Effect of entrance channel parameters on fission fragment angular momentum in medium energy fission

Independent isomeric yield ratios of¹³²I were radiochemically determined in alpha particle induced fission of²³⁸U in the energy range 25–44 MeV. Fission fragment angular momenta were deduced from the measured isomeric yield ratios using spin dependent statistical model analysis. It was seen that angular momentum of¹³²I increases with increase of excitation energy and angular momentum of the fissioning nucleus. Comparison of the present data on¹³²I in²³⁸U(α,f) with the literature data for the same product in²³⁸U(p, f) and²³⁸U(γ, f) at various excitation energies show that fragment angular momentum strongly depends on the input angular momentum in the range of excitation energy considered. Experimental fragment angular momentum at all excitation energies were seen to be in agreement with the theoretical values calculated based on thermal equilibration of the various collective rotational degrees after considering the occurence of multichance fission. Thus, strong effect of input angular momentum as well as the statistical equilibration among the various collective rotational degrees of freedom in medium energy fission is corroborated.     

Level density and collective enhancement factor of a compound nucleus in non-adiabatic approach

In this paper a simple statistical formalism that takes into account the diabatic motion of a compound system to calculate total level density is given. The diabatic motion is introduced by coupling the adiabatic collective motion to an environment consisting of intrinsic degrees of freedom. The collective enhancement of level density is studied. It has anadiabatical coefficient that depends only on the excitation energy and adynamical one that depends on the excitation energy and the coupling between intrinsic and collective modes. Qualitatively, the coefficients of the vibrational enhancement factor forA=240 have been studied. The coupling is understood as the initial effect of the oscillatory motion of the mass asymmetry of fragments on the nucleonic motion. The damping effect of the vibrational motion is taken into account considering the collective motion of the fragments as a zero-sound wave propagating in the Fermiliquid. The intrinsic state in the framework of the Fermi Gas Model (FGM) is described. The Pashkevich’s parametrization is used to describe the binary decay of the compound nucleus.     

Excitation energy dependence of fragment characteristics for the photofission of 232Th

Independent and cumulative product yields were measured for the photofission of ²³²Th with bremsstrahlung with endpoint energies 6.5, 7.0, 8.0, 11.0, 12.0, and 14.0 MeV, applying γ spectrometric techniques on catcherfoils and pneumatically transported ²³²Th-samples. The independent heavy fragment yields for the fission of the ²³²Th compound nucleus at excitation energies in the vicinity of the fission barrier were deduced. Postneutron mass, isobaric charge, isotopic mass distributions, isotonic and elemental yield distributions and proton odd-even effects were obtained from these independent yields. In the mass distributions a maximum yield is observed for mass splits with heavy fragments in the region of A = 142, corresponding with a high production of Ba(Z = 56) - isotopes. A slightly increased yield is also observed for mass splits with heavy mass in the vicinity of A = 134. The latter effect increases with increasing compound nucleus excitation energy. The similarity between the mass distributions of the N = 142 fissioning systems ²³²Th, ²³⁴U and ²³⁶Pu is striking. For low excitation energy the proton odd-even effect in the element distributions amounts to 30%, while on the other hand no sizeable neutron odd-even effect could be deduced from the isotonic distributions. The proton odd-even effects remain constant up to compound nucleus excitation energies of about 7.85 MeV. For higher compound nucleus excitation energies the proton odd-even effect drops rapidly. A possible explanation of these observations in terms of pair breaking at the outer barrier is proposed.     

Isotopic invariance of fission fragment charge distributions for actinide nuclei at excitation energies above 10 MeV

The fragment mass and energy distributions from the proton-induced fission of compound nuclei ²³³Pa, ^{234,236,237,239}Np, ^{239,240,241,243}Am, and ²⁴⁵Bk at proton energy E _p =10.3 and 22.0 MeV have been experimentally studied. It was revealed that the shapes of the asymmetric fission mass distributions are mainly defined by the proton numbers of compound nuclei and demonstrate only a weak dependence on the neutron ones. The detailed study of the fission fragment mass yields for compound nuclei Np and Am isotopic chains has shown that the asymmetric fission fragment charge distributions calculated within the unchanged charge density hypothesis for nuclei with equal Z _C practically coincide.     

