- Email: [email protected]
Electromagnetic transitions in 19Ne
I1.---i-~.4
Nuclear Physics A152 (1970) 369--386; (~) North-Holland Publishing Co., Amsterdam
Not to be reproduced by photoprlnt or microfilmwithout written permission from the publisher
ELECTROMAGNETIC
T R A N S I T I O N S I N 19Nc
R. D. GILL, K. BHARUTH-RAM, K. P. JACKSON, R. A. I. BELL t, B. C. ROBERTSON tt, J. L'ECUYER ~, N. G. CHAPMAN ~:~and H. J. ROSE Nuclear Physics Laboratory, Oxford, England
Received 18 February 1970 (Revised 5 May 1970)
Abstract: The Doppler shift attenuation observed with a Ge(Li) v-ray detector was used to gain information on the decay rates of some of the bound states of 19Ne. The values r = 4.1 +3.5 p s , r = 284-15 fs, r = 180-g60 fs and ~ = 330~130 fs have been determined for the 1508, 1536, 1615 and 2795 keV levels respectively. Level energies and decay schemes are reported and angular correlation studies taken together with the lifetime results and mirror level arguments show that the spin-parity sequence for the levels studied is ~-, ~+, ~-- and ~-+ respectively. The results are compared with model calculations. -
E
1.4-
NUCLEAR REACTIONS 19F(p, n), Ep = 8.48 to 10.4 MeV, 160(~, n), E~ = 15.0 to 19.0 MeV; measured ~r(E; En, E~,, 0ny), Doppler shift attenuation. 19Ne deduced levels, lifetimes, branching ratios, J, zr, 6. Natural targets; Ge(Li) detector.
1. Introduction There have been m a n y theoretical discussions o f mass 19 nuclei m a i n l y because of their p r o x i m i t y to the d o u b l y - c l o s e d 160 nucleus [see ref. 1) a n d further references therein], a n d it is therefore o f interest to p r o v i d e e x p e r i m e n t a l d a t a with which the v a r i o u s m o d e l s m a y be tested. I n 19F the low-lying levels have been extensively investigated by various e x p e r i m e n t a l w o r k e r s while in the m i r r o r 19Ne nucleus the d a t a is r a t h e r meagre. The p o s i t i o n s o f several energy levels have been f o u n d 2 - 7 ) a n d the spins o f the g r o u n d a n d first two excited states have been established 2 s) _ the latter albeit using m i r r o r nuclei arguments. In addition, the lifetime o f the first two 9, l 0), a n d the m a g n e t i c m o m e n t o f the first excited state have been d e t e r m i n e d 9) a n d p a r t i a l v-ray decay d a t a 7) exist for the triplet o f levels at 1.5 M e V a n d for some higher levels. I n view o f the theoretical i m p o r t a n c e o f this nucleus we have undert a k e n a study o f the e l e c t r o m a g n e t i c p r o p e r t i e s o f the 1.5 M e V triplet a n d the state at 2.79 MeV.
2. Experimental method The 19Ne levels studied in the present w o r k were p o p u l a t e d using the 19F(p, n ) l 9Ne a n d 160(~, n)19Ne reactions which have Q-values o f - 4 . 0 2 0 a n d - 1 2 . 1 3 5 MeV, t Present address: Nuclear Physics Department, Canberra, Australia. tt Present address: Nuclear Research Centre, University of Alberta, Edmonton, Canada. Present address: Nuclear Physics Laboratory, University of Montreal, Canada. ~: Present address: Department of Physics, University of Wellington, Wellington, New Zealand. 369
370
R.D. GILL et al.
respectively. The incident beams were supplied by the Oxford University Tandem Van de Graaff Generator at proton energies between 8.4 and 10.4 MeV and at e-particle energies of 15 and 19 MeV. The beams were collimated by a series of annuli and stopped in the target backing. The essentials of the experimental method have been described in detail previously [refs. 11,12)]. Neutrons were detected in either a 12.7 cm diam by 15.3 cm long or a 12.7 cm diam by 5 cm thick N E 213 liquid scintillator, each of which had a detection threshold of ~ 1.5 MeV. G a m m a rays were detected in 40 cm 3 Ge(Li) detectors with resolutions of about 6 keV for the 1.33 MeV, 6°Co line. Fast-slow coincidences were determined between the neutrons and g a m m a rays and the resulting logic signals were used to route and gate a 4096-channel A D C interfaced to a PDP-7 on-line computer. Both real and random coincidence 7-ray spectra were collected. The stability of the system was monitored by collecting concurrently a source spectrum obtained by taking coincidences between the Ge(Li) detector and a 7.6 cm by 7.6 cm NaI(TI) crystal with either an Say or Z2STh radioactive source strapped to its front face. The methods of analysis of the angular correlations and the lifetime data were as described in refs. a l, 12) respectively. TABLE 1 G a m m a - r a y energies and deduced excitation energies of states of X9Ne below 3 MeV Transition (keV) 238 275 1508 1536 1615 1615 2795
~ 0 --~ 0 ~ 275 --~ 238 ~ 275 ~ 0 -+ 238
ref. 7)
Er (keV) present
E~ (keV) present
238.4+0.3 274.8±0.3 1226.04-1.1 1303.24-1.1 1332.24-1.1
238.2i0.2 275.14-0.2 1232.84-0.3 1298.04-0.4 1340.1 4-0.4 1615.44-0.7 2556.24-1.5
238.2±0.2 275.14-t-0.2 1507.94-0.4 1536.34-0.5 1615.3 ± 0 . 5 1615.54-0.7 2794.64-1.5
2537.2±3.4
The last column includes small recoil corrections.
2.1. D E C A Y SCHEMES A N D A N G U L A R C O R R E L A T I O N M E A S U R E M E N T S
The 19F(p, n)l 9Ne reaction with a 10 mg/cm 2 Teflon target and incident proton energies between 8.4 and 10.4 MeV was employed to obtain accurate energies and detailed decay schemes for the a 9Ne levels below 3 MeV. Measurements of the angular correlations of the 7-rays emitted in this reaction were used to obtain information on the spins of the levels. The low yield of the 160(c~ ' n)l 9Ne reaction precluded its use for this part of the experiment. 2.1.1. Energy level measurements. For this part of the experiment the larger neutron detector was positioned at 0 ° to the beam direction with its front face 12 cm from the target while the Ge(Li) detector was at 90 ° and 7 cm from the target. The proton bombarding energy of 8.48 MeV prevented the observation of n-7 coincidences for
19Ne ELECTROMAGNETIC TRANSITIONS
37l
19Ne levels above 3 MeV and severely limited the observation of decays from the 2.79 MeV level. An 88y source spectrum, recorded concurrently in the manner previously described, was used to obtain an energy calibration. Corrections for nonlinearity in the detection system were made at energies below 300 keV with wellknown ?-rays from a lS2Ta source and at higher energies with 6°Co and 228Th sources
13).
The energies obtained for the seven dominant transitions observed are listed in table 1 and are compared with those derived by Olness et al. 7) for ?-rays emitted following the :°Ne(aHe, e)t 9Ne reaction. There is good agreement for the two lowenergy transitions but there are marked differences for the higher-energy transitions. Because of the n-y coincidence requirement, the background from competing reactions was very much lower (cf. fig. 1) than was the case for the data of Olness et al. 7). The energy of the (2795 --* 238) keV transition was determined during the experiment to measure the lifetime of this level (subsect. 2.2.3). 2.1.2. Angular distribution measurements. In order to measure the angular distributions of the major transitions the neutron detector was kept at 0 ° to the incident beam direction but was placed 20 cm from the target. This geometric arrangement and the choice of the 19F(p, n ) l g N e reaction simplified the distributions of the coincident ?-rays ~4) by effectively limiting the population of the magnetic substates of the ~9Ne levels formed to values m = +½, +3- The y-ray spectrum summed over angles is 275 keV (275~0)
19Ne gamma rays 19F(p,n 7 )19Ne Ep = 8 - 4 8 MeV
1233keV (1508 ~ 2 7 5 ) 238 keY (258 ~ O)
1298 keV (/536 ~ 2 3 8 )
o
6 /1340 keV 1615~ 2 7 5 ) (xlO 2) 1615 keY 4 ( 1615~0
~E 1377 keV (16}5~238)
1536 keV (1536~01
,, d
50
150
700
800
Chonnel number ~,~ F i g . l . T h e ) , - r a y spectrum s u m m e d over angles taken coincident with neutrons detected at 0°; Ep = 8 . 4 8 M e V . The unlabelled peak at about channel 650 is due to the c o m b i n a t i o n o f the 1 5 3 6 -+ 2 7 5 k e V a n d 1508 -+ 238 k e V transitions.
19Ne
1556~238
50C
I
200
I
1
I
I
I
1615 --,,-- 275 300
Z
200
I
I
1615 "--,-0
50
1
I
30 °
45 °
OI
I
60 °
I
90 °
cos2 /9 Fig. 2. A n g u l a r correlations observed in coincidence with n e u t r o n s for the decay modes o f th~ 1536 and 1615 keV levels.
4OO
~6 3OO z
1508--4"-275
NNNTI,
2OO
1" I
I
1
I
3o °
45 °
60 °
90 °
cos z 0 Fig. 3. A n g u l a r correlations observed for the decay of the 1508 keV level.
19Ne E L E C T R O M A G N E T I C
TRANSITIONS
373
shown in fig. 1 a n d the a n g u l a r d i s t r i b u t i o n s of the p r o m i n e n t y-rays for energies > 1 MeV observed at a b o m b a r d i n g energy of 8.48 MeV are plotted in figs. 2 a n d 3. Also plotted are the results of least-squares fits of Legendre p o l y n o m i a l s to the data. The e x p a n s i o n coefficients o b t a i n e d from these fits a n d similar fits to the 238 a n d 275 keV transitions are listed in table 2. TABLE 2
Summary of the Legendre coefficients observed Transition
a2
a4 a)
0.238 -+ 0 0.275 -+ 0 1.508 ~ 0 , 2 7 5 1.536 -+ 0 , 2 3 8 1.615 --~ 0 0,275 2.795 -~ 0 , 2 3 8
+0.424-0.04 0.0 ±0.02 +0.46±0.08 --0.15::t:0.08 --0.21±0.20 0.0 ±0.08 +0.16~0.13
--0,11 ±0.05 --0.344-0.11
--0.554-0.18
a) A blank in the a4 column indicates that the fit was not substantially improved by including Legendre polynomials of order higher than two. These coefficients have not been corrected for the effect of the finite size of the ),-detector.
