Shell structure in deformed nuclei and nuclear fission

Some new aspects in the theory of heavy nuclei emerging from studies of nuclear shell structure in the nuclear-fission process are described. Specific subjects cover general understanding of shell structure, the significance of macroscopic modes and the droplet model.     

Recoil studies of fission products formed in the fission of U by protons of energies 25–85 MeV

The recoil properties of ten fission products with masses ranging from 72 to 136 formed in the fission of ²³⁸U with protons of energies 25–85 MeV have been determined radiochemically by the integral-range method. From the recoil properties of the products and the Monte Carlo cascade calculations the average kinetic energy, cascade deposition energy, and anisotropy parameter for each fission product has been calculated. The kinetic energy and the excitation energy of the primary fragments leading to the observed fission product, and the total kinetic energy and the total excitation energy of the primary fragment pair have also been calculated.

The results indicate that up to a bombarding energy of 40 MeV fission takes place predominantly by the compound nucleus mechanism, with an increasing contribution of the direct interaction mechanism as the bombarding energy increases. The kinetic energy deficit was found to decrease with increasing bombarding energy. The fission products formed from the symmetric mode of fission have a larger separation distance between the charge centres of their respective primary fragments than those for the asymmetric mode of fission.     

Radiochemical studies on fission of actinides

Since its discovery in 1939, nuclear fission has been extensively studied by various experimental as well as theoretical groups in several countries leading to an understanding of major aspects of this important and complex nuclear reaction. In Trombay, studies have been carried out in the last 25 years using both physical and radiochemical methods and significant contributions have been made towards a better understanding of this reaction. This paper presents highlights of radiochemical studies on fission of actinides, particularly mass, kinetic energy and charge distribution and fragment angular momentum. Results of these studies brought out the important role played by deformation energy surface, spherical and deformed nuclear shells and nucleon pairing.     

Properties of N=84, even-even nuclei populated in the spontaneous fission of 248Cm

Excited states in the neutron-rich, N=84 nuclei ¹³⁴Sn, ¹³⁶Te and ¹³⁸Xe, populated in the spontaneous fission of ²⁴⁸Cm, were studied to medium spins using the EUROGAM2 array. OXBASH code calculations support the experimental identification of maximum aligned configurations in these isotopes. Empirical shell model calculations agree with the proposed excitation energy of the neutron h_9/2 excitation in the ¹³²Sn region. A discrepancy between the observed and calculated excitation energy of the I^π= 12⁺ level in ¹³⁶Te indicates possible admixtures of collective excitations in this nucleus. Clear signs of collective excitations are observed in ¹³⁸Xe. Received: 10 November 1999 / Revised version: 22 December 1999     

Coulomb effects on the formation of proton halo nuclei

This paper makes some qualitative and quantitative analyses about halo formation rules of some mirror nuclei with the relativistic mean-field (RMF) theory and the Woods--Saxon mean-field model. By analysing two opposite effects of Coulomb interaction on the proton halo formation, it finds that the energy level shift has a larger contribution than that of the Coulomb barrier when the mass number A is small, the hindrance of the Coulomb barrier becomes more obvious with the increase of the mass number A, and the overall effect of the Coulomb interaction almost disappears when A≈39 as its two effects counteract with each other.     

Asymmetry of mass and charge division in spontaneous fission

The order-disorder model has been used to explain asymmetry of mass and charge division and related phenomena in fission. According to this model the fission process involves two steps consisting of charge polarisation into two ‘impending fragment clusters’ with beta stable neutron numbers and subsequent distribution of the balance neutrons between the two. Mode of elemental division of the fissioning nuclei is attributed to the charge polarisation in the first step. Theory of reaction rate has been applied to the system. The frequency term is obtained by applying the conditional stochastic process under charge polarisation constraint and the energy-dependent term is given by the condition of minimum in free energy of the system. Using this, the relative probability of polarisation into given charge pair is arrived at. The model uses stable neutron numbers for the charges as the only input. No explicit assumption or quantification on the preference of formation of shell closure species in fission is necessary. The statistics developed on the principle of equala priori probability of all charge polarisation is used. The shell effects come into play only in deciding a stable neutron number for the charges. The total isotopic yield distribution for a number of fission reactions shows asymmetry in the actinide region which reduces with increasing mass/charge of the fissioning nuclide and bunching of the higherz peaks. Although the mass yields obtained therefrom for a number of fission reactions agree with experimental results, the peaks of the distributions are slightly shifted away from the symmetric point and the distributions are somewhat narrower. Charge distribution parameters obtained from these results are also presented.     

