EC decay of ²⁴⁴Bk

The berkelium isotopes were produced by bombarding rolled metal foils of natural uranium (∼30 mg cm⁻² in thickness) with 63.6 MeV ¹¹B⁵⁺ beam from the BARC-TIFR Pelletron facility. Each irradiation was carried out for about ∼16 h to maximize the production of ²⁴⁴Bk. The beam energy was optimized using EMPIRE II code [13] to get the maximum cross section for ²⁴⁴Bk. However, even at this energy, the predicted fission cross section is about 500 times higher than the formation cross section of the evaporation residues. Figure 1(a) shows the γ-ray spectrum of the target after irradiation. It can clearly be seen that it was not possible to directly measure the γ-rays of the Bk isotopes owing to the presence of a large contribution of γ-rays from the fission products. The presence of the uranium x-rays and γ-rays further complicated the situation. Therefore, the removal of the target and fission products was necessary to study the small amount of Bk isotopes present in the target foil. Radiochemical separation based on ion exchange and solvent extraction was employed for the removal of the majority of the fission products and the uranium.

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After irradiation, the uranium target was dissolved in 10 M HNO₃. A few drops of concentrated HCl was added to facilitate the dissolution. The solution was dried and brought into 8 M HNO₃. The solution was loaded onto an anion exchanger Dowex 1 × 8 column and eluted with 8 M HNO₃. Uranium and some of the fission products were retained in the column. Under these conditions, the Bk isotopes were not retained in the column. The Bk fraction, along with some fission products, was collected and conditioned to 10 M HNO₃. KBrO₃ (equivalent to 0.5 M solution) was added to this aqueous phase, and the Ce-Bk fraction was extracted with two contacts of organic phase containing 0.15 M HDEHP (diethylhexylphosphoric acid) in dodecane. The Ce-Bk fraction was back-extracted from the organic phase with 1.5 M H₂O₂ in 8 M HNO₃. The aqueous phase containing the Bk fraction, along with Ce and a few other fission products, was assayed by γ-spectrometry using HPGe detectors. The average duration for the entire separation procedure was nearly 3 h.

A detection system comprised of three HPGe single-crystal detectors was set up for the singles and coincidence measurement of the γ-rays. All of the three HPGe detectors had a relative efficiency of about ∼30%. A graded shielding, comprised of lead, copper, aluminum and Perspex sheets stacked together one after the other with the lead on the outermost side and the Perspex sheets closest to the detector, was used to minimize the natural γ-ray background for each of the HPGe detectors. The energy and efficiency calibrations of the γ-ray detectors were carried out in the energy range of 121.8–1408 keV with standard γ-ray sources of ¹⁵²Eu^g and ¹³³Ba^g, each of which had a volume of 5 mL. The dead time for the singles measurement was reduced from nearly 50% to about 1% after the radiochemical separation, which substantially improved the relative contribution as well as the peak to total ratios of the γ-rays from the Bk isotopes. The volume of the final solution used for counting was kept as 5 mL. The γ-ray spectrum of the sample after the chemical separation is shown in figure 1(b). It can be seen from this figure that the 217.3 keV γ-ray of ²⁴⁴Bk, which was barely visible before the chemical separation, becomes one of the dominant peaks below the 300 keV region. After separation, a typical count rate of the 217.3 keV γ-ray was around ∼16 cps. Also, the 891.0 keV γ-ray of ²⁴⁴Bk, which was not even visible before the chemical separation, can be clearly seen in the γ-ray spectrum.

The singles spectra were analyzed using the peak area analysis software PHAST [14]. In the γ-ray spectra, the γ-ray energies from ²⁴⁴Bk were the most prominent ones among the different Bk isotopes that were produced. The three most intense γ-lines of ²⁴⁴Bk are 217.3 ± 0.3 keV, 187.4 ± 0.3 keV and 891.0 ± 0.4 keV. In the present work, the half-life of ²⁴⁴Bk was determined using the decay profile of these three γ-ray energies.

