Mass distributions in ¹²C + ²³²Th fission: role of shell effects and excitation energy

Abstract

This article reports the measurement of cross sections of charge and mass identified fission products and the mass distributions in ²³²Th(¹²C,f) reaction at 62.5, 70.7 and 102.9 MeV beam energies to investigate the role of single particle effects. The study was carried out using the recoil catcher technique followed by off-line γ-ray spectrometry. Cross sections of 32, 54 and 64 fission products were measured for 62.5, 70.7 and 102.9 MeV beam energies, respectively. The mass distributions obtained at 62.5 and 70.7 MeV show a flat-top nature indicating significant asymmetric fission contribution (heavy mass peak corresponding to Z range of 54–56), whereas, a nearly Gaussian behaviour was observed at 102.9 MeV indicating dominant contribution from symmetric fission. The experimental mass distributions were in gross agreement with the “GEF, 2021/1.1” calculations which predicted significant asymmetric fission contribution dominated by Z ≈ 55 (‘Standard 2’ mode) at 62.5 and 70.7 MeV. The present study shows the significant role of charge polarization resulting in the deviation of the most probable charge (Z_P) values from those obtained using UCD hypothesis. “GEF, 2023/2.1” calculations were unable to explain the observed mass distributions with significant asymmetric fission contribution due to comparatively lower contribution from higher chance fission resulting from the lower saddle point energies. An attempt has been made to estimate the mass distributions arising from the complete fusion fission and α-transfer induced fission. The trend shows an increase in the α-transfer induced fission contribution with increasing beam energy which is in qualitative agreement with the sum-rule model calculations.

1 Introduction

Study of the mass yield distribution of charge and mass identified fission fragments/products plays an important role in understanding the mechanism of nuclear fission. The presence of the neutron and proton shells guides the formation of the fission fragments/products to a large extent at low to moderate excitation energies. Some of the important observations, like the formation of fission isomers and the new magic numbers in the exotic nuclei, are the results of the shell effects [1, 2]. Recent studies in nuclear fission have been mainly focused on investigating the role of neutron and proton shells in governing the fission process, and it has been proposed that the proton shells have a dominant role in guiding the nuclear fission process [3,4,5]. The effect of the proton and neutron shells has been found to exist up to several tens of MeV of excitation energy in the actinide and the pre-actinide region [4,5,6,7]. With increasing excitation energy of the fissioning system, the shell effect has been found to be gradually washed away along with the increase in the contribution of symmetric fission [8]. Thus, study of the nature of the mass yield distribution as a function of excitation energy can provide useful information regarding the role of shell effects. The mass yield distribution in heavy-ion induced fission of actinides is dominated by the Gaussian distribution which mainly arises from the complete fusion fission (CFF) process [9]. However, along with the CFF, there can also be transfer of nucleons from the projectile to the target, which may result in fission if the target like nucleus is sufficiently excited. Many studies reveal the presence of different transfer induced fission (TF) channels [10,11,12,13,14,15,16,17,18]. The mass distribution arising from the TF process is expected to be asymmetric due to the low excitation energy of the fissioning nucleus due to partial energy transfer to the target nucleus. In off-line measurements of the mass yields, the fission products having contribution from TF can be identified based on their A/Z ratio [16, 17]. Gubbi et al. reported the presence of TF in ¹⁹F + ²³²Th fission at beam energies of 95 and 112 MeV and showed that the contribution from TF relative to CFF decreases with increasing beam energy [17]. Gubbi et al. [17] and Sodaye et al. [18] obtained the contribution from TF by fitting a Gaussian curve to the mass yields corresponding to the products formed exclusively by CFF, and subtracting the CFF yields from the overall product yields to obtain the contribution from TF. Hogan et al. [19] and Todd et al. [20] used the measured ratio of the velocity of the compound nucleus to that of the fission fragment to fractionate the mass yields into CFF and TF components. The contribution of transfer induced fission in the fission fragment angular distribution for ¹³C + ²³²Th and ¹²C + ²³²Th system has been studied using the fission fragment folding angle measurement by Ajith Kumar et al. [21] and Mein et al. [22], respectively. At near and sub-barrier energies, the mass distribution may not show a Gaussian behaviour which may be due to the contribution from both CFF and TF having strong shell effects. However, the mass distribution shows a broad Gaussian behaviour at higher energies which can be attributed to the dominant contribution from the symmetric fission with the contribution from various transfer induced fission channels.

With the semi-empirical code GEF (“GEneral description of Fission observables”) [23, 24], it is possible to obtain information about the pre-neutron as well as the post-neutron mass yields, fission fragment and product yields, prompt neutron emission, isomeric yields and other observables related to nuclear fission. GEF is a Monte-Carlo code based on the principles of quantum mechanics, nuclear dynamics and statistical mechanics, and computes the sequential decay of the fissioning system including the possibility of the multi-chance fission, production of the primary fission fragments, post-scission evaporation and γ-ray emission [24]. As mentioned in ref [24], GEF code can be used to predict the fission observables for a wide range of isotopes from Z = 80 to Z = 112 and beyond, up to excitation energies of about 100 MeV. The GEF code also provides a description of the processes leading to the formation of an excited compound nucleus in reactions induced by neutrons, γ-rays and the charged particles including heavy ions. In the actinide region, GEF considers mainly the four fission channels (modelled as quantum oscillators in the fragment Z degree of freedom) to explain the mass distribution, which are the symmetric super-long (SL) channel, and three asymmetric channels (“standard” S1, S2, and “super-asymmetric” SA) [24]. As the excitation energy of the fissioning system increases, the asymmetric contribution to fission decreases with increasing contribution from the symmetric fission mode. Due to the contribution from multiple reaction channels along with the role of different fission modes, calculations with the GEF code can be very useful to investigate the role of different shells in governing the mass distribution, along with the estimation of the contribution from different fission channels.

