Highly deformed band structures due to core excitations in 123Xe

High-spin states in 123 Xe were populated in the 80 Se( 48 Ca, 5n) 123 Xe reaction at a beam energy of 207 MeV. γ -ray coincidence events were recorded with the Gammasphere spectrometer. Four new high-spin bands have been discovered in this nucleus. The bands are compared with those calculated within the framework of cranked Nilsson-Strutinsky and cranked Nilsson-Strutinsky-Bogoliubov models. It is concluded that the conﬁgurations of the bands involve two-proton excitations across the Z = 50 as well as excitation of neutrons across the N = 82 shell gaps resulting in a large deformation, ε 2 ≈ 0 . 30 and γ ≈ 5 ◦ .


I. INTRODUCTION
Angular momentum in atomic nuclei is generated by the alignment of individual nucleon spins. In nuclei with just a few nucleons outside a closed core, the angular momentum is generally built from the full alignment of a few spin vectors, creating an irregular energy level pattern, whereas in deformed nuclei, far off closed shells, the gradual alignment of many spin vectors gives rise to collective rotation with regular band structures. The competition of these modes of excitation, in particular in the transitional regions between spherical and deformed nuclei, is of special interest [1,2].
The nuclei in the A ≈ 125 mass region are soft toward deformation changes. They lie in the transitional region between spherical (Sn) and deformed (Ce) nuclei. The interplay of a variety of shapes is observed here with the excitation of a few valence nucleons to deformation driving h 11/2 intruder orbitals which are accessible to both protons and neutrons. These h 11/2 nucleons have opposite deformation-driving effects; the protons favor a prolate shape while the alignment of the neutrons drives the nucleus toward an oblate shape [3][4][5].
Shape changes from a weakly prolate shape to an oblate one at medium spin have been reported in several nuclei of this mass region [6][7][8][9][10][11][12][13][14]. With increasing rotational frequency, nucleon pairs are broken and the spin vectors are gradually aligned along the rotational axis, inducing shape changes, until the bands terminate in maximally aligned oblate states where all the valence particles outside the closed 114 Sn core (Z = 50, N = 64) are aligned. Thereafter, higher angular momentum states can only be generated in configurations involving single-particle excitations from the 114 Sn core across the shell gaps.
In this article, we report on the observation of new rotational structures at high spin in 123 Xe. Four highly deformed bands, with characteristics similar to those observed in [124][125][126] Xe, have been found to feed ND levels of 123 Xe [20]. Several decay branches have been observed to emerge at the bottom of the bands, feeding multiple medium-spin band structures. However, they could not be firmly placed in the level scheme due to their weak intensities. Tentative spin and parity assignments, along with the possible configurations of the bands, are discussed within the framework of the CNS and cranked Nilsson-Strutinsky-Bogoliubov (CNSB) models.

II. EXPERIMENTAL DETAILS AND ANALYSIS
High-spin states of 123 Xe were populated in a heavyion fusion evaporation reaction, 80 Se( 48 Ca, 5n) 123 Xe, at the ATLAS accelerator of Argonne National Laboratory, USA. The 48 Ca beam of 207-MeV energy and 4-pnA current bom-barded a target composed of a 0.6 mg/cm 2 thick layer of 80 Se evaporated on a 0.3 mg/cm 2 Au backing. A layer of Au, with a thickness of 0.04 mg/cm 2 , protected the front of the Se target. The target was mounted on four segments of a rotating wheel. In addition, the beam was slightly defocused and wobbled to prevent heat damage of the target [11]. γ -ray coincidence events were recorded with the Gammasphere spectrometer [21], which consisted of 101 Compton-suppressed Ge detectors at the time of the experiment. Over a beam time of 10 days, 2.7 × 10 9 events, with Ge-detector coincidence fold 4, were recorded by the spectrometer. Although the main motivation behind the experiment was to search for hyperdeformed structures in 124 Xe, high-spin states of 123 Xe were populated adequately to carry out the present study. The other dominant channels populated in this experiment were 4n, p4n, and α4n leading to 124 Xe [17], 123 I [11,15], and 120 Te [13], respectively.
The raw data were calibrated and gain matched and were sorted into γ -γ coincidence matrices, γ -γ -γ cubes and γ -γ -γ -γ hypercubes. The offline analysis was carried out with the help of the RADWARE software package [22]. Angular distribution matrices were produced to determine multipolarities of γ rays. Typical values of the angular distribution ratio R θ , defined in Ref. [20], for stretched dipole and stretched quadrupole transitions are around 0.6 and 1.4, respectively. The details of the measurement and data analysis are reported in an earlier publication on 123 Xe [20].

