Investigation of the ²³⁷Np(⁴⁸Ca, xn)^285-xNh reaction: Long-lived state in ²⁷⁴Mt

New isotopes of the elements Rf, Db, and Sg have been previously synthesized in the cold-fusion reactions of the doubly-magic nuclei ²⁰⁸Pb and ²⁰⁹Bi with massive ions having proton numbers Z=22−30 and neutron numbers N=28−40. In addition, new elements from Bh to Nh (Z=107−113) with cross sections ranging from 530 pb to 22 fb (see Reviews [1−4] and the references therein) have been reported. Progress toward more heavy elements was achieved through the fusion reactions of doubly magic ⁴⁸Ca with nuclei from ²³⁸U to ²⁴⁹Cf. In these reactions, approximately 40 new nuclides with Z=104−113 and isotopes of new elements from Fl to Og (Z=114−118) with cross sections from 17 pb to 0.5 pb were synthesized (see Reviews [5, 6] and the references therein).

Since 2007, attempts have been made to synthesize even heavier elements 119 and 120. However, they did not lead to a positive result [7−11]. The reasons for such a relentless interest in the synthesis of new elements is not limited to the desire of researchers to claim the naming rights. The properties of the decay of new elements and, especially, the cross sections of their formation can shed light on one of the fundamental properties of nuclear matter - the magic proton number Z_mag for the heaviest nuclei. As is known, there is still no agreement among theoreticians regarding the Z_mag value; some consider Z_mag = 114, whereas others consider Z_mag = 120−126. It may be expected that as we approach or move away from Z_mag, the value of the fission barrier will increase or decrease, respectively. The magnitude of the fission barrier plays a determining role in the survival probability of the compound nucleus (CN) and, ultimately, in the value of the reaction cross section.

Recently, several studies have focused on choosing the optimal reaction for the synthesis of new elements or testing the facilities where these investigations can be carried out [12−16]. The reactions ²⁴⁹Bk(⁵⁰Ti, 3−4n)^295,296119, ²⁴⁸Cm(⁵¹V, 3−4n)^295,296119, ²⁴³Am(⁵⁴Cr, 3−4n)^{293, 294}119 are considered optimal for the synthesis of element 119.

The first two reactions, after the probable α decay of isotopes ^295,296119, lead to unknown nuclei ^291,292Ts, and then to the known chain of ^287,288Mc – ^267,268Db [17]. The reliable identification of the mother nuclei will be based on the method of genetic relations [17]. The decays of the ²⁴³Am(⁵⁴Cr,3n)²⁹⁴119 reaction products also lead to the known chain of ²⁸⁶Mc – ²⁶⁶Db. However, among the potential products of the 4n reaction channel, i.e., ²⁹³119, only spontaneously fissioning ²⁶¹Lr is considered known. However, it may not be realized if ²⁶⁵Db is also spontaneously fissioning.

In this case, it is important to measure in advance the decay properties of isotopes starting from ²⁸⁵Mc or ²⁸¹Nh, which are products of the 4n channel of reactions of ⁴⁸Ca with ²⁴¹Am or ²³⁷Np, as well as the reaction excitation function. Then, combinations of criteria related to cross-bombardments (or cross-reactions in Ref. [17]), excitation functions or yield curves, properties of heavy ion separators, systematics of experimental results, and theoretical predictions can be used to more reliably prove the synthesis of a new element 119.

The relatively short half-life of ²⁴¹Am (432.6 y [18]) creates some difficulties when using it in an experiment. Therefore, we decided to repeat the ²³⁷Np+⁴⁸Ca experiment that was performed in 2006 with use of position-sensitive detectors and a low time resolution (0.1 ms) [19] but at a slightly higher beam energy, which would correspond to the expected maximum of the 4n-reaction channel. The choice was based on the previously measured excitation functions of the ⁴⁸Ca-induced reactions with the nuclei of actinide elements [5, 6].

In addition to the properties of the new isotopes in the chain ²⁸¹Nh-²⁶⁵Db, clarifying the properties of the nuclei in the chain starting with ²⁸²Nh was of interest. In Refs. [19, 20], we observed two decay chains of ²⁸²Nh in the ²³⁷Np(⁴⁸Ca, 3n) reaction and one after the decay of ²⁸⁶Mc, which is the ²⁴³Am(⁴⁸Ca, 5n) reaction product.

