state) = 31/54 [13] and QEc = (4760 4-100) keV, which ... log ft calculation we used Qec = (5920 _+ 460) keV [9], ..... [-23] and the Davydov-Chaban E24] ones.
Zeitschrift Physik A
Z. PhysikA 284,297- 303 (1978)
9 by Springer-Verlag 1978
Study of the 124Xe and 26Xe Structure Ch. Droste, L. Goettig, T. Morek, J. Srebrny and J. Bucka Institute of Experimental Physics, University of Warsaw, Poland J. Dobaczewski and S.G. Rohozifiski Institute of Theoretical Physics, University of Warsaw, Poland Received August 18, 1977
The level structure of lZ~Xe and 126Xe is studied on the basis of/3 + decay of 124Cs and 126Cs. The Cs isotopes were produced in the Xe(p, n)Cs reactions at a proton energy of E~9.5MeV. Decay schemes are proposed for these nuclei. The available experimental data are compared with the predictions of various models.
1. Introduction The present study of the decay of ~24Cs and 126Cs is a part of our investigation of the level schemes of even-mass xenon isotopes in the neutron-deficient region [1-3]. Levels in 126Xe can be populated from the decay of 126I or from the decay of 126Cs. Because of the relatively low decay energy of 126I only the four lowest levels of 126Xe are populated [4]. The decay of the 126Ba---~126Cs---~126Xe chain was investigated by Arlt et al. [5, 6], Blinowska et al. [3] and recently by Pathak et al. [7]. Levels in ~24Xe have been previously investigated by Droste et al. [2], Arlt et al. [8], and Westgaard et al. [9]. In these experiments the levels of xenon were populated from the decay of ~24Cs and/or the 124Ba__+124Cs~ 124Xe chain. The high-spin levels of 12~Xe and 126Xe are known from in-beam investigations [10]. There was very little information, however, on low-spin levels. Therefore in the present work we investigated the levels populated in the 124'~26Cs ground state decay (U =1 § [11]). The experimental data (our results included) are compared with various models.
previous work [1]. The gaseous target contained nearly 3 % of la4Xe and 3 % of 126Xe (30 times more than in natural xenon). The background was mainly due to 128Cs decay [1]. The exposure and counting times were carefully chosen so as to reduce contamination with 128Cs. The irradiation time was 60s in the case of 126Cs(T1/2 =99s) and 15s in the case of 124Cs(T1/2=26s). Measurements started 25 s after irradiation was terminated. Single spectra were recorded in two successive time channels (3min each for 126Cs and 50s each for 124Cs). This counting regime permitted us to distinguish transitions belonging to the various activities. Targets were irradiated several hundred times to increase the statistics. Measurements encompassed single gamma spectra and, in the case of 126Xe, coincidence gamma-gamma spectra. The same measuring system as previously described [1] was used. In Figure I the gamma spectrum of a caesium source obtained for a sample investigated in time intervals chosen for 124Cs is presented by way of example.
2. Experimental
3. Results
We have produced Cs sources in the (p,n) reaction using a 10MeV Linear Proton Accelerator at the Institute of Nuclear Research at Swierk. The experimental set-up was the same as described in our
3.1. The 126Cs----~126Xe Decay The gamma lines observed in the decay of 126Cs----~126Xe are listed in Table 1. Some transitions
298
Ch. Droste et al.: Study of the a24Xe and J
%
Structure
126Xe
I
.t
~,~__,:..,."
10s i
9
o
m-w-
I
e~
4OO
600
800 ~,
I/I
.-.& ~
~...
~
(..) 10~
~'~:""~n",
""
""
--*-,~'v"
~
~.
"" 9
~a~~
~J ',.~,r
-
....
- "-"~"~'~"---.~,.,.-:4.."
~ ".,~.~.,~ 9
i
I
Channel
"..
31
~
~-
o~o..~
10 ~
-- *'.-~ - o. 9 ...:.-...,.:,.;--..
"
.
I
-.-..- : . . . .
I
i
I
q
t.'-~
~
" * ;.-.~
% ~.'...
:
"~ "
:. -
1600
9
1400
N,
:',.
~
number
9o
""'-'--"' ",.-.'a-~. ...A
9
I
1200
10(11
i
I
I
9
..
9 9
"~'~/',..~.'.....~,.p
. .W~.o.-:~,,a,"
I
.,....