III. RESULTS AND LEVEL SCHEME
The investigation of high-spin states in 123 Xe was based on the same data set as was used for the low-and medium-spin states in Ref. [20]. In the present article, we report the observation of four new highly deformed bands in this nucleus. The partial level scheme of 123 Xe including the new high-spin bands (L1-L4) is displayed in Fig. 1. Some of the low-and medium-spin sequences, receiving decays from the high-spin bands, are included in Fig. 1. The nomenclature of the ND bands has been adopted from the previous work [20].
Band L1 is the most intense and collects approximately 1.5% of the intensity observed for the 617-keV transition of band 9. The second-most intense band is L4, with ≈1% intensity followed by bands L3 and L2, having intensities of less than 1% each. Due to their low intensities and the possible fragmentation of their decay patterns, linking transitions to the ND levels could not be established uniquely. Spin and parity quantum numbers for states in these bands have therefore been estimated from their feeding to ND levels. In this estimate, one or two missing transitions of dipole or quadrupole nature and with energies close to those near the bottom of the high-spin bands have been assumed. Thus, the spins adopted in Fig. 1 have to be considered as lower limits. Furthermore, the relative intensities of the bands have been included in the estimate of the excitation energies. The transition energies, tentative spins, and excitation energies of the bands are summarized in Table I. Angular distribution ratios, R θ , used for determining multipolarities were measured for some of the transitions within bands L1 and L4 and these are also listed in Table I. The ratios are consistent with the   The tentative level energies and spins of L1-L4 have been estimated from the patterns of their decays to ND levels (see text for details). The low-lying structures, numbered 1 to 13, are taken from Ref. [20]. E 2 character of the γ rays. For other transitions of the bands, the ratio could not be determined due to insufficient statistics, and a quadrupole multipolarity has been assumed based on the distinct rotational character of the sequences. With the tentative spins assigned to the bands, they extend to spin I ≈ 60. The highest spins are comparable with those assigned to the high-spin bands in neighboring Xe nuclei [17][18][19].
The level scheme has been constructed using γ -γ coincidence relationships. Quadruple-coincidence conditions have been used to avoid possible contamination from other nuclei populated in this reaction. The in-band transitions have been placed according to their relative intensities. For very weak transitions, e.g., transitions at the top and bottom of the bands, it was difficult to verify coincidence relationships using direct coincidence gates placed on the γ rays involved. These transitions were only observed in summed spectra using gates on a list of other γ rays in the bands. The γ -ray spectra of the four newly established high-spin bands are displayed in Figs. 2-4.

