Coherent bremsstrahlung and GDR width from 252Cf cold fission

The energy spectrum of the high energy gamma-rays in coincidence with the prompt gamma rays has been measured for the spontaneous fission of 252Cf. The nucleus-nucleus coherent bremsstrahlung of the accelerating fission fragments is observed and the result has been substantiated with a theoretical calculation based on the coulomb acceleration model. The width of the giant dipole resonance (GDR) decay from the excited fission fragments has been extracted for the first time and compared with the thermal shape fluctuation model (TSFM) in the liquid drop formalism. The extracted GDR width is significantly smaller than the predictions of TSFM.

Nuclear fission has been a subject of incessant research for decades. This nuclear phenomenon can occur spontaneously as a natural decay process or can be induced through the absorption of a relatively low-energy particle, such as a neutron or a photon. Since large amount of energy is available, the spontaneous fission of 252 Cf has prompted various searches, in particular, for bremsstrahlung emission [1,2,3], neutral pions and charged pions [4,5] and various exotic radioactivities [6]. Photon has evoked an extra attention over pion since it is not seriously affected by absorption phenomenon in the medium.
Hence, it can serve as an excellent probe to study the reaction dynamics in the early stage of the reaction. An accurate measurement of γ-ray emission from spontaneous fission reaction could throw some lights on nuclear dissipation at low temperature. However, in recent decades, a few experiments have been performed to explore the high energy part of the γ-spectrum coming from spontaneous fission. In addition to that, the observations have been found contradictory in nature.
The γ-ray energy spectrum, above 20 MeV, emitted in the spontaneous fission of 252 Cf has been one of the fundamental problems of nuclear fission physics. In a few experiments in the past [2,7], the yield of γ-rays at such high energy could not be detected, while in three other experiments, the energy spectrum could be measured [1,3,8]. The photons with energy 20-120 MeV are associated with the coherent bremsstrahlung of the fission fragments in the Coulomb field. In recent past, detailed macroscopic calculations of the bremsstrahlung yield from the spontaneous fission source has been performed considering different acceleration models (instantaneous, pure Coulomb) [1,2], including fragment-fragment barrier penetration (tunneling) [2]. But the high energy photon spectra extracted from those different theoretical models differ by several orders of magnitude. The conflicting experimental results as well as the theoretical calculations motivate one to carry out further investigation.
The low energy (8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) part of the photon spectrum is mainly associated with direct excitation of the giant dipole resonance (GDR) from the daughter nuclei arising in the fission process. An interesting feature of spontaneous fission is that the fragments are produced at low excitation energies. At these energies, the GDR emission will only be from the first decay step [9,10,11]. As a result, the spontaneous 252 Cf source provides us an unique tool to study the GDR width at low temperature (T) and angular momentum (J), which has been a perplexing topic in recent years. The exploration of the GDR width in fusion evaporation reaction is a complex process as it requires the decoupling of the effects of both J and T on the GDR width. In spontaneous fission, since the angular momentum is very small (∼ 6h), the GDR width will only be affected by temperature.
In this letter, we report on an extensive investigation of high energy γ-ray yield from the coherent nucleus-nucleus bremsstrahlung as well as the decay of GDR from the 252 Cf cold fission. The width of the GDR decay from the excited fission fragments has been extracted for the first time and compared with the Thermal Shape Fluctuation Model (TSFM) [12].
High energy gamma-rays from the spontaneous fission of 252 Cf (3µCi) were detected in coincidence with the low energy discrete γ-rays emitted from the decay of excited fission fragments in order to establish a correlation (photons/fission) between the high energy γ-rays and the fission process. The source was placed as close as possible to the four multiplicity detectors [13], arranged in a 2 × 2 matrix, to get a start trigger in order to separate/reject the neutrons and cosmic pile ups. The high energy γ-rays were measured using the array LAMBDA [14]. The array was assembled in a 7 × 7 matrix and kept at a distance of 35 cm from the 252 Cf source. A master trigger was generated by taking a coincidence between the start trigger and any one of the 49 detectors in the pack above a high threshold of 4 MeV ensuring the selection of fission events and rejection of background. Time of flight measurement distinguished the gamma-rays from neutrons while long/short gate technique was applied to reject the pile up events. Data were collected in this γ -γ coincidence mode for 450 hours. At the photon energies E γ ≥ 25 MeV, cosmic ray showers are the major source of background. Therefore extreme precaution was taken to suppress the background and obtain the experimental data free from cosmic impurity. Lead bricks were used as a passive protection shield from cosmic gamma-rays. Large area plastic scintillator pads (paddle) were used as active shielding that surrounded the LAMBDA array as well as the multiplicity filter to reject the cosmic muons. Further, the cosmic pile up events were rejected using our cluster summing technique [15] in which the energy deposit in each element was required to satisfy the adequate gating employed by the pulse shape discrimination gate and the sharp prompt time gate. Finally, the random coincidence events were rejected by subtracting the background spectrum which was also collected for 450 hours without the fission source in an identical configuration.
