Recoil-decay tagging study of 205 Fr

The nucleus 205 Fr has been studied through γ -ray and electron spectroscopy using the recoil-decay tagging technique. The resulting level scheme presents a spherical structure built on the 9 / 2 − ground state and a rotational structure on top of a short-lived isomer. The isomer, with a spin and parity of 13 / 2 + and a half-life of 80(20) ns, de-excites by an M 2 transition directly to the 9 / 2 − ground state. Another, longer-lived, isomer, with a half-life of 1.15(4) ms, has also been found and assigned a spin and parity of 1 / 2 + . Transitions populating and de-exciting this isomer have been observed as well.


I. INTRODUCTION
Shape coexistence has been studied throughout neutrondeficient nuclei in the lead region. A competition among spherical, oblate, and prolate shapes has been reported to exist in nuclei up to Z = 84 (see Ref. [1] and references therein). The gradual transition between spherical and deformed shapes is believed to be caused by the increasing number of neutron holes, when approaching the neutron mid-shell, coupling to the particle-hole excitations across the proton shell gap. This interaction is attractive and, thus, brings the resulting nuclear states down in energy and increases the collective behavior. The major challenge in studying these proton drip-line nuclei is the decreasing production yield due to the increase of fission.
An onset of oblate ground-state deformation, associated with the 2p-2h excitation across the proton shell gap, has been reported to occur in even-mass polonium nuclei around N 114 [2][3][4]. Low-lying excited states in neutron-deficient radon nuclei have been studied down to 198 Rn [5][6][7][8][9][10]. An increase in collectivity for these states, caused by the increasing number of neutron-hole pairs is reported, showing signs of contributions from the 2p-2h excitation. α-decay properties obtained for 193 Rn [11] and 196 Rn [12] suggest an onset of oblate ground-state deformation in 196 Rn and, further, of prolate deformation in 193 Rn. The chain of corresponding neutron-deficient odd-mass francium nuclei is less well known than the radon isotopes, with 205 Fr being the lightest isotope with in-beam studies reported to date [13][14][15]. No onset of deformation has been observed in these nuclei.
The 1/2 + state, created by exciting a proton from the s 1/2 shell across the proton shell gap, is well known throughout the odd-mass bismuth nuclei. The state is highly nonyrast in 199 Bi and 201 Bi [16]. It comes down in energy with decreasing neutron number and becomes the ground state in 185 Bi [17]. Interesting features have been observed related to this state throughout the isotopic chain, such as very slow M4 transitions to the 9/2 − ground state [16]. In the astatine nuclei the state is first observed in 197 At [18], decaying by α emission, and it becomes the ground state in 195 At [19]. Uusitalo et al. [20] have observed the 1/2 + state in 203 Fr and 201 Fr through α-decay studies. In 201 Fr the level lies at 146 keV, but in 203 Fr the level energy has not yet been established, as the corresponding state in the α-decay daughter 199 At has also not been observed. The 1/2 + state is expected to become the ground state in 199 Fr, leading to oblate ground-state deformation [20].
Another state, characteristic of this region, is the 13/2 + state based on the odd proton excited to the i 13/2 shell. Throughout the odd-mass bismuth and astatine nuclei this state is better known than the 1/2 + state. For instance, when approaching the neutron mid-shell, the 13/2 + state first becomes isomeric in 201 At [21], yrast in 199 At, and α decaying in 193 At [22]. In 199 At and 197 At rotational bands have been observed to be built on the 13/2 + state, with an estimated deformation parameter of β 2 = −0.2 in 197 At [18]. The 13/2 + state has not yet been observed in the odd-mass francium nuclei with A < 213.
The nucleus 205 Fr has previously been reported by Hartley et al. [15], presenting a level scheme with tentative spin and parity assignments constructed up to nearly 10h with a level energy of 1736 keV. The transitions were associated with a francium nucleus based on the x rays visible in the coincidence data and, further, with the nucleus 205 Fr by total γ -ray fold distributions and cross-bombardment. The assignment of this structure was supported by its similarity with the structure of the one assigned for 207 Fr [15].