The activity of a γ-ray decaying with decay constant λ (= 0.693/T_1/2) at any time T_cool can be written as:

$$\begin{eqnarray}&&{{{{A}} }_{{{{{T}} }_{{\rm cool}}}}}=\frac{{{PA}} }{{{LT}} }={{{{A}} }_{0}}\frac{\left( 1-{{{\rm e}}^{-\lambda {{CT}} }} \right)}{\lambda {{CT}} }{{{\rm e}}^{-\lambda {{{{T}} }_{{\rm cool}}}}}{{{{ \varepsilon }} }_{{{ \gamma }} }}{{{{a}} }_{{{ \gamma }} }}\end{eqnarray} \tag{ 1 }$$

where PA is the area under the peak of a given γ-ray energy that has intensity a_γ and detection efficiency _γ; A₀ is the initial activity (at time T = 0, which corresponds to the end of irradiation), CT is the real time and LT is the live time of the detection system. So, the measured activity of a given γ-ray as a function of the cooling time was fitted using a nonlinear least square fitting program with two free parameters, namely λ and (A₀a_γ).

Figure 2 shows the decay of the three γ-lines (217.3 keV, 187.4 keV and 891.0 keV). The half-life of ²⁴⁴Bk has been obtained as 5.07 ± 0.04 h, 5.00 ± 0.13 h and 4.98 ± 0.04 h from the 217.3 keV, 187.4 keV and 891.0 keV γ-rays, respectively. The uncertainties quoted on the half-lives are the fitting errors. The half-life of ²⁴⁴Bk as obtained from the error weighted mean of the above three values is 5.02 ± 0.03 h. This is significantly larger compared to the value of 4.35 ± 0.15 h, as reported earlier in the literature [1, 10]. The newly obtained half-life is closer to the theoretically predicted half-life of 4.78 h [15].

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In order to determine the relative intensities of the γ-rays of ²⁴⁴Bk, γ-ray spectra at different time intervals (acquired for a total duration of about 12 h) were added to improve the statistics. In the summed spectrum, most of the previously reported [1] γ-rays of ²⁴⁴Bk were identified. The re-determined γ-ray energies, along with the energies reported in the literature, are presented in table 1. The uncertainties on the γ-ray energies were due to the variations seen in the singles and coincidence spectra. It can be seen from the table that the uncertainties on the γ-ray energies have been significantly improved in the present data set. It is noteworthy that the differences in the γ-ray energies compared to the values reported earlier were as high as 2–3 keV for some of the γ-rays. In the present work, the peak areas of the γ-ray energies in the sum spectrum were efficiency corrected to determine their intensities relative to the 217.4 keV γ-ray. The relative intensities of the γ-rays thus obtained in the present work, along with the literature values [1], have been listed in table 1. The uncertainties on the relative intensity values are due to counting statistics and efficiency fitting errors. It is evident from table 1 that the relative intensities of the γ-rays, as obtained in the present work, are close to the values reported earlier for several γ-rays. However, significant deviations are also equally abundant. It can also be seen from table 1 that the uncertainties on the relative intensities have now been significantly reduced compared to the values reported earlier [1]. In addition, a few new γ-rays have been assigned to the ²⁴⁴Bk decay scheme based on the coincidence data analysis (described in the next section). Their energies and relative intensities obtained from the sum spectrum are also reported in table 1. In the sum spectrum, it was not possible to resolve a few closely spaced γ-ray energies, which were clearly distinguished in the coincidence data analysis. For such cases, the intensities are quoted for the combined γ-ray energies, as reported in table 1. The relative intensity obtained for the 489.8 keV γ-ray has been corrected for the contribution from ¹⁴³Ce. Two of the γ-ray energies, 144.5 and 745 keV, could not be seen in the singles spectra owing to the overwhelmingly large count rate from the ⁹⁹Mo γ-rays of nearby energies. Also, the 1141 keV γ-ray, which was reported earlier as a γ-ray of ²⁴⁴Bk [1], was not seen in the singles and coincidence spectra.

