- Email: [email protected]
Lifetime measurements of the first excited states of Ti208 and Ra236
LI~T!M~
M~A$~R~M~N'r- OF THI OV "rl~
I. |Otr~ucttott; the Line Shirt M e t ~
in this way are emitted by r~x:,dJ~ng :n~lc],::i.~h~t
gtome{ricat co~,:litio~+~as,~d <~,~ro::thickm>.~;; / woukl ~ u m t y in the id
7.:ii(,~
~d
~. . . . . . . . . . .
" ~
*.
.
.
.
.
.
.
.
.
.
l.n. p~'actic< i i:~~vdm:,:.dby t~vo v~,fb?.+,:tr,,,vhidt c;m is;" taken into accous~r 7v writing / as a prcK}alet of '{wo rv:ductiv~ factors [~ a n d / a : /i is the geome{ricd r~vdact}gn {;,ctor. calculated from the ~;~!id a~gi: sub~en&d by the ~detecting sc~igI1ator {alxiut 2a }~ d 4~,~)and the averages ~ p t a n c e ~mgie d the mag~;e,~c len:~ (27~').. A vMue it ~ 0.69 is fi:mz~d~ h is ihe Nctor by which the ro:oTi vet~<
!~t~ME
~ASm'~TS
403
~. In~iour experiments the position of the centroid of the L-conversion line t: ~ t h ~'s is compared with that of the L-conversion line anti~ t ~ d h ~t s ipbtamed by subtracting the coincidence spectrum from count slx~ctrum). Since some electrons Mth a small component of the re¢~o::~lvel,;~:ity c~mtribtm,, to the anti-coincidence line, this line will also have a ~tnMl D~)I:,pter shift:, It is calculated that as a result of this effect the di:~t~t~e :~t:~een the eentroids of the coincidence and the anti-coincidence tine i~ smaller by !2.:1 ~}.$~that~ extracted from (1). The Doppler shift of the conversion line may be reduced by placing a very thin foil at a small distance d in front of the source. This foil does not affect the conversion electron ~eJt~ity appreciably, but stops M1 recoiling nuclei. By measuring the reduction of the h"n :e shift as a function of source-to-toil distance, lifetimes down to 10"~* ~ can in principle be estimated. in this way Burde and Cohen ~) found T_~ = (lzk0.5) × 10- ~ see for the 40 keV state of T1~s, but as we have pointed out ~) this value should be ~;orn~ted considerably for penetration of source atoms into its backing, which occurs when the source is prepared by the usual recoil collection technique. It aplx~.ared to be worthwhile firstly to repeat the measurement with a ~ u r c e prepared in such a way that no penetration could occur, ~ c o n d l y to compare a result of the line shift method with one of the delayed ~x~incidence method for a case within range of both methods. Such a case is met in the x-decay of Th "02~to the 85 keV state of Ra ~-~a (T.~ ~ 7.5 x 10-~ see) ~). In the next sections details and results of the line shift method and the delayed coincidence measurement are given. 2. Half-life of the 40 keY Level of TI 2°s 2 t. E X P E R I M E N T A L P R O C E D U R E
Fig. 1 shows the source assembly mounted in our spectrometer: "};h,:' ~:mrce-hotder (S) is screwed into a rigid plate (I); the stopping foil-hoMer (T} is mounted on plate (2) which is tightly fixed to the backing-#at,:' at one end. In this way the second plate forms a rather hard flat spring. O~ this a very much softer one (3) is screwed, that can be bent by turning th~~ screw C (pitch 0.33 mm). By turning C over 10° the axis C' is displaced bv 9.2 }, and the stopping foil by about 0.2 #, the movement being quite linear for the range needed. The source foil consisted of 4 ]ayers, the stopping f~i.l of 1 layer of about 5 fig/era °" zapon lacquer. Both foils were covered uitti about 15/,g/cm * At, the aluminized sides facing each other. According t~ measurements by Cohen et al,"), this thickness of the Al-layer is sufiicieri~ t,~ stop all recoiling nuclei. Our T h ( B + C ) sources were prepared in the following way: with a drop ~:~*" very pure HNO3, diluted in some drops conductance water, the activity w~i.~
es
ete
rom
A,)
Fig. I. Mc~unting ~,f sc.~rce a~d ~.*t~ppi~g i~it a~d meeham,~m for va~,ing t h e distance bet~':cc~ t~t~e ~i~.s i~ the. range ~Ji I ~.