In this work, the fission product mass distribution in the ¹²C + ²³²Th reaction system has been studied to investigate the role of the neutron and proton shell closure in governing the fission product mass distribution. Up till now there have been very few studies on the mass distribution of the ¹²C + ²³²Th reaction [25, 26]. A measurement of the fission product mass distribution in the ¹²C + ²³²Th reaction by Manohar et al. at a beam energy of 79 MeV shows a predominantly symmetric mass distribution [25]. However, a measurement of the fission product mass distribution in the ¹²C + ²³²Th reaction by Ramaswami et al. at a beam energy of 72 MeV shows a large deviation from the Gaussian distribution [26]. These observations suggest the requirement of a systematic study over a broad energy range to obtain a deeper insight of the role of the shell effects in governing the nature of the mass distributions. The experiment was carried out using the recoil catcher technique followed by off-line γ-ray spectrometry with the identification of mass and charge of the measured fission products, which can be very useful for the comparison with future on-line measurements of the ¹²C + ²³²Th fissioning system using other facilities such as VAMOS++ [27] or gamma detector arrays [28]. Off-line measurements using the γ-ray spectrometry have been extensively carried out to measure the fission product cross sections in the recent past [29,30,31,32,33,34,35]. In the present study, yields of 32, 54 and 64 fission products have been measured at the beam energies of 62.5, 70.7 and 102.9 MeV, respectively. The contribution from α-transfer induced fission was estimated from the experimentally measured overall yields of the fission products using the respective yield ratios of the fission products, obtained using the GEF code for the fission of ²⁴⁴Cm (formed by CFF) and ²³⁶U (formed by α transfer). The deviation of the most probable charge (Z_P) from that predicted using the Unchanged Charge Distribution (UCD) hypothesis ‘Z_UCD’ [7], has been investigated. A detailed comparison has been carried out between the experimental mass distributions and the GEF calculations predicting contributions from various fission modes governed by the different nucleon shells.

2 Experimental method

The present experiments were performed at the BARC-TIFR Pelletron-LINAC facility at Tata Institute of Fundamental Research, Mumbai, India. Three self-supporting ²³²Th targets of thickness 2.02, 1.88 and 1.95 mg/cm² were used for the irradiation at three beam energies 62.5, 70.7 and 102.9 MeV, respectively. Each ²³²Th target was sandwiched between two aluminium catcher foils of thickness 6.75 mg/cm² (to stop the fission products recoiling out of the target in the forward and backward directions) and was fixed at an inclination of 45° on a target stand placed inside the irradiation chamber. The samples were irradiated with the ¹²C beam of energies 80.0, 87.0 and 115.3 MeV for approximately 21.5, 17.0 and 11.7 h, respectively. The beam energies incident at the ²³²Th target after loss in the backward Al catcher foil were calculated using the code SRIM [36] and were found to be 62.5, 70.7 and 102.9 MeV, respectively. The excitation energies corresponding to the three beam energies were calculated to be approximately 36.4, 44.3 and 74.8 MeV, respectively. An upper limit of the uncertainty in the beam energy was estimated to be about 1.3 MeV (3σ), which comprises of the uncertainty in the beam energy from the accelerator as 1.2 MeV (3σ) and the energy straggling in the backward Al catcher foil which was found to be 0.5 MeV (3σ) [37]. Similarly, the maximum uncertainty on the beam energy, when translated to the excitation energy, was found to be 1.2, slightly less than that of the incident beam energy. After the irradiation, the backward Al catcher foil along with ²³²Th target and the forward Al catcher foil were mounted separately on perspex plates and were counted alternatively using pre-calibrated high-resolution γ-ray spectrometers coupled to a PC based multi-channel analyser (MCA). Two different co-axial high purity germanium detectors with the relative efficiency of approximately 30% and energy resolution of 2 keV FWHM at 1332 keV γ-ray energy of ⁶⁰Co were used for the γ-ray spectrometry. The energy as well as the absolute efficiency calibration of the HPGe detectors was carried out by counting standard ¹⁵²Eu^g and ¹³³Ba^g sources in the identical geometry as that of sample. The dead time of the detector for the measurement of the sample was kept < 1% to avoid the pile-up effect. The γ-ray spectrometric measurements were carried out over a period of cooling time ranging from ~ 5 min to ~ 50 days for unambiguous identification of the fission products by matching their characteristic half-lives in addition to the γ-ray energies. The acquired γ-ray spectra were analysed using the peak fitting software PHAST developed at BARC, Mumbai [38] to generate the peak reports containing the peak areas corresponding to the characteristic γ-ray energies of various fission products. The detailed experimental setup of the γ-ray spectrometric measurements can be found in ref [44].

The nuclear data of the fission products measured in the present study (Table 1) have been taken from the NUDAT database [39] unless otherwise mentioned.