The offline analysis of the experimental coincidence data was done using the RADWARE software package [16, 17]. The acquired data after presorting (i.e. the energy calibration followed by the software gain matching over the entire energy range), were sorted into a conventional γ–γ coincidence matrix. The matrix was then used to determine the correlation between the two coincident γ-rays. A typical γ-ray spectrum gated with the 217.3 keV γ-ray is shown in figure 3. Various decay γ-rays of ²⁴⁴Bk and the x-rays of the daughter product, ²⁴⁴Cm, are marked in the figure. As seen from the figure, the x-ray peaks are the most dominant. Also, the absence of the most intense γ-ray peaks of the singles spectra in the gated spectrum indicates that the contributions from the chance coincidence are negligibly small.

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In a twofold coincidence requirement, it may be possible that γ-rays from some other products may wrongly be assigned to ²⁴⁴Bk if they emit γ-rays with energies close to any of the γ-rays of ²⁴⁴Bk. In order to unambiguously identify the γ-rays of ²⁴⁴Bk, an additional condition was imposed, which is as follows: either the γ-ray should be present in the spectra gated by the x-rays of Cm or when gated with a particular γ-ray energy; the x-rays of Cm should be present in the spectrum. The second condition was required to identify weak γ-rays in the low energy region. These γ-rays may be missed while gating with the x-rays due to the large Compton background present in the low energy region. However, it should be mentioned here that if a γ-ray is not in coincidence with any of the γ-rays that belong to one of the cascades that contains 187.4, 217.3 or 891.0 keV (for which half-lives have been measured) as members, the possibility of its origin from the neighboring Bk isotopes, like ²⁴³Bk and ²⁴⁵Bk, cannot be completely ruled out. The energy of such γ-rays were 334.2, 985.9, 1040.9, 1136, 1177.2, 1205.3, 1232.7 and 1502.3 keV. However, none of these were of the same energy as any of the known γ-rays of ²⁴⁵Bk (T_1/2 = 4.94 days) or ²⁴³Bk (T_1/2 = 4.5 h). Also, the observed count rates of the known γ-rays of ^243,245Bk were very low in the summed spectrum, and none of the above listed γ-rays were in coincidence with any known γ-rays of ^243/245Bk. Therefore, their possible origins from either of these two neighboring isotopes were ruled out.

Thus, in the present work, a γ-ray has been assigned to the decay scheme of ²⁴⁴Bk if it satisfies one of the following conditions:

• (i)  
  it follows the half-life of ²⁴⁴Bk;
• (ii)  
  it is in coincidence with a γ-line that follows the half-life of ²⁴⁴Bk;
• (iii)  
  it is in coincidence with any of the γ-lines that belongs to the cascade that has the γ-line that follows the half-life of ²⁴⁴Bk;
• (iv)  
  it is in coincidence with the previously reported γ-lines [6].

The coincident γ-rays of ²⁴⁴Bk are listed in table 2. The γ-ray energy in the second column indicates the gated γ-ray (E_γ ± 1 keV), and the γ-rays in coincidence with the gated γ-ray are listed in the third column. Based on the statistics, the coincidences have been categorized as strong (>50 counts) or weak (<50 counts). Strong coincidences have been marked as bold letters in the table.

