeV state would be observed in addition to those from the 5.80 MeV state. Inspection of fig. 1 suggests that the tail of the 5.63 MeV state is clown by a factor ~ 500 below the intensity of the 5.80 MeV state at the position of the arrow which indicates the spectrometer field at which runs were made. This factor combined with the result for the 5.63 MeV state given in table 2 would lead to an apparent F~/F for the 5.80 MeV state of 1.5 × 10 -4. A correction of this magnitude has been made at the bottom of table 2. The errors quoted in table 2 are statistical only and do not include possible systematic errors in efficiency calibration and estimating background "tails". In the case of the 5.63 MeV state a realistic probable error from all sources in the mean value of the ratio F~/F is estimated to be +0.008. Similarly an allowance for systematic errors somewhat increases the limit on Fy/F for the 5.80 MeV state over the value given in table 2. The most realistic estimates are 5.63 MeV state 5.80 MeV state

Fr/F F~/F

= 0.077(_0.008), < 3 × 10 -4.

4. Discussion The life-time of the 5.63 MeV state has been measured by Evans et al. 3) to be 3.4x 10-13s which corresponds to a total width F of 1.9 meV for this state. This result together with our value for the branching ratio yields the values of partial widths that are listed in table 3 together with the "single-particle" estimate Fsp for the alpha-particle channel. This estimate was made using a computer programme to calculate the Coulomb-barrier penetrabilities for the alpha particles of appropriate angular m o m e n t u m assuming a radius 5.0 fm for the 016 + ~ system and taking the reduced width 7 z = h2/igR2 to be 0.53 MeV. N o experimental determination of the width of the 5.80 MeV state is available. Assuming that the "single-particle" estimate is an upper limit for /',, the widths shown in brackets are derived f r o m the ratio measurement as corresponding upper limits. Since it is generally found in light nuclei that the measured alpha-particle widths are less than 10 ~o of the single-particle unit, (see for example the result for TABLE 3 Widths o f 5.63 and 5.80 MeV levels

Level

Fr/F

F (eV)

T~ (eV)

T~ (eV)

Fsp (eV)

5.63(3--)

0.077

1.9 x 10 -3

0.15 x 10 -8

1.8 x 10 -3

28 x 10 -3

5.80(1--)

< 3 x 10 -~

( < 16)")

( < 5 x 10-8) a)

( < 16) ~)

16

a) These limits are based o n the assumption that the alpha-particle width is the "single-particle" estimate given in the right-hand column; usually observed values are < 0.1 o f this in light nuclei.

154

E. ALMQVIST AND J. A. KUEHNER

the 5.63 MeV state in table 3), the upper limits shown are probably high by a factor of ten or more. It is noted that this paper contains additional measurements to those that had been completed at the time of the Rutherford Conference report 5) and therefore permits a limit that is a factor of ten lower than that previously set on the ratio FT[F for the 5.80 MeV state. An upper limit to the E1 branch of the radiative width is given by F r in table 3. These limits, expressed in terms of Weisskopf units Fw(EI) = 0.068A~E~ are for the most energetic E1 transitions 5.63(3-)~

•

1.63(2 +)

5 . 8 0 ( 1 _ ) ~ 0 ( 0 +)

IMI 2 ~ 5 x 1 0 -6,

Igl z < 5 × 1 0 - s .

For the reasons just mentioned in the previous paragraphs the latter limit is probably a factor of 10 too high. Both these levels, therefore, appear to have similarly strongly inhibited E1 de-excitation rates. This strong inhibition probably reflects in great part the operation of the isobaric spirt selection rule on E1 transitions between T = 0 states in self-conjugate nuclei. In addition a rotational band interpretation s) of the levels of Ne 2 o would suggest an inhibition by the K-selection rule of the E1 transitions from the K = 2, ( 3 - ) 5.63 MeV state to members of the K = 0, positive parity ground state band but not from the K = 0 ( 1 - ) 5.80 MeV state. The fact that the latter appears as inhibited as the former suggests that the K-selection rule itself is not a predominant factor. It appears likely that the reduced alpha-particle width of the 5.80 MeV state like that at 5.63 MeV excitation has a magnitude of at least 5 % of a single-particle unit h2/MR 2, otherwise the E1 transition from the 5.80 MeV state becomes the most inhibited known e.g. an alpha-particle width of 1% of the single-particle estimate leads to IMI 2 < 5 x 10 -7 for the E1 transition using the measured ratio of F~/F. F r o m the astrophysical point of view the limits to the radiative widths set by this work are such as to permit both of these levels to contribute significantly to the formation of Ne 2 o in stars in thermonuclear explosions only where temperatures greater than 5 x 10 s °K are reached 9). This result m a y be of importance since the 2 - assignment to the 4.97 MeV state by Gove et aL xo) rules out participation of this level in thermonuclear reactions involving O 1 6 + H e 4.

References 1) J. A. Kuehner, Phys. Rev. 125 (1962) 1650 2) Clark, Gove and Litberlaad, Can. J. Phys. 39 (1961) 1241, 1243, 1249; Almqvist and Kuehner, Can. J. Phys. 39 (1961) 1246 3) Evans, Gove, Litherland, Broude and Eswaran, (1963) to be published 4) S. F. Eccles and D. Bodansky, Phys. Rev. 113 (1959) 608 5) J. A. Kuehner and E. Almqvist, in Proc. Rutherford Jubilee Conf., ed. by J. B. Birks (Academic Press, New York, 1961) p. 793 6) Pearson, Almqvist and Kuehner, (1963) Can. J. Phys. 42 (1964) 489 7) H. A. Enge, Rev. Sci. Inst. 29 (1958) 885 8) Litherland, Kuehner, Gove, Clark and Almqvist, Phys. Rgv. Lett. 7 (1961) 98 9) A. G. W. Cameron, private communication (1961) 10) Gove, Litherland and Clark, Nature 191 (1961) 1381