Investigation of the 208Pb(18O, f) fission reaction: Mass-energy distributions of fission fragments and their correlation with the gamma-ray multiplicity

The mass-energy distributions of fragments originating from the fission of the compound nucleus ²²⁶Th and their correlations with the multiplicity of gamma rays emitted from these fragments are measured and analyzed in ¹⁸O + ²⁰⁸Pb interaction induced by projectile oxygen ions of energy in the range E _lab = 78–198.5 MeV. Manifestations of an asymmetric fission mode, which is damped exponentially with increasing E _lab, are demonstrated. Theoretical calculations of fission valleys reveal that only two independent valleys, symmetric and asymmetric, exist in the vicinity of the scission point. The dependence of the multiplicity of gamma rays emitted from both fission fragments on their mass, M_γ(M), has a complicated structure and is highly sensitive to shell effects in both primary and final fragments. A two-component analysis of the dependence M_γ(M) shows that the asymmetric mode survives in fission only at low partial-wave orbital angular momenta of compound nuclei. It is found that, for all E _lab, the gamma-ray multiplicity M_γ as a function of the total kinetic energy (TKE) of fragments, M_γ(TKE), decreases linearly with increasing TKE. An analysis of the energy balance in the fission process at the laboratory energy of E _lab = 78 MeV revealed the region of cold fission of fragments whose total kinetic energy is TKE ～Q _max.     

Orientation windows in the cold synthesis and decay of heavy elements

Due to the multipolar ground state nuclear deformations (β ₂, β ₃, β ₄,...) the cold synthesis of heavy and superheavy elements is dependent on the mutual orientation of target and projectile. When going from lower bombarding energies to higher bombarding energies, windows for orientations are occurring and others are disappearing. The cold fission is also strongly dependent on the deformation but is more selective in respect to orientation of fragments at scission. The measured cold fission yields of ²⁵²Cf show that only one orientation window is active. I propose a qualitative receipt based on the orientation windows of the driving potential which serves as a guidance in understanding the fission and quasifission mass distributions in the synthesis of heavy and superheavy elements.     

Cold fission as heavy ion emission

The last version of the analytical superasymmetric fission model is applied to study cold fission processes. Strong shell effects are present either in one or both fission fragments. A smooth behaviour is observed when the proton or the neutron numbers are changed by four units. IncreasingZ andN, in the transuranium region, a sharp transition from asymmetry with a large peak-to-valley ratio to symmetry atZ=100 and/orN=164 is obtained. The transition toward asymmetry at higherZ andN is much smoother. The most probable cold fission light fragments from²³⁴U,²³⁶U,²³⁹Np and²⁴⁰Pu are¹⁰⁰Zr,¹⁰⁴Mo,¹⁰⁶Mo and¹⁰⁶Mo, respectively, in good agreement with experimental data. The unified treatment of alpha decay, heavy ion radioactivities and cold fission is illustrated for²³⁴U — the first nucleus in which all three groups have been already observed.     

Calculation of multidimensional potential energy surfaces for even-even transuranium nuclei: systematic investigation of the triaxiality effect on the fission barrier

Static fission barriers for 95 even-even transuranium nuclei with charge number Z = 94-118 have been systematically investigated by means of pairing self-consistent Woods-Saxon-Strutinsky calculations using the potential energy surface approach in multidimensional(β_2, γ, β_4) deformation space. Taking the heavier (252)~Cf nucleus(with the available fission barrier from experiment) as an example, the formation of the fission barrier and the influence of macroscopic, shell and pairing correction energies on it are analyzed. The results of the present calculated β_2 values and barrier heights are compared with previous calculations and available experiments. The role of triaxiality in the region of the first saddle is discussed. It is found that the second fission barrier is also considerably affected by the triaxial deformation degree of freedom in some nuclei(e.g., the Z =112-118 isotopes). Based on the potential energy curves, general trends of the evolution of the fission barrier heights and widths as a function of the nucleon numbers are investigated. In addition, the effects of Woods-Saxon potential parameter modifications(e.g.,the strength of the spin-orbit coupling and the nuclear surface diffuseness) on the fission barrier are briefly discussed.     