lam~,. In order to avoid the forraing of a ridge along the edge of the dro p, thisedge ~ s shielded somewhat from the heating lamp. In this way we got sources of sufficient aetivity~ inv~,sib~eunder a microscope. From the observed maximum line shiR, a mean velocity toss oft_he recoil~nuclei of abo~t
! 0 ~i}{~:oftheinitial velocity was deduced ([, = 0.9), showing that the sources: were very thin. A f t e r screwing the source-holder ( S ) i n t o the backing-plate, plate (2} ~ t h stopping-foil holder (T) was fastened tightly to it. The stopping foil w ~ s a d j u s t e d parallel to the source foil with three screws B (one of t h e m is d r a w n i n fig. 1) looking at Che interference pattern w;+h a simple interferometer, Both foil-surfaces had to be absolutely dust-free, since dust particles would prevent us from bringing the foils in contact over tile whole surfr~ce at the same time. As the exact location of the source could not be seen, it proved to be ver? useful to be able to shift the source assembly perpendicular to the axis of the spectrometer. This m o v e m e n t was provided by excentric pin:~ at the end ~ ~:ff the shafts Ax and A~. Thus the source could be adjusted frora the outsid,!~ t~:~ give a well-shaped conversion-line; the F-line of ThB was used iigr this purpose. The diaphragms were set to give a hne-width of about 1 "~: (tr:ans.-. mission a b o u t 2 %). 2,~. L I N E S H I F T R E S U L T S
Fig. 2a summarizes the measurements with two sources. The horiz, mtai errors include the inaccuracy in the zero foil distance .s~'t*ing~ ~. _. The tilw ~l:~i~t as a function of the stopping foil distance d from the sotu:ce is t~xt.rc~,s~:d hv [(d). if(m) = [.) In a first approximation one expects a dependence i .... (/(d)ff) = e -~ with A = d In 2/17T~ (broken line in fig. 2b). A more earefN analysis, accounting for the contributions of the various directions of n~c~;d~ nuclei to the Doppler shift yields a theoretical dependence of ](d)ff o,~ 3 represented b y the solid lines in figs. 2a and 2b. Using the vMue ~:' obt~d~:t~:x! from eq. (1) b y p u t t i n g / = / ~ / 2 = 0.69× 0.90 = 0.62 the best fit l:~,}:w~ the broken line of fig. 2b and the experimental points is obtained f~,~ T½ = 2.6 × 10 -xz sec with an estimated standard de~4atiort of ~3:1.~):~,~:t:~3~':~ see.
3. Half-life of the 85 keV level of Ra 2u 3.1. M E A S U R E M E N T W I T H T H E L I N E S H I F T METHOD
As this half-life is about a00 times longer than the forrncl~ life di:~t,,~:~:~: between source and stopping foil must be made larger by the sam~: fa,:l,~ Therefore we did not use the flat springs (2 and 3), but att~rh~'d ~ h&d~:~ carrying t h e stopping foil directly to axis C'. Sources were prepared by adding some drops of condtiq~:~ *~'~°~,~fA,~ },:~) carrier-free R d T h (obtained from Harwell) and p~ttting on~:~dmph~, ~,~'~. ~ 0.8 m g / c m ~ mica foil, This was dried under an hffra wd h~a~*~ k ~ } ~ ],'hen t h e mica foil was pressed against a tungsten rib!:~×m,.~.~t t**~;~U.-~~i~ v a c u u m to a temperature of about 1000 ':~C. In this 'way we m ~ e ~ : i ~,~ ~:v*
--:
/i~i:: ~ ii ¸:I~: ?::i~ ....
'1 1 d
0.05
s : ~ ¸~
t
÷ ~
v.T~ Fig~ ~. R e ~ ; t of the ffr.c sh~ft meas~rement of t h e 4 0 :keV ]eve! of T J ~ . ~.. obse~,ed ~ine s~ift reIative to the : n a h u m Shier: plotted as a. fuaction :of source~to-fe~ b~ iL'~eShift plotted on a l ~ r i t h m ~ c sc=Aea~:a function i~ The t ~ t fit is o b t ~ n ~ ~, The ~o~d lines g~ve the ~heoreticai dependence
the degree :of purification of the source foil from ~e Carlo of the intensity of the well-known F-~ne L-lines. Oft,he:order of 1 pC. The diaphragms of the magnetic spectrometer were;
~,--t
=
"
~
I
a~
'7
v', SOURCEI SOURCE 2
LINE W!DTH ..2A~
~9=,~ " O SOURCE3 LINE WIDTH O.il~
0.4
0
t
I
200
0.~!
