Photonuclear reactions of actinide and pre-actinide nuclei at intermediate energies Tapan Mukhopadhyay1 and D.N. Basu2 Variable Energy Cyclotron Centre, 1/AF Bidhan Nagar, Kolkata 700 064, India ∗ (Dated: August 9, 2021) Photonuclear reaction is described with an approach based on the quasideuteron nuclear pho- toabsorption model followed by the process of competition between light particle evaporation and fission for the excited nucleus. Thus fission process is considered as a decay mode. The evaporation- fission process of the compound nucleus is simulated in a Monte-Carlo framework. Photofission reaction cross sections are analysed in a systematic manner in the energy range ∼ 50-70 MeV for the actinides 232Th, 233U, 235U, 238U and 237Np and the pre-actinide nuclei 208Pb and 209Bi. The study reproduces satisfactorily well the available experimental data of photofission cross sections at energies ∼ 50-70 MeV and the increasing trend of nuclear fissility with the fissility parameter Z2/A for the actinides and pre-actinides at intermediate energies [∼ 20-140 MeV]. Keywords: Photonuclear reactions; Photofission; Nuclear fissility; Monte-Carlo PACS numbers: 25.20.-x, 27.90.+b, 25.85.Jg, 25.20.Dc, 24.10.Lx I. INTRODUCTION Isotopes of plutonium and other actinides tend to be long-lived with half-lives of many thousands of years, whereas radioactive fission products tend to be shorter- In recent years the study of photofission has attracted lived (most with half-lives of 30 years or less). Many of considerable interest. When a gamma (photon) above the actinides are very radiotoxic because they also have the nuclear binding energy of an element is incident on long biological half-lives and are α emitters as well. In that element, fission may occur along with the emission transmutation the intention is to convert the actinides of neutrons and the number of neutrons released by each into fission products. The fission products are very ra- fission event is dependent on the element. With high dioactive, but the majority of the activity will decay enough photon energy it is possible to induce fission in away within a short time. From a waste management most elements. For lighter elements the cross sections are viewpoint, transmutation of actinides eliminates a very quite small. There is also the difficulty in distinguishing long-term radioactive hazard and replaces it with a much fission from various fragmentation processes, particularly shorter-term one. Accelerated radioactive decay has been for light elements. These reasons practically limit all in- proposed by bombarding spent fuel with electromagnetic vestigations to the upper half of the Periodic Table. Re- (photon) rays. The γ-rays have also been suggested to cently the experimental techniques are improved by using be very effective, but γ-rays are very difficult to produce the solid state track and parallel plate avalanche detec- and may need to be precisely tuned to the target actinide tors which make it possible to study fission with very or fission product. low yields. Moreover, the production of highly neutron- The aim of the present work is to obtain photofission rich radioactive nuclei through photofission will open new cross section. From the photonuclear reactions, it is pos- perspectives to explore very exotic nuclei far away from 78 sible to gain insight into the fission mechanism, especially the valley of stability, especially in the vicinity of Ni. about how the barrier varies. Information can also be The use of the energetic electrons is a promising mode obtained about the excitation of a nucleus by absorp- to get intense neutron-rich ion beams [1]. The reason is tion of a high-energy quantum and the subsequent de- arXiv:0709.4155v1 [nucl-th] 26 Sep 2007 excitation process. At intermediate energies [ 20-140 that although the fission cross section at the giant dipo- ∼ lar resonance energy is 0.16 barn for 238U (against MeV] such a reaction can be described as a two step pro- 1.6 barn for 40 MeV neutrons≈ induced fission) but the cess. The incoming photon is assumed to be absorbed by electrons/≈ γ-photons conversion efficiency is much more a neutron-proton [n-p] pair inside nucleus, followed by a significant than that of the deuterons/neutrons. The en- mechanism of evaporation-fission competition. Photofis- ergetic beam ( 50 MeV ) of incident electrons can be sion cross sections of various nuclei are calculated using a slowed down in∼ a tungsten (W) converter or directly in Monte-Carlo method for the evaporation-fission calcula- the target (U), generating Bremsstrahlung γ-rays which tion and compared with the available experimental data at energies 50-70 MeV. may induce fission. In the photofission method for the ∼ (neutron-rich) radioactive ion beam production, nuclei are excited by photons covering the peak of the giant II. THE PHOTOABSORPTION MECHANISM dipolar resonance. The dominant mechanism for nuclear photoabsorp- tion at intermediate energies is described by the ∗E-mail 1: [email protected]; E-mail 2: [email protected] quasideuteron model [2] which is employed to evaluate 2 the total photoabsorption cross section in heavy nuclei. III. THE NUCLEAR EXCITATION AND It is based on the assumption that the incident photon FISSION PROBABILITY is absorbed by a correlated n-p pair inside the nucleus, leaving the remaining nucleons as spectators. Such an After absorption of a photon (γ) with incident energy assumption is enforced when wavelength of the incident Eγ (as measured in the laboratory frame), the nucleus photon is small compared to the nuclear dimensions. The with rest mass m0 recoils with a velocity vr given by T total nuclear photoabsorption cross section σa is then proportional to the available number of n-p pairs inside nucleus and also to the free deuteron photodisintegration Eγ c vr = 2 (5) 0 cross section σd(Eγ ) and is given by : [Eγ + m c ] which is also the velocity of the centre of mass vcm of the T L γ-nucleus system where c is the speed of light in vacuum. σa = NZσd(Eγ )fP (Eγ ) (1) A In the centre of mass frame, momenta of the γ and the where Eγ is the incident photon enegy, N, Z and A nucleus are the same and equal to pcm: are the neutron, proton and mass numbers respectively, L/A factor represents the fraction of correlated n-p pairs. Eγm0c Thus, Levinger’s constant [2] L is a factor which measures pcm = 2 2 (6) the relative probability of two nucleons being near each [m0c (2Eγ + m0c )] other in a complex nucleus compared with that in a free p and the kinetic energy Er of the recoiling nucleus in the deuteron. The function fP (Eγ ) accounts for the reduc- laboratory frame is tion of the n-p phase space due to the Pauli exclusion principle. A systematic study of the total nuclear pho- ′ 2 toabsorption cross section data [3] in the intermediate m0c ′ 2 Er = m0c energy range shows that 1 v2/c2 − − r p 2 2 2 1/2 = Eγ + m0c [m0c (2Eγ + m0c )] (7) −D/Eγ 0.81 fP (Eγ )= e where D =0.72A MeV. (2) − ′ where m0 and m0 are the rest masses of the nucleus be- For photon energies upto the pion threshold, the Eq. (2) fore and after the photon absorption respectively. along with the damping parameter D provided above The recoiling nucleus can be viewed as a compound nu- agrees reasonably well with the approach based upon cleus having the same composition as the target nucleus phase space considerations [4] using Fermi gas state den- but with the excitation energy sities that conserve linear momentum for the Pauli block- ing effects in the quasideuteron regime of hard photon ∗ ′ 2 2 2 2 1/2 absorption. E = m0c m0c = m0c [(1 + 2E /m0c ) 1] − γ − The free deuteron photodisintegration cross section [5] 2 2 1/2 2 = [m0c (2E + m0c )] m0c (8) is given by γ − and in this case E∗ is also equal to the kinetic energy 3/2 61.2 [Eγ B] in the centre of mass frame (which is sum of the kinetic σd(Eγ )= 3− [mb] (3) energies of the γ and the nucleus moving in the centre Eγ of mass frame). The kinetic energy Er of the recoiling where B=2.224 MeV is the binding energy of the nucleus in the laboratory frame can now be rewritten as deuteron. The quasideuteron model of nuclear photoab- the obvious result sorption is used together with the modern root-mean- square radius data to obtain Levinger’s constant ∗ E = E E . (9) r γ − −2/3 −4/3 L =6.8 11.2A +5.7A (4) This excited compound nucleus then undergoes succes- − sive evaporation of neutrons and other light particles or of nuclei throughout the Periodic Table and is in good fission. Thus, the fission is considered as a decay mode. agreement [6] with those obtained from the experimen- The photofission cross section σ is a product of the nu- tally measured σT values. At the quasideuteron energy f a clear photoabsorption cross section σT and the total fis- range, as a consequence of the primary photointerac- a sion probability (fissility) f and is, therefore, given by tion, γ+(n+p) n*+p*, in most of the cases excited com- pound nuclei are→ formed with the same composition as target nucleus where both neutron and proton are re- T σf = σ f. (10) tained inside the nucleus and the probabilities that either a neutron escapes or proton escapes or both neutron and The statistical approach for nucleon and light-particle proton escape from the nucleus are extremely low. evaporation and nuclear fission is an appropriate scheme 3 ∗ ∗ ∗ ∗ for calculation of the relative probabilities of different where En = E Bn and Ef = E Bf are the nu- decay modes of the compound nucleus.