Influence of shell effects on the angular distributions of fission fragments

A dynamical-statistical model is used to analyze the experimental angular distributions of fission fragments in the reactions α + ²³⁸U, ²³⁷Np at E _α = 20–100 MeV, as well as to determine the Am isotope fission probabilities and the shape isomer yields in the reactions d + ^242,240Pu at E _d = 20–30 MeV. Manifestations of shell effects are found in the fission barrier structure up to the excitation energies of 50–60 MeV.     

Study of isotope shifts,isotone shifts and nuclear compressibility from the analysis of muonic x-ray transitions

Muonic x-ray transitions in various spherical nuclei in the region 13?Z?83 have been analysed and the isotope and isotone shifts in charge radiusR are investigated. AssumingR=r ₀ A ^1/3, the isotopic and isotonic behaviour of the parameterr ₀ (=RA ^?1/3) is also studied. The variation ofr ₀ with mass numberA reveals the variation of average nucleon density, which in turn sheds light on the compressibility of nuclear matter. The isotope and isotone shifts inR exhibit the shell effects in the vicinity of magic neutron and proton numbers: 20, 28, 50, 82 and 126. The results indicate that neutron-proton interaction is maximum at the beginning of a major neutron shell and decreases gradually as the shell gets filled up. The behaviour of parameterr ₀ clearly suggests that low-Z nuclei are highly compressible while high-Z nuclei are more or less incompressible. The parameterr ₀ too is observed to exhibit profound shell effects.     

Energy fluctuations in multichannel fission and heavy ion collisions

A simple theory for the variance σ_E² of the total kinetic energy distribution of the fission fragments is given and compared with the data. It seems to explain the observed variation of σ_E with the mass number as well as the differences of σ_E for the different fission channels due to shell effects. The physical origin of σ_E is supposed to be the permanent thermal noise along the path from the barrier to scission. The same theory is applied to deep inelastic collisions and leads to much larger σ_E in agreement with measurements.     

Analysis of fission excitation functions and the determination of shell effects at the saddle point

A method is proposed to deduce the shell correction energy corresponding to the fission transition state shape of nuclei in the mass region around 200, from an analysis of the first chance fission values of the ratio of fission to neutron widths, (Γ _f /Γ _n )₁. The method is applied to the typical case of the fissioning nucleus²¹²Po, formed by alpha bombardment of²⁰⁸Pb. For the calculation of the neutron width, the level densities of the daughter nucleus after neutron emission were obtained from a numerical calculation starting from shell model single particle energy level scheme. It is shown that with the use of standard Fermi gas expression for the level densities of the fission transition state nucleus in the calculation of the fission width, an apparent energy dependence of the fission barrier height is required to fit the experimental data. This energy dependence, which arises from the excitation energy dependence of shell effects on level densities, can be used to deduce the shell correction energy at the fission transition state point. It is found that in the case of²¹²Po, the energy of the actual transition state point is higher than the energy of the liquid drop model (LDM) saddle point by (3 ± 1) MeV, implying significant positive shell correction energy at the fission transition state. Further, the liquid drop model value of level density parametera is found to be a few per cent smaller for the saddle point shape as compared to its spherical shape.     

Fragment stiffness-parameters Cγ at scission

The fragment deformation β at scission and the stiffness parameters C_γ are calculated for the fission of ²³⁶U and ²⁵²Cf. The results show that in both compound nuclei the stability against axial asymmetric deformations is determined by fragment shell effects in the β-values.     

The scission neutron spectrum of252CF (SF)

The scission neutron spectrum was obtained as a difference between the integral experimental fission neutron spectrum evaluated by Mannhart based on measurements in the laboratory reference system from several authors in the different neutron energy ranges, and the laboratory fission neutron spectrum stemming only from those neutrons which are evaporated from the fully accelerated fission fragments. The scission neutron spectrum was represented by a Weisskopf evaporation spectrump _s(? _l )=P ₀/(T _s)²·?_l·exp(??_l/T_s). A least squares fit gave for the fraction of scission neutrons with respect to all fission neutrons a value ofp ₀=(0.011±0.003) and for the pseudo scission neutron temperature a value ofT _s=(0.20±0.03) MeV. The low pseudo temperature is compatible with a cold nuclear matter of the prescission configuration. The low energy of the scission neutrons indicates that they come from a slowly moving source. The width of the distribution suggests that the source is small: radius of about 5 fm. This information conforms with the idea of satellite droplets which are formed when the neck snaps.     