Table 1 The nuclear data used for the fission products identified in the present study [39,40,41]

3 Data analysis

3.1 Calculation of the formation cross section of the fission products

The activities (A_i) at the end of irradiation of the various fission products were calculated using the peak areas of their characteristic γ-rays obtained from the analysed spectra acquired at different cooling times using Eq. (1).

$$\begin{aligned}{A}_{i}&=PA\times \left(\frac{CT}{LT}\right)/\left[\vphantom{\left(\frac{CT}{LT}\right)}{a}_{\gamma }\cdot {\varepsilon }_{\gamma }\cdot [\mathit{exp}\left(-\lambda \cdot {T}_{cool}\right)] \right.\\& \left.\quad \cdot \left[\frac{\left(1-\mathit{exp}\left(-\lambda \cdot CT\right)\right)}{\lambda }\right]\right]\end{aligned}$$

(1)

where, PA is the peak area of the characteristic γ-ray of the fission products, CT and LT are the clock time and live time of the spectra acquisition, respectively, ${a}_{\gamma }$ is the abundance (photons/disintegration) of the corresponding γ-ray, ${\varepsilon }_{\gamma }$ is the efficiency of the detector for the corresponding γ-ray, $\lambda$ is the decay constant of the fission product and T_cool is the cooling time from the end of irradiation till the start of the spectra acquisition.

The formation cross section, σ_i for the various identified fission products was calculated considering the equilibrium charge state of the projectile ions after passing through the target-catcher assembly [42, 43]. The equilibrium charge states used for the fission product cross section calculations were 5.97, 5.97 and 5.99 for the beam energies of 62.5, 70.7 and 102.9 MeV, respectively. The formation cross section, σ_i was obtained using the Eq. (2).

$${\sigma }_{i}=\frac{{A}_{i}}{N\sum_{k=1}^{M}\left(1-\mathit{exp}(-\lambda \Delta t\right)){\phi }_{k}\mathit{exp}\left(-\lambda \left({T}_{irr}-{T}_{k}\right)\right)}$$

(2)

where, N is the number of target atoms per cm², λ is the decay constant, T_irr is the duration of irradiation, and Φ_k is the number of beam particles incident per unit time in kth time interval, Δt is the duration of the time interval, T_k is the clock time at the end of kth interval and M (= T_irr/Δt) is the number of intervals in the irradiation time [44]. Beam intensity was continuously monitored during irradiation to account for the fluctuations, if any, during the irradiation. The beam intensity was measured every 30 s for 62.5 and 70.7 MeV energy while for 102.9 MeV energy, it was recorded every 60 s. The average beam intensities were found to be (4.42 ± 0.59) × 10¹⁰, (3.85 ± 0.45) × 10¹⁰ and (2.39 ± 0.36) × 10¹⁰ beam particles/s for the beam energies 62.5, 70.7 and 102.9 MeV, respectively. The variation in the beam intensity during irradiation is accounted while determining the formation cross sections of the fission products. The formation cross section was calculated using Eq. (2) for the fission products in the backward catcher foil along with the target and the forward catcher foil separately. Total cross section of the fission product was calculated by summing up the cross sections in the backward foil along with the target and the forward catcher foil. For some of the fission products, cross sections could not be measured in the forward catcher foil due to the larger Compton background arising from the γ-rays of the undesired products from ¹²C + ²⁷Al reaction. Therefore, the measured cross sections of such fission products in the backward catcher foil was scaled up using the average of the ratios of forward to backward catcher foil cross sections to obtain the overall formation cross sections. Formation cross sections of the fission products measured in the present study at three beam energies are given in Table 2.

Table 2 Formation cross sections of the fission products measured in the present study in ¹²C + ²³²Th reaction at three different beam energies

3.2 Calculation of the charge distribution parameters

From the measured formation cross sections of the fission products shown in Table 2, mass yields of various isobaric chains can be calculated using Eqs. (3–6) which requires information about the charge distribution parameters i.e., most probable charge, Z_P and the width parameter, σ_z for the isobaric chains.

$$FIY\left(A,Z\right)=\frac{1}{\sqrt{2\Pi {\sigma }_{z}^{2}}}\underset{z-0.5}{\overset{z+0.5}{\int }}{e}^{-{\left(z-{z}_{P}\right)}^{2}/2{\sigma }_{z}^{2}}dz$$

(3)

$$FCY(A,Z)=\frac{1}{\sqrt{2\Pi {\sigma }_{z}^{2}}}\underset{-\infty }{\overset{z+0.5}{\int }}{e}^{-{\left(z-{z}_{P}\right)}^{2}/2{\sigma }_{z}^{2}}dz$$

(4)

$$Y\left(A\right)=\frac{IN\left(A,Z\right)}{FIY\left(A,Z\right)}$$

(5)

$$Y\left(A\right)=\frac{CU\left(A,Z\right)}{FCY\left(A,Z\right)}$$

(6)

where, CU(A,Z) and IN(A,Z) are the experimentally determined cumulative and independent formation cross sections of the fission product, respectively, FCY(A,Z) and FIY(A,Z) are the fractional cumulative and independent yields of the fission product, respectively.

