- EPJ Web of Conferences

EPJ Web of Conferences 93, 010 0 6 (2015)
DOI: 10.1051/epjconf/ 201 5 93 0100 6
C Owned by the authors, published by EDP Sciences, 2015
Spectroscopy of the Cadmium isotopes
John L. Wood
School of Physics, Georgia Institute of Technology, Atlanta, GA 30332-0430, USA
Abstract. The cadmium isotopes have now been characterized across the entire 50 < N < 82 shell. A brief review is
given of the identifiable structures. Some discussion of open questions is made, especially of vibrations.
1 Introduction
The cadmium (Z = 48) isotopes have been a focus of
interest in nuclear structure for many decades. This is
because they exhibit collective excitations and are located
adjacent to the closed shell at Z = 50.
At the closed neutron shells, N = 50, 82, pairing
dominates and is manifested as excitations with good
seniority. Moving towards the mid-neutron shell at
N = 66, collectivity emerges; but exactly how and what
kind is an open question. In the vicinity of the mid-shell,
the former view of the structure of the Cd isotopes was
one of near-harmonic quadrupole collective vibrations:
this view has been refuted [1]. However, exactly what is
the collective character of the mid-shell Cd isotopes,
remains an open question. The present paper discusses
these issues.
2 A global view of the Cd isotopes
Figure 1 presents seniority structures due to the g9/2-2
configuration as manifested in 98-130Cd. Figure 2 presents
.
E(MeV)
(nm)
4
8+
8+
d, 3He 8+
8+ g9/22
+10.32
2
10+ h11/22
(nm)
1.04
2
6
4
1
2
6
4
4
2
0
2
0
98
102
106
110
114
118
122
126
130
Figure 2. Seniority structures in
resulting from g7/2+2,
-2, and g d
h11/2
7/2 5/2 configurations. The data are taken from
Nuclear Data Sheets.
102-128Cd
In the mid-shell region of the Cd isotopes shape
coexistence is well-established and is interpreted as
resulting from a proton-pair excitation across the Z = 50
shell gap [2]. This is shown in Fig. 3.
The major open question is the nature of the collective
structures built on the Cd ground states. Maps
coexis ng collec ve
structures AND mixing
8
3
4
2
2
10
8
4
4
8
6
4
2
10+
6+, 10+
g7/2d5/2
3He,
1
% gs
6
4
2
0
2
17%42%
n 0+
6
4
0 0
98
102
106
110
114
118
122
126
130
Figure 1. Seniority structures in the Cd isotopes resulting from
g9/2-2 configurations. The data are taken from Nuclear Data
Sheets.
+2
seniority structures due to the g7/2 , g 7/2d5/2, and
h11/2-2 configurations as manifested in 100-128Cd. These
are characterized spectroscopically by one-nucleon
transfer reactions, magnetic moments, and lifetimes.
a
6+
10
3
.
E(MeV)
8
6
4
2
4
8
+9.95
3
6+ g7/2+2
.
E(MeV
1
0
55%
2
0
98
102
106
110
114
118
122
126
130
108-118Cd
Figure 3. Deformed structures in
resulting from a (2p4h) configuration. The data are taken from Nuclear Data Sheets.
of B(E2) values provide a powerful summary of the
collective character of a series of isotopes. These are
Corresponding author: [email protected]
!
Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/20159301006
EPJ Web of Conferences
shown for the Cd isotopes in Figs. 4, 5, 6, 7, 8, and 9.
While the energy pattern of excited states suggests
emerging
collec vity
.
E(MeV)
the subject of the contribution by Andrey Blazhev to
these Proceedings.
emerging
collec vity
E(MeV)
4
B20 W.u.
2
3
6
2+
6
2
4
2
4
2
1
0
20
0
204 259
98
102
25
27
27
106
110
30 31 34 33
114
27
118
23
19
122
2
14
126
130
305
153
226
25
27
106Cd
108Cd
27
30
31
0+
110Cd
+Î
112Cd
2510
114Cd
34
33
116Cd
118Cd
Figure 7. Map of B(E2; 22
21 and B(E2; 21 Î 01
expressed in W.u. The data are taken from Nuclear Data Sheets
+)
+
+)
B2’0 / B2’2
0+
E(MeV)
0.22
0.11
0.045
2+
0
0
2+
0+
2+
4+
1
175
2+
Figure 4. Map of B(E2; 21+ Î 01+ ) = B20 expressed in W.u.