Influence of the odd neutron on the fragment characteristics in the photofission of 235U

Cumulative and independent post-neutron product yields were measured for the photofission on ²³⁵U with 6.5, 7.0, and 8.4 MeV bremsstrahlung, applying γ-spectrometric methods on catcherfoils and pneumatically transported ²³⁵U-samples. The independent yields for the heavy (A = 128–149) fragments were deduced. Post-neutron mass and isotonic yield distributions were studied together with the elemental yield distributions and the proton odd-even effect. The mass distribution shows about an equal yield for the mass regions around A = 134 (N = 82) and A = 142 (N = 86–88). The proton odd-even effect for the fission of this odd-A nucleus remains at a constant value δ_p = 25% in the studied compound nucleus excitation energy region, indicating that the odd neutron does not influence the energy transfer between the different degrees of freedom during the descent from saddle to scission point in a substantial way.     

Experimental study of some important characteristics of the thermal neutron induced fission of 237Np

Fission fragment mass and kinetic energy distributions and their correlations have been studied for the thermal neutron induced fission of ²³⁷Np. The global mass distribution is rather smooth, apart from a weak shoulder at μ_H = 140–141. When low excitation events are selected, fine structures associated with the charge of the fragments are observed. Furthermore, there is a sudden increase in E_k for μ_H > 155, which is probably due to a spherical shell N = 50 in the light fragment and the corresponding deformed (but stable) heavy fragments with masses in the rare earth region. For the average (pre-neutron emission) total fragment kinetic energy, a value of 176.4 ± 0.6 MeV has been obtained, in agreement with the systematics.Also the prompt neutron emission curve $\text{v(m}{}^1\text{)}$ has been calculated, which shows the well-known saw-tooth shape. Finally, the energy distribution and the emission probability of the ternary α-particles have been determined.     

Division of nuclear charge in the thermal neutron fission of U235

The mean primary nuclear charges of fragments from thermal neutron fission of U²³⁵ as a function of initial mass in the range 88–105 have been determined from theK-ray energy spectra of the light fragments.K- rays were registered with an argon-methane filled proportional counter in coincidence with the pulses from a pair of semiconductor detectors for complementary fission fragments. The deviation of the mean primary charge of the fragments from the “unchanged charge density” value as compared to the density of the parent nucleus U²³⁶ was found to be 0.54±0.14 charge units independent of mass in the range 88–105. No closed shell effect on the mean primary charge was found. Within about 10^?9 sec after fission aK-X ray yield of 0.057±0.012 per fission in the light fragment group was measured. The yields are nearly independant of mass in the range 88–95 corresponding to a value of 0.04 per fragment and increase up to 0.09 in the mass range 95–104, the relative accuracy being 3 to 4%.     

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.     

Spinon and <Emphasis Type="Italic">η</Emphasis>-spinon correlation functions of the Hubbard chain

We calculate real-space static correlation functions of spin and charge degrees of freedom of the one-dimensional Hubbard model that are described by operators related to singly occupied sites with spin up or spin down (spinons) and unoccupied or doubly occupied sites (η-spinons). The spatial decay of their correlation functions is determined using density matrix renormalization group results. The nature and spatial extent of the correlations between two sites on the Hubbard chain is studied using the eigenstates and eigenvalues of the two-site reduced density matrix. The results show that the spinon-spinon correlation functions decay algebraically and the η-spinon correlation functions decay exponentially, both in the half-filling and metallic phases. The results provide evidence that these degrees of freedom are organized in boundstates in the interacting system.     

Effect of shell structure on energy dissipation in heavy-ion collisions

The effect of shell structure on the distribution of the excitation energy between fragments of the deep inelastic collisions is analysed in the microscopic approach. It is shown that the density of the single-particle levels of the proton and neutron subsystems near the Fermi surface determines the ratio between the excitation energies of fragments at the initial stage of the collision. It is shown also that the shell structure strongly influences the correlations between the width of the charge distributions and the total kinetic energy losses. Calculations are performed for the ^40,48Ca+²⁴⁸Cm reactions. The results obtained suggest a possible interpretation for the observed concentration of the excitation energy in the light fragment in deep inelastic collisions for a wide range of the total kinetic energy losses. Received: 27 July 1999 / Accepted: 29 March 2000     

Classical behaviour of the soliton density in Rb2ZnCl4 studied by 87Rb NMR

The temperature dependence of the soliton density n_s(T) which has been studied in Rb₂ZnCl₄ by ⁸⁷Rb NMR could be fitted to a classical formula using only one fit parameter. From our data we cannot confirm recent experimental results which yield a critical exponent $\text{1}\text{2}$ for the soliton density. The results are discussed with respect to the free energy where the soliton density acts as the order parameter. Moreover, couplings to other degrees of freedom, e.g. the elastic strains, are considered.     