In an ideal case for the calculation of the charge distribution parameters, the independent yields of atleast three members of a single isobaric chain is required which is usually very difficult to obtain experimentally. Therefore, a different approach was applied to obtain the charge distribution parameters, Z_P (most probable charge) and σ_z (width parameter) in this study. In order to calculate Z_P for an isobaric chain with the mass number A, the total number of neutrons evaporated per fission, ν_T was estimated by taking the average of the values calculated using the prescription of Kozulin et al. [45] and the GEF code. The values of ν_T for the beam energies of 62.5, 70.7 and 102.9 MeV were found to be 6.5 ± 0.5, 7.2 ± 0.5 and 10.3 ± 1.1, respectively. After determination of ν_T, Z_P was calculated using the Eqs. (7) and (8) based on the unchanged charge distribution (UCD) hypothesis [7].

$$ Z_{p} \left( A \right) = A/\left( \frac{A}{Z} \right)_{p} $$

(7)

$${\left(\frac{A}{Z}\right)}_{p}=\frac{{A}_{C}-{\nu }_{T}}{{Z}_{C}}$$

(8)

where, A_C and Z_C are the mass and atomic numbers of the compound nucleus. The value of σ_z was estimated by reproducing the ratio of experimental yields of ¹³¹Te and ¹³¹I which were obtained by solving the parent-daughter decay-growth equation by fitting the measured activity of ¹³¹I at different cooling times. The yield ratios at the three beam energies were fitted together to obtain the width parameter ‘σ_z’. Expected precursor contribution to the measured experimental yield of ¹³¹Te was less than 7% and was therefore, ignored during the fitting. The σ_z value, thus obtained by the least square fit was 0.84 ± 0.05 which was used to convert the experimentally measured fission product cross sections to the corresponding mass yields. The average value of σ_z, obtained from the GEF predicted independent yields of the fission products, was found to be 0.79 ± 0.07 which is in agreement with the σ_z value used in the present study. The values of the width parameter (σ_z) for similar fissioning systems have been reported earlier in literature [14, 25, 26]. Manohar et al. [25] used σ_z value of 0.88 for the same fissioning system at 79 MeV energy while Ramaswami et al. [26] used σ_z value of 0.85 for ¹²C + ²³²Th fission at a beam energy of 72 MeV. Gubbi et al. [14] used the value of σ_z as 0.84 for ¹¹B + ²³²Th reaction at 72 MeV beam energy. Thus, the value of σ_z determined in the present study is reasonably close to the values obtained in the similar fissioning systems.

4 Results and discussion

4.1 Mass distribution of the fission products for ¹²C + ²³²Th reaction at 62.5 MeV beam energy

The formation cross sections of the fission products obtained at 62.5 MeV beam energy (E_excitation = 36.4 MeV) were converted into the corresponding mass yields using Eqs. (3–6) and the charge distribution parameters, Z_P and σ_z. The uncertainties on the estimated mass yield of the fission products include the uncertainties associated with formation cross sections of the fission products, the most probable charge (Z_P) and the width parameter (σ_z). It should be mentioned here that isomeric yields predicted by the “GEF, Version 2021/1.1” calculation were used to correct the measured formation cross sections of few of the fission products to account for the unmeasured fission isomers undergoing β-decay. In most of such cases, major isomer (isomer with higher yield) of the fission products was measured and the correction in measured cross section was within 15%. However, the minor isomers were detected for ¹¹³Ag, ¹²⁴Sb and ¹³⁸Cs (not detected at the lowest beam energy). The measured yields of these fission products were underestimated, respectively, by approximately 33%, 22% and 17% at 70.7 MeV energy while approximately 35%, 19% and 24% at 102.9 MeV energy due to the β⁻ decay of the unmeasured isomers for which the correction in the measured cross sections of such fission products were carried out accordingly. The corrections in the formation cross sections of ¹¹³Ag and ¹²⁴Sb was carried out by approximately 32% and 17%, respectively at 62.5 MeV beam energy. The experimental mass distribution at 62.5 MeV beam energy has been shown in Fig. 1. The experimental mass distribution was fitted using the Gaussian function to observe the contribution from the asymmetric fission modes along with the symmetric mode of fission (Fig. 1a). The deviations of the experimental data from the Gaussian function has been plotted as the ratio of experimental mass yields and the corresponding Gaussian fit value which clearly shows a double peak like structure having peaks approximately around 103 and 135 for the light and heavy mass region, respectively arising from the asymmetric fission contribution (Fig. 1b). The peak positions observed in this study was found to be in concordance with the observations reported by Ramos et al. [46] for the mass distribution of ²⁴⁴Cm at 23.0 MeV showing a predominantly double humped mass distribution. Based on the UCD hypothesis, the Z value corresponding to the heavy mass peak was estimated to be in the range of 54–56 indicating dominant contribution from the S2 asymmetric mode. The presence of the asymmetric component in overall mass yields can be attributed to the role of the shell effects. In order to investigate further, experimental mass distribution obtained at 62.5 MeV beam energy has been compared with the calculations of two versions of GEF namely “GEF, Version 2021/1.1” and “GEF, Version 2023/2.1”. For comparison, experimentally determined mass distribution was normalized by a factor calculated by taking the ratio of the sum of the experimentally obtained mass yields to the sum of % yields of the fission products calculated by the GEF code. The experimental mass distribution obtained at 62.5 MeV along with the GEF prediction has been shown in Fig. 2.

Fig. 1

Experimental mass distribution for ¹²C + ²³²Th reaction at beam energy of 62.5 MeV along with a Gaussian fit (a) and, Ratio of the experimental mass yields and the corresponding Gaussian fit value (b)

Fig. 2

Mass distribution for ¹²C + ²³²Th reaction at beam energy of 62.5 MeV along with the calculations of “GEF, Version 2021/1.1” code (a) and with “GEF, Version 2023/2.1” code (b) (shown with black solid line) for comparison