The present work investigates the possible shape coexistence in 205 Fr. Isomeric states generated by the i 13/2 and the intruding s 1/2 orbitals are presented, with excited states built on these isomers. Transitions to the ground state are also presented. The present work disagrees entirely with the previous study presented by Hartley et al. on the excited states in 205 Fr. This disagreement will be discussed as well.

II. EXPERIMENTAL DETAILS
The measurements were conducted in the Accelerator Laboratory at the Department of Physics of the University of Jyväskylä (JYFL), Finland. The nucleus 205 Fr was produced in the fusion-evaporation reaction 169 Tm( 40 Ar, 4n) 205 Fr. The 40 Ar ion beam, provided by the K-130 cyclotron, was accelerated to an energy of 180 MeV with an average beam current of 14 particle-nA (pnA), during an irradiation time of 60 h. The self-supporting 169 Tm target had a thickness of 410 μg/cm 2 , and a 50-μg/cm 2 -thick carbon reset foil was used behind the target. The 205 Fr isotopes were produced with a cross section of 1.3 mb. The rate of detected fusion-evaporation products was estimated to be 27 Hz.
The JUROGAM Ge-detector array was used to detect prompt γ rays at the target position. The array consisted of 43 Compton-suppressed high-purity germanium (HPGe) detectors of EUROGAM phase one [23] and GASP [24] type. The recoiling fusion-evaporation products were separated from beam particles and other unwanted reaction products by the gas-filled recoil separator RITU [25] and transported to the GREAT spectrometer [26] at its focal plane. When arriving in GREAT, the recoils passed through a multiwire proportional counter (MWPC) and were finally implanted into a 300-μm-thick double-sided silicon strip detector (DSSD), which has 4800 pixels in total. The horizontal strips of the DSSD were set to measure α-decay energies and the vertical strips to measure conversion-electron energies, by adjusting the gain ranges of the amplifiers. A clover and a planar germanium detector were used to detect delayed γ rays close to the DSSD, and a silicon PIN-detector array, situated upstream in a box arrangement at the edges of the DSSD, was used for detecting conversion electrons. The PIN detectors and the vertical strips of the DSSD were calibrated using a 133 Ba source. All data channels were recorded synchronously using the triggerless total data readout (TDR) [27] data acquisition system, which gives each event an absolute time stamp with a time resolution of 10 ns.

III. RESULTS
The measurement data were analyzed using the recoildecay tagging (RDT) technique [28] and processed using the GRAIN [29] and RADWARE [30,31] software packages. The recoiling fusion-evaporation products were selected by their time of flight between the MWPC and the DSSD and their energy loss in the MWPC. Furthermore, the different isotopes were identified by linking the recoils with their subsequent α decays in the DSSD, using spatial and temporal correlations. The α-decay branch of 98.5% [32] and half-life of 3.80(3) s [33] for the 9/2 − ground state allowed for an effective identification of the 205 Fr recoils using a maximum correlation time of 12 s between the recoil and its subsequent α decay. The MWPC-vetoed α-particle energy spectrum obtained from the 40 Ar + 169 Tm reaction is shown in Fig. 1. Prompt and delayed γ rays belonging to 205 Fr were identified based on their time correlation with the α-tagged recoil observed in the DSSD.
The delayed γ -ray and electron spectra in Fig. 2 are collected from recoil-correlated events detected in the GREAT clover detector and the PIN-detector array, respectively. The 440-keV peak in the electron spectrum represents the K-shell conversion of the 544-keV isomeric transition. An internal K-shell conversion coefficient of 0.25 (10) can be obtained by comparing the intensities of the peaks in the two spectra (simulated efficiencies were used for the PIN-detector array; see Ref. [34]). This result suggests an M2 multipolarity for the isomeric transition [35]. The half-life of the isomer could not be directly determined, due to poor statistics. Based on the feeding of the isomer detected in the JUROGAM array, the number of events detected in the GREAT clover detector and the flight time of the recoil through RITU, a value of 80 (20) ns can be estimated for the half-life of the isomer. The estimates assume roughly equal efficiencies for the JUROGAM array and the GREAT clover detector  See text for further details. [34]. Based on the results obtained, a transition strength of 0.17(4) W.u. was determined for this M2 transition. This value is comparable with those obtained for M2 transitions depopulating the 13/2 + isomer directly to the 9/2 − ground state in odd-mass astatine nuclei. For example, the values 0.182(22) W.u. for 201 At [36], 0.16(5) W.u. for 199 At [37], and 0.086(13) W.u. for 197 At [18] have been reported. Based on these observations the spin and parity of the fast isomer is assigned to be 13/2 + .