The high energy γ spectrum measured upto 80 MeV is shown in Fig.1 Equation 1 gives the exact energy spectrum, in the classical nonrelativistic limit, of the bremsstrahlung produced from the acceleration of the two charged fission fragments [2]. In ref [17], the analogous case of alpha emission was discussed in detail. Here we take only an approximate approach. In order to solve the above equation, time (t) was expressed as a function of the distance (x) between the two fragments. The motion of the fragments was determined by solving the differential equation for the two particles under the influence of a repulsive Coulomb potential where k is Z 1 Z 2 e 2 and E is the total energy of the system. In order to calculate the emission of gamma-rays from the decay of GDR accompanying the spontaneous fission of 252 Cf, a modified version of the statistical code CASCADE [21] was used. Here, only the emission of γ-rays from the excited fission fragments has been considered, neglecting the pre-scission γ contribution. The latter was found to be very small even by increasing the scission time scale [22]. The total γ-ray spectrum was generated by summing all the gamma spectra calculated independently for all the possible fission fragments and weighed according to corresponding masses. For each fragment the charge number has been estimated from the relation Z f rag =A f rag 98/252 [22,23]. In all the nuclei, Reisdorf-Ignatuyk level density prescription [24,25] has been used to incorporate the mass and the excitation energy dependence of the level density parameter. The GDR strength function was calculated using a Lorentzian having a centroid energy (E GDR ) and width (Γ GDR ). The parameters were calculated dynamically for each fragment mass inside the CASCADE using the systematics E GDR = 18.0A −1/3 + 25.0A −1/6 [9] and Γ GDR = 4.8 + 0.0026E * 1.6 [26]. The high energy photon spectrum, estimated above, was folded with the detector response and is shown in Fig.2. The bremsstrahlung component has been extrapolated to the lower energies while reconstructing the gamma spectrum. The present calculation represents the experimental data quite well. The linearized GDR lineshape along with the CASCADE prediction is shown in Fig. 2.
In order to understand the emission of GDR photons from the fission fragments, the mass dependent excitation energy was obtained from ref [16] (top panel of Fig. 3). The GDR decay probability was calculated [27] for each mass based on the available excitation energy and is shown in Fig. 3(bottom panel) after weighing over the corresponding mass yield. The solid line in Fig. 3 MeV) for A=109-124. Thus, the measured width actually provides an average width for the mass region 109-124. The temperature was calculated from the initial excitation energy of the fragments after subtracting the rotational en-ergy and the corresponding GDR centroid energy. The average temperature and mass of the region 109-124 were found to be 0.68 MeV and 117 , respectively. These mean values were also estimated by weighing over the GDR emission probability shown in the bottom panel of Fig. 3. The extracted GDR width of the average mass ∼ 117 is found to be 5.24 ± 1 MeV. It is observed that the GDR width measured in this experiment is appreciably smaller than the TSFM predictions ( Table 1). The phenomenological description based on the thermal fluctuation theory, describes on the average, many experimental results but it fails to reproduce the data corresponding to the lowest temperatures showing the limitation of the model [12].
In conclusion, the nucleus-nucleus coherent bremsstrahlung from 252 Cf cold fission has been observed and the result has been corroborated with a theoretical calculation based on the Coulomb acceleration model. The 252 Cf source provides us an unique tool to study the GDR width at low temperature which has been an intriguing topic in the recent years. The GDR widths from the decay of excited fission fragments have been extracted in order to test the thermal shape fluctuation theory at low temperature. The model overpredicts the variation of GDR width at low temperature.
The authors wish to thank Dr.A.K.Sinha of UGC-DAE CSR for providing