From Fig. 2, it has been observed that the experimentally obtained mass distribution which has a flat-top nature is in better agreement with the calculations of “GEF, Version 2021/1.1” code (Fig. 2a) which also shows a flat-top nature while a significant deviation has been observed with that predicted by the “GEF, Version 2023/2.1” code (Fig. 2b) which shows strongly symmetric Gaussian mass distribution. The flat-top nature indicates significant asymmetric fission contribution. According to the GEF calculations, these fission modes correspond to Z ≈ 52 (Standard 1), Z ≈ 55 (Standard 2) and Z ≈ 28 (Super-asymmetric) among which Z ≈ 55 (Standard 2) fission mode was found to have dominant effect. The variation in the results of the two versions of the GEF code can be attributed to the difference in the saddle point energies of ²⁴⁴Cm. The saddle point energies are higher in the “GEF, Version 2021/1.1”, resulting in the larger contribution from higher chance fission, which have large contribution from asymmetric fission modes as seen from Table 3. On the contrary, in the “GEF, Version 2023/2.1” version, the saddle point energies are lower, thereby decreasing the contribution from higher chance fission and thus reduced asymmetric fission contribution. As “GEF, Version 2021/1.1” with higher saddle point energies describes the experimental mass distribution better than the “GEF, Version 2023/2.1”, “GEF, Version 2021/1.1” has been used further in the present work for comparison with the experimental results.

Table 3 Contribution from different chance fission in the mass distribution at 62.5 MeV energy as predicted by the two versions of the GEF code

4.2 Mass distribution of the fission products in ¹²C + ²³²Th reaction at 70.7 MeV & 102.9 MeV beam energy

The experimental cross sections of the fission products for the beam energies 70.7 and 102.9 MeV were transformed to the corresponding mass yields using charge distribution parameters as discussed earlier and the mass distributions for both the energies have been shown in Fig. 3a and b, respectively. The uncertainties on the mass yields of the fission products include the uncertainties associated with formation cross sections of the fission products, the most probable charge (Z_p) and the width parameter (σ_z). Also, the correction in the measured fission cross section have been carried out to account for the unmeasured isomers while obtaining the mass yields, as mentioned earlier.

Fig. 3

Mass distributions for ¹²C + ²³²Th reaction at beam energy of 70.7 MeV (a) and 102.9 MeV (b) along with the comparison with calculations of “GEF, Version 2021/1.1”code (shown with black solid line)

As seen from Fig. 3a, the experimental mass distribution obtained at 70.7 MeV is in gross agreement with the predictions of “GEF, Version 2021/1.1” code with flat top nature indicating contribution from various asymmetric fission modes out of which ‘Standard 2’ mode corresponding to Z ≈ 55 has dominant contribution. The mass distribution at 102.9 MeV (Fig. 3b) follows a broad Gaussian curve as predicted by “GEF, Version 2021/1.1” calculations. The significantly large uncertainty on some of the mass yields is mainly due to the uncertainty in Z_P values arising from the uncertainty in the ν_T values. As seen from Fig. 3b, some of the mass yields in the mass region 132–145 are anomalously higher than that predicted by the GEF code which is a signature of the significant contribution from transfer induced fission (TF) at beam energy of 102.9 MeV which has been discussed later. Relative contributions of the different fission modes for CFF (Super long, Standard 1, Standard 2 and Super asymmetric mode) in the mass yields, as calculated using “GEF, Version 2021/1.1” code for the various energies have been given in Table 4 which show ‘Standard 2’ mode as the dominant ‘asymmetric’ fission mode. As seen from the Figs. 2a and 3a & b, experimental mass distributions obtained for the three energies are in gross agreement with that predicted by the “GEF, Version 2021/1.1” code.

Table 4 Contribution from the different fission modes in the mass distributions at various beam energies as calculated using “GEF, Version 2021/1.1”

4.3 Estimation of the contribution of transfer induced fission in the overall fission product yields

The anomalously large mass yields in the mass region around 132–145, most pronounced at 102.9 MeV beam energy, indicate the presence of transfer induced fission (TF) as pointed out in earlier studies [10,11,12,13,14,15,16,17,18]. When cross sections of the fission products, predominantly formed in the transfer channel, are converted into the corresponding mass yields using charge distribution parameters for CFF, it results in the anomalously large mass yields due to the difference in the A/Z ratio of the fissioning system populated in CFF and TF. This overestimation would increase with increasing difference in the A/Z and, thus, is expected to be most pronounced for the light mass transfer channels. The asymmetric nature of the mass distribution in the light mass transfer channels due to the lower excitation energy of the fissioning system would further add to this deviation around A = 140. In principle, similar deviation should be observed around the asymmetric peak in the lighter mass region, however, the effect is less pronounced in the lighter mass region due to comparatively lower A/Z of the measured fission products in the lighter mass region. As fission products formed in TF are more neutron rich compared to those formed in CFF, it would result in less relative contribution of TF in the measured yield of the fission products with comparatively lower A/Z. Sum-rule model was used to obtain the cross sections for complete and incomplete fusion channels (including the pick-up as well as strip** channels) [47]. The sum-rule model considers the localization of different incomplete fusion channels, with decreasing transferred mass, in the successive angular momentum window beyond critical angular momentum for complete fusion [47]. However, it should be mentioned here that this model underestimates the cross sections for light mass transfer at beam energies below approximately 10 MeV/nucleon [48]. Thus, the probability for proton and α transfer channels are expected to be larger compared to that predicted by the sum-rule model. The sum-rule model calculations showed that, apart from the complete fusion fission (CFF) channel being the major contributor, ¹¹B, ⁸Be (2α), ⁴He (α) and proton transfer channels are the dominant channels. A plot of transfer/pick-up probability for different channels relative to complete fusion is shown in Fig. 4. While plotting the transfer probabilities, transfer or pick-up probabilities for different A were added for a given Z for clarity of presentation. The cross sections for the pick-up channels were found to be negligible as compared to those involving nucleon transfer from projectile to target. Also, at the sub-barrier energy of 62.5 MeV, sum rule model didn’t predict any contribution from incomplete fusion.