1500
o
"S
•
:3
z
I00( 2794
MeV level
2794
---,.,- 0 ' 2 5 8
i
i
i
i
ZO
45
60
90
cos2 8 Fig. 4. Angular correlation observed in coincidence with neutrons for the 2795 --~ 238 keV transition. The spectrum was taken at a proton energy of 10.4 MeV.
O n the basis o f a c o m p a r i s o n with the m i r r o r nucleus 19F, the spins a n d parities of the 238 a n d 275 keV levels in x 9Ne have been assigned as ~+ a n d ½-, respectively, f r o m i n f o r m a t i o n o n the lifetimes 2) a n d relative internal conversion coefficients s) of
R.D. GILL et al.
374
the two levels. The observations in the present experiments, of a significant a4 coefficient for the 238 -~ 0 keV transition and isotropy for the 275 --, 0 keV transition support both these spin assignments. N o more detailed attempt was made to analyse the 238 ~ 0 keV transition since the level was strongly populated by cascade radiation and also because the correlation could well be perturbed considering the long lifetime of the 238 keV state. The non-zero a4 coefficient for the 1508 ~ 275 keV transition requires J >__ ) for the 1508 keV level and similarly the a2 coefficient observed in the decay to the 238 keV state implies J ->_ ~ for the 1536 keV level. The correlations observed in the decay of the 1615 keV level are consistent (to one standard deviation) with the assignments J = ½, ~ or a2. The significance of these correlations is discussed further in sect. 3. TABLE 3 Decay modes of some of the lower levels of 19Ne
E~l/Exf
1508
1536
1615
2794
0 238 275 1508 1536 1615
<3 12~3 88±3
<6 95 ± 3 5±3
20±3 10~3 70±4
<10 100 <10 <12 <10 <10
Fig. 4 shows the angular distribution of the 2795 ~ 238 keV transition observed in coincidence with neutrons detected with the neutron counter at 0 ° and 14 cm from the target. The same Teflon target and a bombarding energy of 10.4 MeV were used. The result of the fit of Legendre polynomial coefficients to this data is shown in fig. 4 and listed in table 2. F r o m the observed a 4 coefficient, it follows that the spin of the 2795 keV level must be > ~. 2.1.3. Branehin9 ratio measurements. The excitation energies of the 19Ne levels below 3 MeV derived from the present experiment are listed in the final column of table 1. The major decay mode of each of the 4 levels between 1 MeV and 3 MeV has been identified by Olness et al. 7). In addition to these previously identified transition, the weaker 1615 ~ 0 keV transition is evident in the data of fig. 1. F r o m the measured energies of each of the levels the anticipated position in the coincident y-ray spectrum for all the possible decay modes of each level were calculated. In order to obtain the relative intensities of these weaker transitions the spectra used to obtai~ the angular distributions of the prominent transitions were summed, and account was taken of the effects of angular correlations and the relative efficiency as a function of energy of the Ge(Li) detector. Additional information was obtained from a spectrum taken with the Ge(Li) detector at 125°: the expected centroid of the peak corresponding to the one at channel 650 in fig. 1 was calculated by assuming that it was composed of the 1536 --*
Effective charge
Porat e l o /
/
3.0
Z
"6
2
820
r~,:.
I
t
",.
*-
°
86O
•
-eat'.
•
•
•e
t
'/
82O
.'_%..,,," -.
Thick target
•
860
Fig, 6, Singles spectra o f the 1346 -+ 110 keY transition t a k e n with the Ge(Li) detector at 0 ° a n d 90 ° with respect to the b e a m direction with b o t h the thick a n d t h e thin target. T h e spectra were a c c u m u l a t e d at E~ = 15 MeV.
2'.0
,
~
/
× in
o
Fig. 5. T h e energy loss of 2°Ne ions in T u n g s t e n . T h e effective charge m e t h o d a n d the f o r m u l a due to L i n d h a r d et al. ~7) have been used. T h e experimental data o f P o r a t et al. ~6) is also shown. T h e solid line indicates the adopted values.
Ii0
/
//////
/ i ~
.rL
Channel number
/
.I
2ONe in W
i
o
a : 90 °
E,I/2 (MeV ~)
0 - -
10
o, 2-0 :::t. >
T''
30
i
f
~= 0 °
Thin to,rget
r60(.~,p)19F 1346 --,,-'-IlO key
T
z
©
f'l
z
O
z
376
R. D. GILL et al. TABLE 4 T h e (dE/dx)e values used in the analysis o f the lifetime data Incident ion
Stopping material
(dE/dx)e ( k e V . / ~ g - 1 . c m 2) for 1 M e V ion energy
2°Ne
W O F Pb CaF2
1.15 6.10 5.02 0.925 3.70
19F
W O Pb
1.12 5.80 0.890
TABLE 5 Lifel~me results Nucleus
Level
E./
Incident
Energy
(keV) a)
(keV) ~
particle
(MeV)
Target
F(T)
"c (ps)
19F
1346
1236
~
15
thin
0.04±0.01
6.5+3:5
19Ne
1508
1233
c~
19
WO 3 thin
0.08-4-0.05
a ~+6.5
0.89=t=0.10
0.043 =t=0.043
0.584-0.06
0.31~0.10
WO 3 1536
1298
1615
1340
19F
1346
1236
15
thick
19Ne
1508
1233
19
thick
1536
1298
1615
1340
1508
1233
1536
1298
0.92±0.09
1615
1340
0.654-0.07
1508
1233
1536
1298
0.254-0.03
WO 3 0.264-0.02
4 ~+3.0 "~- 1.8
0.924-0.05
0.0344-0.024
0.804-0.05
0.10 4-0.04
WO 3
X9Ne
p
8.75
thick
0.224-0.06
CaF2
t9Ne
p
10.4
thick
0.038 +0.052 --0.038 0.234-0,08
0.184-0.05
CaF2 0.974-0.05
1615
1340
0.714-0.05
2795
2556
0.57i0.06
a) T h e 19F energies are t a k e n f r o m ref. 19).
0.015 +0.025 -0.015 0.184-0.06 0.334-0.10
19Ne ELECTROMAGNETIC TRANSITIONS
377
275 keV and 1508 ~ 238 keV transitions. The relative intensities of these two ~-rays was then found by comparing the calculated centroid with the one found in the experimental spectrum. The final branching ratios derived from all the available data are listed in table 3. 2.2. L I F E T I M E M E A S U R E M E N T S
2.2.1. The thin target measurements. The lifetimes of the 1.5 MeV triplet in 19Ne and the 1346 keV state in 19F were investigated with a 500#g. cm -z, WO3 target evaporated onto a thick lead backing and with the 160(e, n ) a n d 160(e, p) reactions, respectively. The c~-particle energy was 19 MeV for the ~gNe states and the Ge(Li) detector was operated in coincidence with the larger neutron detector, which was 13 cm from the target and at 0 °. A 6°C0 source placed near the target provided a continuous monitor of the gain of the system. The F(z) values were extracted from spectra taken at forward and backward angles: the maximum possible shifts were calculated by averaging the possible values of the initial velocity and assuming an isotropic reaction yield while the error in this value was estimated by assuming that the reaction yield over the face of the neutron detector varied by a factor of not more I
~ . ~
.. >.
!gNe in WO 3
"~...
Vo=5.2xlO cnn sec
F (rl
0
I 0.1
I.O v (ps)
Fig. 7. The
F(z)
versus z curve for 19Ne ions in W O a . The broken line shows the corrected F(T) curve which was used in the analysis o f the thick target measurements.
than three. The F(z) versus z curves were calculated from the electronic and nuclear dE/dx values and gave the lifetimes shown in table 5 where an error of 10 ~ was allowed on the electronic dE/dx values which had been calculated both by using the effective charge method ~5) and by interpolation of the 2 ONe data of Porat et al. ~6). These methods were in substantial agreement (see fig. 5), and this was also found to be the case for the other dE/dx values (table 4) which were calculated in this way. The nuclear dE/dx values were calculated using ref. ~7) and were allowed a 15 error. The accuracy of the results was poor due to the low reaction yield and for this reason this part of the experiment was repeated with thick targets. The 19F lifetime was investigated in a singles experiment at 15 MeV (fig. 6). At this energy the uncertainties in the initial ion velocity due to the different possible
378
GILL et al.
R.D.
recoil directions of the out-going proton were small since the threshold for production of this state is 11.8 MeV in the laboratory system and, further, the level of interest could not have been populated by cascade radiation. The effect of the recoils of the excited 19 F nuclei into the lead backing was negligible since the F(z) curves for WO3 and Pb were found to be virtually identical. Our measurement (r --- a. . .a+3.5 . t.5 ps) is consistent with the average 18,19) of the previous measurements: z = 4.9+0.5 ps. 2.2.2. The thick target measurements: the (~, n) reaction. The experiment described in the previous subsection was repeated with 10 rag- cm-2, WO 3 targets prepared by depositing a slurry of WO3 in water on to a lead backing and then heating to drive off the water. The composition of the target was checked by remeasuring the F(r) value for the 19F, 1346 ~ 110 keV transition again at 15 MeV. As a substantial difference from the thin target measurement was found both for the lineshape (fig. 6) and for the F(~) value (table 5), this result was only used to correct the F(z) curves used in the 19Ne part of the experiment (fig. 7). The difference between the two
Ey : 2 5 5 6 k e V (2794 ~ 238) I00
•
•
•
~n = 0 ° 87 = 90 °
o•
50 •
•
OlD
"5 E =
Z
0
I
I
8n = 9 0 ° •
8;,. = 3 0 °
50 •
o•
O•
•
•
I
2500
OlD
I
2600
Channel number Fig. 8. The neutron coincident 7-ray spectrum o f the 2 7 9 5 --> 2 3 8 k e V transition. The p h o t o p e a k is s h o w n and sits on a b a c k g r o u n d w h i c h was t h o u g h t to be due to various l o w Z impurities in the b e a m stopper.