Multifragmentation of Gold nuclei in the interactions with photoemulsion nuclei at 10.7 GeV/nucleon

Recent results from the EMU-01/12 collaboration are presented for 10.7 GeV/nucleon gold nuclei interactions in emulsion. The distributions of “bound” charge (Z _bound , Z _b3 ), multiplicity distributions, fragment correlations and fluctuations are discussed. The data are compared to similar results obtained on the ALADIN setup at 600 MeV/nucleon. It is shown that multifragmentation of gold nuclei at high and intermediate energies has common features. It is also obtained that the IMFs have reduced multiplicity at high energies. The data are analyzed within the scope of the statistical model of multifragmentation. This model requires the following predetermined model ingredients: mass, charge and excitation energy of nuclear residuals. The simple estimation method of these characteristics is proposed in the framework of the Glauber approach. It is shown that the multifragmentation model reproduces qualitatively the present data. A dramatic discrepancy between the predicted and experimental yield of two charged fragments is found. The evolution of transverse momentum of fragments as a function of Z _bound is presented. It is shown that the model greatly underpredicts the transverse momentum of fragments. It is interpreted as evidence of a strong radial flow of spectator fragments.     

A transverse gluonium potential model with Breit-fermi hyperfine effects

We introduce a potential model of bound transverse gluons with a fictitious constitutent mass. The gluonic Breit hamiltonian due to one gluon exchange is derived, and its effect on thegg spectrum is estimated; hyperfine corrections are large, but not nonperturbatively so. We find a degenerate (0⁺⁺, 0^?+) ground state and a first 2⁺⁺ excitation at ～1.2M ₀. Our list ofgg states disagrees with some sources, due to the absence of unphysical longitudinal degrees of freedom in the model.     

Charge vibrations in the liquid-drop model of fission

The two-spheroid liquid-drop model of fission developed by Nix and Swiatecki has been extended to include charge vibrations. Using the Myers-Swiatecki mass formula, the appropriate stiffness constants have been obtained in analytic form. The effective mass, M_Δ, associated with charge vibrations for fission shapes was deduced from eigenenergies for the giant dipole resonance calculated by Updegraff and Onley, assuming that the eigenenergy is given by

$\text{h}\text{?}\text{ω}{}_{\mathrm{dipole}}\text{=}\text{h}\text{?}\text{K}{}_{\mathrm{\Delta \Delta }}\text{M}{}_{\mathrm{\Delta }}$

,where K_ΔΔ is the stiffness for charge vibrations. To account for the experimental charge dispersion widths a highly constricted fission shape was chosen. The dependence of fragment deformation energy on mass increases more rapidly than in the Nix and Swiatecki treatment when the eigenvalues of two new normal modes have similar values; it is concluded that this, together with spherical closed-shell effects, may explain the discrepancy between the Nix and Swiatecki values and experimental data. Various other aspects of the effect of charge vibrations are discussed.     

Mean field model with excluded volume correction for a multicomponent hadron gas

A phenomenological mean field formalism developed to incorporate the excluded volume correction arising due to a hard-core repulsion between a pair of baryons has been extended for a multicomponent hadron gas involving strangeness degrees of freedom. The resulting equation of state (EOS) is used to study the medium modifications of the nucleon and hyperon masses with the temperature T and the chemical potential μ. The variations of the effective masses of the baryons with respect to the temperature at μ = 0 shows a striking difference from that obtained in the Walecka model for T > 150 MeV. Similar difference can also be noticed in the variations of the baryon density with temperature.     