Fig. 4

Relative probability of the various transfer channels with respect to the complete fusion obtained using the sum rule model [47] as a function of the atomic number (Z) of the transferred nucleon or cluster in ¹²C + ²³²Th reaction at 70.7 and 102.9 MeV beam energy (negative Z represents the pick-up channels and positive Z represents the strip** channels)

Since, the target like products formed due to the transfer of ¹¹B and ⁸Be do not differ significantly in mass compared to that of the compound nucleus formed in CFF, and the fissioning systems are also expected to have high excitation energy, the nature of the mass distribution for the CFF and heavy mass transfer induced fission would be similar and would, therefore, be difficult to estimate their contribution. However, in the case of proton and α transfer induced fission, the nature of the mass distribution would be expected to be very different compared to that for CFF due to the comparatively much lower excitation energy of the fissioning nuclei in these transfer channels. Approximate excitation energies of the corresponding fissioning nuclei ²³³Pa and ²³⁶U formed in proton and α transfer channels were calculated assuming that the outgoing PLFs formed in the respective transfer channels keep moving with the beam velocity. This assumption allows the fractionation of the projectile energy between the transferred nucleon/cluster and the outgoing PLF according to their mass ratio. Thus, excitation energy of the target like product, E_excitation,1 can be calculated using Eqs. (9) and (10).

$$ E_{{{\text{TN}}}} = \left( {E_{{{\text{beam}}}} *M_{{{\text{TN}}}} /M_{{{\text{proj}}}} } \right) $$

(9)

$$ E_{{{\text{excitation}}}} = \left( {E_{{{\text{TN}}}} *A_{{{\text{target}}}} /A_{{{\text{TLP}}}} } \right) + Q_{{{\text{gg}}}} $$

(10)

where, E_beam is the beam energy, M_TN is the mass of transferred nucleons, M_proj is the mass of projectile, A_target is the mass number of ²³²Th target, A_TLP is the mass number of the target like product. In an alternative approach, the excitation energy, E_excitation,2 of the target like product following the transfer of nucleons can be assumed to have a Gaussian distribution with the centroid at Q_gg-Q_opt [10, 17] where, Q_gg is the Q-value for the ground state transfer and Q_opt can be calculated using the Eq. (11) as:-

$$ Q_{{{\text{opt}}}} = E_{{{\text{CM}}}} * \, \left[ {\left( {z^{\prime } Z^{\prime } /zZ} \right){-}{1}} \right] $$

(11)

where, E_CM is the projectile energy in the centre of mass frame of reference, z and z′ are the proton numbers of the projectile and the outgoing PLF, respectively. Z and Z′ are the proton numbers of target and the target like product formed after transfer of nucleons. The values of E_excitation, calculated using the two approaches, were found to be close as seen from Table 5. The excitation energies for the proton transfer channel were found to be lower than the fission barrier for all the three beam energies. Therefore, attempt was made to obtain the mass distribution for only α-transfer channel and the corresponding excitation energies of the target like product (²³⁶U) have been given in Table 5.

Table 5 The excitation energies of the target-like product ²³⁶U formed in the alpha (α) transfer channel at different beam energies. E_excitation,1 and E_excitation,2 refer to the excitation energies calculated using two different approaches (see text for details)

In order to estimate the contribution from the CFF and α-TF, the experimentally measured cross sections of the fission products were fractionated according to the ratio of respective fission product yields for CFF (²⁴⁴Cm) and TF (²³⁶U) as calculated using the code “GEF, Version 2021/1.1”. In this procedure, the relative contribution from TF was estimated by imposing the condition of best possible agreement between the estimated experimental yields of fission products for CFF (after removing TF contribution) and the “GEF, Version 2021/1.1” calculations for CFF as judged by the least chi-square. Cross sections of the fission products formed in α-TF as obtained from the above exercise for the beam energies at 62.5, 70.7 and 102.9 MeV are given in Table 6.

Table 6 Formation cross sections of the fission products formed in alpha (α) transfer induced fission (TF) at different excitation energies. (See text for details about the estimation of cross sections of fission products formed in α-TF)

The contribution of α-TF in overall fission cross section at different beam energies are given in Table 5. Uncertainty on the α-TF as given in Table 5 as well as on the formation cross sections of the fission products formed in α-TF, as given in Table 6, also include the uncertainty due to the variation in the excitation energy of the target like product (²³⁶U) calculated using the two different approaches which are given in Table 5. As seen from Table 5, contribution from α-TF was similar (approximately 3%) at the lower beam energies of 62.5 and 70.7 MeV and increased significantly to approximately 12% at the beam energy of 102.9 MeV (Table 5). In the study of ¹¹B, ¹⁹F + ²³²Th reactions by Gubbi et al., the contribution of transfer fission in the overall fission cross section was observed to decrease with increasing beam energy [14, 17]. Variation of TF cross section with beam energy would depend on the variation in the transfer cross section relative to the complete fusion cross section and the excitation energy of the fissioning nucleus formed in the transfer channel. In the case of ¹²C + ²³²Th reaction, the Q_gg value for the proton transfer channel is much more negative (-10.7 MeV) compared to that in ¹⁹F + ²³²Th reaction for which Q_gg for the proton transfer channel is -2.7 MeV. Thus, in the case of the latter reaction, proton transfer channel also significantly contributes to fission at lower beam energies where proton transfer would dominate. Thus, observed decrease in the TF cross section relative to CFF at lower energies can be attributed to the absence of the TF contribution from the proton transfer channel in the present study. After the CFF and α-TF contributions in the experimentally measured formation cross sections of fission products were estimated using the GEF predicted yield ratios, mass yields for CFF and α-TF were obtained using the charge distribution parameters for CFF and TF, respectively. For CFF contribution, Z_P for the isobaric chain was obtained with Eq. (7) & (8) taking the value of the pre-fission neutrons, ${\nu }_{T}$ as the average of the values obtained using the prescription of Kozulin et al. [45] and the GEF calculation and, the width parameter, σ_z was taken as 0.84 ± 0.05, as discussed earlier. However, the parameters for the TF contribution, Z_P and σ_z, (as given in Eq. 3), for each isobaric chain were obtained by fitting the independent yields calculated using the GEF code for the fission of ²³⁶U.

