3.1. Se
For the study of the structure and dynamics of the lowest few 0
, 2
, and 4
states in
Se, up to 22 orthogonal
Excited Vampir configurations have been independently built for each considered symmetry. For each spin, the final solutions displaying the mixing of configurations of different deformations in the intrinsic system have been obtained by the diagonalization of the residual interaction between the corresponding many-nucleon EXVAM wave functions. The EXVAM spectrum of the lowest few 0
, 2
, and 4
states is compared with the available data in
Figure 1. For the explored lowest two 0
, 2
, and 4
states, the EXVAM spectrum indicates good agreement with the experimental one [
20]. The development of the shape mixing with increasing excitation energy and spin is displayed by the structure of the wave functions for the analyzed states in
Table 1. In this table, the contribution of differently deformed prolate (p) and oblate (o) EXVAM configurations in the intrinsic system as a percentage of the total amplitude is illustrated. The amount of mixing of the configurations contributing at least 2% to the structure of the wave function for a state of a given spin and parity are indicated in parentheses in decreasing order. The structure of the wave functions of the lowest six 0
states reveals a variable mixing of configurations characterized by prolate and oblate deformation in the intrinsic system. Almost equal prolate and oblate content characterizes the ground state (altogether 53% oblate content, including the configurations that each contribute less than 2%) and the first excited state (altogether 55% prolate content, including the configurations that each contribute less than 2%); the third, the fourth, and the sixth state are dominated by prolate deformed configurations, whereas the fifth 0
state is dominated by oblate ones.
The configuration mixing for the investigated 2 states indicates prolate dominating content for the yrast (altogether 58% prolate configurations) and the sixth state, oblate dominating one for the second 2 state, almost equal prolate and oblate contribution for the fourth state, almost pure prolate mixing for the third 2, and almost pure oblate one for the fifth state. Similar behavior characterizes the lowest five 4 states, but oblate dominant content is obtained for the sixth state. For the spin 2, the quadrupole deformation parameter is changing from to for the oblate deformed EXVAM configurations, whereas for the prolate ones, it is changing from to .
The variety of mixing of the differently deformed prolate and oblate configurations in the structure of the 2
and 4
states is reflected by the spectroscopic quadrupole moments presented in
Table 2. Based on the experimental data in the mass region, effective charges of
and
were used. The third and the fifth 2
and 4
states dominated (∼90% contribution) by configurations of prolate and oblate deformation in the intrinsic system, respectively, manifest large spectroscopic quadrupole moments. The other investigated low-lying 2
and 4
states showing strong prolate–oblate mixing of differently deformed configurations are characterized by small positive or negative spectroscopic quadrupole moments. The first experimental investigations on the spectroscopic quadrupole moment of the yrast 2
state in
Se concluded that there is no evidence for oblate shape [
16]. Improved experimental results indicate evidence for oblate shapes and suggest shape coexistence scenario for low spin states in
Se [
17].
The EXVAM results show that, in
Se, shape coexistence and mixing are the dominant characteristics, not only for the investigated 0
states, but also for the lowest few 2
and 4
states. Consequently, we investigated the
transition strengths connecting not only the 0
states, but also the low-lying 2
and 4
states.
Table 3 presents the strengths (
) for the calculated
transitions linking the EXVAM states larger than 5 milliunits. The strongest
transitions between the lowest 0
states connects the fourth and the second 0
state. Weaker transitions are linking the second 0
and the ground state as well as the higher lying and the lowest three 0
states. Concerning the
transitions between the 2
states, we found maximum strengths linking the second and the yrast 2
and the fourth to the second 2
state. Weaker transitions connect the higher lying 2
states with the lowest three 2
states. For the
transitions connecting the 4
states, maximum strength links the second and the yrast 4
state.
The latest measurements concerning the
decay of the yrast states indicate for the
strengths the values 342(19) and 370(24)
for the 2
and 4
states, respectively [
17,
19]. The corresponding calculated EXVAM values are 473 and 706
for the 2
and 4
states, respectively. The strong shape mixing identified in the structure of the wave functions for the 2
and 4
states could induce significant
transition strengths linking the EXVAM states displayed in
Table 3. The strongest EXVAM
values are connecting the lowest two states of spin 2
and 4
, 636 and 617
, respectively, and the experimental value for the first amounts to 565 (240)
[
20]. The significant
and
,
EXVAM transition strengths decaying higher lying 2
states amount to:
= 23
;
= 64
;
= 20
and for
,
= 0.011
. The results for the 4
states indicate
= 30
,
= 29
, and for the M1 branches
= 0.042
. Experimental investigations concerning the
transitions in
Se are currently being performed at TRIUMF-ISAC.
3.2. Kr
Our previous investigations on the interplay between shape coexistence and isospin-symmetry breaking effects in the A = 70 isovector triplet revealed a shape change along the isobars [
13]. The evolution of the shape mixing in the structure of the analog states explains the anomaly identified in the Coulomb energy differences. Our studies concerning the effects of shape coexistence and mixing on the analog states are extended to investigate the
transitions between the lowest few 0
, 2
, and 4
states in
Kr, the mirror nucleus of
Se. In independent variational chains, up to 22
Excited Vampir configurations for each spin have been built. The EXVAM spectrum presented in
Figure 2 compares well with the available experimental results [
18].
The amount of mixing of differently deformed prolate and oblate EXVAM configurations in the structure of the lowest six 0
, 2
, and 4
states is presented in
Table 4. The investigated states manifest, as in
Se, variable, in some cases very strong, prolate–oblate mixing, but the prolate content is larger for the corresponding states in
Kr. This feature appears already in the structure of the the wave functions of the analog states: the prolate content for the ground state, yrast 2
, and yrast 4
state amounts to 72%, 73%, and 78%, respectively. For the spin 2
, the quadrupole deformation parameter for the oblate EXVAM configurations varies from
to
; for the prolate ones, from
to
.
The oblate–prolate mixing is reflected by the spectroscopic quadrupole moments of the investigated 2
and 4
states displayed in
Table 5.
The strengths of the
transitions linking the investigated states larger than 5 milliunits are presented in
Table 6. The trend in
Kr is similar to the one obtained for
Se, but the transition linking the lowest two 0
states is two times stronger. The EXVAM value for the
amounts to 589
, in good agreement with the measured value of 545 (90)
[
17,
19]. Concerning the
transitions, the strongest connect the lowest two 2
and 4
states: 636
and 495
, respectively. Significant
and
,
EXVAM strengths for the higher lying 2
and 4
states are:
= 41
;
= 422
,
= 0.018
, and
= 31
.