Collectivity is evidently emerging by 102Cd and 124Cd. The data
are taken from Nuclear Data Sheets and [3,4].
E(MeV)
143
1
2
0.040
0.022
0+
2+
4+
2
2+
1
110Cd
114Cd
112Cd
116Cd
118Cd
0
Figure 5. Map of B(E2; 22 Î 01 ) / B(E2; 22 Î 21 ) =
+
+
+
146 or <10
0.0099
2+
0+
108Cd
0+
0.044
0+
106Cd
2+
0+
+
5.38
0+
106Cd
B2’0 / B2’2. Intruder states are shown in red. The data are taken
from Nuclear Data Sheets.
0.0025 0.79
108Cd
110Cd
112Cd
114Cd
116Cd
118Cd
Figure 8. Map of B(E2; 0vib+ Î 21+) expressed in W.u. for 0+
states that are candidate two-phonon states. The data are taken
from Nuclear Data Sheets.
E(MeV)
E(MeV)
2
4+
2
466
1
( ) 416
429
616
2+
25
0
27
27
30
0+
106Cd
108Cd
110Cd
112Cd
624
31
114Cd
5614
34
116Cd
( )
0+
2+
0+
> 61 1
33
5114
2+
272
306
118Cd
Figure 6. Map of B(E2; 41+ Î 21+) and B(E2; 21+ Î 01+)
expressed in W.u. Good candidates for harmonic quadrupole
vibrators are indicated by check marks. The data are taken from
Nuclear Data Sheets.
near-harmonic quadrupole vibrational behavior, the
B(E2) pattern does not support this. Undertaking a
characterization of just what is the nature of the collective
nuclear structure built on the Cd ground states has proven
to be one of the most highly demanding tasks in nuclear
spectroscopy, probably, that has ever been undertaken.
Some details are given in the next section.
A further issue that arises in the Cd isotopes is the
possibility of elucidating the emergence of collectivity
from its incipient appearance. To this end, the
spectroscopy of 100-108Cd is of particular interest. This is
0
0+
106Cd
108Cd
110Cd
112Cd
114Cd
116Cd
118Cd
Figure 9. Map of B(E2; 0def+ Î 21+) expressed in W.u. for 0+
states that are deformed states. The data are taken from Nuclear
Data Sheets
3 Detailed spectroscopic studies of the Cd
isotopes
Detailed spectroscopic data for the Cd isotopes have
begun to be acquired, especially by the technique of
inelastic neutron scattering as carried out at the Univ. of
Kentucky Accelerator Laboratory [5-8] (and see the paper
by Steven Yates in these Proceedings). These data have
01006-p.2
CGS15
been combined with ultra-weak -ray decay branch
measurements following decay [9,10]. An outcome of
these studies is presented in Fig. 10, which summarizes
pertinent data that are a first look beyond a vibrational
interpretation of 110-116Cd.
Fortune PR C35 2318 1987
02+
pt(02+)
01+
pt(01+)
0 1+
114Cd
(p,t)
116Cd
VJ=0
~
330 keV
0 / 0
~
0.28
02 + 02 = 1
02+ 1135
0def+ Ed
0sph
To move beyond the present status of the structure of
the Cd isotopes will be even more demanding of
spectroscopic techniques. An obvious direction is multistep Coulomb excitation. At present, such data only exist
for 114Cd [11]. A less obvious direction is transfer
reaction
+
0Î 02 (E0) ~ [<r2 >]2 02 02
E0
Es
0 1+
<r2 > = <r2 >def <r2 >sph [unknown]
0
114Cd(expt)
0Î 02 (E0) 103 = 19 = 482 [<r2 >]2 103 [0.28 x 0.96]2
[1.2 x 1141/3]4
<r2 > ~ 0.4 fm2 [first es mate]
JÎ J2 (E0) 103 ~ 300 J2 J2
E(MeV)
trans.
6d+
2
4d+
2d+
0+,3+,
4+,6+
41+
23+
02+
0d+
1
2p4h
22+
21+
0
110Cd
4d2d 11535
2302
242
2341 < 5
2322 < 0.76
2h p1/22
112Cd
0221 < 7.9
2101
27
114Cd
116Cd
harm.
vib.
Figure 11. Electric monopole transition strength, 2(E0)*103 in
114Cd and its origin through configuration mixing.