Based on the Nilsson single-particle level scheme, two possible values for the ground state spin of ²⁴⁴Bk have been proposed [18]. The assignment given by Sood et al is (1⁻) (3/2⁻[521]π ⨂ 1/2⁺[631]ν) and that given in the ENSDF table is (4⁻) (3/2⁻[521]π ⨂ 5/2⁺[622]ν) [18]. If the ground state spin of ²⁴⁴Bk is assumed to be 1⁻, then the majority of the EC decay should have directly fed the ground state (I^π = 0⁺) and the 43.0 keV (I^π = 2⁺) levels of ²⁴⁴Cm. The observation of several strong γ-rays and the absence of the 942 keV γ-ray (reported for ²⁴⁴Am (1+) → ²⁴⁴Cm decay) suggest the ground state spin of ²⁴⁴Bk to be 4⁻ rather than 1⁻. The strongest coincidence was observed between the 217.4 and 891.0 keV γ-ray energies (∼3700 counts). Also, the 187.4 and 920.8 keV transitions showed a coincidence count of ∼480. The energy summing indicates that the origin of these two cascades is from the same level (E_x = 1108.3 + x keV). This level de-excites to 920.8 + x and 891.0 + x keV levels by emitting 187.4 and 217.3 keV γ-rays, respectively. The large coincidence counts and relative intensities of the γ-rays suggest a large direct feeding to the 1108.3 + x keV level of ²⁴⁴Cm by the EC-decay of the ²⁴⁴Bk. Based on this, the 1108.3 + x keV level was assigned a tentative spin of '4,' as this level has the largest direct feeding by EC-decay of the ²⁴⁴Bk. Also, a transition of 1107.6 keV was observed, which was assumed to originate from the 1108.3 + x keV level. Due to the large spin value of the 1108.3 + x keV level, it is not expected to directly de-excite to the ground state, i.e. x is not equal to zero. As the 1107.6 keV transition was very weak, it was not likely to decay to the 142.3 keV (I^π = 4⁺) state; rather, it should be a transition to the 43.0 keV (I^π = 2⁺) state. Based on this, the proposed value of 'x' is 43.0 keV. However, the transition from 43.0 to the ground state could not be detected in the present experiment due to the higher energy thresholds of the timing circuit.

Based on the above discussion, the 1151.0 keV level was added to the level scheme of the ²⁴⁴Cm. The de-excitation of the 1151.0 keV level to 934.0 keV levels with maximum intensity indicates that the tentative spin of the 934.0 keV level could be 3 or 4. Another transition of 187.4 keV from the 1151.0 keV level to the 963.8 keV level has a relative intensity of about 16.5%, which indicates the spin of this level to be 2 or 3. The difference in the intensities of the two transitions suggests different multipolarities arising from the difference in the spin/parity values of the levels involved. Based on this discussion and the relative transition intensities, tentative spins of (3, 4) and (2, 3) were assigned to the 934.0 and 963.8 keV levels, respectively. The coincidence between 187.4 keV and 891.0 keV requires that the levels at 963.8 and 934.0 keV are linked. It is assumed that they are linked through a low energy transition (∼30 keV), which could not be detected in the present measurement.

The 1295.6 keV level de-excites to the 1151.0 keV level by emitting a 144.6 keV γ-ray and to the 142.3 keV (I^π = 4⁺) level with the emission of the 1153.4 keV γ-ray. Also, there is a direct transition of 1252.5 keV from the 1295.6 keV level to the 43.0 keV (I^π = 2⁺) level. Based on this, the most likely spin of the 1295.6 keV level would be 3 or 4. Since the 489.8 keV γ-ray is in coincidence with all of the γ-rays originating from the 1295.6 keV level, it would be a transition from the 1785.4 keV level to the 1295.6 keV level. The γ-ray of 176.7 keV was observed to be in coincidence with all of the γ-rays of the decay cascades that started from the 1151.0 level. This observation suggested that the 1327.7 keV level decays directly to the 1151.0 keV level. Another transition of 690.7 keV seen in coincidence with 920.8 keV suggests that it originated from a level at 1654.5 keV.

A tentative partial level scheme for the ²⁴⁴Bk → ²⁴⁴Cm decay with eight new levels was determined, which is shown in figure 4. Only a few transitions among the existing levels of ²⁴⁴Cm [1, 19] were observed. Therefore, only two reported levels of ²⁴⁴Cm (2⁺ and 4⁺) were included, as they fit well with the transitions seen in the present study. These levels and γ-ray energies are marked with an asterisk (*) in the figure. Several γ-rays of ²⁴⁴Bk, particularly with large relative intensities, have been placed in this level scheme. The γ-rays, which could not be placed, are underlined in table 2. Also, based on the relative intensities of the γ-rays and accounting for the unplaced γ-rays that could not be placed in the level scheme, a lower limit of the branching intensity (>40%) of the EC-decay was assigned to the 1151.0 keV level of ²⁴⁴Cm. A measurement of the conversion electrons in coincidence with these γ-rays will further confirm the proposed decay to the 43.0 keV (I^π = 2⁺) level of ²⁴⁴Cm and the ground state assignment of ²⁴⁴Bk.

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