% . . .
--
1
1800
2000 ,o
i
(.)
~o ~
0"~
9
.
~,,,~..,,~)..tr
L
~'~'
9 : ""4
.,.t
9 , ". .o ". -,.~..v.~'~ ..r 9 9 "-" ~
t
-
9
~.'. :"
"",~.'-t,.'...~.r vq.~:-. "~.'-
" ".:"..
."...
-. ,.-......,.~,.~ .'~. ... ~.~r
b
I02~
: 9
.
~.
~ l~
9 9
.
9
.'.
9176 9 :
g , ".,*'
I
I
I
2200
I
2400
Channel
i
2600
number
Fig. l a and b. Gamma-ray spectrum of Cs decay. Peaks with assigned energies belong to the decay of ~24Cs, peaks with assigned energies and provided with asterisks belong to the decay of ~26Cs
from this list d e m a n d s o m e c o m m e n t s . The w e a k line at 434 keV was o b s e r v e d in o u r m e a s u r e m e n t s o n l y in the first time channel. Its a s s i g n m e n t to 1 2 6 X e is b a s e d on the results of a previous w o r k [3]. W e o b s e r v e d the 6 8 2 k e V line with an intensity m u c h
lower t h a n in the decay chain 126Ba--+ 1 2 6 C s - - + 1 2 6 X e [-3, 6, 7]. It is possible t h a t t r a n s i t i o n s with the same energy occur b o t h in the 1 2 6 C s a n d 126Xe nuclei. The 1290keV t r a n s i t i o n was p l a c e d in the level scheme after [61. In o u r s p e c t r u m this line is m a s k e d by a
Ch. Droste et al.: Study of the ~2~Xe and t26Xe Structure
299
Table 1. Energies and intensities of the gamma transitions observed in 126Cs~126Xe decay
Table 2. Energies and intensities of the gamma transitions observed in 124Cs-~ lZ~Xe decay
E~ (keV)
E~ (keY)
I~
353.9 422.5 492.5 736.6 846.2 914.8 950.7 1133.1 1274.2 1336.2 1358.7
I00 1.0 7.3 1.0 3.2 9.9 1.6 1.2 I.i 1.43 0.37
388.6 434.1 491.2
(2) (3) ~ (2)
682.5 798.1 879.8 925.2 1622.8 1678.3 1958.9 2067.0 2407.1 2566.1
(4) ~ (1) (1) (2) (3) (2) (2) (2) (3) (3)
I~ 100 1.6 10.8
(6) (3)
0.78 1.24 3.12 9.64 0.59 1.89 0.50 0.80 0.33 0.17
(11) (8) (12) (16) (7) (7) (6) (7) (3) (2)
(2) (4) a (4) (2) (2) (1) (3) (2) (2)" (2) (4)
1689.0 (3) 2019.9 (2)
The assignment of this line to 126Xe is uncertain
I§
(3) (6) (2) (5) (2) (3) (i) (I) (8) (8)
1.2 (1) 1.9 (1)
The assignment of the line to 12~Xe is uncertain, supported by the results of Arlt et al. [-8]
26.5s
1"
1255c09
'EC ~
c=5920t460
98.6s
55Cs 71 Clec=4760 _ 70
sO-4~
O0
.4. 04
,.-:
log ft
log ft A
~ 6 "=.4 (1,2 § - - ~ ~- ~ ~ ~ 03
co
9
1689.7
- 5.6
1268.7
5.5
846.2
5.8
2*
i I I l I I I
353.9
5.0
2*
I
5.0
O*
(1,2+)
1678.3
-5.7
1313.7
5.4
879.8
5.8
388.6
5.1
up
§ § §
(0,1 ,2*)
~ 4 04 ~
2* _ _
, .4 o~
-4-~
2 _ _
0§ ~
.0
10,1 ,2)
124x
54 eTo Fig.2. Decay schemes of la4es and 126Cs
double-escape peak due to the 2312.5 keV 7-ray from 140 decay. We could not see some weak transitions reported by Pathak et al. [7] because of the relatively high level of background in our spectra. The decay scheme shown in Figure 2 was constructed basing on sums and differences of gamma ray energies and on coincidence data. The coincidence data show that 491 and 925keV transitions feed the
e4 j
i ~ iQo~ ic~I ~ ~ ~
'~ co m
126Xe 54 72
5.0
388keV level and that the 879keV transition feeds the ground state. The log ft values were obtained by taking T1/2= (98.6 _+0.1) s [12], I~ +(388)/I~ + (ground state) = 31/54 [13] and QEc= (4760 4-100) keV, which is the average value between Q~c=(4690_+140)keV [9] and Q~c=(4830___ 140) keV [14]. The log f values were taken from tables given by Gove et al. [15, 16]. Transitions of the total intensity 3.2 which are not
300
Ch. Droste et al.: Study of the 124Xe and 126Xe Structure
located in our level scheme do not change the spin assignments. Spin of the 388 and 879keV levels was established earlier [10, 22] as 2 +.