0.2
LiNE
....... ~ - -
400 FOiL DISTANCE d
500
~
............
-~ ~'~:~ ~,~
i
"i
-
1]
~-~ 03 gob
,t
0"040
"t
:Fig . : '
. ;
3 .
"
Result .
p
2
of the
3
line shif~ measurement
4
o f t h e 8 ~ k ~ V tc~:'i~
d i s t a n c e d. o n a I o a r i t h m i c s c a l e a s a i t m c t i o n o I tt~e ~ u t ~ e * : ~
':1~-*.~~,~:~/:';~'~:~*~ ~:~: ~>':*~;:;~::~
i DELAYEI) CO~N{, CURVE ~=Tna==
I,d'
~O~PT COINC. CURVE
t0
8
6
4
2
....J O'
,,,[ 2
CO~
..... J 4
,,,
..i 6
~ S
~
7 12
10 -
DELAY (IO-S $ec ) de~:~y C~x~r_~cec~ci~lcz~ce~h;~ve i~en silbtracted~
oLrserved maximum shift with the c a l c u l a t e d o n e . T h e average velocity loss was (t 2 i 12) % f~r the the:~e ~bffi,,.rent sources used, ( ; i i = 0.88:~:0.t2). Thi~ ~ ~ '~ :~ value was used in comr~si~g fig. 3 from the three series of measurements. -
described in ~¢~'c,tion2 . 2 .
:
~:
....
-
.... ..........
~,~rm~ ~^~tr~M~:rs
::i 4o~
t THI~ DELAYED FAST-SLOW COINCIDENCE METHOD
a fast slow coincidence circuit similar to that introd~i b y Bell, Graham and Petch ~) was used. The magnetic lens spectro: m e t ~ , ' n o w adjusted to 6 % transmission, again selected the L-conversion 6 1 e c t r o ~ , : = d a plastic scintillator, now 2 m m thick, accepted the ~-particles within a ~ i d angle close to 30 % of 4z,. Some details of tiffs measurement }een given previously*). ~ e delayed coincidence curve of RdTh was carefully compared with one o b t a i n e d from a Co ~ source by measuring coincidences between t-particles focused o n t h e electron detector and Compton electrons accepted by the plastic seintiUator. A 80 mg/cm ~ Al-absorber was placed between source and plas~c t o prevent any t-particle from reaching the scintillator. Exactly the same a d j u s t m e n t of the whole apparatus was used in both cases. The centroid shift of the RdTh-curve relative to the Co~° curve (fig, ~) which equals the experimental lifetime ~) was found to be Vexp -~- (10.2~ 1.6) × 10 -~° sec while a Newton
7)
analysis yields vexp = (11.4~1.6) × 10 -1° sec.
Averaging these two values we obtain "gexp
==
(10.8~2.2) × 10 -I° sec
T½ :
(7.5:k 1.5) × 10 -~° sec.
or
4. Discussion
We see t h a t the measurements of the half-life of the 85 keV ex(hted state of Ra ~2~ using two different methods are in good agreement, which adds to our confidence in the result for the half-life of the 40 keV st~tte oi Tt ~ Asaro, Perlman and Stephens 8) find an experimental totM converskm coefficient atot = 16 for the 85 keV transition in R a ~4. Using this vMu¢: we propose a lifetime ~ (1 ~. ~~ 2.5) × 10 -~ sec, as an average of I~:~th meagre,:, merits. F r o m t h i s an intrinsic quadruple m o m e n t IQoi = (7~3d=0.7} ~< tO ~* c m * i s deduced for the nucleus Ra 2~4, fitting well in the Qo versus A ,;'llr~*~ given b y A l d e r et a/.9).