用动力学模型计算10.6MeV/u~(84)Kr(~(27)Al,准裂变)反应的裂变时间

用单体耗散模型对１０．６ＭｅＶ／ｕ８４Ｋｒ在２７Ａｌ上引起的准裂变反应进行了计算，结果表明该准裂变反应的准裂变时间大于２００×１０－２２ｓ．发现对本反应系统，准裂变的出现至少需要８ＭｅＶ／ｕ阈能     

Equivalence between local Fermi gas and shell models in inclusive muon capture from nuclei

Motivated by recent studies of inclusive neutrino nucleus processes and muon capture within a correlated local Fermi gas model (LFG), we discuss the relevance of nuclear finite-size effects in these reactions at low energy, in particular for muon capture. To disentangle these effects from others coming from the reaction dynamics we employ here a simple uncorrelated shell model that embodies the typical finite-size content of the problem. The integrated decay widths of muon atoms calculated with this shell model are then compared for several nuclei with those obtained within the uncorrelated LFG, using in both models exactly the same theoretical ingredients and parameters. We find that the two predictions are in quite good agreement, within 1-7%, when the shell model density and the correct energy balance is used as input in the LFG calculation. The present study indicates that, despite the low excitation energies involved in the reaction, integrated inclusive observables, like the total muon capture width, are quite independent of the fine details of the nuclear wave functions. An erratum to this article is available at .     

The isospin admixture of the ground state and the properties of the isobar analog resonances in medium and heavy mass nuclei

Within the framework of quasiparticle random phase approximation (QRPA), Pyatov-Salamov method [23] for the self-consistent determination of the isovector effective interaction strength parameter, restoring a broken isotopic symmetry for the nuclear part of the Hamiltonian, is used. The isospin admixtures in the ground state of the parent nucleus, and the isospin structure of the isobar analog resonance (IAR) state were investigated with the inclusion of the pairing correlations between nucleons for the medium and heavy mass regions: 80 <A < 90, 102 <A < 124, and 204 <A < 214. It was determined that the influence of the pairing interaction between nucleons on the isospin admixtures in the ground state and the isospin structure of the IAR state is more pronounced for the light isotopes (N ≈ Z) of the investigated nuclei     

Production of neutron-rich nuclei in fission induced by neutrons generated by the p + <Superscript>13</Superscript>C reaction at 55 MeV

Cross-sections for the production of neutron-rich nuclei obtained by neutron-induced fission of natural uranium have been measured. The neutrons were generated by bombarding a ¹³C target with 55 MeV protons. The results, position of the maximum in the (Z, A)-plane, width and magnitude, are very comparable with those where the neutrons are generated by bombardment of natural ¹²C graphite with 50 MeV deuterons. Depending on the geometry of the converter/target assembly the isotope yields, however, are a factor of 2-3 lower due to less efficient production of neutrons per primary projectile, especially at small forward angles. Received: 8 November 2002 / Accepted: 20 December 2002 / Published online: 15 April 2003     

Nuclear magnetic resonance study of the relaxation mechanisms of the Be, Al, and Si nuclei in Cr-doped Be3Al2Si6O18 crystals

The variations with temperature of the relaxation mechanisms of the ⁹Be, ²⁷Al, and ²⁹Si nuclei in emerald (Be₃Al₂Si₆O₁₈:Cr³⁺) single crystals were investigated by using a pulse NMR spectrometer. The values of the spin-lattice relaxation rates for the three nuclei are different, and these differences are attributed to the differences between their Larmor frequencies and their local nuclear environments. The relaxation rates of the ⁹Be and ²⁷Al nuclei undergo no abrupt changes within the temperature range 180-400 K, which indicates that there are no phase transitions within this temperature range. The spin-lattice relaxation rates of ⁹Be and ²⁷Al were found to be proportional to temperature. Therefore, the nuclear spin-lattice relaxation processes of these two nuclei proceed via single-phonon processes.     

Reliability of the pseudospin symmetry in atomic nuclei

The reliability of the pseudospin symmetry (PSS) in atomic nuclei is analyzed in the framework of the relativistic Hartree approach. We find that the nuclear surface strongly increases the effect of the pseudospin-orbit potential (PSOP), spoiling the possibility of the exact realization of the PSS even in the limit of a vanishing PSOP. It is also shown that the PSS cannot be explained by the fact that Σ_S ≃ - Σ. New arguments to explain the PSS in finite nuclei are given. The important role the spin-orbit interaction plays in the achievement of the PSS is also discussed. Received: 22 July 2002 / Accepted: 18 February 2003 / Published online: 20 May 2003     