The influence of pairing and nuclear structure on the thermal-neutron-induced fission of235U

The mass separated fission product beam provided by the mass separator “Lohengrin” has been used to determine the nuclear charge distribution for the thermal-neutron-induced fission of²³⁵U for all light fission products in the region 80≦A≦107. The measurements were performed at the most probable kinetic energy of the fission products. By using the known fission product mass yields, the independent yields for a total number of 100 nuclides were obtained under the condition of the most probable kinetic energy. The proton pairing effect modulates the average nuclear charge of the fission fragments and the isobaric charge distribution widths in a regular fashion. The probabilities of breaking a pair and of forming fragments with an energetically unfavourable neutron-to-proton ratio are found to compete with each other. Both probabilities depend on the mass split and reach their maximum values in the region of the most probable masses. The odd-even-proton effect is found to vary smoothly between 16% for the most abundant mass splits and 40% for the rare mass splits. The odd-even-neutron effect exhibits maxima nearN=50 andN=60, where it reaches 16%. These maxima and the extremely low Tcyield (0.13±0.05%) are discussed with regard to fragment shell effects.     

Isospin and symmetry energy effects on nuclear fragment production in liquid-gas-type phase transition region

We have shown that the isospin of nuclei influences the fragment production during the nuclear liquid-gas phase transition. Calculations for Au¹⁹⁷, Sn¹²⁴, La¹²⁴ and Kr⁷⁸ at various excitation energies were carried out on the basis of the statistical multifragmentation model (SMM). We analyzed the behavior of the critical exponent τ with the excitation energy and its dependence on the critical temperature. Relative yields of fragments were classified with respect to the mass number of the fragments in the transition region. In this way, we have shown that nuclear multifragmentation exhibits a “bimodality” behavior. We have also shown that the symmetry energy has a small influence on fragment mass distribution; however, its effect is more pronounced in the isotope distributions of produced fragments.     

Nuclear charge distribution of heavy fission fragments from thermal-neutron-induced fission of235U

Fragments from thermal-neutron induced fission of²³⁵U have been separated by a mass spectrometer with respect to their masses and kinetic energies within 1 μsec. The separation principles are briefly described. For masses 130 to 139 amu the charge distributions have been determined by counting the number of beta tracks emitted from the individual mass selected fission fragments in a nuclear photographic emulsion. In another method, the average number of beta particles for each fragment mass is determined by use of a 4π-proportional counter. The mean nuclear charge as a function of mass is compared with other experimental results and theoretical curves. Contradictory to the radiochemical results, this experiment yields a dip in the mean nuclear charge versus mass curve at mass 132 amu corresponding to the doubly magic nucleus (N=82,Z=50)¹³²Sn. Recent theoretical calculations of Nörenberg are in agreement with this finding.     

Threshold dependence of the vibrational excitation of molecules on laser radiation intensity

The collisionless vibrational excitation of a polyatomic molecule in an IR laser radiation field has been theoretically studied. It has been shown that (i) the degree of vibrational excitation (namely, number 0000 of vibrational quanta of a molecular mode near-resonant with the IR laser field that are absorbed by the molecule) is low if laser pulse intensity P (energy flux density in the laser beam) is lower than a certain critical value P _cr; (ii) the degree of excitation abruptly increases after crossing the boundary where P = P _cr; (iii) this effect is attributed to two properties inherent in polyatomic molecules, namely, the anharmonicity of the vibrational mode interacting with the laser field and the energy exchange with other modes; and (iv) at P > P _cr, number 00000 is determined only by energy density Φ = Pτ_P, where τ_P is the laser pulse duration, 00000 monotonically increases with increasing Φ. The model is in good agreement with the experimental data.     

Design and commissioning of a timestamp-based data acquisition system for the DRAGON recoil mass separator

The fission fragment mass distribution followed by neutron emission is studied for the ²³⁸U(¹⁸O,f) reaction using the asymmetric two-center shell model. Within the thermodynamic approach, excitation energy carried by the compound nucleus is dissipated in the emission of a pair of neutrons in several consecutive steps. Therefore, we have considered 2–12 (in step of 2) neutron emission channels in our formalism. The mass distribution corresponding to 8-neutron emission channel compares reasonably well with the experimental data. The observed fine structure dips corresponding to shell closure (Z = 50 and N = 82 of individual fission fragment arise mainly due to shell structure in the mass parameters. However, an exact location and magnitude of the dip at A = 124 in the mass distribution depends on how the temperature modifies masses and, also, on the precise information of pre- and post-neutron emission data. This suggests a possible importance of extending these calculations to get new insight into an understanding of the dynamical behaviour of fragment formation in the fission process.