Another, longer-living, isomeric state was also observed by studying 205 Fr α-tagged delayed electrons and γ -ray At. The spectra in Figs. 3(b) and 3(d) provide a means for internal calibration of the spectrum in Fig. 3(a). It is worth noting that since the FWHM is close to 12 keV for the obtained electron peaks, the Land higher shell conversion electrons will not be separated, and a sum peak representing all these events should situate roughly 12-13 keV below the corresponding transition energy. In this special case, the internal conversion takes place inside the DSSD. Therefore, the energy deposited by the Auger electrons and low-energy x rays, released in the internal conversion process, sum up with the energy deposit of the conversion electron, giving an additional ∼10 keV to the total energy deposit. As a result, the electron peak representing emission from the L + M (+higher) shells is found close to 2-3 keV below the corresponding transition energy. This effect is also confirmed in simulations performed for the cases presented above. Figure 4 presents the time difference between the recoil implantation and the electrons in Fig. 3(a). Using the logarithmictime method [40] a half-life of 1.15(4) ms was obtained for the isomeric decay. Based on the half-life the assumption can be made that the longer living isomer is actually the 1/2 + isomer. Figure 5 depicts the spectrum of delayed γ rays obtained from the GREAT planar and clover detector tagged with the isomeric electrons in Fig. 3(a). Two γ -ray transitions with energies of 209 and 235 keV are clearly visible together with a weaker 444-keV peak. To understand the complicated structure of the electron spectrum in Fig. 3(a), the 209-and 235-keV transitions need to be in a cascade with an additional highly converted (M2 or E3) transition depopulating the 1.15(4)-ms isomer. This observation is supported by the presence of an intense 169-keV peak in Fig. 3(a). If the electrons generating the 169-keV peak originated from K-shell conversion, a corresponding γ -ray peak should be visible in Fig. 5; however, no such peak has been observed. The 444-keV transition energy equals the sum of the 209-and 235-keV transition energies, and, therefore, the transition is set to proceed alongside the 209-and 235-keV transitions. Based on similar cases in the odd-mass bismuth isotopes [41], we propose that the 1.15(4)-ms isomer de-excites to the 9/2 − ground state via a cascade consisting of an M2 transition and two M1 transitions with energies of 209 and 235 keV, respectively. The 209-keV transition is also observed in the prompt γ -ray data; therefore, it is set to populate the ground state. The suggested structure of the cascade is presented in Band 3 of Fig. 6.
GEANT4 [42] simulations were performed to reproduce the conversion-electron and γ -ray spectrum of the de-excitation of the 1/2 + state with the decay characteristics discussed above; see Fig. 7. As a test, the simulations reproduced the calibration spectra in Figs. 3 The results from the simulations support our interpretation of the deexcitation path of the 1/2 + isomer, with a transition energy of 165(5) keV for the depopulating M2 transition and a 35(10)% branching ratio for the 444-keV E2 transition. Figure 7(a) presents the scenario discussed above. As a comparison, the above-discussed scenario, without the parallel E2 transition, was simulated; see Fig. 7(b). In this scenario, 169-keV peak is clearly not as enhanced as in Figs. 7(a) and 3(a). To verify these results, spectra were generated for a scenario where the 1/2 + state is assumed to de-excite by a 235-keV E3 transition (100% branching) to the 7/2 − state. This result, presented in Fig. 7(c), clearly does not resemble the experimental results. A transition strength of 3.5(2)×10 −4 W.u. was obtained for the 165-keV M2 transition, by assuming a 100% branching ratio. This result agrees well with the value of 9.96(14)×10 −4 W.u. for the corresponding transition in 205 Bi [41]. There is a possibility for a ∼400-keV E3 transition to occur between the 1/2 + state and the 7/2 − state (see Fig. 6). With a transition strength as for similar transitions in neutron-deficient odd-mass thallium [36,43], bismuth [44], and astatine [44] nuclei, a branching ratio of 5-40% can be estimated for this competing transition. However, the setup was not sensitive enough to resolve the possible E3 branch.  205 Rn (peaks denoted by diamonds). The events belonging to 205 Rn are eliminated when tagging with the 205 Fr α decay, as shown in Fig. 8(b). Events from the Coulomb-excited 169 Tm target ions still leak through despite α-decay tagging. The strongest of these peaks are denoted by open circles. The fusion-evaporation reaction also produces neutrons which excite the germanium nuclei in the HPGe detector material. The resulting γ rays cannot be completely filtered out, and, thus, two broad peaks close to 600 and 840 keV [47,48] are visible in Fig. 8 (and in the inset of Fig. 5).