However, in the first chain of the ²³⁷Np+⁴⁸Ca reaction, the α-particle energy E_α of ²⁷⁴Mt was measured only by the side detector with a low accuracy (1.08 MeV). In the second chain, the α particle of ²⁷⁸Rg was registered by the focal detector and the energy of ²⁷⁴Mt was 9.76 MeV, although one would expect a value of 10.45±0.23 MeV, almost 0.7 MeV higher, according to Ref. [21]. In the decay chain of ²⁸⁶Mc, the α particle of ²⁷⁴Mt escaped the focal detector, leaving 0.963 MeV, and did not enter the side detector (the location of similar detectors is described below). In addition, from the extrapolation of the half-life T_α of ^275,276,278Mt, one would expect T_α of several milliseconds for ²⁷⁴Mt [1−6, 16, 18−20]. However, the decay times of ²⁷⁴Mt in the three decay chains were in the range of 0.47−1.48 s. Such differences in the energy and half-life of ²⁷⁴Mt from the expected values may indicate the presence of a long-lived state. Thus, the clarification of the decay properties of ²⁷⁴Mt was also of interest from the point of view of studying the structure of superheavy nuclei.

The ²³⁷Np+⁴⁸Ca reaction was studied using the Dubna gas-filled separator DGFRS-2 [22, 23] and the cyclotron DC280 of the SHE Factory at FLNR, JINR [24]. Some parameters of the experiment and results are listed in Table 1.

Similar to the experiments [13, 14, 20], the ²³⁷Np target consisted of twelve segments, which were produced by electrodeposition on 0.6-mg/cm² Ti backing and mounted on a disk with a diameter of 24 cm, rotated at 980 rpm. The reaction products, before implantation into focal detectors, passed through the H₂ gas-filled DGFRS-2 separator at a pressure of 0.9 mbar. The separator had a 0.7-μm mylar separating foil and two multiwire proportional chambers located in pentane at a pressure of 1.6 mbar. For reducing the counting rate of low-energy particles, which are the dominant background source on the detectors, a 0.2 mg/cm² thick Al foil was installed in front of the detectors before observing the third chain of ²⁸²Nh in this experiment (see below). Al foil led to a slight decrease in the implantation energy of the nucleus and a 6-fold decrease in the background. The transmission efficiency was estimated to be approximately 0.35 for a 0.89 mg/cm² thick target and the detector used in the experiment [23]. The typical beam intensity in front of the target was approximately 3 pμA.

After the experiment, an analysis of the target material was conducted. In the ²³⁸U+⁴⁸Ca experiment [26] with a maximum beam intensity of 6.5 pμA and beam dose of 2.6×10¹⁹, the target thickness decreased by 3%, and the thickness of the backing increased slightly. In this experiment, the layers of Np and Ti were damaged after a total beam dose of 2.1×10¹⁹. Approximately 20% of the thick Np material was lost in the beam spot area, and the Ti backing was damaged by 5%−80% across different sectors. For this reason, the data of the first part of the experiment with the dose of 1×10¹⁹ ions were used in the analysis. Beyond this point, the experimental conditions changed, as both the beam energy inside the target and amount of target material became poorly defined. No events were observed after a dose of 1×10¹⁹ ions.

Two double-sided silicon strip detectors (DSSDs) with an active area of 60 mm×120 mm and a thickness of 0.3 mm were installed close to each other in the focal plane of the separator. Thus, the total horizontal width was 240 mm. These detectors had 48 1.25-mm horizontal strips at the front of the detector and 48 2.5-mm vertical strips at the back, which were used to determine the vertical and horizontal positions of the nuclei on the detectors, respectively. The focal detector was surrounded by ten 60 mm×120-mm side silicon detectors (SSDs), each with eight strips, constituting a box with a depth of 120 mm. The signals in the focal and side detectors with amplitudes above the thresholds of ≈0.5 and ≈2.7 MeV, respectively, were recorded independently by digital and analog data acquisition systems.