A. Band L1
Band L1, consisting of a cascade of 12 γ rays, is the most intense sequence above I = 30 in this nucleus. A summed triple-gated coincidence spectrum with gates on the transitions of band L1 is presented in Fig. 2(a). The decay of L1 is fragmented and the total intensity of the band is divided among several cascades feeding to bands 1, 2, 6, 7, 8, and 9, respectively. This is observed in Fig. 2(a), where the intensities of the transitions below the 1287-keV γ ray drop drastically. Parallel branches, labeled L1a and L1b, have been detected in the lower part of this structure. The 1294-keV transition is missing in the 1287-keV coincidence spectrum and has been placed in parallel to it. The presence of the 1366-and 1286-keV γ rays has been established in coincidence spectra with respective gates on the 1367-and 1287-keV transitions of the band. The 1366-keV transition was not observed in gates involving both the 1367-and 1287-keV transitions and, therefore, it is placed in parallel to the 1287-keV γ rays. The TABLE I. γ -ray energies, tentative level energies, and spin assignments to the levels of the four high-spin bands in 123 Xe. Angular distribution ratios and deduced multipolarities of the transitions are listed in columns 4 and 5, respectively. The initial level energies and spins of the bands have been estimated from their feeding to ND levels (see Ref. [20] and the text of this paper). W , X , Y , and Z are unknown excitation energies.

Energy
Initial level energy Spin assignment Angular distribution ratio Multipolarity band L1 also forks into two branches at high spin, where the parallel branch is labeled L1c. In a triple-gated coincidence spectrum, produced with a list of all the transitions of band L1 [see Fig. 2(a)], the transitions of band 1 up to the 1232-keV transition and of band 2 up to the 1216-keV transition along with some of the intermediate M1 γ rays have been observed. A fraction of the band intensity is feeding the 55/2 − state of band 9 and the 59/2 − level of band 7. In a triple-gated spectrum with two transitions of band L1 and the third one of 402 keV of band 6, all the transitions of band L1 along with those of 955, 632, and 831 keV of bands 7 and 8 were observed. Furthermore, the 955-keV transition is present in a triple-gated spectrum with a gate on the 1287 line and two gates on the rest of the transitions of band L1 but the 632-and 831-keV γ rays are absent. This indicates that the 1287-keV transition is feeding the 59/2 − level of band 7. Assuming a missing linking transition of dipole nature and energy around 1300 keV, a tentative spin of 61/2 − and an excitation energy of about 12.4 MeV can be assigned to the lowest level of band L1. With a possibility that the missing transition is of quadrupole character or that an additional linking γ ray is present, the uncertainty in the spin assignment is 1-3h and that for excitation energy about 1-2 MeV.

B. Band L2
Band L2 is the least intense of the four high-spin bands and it is difficult to conclude exactly where this band is feeding to ND levels. Only the strongest transitions of the yrast band 9 are visible in a triple-gated spectrum produced with a list of γ rays of band L2 [see Fig. 2(b)]. The strongest γ rays of 124 Xe are also visible due to overlapping energies with some of the transitions of the L2 band. The spin and excitation energy of the band have been adjusted to place this sequence above all other bands observed in this nucleus. A tentative spin of 63/2 and an energy around 13.3 MeV are being proposed for the band head in the level scheme (see Fig. 1).

C. Band L3
Band L3 exhibits regular energy spacings above the 1493-keV transition with nearly 100-keV energy difference between successive γ rays. The energy difference becomes irregular in its extension toward lower energy, marked as L3a. The ordering of γ rays below the 1493-keV transition is based on their intensities in different coincidence spectra. However, a possible reordering cannot be ruled out due to their weak intensities. A 1390-keV γ ray, forming a parallel decay branch is observed at the bottom of the band.
Band L3 decays primarily to band 9 but it also feeds bands 6 and 7. A summed triple-gated coincidence spectrum with gates on all the transitions of the band is displayed in Fig 3(a). The strongest γ rays of band 9 and the 402-, 778-, and 955-keV transitions of band 7 are clearly visible. A triple-gated spectrum with two gates placed on a list of transitions of band L3 and the third gate on the 402-keV transition of band 7 confirms the presence of the 778-, 955-, and 1402-keV γ rays of band 7 along with all those of band L3 [see Fig. 3 A very small peak at 1440 keV, the transition placed below the 1493 keV one in L3, is also visible in that spectrum. Furthermore, a summed triple-gated spectrum with gates on 402-and 1402-keV γ rays and on one transition from band L3 confirms the presence of the 1440-keV line of L3. Therefore, assuming a missing dipole transition of 1200 keV, a spin 65/2 and 13.7 MeV of excitation energy is proposed to the lowest level of band L3.