379
19Ne ELECTROMAGNETIC TRANSITIONS
19F
(p,n)!gNe
Ep = 8.75 MeV
~,, = 150 °
1298 (1556 ~
100
i233 keV ( 1 5 C ~ E ~ 275) £
275 2:58 0
I/a- 5 + ~/z+ /z
258 ) 1340 keV 0615~275)
i,~ 1'1
O>.= 120 ° ]615 keV (1615~0)
.~
, •
•
0
(3&-)(3&+
(%-)
keY
50
8 "3
z
r6i5 _ _ ,5o8
°
__
I
° •
~ " °° I I
°
I I
L~
I I
.I],
I i"
*,,"
t
/I
°~. I --
°,1' •
I I
o~,~'-.•=s °°
~",-'Y~ •
Ir
I
L_ 7 I
100
Io I 1
Or=50 °
J
• .-..
.-
.
/'.
,.'5 • "g-~
1150
1200
1250
1500
°
1550 ChGnnel
--°'~,,~
•
14001560
° ° ," • •
1600
."i
~*
°"
1650
number
Fig. 9. N e u t r o n coincident 7-ray spectra taken at a proton energy of 8 . 7 5 M e V . The upper half corresponds t o 0~ = 1 5 0 °, = 1 2 0 ° whilst the lower half has 0~ = 1 5 0 ° a n d 0 T = 30 °.
07
results was attributed to the escape of some o f the 19 F ions from the grains which made up the target before they had been properly slowed down. This supposition was reasonable in as much as the mean grain size was comparable with the range of the excited 19 F ions. A detailed description of the corrections made to the calculated F(z) curves to account for structural effects in the targets appears as the appendix. The t 9Ne levels were studied at a beam energy of 19 MeV with the larger neutron detector at 0 °, 13 cm from the target. The F ( 0 values were extracted from spectra taken at forward and backward angles. The a9Ne, 1508 -* 275 keV transition was found to have an F(z) value of 0.26_+ 0.02 which, with the corrected curve (see fig. 7), gave a lifetime z . . . .m . ~+3.0 1.4 ps in agreement with the thin target measurement. The error on this value was increased because of the large corrections which had been made to the F(~) curve, which gives z = 4.1+3"5-1.4ps on combining the two results. The 1536 and 1615 keV level decay y-rays were also affected by the correction but, as their F(T) values were much larger, the correction was relatively less important since the mean range of the excited 19Ne nuclei was much smaller. 2.2.3. The (p, n) reaction. As it was impossible to populate the 2795 keV level at the available a-particle energies, this level was studied using protons of 10.4 MeV and a thick CaF2 (10 rag" cm -2) target on a gold backing. The smaller neutron
R.D. GILLet al.
380
detector was used at 90 ° with its plane faces vertical a n d its edge facing the target. This reduced the u n c e r t a i n t y in the m e a n initial recoil velocity of the 19Ne ions due to the v a r i a t i o n of n e u t r o n angle in the horizontal plane. The G e ( L i ) detector was at 30 ° opposite the n e u t r o n c o u n t e r whilst the positions of the unshifted peaks (from which the energy of the 2795 keV level was determined) were f o u n d using 0 n = 0 ° a n d 0e = 90 ° (fig. 8). Data were also a c c u m u l a t e d for the t9Ne, 1.5 MeV triplet and,
TABLE6 Transition strengths in 19Ne derived from the present experiment Initial state Exl
j~r
(keV)
Final state
rm
F,°tal (meV)
multipole
"~7 +1"8 -0.9
0 238 275 0 238 275 0
3+ ~+ ½½+ ~+ ½½+
M2 E1 E2 M1 M1 E1 E1
<9•0 (2.0± 1.0) × 10-5 214-10 <4.1 N: 1 0 - 2 0• 50 -+0.56 0.17 (1.2+2: O) × 10 -3 + 1 o9) × 10-4 (3.6_11
20 +1"3 • -0.6
238 275 238
:)+ ½.~+
E1 M1 E2
+1 7 × 10-4 (2.9_a~1) +2 6) × 10-2 (5•1 _1:3 7 4 +4.8
(keV)
1508
~-
4• 1+3.5 --1•4-
1536
~-+
0.028~0.015
1615
~r-
0•18 4-0.06 . . .
2795
2+
0.33 4-0.13
[M[Z t,)
jzr
(ps) a)
Exf
Lowest
0.17=t=0.08 24_+827
.
-•---2•2
") The values of the lifetimes quoted in this column are weighted averages of those in table 5 and the quoted uncertainties include estimates of both the systematic and random errors• b) The transition strengths are expressed in Weisskopf units 20) and the errors reflect both the uncertainties in the lifetime measurements and in the branching ratios listed in table 3. now, the long-lived 1508 keV state data were used to correct the F(z) curve. The results are s u m m a r i z e d in table 5. The experiment o n the triplet was repeated at a lower b e a m energy this time with the smaller n e u t r o n detector edge-on at 150 ° a n d 13 cm f r o m the target. Some of the data are shown in fig. 9. The lifetime results f r o m this a n d the previous part of the experiment were c o m b i n e d a n d are s h o w n in table 6.
3. Synthesis of experimental results 3.1. THE 1508 keV LEVEL As n o t e d in subsect. 2.1.2 the a n g u l a r correlation data restricted the spirt of this level to J ~ ~z a n d the lowest order multipole r a d i a t i o n c o n t r i b u t i n g to the t r a n s i t i o n to the ½-, 275 keV level is therefore E2 or M2 according to the parity of the state. U s i n g our measured width a n d the Weisskopf single-particle estimates 2o) it can be
3’
3-
8’
1508
1536
1615
2795
b, Ref. g). e, Ref. 26).
4’ *.$-
238 215
“) Ref 25) r) Ref. 27):
Jr”
Initial level (rgNe) (keV)
“) Ref. lo). “) Refs. 24*28).
238
t+
238 275 0 238 275
TABLE 7
7.4
0.5 1.2x lo-3 3.6x lO-4 2.9 x lO-4 5.1 x10-2
<-10’ <4.1 x lo-2
M3 Ml E2
<9.0 2x 10-5 21
Ml El El El Ml E2 E2
r9Ne
13.4 a*y 1.07 x 10-3 ‘)
exp. IMj2
El E2
M2 E3
E2 El
Assumed multipole
12x 10-Z 26.1 22.1
1.59
1.13x 10-Z 20.4
25.9
19.7
theor. jMjZ
of the mass-19 data with Benson’s model 19F
2.65 ‘) 5.3 x 10-S ‘) 1.17x 10-a ‘) 8.75 x lO-4 ‘) 9.6x lO-2 “) 23.2 p, 8.8 b)
3.9 x‘) 10-Z ‘) 6.8
6.0x lO-6 ‘) 18.1 ‘)
<2.9 ‘) 7.6 ‘)
6.7 “) 1.02x 10-3 d)
exp. [Ml2
17x 10-Z 26.8 7.1
2.10
7.2 1.19x10-‘
27.5
10
8.0
theor. lM/’
d, Ref. 21). ‘) The averaged values for the branching ratios and lifetimes as quoted in ref. r9). The numbers in the theoretical columns are discussed in sect. 4.
%+
+ :3’ 3-
3’
4’ 8-
;:
*+
JP
0
238 275
0
0 0
Final level (r9Ne) (keV)
Comparison
;
; =!
2
3
z ,z F z A” P !j
382
R.D. GILLe t
al.
seen that the radiation must be E2; M2 radiation would require a n IMI 2 > 500 which may be excluded since enhancements of this order have never been encountered in light nuclei 22). Since higher multipolarities may be excluded on similar grounds we conclude that J ~ = 5 - for this level. The angular correlation data for the 1508 ~ 275 keV transition were analysed as described in ref. ~a) for an initial spin of 5. The relative populations of the m = +__½ and +__~substates of the initial state had to be determined from the data. The value of the M3/E2 mixing ratio, 6, was found to have the solutions + 0.1 + 0.2, -0.6___ 0.2, " 4 +~'~ z. -0.8 and - 5 _+2 4 for the 1508 ~ 275 keV transition where the phase convention of ref. zl) has been used. All solutions except the first may be discarded since even the value 6 = - 0 . 6 would imply an M3 enhancement of 2.5 x 10 v. The transition strengths observed in the decay of the 1508 keV level expressed in Weisskopf units, are shown in table 7. 3.2. THE 1536 AND 1615 keV LEVELS The angular correlation data for the 1536 keV level indicates that J > 3. The partial width for the 95 ~ branch to the ~+, 238 keV state is 0.02 eV. F r o m a comparison with Weisskopf estimates this transition must be predominantly dipole since a pure E2 transition would imply an enhancement factor of greater than 2000. Hence the values of J are limited to z2, -~-or -~. The angular correlation data were analysed for these spin values. For J = 5, 6 was greater than 0.27 which, for positive parity, would require an E2 enhancement of 200 which is unlikely, while, for negative parity, an even larger enhancement would be required for the M2 radiation. For similar reasons all the solutions for J = -~ ( + o c , ~ 0 or + 5 . 8 ) w e r e discarded except for 6 ~ 0. For J = 3 the value of 6 was not restricted. At this point we must resort to mirror level arguments: the triplet of states in 19 F at ~ 1.5 MeV has the spin parity sequence 2) 5 - , 3 - and ~+ with the first state corresponding to the 19Ne, 1508 keV state, implying that both the remaining ~9Ne states have J = ~. F r o m a comparison of the decay schemes 2,19) and lifetimes 19) in the two nuclei it is clear that the 1536 and 1554 keV states (J~ = ~+) correspond and that the 1615 and 1459 keV states also form a mirror pair (J~ = z2-). The angular distributions of the 1615 keV decay modes were then analysed assuming J(1615) = -~ but no information on the mixing ratio was obtained. Again, the decay widths have been collected in table 7. 3.3. THE 2795 keV LEVEL The angular distribution of the 2795 ~ 238 keV transition shows an a 4 term implying that J > 5 and that the transition proceeds appreciably via quadrupole radiation 22). The measured lifetime further restricts the multipolarity of the transition to El, M1 or E2 (for M2, [ M I 2 = 170 which can be excluded) which then implies that the possible spin parity assignments are J ~ = ~+, ~+ or 3 +. In the
19Ne ELECTROMAGNETICTRANSITIONS
383
~,fe reaction this state was apparently seen to be excited b;y an l = 4 j which would agree with the last two possibilities. The mirror state in ~Nel~l~y 24) has J = -~-thus implying J~ = 3 + for the 19Ne level. e~orrelation was analysed with this initial spin value and the solutions ~ = _+_0.5, < - 2 . 7 and > +5.7 were found of which the latter pair may be dis.cded since they both imply an M3, IM[ z > 107. Hence, 6 = - 0 . 1 0 . 5 . A level scheme combining the results of this section is shown in fig. 10. 9/~
I00
-
70 I0 20 5 95 88 12
%-
I/2 5/2
2794
1615 1556 1508
2.75 238
~'
I/2+ ~gNe
Fig. 10. 19Ne decay modes observed in this work.