3.2. The
124Cs--+t24Xe
strong coupling between v-vibrations and rotation [18] and that a very important role is played by the v-dependence of the kinetic energy part of the collective Hamiltonian [19]. This is why we used the collective model described by Dobaczewski et al. [20] (model I) for calculating the energy of levels and B(E2) transition probabilities in 126Xe and 124Xe. In this model the v-independent potential of the form
Decay
Table 2 presents a list of energies and intensities of gamma transitions in 124Xe. Sums and differences of the gamma ray energies allowed us to construct the decay scheme shown in Figure 2. Spin of the 353 and 846keV levels is known from [10, 22] as 2 +. For the log ft calculation we used Qec = (5920 _+460) keV [9], T1/2=(26.5+l.5)s [12] and 1~+(353)/In+ (ground state)=37/58 [2]. Transitions of the total intensity 6.1 not located in our level scheme do not change the spin assignments.
(1)
V(fi)= 89
was assumed. For easier physical interpretation we used instead of C 8, G, a and C 2 a different set of parameters, viz. equilibrium deformation fi0, depth of the potential D = -V(flo), stiffness of the potential at equilibrium point C=(d2V(fi)/d2fi)e=l~ o. I f C 8 = 0 then both sets of parameters G, a, C 2 and/3 o, D, C can be transformed into each other in a unique way. As regards the kinetic energy part of the collective Hamiltonian the following assumption was made
4. Comparison with Theoretical Models
[20]:
Even-even isotopes of xenon are a typical example of transitional nuclei. The potential energy surface (PES) calculated by the macroscopic-microscopic method [17] shows a very weak dependence on Vdeformation. These calculations reveal a tendency to
Bpa (/3, y) = B = const
Bp~(/3, v) = 0
(2)
B=(/3, V)=B~(fi, 7)=fBmi~
"P)+b
126 , , 54xe72
E(MeV) 3.0
O4
3.245
84 74
2.990 2.880
8*
2 w64
4+ 3§ w 04jr...-~_
o
-
6§
2.780
8" 2444 5.648 .,
2.187 2.095 2.01.7 1.992
2.0
3.228
2.925
2.409
6" 54
1.0
7+8+10+
1o*
1.637 1.460 1. 390 1.368
2.195
0+3*4+64
1.517
5*
1.923
4 * _ _ 6§
1.703 1.633 1.591
o§
4*
2.383
8*
2.435
(6+} -
-
2.214
(5*) -
-
1.903
5*
2.174
o§
2 .og4
4* 6+
1.803 1.632
3+
1.354
2+
o.o - -
o§
w2§
0.392
2+
0.389
2*
o.o
V
I b
2.562
0.388
0.907
o§
(7+)
4§ 2+
2+4'
-
2.641
1.1 45
0.954 0.830
o.o -
2"
0.980 0.851
~4 § 2*
la
2.867
3§
4§ 2+
0.
2.415
6*
II
-
Ill
2+ 6+ 4§ 3+-.~ p (Otl~ 2 ~ - -
1.678 1.630 1.488 1.317 1. 313
0.944 0.890
4+ 2*
0.940 0.880
0.388
2+
0.388
o . o - -
0.