D. Band L4
Among the high-spin bands, L4 has the longest chain of in-band transitions. The band is regular in energy at the beginning with successive γ -ray energy differences of the order of 100 keV. The difference gradually decreases to 80 keV toward higher spin. The γ -ray energies become irregular at higher spin indicating the presence of a band crossing. The top two transitions of the band, i.e., the 2152-and 2190-keV γ rays, were observed only in summed triple-gated spectra produced using a list of the other transitions of the band. Due to low statistics in the resulting spectra, a unique placement of the 2152-and 2190-keV transitions was not possible. The most probable placement is that they are extensions of band L4 on top of the 2065-keV line, although a placement in parallel to that transition cannot be excluded.
Band L4 predominantly decays to bands 12 and 13. A summed triple-gated coincidence spectrum, created with a list of transitions of band L4, is found in Fig. 4(a). The transitions of bands 12 and 13 can be seen in coincidence with the transitions of the sequence. A triple-gated spectrum with two gates on transitions of L4 and the third gate on the 180-keV transition of bands 12 and 13 also shows γ rays of band L4 along with transitions of bands 12 and 13. Similar to other high-spin bands in this nucleus, the decay of L4 is also fragmented and several decay branches below the 1354-keV transition have been observed in the coincidence analysis. The presence of a second 1354-keV γ ray is shown in the inset of Fig. 4(a). A decay branch of 1294-and 1483-keV γ rays has been observed in parallel to the 1343-and 1433-keV transitions. The transitions below the 1433-keV γ ray of L4a were not only in coincidence with the band transitions but also with themselves. Due to overlapping energies of some of the γ rays, e.g., the 1343-, 1351-, and 1354-keV lines and the 1079-and 1080-keV decay transitions of bands 12 and 13, clean gates could not be placed on individual transitions. Therefore, the ordering of the transitions in the lower part of the band remains uncertain.
In order to estimate the spin of the band, feedings from band L4 to bands 12 and 13 have been searched for in the coincidence spectra. It is observed in Fig. 4(a)    proposed to the level below the 1354-keV transition. If the average energy of these two transitions is 1300 keV, an excitation energy of roughly 12.0 MeV can be estimated to the level. Assuming a quadrupole nature of the transitions of band L4a, the lowest level of the band can be proposed to have spin 37/2 at an excitation energy of about 4.64 MeV. With these assumptions for spin and excitation energy, the lower portion of L4a is lower in energy by nearly 0.8 MeV relative to bands 12 and 13. The parity of the band has been assumed to be positive.

IV. DISCUSSION
In this section, the observed bands will be compared with the lowest-energy bands calculated within the cranked Nilsson-Strutinsky (CNS) [23][24][25] and cranked Nilsson-Strutinsky-Bogoliubov (CNSB) [26,27] formalisms. The tentative spins and parities assigned to the bands in Fig. 1 will be compared with those suggested from the theoretical analysis. A brief discussion on the impact of the pairing interaction in the calculated bands will be made by comparing results of the CNS and CNSB models.