4. Discussion
The positive parity states of the mass-19 nuclei have been successfully described [refs. 2,29,30)] by intermediate coupling calculations in which the three valence particles outside the doubly closed 260 core were allowed to move in the (2s, ld) shell. In the early calculations 29,30) these particles were allowed to interact via a residual force the parameters of which were then adjusted to give the best overall agreement between the experimental and theoretical spectra. In particular, these calculations predict low-lying levels with J~ = ½+, ~+, ~+ and 29-+ which may be identified with the lowest positive parity states in 19F and 19Ne" The Nilsson rotational model has also been used to describe the low-lying positive parity states as mixtures of the K = ½+ and ~+ bands 31). The relationship between these two models has been discussed in ref. 2). The low-lying negative parity states in the mass-19 spectra were first described by Harvey 32) who used an SU3 model and, more recently, by Benson and Flowers 1). The latter described these levels as mixtures of the K = ½- and ~ - rotational bands formed by coupling a p½ or pl hole on to the
384
R.D. GILLet aL
ground state rotational band of 2°Ne. It was found that, for the lowest few states, these wave functions had a large overlap with those of ref. 32). The calculations of ref. 1) have been repeated for 19Ne t again with the KallioKolltveit potential and the Moszkowski-Scott separation method to deal with the hard core. Harmonic oscillator wave functions were used with a radius parameter of 1.69 fm. The electromagnetic transition rates, however, were calculated with the Woods-Saxon single-particle wave functions. This is reasonable in view of the fact that the electromagnetic decay rates are very sensitive to the fall-off of the wave functions at large distances. An effective charge of 0.25e was used for both proton and neutron: this value, which is larger than the 0.1e used for the 2°Ne rotational 5+ ~ ~o 1+ and zo a+ ~ ~o ~+ E2 decay band x), was originally chosen 1) by fitting the ~o rates in t9F. The theoretical and experimental results are compared in table 7; the 19F predictions have been taken from ref. 1). It can be seen from table 7 that the general features of the M 1 and E2 decays of the positive parity states are well described a + transition; by the model which, for example, explains the weakness of the ~ - ~ ~o s+ and To 1+ is 1.4~o which the theoretical branching ratio for the decays to the ~o compares with the experimental value of < 6 ~o which just approaches the region ot interest. This feature also emerges from the early Elliott and Flowers 29) calculation and can be readily understood in terms of the relative amplitudes of the different components of the appropriate wave functions. The 2.79 MeV E2 decay is slower than predicted by a factor of about 3. This is well outside the experimental error although the theoretical value could presumably be reduced by using a smaller effective charge. Of the data which can be compared with theory in 19Ne this is the only real discrepancy. As has been noted in ref. 1), the lowest negative parity states are predominantly composed of the K = ½- band. Transitions between states in the same band are characterised by large E2 strengths and vanishing M1 strengths. This rule is obeyed well for both the-~o and ~o states: the observed and calculated M1 strengths are then due to the small amount of K = ½- and ~ - band mixing which occurs. We would like to thank Drs. D. A. Hukin and G. Garton for discussions concerning the target structure. One of us (K.B.R.) would like to thank the CSIR (South Africa) for financial support and another (K.P.J.) is indebted to the N R C (Canada) for an overseas postdoctoral fellowship.
Appendix As has been mentioned in subsect. 2.2 the theoretical F(z) for a given material must be corrected for structural effects in the target materials which may arise from the method of preparation. While for evaporated thin targets of the WO 3 layers are likely to be unitbrm with a grain size smaller than 1 p m and an average density which t We are indebted to Dr. H. G. Benson for these calculations.
19Ne ELECTROMAGNETIC TRANSITIONS
385
is between 1 and 2 70 lower than the bulk density, thick targets show grain sizes between I and 5/tin. The density of the grains is exactly the density of the single crystals, but there are spacings between the grains and consequently corrections must be applied. The change of the experimental F(~) for the ~9F, 1236 keV transition (cf. table 5 and subsect. 2.2) provides one empirical point for the (corrected) thick target F(z) function in the region where this function is most sensitive to structural effects (fig. 7). The shape of the corrected thick target F(r) curve relative to the thin target curve is then obtained as described below. We consider the modifications to be made to F ( z ) when the initial excited nuclei are produced in a slab of thickness, l, which is greater than the mean range, R, of the nuclei. If nuclei at a distance x from the front surface of the slab are produced with a velocity Vo and escape with a velocity v¢ (both velocities are perpendicular to the faces of the slab) then it can easily be shown that the observed F'(T) may be related to the F(v) value when no particles escape by ~'(T)
=
F(T)-~
/'/eve ( I - - F ~ ) ,
(1)
IIOV0
where no and n~ are the initial number and number of escaping nuclei and Fe(z) is the F(r) value with respect to an initial velocity, G, the n~ particles would have had had they recoiled in the solid medium. To obtain the observed F ' ( v ) the above equation must be integrated over the dimensions of the slab but we will first introduce the following: (i) We assume that G = Vo e -t/~ where c~ is chosen to include the effects of nuclear scattering. Empirically, this is a reasonably good approximation. (ii) G = no e-t/L (iii) We assume that Fe(~) is independent of G and further, that F~(r) is equal to the value of F(r) evaluated for v = vo. If the effects of nuclear scattering were not present then this assumption would be correct in the cases in which the energy loss was proportional to the velocity. In terms of x we then obtain: =
o(1
-OCVo
,
l)e =
V0
(
1--
. C(Vo
Integrating equation (1) with respect to x gives F ' ( Q = F ( r ) + (1--F¢) R (2+ oc/r) l
(2)
This equation still does not take into account the possibility that the particles which compose the target are of varying sizes. Due to a lack of detailed information this is usually best taken care of by using the formula F ' ( Q = F ( r ) + f l 1 - F(z), 2 + c~/r
(3)
386
R.D. GILL et al.
a n d t r e a t i n g / 3 as a p a r a m e t e r t o b e d e t e r m i n e d f r o m t h e e x p e r i m e n t . T h i s h a s b e e n done in the present experiment.
References 1) H. G. Benson and B. H. Flowers, Nucl. Phys. A126 (1969) 305 2) F. Ajzenberg-Selove and T. Lauritsen, Nucl. Phys. 11 (1959) 1; T. Lauritsen and F. Ajzenberg-Selove, Nuclear data sheets, compiled by K. Way et al. (National Academy of Sciences, National Research Council, Washington D.C., 1962, sets 5 and 6) 3) J. M. Freeman and D. West, Nucl. Phys. 38 (1962) 89 4) J. J. Wesolowski et al., Nucl. Phys. 71 (1965) 586 5) M. W. Greene and E. B. Nelson, Phys. Rev. 153 (1967) 1068 6) K. Gul, B. M. Armitage and B. W. Hooton, Nucl. Phys. A122 (1968) 81 7) J. W. Olness, A. R. Poletti and E. K. Warburton, Phys. Rev. 161 (1967) 1131 8) W. W. Givens, R. C. Bearse, G. C. Phillips and A. A. Rollefeson, Nucl. Phys. 43 (1963) 553 9) J. Bleck et al., Nucl. Phys. A123 (1969) 65 10) R. J. Nickles, Nucl. Phys. A134 (1969) 308 11) O. H~iusser, J. S. Lopes, H. J. Rose and R. D. Gill, Oxford Nuclear Physics lab. rep., 1966, unpublished 12) B. C. Robertson et al., Nucl. Phys. A126 (1969) 431 13) J. B. Marion and F. C. Young, Nuclear reaction analysis (North-Holland, Amsterdam, 1968); C. M. Lederer, J. M. Hollander and I. Perlman, Table of isotopes 6th ed. (Wiley, New York, 1967) 14) A. E. Litherland and A. J. Ferguson, Can. J. Phys. 32 (1961) 378 15) R. D. Gill, J. S. Lopes, O. H/iusser and H. J. Rose, Nucl. Phys. A121 (1968) 209; L. C. Northcliffe, Ann. Rev. Nucl. Sci. 13 (1963) 67 16) D. I. Porat and K. Ramavataram, Proc. Phys. Soc. 77 (1961) 1135 17) J. Lindhard, M. Scharff and H. E. Schiott, Mat. Fys. Medd. Dan. Vid. Selsk. 33 No. I0 (1963) 18) K. W. Jones, A. Z. Schwarzschild, E. K. Warburton and D. B. Fossan, Phys. Rev. 178 (1969) 1773 19) A. R. Poletti, J. A. Becker and R. E. McDonald, Phys. Rev. 182 (1969) 1054 20) D. H. Wilkinson, Nuclear spectroscopy, Part B, ed. F. Ajzenberg-Selove (Academic Press, New York, 1960) 21) S. J. Skorka, J. Hertel and T. W. Retz-Schmidt, Nucl. Data 2 (1966) 347 22) H. J. Rose and D. M. Brink, Rev. Mod. Phys. 39 (1967) 306 23) D. J. Baugh, J. Nurzynski, D. M. Rosalky and C. H. Osman, Austral. J. Phys. 22 (1969) 555 24) D. D. Tolbert, P. M. Cockburn and F. W. Prosser, Phys. Rev. Lett. 21 (1968) 1535 25) J. A. Becket, J. W. Olness and D. H. Wilkinson, Phys. Rev. 155 (1967) 1089 26) J. D. Prentice, N. W. Gebhie and H. S. Caplan, Phys. Lett. 3 (1963) 201 27) T. K. Alexander, O. H/iusser, K. W. Allen and A. E. Litherland, Can. J. Phys. 47 (1969) 2335 28) K. P. Jackson, K. Bharuth-Ram, P. G. Lawson, N. G. Chapman and K. W. Allen, Phys. Lett. 30B (1969) 162 29) J. P. Elliott and B. H. Flowers, Proc. Roy. Soc. A229 (1955) 536 30) M. G. Redlich, Phys. Rev. 99 (1955) 1427 31) E. B. Paul, Phil. Mag. 2 (1957) 311 32) M. Harvey, Nucl. Phys. 52 (1964) 542
Nuclear Physics A152 (1970) 369--386; (~) North-Holland Publishing Co., Amsterdam
Not to be reproduced by photoprlnt or microfilmwithout written permission from the publisher
ELECTROMAGNETIC
T R A N S I T I O N S I N 19Nc
R. D. GILL, K. BHARUTH-RAM, K. P. JACKSON, R. A. I. BELL t, B. C. ROBERTSON tt, J. L'ECUYER ~, N. G. CHAPMAN ~:~and H. J. ROSE Nuclear Physics Laboratory, Oxford, England
Received 18 February 1970 (Revised 5 May 1970)
Abstract: The Doppler shift attenuation observed with a Ge(Li) v-ray detector was used to gain information on the decay rates of some of the bound states of 19Ne. The values r = 4.1 +3.5 p s , r = 284-15 fs, r = 180-g60 fs and ~ = 330~130 fs have been determined for the 1508, 1536, 1615 and 2795 keV levels respectively. Level energies and decay schemes are reported and angular correlation studies taken together with the lifetime results and mirror level arguments show that the spin-parity sequence for the levels studied is ~-, ~+, ~-- and ~-+ respectively. The results are compared with model calculations. -
E
1.4-
NUCLEAR REACTIONS 19F(p, n), Ep = 8.48 to 10.4 MeV, 160(~, n), E~ = 15.0 to 19.0 MeV; measured ~r(E; En, E~,, 0ny), Doppler shift attenuation. 19Ne deduced levels, lifetimes, branching ratios, J, zr, 6. Natural targets; Ge(Li) detector.