o.o
EXPERIMENT
Fig. 3. Comparison of the experimental data with theoretical predictions of various models for energy levels of 126Xe. I. Model of Dobaczewski et al. [20]. a) The calculation made with ?-dependent inertial functions (levels marked by asterisks were used to establish model parameters), b) Calculation made with the simplifying assumption B ~ = B x = By = B z = B . . . . . II. Model of Davydov and Chaban [24]. III. Model of Gneuss and Greiner. The results are taken from papers [26, 27]
Ch. Droste et al.: Study of the 124Xe and 126Xe Structure
301
Table3. Comparison of the experimental data and various theoretical predictions of the E2 transition probabilities for 126Xe. Assignments of the model are the same as in Figure 3 Model I
Model II Model III
Experiment
a
b
B(E2;2[~O[) e2b2
0.162
0.14
0.153
0.15
0.153 (6)
B(E2; 2~---+0[) B(E2; 22+~ 2 ] ) B(E2; 3[--+2/) B(E2; 3~ --+2~-) B(E2; 3 + ~ 2 +) B(E2; 3 + --+4+) B(E2; 3+ --+2~) B(E2; 3~ --+4+)
0.013
0.004
0.045
0.005
0.016 (2)
0.024
0.006
0.040
0.004
0.013 (4) 0.12 (3)
0.061
0.016
0.18
0.007
>0.027
2.5
2.5
1.8
>1.7
B(E2;4~---+22) B(E2; 42+ ~22+) B(E2;4+--+2 +) B(E2; 42~--+4[) B(E2; 42+--, 22+) B(E2; 42+--+4 +) B(E2; 6~--+4 +) B(E2; 6+ ~42+) B(E2; 0+ --+2+) B(E2; 0~ --+2~-)
0.017
0.006
0.044
0.005
0.017
0.007
0.061
0.006
1.0
1.1
1.4
1.4
0.010
0.004
0.002
-
0.009 (4)
0.003
0.006
-
-
0.10
B(E2; 6~ --+4[) B(E2; 6~--+6~) B(E2; 6+ --+42+) B(E2;6~- --+6~-) B(E2; 6~ --+4[) B(E2; 6+ --+5+) B(E2; 5+ --, 3~) B(E2; 5~-+ 4~-) B(E2; 5~-+3/) B(E2; 5+ --, 4~) B(E2; 7 + --+5 [) B(E2; 7~ ~6~) ( Q 2 + ) eb
0.021
0.009
0.014
-
>0.005
2.1
2.1
6.2
-
>0.9
8.0
1.4
0.04
-
> 0.0004
2.1
1.6
140.0
-
>0.8
2.1
2.2
0.9
-
>0.7
5.20
5.70
1.70
-
> 0.13
-0.03
-0.06
-0.52
-0.13
-
45
w h e r e c~ stands for each of the subscripts 7Y, x, y, z, a n d Bmicr(fl, 7) is t a k e n from the m i c r o s c o p i c calcul a t i o n [21]. T h e value fl was t a k e n equal to 0.2. This value is close to the average value o f / 3 in the lowlying states. F o r 126Xe we u s e d / 3 o = 0 . 1 4 5 a n d D = 0 . 7 M e V which result from m i c r o s c o p i c c a l c u l a t i o n of PES [-17]. The o t h e r four p a r a m e t e r s C = 2 2 8 MeV, B = 4 3 M e V - 1 , f = 7 . 3 5 a n d b = 1 2 4 . 5 M e V - 1 were chosen to fit the e x p e r i m e n t a l values of B ( E 2 ; 2+--+0 +) [22] a n d energy of 7 levels. T h e results of c a l c u l a t i o n s of the level energies, t r a n s i t i o n p r o b a b i l i t i e s B(E2) a n d b r a n c h i n g ratios are shown in F i g u r e 3 (part I a) a n d in T a b l e 3 (part I a). It is seen t h a t a g r e e m e n t b e t w e e n m o d e l I a n d the e x p e r i m e n t a l d a t a is quite satisfactory. F o r ~24Xe we used the s a m e p h e n o m e n o l o g i c a l pa-
or
0.010 (2) 0.024 0.012 2.3 1.2
(6) (3) (3) (1)
or
or
(4)
r a m e t e r s f, b a n d B of the inertial functions as for 126Xe. T h e d e p t h of PES D = 0 . 9 7 M e V was t a k e n from m i c r o s c o p i c calculations, the o t h e r two p a r a m e ters, /3o=0.174 a n d C = 2 5 6 M e V , were chosen to fit the e x p e r i m e n t a l data. This m e a n s t h a t for 1/4Xe o n l y two a d d i t i o n a l p a r a m e t e r s were fitted specially for this isotope. M o r e o v e r , the fitted/3o value is very close to the m i c r o s c o p i c one,/3~icr =0.177. T h e experi m e n t a l d a t a a n d the results of c a l c u l a t i o n s for i24Xe are p r e s e n t e d in F i g u r e 4 a n d T a b l e 4. T h e shapes of the p o t e n t i a l used in m o d e l I a n d of the m i c r o s c o p i c p o t e n t i a l are s h o w n in F i g u r e 5. It is seen t h a t to fit the e x p e r i m e n t a l d a t a by m o d e l I it is necessary to use a p o t e n t i a l m o r e stiff to t h e / 3 d e f o r m a t i o n t h a n the m i c r o s c o p i c one. T o e m p h a s i s e the i m p o r t a n c e of the 7 - d e p e n d e n c e of
302
Ch. Droste et ai.: Study of ihe *24Xe and 126Xe Structure Table 4. Comparison of experimental data and predictions of model I for ~24Xe 124, 54 A e 70
E(MeV) 8"
2.832
B(E2; B(E2; B(E2; B(E2; B(E2;
2[ -,0+) e2b z 22--+0 +) 2~ -+21+) 3[ -+ 2+) 3+--+2 +)
B(E2; B(E2; B(E2; B(E2;
3+ -+2 +) 3+ -+4 +) 3+--+22) 3[--+4+)
2.5 8+ 8+ 5+
2.0
~
2.103
6 + ~
2.066
4.'.