A. The CNS and CNSB models
Within the CNS formalism, the Hamiltonian has the form [23][24][25] where H MO is the modified oscillator Hamiltonian [28] and ω j x is the cranking term for rotation around the principal x axis. The κ and μ parameters derived for the A ≈ 110 region have been applied [24]. The total energy is defined as the sum of the shell energy and the rotating liquid drop energy. This shell energy is calculated using the Strutinsky method [29,30]. The Lublin-Strasbourg drop (LSD) model [31] is used for the static liquid drop energy with the rigid-body moment of inertia calculated with a radius parameter r 0 = 1.16 fm and diffuseness parameter a = 0.6 fm [25]. The total energy is minimized with respect to the deformation parameters (ε 2 , ε 4 , γ ) for each configuration and for each spin value. Special methods, based on exact and approximate quantum numbers, are introduced [23,32] to fix diabatic configurations in a detailed way. These calculated configurations are labeled as [(p 1 )p 2 p 3 ; n 1 n 2 (n 3 n 4 )] relative to a Z = 50 and N = 70 core, where p 1 is the number of proton holes in orbitals of g 9/2 character, p 2 is the number of dg protons (i.e., protons with dominant amplitudes in the d 5/2 and g 7/2 shells), and p 3 is the number of protons in h 11/2 orbitals. Furthermore, n 1 is the number of N = 4 neutron holes, n 2 is the number of h 11/2 neutrons, and n 3  x/x/180   [20] for detail level scheme) to which band L4 decays. and h 9/2 shells. Numbers in parentheses are not shown when they are equal to zero. When appropriate, the signature for an odd number of particles in a certain group is denoted by a subscript, + or −. In previous publications, when signature was not specified, a shorter form [p 1 p 3 , n 2 (n 3 n 4 )] was used to label the configuration; e.g., see Refs. [15][16][17]. It is generally assumed that each of the labels, p 1 , p 2 , etc. has only one digit. In the event that a label has two digits, e.g., 10 holes in the N = 4 neutron shell, an asterisk ( * ) is added as a subscript.
In the CNSB formalism [26,27], the same potential as in CNS plus a monopole pairing term are used, (2) where P † (P) andN are the pair creation (annihilation) and particle number operators, respectively. The formalism is based on the ultimate cranker method developed by T. Bengtsson [33]. In the CNSB formalism, the microscopic energy, after particle number projection, is minimized not only in the deformation space, but also in a mesh of the pairing parameters, Fermi energies λ p and λ n , and pairing gaps p and n . According to the Hamiltonians in Eqs. (1) and (2), the only difference between the CNS and the CNSB yrast configurations is the pairing energy. In the CNSB formalism, the only preserved quantum numbers are parity π and signature α for protons and neutrons. Thus, it is possible to form 16 different configurations which can be labeled (π, α) p (π, α) n .

B. The pairing energy
As discussed in Ref. [17], the configurations with two holes in the g 9/2 shell are favored in energy and one should consider those to find an interpretation for the high-spin collective bands in the Xe region. Such configurations form minima for I ≈ 30-60 at ε 2 ≈ 0.30 ± 0.05 and γ ≈ 0 ± 15 • . If the energy of these minima is calculated in the CNS and CNSB formalisms, i.e., with and without pairing (see Fig. 5), it turns out that the pairing energy is always small and moreover that it follows a smooth trend with spin. Thus, for I > 30 and for all 16 combinations of parity and signature for protons and neutrons, (π, α) p (π, α) n , Fig. 5 indicates that the pairing energy is generally smaller than 0.7 MeV and it comes close to zero when the spin approaches I = 60. In particular, it can be fitted with an exponential function, energies lie close to the energies with the proper pairing energy. However, by considering the unpaired configurations, it becomes possible to trace these in a detailed way. This also allows us to consider configurations which are not yrast within the paired configurations (π, α) p (π, α) n . We will refer to these calculations within the CNS formalism but with addition of an average pairing, as the CNS(B) formalism.