1. Introduction There have been m a n y theoretical discussions o f mass 19 nuclei m a i n l y because of their p r o x i m i t y to the d o u b l y - c l o s e d 160 nucleus [see ref. 1) a n d further references therein], a n d it is therefore o f interest to p r o v i d e e x p e r i m e n t a l d a t a with which the v a r i o u s m o d e l s m a y be tested. I n 19F the low-lying levels have been extensively investigated by various e x p e r i m e n t a l w o r k e r s while in the m i r r o r 19Ne nucleus the d a t a is r a t h e r meagre. The p o s i t i o n s o f several energy levels have been f o u n d 2 - 7 ) a n d the spins o f the g r o u n d a n d first two excited states have been established 2 s) _ the latter albeit using m i r r o r nuclei arguments. In addition, the lifetime o f the first two 9, l 0), a n d the m a g n e t i c m o m e n t o f the first excited state have been d e t e r m i n e d 9) a n d p a r t i a l v-ray decay d a t a 7) exist for the triplet o f levels at 1.5 M e V a n d for some higher levels. I n view o f the theoretical i m p o r t a n c e o f this nucleus we have undert a k e n a study o f the e l e c t r o m a g n e t i c p r o p e r t i e s o f the 1.5 M e V triplet a n d the state at 2.79 MeV.
2. Experimental method The 19Ne levels studied in the present w o r k were p o p u l a t e d using the 19F(p, n ) l 9Ne a n d 160(~, n)19Ne reactions which have Q-values o f - 4 . 0 2 0 a n d - 1 2 . 1 3 5 MeV, t Present address: Nuclear Physics Department, Canberra, Australia. tt Present address: Nuclear Research Centre, University of Alberta, Edmonton, Canada. Present address: Nuclear Physics Laboratory, University of Montreal, Canada. ~: Present address: Department of Physics, University of Wellington, Wellington, New Zealand. 369
370
R.D. GILL et al.
respectively. The incident beams were supplied by the Oxford University Tandem Van de Graaff Generator at proton energies between 8.4 and 10.4 MeV and at e-particle energies of 15 and 19 MeV. The beams were collimated by a series of annuli and stopped in the target backing. The essentials of the experimental method have been described in detail previously [refs. 11,12)]. Neutrons were detected in either a 12.7 cm diam by 15.3 cm long or a 12.7 cm diam by 5 cm thick N E 213 liquid scintillator, each of which had a detection threshold of ~ 1.5 MeV. G a m m a rays were detected in 40 cm 3 Ge(Li) detectors with resolutions of about 6 keV for the 1.33 MeV, 6°Co line. Fast-slow coincidences were determined between the neutrons and g a m m a rays and the resulting logic signals were used to route and gate a 4096-channel A D C interfaced to a PDP-7 on-line computer. Both real and random coincidence 7-ray spectra were collected. The stability of the system was monitored by collecting concurrently a source spectrum obtained by taking coincidences between the Ge(Li) detector and a 7.6 cm by 7.6 cm NaI(TI) crystal with either an Say or Z2STh radioactive source strapped to its front face. The methods of analysis of the angular correlations and the lifetime data were as described in refs. a l, 12) respectively. TABLE 1 G a m m a - r a y energies and deduced excitation energies of states of X9Ne below 3 MeV Transition (keV) 238 275 1508 1536 1615 1615 2795
~ 0 --~ 0 ~ 275 --~ 238 ~ 275 ~ 0 -+ 238
ref. 7)
Er (keV) present
E~ (keV) present
238.4+0.3 274.8±0.3 1226.04-1.1 1303.24-1.1 1332.24-1.1
238.2i0.2 275.14-0.2 1232.84-0.3 1298.04-0.4 1340.1 4-0.4 1615.44-0.7 2556.24-1.5
238.2±0.2 275.14-t-0.2 1507.94-0.4 1536.34-0.5 1615.3 ± 0 . 5 1615.54-0.7 2794.64-1.5
2537.2±3.4
The last column includes small recoil corrections.
2.1. D E C A Y SCHEMES A N D A N G U L A R C O R R E L A T I O N M E A S U R E M E N T S
The 19F(p, n)l 9Ne reaction with a 10 mg/cm 2 Teflon target and incident proton energies between 8.4 and 10.4 MeV was employed to obtain accurate energies and detailed decay schemes for the a 9Ne levels below 3 MeV. Measurements of the angular correlations of the 7-rays emitted in this reaction were used to obtain information on the spins of the levels. The low yield of the 160(c~ ' n)l 9Ne reaction precluded its use for this part of the experiment. 2.1.1. Energy level measurements. For this part of the experiment the larger neutron detector was positioned at 0 ° to the beam direction with its front face 12 cm from the target while the Ge(Li) detector was at 90 ° and 7 cm from the target. The proton bombarding energy of 8.48 MeV prevented the observation of n-7 coincidences for
19Ne ELECTROMAGNETIC TRANSITIONS
37l
19Ne levels above 3 MeV and severely limited the observation of decays from the 2.79 MeV level. An 88y source spectrum, recorded concurrently in the manner previously described, was used to obtain an energy calibration. Corrections for nonlinearity in the detection system were made at energies below 300 keV with wellknown ?-rays from a lS2Ta source and at higher energies with 6°Co and 228Th sources
13).
The energies obtained for the seven dominant transitions observed are listed in table 1 and are compared with those derived by Olness et al. 7) for ?-rays emitted following the :°Ne(aHe, e)t 9Ne reaction. There is good agreement for the two lowenergy transitions but there are marked differences for the higher-energy transitions. Because of the n-y coincidence requirement, the background from competing reactions was very much lower (cf. fig. 1) than was the case for the data of Olness et al. 7). The energy of the (2795 --* 238) keV transition was determined during the experiment to measure the lifetime of this level (subsect. 2.2.3). 2.1.2. Angular distribution measurements. In order to measure the angular distributions of the major transitions the neutron detector was kept at 0 ° to the incident beam direction but was placed 20 cm from the target. This geometric arrangement and the choice of the 19F(p, n ) l g N e reaction simplified the distributions of the coincident ?-rays ~4) by effectively limiting the population of the magnetic substates of the ~9Ne levels formed to values m = +½, +3- The y-ray spectrum summed over angles is 275 keV (275~0)
19Ne gamma rays 19F(p,n 7 )19Ne Ep = 8 - 4 8 MeV
1233keV (1508 ~ 2 7 5 ) 238 keY (258 ~ O)
1298 keV (/536 ~ 2 3 8 )
o
6 /1340 keV 1615~ 2 7 5 ) (xlO 2) 1615 keY 4 ( 1615~0
~E 1377 keV (16}5~238)
1536 keV (1536~01
,, d
50
150
700
800
Chonnel number ~,~ F i g . l . T h e ) , - r a y spectrum s u m m e d over angles taken coincident with neutrons detected at 0°; Ep = 8 . 4 8 M e V . The unlabelled peak at about channel 650 is due to the c o m b i n a t i o n o f the 1 5 3 6 -+ 2 7 5 k e V a n d 1508 -+ 238 k e V transitions.
19Ne
1556~238
50C
I
200
I
1
I
I
I
1615 --,,-- 275 300
Z
200
I
I
1615 "--,-0
50
1
I
30 °
45 °
OI
I
60 °
I
90 °
cos2 /9 Fig. 2. A n g u l a r correlations observed in coincidence with n e u t r o n s for the decay modes o f th~ 1536 and 1615 keV levels.
4OO
~6 3OO z
1508--4"-275
NNNTI,
2OO
1" I
I
1
I
3o °
45 °
60 °
90 °
cos z 0 Fig. 3. A n g u l a r correlations observed for the decay of the 1508 keV level.
19Ne E L E C T R O M A G N E T I C
TRANSITIONS
373
shown in fig. 1 a n d the a n g u l a r d i s t r i b u t i o n s of the p r o m i n e n t y-rays for energies > 1 MeV observed at a b o m b a r d i n g energy of 8.48 MeV are plotted in figs. 2 a n d 3. Also plotted are the results of least-squares fits of Legendre p o l y n o m i a l s to the data. The e x p a n s i o n coefficients o b t a i n e d from these fits a n d similar fits to the 238 a n d 275 keV transitions are listed in table 2. TABLE 2
Summary of the Legendre coefficients observed Transition
a2
a4 a)
0.238 -+ 0 0.275 -+ 0 1.508 ~ 0 , 2 7 5 1.536 -+ 0 , 2 3 8 1.615 --~ 0 0,275 2.795 -~ 0 , 2 3 8
+0.424-0.04 0.0 ±0.02 +0.46±0.08 --0.15::t:0.08 --0.21±0.20 0.0 ±0.08 +0.16~0.13
--0,11 ±0.05 --0.344-0.11
--0.554-0.18
a) A blank in the a4 column indicates that the fit was not substantially improved by including Legendre polynomials of order higher than two. These coefficients have not been corrected for the effect of the finite size of the ),-detector.