Mass distributions obtained for CFF and TF after obtaining the corresponding mass yields from the estimated CFF and α-TF cross sections using the respective charge distribution parameters have been plotted in Fig. 5a–c for the beam energies 62.5, 70.7and 102.9 MeV, respectively. As can be seen from the plots, the mass distributions for the TF are asymmetric for all the beam energies due to low excitation energies of the fissioning system. However, the mass distribution for CFF is symmetric at 102.9 MeV as expected due to the washing out of the shell effects but the mass distributions at 62.5 and 70.7 MeV energies show flat-top nature indicating the significant contribution from the asymmetric modes of fission due to the presence of the shell effects in CFF. The comparison of GEF results with experimental mass distributions for CFF in Fig. 5a–c for the three beam energies suggests experimental mass distributions are grossly consistent with the GEF calculations which attribute asymmetric mass distribution to the above-mentioned proton shells.

Fig. 5

Mass distributions for complete fusion fission (CFF) (black circle) and α-transfer induced fission (TF) (blue upper triangle) for ¹²C + ²³²Th reaction at beam energy of 62.5 MeV (a), 70.7 MeV (b) and, 102.9 MeV (c) along with calculations of “GEF, Version 2021/1.1”code for CFF (black solid line) and TF (blue solid line). The red solid line in a & b is the 4th order polynomial fit to the experimental CFF data and that in c is the 3rd order polynomial fit to the CFF experimental data

The contribution from the different symmetric and asymmetric components for CFF as predicted by GEF has been given in Table 4. It has been observed that S2 component (Z ≈ 55) of the asymmetric modes has dominant contribution in the fission of heavy actinides. It is important to note that the agreement of the mass yields obtained from the experimentally measured cross sections of the fission products requires that the yields of the individual fission products, calculated by “GEF, Version 2021/1.1”, are also in reasonable agreement with the experimentally measured fission product yields, which also validates the estimation of the CFF and α-TF mass distributions using GEF calculated fission product yields. It should be mentioned here that, for many fission product yields, particularly for independent yields, the charge distribution correction factors are very large, therefore, even a small difference in yields at the product stage would result in a large difference in the experimental and calculated mass yields. As discussed earlier, with the detailed comparison of the experimental fission product yields with GEF calculations, it had been possible to estimate the contribution from transfer induced fission at different beam energies.

4.4 Effect of charge polarization on the mass yield distribution

With the help of GEF calculations, it is possible to look into the specific disagreements/deviations in more detail. A closer look of the mass distributions in Fig. 5a–c shows that some of the mass yields do not follow the systematic behaviour of the majority of the mass yields and also deviate significantly from GEF calculations as well. One of the possible reasons for this behaviour can be the deviation of the Z_P values obtained using unchanged charge distribution (UCD) hypothesis [7], with the ν_T values calculated using the prescription of Kozulin et al. [45] and the GEF code, from the actual values due to charge polarization effect [49]. According to the Unchanged Charge Distribution (UCD) hypothesis, the A/Z ratio of the fission fragments remains same as that of fissioning nucleus [7]. However, due to the charge polarization effect, the A/Z ratio changes resulting in a positive deviation of the Z_P values for lighter fission fragments and negative deviation for the heavier fission fragments in the fission of actinides [6]. Thus, “GEF, Version 2021/1.1” code also provides an opportunity to investigate the charge polarization effects in detail as discussed in the following. In order to achieve the best agreement of the experimental mass yields with the corresponding GEF values, the most probable charge, Z_P as obtained from UCD hypothesis (Z_UCD), was varied in the range of ± 1 unit while performing the charge distribution correction to obtain the mass yields for the CFF. As can be seen from the plots in Fig. 6a–c, most of the mass yields obtained using the charge distribution parameters could be matched with those predicted by GEF calculation by this procedure. It should be mentioned here that uncertainty on Z_P value has not been considered here as Z_P values were varied to achieve best possible agreement of the experimental mass yields with corresponding GEF values. However, the uncertainties on σ_z has been considered in the estimation of mass yields. The deviation of Z_P values from the corresponding Z_UCD values obtained using this procedure is plotted in Fig. 6d–f for the three beam energies. The uncertainty on the values corresponds to the uncertainty on the experimental fission product cross sections and due to the uncertainties on σ_z.