11912
278
175
3510
42
< 0.4
< 0.3
<7
31
<2
2.84
0.009944 0.00264
30
31
2.06
17
0.554
60
34
30 (norm)
analysis to states with spin other than zero is presented in
Fig. 12. In particular, note that the input quantity, <r2>
2(E0) 103 max ~ 100 (obs.)
2(E0) 103
E(MeV)
114Cd
JÎ J2 (E0) 103 ~ 400 J2 J2
0 1+
<120
<r2 > ~ 0.45 fm2 [2nd est.]
2
Figure 10. Electric quadrupole transition strengths in 110-116Cd
deduced from lifetime measurements and -ray transition
intensities. The data are taken from Nuclear Data sheets and
references given in the text.
3+ 2205
4+ 2152
2+ 1842
4+ 1932
0 / 0 ~ 0.23
4+ 1732
3+ 1864
8912
12020
2+ 1364
0+ 1306 4+ 1284
0.655
<130
0+ 1135
255
2+ 1210
1
438
1.8313
2+
558
0+
0
192
0
spectroscopy, using both one- and multi-nucleon transfer
(see the paper by Paul Garrett in these Proceedings). A
particular outcome of such measurements is that they
reveal the non-collective states in weakly collective
nuclei such as the Cd isotopes.
Figure 12. Electric monopole transition strengths, 2(E0)*103 in
114Cd for all strong E0 transitions and the fine-tuning of its
strength (see text). The data are taken from [12,14].
A rarely conducted type of spectroscopy that has been
carried out for many decades is conversion electron
spectroscopy, which, besides the familiar outcome of
transition multipolarities, is uniquely able to quantify E0
transition strengths (given that the lifetime of the parent
level is known). Such strengths are a sensitive and modelindependent view of shape coexistence and mixing (see,
e.g., [12]).
is taken to be spin independent and is fine-tuned to the
largest observed value of 2(E0)*103 and the presumption
that this corresponds to = = 0.50, i.e., maximal
mixing. From this, one can deduce mixing of pairs of
configurations as shown in Fig. 13. Also shown in Fig. 13
are mixing strengths from an IBM-MIX calculation [15].
Evidently, the IBM-MIX calculation (which was directed
at fitting E2 strengths) seriously fails to describe the
pattern of mixing (note that the IBM-MIX calculations
are multi-state mixing).
An analysis for the E0 transition strengths is presented
here for 114Cd. It relies on having information for mixing
amplitudes for 0+ states from two-neutron transfer data
[13]. The essential theory and the input data are
summarized in Fig. 11. The extension of the mixing
E(MeV)
2
2(E0) 103
expt
J2
J2
0102 0.95
0.05
2123 0.88
0.12
4142 0.67
0.33
2224 0.50
0.50
2223 0.93
0.07
mixing is 2state
<120
3+ 2205
4+ 1732
12020
2+
0+ 1306 4+ 1284
4+ 2152
2+ 1842
3+ 1864
8912
0.655
<130
4+ 1932
0+
1364
1135
2+ 1210
255
114Cd
th
J2
J2
0102
0.97 0.02
2123
0.94 0.03
4142
0.93 0.05
2224
0.85 0.03
2223
0.85 0.10
mixing is mul state
1
438
1.8313
2+
558
0+
0
192
0
Figure 13. Mixing strengths in 114Cd deduced from electric
monopole transition strengths, 2(E0)*103 for all strong E0
transitions and comparison with mixing strengths from an IBMMIX calculation [15].
01006-p.3
EPJ Web of Conferences
4 Future work and conclusions
From the emerging pattern of E2 and E0 decay strengths
in the mid-shell Cd isotopes it is evident that
considerably more spectroscopic study is needed. A first
major direction will be multi-step Coulomb excitation.
Such data will identify which excited states are
connected by strong E2 transitions. In addition, one- and
multi-nucleon transfer data are needed to identify noncollective, i.e., broken pair states.
An issue that impacts nuclear structure more widely
and involves the Cd isotopes is the question; “Do we
understand excited 0+ states in nuclei?” An initial
exploration of this was made in [16]. It would appear
that, from a shell model perspective, the location of shell
and subshell gaps is important for answering this
question. However, from a more global perspective, the
symplectic shell model may provide a unified way
forward (see, e.g., [17]).
The author wishes to acknowledge collaborations with
Mitch Allmond (Oak Ridge National Lab), Paul Garrett
(U. Guelph), Kris Heyde (U. Gent), and Steve Yates (U.
of Kentucky) on the study of the Cd istopes.
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