Effect of Co doping on the magnetic properties of La0.85Ag0.15(Mn1−yCoy)O3

The mixed valent manganites (La_0.85Ag_0.15)MnO₃ with perovskite structure has been prepared by doping up to 50% of Co at the Mn site. Paramagnetic (PM) to ferromagnetic (FM) transitions have been observed in all the prepared materials. However, the long-range magnetic ordering observed in (La_0.85Ag_0.15)MnO₃ is systemically reduced to cluster glass-type (short-range) of FM ordering due to the introduction of Co. The FM transition temperature was found to decrease with increase in Co doping up to 20% and for further increase in Co doping, the T_c was found to increase. They are explained on the basis of competition between FM double exchange interactions in Mn–O–Mn and Co–O–Co networks. In addition to PM–FM transition, evidences of FM to antiferromagnetic (AFM), and AFM to reentrant spin-glass transitions have been observed. The shift in spin-glass freezing temperature, T_f has been observed from the frequency variation of ac susceptibility measurements. The observed magnetic transitions are explained on the basis of magnetic interactions in different Mn–O–Mn, Mn–O–Co and Co–O–Co networks and such transitions are also observed from the measurement of third harmonic susceptibility. Metal–insulator transition and colossal magneto-resistivity have been observed up to 10% of Co doping.     

DTA and NQR studies of polymorphism in p-chlorofluorobenzene

Differential thermal analysis, and the ³⁵Cl Nuclear Quadrupole Resonance frequency (ν_Q) and spin-lattice relaxation time (T₁) were measured as a function of temperature in p-chlorofluorobenzene. Three different phases were found according to the thermal history of the sample and only one was stable up to the melting point. In one of the phases, the presence of molecular reorientations can be inferred from T₁ data with activation energy of 3.7 kcal/mol. A value of 13.9 kJ/mol for the fusion heat of this compound has been obtained.     

Structure of unstable nuclei in the sd-pf shell region by shell model with proper tensor force

Focusing on the importance of the tensor force in the effective interaction, we investigate the structure of unstable nuclei around N=28 with large-scale shell-model calculations. From the analysis of the spin-tensor decomposition for some interactions, the tensor force in the effective interaction should be close to the π+ ρ force, whereas it is much weaker in the Millener-Kurath (MK) interaction which is often used as the cross-shell interaction. The significance of the tensor force appears in the structure around ⁴²Si: the proper tensor force predicts that it is deformed contrary to the result from MK.     

Prompt neutron emission spectra and multiplicities in the thermal neutron induced fission of235U

The emission spectra of prompt fission neutrons from mass and kinetic energy selected fission fragments have been measured in²³⁵U(n _th,f). Neutron energies were determined from the measurement of the neutron time of flight using a NE213 scintillation detector. The fragment energies were measured by a pair of surface barrier detectors in one set of measurements and by a back-to-back gridded ionization chamber in the second set of measurements. The data were analysed event by event to deduce neutron energy in the rest frame of the emitting fragment for the determination of neutron emission spectra and multiplicities as a function of the fragment mass and total kinetic energy. The results are compared with statistical model calculations using shell and excitation energy dependent level density formulations to deduce the level density parameters of the neutron rich fragment nuclei over a large range of fragment masses.     

Mass distribution in the bremsstrahlung-induced fission of Th,U and Pu

The yields of various fission products in the 10 MeV bremsstrahlung-induced fission of ²³²Th, ²³⁸U and ²⁴⁰Pu were determined using a recoil catcher and off-line γ-ray spectrometric techniques. From the yield data, mass yield distributions were obtained using charge distribution corrections. The higher yields of fission products around mass numbers 133–135, 138–140, 143–145 and their complementary products in the neutron and bremsstrahlung-induced fission of ²³²Th, ²³⁸U and ²⁴⁰Pu were interpreted based on nuclear structure effects. From the mass yield distribution, the peak-to-valley (P/V$P/V$) ratio was also obtained for the above fissioning systems. The present data, along with data from the literature on different bremsstrahlung- and mono-energetic neutron-induced fissions of ²³²Th and ²³⁸U are interpreted to examine the influence of excitation energy on the peak to valley ratio. For the same compound nucleus ²⁴⁰Pu^?, the data in the 10–30 MeV bremsstrahlung-induced fission of ²⁴⁰Pu were compared with similar data of thermal to 14 MeV neutron-induced fission of ²³⁹Pu and the spontaneous fission of ²⁴⁰Pu to examine the role of excitation energy due to bremsstrahlung radiation and mono-energetic neutrons.     

Central cell effects on the polarizabilities of shallow donors in silicon

With the Topp and Hopfield form for the ionic pseudopotentials, the screened impurity pseudopotentials of the shallow donors P, As and Sb in silicon are obtained in closed form in the linearized Thomas-Fermi model. The results are compared with the screening using a k-dependent dielectric function. Using these impurity pseudopotentials in the multivalley effective mass equation, the binding energies of these donors in Si are estimated variationally. Adopting the Hasse variational method, the polarizabilities of the P, As and Sb donors in Si are computed and are found to be in excellent agreement with the polarizability values of isolated P and Sb in Si, deduced from recent piezocapacitance measurements.