1500
o
"S
•
:3
z
I00( 2794
MeV level
2794
---,.,- 0 ' 2 5 8
i
i
i
i
ZO
45
60
90
cos2 8 Fig. 4. Angular correlation observed in coincidence with neutrons for the 2795 --~ 238 keV transition. The spectrum was taken at a proton energy of 10.4 MeV.
O n the basis o f a c o m p a r i s o n with the m i r r o r nucleus 19F, the spins a n d parities of the 238 a n d 275 keV levels in x 9Ne have been assigned as ~+ a n d ½-, respectively, f r o m i n f o r m a t i o n o n the lifetimes 2) a n d relative internal conversion coefficients s) of
R.D. GILL et al.
374
the two levels. The observations in the present experiments, of a significant a4 coefficient for the 238 -~ 0 keV transition and isotropy for the 275 --, 0 keV transition support both these spin assignments. N o more detailed attempt was made to analyse the 238 ~ 0 keV transition since the level was strongly populated by cascade radiation and also because the correlation could well be perturbed considering the long lifetime of the 238 keV state. The non-zero a4 coefficient for the 1508 ~ 275 keV transition requires J >__ ) for the 1508 keV level and similarly the a2 coefficient observed in the decay to the 238 keV state implies J ->_ ~ for the 1536 keV level. The correlations observed in the decay of the 1615 keV level are consistent (to one standard deviation) with the assignments J = ½, ~ or a2. The significance of these correlations is discussed further in sect. 3. TABLE 3 Decay modes of some of the lower levels of 19Ne
E~l/Exf
1508
1536
1615
2794
0 238 275 1508 1536 1615
<3 12~3 88±3
<6 95 ± 3 5±3
20±3 10~3 70±4
<10 100 <10 <12 <10 <10
Fig. 4 shows the angular distribution of the 2795 ~ 238 keV transition observed in coincidence with neutrons detected with the neutron counter at 0 ° and 14 cm from the target. The same Teflon target and a bombarding energy of 10.4 MeV were used. The result of the fit of Legendre polynomial coefficients to this data is shown in fig. 4 and listed in table 2. F r o m the observed a 4 coefficient, it follows that the spin of the 2795 keV level must be > ~. 2.1.3. Branehin9 ratio measurements. The excitation energies of the 19Ne levels below 3 MeV derived from the present experiment are listed in the final column of table 1. The major decay mode of each of the 4 levels between 1 MeV and 3 MeV has been identified by Olness et al. 7). In addition to these previously identified transition, the weaker 1615 ~ 0 keV transition is evident in the data of fig. 1. F r o m the measured energies of each of the levels the anticipated position in the coincident y-ray spectrum for all the possible decay modes of each level were calculated. In order to obtain the relative intensities of these weaker transitions the spectra used to obtai~ the angular distributions of the prominent transitions were summed, and account was taken of the effects of angular correlations and the relative efficiency as a function of energy of the Ge(Li) detector. Additional information was obtained from a spectrum taken with the Ge(Li) detector at 125°: the expected centroid of the peak corresponding to the one at channel 650 in fig. 1 was calculated by assuming that it was composed of the 1536 --*
Effective charge
Porat e l o /
/
3.0
Z
"6
2
820
r~,:.
I
t
",.
*-
°
86O
•
-eat'.
•
•
•e
t
'/
82O
.'_%..,,," -.
Thick target
•
860
Fig, 6, Singles spectra o f the 1346 -+ 110 keY transition t a k e n with the Ge(Li) detector at 0 ° a n d 90 ° with respect to the b e a m direction with b o t h the thick a n d t h e thin target. T h e spectra were a c c u m u l a t e d at E~ = 15 MeV.
2'.0
,
~
/
× in
o
Fig. 5. T h e energy loss of 2°Ne ions in T u n g s t e n . T h e effective charge m e t h o d a n d the f o r m u l a due to L i n d h a r d et al. ~7) have been used. T h e experimental data o f P o r a t et al. ~6) is also shown. T h e solid line indicates the adopted values.
Ii0
/
//////
/ i ~
.rL
Channel number
/
.I
2ONe in W
i
o
a : 90 °
E,I/2 (MeV ~)
0 - -
10
o, 2-0 :::t. >
T''
30
i
f
~= 0 °
Thin to,rget
r60(.~,p)19F 1346 --,,-'-IlO key
T
z
©
f'l
z
O
z
376
R. D. GILL et al. TABLE 4 T h e (dE/dx)e values used in the analysis o f the lifetime data Incident ion
Stopping material
(dE/dx)e ( k e V . / ~ g - 1 . c m 2) for 1 M e V ion energy
2°Ne
W O F Pb CaF2
1.15 6.10 5.02 0.925 3.70
19F
W O Pb
1.12 5.80 0.890
TABLE 5 Lifel~me results Nucleus
Level
E./
Incident
Energy
(keV) a)
(keV) ~
particle
(MeV)
Target
F(T)
"c (ps)
19F
1346
1236
~
15
thin
0.04±0.01
6.5+3:5
19Ne
1508
1233
c~
19
WO 3 thin
0.08-4-0.05
a ~+6.5
0.89=t=0.10
0.043 =t=0.043
0.584-0.06
0.31~0.10
WO 3 1536
1298
1615
1340
19F
1346
1236
15
thick
19Ne
1508
1233
19
thick
1536
1298
1615
1340
1508
1233
1536
1298
0.92±0.09
1615
1340
0.654-0.07
1508
1233
1536
1298
0.254-0.03
WO 3 0.264-0.02
4 ~+3.0 "~- 1.8
0.924-0.05
0.0344-0.024
0.804-0.05
0.10 4-0.04
WO 3
X9Ne
p
8.75
thick
0.224-0.06
CaF2
t9Ne
p
10.4
thick
0.038 +0.052 --0.038 0.234-0,08
0.184-0.05
CaF2 0.974-0.05
1615
1340
0.714-0.05
2795
2556
0.57i0.06
a) T h e 19F energies are t a k e n f r o m ref. 19).
0.015 +0.025 -0.015 0.184-0.06 0.334-0.10
19Ne ELECTROMAGNETIC TRANSITIONS
377
275 keV and 1508 ~ 238 keV transitions. The relative intensities of these two ~-rays was then found by comparing the calculated centroid with the one found in the experimental spectrum. The final branching ratios derived from all the available data are listed in table 3. 2.2. L I F E T I M E M E A S U R E M E N T S
2.2.1. The thin target measurements. The lifetimes of the 1.5 MeV triplet in 19Ne and the 1346 keV state in 19F were investigated with a 500#g. cm -z, WO3 target evaporated onto a thick lead backing and with the 160(e, n ) a n d 160(e, p) reactions, respectively. The c~-particle energy was 19 MeV for the ~gNe states and the Ge(Li) detector was operated in coincidence with the larger neutron detector, which was 13 cm from the target and at 0 °. A 6°C0 source placed near the target provided a continuous monitor of the gain of the system. The F(z) values were extracted from spectra taken at forward and backward angles: the maximum possible shifts were calculated by averaging the possible values of the initial velocity and assuming an isotropic reaction yield while the error in this value was estimated by assuming that the reaction yield over the face of the neutron detector varied by a factor of not more I
~ . ~
.. >.
!gNe in WO 3
"~...
Vo=5.2xlO cnn sec
F (rl
0
I 0.1
I.O v (ps)
Fig. 7. The
F(z)
versus z curve for 19Ne ions in W O a . The broken line shows the corrected F(T) curve which was used in the analysis o f the thick target measurements.
than three. The F(z) versus z curves were calculated from the electronic and nuclear dE/dx values and gave the lifetimes shown in table 5 where an error of 10 ~ was allowed on the electronic dE/dx values which had been calculated both by using the effective charge method ~5) and by interpolation of the 2 ONe data of Porat et al. ~6). These methods were in substantial agreement (see fig. 5), and this was also found to be the case for the other dE/dx values (table 4) which were calculated in this way. The nuclear dE/dx values were calculated using ref. ~7) and were allowed a 15 error. The accuracy of the results was poor due to the low reaction yield and for this reason this part of the experiment was repeated with thick targets. The 19F lifetime was investigated in a singles experiment at 15 MeV (fig. 6). At this energy the uncertainties in the initial ion velocity due to the different possible
378
GILL et al.
R.D.
recoil directions of the out-going proton were small since the threshold for production of this state is 11.8 MeV in the laboratory system and, further, the level of interest could not have been populated by cascade radiation. The effect of the recoils of the excited 19 F nuclei into the lead backing was negligible since the F(z) curves for WO3 and Pb were found to be virtually identical. Our measurement (r --- a. . .a+3.5 . t.5 ps) is consistent with the average 18,19) of the previous measurements: z = 4.9+0.5 ps. 2.2.2. The thick target measurements: the (~, n) reaction. The experiment described in the previous subsection was repeated with 10 rag- cm-2, WO 3 targets prepared by depositing a slurry of WO3 in water on to a lead backing and then heating to drive off the water. The composition of the target was checked by remeasuring the F(r) value for the 19F, 1346 ~ 110 keV transition again at 15 MeV. As a substantial difference from the thin target measurement was found both for the lineshape (fig. 6) and for the F(~) value (table 5), this result was only used to correct the F(z) curves used in the 19Ne part of the experiment (fig. 7). The difference between the two
Ey : 2 5 5 6 k e V (2794 ~ 238) I00
•
•
•
~n = 0 ° 87 = 90 °
o•
50 •
•
OlD
"5 E =
Z
0
I
I
8n = 9 0 ° •
8;,. = 3 0 °
50 •
o•
O•
•
•
I
2500
OlD
I
2600
Channel number Fig. 8. The neutron coincident 7-ray spectrum o f the 2 7 9 5 --> 2 3 8 k e V transition. The p h o t o p e a k is s h o w n and sits on a b a c k g r o u n d w h i c h was t h o u g h t to be due to various l o w Z impurities in the b e a m stopper.