The analog system, along with ordinary signal processing, was also used for the online registration of the correlations of the evaporation residues (ERs) and α particles registered with full energy in the DSSD, with the energies and ER-α time interval expected for implantation in the DSSD and subsequent α decays of the parent or daughter nuclei. This pair of events caused the beam to be switched off in approximately 0.1 ms to observe the decays of the descendant nuclei under low background conditions.

The energies of the α particles and spontaneous fission (SF) fragments and decay times of the nuclei in the decay chains observed in this study are shown in Fig. 1(d-f). The same details are shown for the nuclei obtained in Ref. [19] and Ref. [20] in Fig. 1(a,b) and Fig. 1(c), respectively, for comparison.

Figure 1.  (color online) Decay chains originating from ²⁸⁶Mc and ²⁸²Nh observed in the ²⁴³Am + ⁴⁸Ca and ²³⁷Np + ⁴⁸Ca reactions, respectively. Chains (a, b) and (c) were published in Ref. [19] and Ref. [20], respectively. Chains (d-f) are results of this study. The upper rows show the ER energy in chains (a-f) and vertical and horizontal positions on the detector in chains (d-f). The left rows provide the α-particle [in yellow (light gray)] and SF [in green (dark gray)] energies and time intervals between the events. The energies of the summed signals (in DSSD + SSD) are given in parentheses. The events marked with a shadow were registered during the beam-off period. The α-particle energy errors (standard deviations) are shown by smaller italic numbers. The decays of ²⁷⁰Bh and ²⁶⁶Db in chain (b) were not recorded in Ref. [19].

The number of random sequences imitating any of the chains in Fig. 1(d-f) was estimated based on the average counting rates of the beam-on full energy α particles (E_α = 8.5−11 MeV) and SF events registered in the DSSD (E_SF > 120 MeV). Time intervals of 10 s for the first three α decays and 1000 s for the fourth α decay and SF were used. Under these conditions, the number of random sequences was found to be less than 10^–14 [27]. Observing each α particle during the beam-off interval or registering it simultaneously by the DSSD and SSD reduces this probability by an additional factor of 10 or 2, respectively.

The energy spectra and lifetime distributions of the α particles of ²⁸²Nh, ²⁷⁸Rg, ²⁷⁴Mt, ²⁷⁰Bh, and ²⁶⁶Db (only lifetime distribution) observed in Refs. [19, 20] and this study are shown in Fig. 2. Note that the distributions of the decay times for all of the observed isotopes from ²⁸²Nh to ²⁶⁶Db satisfy the criterion for a single radioactive species suggested in Ref. [28].

Figure 2.  (color online) Alpha-particle energy spectra (left-hand panel) and decay-time distributions on a logarithmic scale (right-hand panel) for ²⁸²Nh and descendant nuclei. The events originating from ²⁸²Nh observed at DGFRS-2 in Ref. [20] and this study are shown by full red histograms; previous results obtained at DGFRS [19] are shown by open histograms. For α-particle spectra, events with an energy resolution of $\leqslant $45 keV were selected. At the top of each spectrum, the average E_α value and uncertainty interval recalculated from the Q_α value according to Ref. [21] are shown. Alpha-particle energy intervals given on the left-hand panels for each isotope are determined from all known events. Regarding the distribution of the decay times, the smooth curves are the time distributions for exponential decays calculated with the half-lives T_1/2 shown in the figures.

The α-particle energies of the nuclei observed in this study are consistent with those in Refs. [19, 20]. In addition, the measured decay times in this and previous experiments do not contradict each other. The energies E_α and intervals recalculated from the α-decay energies Q_α according to Ref. [21] are shown above the energy spectra. There is a good agreement between the experimental results and calculations for all nuclei except ²⁷⁴Mt. From Ref. [21], the E_α value of 10.45±0.23 MeV is obtained, although the measured values range from 9.57 to 10.10 MeV.

In addition, the decay times of ²⁷⁴Mt are in the range of 0.3−2.5 s, which is significantly higher than the half-life according to the systematics of T_1/2 for neighboring odd-Z nuclei (Fig. 3). As stated above, from the dependence of T_1/2 of isotopes ^275,276,278Mt on the number of neutrons, this value for ²⁷⁴Mt could be several milliseconds. However, the T_1/2 value determined for all six decays was $0.8^{+0.52}_{-0.23} $ s, i.e., two orders of magnitude higher.