C. General features when comparing observed and calculated bands
As suggested from the single-particle diagram for neutrons, the low-lying configurations have up to three neutrons excited across the N = 82 gap (see Fig. 12 in Ref. [17]). A large number of such configurations combined with proton configurations with two g 9/2 holes have been calculated in the CNS formalism and those which are relatively low lying in energy have been selected. With the average pairing energy added, these configurations are displayed relative to the rotating liquid drop energy in Fig. 6. The configurations with four excited neutrons across the N = 82 shell gap appear to be favored in energy at much higher spin and are not of interest for the interpretation of the high-spin bands.
The excitation energies of the high-spin bands in 123 Xe, shown in Fig. 1 as L1-L4, have been plotted relative to the rotating liquid drop energy as a function of spin in Fig. 7. Note that the bands are not linked and their spins and excitation energies represent lower limits which have been proposed assuming that one or two missing transitions feed the levels of the ND bands. The relative energies of selected ND bands have been included in Fig. 7 for reference. The general features of the high-spin bands are similar to those of the calculated ones in Fig. 6, i.e., smooth curves with a minimum for I = 35-45. This is especially true for bands L1 and L3 while bands L2 and L4 are more irregular, suggesting that they might be built from two or three interacting bands. Furthermore, for the calculated bands which are most favored in energy, the minimum is located at a higher spin values, I ≈ 50. This suggests that the spin values of the observed bands might be larger than the experimental values suggested in Figs. 1 and 7. This is not unexpected considering that the experimental values are lower limits.
An interesting feature of the observed bands is the sections at low spin forming short sequences, especially band L4a with five transitions and band L3a with two transitions. The fact that these bands are not linked to the ND bands suggests that they are not associated with excitations in the valence space. Thus, like the high-spin bands, it is assumed that they are built from configurations with two proton holes in the g 9/2 orbitals. As evident from Fig. 6 7. The observed collective bands in 123 Xe, with spin and excitation energies according to the experimental analysis, are drawn relative to the rotating liquid drop reference. In addition, some selected ND bands [20] are shown relative to the same reference. [24,32]. In this configuration, it is rather straightforward to distinguish between dg and sd neutrons, i.e., neutrons which have their dominating amplitudes in the d 5/2 , g 7/2 shells and in the s 1/2 , d 3/2 shells, respectively. With such a distinction, the [(2)42; 87] configuration can be written relative to a 114 Sn core as π (g 9/2 ) −2 8 (dg) 4 10 (h 11/2 ) 2 10 28 ⊗ν (dg) −4 10 (sd ) 2 2 (h 11/2 ) 7 16.5,17.5 28.5,29.5 , where the maximum spin value is denoted as a subscript. Adding these spin contributions, a highest value for the total spin can be calculated, I max = 56.5, 57.5. Thus, these configurations will terminate at relatively very high spin values where they are high above the yrast line and probably cannot be observed as discrete states.

D. Bands L3 and L4
In order to assign configurations to the branches of L3 and L4 at lower spin, labeled as L3a and L4a in Fig. 1, these are compared in Fig. 8 to the calculated configurations which are lowest in energy in the spin range I = 20-30 of Fig. 6, i.e., the two signatures of the [(2)42; 87] configuration where the occupation of the j shells is spelled out above. It is appropriate to assign the favored signature of this configuration to the best developed low-spin band L4a where the difference curve between experiment and calculation [see Fig. 8 Figs. 1 and 7. Consequently, the L3a band will have signature α = 1/2, and if all the transitions of L3a and L3 are of stretched E 2 character, the full spin range of the L3 band has this signature. Therefore, above the crossing, the L3 band can be assigned to the configuration, [(2)42; 9 − 6(1 + 1 + )], i.e., π [(g 9/2 ) −2 (dg) 4 (h 11/2 ) 2 ] ⊗ ν[(sdg) −9 (h 11/2 ) 6 (h f ) 1 (i 13/2 ) 1 ], which is the next lowest calculated configuration for I = 40-50; see Fig. 6. With a spin value which is two units higher than that suggested in Fig. 1, the energy difference for band L3 is very close to constant. Furthermore, if the energy of the bands is increased by 0.8 MeV for each added spin unit, the difference curve has essentially the same value as for the L4a band. It appears that the crossing region between the [(2)42; 87 + ] and [(2)42; 9 − 6(1 + 1 + )] configurations, i.e., between L3a and L3, is smoothed by the [(2)42; 86(1 + 0)], or