Angular-distribution measurements were performed for a number of strong γ -ray transitions. The prompt γ -ray data were sorted according to the four detector rings (at angles of 158 • , 134 • , 108 • , and 94 • with respect to the beam direction) of the JUROGAM array. The relative-efficiency corrected data for each transition were studied relative to the detector angle. Legendre polynomials according to the method presented in the work by Yamazaki [49] were fitted to the data to obtain the value of the A 2 coefficient. The A 4 coefficient was set to zero as the aim was to distinguish between the possible stretched dipole and stretched E2 character of the transition and not to consider quadrupole mixing. The obtained values for the Legendre polynomial A 2 coefficient, where the procedure was possible, are presented in Table I, with a negative value usually presenting a stretched dipole transition and a positive value a stretched E2 transition. The level scheme resulting from the analysis is presented in Fig. 6 and further details for each transition are presented in Table I. Figure 8(c) presents the spectrum of coincident γ rays obtained by setting an energy gate on the 517-keV peak, which is the strongest of the γ -ray transitions associated with the  Table I) and are, thus, assigned an E2 multipolarity. This sequence of transitions is placed on top of the 9/2 − ground state, and it forms a regular level pattern up to a 21/2 − state  Fig. 8(b).
(see Band 1 in Fig. 6). A 275-keV stretched dipole (presumably of M1 multipolarity) transition is in coincidence with each of these transitions and is, therefore, assigned to depopulate a 23/2 − state. Figure 8(c) shows a 653-keV transition in clear coincidence with the 517-keV transition but not with the other transitions in Band 1. Therefore, it is set to precede the 517-keV transition. It is evident that the 653-keV peak must be a doublet by comparing its intensity with the intensity of the 580-keV transition between Figs. 8(b) and 8(c). A 606-keV transition was observed to populate the 23/2 − state. High-energy transitions (with energies of 719, 942, 983, and 1076 keV) were observed in coincidence with the low-lying ground-state band transitions. It is evident that some of the most intense peaks in Fig. 8(b) are not visible in Fig. 8(c), implying that the transitions in Fig. 8(b) can be divided into two dominating structures. Figures 8(c) and 8(d) indicate that the intense 477-keV transition in Fig. 8(b) is not in coincidence with the 517-keV transition or with any of the other transitions in Band 1. This M1 transition is assumed to populate the 13/2 + state. Coincidence and energy relations produce a strongly coupled band, up to a spin and parity of 23/2 + , including γ -ray transitions with energies of 176, 184, 358, 447, 477, 542, 623, 631, and 653 keV. Angular distribution measurements support the multipolarity assignments for several of these transitions. This sequence is indicated as Band 2 in Fig. 6. Figure 6 presents several transitions feeding into Band 2, of which the most intense is the 568-keV transition. It is also one of the most intense peaks in Fig. 8(d) produced by setting a gate on the 477-keV transition. It is not in coincidence with the other transitions in Band 2 and is, therefore, set to populate the 15/2 + state. Results from angular-distribution measurements provide a stretched dipole character for the transition, and it is, thus, placed to depopulate a 17/2 + state. A weaker 391-keV transition can be assigned to depopulate this state to the 17/2 + state in Band 2. A γ -ray peak at 601-keV is the strongest peak visible in the spectrum gated on the 568-keV transition.
A 163-keV E2 transition is clearly visible when setting an energy gate on the 358-keV transition. This transition is, furthermore, in coincidence with the 447-, 631-, and 653-keV transitions. The transition is placed to depopulate a 27/2 + state to the 23/2 + state in Band 2. Similarly, the rest of the transitions in these cascades are placed based on coincidence studies.