Figure 3.  (color online) Partial half-lives T_α vs neutron number N for the isotopes of odd-Z elements Bh–Ts (Refs. [1-6, 16, 18-20]. Full and open symbols refer to nuclei produced in the reactions with ⁴⁸Ca and other reactions, respectively. The lines are drawn to guide the eye. Vertical dotted brown line shows the deviation of T_α for ²⁷⁴Mt from the systematics.

In addition to ²⁷⁴Mt, among the remaining 37 odd-Z nuclei with Z=107−117, two states with different half-lives are known only for ²⁶²Bh and presumably for its precursor ²⁶⁶Mt (see, e.g., Refs. [18, 29−32]). Furthermore, it remains unclear which of the states belongs to the ground one (g.s.) and which is an isomeric (i.s.) state [32].

To extract information about the nuclear structure from our experimental data, we used a cluster model based on a dinuclear system approach. As shown in Refs. [33−38], the cluster model well describes the experimental half-lives of the α decay and SF from the ground and isomeric states of nuclei with even atomic numbers Z. Moreover, new calculations within the cluster model also demonstrate good descriptions of T_α and T_SF for odd-Z nuclei (see Table 2).

Within the cluster model, one can determine the possible K value of a nuclear state using the experimental values of the Q_α energy and α decay half-life T_α, as well as the SF half-life T_SF. In this regard, we vary the K value so that the calculated $ T_{a}^{\rm th} $ values and/or $ T_{\rm SF}^{\rm th} $ half-lives become close to the experimental values of T_α and/or T_SF, respectively. The same extraction method was used in Ref. [40] for the α-decay chains of ^273,275Ds.

In some cases, the experimental uncertainties in T_α are large enough to affect the K value. In that case, the corresponding K range can be obtained. All calculated half-lives compared with experimental values, along with the respective K, are presented in Table 3. A decay scheme is also proposed and shown in Fig. 4. Note, that the cluster model cannot provide definite information about the state (ground, isomeric or low-lying ones) of a nucleus.

Figure 4.  (color online) Possible α-decay scheme for ²⁸⁶Mc. γγ’ represents γ-cascade. Extracted spin values with their corresponding uncertainties are shown. For the nuclei ²⁷⁸Rg, ²⁷⁴Mt, and ²⁷⁰Bh, only one spin value is possible according to the experimental half-life error bars.

For the observed decays of ²⁷⁴Mt, with K = 9, which is higher than that of the neighboring nuclei in the isotopic chain, e.g., for ²⁷⁵Mt, the K of around 3/2 is predicted. Therefore, its robustness to α decay is lower. This is the main reason for the “increased” stability of this transition of ²⁷⁴Mt.

The energies of the observed decays of ²⁷⁴Mt are noticeably lower than that obtained from the Q_α value predicted in Ref. [21] (Q_α = 10.60±0.23 MeV), as shown in Fig. 2. For this Q_α value and T_α of a few ms (in particular, 6.7 ms according to calculations), we get K = 7. Thus, we can assume an α transition from the state with K = 7 in ²⁷⁴Mt to the state with K = 7 in ²⁷⁰Bh. This transition was not observed in this and previous [19, 20] experiments, which may be because of insufficient statistics. One may assume that K=9 is the isomeric state for ²⁷⁴Mt and ²⁷⁰Bh, and the ground state in ²⁷⁴Mt will be at K=7. However, in this case, a short decay would be observed in the experiment, as the transition from ²⁷⁸Rg is from the state with K=7. In the case where K=7 lies higher, the transition to a lower-energy state with K=9 is acceptable and probably proceeds quickly enough. Thus, no decay from K=7 is observed in the experiment.