~t~t ~ !9;6, De Shalit 10) has calculated lifetimes f o r , e~erM rn,~s~th' c,:,*:~.*: figurations of the nucleus TI ~°s on the basis of the shell model. Oar r ~ u i t
~ree~ ~ t with the value ~ (s~, g|)~onfiguration . . . . 5. F i ~
1.sx ]0 :~°~° ~
which::~s:~fou~ for a .... , ,
Remarks
gi,l.' R E S I D U A L L!NI~ S I I I F T
A smal! line shift remains for d = 0. ('rite figs. 2 and 3 are corrected for this residual shift,) .In our measurements this is' a N m t 5 % for T I ~ * and for Ra~"** about 10 % of the maximum shift observed. This residual shift can be expla/ned by ~:;)different absorption o~ the com,ersion electrons emitted by "coincident" and "anti,coincident" mu:lei ~4.~et~vcly, b) the additional velocity of the very small fraction of electrons emitted by excited nuclei in the source- and stopping-foil respectively before theehave come to rest. The latter effect ~comes smaller as the lifetime cf the excited state becomes larger and may be entirely neglected in the Ra m * measurement. Using for this case a figure of Paul and Steinwedel ~), we find that thi~ residual shift corresponds to an energy difference of ,~ 20 eV of the coincident and anti-coincident electrons. From this a mean recoil range ~ /~g/cm~ for thc Ra s~* nuclei in mica and A1 is deduced. This agrees reasonably with the value reported by Cohen et a/.S). 5.2. DUST.-FREE SOURCES
It is hard to make dust-free sources, therefore all foils and sources have to be prepared in a dust-free box. Yet, only 2 out of more than 20 Th(B+CI~ sources made for the TI* lifetime measurement proved to be clean. 5.3. A P P L I C A B I L I T Y O F METHOD
The most important difficulties arising in this kind of experiments are that i) the measurements consume a long time, and that 2) the sources must be verg lhin. These circumstances }imit the applicability to cases in which the parent nucleus has a lifetime not shorter than about one daj¢ nor longer than a few decades. The transition considered shouId be fed by a nice ~-branch and it should be appreciabl 7 converted. in some cases the result may be affected by :t's feeding a higher excited state that decays by ), or e- emission to the excited state consideredo In the RdTh-decay the 217 and -53 keV states are such, but here the correction for these "'false" coincidences is negligible. In table I cases are summarized where the line shift method as described above is applicable. Using a double focusing electron spectrometer with extreme resolution a,s
::i)ii::17/i ?arch ~ tuclcu
13i~u fli':t ~ Ra ms
:l:.h: I::".¢,e.s :l)a
g e
t':":
,=s:t:on t fo i.g { *
s ate
TI,*, :
o.273
TI ~°~ R n ~*
6.04 5.704 5.569 5.6 6.220 5.972 5.338 5.813 5.26I 5.75 5.452
Fr ~ lta ~
ira ~ R a "~* Th ~
U~m pu~3 ~
:/
Th :~
U ~'~ U ~a~
:
de-exciting t h e state
~11 (+ E2) M1
M1 (+ E2) m(+E2) E2 E2 E2 E2 E2 E2 E2
{ shift in I
t
] t
Half-life observed
Halfdife " expec:ed
{ .... ~:::~":3~<~:~.... :~ ~ *~. . . .
I 353 40 154 268 220 111. 61.~ 84.47 72 57.9 45
0.11 0.36 0.23 0.18 0.14 0.17 0.24 0A8 0.21 0.23 0.3~.
42,6i o . ~
eg e~ e~
(..LoN 10 'a~
s~.
< 1 0 -~ r } <: 1.5 :< 10"' {
i.':>r:,l.~;:~ {
'i
eL % % %
< 2 :< 1.0"~ < 5 .*: 10 ° ~
described e.g. by Siegbahn and Edvarson x-~)to measure line shifts, iik;tim ~ might be determined for some additional cases. The authors owe Professor H, Brinkman a great debt of grati~de fi:~r having made it possible for them to perform these measurements and. fi~-.~' reading the manuscript. Many thanks are also due to ML A, j~ Wa~i:~c~' Mr. K. G. Dik and Mr. G. T. Pott for their able and untiring ~ s t ~ , : ~ v during various stages of the experiments and calculations, References 1) J. B u r d e a n d S. G. Cohen, Phys. Rev. 104 (1956) 1093 2) S. G. C o h e n , Proc. R e h o v o t h Conf. on Nuclear Structure, Ed, Ilo J, L:~k~ {......... lmabl. Comp., A m s t e r d a m , 1958) p. 571 3) J . G. S i e k m a n a n d H. de Waard, Phys. Rev. 107 (1957} 17:¢i 4} J, G. S i e k m a n a n d H. de Waard, Proc, R e h o v e t h CoM, on Nuciear S~':r:¢:ct~_~:,~: i ~. ~,,;4,~:~ a n d t , P e N m a n , Phys. Rev. 96 (1954) 1568 9 ) K . Alder, A. I~)hr, T. Huus, B. Mottetsoa a n d A~ Win0~er~ Re~:s, ::M ~ ~:% ~- 1~ i:!~A~, 532, fig. V , 6 10) :A, d e Shalit, P h y s . Rev. 105 {1957) 15~1 !l): ~W- P a u l a n d It. Steinwedel, Beta- and Gamma~raY Spo:::t~>c~py l:d., ~:L ':~ ~,~>~¢>/~ ( N o r t h - H o l i . Publ. Comp,, A m s t e r d a m , 19511) Ch. L ;p~ 1~} 12) IK, S i e g b a h n a n d K. Edvarson, Nuclear Physics I (lgaa? ~:*:
{: e,
M~A$~R~M~N'r- OF THI OV "rl~
I. |Otr~ucttott; the Line Shirt M e t ~
in this way are emitted by r~x:,dJ~ng :n~lc],::i.~h~t
gtome{ricat co~,:litio~+~as,~d <~,~ro::thickm>.~;; / woukl ~ u m t y in the id
7.:ii(,~
~d
~. . . . . . . . . . .