379
19Ne ELECTROMAGNETIC TRANSITIONS
19F
(p,n)!gNe
Ep = 8.75 MeV
~,, = 150 °
1298 (1556 ~
100
i233 keV ( 1 5 C ~ E ~ 275) £
275 2:58 0
I/a- 5 + ~/z+ /z
258 ) 1340 keV 0615~275)
i,~ 1'1
O>.= 120 ° ]615 keV (1615~0)
.~
, •
•
0
(3&-)(3&+
(%-)
keY
50
8 "3
z
r6i5 _ _ ,5o8
°
__
I
° •
~ " °° I I
°
I I
L~
I I
.I],
I i"
*,,"
t
/I
°~. I --
°,1' •
I I
o~,~'-.•=s °°
~",-'Y~ •
Ir
I
L_ 7 I
100
Io I 1
Or=50 °
J
• .-..
.-
.
/'.
,.'5 • "g-~
1150
1200
1250
1500
°
1550 ChGnnel
--°'~,,~
•
14001560
° ° ," • •
1600
."i
~*
°"
1650
number
Fig. 9. N e u t r o n coincident 7-ray spectra taken at a proton energy of 8 . 7 5 M e V . The upper half corresponds t o 0~ = 1 5 0 °, = 1 2 0 ° whilst the lower half has 0~ = 1 5 0 ° a n d 0 T = 30 °.
07
results was attributed to the escape of some o f the 19 F ions from the grains which made up the target before they had been properly slowed down. This supposition was reasonable in as much as the mean grain size was comparable with the range of the excited 19 F ions. A detailed description of the corrections made to the calculated F(z) curves to account for structural effects in the targets appears as the appendix. The t 9Ne levels were studied at a beam energy of 19 MeV with the larger neutron detector at 0 °, 13 cm from the target. The F ( 0 values were extracted from spectra taken at forward and backward angles. The a9Ne, 1508 -* 275 keV transition was found to have an F(z) value of 0.26_+ 0.02 which, with the corrected curve (see fig. 7), gave a lifetime z . . . .m . ~+3.0 1.4 ps in agreement with the thin target measurement. The error on this value was increased because of the large corrections which had been made to the F(~) curve, which gives z = 4.1+3"5-1.4ps on combining the two results. The 1536 and 1615 keV level decay y-rays were also affected by the correction but, as their F(T) values were much larger, the correction was relatively less important since the mean range of the excited 19Ne nuclei was much smaller. 2.2.3. The (p, n) reaction. As it was impossible to populate the 2795 keV level at the available a-particle energies, this level was studied using protons of 10.4 MeV and a thick CaF2 (10 rag" cm -2) target on a gold backing. The smaller neutron
R.D. GILLet al.
380
detector was used at 90 ° with its plane faces vertical a n d its edge facing the target. This reduced the u n c e r t a i n t y in the m e a n initial recoil velocity of the 19Ne ions due to the v a r i a t i o n of n e u t r o n angle in the horizontal plane. The G e ( L i ) detector was at 30 ° opposite the n e u t r o n c o u n t e r whilst the positions of the unshifted peaks (from which the energy of the 2795 keV level was determined) were f o u n d using 0 n = 0 ° a n d 0e = 90 ° (fig. 8). Data were also a c c u m u l a t e d for the t9Ne, 1.5 MeV triplet and,
TABLE6 Transition strengths in 19Ne derived from the present experiment Initial state Exl
j~r
(keV)
Final state
rm
F,°tal (meV)
multipole
"~7 +1"8 -0.9
0 238 275 0 238 275 0
3+ ~+ ½½+ ~+ ½½+
M2 E1 E2 M1 M1 E1 E1
<9•0 (2.0± 1.0) × 10-5 214-10 <4.1 N: 1 0 - 2 0• 50 -+0.56 0.17 (1.2+2: O) × 10 -3 + 1 o9) × 10-4 (3.6_11
20 +1"3 • -0.6
238 275 238
:)+ ½.~+
E1 M1 E2
+1 7 × 10-4 (2.9_a~1) +2 6) × 10-2 (5•1 _1:3 7 4 +4.8
(keV)
1508
~-
4• 1+3.5 --1•4-
1536
~-+
0.028~0.015
1615
~r-
0•18 4-0.06 . . .
2795
2+
0.33 4-0.13
[M[Z t,)
jzr
(ps) a)
Exf
Lowest
0.17=t=0.08 24_+827
.
-•---2•2
") The values of the lifetimes quoted in this column are weighted averages of those in table 5 and the quoted uncertainties include estimates of both the systematic and random errors• b) The transition strengths are expressed in Weisskopf units 20) and the errors reflect both the uncertainties in the lifetime measurements and in the branching ratios listed in table 3. now, the long-lived 1508 keV state data were used to correct the F(z) curve. The results are s u m m a r i z e d in table 5. The experiment o n the triplet was repeated at a lower b e a m energy this time with the smaller n e u t r o n detector edge-on at 150 ° a n d 13 cm f r o m the target. Some of the data are shown in fig. 9. The lifetime results f r o m this a n d the previous part of the experiment were c o m b i n e d a n d are s h o w n in table 6.
3. Synthesis of experimental results 3.1. THE 1508 keV LEVEL As n o t e d in subsect. 2.1.2 the a n g u l a r correlation data restricted the spirt of this level to J ~ ~z a n d the lowest order multipole r a d i a t i o n c o n t r i b u t i n g to the t r a n s i t i o n to the ½-, 275 keV level is therefore E2 or M2 according to the parity of the state. U s i n g our measured width a n d the Weisskopf single-particle estimates 2o) it can be
3’
3-
8’
1508
1536
1615
2795
b, Ref. g). e, Ref. 26).
4’ *.$-
238 215
“) Ref 25) r) Ref. 27):
Jr”
Initial level (rgNe) (keV)
“) Ref. lo). “) Refs. 24*28).
238
t+
238 275 0 238 275
TABLE 7
7.4
0.5 1.2x lo-3 3.6x lO-4 2.9 x lO-4 5.1 x10-2
<-10’ <4.1 x lo-2
M3 Ml E2
<9.0 2x 10-5 21
Ml El El El Ml E2 E2
r9Ne
13.4 a*y 1.07 x 10-3 ‘)
exp. IMj2
El E2
M2 E3
E2 El
Assumed multipole
12x 10-Z 26.1 22.1
1.59
1.13x 10-Z 20.4
25.9
19.7
theor. jMjZ
of the mass-19 data with Benson’s model 19F
2.65 ‘) 5.3 x 10-S ‘) 1.17x 10-a ‘) 8.75 x lO-4 ‘) 9.6x lO-2 “) 23.2 p, 8.8 b)
3.9 x‘) 10-Z ‘) 6.8
6.0x lO-6 ‘) 18.1 ‘)
<2.9 ‘) 7.6 ‘)
6.7 “) 1.02x 10-3 d)
exp. [Ml2
17x 10-Z 26.8 7.1
2.10
7.2 1.19x10-‘
27.5
10
8.0
theor. lM/’
d, Ref. 21). ‘) The averaged values for the branching ratios and lifetimes as quoted in ref. r9). The numbers in the theoretical columns are discussed in sect. 4.
%+
+ :3’ 3-
3’
4’ 8-
;:
*+
JP
0
238 275
0
0 0
Final level (r9Ne) (keV)
Comparison
;
; =!
2
3
z ,z F z A” P !j
382
R.D. GILLe t
al.
seen that the radiation must be E2; M2 radiation would require a n IMI 2 > 500 which may be excluded since enhancements of this order have never been encountered in light nuclei 22). Since higher multipolarities may be excluded on similar grounds we conclude that J ~ = 5 - for this level. The angular correlation data for the 1508 ~ 275 keV transition were analysed as described in ref. ~a) for an initial spin of 5. The relative populations of the m = +__½ and +__~substates of the initial state had to be determined from the data. The value of the M3/E2 mixing ratio, 6, was found to have the solutions + 0.1 + 0.2, -0.6___ 0.2, " 4 +~'~ z. -0.8 and - 5 _+2 4 for the 1508 ~ 275 keV transition where the phase convention of ref. zl) has been used. All solutions except the first may be discarded since even the value 6 = - 0 . 6 would imply an M3 enhancement of 2.5 x 10 v. The transition strengths observed in the decay of the 1508 keV level expressed in Weisskopf units, are shown in table 7. 3.2. THE 1536 AND 1615 keV LEVELS The angular correlation data for the 1536 keV level indicates that J > 3. The partial width for the 95 ~ branch to the ~+, 238 keV state is 0.02 eV. F r o m a comparison with Weisskopf estimates this transition must be predominantly dipole since a pure E2 transition would imply an enhancement factor of greater than 2000. Hence the values of J are limited to z2, -~-or -~. The angular correlation data were analysed for these spin values. For J = 5, 6 was greater than 0.27 which, for positive parity, would require an E2 enhancement of 200 which is unlikely, while, for negative parity, an even larger enhancement would be required for the M2 radiation. For similar reasons all the solutions for J = -~ ( + o c , ~ 0 or + 5 . 8 ) w e r e discarded except for 6 ~ 0. For J = 3 the value of 6 was not restricted. At this point we must resort to mirror level arguments: the triplet of states in 19 F at ~ 1.5 MeV has the spin parity sequence 2) 5 - , 3 - and ~+ with the first state corresponding to the 19Ne, 1508 keV state, implying that both the remaining ~9Ne states have J = ~. F r o m a comparison of the decay schemes 2,19) and lifetimes 19) in the two nuclei it is clear that the 1536 and 1554 keV states (J~ = ~+) correspond and that the 1615 and 1459 keV states also form a mirror pair (J~ = z2-). The angular distributions of the 1615 keV decay modes were then analysed assuming J(1615) = -~ but no information on the mixing ratio was obtained. Again, the decay widths have been collected in table 7. 3.3. THE 2795 keV LEVEL The angular distribution of the 2795 ~ 238 keV transition shows an a 4 term implying that J > 5 and that the transition proceeds appreciably via quadrupole radiation 22). The measured lifetime further restricts the multipolarity of the transition to El, M1 or E2 (for M2, [ M I 2 = 170 which can be excluded) which then implies that the possible spin parity assignments are J ~ = ~+, ~+ or 3 +. In the
19Ne ELECTROMAGNETICTRANSITIONS
383
~,fe reaction this state was apparently seen to be excited b;y an l = 4 j which would agree with the last two possibilities. The mirror state in ~Nel~l~y 24) has J = -~-thus implying J~ = 3 + for the 19Ne level. e~orrelation was analysed with this initial spin value and the solutions ~ = _+_0.5, < - 2 . 7 and > +5.7 were found of which the latter pair may be dis.cded since they both imply an M3, IM[ z > 107. Hence, 6 = - 0 . 1 0 . 5 . A level scheme combining the results of this section is shown in fig. 10. 9/~
I00
-
70 I0 20 5 95 88 12
%-
I/2 5/2
2794
1615 1556 1508
2.75 238
~'
I/2+ ~gNe
Fig. 10. 19Ne decay modes observed in this work.