Similarly, we can propose a decay scheme for the isotope ²⁶²Bh, for which two states are assumed. The ²⁵⁸Db nucleus is formed as a result of the α decay of ²⁶²Bh. As is known, ²⁵⁸Db has a state with an energy of 156.5 keV and a spin range from 4 to 7 [32]. The half-lives obtained from the cluster model show (see Table 4) that the shorter-lived state in ²⁶²Bh can be well described as an isomer with an energy of 0.25 MeV and K = 7. Moreover, Q_α = 10.41 MeV, which is consistent with the experimental value of Q_α for this state (in the range from 10.4 to 10.53 MeV) [41]. Therefore, the longer-lived state of the ²⁶²Bh nucleus is assumed to be the ground state. In this case, α decay can occur to the 222 or 358 keV levels [32], leading to Q_α = 10.1 or 9.95 MeV, which are consistent with the experimental data (covering the range from 9.8 to 10.22 MeV) [32]. The α-decay scheme of ²⁶²Bh is shown in Fig. 5 and Table 4. The higher stability of the ground state of ²⁶²Bh is explained by the higher spin K = 9, corresponding to $ T_{a}^{\rm th} $ = 1.40 × 10⁻¹ s.

Figure 5.  (color online) Possible α-decay scheme for ²⁶²Bh.

The ²³⁷Np+⁴⁸Ca reaction cross sections, measured in Ref. [19] and this study, are listed in Table 1 and Fig. 6. An increase in E^* of the ²⁸⁵Nh CN by 3 MeV led to a decrease in the cross section of the 3n channel by approximately 2 times. Only the upper limit is set for the 4n reaction channel (Table 1). These cross sections are consistent with the predictions [49] made before the experiment [19] (see, e.g., Refs. [5, 6]). In numerous subsequent theoretical studies, the measured cross sections were reproduced well by different authors.

Figure 6.  (color online) Cross sections for the 2n- to 5n-evaporation channels for the ²⁴³Am (a), ²⁴²Pu (b), ²³⁷Np (c), ²³⁸U (d), and ²³²Th+⁴⁸Ca (e) reactions. Vertical error bars correspond to total uncertainties. The symbols with arrows show the upper cross-section limits. The data are represented by open (from Refs. [42−45]), half-closed (from Refs. [46, 47]), and closed symbols (from Refs. [19, 20, 26, 40] and this study). The dashed lines through the data are drawn to guide the eye. Panel (f) shows the difference between the fission barriers B_f and neutron binding energy B_n for the compound nuclei and neutron evaporation products of the ²⁴³Am, ²⁴²Pu, ²³⁷Np, ²³⁸U, ²³²Th, and ²²⁶Ra reactions with ⁴⁸Ca [48].

As can be seen in Fig. 7, the ²³⁷Np+⁴⁸Ca reaction cross section was slightly smaller than the cross sections for the nuclei of the neighboring elements Cn and Fl. The reason for this may be the lower number of neutrons in ²³⁷Np than those in ²³⁸U and ^242.244Pu. Thus, the reaction with ²³⁷Np leads to a more neutron-deficient compound nucleus ²⁸⁵Nh, which is farther from the influence of the magical neutron shell at N=184. As a result, there is a smaller difference (B_f-B_n), which determines the survival probability of CN in the process of deexcitation, as shown in Fig. 6(f). The cross sections for the elements Hs-Og (the maximum total cross section of the xn-channels), shown in Fig. 7, were obtained from the fusion-evaporation reactions of ²²⁶Ra, ²³²Th, ²³⁸U, ²³⁷Np, ^242,244Pu, ²⁴³Am, ^245,248Cm, ²⁴⁹Bk, and ²⁴⁹Cf with ⁴⁸Ca projectiles, which led to the synthesis of isotopes with Z=108, 110, and 112−118.

Figure 7.  (color online) Maximum production cross sections for the isotopes of heavy elements in the ⁴⁸Ca-induced reactions with ²²⁶Ra, ²³²Th, ²³⁸U, ^242,244Pu, ²⁴³Am, ^245,248Cm, ²⁴⁹Bk, and ²⁴⁹Cf. Data measured at DGFRS and DGFRS-2 are shown by red squares [5, 6, 19, 20, 26, 40, 46, 47, 50], whereas the results obtained at SHIP, BGS, TASCA, and GARIS are shown by blue circles [15, 41, 45, 51-53]. The dashed line through the data is drawn to guide the eye.