" ~
*.
.
.
.
.
.
.
.
.
.
l.n. p~'actic< i i:~~vdm:,:.dby t~vo v~,fb?.+,:tr,,,vhidt c;m is;" taken into accous~r 7v writing / as a prcK}alet of '{wo rv:ductiv~ factors [~ a n d / a : /i is the geome{ricd r~vdact}gn {;,ctor. calculated from the ~;~!id a~gi: sub~en&d by the ~detecting sc~igI1ator {alxiut 2a }~ d 4~,~)and the averages ~ p t a n c e ~mgie d the mag~;e,~c len:~ (27~').. A vMue it ~ 0.69 is fi:mz~d~ h is ihe Nctor by which the ro:oTi vet~<
!~t~ME
~ASm'~TS
403
~. In~iour experiments the position of the centroid of the L-conversion line t: ~ t h ~'s is compared with that of the L-conversion line anti~ t ~ d h ~t s ipbtamed by subtracting the coincidence spectrum from count slx~ctrum). Since some electrons Mth a small component of the re¢~o::~lvel,;~:ity c~mtribtm,, to the anti-coincidence line, this line will also have a ~tnMl D~)I:,pter shift:, It is calculated that as a result of this effect the di:~t~t~e :~t:~een the eentroids of the coincidence and the anti-coincidence tine i~ smaller by !2.:1 ~}.$~that~ extracted from (1). The Doppler shift of the conversion line may be reduced by placing a very thin foil at a small distance d in front of the source. This foil does not affect the conversion electron ~eJt~ity appreciably, but stops M1 recoiling nuclei. By measuring the reduction of the h"n :e shift as a function of source-to-toil distance, lifetimes down to 10"~* ~ can in principle be estimated. in this way Burde and Cohen ~) found T_~ = (lzk0.5) × 10- ~ see for the 40 keV state of T1~s, but as we have pointed out ~) this value should be ~;orn~ted considerably for penetration of source atoms into its backing, which occurs when the source is prepared by the usual recoil collection technique. It aplx~.ared to be worthwhile firstly to repeat the measurement with a ~ u r c e prepared in such a way that no penetration could occur, ~ c o n d l y to compare a result of the line shift method with one of the delayed ~x~incidence method for a case within range of both methods. Such a case is met in the x-decay of Th "02~to the 85 keV state of Ra ~-~a (T.~ ~ 7.5 x 10-~ see) ~). In the next sections details and results of the line shift method and the delayed coincidence measurement are given. 2. Half-life of the 40 keY Level of TI 2°s 2 t. E X P E R I M E N T A L P R O C E D U R E
Fig. 1 shows the source assembly mounted in our spectrometer: "};h,:' ~:mrce-hotder (S) is screwed into a rigid plate (I); the stopping foil-hoMer (T} is mounted on plate (2) which is tightly fixed to the backing-#at,:' at one end. In this way the second plate forms a rather hard flat spring. O~ this a very much softer one (3) is screwed, that can be bent by turning th~~ screw C (pitch 0.33 mm). By turning C over 10° the axis C' is displaced bv 9.2 }, and the stopping foil by about 0.2 #, the movement being quite linear for the range needed. The source foil consisted of 4 ]ayers, the stopping f~i.l of 1 layer of about 5 fig/era °" zapon lacquer. Both foils were covered uitti about 15/,g/cm * At, the aluminized sides facing each other. According t~ measurements by Cohen et al,"), this thickness of the Al-layer is sufiicieri~ t,~ stop all recoiling nuclei. Our T h ( B + C ) sources were prepared in the following way: with a drop ~:~*" very pure HNO3, diluted in some drops conductance water, the activity w~i.~
es
ete
rom
A,)
Fig. I. Mc~unting ~,f sc.~rce a~d ~.*t~ppi~g i~it a~d meeham,~m for va~,ing t h e distance bet~':cc~ t~t~e ~i~.s i~ the. range ~Ji I ~.