4. Discussion
The positive parity states of the mass-19 nuclei have been successfully described [refs. 2,29,30)] by intermediate coupling calculations in which the three valence particles outside the doubly closed 260 core were allowed to move in the (2s, ld) shell. In the early calculations 29,30) these particles were allowed to interact via a residual force the parameters of which were then adjusted to give the best overall agreement between the experimental and theoretical spectra. In particular, these calculations predict low-lying levels with J~ = ½+, ~+, ~+ and 29-+ which may be identified with the lowest positive parity states in 19F and 19Ne" The Nilsson rotational model has also been used to describe the low-lying positive parity states as mixtures of the K = ½+ and ~+ bands 31). The relationship between these two models has been discussed in ref. 2). The low-lying negative parity states in the mass-19 spectra were first described by Harvey 32) who used an SU3 model and, more recently, by Benson and Flowers 1). The latter described these levels as mixtures of the K = ½- and ~ - rotational bands formed by coupling a p½ or pl hole on to the
384
R.D. GILLet aL
ground state rotational band of 2°Ne. It was found that, for the lowest few states, these wave functions had a large overlap with those of ref. 32). The calculations of ref. 1) have been repeated for 19Ne t again with the KallioKolltveit potential and the Moszkowski-Scott separation method to deal with the hard core. Harmonic oscillator wave functions were used with a radius parameter of 1.69 fm. The electromagnetic transition rates, however, were calculated with the Woods-Saxon single-particle wave functions. This is reasonable in view of the fact that the electromagnetic decay rates are very sensitive to the fall-off of the wave functions at large distances. An effective charge of 0.25e was used for both proton and neutron: this value, which is larger than the 0.1e used for the 2°Ne rotational 5+ ~ ~o 1+ and zo a+ ~ ~o ~+ E2 decay band x), was originally chosen 1) by fitting the ~o rates in t9F. The theoretical and experimental results are compared in table 7; the 19F predictions have been taken from ref. 1). It can be seen from table 7 that the general features of the M 1 and E2 decays of the positive parity states are well described a + transition; by the model which, for example, explains the weakness of the ~ - ~ ~o s+ and To 1+ is 1.4~o which the theoretical branching ratio for the decays to the ~o compares with the experimental value of < 6 ~o which just approaches the region ot interest. This feature also emerges from the early Elliott and Flowers 29) calculation and can be readily understood in terms of the relative amplitudes of the different components of the appropriate wave functions. The 2.79 MeV E2 decay is slower than predicted by a factor of about 3. This is well outside the experimental error although the theoretical value could presumably be reduced by using a smaller effective charge. Of the data which can be compared with theory in 19Ne this is the only real discrepancy. As has been noted in ref. 1), the lowest negative parity states are predominantly composed of the K = ½- band. Transitions between states in the same band are characterised by large E2 strengths and vanishing M1 strengths. This rule is obeyed well for both the-~o and ~o states: the observed and calculated M1 strengths are then due to the small amount of K = ½- and ~ - band mixing which occurs. We would like to thank Drs. D. A. Hukin and G. Garton for discussions concerning the target structure. One of us (K.B.R.) would like to thank the CSIR (South Africa) for financial support and another (K.P.J.) is indebted to the N R C (Canada) for an overseas postdoctoral fellowship.
Appendix As has been mentioned in subsect. 2.2 the theoretical F(z) for a given material must be corrected for structural effects in the target materials which may arise from the method of preparation. While for evaporated thin targets of the WO 3 layers are likely to be unitbrm with a grain size smaller than 1 p m and an average density which t We are indebted to Dr. H. G. Benson for these calculations.
19Ne ELECTROMAGNETIC TRANSITIONS
385
is between 1 and 2 70 lower than the bulk density, thick targets show grain sizes between I and 5/tin. The density of the grains is exactly the density of the single crystals, but there are spacings between the grains and consequently corrections must be applied. The change of the experimental F(~) for the ~9F, 1236 keV transition (cf. table 5 and subsect. 2.2) provides one empirical point for the (corrected) thick target F(z) function in the region where this function is most sensitive to structural effects (fig. 7). The shape of the corrected thick target F(r) curve relative to the thin target curve is then obtained as described below. We consider the modifications to be made to F ( z ) when the initial excited nuclei are produced in a slab of thickness, l, which is greater than the mean range, R, of the nuclei. If nuclei at a distance x from the front surface of the slab are produced with a velocity Vo and escape with a velocity v¢ (both velocities are perpendicular to the faces of the slab) then it can easily be shown that the observed F'(T) may be related to the F(v) value when no particles escape by ~'(T)
=
F(T)-~
/'/eve ( I - - F ~ ) ,
(1)
IIOV0
where no and n~ are the initial number and number of escaping nuclei and Fe(z) is the F(r) value with respect to an initial velocity, G, the n~ particles would have had had they recoiled in the solid medium. To obtain the observed F ' ( v ) the above equation must be integrated over the dimensions of the slab but we will first introduce the following: (i) We assume that G = Vo e -t/~ where c~ is chosen to include the effects of nuclear scattering. Empirically, this is a reasonably good approximation. (ii) G = no e-t/L (iii) We assume that Fe(~) is independent of G and further, that F~(r) is equal to the value of F(r) evaluated for v = vo. If the effects of nuclear scattering were not present then this assumption would be correct in the cases in which the energy loss was proportional to the velocity. In terms of x we then obtain: =
o(1
-OCVo
,
l)e =
V0
(
1--
. C(Vo
Integrating equation (1) with respect to x gives F ' ( Q = F ( r ) + (1--F¢) R (2+ oc/r) l
(2)
This equation still does not take into account the possibility that the particles which compose the target are of varying sizes. Due to a lack of detailed information this is usually best taken care of by using the formula F ' ( Q = F ( r ) + f l 1 - F(z), 2 + c~/r
(3)
386
R.D. GILL et al.
a n d t r e a t i n g / 3 as a p a r a m e t e r t o b e d e t e r m i n e d f r o m t h e e x p e r i m e n t . T h i s h a s b e e n done in the present experiment.
References 1) H. G. Benson and B. H. Flowers, Nucl. Phys. A126 (1969) 305 2) F. Ajzenberg-Selove and T. Lauritsen, Nucl. Phys. 11 (1959) 1; T. Lauritsen and F. Ajzenberg-Selove, Nuclear data sheets, compiled by K. Way et al. (National Academy of Sciences, National Research Council, Washington D.C., 1962, sets 5 and 6) 3) J. M. Freeman and D. West, Nucl. Phys. 38 (1962) 89 4) J. J. Wesolowski et al., Nucl. Phys. 71 (1965) 586 5) M. W. Greene and E. B. Nelson, Phys. Rev. 153 (1967) 1068 6) K. Gul, B. M. Armitage and B. W. Hooton, Nucl. Phys. A122 (1968) 81 7) J. W. Olness, A. R. Poletti and E. K. Warburton, Phys. Rev. 161 (1967) 1131 8) W. W. Givens, R. C. Bearse, G. C. Phillips and A. A. Rollefeson, Nucl. Phys. 43 (1963) 553 9) J. Bleck et al., Nucl. Phys. A123 (1969) 65 10) R. J. Nickles, Nucl. Phys. A134 (1969) 308 11) O. H~iusser, J. S. Lopes, H. J. Rose and R. D. Gill, Oxford Nuclear Physics lab. rep., 1966, unpublished 12) B. C. Robertson et al., Nucl. Phys. A126 (1969) 431 13) J. B. Marion and F. C. Young, Nuclear reaction analysis (North-Holland, Amsterdam, 1968); C. M. Lederer, J. M. Hollander and I. Perlman, Table of isotopes 6th ed. (Wiley, New York, 1967) 14) A. E. Litherland and A. J. Ferguson, Can. J. Phys. 32 (1961) 378 15) R. D. Gill, J. S. Lopes, O. H/iusser and H. J. Rose, Nucl. Phys. A121 (1968) 209; L. C. Northcliffe, Ann. Rev. Nucl. Sci. 13 (1963) 67 16) D. I. Porat and K. Ramavataram, Proc. Phys. Soc. 77 (1961) 1135 17) J. Lindhard, M. Scharff and H. E. Schiott, Mat. Fys. Medd. Dan. Vid. Selsk. 33 No. I0 (1963) 18) K. W. Jones, A. Z. Schwarzschild, E. K. Warburton and D. B. Fossan, Phys. Rev. 178 (1969) 1773 19) A. R. Poletti, J. A. Becker and R. E. McDonald, Phys. Rev. 182 (1969) 1054 20) D. H. Wilkinson, Nuclear spectroscopy, Part B, ed. F. Ajzenberg-Selove (Academic Press, New York, 1960) 21) S. J. Skorka, J. Hertel and T. W. Retz-Schmidt, Nucl. Data 2 (1966) 347 22) H. J. Rose and D. M. Brink, Rev. Mod. Phys. 39 (1967) 306 23) D. J. Baugh, J. Nurzynski, D. M. Rosalky and C. H. Osman, Austral. J. Phys. 22 (1969) 555 24) D. D. Tolbert, P. M. Cockburn and F. W. Prosser, Phys. Rev. Lett. 21 (1968) 1535 25) J. A. Becket, J. W. Olness and D. H. Wilkinson, Phys. Rev. 155 (1967) 1089 26) J. D. Prentice, N. W. Gebhie and H. S. Caplan, Phys. Lett. 3 (1963) 201 27) T. K. Alexander, O. H/iusser, K. W. Allen and A. E. Litherland, Can. J. Phys. 47 (1969) 2335 28) K. P. Jackson, K. Bharuth-Ram, P. G. Lawson, N. G. Chapman and K. W. Allen, Phys. Lett. 30B (1969) 162 29) J. P. Elliott and B. H. Flowers, Proc. Roy. Soc. A229 (1955) 536 30) M. G. Redlich, Phys. Rev. 99 (1955) 1427 31) E. B. Paul, Phil. Mag. 2 (1957) 311 32) M. Harvey, Nucl. Phys. 52 (1964) 542