Fission of 232Th, 238U and 235U induced by negative muons

The absolute yields of prompt and delayed fission induced by negative muons in ²³²Th, ²³⁸U and ²³⁵U have been measured. The delayed fission yields are much lower than could be predicted from Γ_n/Γ_f systematics for 15–20 MeV nuclear excitation. The systematics of prompt fission yields are compared with recently obtained photofission data. It is suggested that prompt fission can be used for investigating the channel structure of the fission barrier.     

Quasi-fission and other strongly damped collisions between 63Cu ions and 197Au nuclei

The interaction of ⁶³Cu ions with ¹⁹⁷Au nuclei have been studied experimentally at incident energies of 365 and 443 MeV (1.1 and 1.4 times the Coulomb barrier). Mass and kinetic energy distributions of reaction products have been measured at several angles. Near the grazing angle, a continuous transition was found from elastic events to partially damped (PD) events, and to fully damped events (quasi-fission, QF). Away from the grazing angle a clean separation between elastic and QF events was observed. Events that may be due to fission following fusion (CF) were also obtained. Results are discussed in terms of decomposition into PD, QF, and CF components. The QF kinetic energy is independent of the incident energy (implying full damping of the initial relative motion). It is lower than the Coulomb barrier and close to the kinetic energies from the fission of similar systems. The angular distribution is peaked somewhat forward of the grazing angle for low mass transfers. For large mass transfers the yield increases slowly with decreasing angle. At 443 MeV a large contribution from negative angles is present. σ_QF accounts for more than 65 % of the reaction cross section σ_R at 443 MeV and for more than 50 % at 365 MeV. The upper limit on CF is about 10 % of σ_R, and σ_PDis of the order of 25 % of σ_R.     

Sub-Coulomb transfer and fission in collisions of129Xe,132Xe and136Xe with238U

Integral cross sections for fission and for one- and two-neutron transfer reactions in the system¹³²Xe+²³⁸U were measured radiochemically in the energy range 0.7≦E/E _Coul≦1. The excitation functions for fission and transfer are found to be essentially parallel below 0.85×E _Coul. Even at the lowest energies the transfer cross sections exceed the fission cross section by more than one order of magnitude. With the other projectiles¹²⁹Xe and¹³⁶Xe different transfer cross sections illustrating their sensitivity for the ground stateQ-values,Q _gg , are observed while the fission cross sections are the same as in the¹³²Xe +²³⁸U reaction. The fission data are interpreted in terms of a continuous transition between Coulomb fission and several transfer-induced fission processes.     

Role of the quasiparticle structure in α-decays of superheavy nuclei

The one-quasiparticle structures of nuclei in the α-decay chains of ²⁸⁷114 and ²⁹³116 are studied using a modified two-center shell model. Two-quasiparticle states are revealed in the α-decay chain of even-even nuclei ^286,288114. The calculated values for Q _α are compared to the available experimental data. The termination of the α-decay chains by spontaneous fission is analyzed.     

Nuclear charge radii of Al and Si from elastic electron scattering between 25 and 60 MeV

Elastic electron scattering cross sections of²⁷Al and Si (natural isotopic mixture) have been measured relative to carbon. The rms charge radiiR _m , deduced with partial wave calculations, are (3.01±0.05) fm for²⁷Al and (3.06±0.05) fm for Si, in good agreement with results from muonic X-ray energies. The values given are those for a Fermi charge distribution with skin thickness 2.5 fm; harmonic oscillator shell model distributions yield radii smaller by 0.03 fm. The ratioR _m (²⁷Al)/R_m(Si) is 0.984±0.016.     

On the stability of the nuclei of element 108 withA=263–265

In bombarding²⁰⁹Bi and^{207, 208}Pb targets by⁵⁵Mn and⁵⁸Fe ions the yields of “cold fusion” reactions have been determined using a sensitive technique for detectingT _1/2≧1 ms spontaneous fission and theα-decay of heavy actinide elements. It has been shown that theA = 263–265 isotopes of element 108, including the even-even isotope²⁶⁴108, undergo mainlyα-decay. The obtained results, together with the known data on the properties of the isotopes of elements 104 and 106, provide evidence for the enhanced stability of theZ=108 nuclei against spontaneous fission.     