lam~,. In order to avoid the forraing of a ridge along the edge of the dro p, thisedge ~ s shielded somewhat from the heating lamp. In this way we got sources of sufficient aetivity~ inv~,sib~eunder a microscope. From the observed maximum line shiR, a mean velocity toss oft_he recoil~nuclei of abo~t
! 0 ~i}{~:oftheinitial velocity was deduced ([, = 0.9), showing that the sources: were very thin. A f t e r screwing the source-holder ( S ) i n t o the backing-plate, plate (2} ~ t h stopping-foil holder (T) was fastened tightly to it. The stopping foil w ~ s a d j u s t e d parallel to the source foil with three screws B (one of t h e m is d r a w n i n fig. 1) looking at Che interference pattern w;+h a simple interferometer, Both foil-surfaces had to be absolutely dust-free, since dust particles would prevent us from bringing the foils in contact over tile whole surfr~ce at the same time. As the exact location of the source could not be seen, it proved to be ver? useful to be able to shift the source assembly perpendicular to the axis of the spectrometer. This m o v e m e n t was provided by excentric pin:~ at the end ~ ~:ff the shafts Ax and A~. Thus the source could be adjusted frora the outsid,!~ t~:~ give a well-shaped conversion-line; the F-line of ThB was used iigr this purpose. The diaphragms were set to give a hne-width of about 1 "~: (tr:ans.-. mission a b o u t 2 %). 2,~. L I N E S H I F T R E S U L T S
Fig. 2a summarizes the measurements with two sources. The horiz, mtai errors include the inaccuracy in the zero foil distance .s~'t*ing~ ~. _. The tilw ~l:~i~t as a function of the stopping foil distance d from the sotu:ce is t~xt.rc~,s~:d hv [(d). if(m) = [.) In a first approximation one expects a dependence i .... (/(d)ff) = e -~ with A = d In 2/17T~ (broken line in fig. 2b). A more earefN analysis, accounting for the contributions of the various directions of n~c~;d~ nuclei to the Doppler shift yields a theoretical dependence of ](d)ff o,~ 3 represented b y the solid lines in figs. 2a and 2b. Using the vMue ~:' obt~d~:t~:x! from eq. (1) b y p u t t i n g / = / ~ / 2 = 0.69× 0.90 = 0.62 the best fit l:~,}:w~ the broken line of fig. 2b and the experimental points is obtained f~,~ T½ = 2.6 × 10 -xz sec with an estimated standard de~4atiort of ~3:1.~):~,~:t:~3~':~ see.
3. Half-life of the 85 keV level of Ra 2u 3.1. M E A S U R E M E N T W I T H T H E L I N E S H I F T METHOD
As this half-life is about a00 times longer than the forrncl~ life di:~t,,~:~:~: between source and stopping foil must be made larger by the sam~: fa,:l,~ Therefore we did not use the flat springs (2 and 3), but att~rh~'d ~ h&d~:~ carrying t h e stopping foil directly to axis C'. Sources were prepared by adding some drops of condtiq~:~ *~'~°~,~fA,~ },:~) carrier-free R d T h (obtained from Harwell) and p~ttting on~:~dmph~, ~,~'~. ~ 0.8 m g / c m ~ mica foil, This was dried under an hffra wd h~a~*~ k ~ } ~ ],'hen t h e mica foil was pressed against a tungsten rib!:~×m,.~.~t t**~;~U.-~~i~ v a c u u m to a temperature of about 1000 ':~C. In this 'way we m ~ e ~ : i ~,~ ~:v*
--:
/i~i:: ~ ii ¸:I~: ?::i~ ....
'1 1 d
0.05
s : ~ ¸~
t
÷ ~
v.T~ Fig~ ~. R e ~ ; t of the ffr.c sh~ft meas~rement of t h e 4 0 :keV ]eve! of T J ~ . ~.. obse~,ed ~ine s~ift reIative to the : n a h u m Shier: plotted as a. fuaction :of source~to-fe~ b~ iL'~eShift plotted on a l ~ r i t h m ~ c sc=Aea~:a function i~ The t ~ t fit is o b t ~ n ~ ~, The ~o~d lines g~ve the ~heoreticai dependence
the degree :of purification of the source foil from ~e Carlo of the intensity of the well-known F-~ne L-lines. Oft,he:order of 1 pC. The diaphragms of the magnetic spectrometer were;
~,--t
=
"
~
I
a~
'7
v', SOURCEI SOURCE 2
LINE W!DTH ..2A~
~9=,~ " O SOURCE3 LINE WIDTH O.il~
0.4
0
t
I
200
0.~!