(c)] becomes relatively constant if the spin value of band L4a is increased by three units compared to the values in
configuration. Thus, starting at low spin from the L3a band, first a neutron is excited from h 11/2 to the h f orbitals and then another neutron is lifted from N = 4 to N = 6.
A reasonable interpretation for band L4 becomes difficult if all the transitions are assumed of stretched E 2 character, and parity and signature are the same throughout L4a and L4. However, if the 1343-keV transition, connecting L4a and L4, is assumed to be a I = 1, E 1 transition, the L4 band can be assigned a configuration [(2)42; 86(01 + )] or π [(g 9/2 ) −2 (dg) 4 (h 11/2 ) 2 ] ⊗ ν[(sdg) −8 (h 11/2 ) 6 (i 13/2 ) 1 ], which means that an h 11/2 neutron is lifted to i 13/2 in the transition from the L4a to the L4 band. With this assignment, the difference curve will essentially overlap with that for the L3 band; see Fig. 8. The agreement is seen up to I ≈ 48 where a band crossing is apparent in the L4 band. A band crossing is also observed in the calculation for the [(2)42; 85 − (1 + 1 + )] configuration, where the calculated crossing is much sharper than the observed one. However, because the experimental values are rather uncertain at these high spin values, this should not be viewed as a serious disagreement.
Band L2 is much shorter and more irregular, which means that any assignment will be uncertain. As shown in Fig. 9, if its spin value is decreased by 1h relative to the value in  Fig. 1, it might be assigned to the [(2)42; 7 + 6] configuration at low spin and possibly to a configuration with one neutron lifted from N = 4 to N = 6 at higher spins. However, the calculated crossing appears sharper than the observed one. Furthermore, the suggested configuration above the crossing was already assigned to band L4. Thus, if that assignment is correct, another interpretation for the highest spin states in the L2 band is needed. However, as the observed values for the highest spin states in the L2 band are rather uncertain, we will not try to propose an alternative interpretation.

F. Energies and energy surfaces in the CNSB formalism
If a configuration assigned to an observed band is the lowest one in a (π, α) p (π, α) n group, it is straightforward to compare it with the full CNSB calculations. This is demonstrated for bands L1 and L3 in Fig. 10, which can be compared with the corresponding curves in Figs. 9 and 8, respectively. Considering that the full pairing can be described by the average pairing with a good accuracy (see Fig. 5), the difference between calculations and experiment will be similar to that of the CNS calculations with the average pairing energy added, i.e., the CNS(B) calculations. The change in CNS configuration at low spin in the L3 band can be seen in the energy surface for the (+,0)(−,1/2) configuration in Fig. 11, calculated in the full CNSB formalism. For I = 34.5, the lowest energy configuration is [(2)42; 86(1 + 0)] corresponding to the deformation ε 2 ≈ 0.28, γ ≈ 3 • while the minimum at ε 2 ≈ 0.32, γ ≈ 10 • for I = 44.5 is formed with a neutron excited from N = 4 to N = 6, i.e., in the [(2)42; 9 − 6(1 + 1 + )] configuration. At intermediate spins, I = 38.5, 40.5, coexistent minima are calculated.