The inset of Fig. 5 presents prompt γ rays associated with the 1/2 + isomer. Lack of statistics did not allow for an adequate γ -γ coincidence analysis, although some weak evidence for coincidences between the 154-and 413-keV transitions was found. The ordering of the transitions is purely based on their intensities. The strength of the x-ray peak suggests an E2 multipolarity for the 154-keV transition. There is, however, a weak γ -ray peak close to an energy of 200 keV. If a considerable amount of the x-ray intensity originates from the internal conversion of this peak, the total internal conversion coefficient of the 154-keV transition will be lower and the multipolarity could approach the value of an E1 transition. The spin and parity assignments of the states remain, therefore, tentative.
The γ -ray transitions reported by Hartley et al. [15] were not observed in the present work among the transitions associated with 205 Fr. In the previous work RDT-type tagging methods were not used; instead, the identification of the studied isotopes relied on excitation-function analysis. We have found that the γ -ray transitions identified in the previous study actually belong to the neighboring isotope 206 Fr as shown in Fig. 8(e), where observed transitions include the 503-, 507-, and 777-keV transitions previously reported as belonging to 205 Fr. The 384-keV transition reported by Hartley et al. to belong to 206 Fr is clearly visible in this spectrum, with the 262-, 267-, 278-, and 294-keV transitions reported as part of the shears band. Furthermore, the 438-keV transition and the group of transitions close to 600-keV have not been previously reported. There are three α-decaying states in 206 Fr [38]; unfortunately, the lack of statistics in the present work and the overlap of the α-decay energies prevent us from associating the above-mentioned γ -ray transitions with the corresponding α-decaying state.

IV. DISCUSSION
The level scheme obtained for 205 Fr, shown in Fig. 6, presents separate positive-parity and negative-parity structures. This scheme differs from what has earlier been found for heavier francium nuclei [13,14], where the positive-parity states de-excite toward the ground state through high-lying negative-parity states. The origin of this change is in the lowering of the 13/2 + state, which de-excites to the ground state. A similar transformation has been observed in the odd-mass astatine nuclei when comparing 199 At [37] with  [5,[8][9][10]51]. The data for the heavier francium nuclei are taken from the studies in Refs. [13][14][15]. The lines connect yrast states without specifying the configuration of the states. heavier astatine isotopes (see Refs. [21,50] and references therein). Figure 9 presents energy systematics of negative-parity states in odd-mass francium nuclei compared with yrast levels in their radon isotones. The increasing number of valence neutron holes lowers the level energies when moving away from the closed neutron shell. The first sign of the effect is visible in the drastic drop of the 2 + state in 210 Rn, caused by the opening of the first neutron shell. While the corresponding state in 212 Rn is still purely a (πh 9/2 ) 4 state, the neutron holes generate components in the wave function of the 2 + state bringing the state down in energy. This scheme is followed by the francium isotones, with a clear analogy visible for the 13/2 − state. The same effect appears in the radon 4 + states at 208 Rn, where both the proton state and the yrast neutron state have been observed. The nonyrast proton state is still known in 206 Rn, but as the neutron states decrease in energy, the proton state is nonyrast and is not observed in the lighter even-mass radon isotopes. Again, the 17/2 − states in the francium isotones show a similar behavior with a change between proton and neutron-hole configuration in 209 Fr. Although collectivity increases with each new neutron hole, the level spacing between the 2 + and 4 + states in the radon nuclei indicates that no sign of the proton intruder configuration, visible in 198 Rn [10], is yet to be expected this far from the neutron mid-shell in the francium nuclei. Further up in energy, the 6 + states show signs of neutron-hole configurations in 202 Rn, where a down bend in the energy curve is visible. Francium systematics do not reach this far yet, and the 21/2 − state in 205 Fr could still originate from the (πh 9/2 ) 3 configuration. Furthermore, the 23/2 − state could originate from the (πh 9/2 ) 2 f 7/2 configuration.