0.2
LiNE
....... ~ - -
400 FOiL DISTANCE d
500
~
............
-~ ~'~:~ ~,~
i
"i
-
1]
~-~ 03 gob
,t
0"040
"t
:Fig . : '
. ;
3 .
"
Result .
p
2
of the
3
line shif~ measurement
4
o f t h e 8 ~ k ~ V tc~:'i~
d i s t a n c e d. o n a I o a r i t h m i c s c a l e a s a i t m c t i o n o I tt~e ~ u t ~ e * : ~
':1~-*.~~,~:~/:';~'~:~*~ ~:~: ~>':*~;:;~::~
i DELAYEI) CO~N{, CURVE ~=Tna==
I,d'
~O~PT COINC. CURVE
t0
8
6
4
2
....J O'
,,,[ 2
CO~
..... J 4
,,,
..i 6
~ S
~
7 12
10 -
DELAY (IO-S $ec ) de~:~y C~x~r_~cec~ci~lcz~ce~h;~ve i~en silbtracted~
oLrserved maximum shift with the c a l c u l a t e d o n e . T h e average velocity loss was (t 2 i 12) % f~r the the:~e ~bffi,,.rent sources used, ( ; i i = 0.88:~:0.t2). Thi~ ~ ~ '~ :~ value was used in comr~si~g fig. 3 from the three series of measurements. -
described in ~¢~'c,tion2 . 2 .
:
~:
....
-
.... ..........
~,~rm~ ~^~tr~M~:rs
::i 4o~
t THI~ DELAYED FAST-SLOW COINCIDENCE METHOD
a fast slow coincidence circuit similar to that introd~i b y Bell, Graham and Petch ~) was used. The magnetic lens spectro: m e t ~ , ' n o w adjusted to 6 % transmission, again selected the L-conversion 6 1 e c t r o ~ , : = d a plastic scintillator, now 2 m m thick, accepted the ~-particles within a ~ i d angle close to 30 % of 4z,. Some details of tiffs measurement }een given previously*). ~ e delayed coincidence curve of RdTh was carefully compared with one o b t a i n e d from a Co ~ source by measuring coincidences between t-particles focused o n t h e electron detector and Compton electrons accepted by the plastic seintiUator. A 80 mg/cm ~ Al-absorber was placed between source and plas~c t o prevent any t-particle from reaching the scintillator. Exactly the same a d j u s t m e n t of the whole apparatus was used in both cases. The centroid shift of the RdTh-curve relative to the Co~° curve (fig, ~) which equals the experimental lifetime ~) was found to be Vexp -~- (10.2~ 1.6) × 10 -~° sec while a Newton
7)
analysis yields vexp = (11.4~1.6) × 10 -1° sec.
Averaging these two values we obtain "gexp
==
(10.8~2.2) × 10 -I° sec
T½ :
(7.5:k 1.5) × 10 -~° sec.
or
4. Discussion
We see t h a t the measurements of the half-life of the 85 keV ex(hted state of Ra ~2~ using two different methods are in good agreement, which adds to our confidence in the result for the half-life of the 40 keV st~tte oi Tt ~ Asaro, Perlman and Stephens 8) find an experimental totM converskm coefficient atot = 16 for the 85 keV transition in R a ~4. Using this vMu¢: we propose a lifetime ~ (1 ~. ~~ 2.5) × 10 -~ sec, as an average of I~:~th meagre,:, merits. F r o m t h i s an intrinsic quadruple m o m e n t IQoi = (7~3d=0.7} ~< tO ~* c m * i s deduced for the nucleus Ra 2~4, fitting well in the Qo versus A ,;'llr~*~ given b y A l d e r et a/.9).