G. Summary of the assignments
The spin values and corresponding excitation energies which are suggested from the CNS calculations are summarized in Table II. In the determination of the excitation energies we started from the experimental values specified in Fig. 1 and 0 in bands L4 and L4a have been increased by 3 × 0.8 MeV, considering that the spin values in band L4a are increased by 3h. Note, however, that the values in the L4 band are increased by only 2h. In any case, with these energies, the difference between experiment and calculations has essentially the same value in all bands; see Figs. 8(c) and 9(c). Using the values in Table II, the collective bands are displayed together with selected ND bands in Fig. 12. Compared with the calculated bands in Fig. 6, the assignments for bands L1 and L3 appear convincing, since they agree with the two configurations calculated lowest in energy for I ≈ 40-50. The observed bands evolve smoothly with spin for at least 20 spin units and, in this spin range, the configurations assigned to them do not cross with any other ones having the same parity and signature. Furthermore, it is gratifying that the most intense band, L1, is assigned to the configuration which is calculated to be lowest in energy. However, the third most intense band, L3, is assigned to a configuration which is calculated 0.5-1.0 FIG. 11. Total energy surfaces calculated in the CNSB formalism with constraints of parity and signature for protons and neutrons, (π, α) p (π, α) n = (+, 0)(−, 1/2). This is the configuration assigned to the L3 band. The contour line separation is 0.2 MeV.
MeV higher in the spin range I = 30-50. The relative energies are rather sensitive to parameter changes while moments of inertia that reflect the overall features of the E − E rld plots are much more stable toward changes in parameters.
For the assignment of bands L4 and L4a, it would be important to measure the multipolarity of the 1343-keV transition connecting these two bands. Band L1 is mainly feeding negative-parity states, which might suggests that it has negative parity contrary to the assignment of a positive-parity configuration. However, it is not unlikely that the band is linked through an E 1 transition. For the other bands where the feeding can be analyzed, L3 and L4, the suggested parity appears in line with the assumption that it is not changed by the connecting transitions.

V. SUMMARY
High-spin states in 123 Xe were populated in a heavyion induced fusion-evaporation reaction and γ -γ coincidence relationship were measured with the Gammasphere spectrometer. Four new highly deformed rotational bands have been observed up to high spins which feed previously known lev- els of ND bands [20] around spin I ≈ 30. However, linking transitions between the high-spin bands and the levels of known spin and parity could not be established. Excitation energies and spin values of the bands are estimated on the basis of their feeding to ND levels under the assumption of a de-excitation through one or two unobserved γ -ray transitions.
The properties of the bands are compared with those calculated within the CNS and CNSB formalisms, where the method with an average pairing added to the CNS energies, CNS(B) appears to be particularly useful. The calculations indicate that the bands correspond to deformed minima around ε 2 ≈ 0.3 and γ ≈ 5 • which are formed by excitation of two protons from the g 9/2 orbitals across the Z = 50 shell gap along with neutron excitations across the N = 82 gap to the f h ( f 7/2 h 9/2 ) and i 13/2 orbitals. Indeed, all the observed bands are assigned to the proton configuration labeled "(2)42," i.e., with four particles in dg (d 5/2 g 7/2 ) orbitals and two in h 11/2 orbitals.
In order to find a satisfactory agreement between experiment and theory, the estimated spin values of bands L1, L3, and L4 were increased by 2-3h, i.e., within the limits allowed by the experimental data, with a corresponding increase of the excitation energies.
The neutron configuration calculated lowest in energy for I = 38-54 with three particles excited across the N = 82 gap, two in h f orbitals and one in the i 13/2 state, is assigned to the most intense band L1 while the L3 band is assigned to the next lowest band in this spin range with one h f and one i 13/2 particle. The low-spin extensions of bands L3 and L4, L3a and L4a, are assigned to the two signatures of the lowest energy configuration with no neutrons excited across the N = 82 gap. All these assignments result in a fair agree-ment between experiment and calculations, but, even so, they must be considered as tentative in view of the freedom to adjust spin values and excitation energies of the observed bands.
The band crossing observed from L3a to L3 is suggested to occur via an intermediate configuration with only one h f and no i 13/2 neutrons. A reasonable interpretation of the bandcrossing from L4a to L4 is obtained if the connecting 1343-keV transition is assumed to be of electric dipole character. In that case, an excitation of a neutron from an h 11/2 to an i 13/2 orbital is assumed in the transition from the L4a to the L4 band. For the L2 band, it is proposed that its spin values should be decreased by 1h, in which case, its lower spin region might be assigned to the next lowest configuration with no neutrons excited across the N = 82 gap while its less regular higher spin region appears to be even more uncertain.