Cold deformed fission in232U(n,f) and239Pu(n,f)

Masses, charges and kinetic energies of light fission fragments from the reactions²³²U(n, f) and²³⁹Pu(n, f) induced by thermal neutrons have been measured on the Cosi fan tutte spectrometer of the Institut Laue-Langevin in Grenoble. Both at very high and very low kinetic energies marked fine structures in the mass yields and odd-even staggerings in the charge yields are observed. In the framework of a scission point model the results are shown to point to compact and deformed scission configurations, respectively, where at scission the fragments carry no intrinsic excitation energy. The two limiting processes may, therefore, be called cold compact fission (usually known as cold fission) and cold deformed fission. The latter process as a general phenomenon of low energy fission has come into focus only recently.     

Neutron and proton shell closure in the superheavy region via cluster radioactivity in <Superscript>280–314</Superscript>116 isotopes

Based on the concept of cold valley in fission and fusion, the radioactive decay of superheavy^280–314116 nuclei was studied taking Coulomb and proximity potentials as the interacting barrier. It is found that the inclusion of proximity potential does not change the position of minima but minima become deeper which agrees with the earlier findings of Gupta and co-workers. In addition to alpha particle minima, the other deepest minima occur for ⁸Be, ^12,14C clusters. In the fission region two deep regions are found each consisting of several comparable minima, the first region centred on ²⁰⁸Pb and the second is around ¹³²Sn. The cluster decay half-lives and other characteristics are computed for various clusters ranging from alpha particle to ⁷⁰Ni. The computed half-lives for alpha decay match with the experimental values and with the values calculated using Viola-Seaborg-Sobiczewski (VSS) systematic. The plots connecting computed Q values and half-lives against neutron number of daughter nuclei were studied for different clusters and it is found that the next neutron shell closures occur at N = 162, 172 and 184. Isotopic and isobaric mass parabolas are studied for various cluster emissions and minima of parabola indicate neutron shell closure at N = 162, 184 and proton shell closure at Z = 114. Our study shows that ₁₆₂²⁷⁶114 is the deformed doubly magic and ₁₈₄²⁹⁸114 is the spherical doubly magic nuclei.      

Nucleon-content effect on the fission lifetime of excited nuclei

It was shown previously that the fission lifetime of a nucleus excited to about 100 MeV depends strongly and nonmonotonically on the initial value of its angular momentum L ₀. This result was obtained on the basis of a refined version of the combined dynamical and statistical model. The present study is devoted to a theoretical analysis of the dependence of the fission time on the nucleonic composition of the nucleus involved. The respective calculations were performed within the same model. The dependence of the average fission time 〈t _f 〉 on the initial fissility parameter (Z ²/A)₀ appears to be of a resonance type and is similar to its dependence on L ₀. This dependence of the average fission time on (Z ²/A)₀ stems both from statistical calculations and from a dynamical simulation of the fission mode with allowance for friction. The conditions under which the average fission time reaches a maximum are specified. The dependence of the average fission time on (Z ²/A)₀ remains nonmonotonic in the fusion-fission reaction as well, in which case the distribution of compound nuclei with respect to the initial angular momentum is broad.     

Measurement of fast neutron induced fission cross section of thorium using Lexan plastic track detector

Fission-track registration characteristics of Lexan solid state nuclear track detectors have been used to measure the fast neutron induced fission cross section of²³²Th. The fast neutrons (?14.2MeV) were produced with the help of an AN-400 model Van-de-Graaff accelerator at Banaras Hindu University laboratory using³H(²H,n)⁴He reaction and were used to irradiate the fissile target deposited on the plastic detector. The track densityT, registered on the plastic detector is related to the fission cross sectionσ _f, through the relationT=knσ _føt wheren is the number of fissile atoms per cm² in the deposit, ø is the neutron flux,k is fission track registration efficiency andt is the time of irradiation. The fission cross sectionσ _f of²³²Th, relative to the well measured fission cross section of²³⁸U, was found to be 0.36±0.04 barn.