~t~t ~ !9;6, De Shalit 10) has calculated lifetimes f o r , e~erM rn,~s~th' c,:,*:~.*: figurations of the nucleus TI ~°s on the basis of the shell model. Oar r ~ u i t
~ree~ ~ t with the value ~ (s~, g|)~onfiguration . . . . 5. F i ~
1.sx ]0 :~°~° ~
which::~s:~fou~ for a .... , ,
Remarks
gi,l.' R E S I D U A L L!NI~ S I I I F T
A smal! line shift remains for d = 0. ('rite figs. 2 and 3 are corrected for this residual shift,) .In our measurements this is' a N m t 5 % for T I ~ * and for Ra~"** about 10 % of the maximum shift observed. This residual shift can be expla/ned by ~:;)different absorption o~ the com,ersion electrons emitted by "coincident" and "anti,coincident" mu:lei ~4.~et~vcly, b) the additional velocity of the very small fraction of electrons emitted by excited nuclei in the source- and stopping-foil respectively before theehave come to rest. The latter effect ~comes smaller as the lifetime cf the excited state becomes larger and may be entirely neglected in the Ra m * measurement. Using for this case a figure of Paul and Steinwedel ~), we find that thi~ residual shift corresponds to an energy difference of ,~ 20 eV of the coincident and anti-coincident electrons. From this a mean recoil range ~ /~g/cm~ for thc Ra s~* nuclei in mica and A1 is deduced. This agrees reasonably with the value reported by Cohen et a/.S). 5.2. DUST.-FREE SOURCES
It is hard to make dust-free sources, therefore all foils and sources have to be prepared in a dust-free box. Yet, only 2 out of more than 20 Th(B+CI~ sources made for the TI* lifetime measurement proved to be clean. 5.3. A P P L I C A B I L I T Y O F METHOD
The most important difficulties arising in this kind of experiments are that i) the measurements consume a long time, and that 2) the sources must be verg lhin. These circumstances }imit the applicability to cases in which the parent nucleus has a lifetime not shorter than about one daj¢ nor longer than a few decades. The transition considered shouId be fed by a nice ~-branch and it should be appreciabl 7 converted. in some cases the result may be affected by :t's feeding a higher excited state that decays by ), or e- emission to the excited state consideredo In the RdTh-decay the 217 and -53 keV states are such, but here the correction for these "'false" coincidences is negligible. In table I cases are summarized where the line shift method as described above is applicable. Using a double focusing electron spectrometer with extreme resolution a,s
::i)ii::17/i ?arch ~ tuclcu
13i~u fli':t ~ Ra ms
:l:.h: I::".¢,e.s :l)a
g e
t':":
,=s:t:on t fo i.g { *
s ate
TI,*, :
o.273
TI ~°~ R n ~*
6.04 5.704 5.569 5.6 6.220 5.972 5.338 5.813 5.26I 5.75 5.452
Fr ~ lta ~
ira ~ R a "~* Th ~
U~m pu~3 ~
:/
Th :~
U ~'~ U ~a~
:
de-exciting t h e state
~11 (+ E2) M1
M1 (+ E2) m(+E2) E2 E2 E2 E2 E2 E2 E2
{ shift in I
t
] t
Half-life observed
Halfdife " expec:ed
{ .... ~:::~":3~<~:~.... :~ ~ *~. . . .
I 353 40 154 268 220 111. 61.~ 84.47 72 57.9 45
0.11 0.36 0.23 0.18 0.14 0.17 0.24 0A8 0.21 0.23 0.3~.
42,6i o . ~
eg e~ e~
(..LoN 10 'a~
s~.
< 1 0 -~ r } <: 1.5 :< 10"' {
i.':>r:,l.~;:~ {
'i
eL % % %
< 2 :< 1.0"~ < 5 .*: 10 ° ~
described e.g. by Siegbahn and Edvarson x-~)to measure line shifts, iik;tim ~ might be determined for some additional cases. The authors owe Professor H, Brinkman a great debt of grati~de fi:~r having made it possible for them to perform these measurements and. fi~-.~' reading the manuscript. Many thanks are also due to ML A, j~ Wa~i:~c~' Mr. K. G. Dik and Mr. G. T. Pott for their able and untiring ~ s t ~ , : ~ v during various stages of the experiments and calculations, References 1) J. B u r d e a n d S. G. Cohen, Phys. Rev. 104 (1956) 1093 2) S. G. C o h e n , Proc. R e h o v o t h Conf. on Nuclear Structure, Ed, Ilo J, L:~k~ {......... lmabl. Comp., A m s t e r d a m , 1958) p. 571 3) J . G. S i e k m a n a n d H. de Waard, Phys. Rev. 107 (1957} 17:¢i 4} J, G. S i e k m a n a n d H. de Waard, Proc, R e h o v e t h CoM, on Nuciear S~':r:¢:ct~_~:,
{: e,