Fig. 6

CFF Mass yield distribution for ¹²C + ²³²Th system at beam energy of 62.5 MeV (a), 70.7 MeV (b) and, 102.9 MeV (c) after accounting the charge polarization effect to achieve best possible agreement between experimental and “GEF, Version 2021/1.1” predicted mass yields by varying the Z_P values based on UCD hypothesis within ± 1 unit, and the corresponding plot of (Z_P−Z_UCD) versus the mass number at beam energy of 62.5 MeV (d) 70.7 MeV (e) and, 102.9 MeV (f)

As seen from these figures, the deviations follow, in general, the expected trend, though some of the values are very off (Fig. 6d–f). It is also important to note from Fig. 6a–c, even after allowing variation in the Z_P values, some of the mass yields can’t be matched with the GEF calculation and still show large positive deviation from the systematic trend of the experimental data. The positive deviation of mass yields corresponding to the fission products ⁹⁸Nb, ¹⁰⁵Rh, ¹¹³Ag, ¹²⁴Sb, ¹³⁵Cs and ¹⁵⁰Pm from the GEF calculations may be due to the role of specific neutron or proton configurations, particularly due to the neutron evaporation during the de-excitation process, as the effect is most pronounced at the highest beam energy. Study of the fission fragment gated neutron multiplicity can provide further information about this observation. The large scatter in the plot of Z_P-Z_UCD values may also be possibly attributed to the secondary de-excitation of fragments. Understanding of this effect would require further investigations such as fission fragment gated neutron multiplicity measurements as mentioned earlier.

The fission cross sections for the ¹²C + ²³²Th reaction was obtained by fitting the experimental CFF mass yields with 4th order polynomial for the beam energies of 62.5 and 70.7 MeV. The cross section at the beam energy of 102.9 MeV was obtained by the 3rd order polynomial fit to the experimental CFF mass distribution which resembled a symmetric broad Gaussian curve and was also found to be consistent with the GEF predictions. The obtained fission cross sections for the fissioning system at 62.5, 70.7 and 102.9 MeV were found to be 45.4 ± 3.0, 504 ± 24 and 1703 ± 138 mb, respectively. The uncertainty quoted on the fission cross section was obtained by fitting the lower and upper limits of the mass yields obtained using the uncertainty on the individual mass yields. In addition to the uncertainty on the absolute fission cross sections for the three beam energies as mentioned above, a maximum systematic bias of 12% may arise due to the target thickness. The fission cross section for the same fissioning system reported in literature by Ramaswami et al. was 386 ± 25 mb at 72 MeV beam energy [26] which is lower than the value obtained at 70.7 MeV in the present study. It should be mentioned here that the cross section in ref [26] measured at the beam energy of 72 MeV were obtained assuming a purely Gaussian distribution. However, the present study at beam energy of 70.7 MeV which is very close to that in ref [26], show flat-top nature of the mass distribution. The fusion cross sections calculated using CCFUS [50] were found to be 47.8, 475 and 1785 mb at 62.5, 70.7 and 102.9 MeV, respectively. The curvature of the fusion barrier was adjusted in the CCFUS calculations to achieve an overall agreement. The experimental cross sections at 62.5, 70.7 and 102.9 MeV were found to reasonably agree with the CCFUS calculations.

5 Conclusions

The cross sections of the mass and charge identified fission products were measured using the recoil catcher technique followed by off-line γ-ray spectrometry at different beam energies of 62.5, 70.7 and 102.9 MeV. The cross sections of 32, 54 and 64 fission products were measured for the beam energies of 62.5, 70.7 and 102.9 MeV, respectively. The estimation of the mass yields of the isobaric chain was carried out using the experimentally measured cumulative and independent fission product cross sections and the charge distribution parameters. Experimental mass distribution at 62.5 MeV showed significant deviation from the Gaussian Fit to the experimental data. Experimental mass distributions showed a flat-top nature at the two lower beam energies of 62.5 and 70.7 MeV indicating significant contribution from asymmetric fission. The experimental mass distribution at the beam energy of 62.5 MeV was compared with the two versions of the GEF code i.e., “GEF, Version 2021/1.1” and “GEF, Version 2023/2.1” having difference in the saddle point energies for the compound nucleus ²⁴⁴Cm and was observed to be in better agreement with the “GEF, Version 2021/1.1” predicting significant contribution from asymmetric modes (Standard 1, Standard 2 and the Super-asymmetric modes) with Standard 2 (Z ≈ 55) mode having the dominant contribution. At the beam energy of 102.9 MeV, mass distribution was observed to follow a Gaussian behaviour for CFF indicating dominant contribution from the symmetric mode of fission. The experimental mass distributions were in gross agreement with that calculated using the GEF code. However, anomalously higher mass yields were observed in the mass region 132–145 at 102.9 MeV beam energy which was attributed to the contribution from transfer induced fission. With the help of the mass distributions calculated using the GEF code for the complete fusion fission (CFF) and α transfer induced fission (α-TF), mass distribution for the α transfer induced fission as well as for CFF could be separately estimated. Mass distribution for α-TF was observed to be asymmetric and was in agreement with the GEF calculations. The TF contributions in the overall yields were estimated as 3.2 ± 1.2%, 2.5 ± 0.9% and 11.9 ± 1.4% at beam energies of 62.5, 70.7 and 102.9 MeV, respectively. The decrease in the TF contribution relative to CFF at lower beam energies can be attributed to the absence of the fission contribution from proton transfer channel at lower beam energies due to the highly negative Q_gg value for the same. In order to investigate the effect of the charge polarization, the most probable charge ‘Z_P’, as estimated based on the UCD hypothesis for different mass chains, was varied in the range of ± 1 unit while converting the formation cross sections to the mass yields using the charge distribution parameters. Variation in the Z_P values improved the agreement between the calculated and the experimental mass distributions. The overall fission cross sections were found to be in reasonable agreement with the CCFUS calculations.