Band 1 includes states feeding into the cascade mentioned above. A (25/2 − ) state has been observed at a level energy of 2481 keV and can be interpreted as originating from the maximum alignment of the five h 9/2 protons. This state is expected to lie approximately 750 keV above the 21/2 − state in odd-mass francium nuclei [13]. It has not been observed in 213 Fr and 211 Fr [14], but it has been observed in 209 Fr [13] at a level energy of 2559 keV (that is 795 keV above the 21/2 − state). The level-energy difference of 719 keV between the (25/2 − ) and 21/2 − states in 205 Fr agrees well, therefore, with these observations. The (27/2 − ) state in 205 Fr, at a level energy of 2643 keV, is observed to de-excite to the 23/2 − state discussed earlier. It is interpreted as originating from the π (h 9/2 ) 4 f 7/2 [or the π (h 9/2 ) 2 f 7/2 ⊗ 2 + ] configuration. Similar states have earlier been observed in 209 Fr and in 213 Fr at level energies of 2599 and 2740 keV, respectively.
Strongly coupled bands have been observed on top of the 13/2 + state in 197 At and 199 At, indicating an oblate deformation for the 13/2 + state [37]. A similar, but slightly weaker, coupling is observed for the band built on top of the 13/2 + state in the present work (Band 2), indicating that the 13/2 + state in 205 Fr originates from the odd proton in the 13/2 + [606] Nilsson state. Plots of kinematic moments of inertia I (1) , extracted from the level energies, for Band 2 in 205 Fr compared with similar bands in neighboring nuclei are presented in Fig. 10. The result for 205 Fr follows the same, quite linear, behavior as the other nuclei, with collective characteristics similar to those of 199 At. The high-spin point, with a I (1) value close to 40h 2 MeV −1 , shows a clear deviation from the smooth behavior. This deviation may suggest that the 23/2 + state is no longer part of the structure of Band 2.
The 1/2 + state has been identified and assigned as originating from a proton-hole in the s 1/2 shell. The corresponding state has been observed in odd-mass bismuth isotopes. In 205 Bi this 1/2 + state de-excites by a hindered M2 transition to a 5/2 − state [41]. In 203 Bi a competing E3 transition to a 7/2 − state has additionally been observed [41]. In 201 Bi and 199 Bi these two states lie above the 1/2 + state, and the 1/2 + state (with a half-life of tens of minutes) decays mainly by electron capture but also de-excites by a strongly hindered M4 transition to the 9/2 − ground state. In the present work, the 5/2 − state is assigned to belong to the πh 9/2 ⊗ 2 + multiplet as in the isotopes 199 Bi to 205 10. Experimental kinematic moments of inertia of the rotational band feeding the 13/2 + isomer in 205 Fr compared with neighboring oblate deformed nuclei. The data for the astatine nuclei are taken from Ref. [37] and the bismuth data from Ref. [52]. lies further away from the 5/2 − state, which indicates that it is not part of the multiplet. It is, therefore, assumed to originate from the odd proton on the f 7/2 shell as in the lighter bismuth and astatine nuclei [19,22]. Similarly to the behavior in the bismuth nuclei, the 1/2 + state in 205 Fr continues the rising trend in level energy when approaching the closed neutron shell. This is a characteristic feature of the intruder states involving proton excitations across the Z = 82 shell gap. Finally, no additional higher-spin isomers, as reported in the heavier odd-mass francium nuclei, were observed in the present study. If such isomers exist in 205 Fr, they would need to be as fast as to decay inside the RITU separator but as slow as not to be seen by the JUROGAM array (Table II).

V. CONCLUSIONS
The nucleus 205 Fr has been studied using both in-beam γ -ray and delayed γ -ray and electron spectroscopy. We present results of the de-excitation of the 13/2 + isomer, with a weakly deformed band built on top of the isomer. A series of transitions to the 9/2 − ground state have also been observed. This result indicates that the ground-state band is still dominated by spherical structures in 205 Fr and pushes the onset of ground-state deformation in francium nuclei further toward the neutron mid-shell. Using highly selective electron-γ coincidence methods, the 1/2 + isomer was observed and it continues the tendency of a rising level energy, when approaching the closed neutron shell, as expected when comparing with odd-mass bismuth isotopes. The systematic study of the odd-mass francium isotopes would highly benefit from a deeper examination of the properties of 207 Fr. Certainly a continued, although challenging, search toward the proton drip line in both radon and francium nuclei would present data of high interest.