2.'.
2.036 1.908
6
1.500 1.415
+ --,,
~+
1.5
2.331
Z218
/-
(5§
1.837
(1,'2§
1.690
6+
1.548 1.437
4+
1.387(0 ,§1, 2 ~ ) ~ 1.236 3''- /
0+'
B(e2; 4+ -+27/
1.269
B(E2; B(E2; B(E2; B(E2; B(E2; B(E2; B(E2;
X._ 1.248
1.0
4§
- 2+84
0.872 0.812
2+
2"
0.360
2"
4+
0.879 0.846
~
0.5 0.354
0.1
2.5
>1.1
0.045
< 0.007
1.1
> 1.0
68
>25
2.5
>1.0
0.15
-
-
Fig.4. Comparison of the experimental energy levels and predictions of model I for 124Xe
f
2
I
I
l
,
; I
~
t
",,:3o"
/ / ~ //9~-'/-
2
_
\
\It= 60" r
-2
\
\
-.
\
-4
\
\\
\
-6 -8
i
-2
l / It
I
-4
I=25"
126,,_
I
-6
124 .
54X~70
54XI~72 -8
\\
// 1 "-~
o.1
I I
\\4~ ,. M \
iF=60"
t o
\
, ~=0"
/I \
\
I I
0
02
i
t
0.3
0.4
0
1
1
L
I
0.1
0.2
0.3
0.4
P Fig. 5. The fi-dependence of the potential for 124Xe and 126Xe" Normal solid lines-results of microscopic calculation for 7 = 0~ 30~ 60~ Bold solid l i n e - result of fit of model I to the experimental data. Dashed lines - results of fit of model III [26, 27] to the experimental data. Potentials for 7 =0~ 25~ 60~ are presented. There are no data for lZ~Xe in [26, 27]
inertial functions BT~, Bx, By, Bz, the results obtained using model I with B~v = B x = By= B z = const = B . . . . = 1 7 5 M e V -1 are shown for 126Xe in F i g u r e 3 (part Ib) and in T a b l e 3 (part Ib). It is clearly seen that the inclusion of the 7-dependence of inertal functions splits the degenerated multiplets.
There are simple phenomenological models which contain the 7-deformation dependence of the collective Hamiltonian, these are the D a v y d o v - F i l i p o v [-23] and the D a v y d o v - C h a b a n E24] ones. We tried to use the second one to analyze the properties of 126Xe. The results of calculations in terms of the
Ch. Droste et al.: Study of the t24Xe and t26Xe Structure
Davydov-Chaban model (model II) are shown in Figure3 (part II) and in Table 3 (part III). The following four parameters of the model were used: #=0.40, V=25 ~ and according to experimental data E2~=0.388MeV, B(E2; 2~-~O~)=O.153e2b z. One can see that such a simple model reproduces the main features of the level spectrum. However, this model is purely phenomenological because the physical meaning of # and V strongly depends on the simplifications made during solving the collective Schr6dinger equation [25]. Another attempt to interpret the properties of lowlying excited levels for even-even nuclei from the 50