Cross-section variations, seen in Fig. 7, depend on both the properties of the interacting nuclei and the CN resulting from their complete fusion. These features of the nuclei determine the capture of interacting nuclei, formation of an almost spherical CN, and its survival during deexcitation. According to the theory (see e.g., Refs. [54−56] and recent papers [57−60]), the drop in the ⁴⁸Ca-induced complete-fusion reaction cross sections, caused by the survivability of CN during deexcitation, are by orders of magnitude higher than the drop owing to the formation probability of compound nuclei. Thus, the changes in the reaction cross sections are largely determined by the survival of CN, which, in turn, depends on their fission barriers. As can be seen in Fig. 7, the dependence of the cross sections on the atomic number of CN is a rather narrow function. A deviation from the presumed magic number Z=114 by 1−2 units leads to noticeable drops in the cross sections. This fact may indicate the magical value of Z = 114. The increase in the reaction cross section for Hs, produced in the ²²⁶Ra+⁴⁸Ca reaction, may also be due to the influence of the shells at Z = 108 and N = 162.

The objective of this study was to measure the decay properties of the daughter products of the ²⁴³Am + ⁵⁴Cr reaction, which can be used for the synthesis of element 119. The ²³⁷Np+⁴⁸Ca reaction has been studied using the gas-filled separator DGFRS-2 at the SHE Factory (FLNR, JINR). We obtained three chains of consecutive α decays of ²⁸²Nh, ²⁷⁸Rg, ²⁷⁴Mt, and ²⁷⁰Bh, which stopped by the SF of ²⁶⁶Db. The results of this experiment are consistent with our previous data [19, 20]. The half-lives of ²⁸²Nh, ²⁷⁸Rg, and ²⁷⁰Bh are consistent with the values that can be expected for them based on the systematics of the experimental properties of odd-Z nuclei. However, the half-life of ²⁷⁴Mt is two orders of magnitude longer than expected. Such a large difference has been observed for the first time for the heaviest nuclei.

The decay schemes for some heavy odd-Z nuclei were extracted by using the experimental Q_α and T_α values and the cluster model based on the dinuclear system approach. As it follows from the model, the observation of a lower E_α value for ²⁷⁴Mt, when compared with the predictions [21], and longer decay times than those expected from systematics (Fig. 3), may be owing to the decays of ²⁷⁴Mt and ²⁷⁰Bh into i.s. with K=9. The transition to g.s. from K=7 to the state with K=9 may occur owing to a rapid γ decay, as a result of which the decay from the state with K=7 was not observed.

The measured cross section of $0.43^{+0.46}_{-0.25}$ pb at E^* = 42 MeV is consistent with the behavior of the excitation functions for the 3n channel in the ⁴⁸Ca-induced reactions. An increase in E^* of the ²⁸⁵Nh CN by 3 MeV when compared with the observation in Ref. [19] at E^* = 39 MeV led to a decrease in the cross section of the 3n channel by approximately 2 times.

The upper cross-section limit of the 4n reaction channel was 0.28 pb. The decay chain of the unknown isotope ²⁸¹Nh has not been detected, although the decay properties of the odd-even isotopes ²⁸¹Nh, ²⁷⁷Rg, ²⁷³Mt, and ²⁶⁹Bh are of great interest. The isotope ²⁷⁷Rg (N = 166) may be the least stable of all odd-Z heavy nuclei (see Fig. 3), as the Rg isotopes have the largest drop in T_1/2 with decreasing N. The half-life of ²⁷³Mt (N = 164) may correspond to the T_1/2 trend for the isotopes of Mt and reach approximately 1 ms if its decay is not hindered to the extent as in the case of ²⁷⁴Mt. Isotope ²⁶⁹Bh (N=162) may be the first of the isotopes of odd-Z elements with a magic number N = 162. However, the small reaction cross section may cause a serious challenge for future research.

The previously observed lower cross section for Nh than those for the isotopes of neighboring elements Cn and Fl (Fig. 7) may be owing to the relatively small number of neutrons in ²³⁷Np and CN, respectively (Fig. 6). This should lead to a decrease in the fission barriers of CN when moving away from the magic neutron number N = 184 and a decrease in the survival probability of CN.