Langevin description of the charge distribution of fragments originating from the fission of excited nuclei

The charge distribution of fragments originatingfrom the fission of the ²³⁶U compound nucleus is calculated within a stochastic approach based on Langevin equations. The elongation coordinate, the neck-thickness coordinate, and the charge-asymmetry coordinate are chosen as collective variables. The friction parameter of the charge mode is calculated on the basis of two nuclear-viscosity mechanisms, that of one-body and that of two-body dissipation. It is shown that the Langevin approach is applicable to studying isobaric distributions. In addition, the charge distribution in question is studied as a function of the excitation energy of the compound nucleus and as a function of the coefficient of two-body viscosity.     

Theory of mean primary charge distribution in low energy fission of even-even nuclei

A molecular model of fission is introduced in which the compound nucleus before scission is described. The ground state wave function is assumed to be a BCS wave function. The single particle wave functions are expanded in terms of eigenfunctions of the unperturbed spherical fragments. The BCS wave function is determined from the minimum condition for the total energy. The fragment masses, the centers of mass, and the total proton and neutron numbers are kept constant. The resulting BCS and Hartree-Bogoliubov equations are solved approximately within the framework of an extended Nilsson model. The numerical results for the charge distribution in low energy fission of²³⁶U are in agreement with experiments. The heavier (lighter) fragment has on the average 0.5 protons less (more) than expected on the basis of the socalled unchanged charge distribution (UCD). At magic configurations the charge distribution shows characteristic deviations from the average value due to the shell structure of the fragments. The charge distribution seems to result mainly from three competing effects:

1. a)
   from the level density of the unperturbed fragments in the vicinity of the Fermi energy.     
   
   

Isovector coupling channel and central properties of the charge density distribution in heavy spherical nuclei

The influence of the isovector coupling channel on the central depression parameter and the central value of the charge density distribution in heavy spherical nuclei was studied. The isovector coupling channel leads to about 50% increase of the central depression parameter, and weakens the dependency of both central depression parameter and central density on the asymmetry, impressively contributing to the semibubble form of the charge density distribution in heavy nuclei, and increasing the probability of larger nuclei with higher proton numbers and higher neutron-to-proton ratios stable.     

Correlation effects on the charge radii of exotic nuclei

The structures and distributions of light nuclei are investigated within a microscopic correlation model. Two particle correlations are responsible for the scattering of model particles either to low momentum- or to high momentum-states. The low momentum states form the model space while the high momentum states are used to calculate the G-matrix. The three and higher order particle correlations do not play a role in the latter calculation especially if the correlations induced by the scattering operator are of sufficient short range. They modify however, via the long tail of the nuclear potential, the Slater determinant of the (A) particles by generating excited Slater’s determinants.      

Translationally invariant treatment of the charge density in nuclei

An expression is derived for the translationally invariant (transition-) charge density in the center of mass rest frame of the nucleus in between arbitrary wave functions. An explicit formulation is given for the charge density of spherically symmetric Hartree-Fock type ground states. The method is applied to the nuclei⁴He,¹⁶O,⁴⁰Ca and⁹⁰Zr using Woods-Saxon single nucleon orbits for the construction of the ground state wave functions. For the two lighter nuclei in addition realistic Hartree-Fock wave functions are investigated. The results are compared to those obtained with various approximate treatments of the center of mass motion. It turns out that at least in the lighter nuclei the usual center of mass correction, which is based on the assumption of pure non-spurious oscillator configurations and commonly used in the analysis of, e.g., electron scattering data, does not produce reliable (or even predictable) results. Thus here indeed the full translationally invariant treatment seems to be required. For the heavy nucleus⁹⁰Zr on the other hand, as expected, the center of mass effects become negligibly small.     

On the charge distribution of static axial and mirror symmetric monopole systems

It has been shown that the imposition of axial and mirror symmetry on the static magnetic SU (2) Yang-Mills-Higgs system reduces the usual first order (“self-dual”) Bogomolny equations to five equations for five unknown (gauge-invariant) functions. In this note we show that, for a differentiable Higgs field, the five field equations and the topology rule out all charge-distribution along the axis of symmetry except a single-point distribution, and the boundary conditions at the single point distribution are discussed.     

Nuclear charge asymmetry in the a = 3 nuclei

The nuclear charge asymmetry in the A = 3 system is determined by making a perturbative estimate of the direct electromagnetic (e.m.) contribution to the ³He-³H binding energy difference. All local e.m. contributions are estimated in an almost model-independent way using experimental charge form factors and the relation exploited previously by Fabre de la Ripelle and Friar only for the contribution of the static Coulomb interaction. Model-dependent wave functions are used for the contribution of the small non-local terms of the e.m. interaction and the proton-neutron mass difference. Only 81 ± 29 keV of the experimental binding-energy difference has to be attributed to nuclear charge asymmetry, an amount smaller than previous estimates. The nearly model-independent method is used to estimate the contribution of some two-body charge asymmetric potentials, both theoretical and phenomenological, to the binding-energy difference.     

Scenario of charge distributions of f-p shell nuclei

Using the experimental occupation probabilities for the single particle states near the Fermi surface, the charge distribution of⁵⁴Fe,^58–64Ni and^64,66Zn have been calculated on the basis of an optimized one body potential. Excellent agreement with the experimental values have been found both in the case of single particle (-hole) energies and rms charge radii of the nuclei under consideration. Calculated values of Barrett moments and equivalent radii are in good agreement with the experiment. The details of the charge distributions have been evaluated by Fourier-Bessel analysis.The author wishes to thank the Research and Publication Committee of University of Botswana for a research grant. The interesting comments of the respected referee for the betterment of the paper is also acknowledged with thanks.     

Inclusive charge longitudinal response in finite nuclei

The experimental dynamic and static longitudinal structure factors of ¹²C, ⁴⁰Ca and ⁵⁶Fe are investigated with a semiclassical RPA theory.The ph interaction is linked at zero momentum to the nuclear compression modulus and symmetry energy. Its momentum evolution is handled phenomenologically, as well as the position-dependent nucleon effective mass.Quite reasonable values of these quantities allow a satisfactory account of the experimental data over a wide range of momentum transfers in all the three nuclei.In order to achieve this result the proton root mean square radius has to be increased of about 13% in ¹²C, 23% in ⁴⁰Ca and 21% in ⁵⁶Fe.     

Potential and charge deformations in light nuclei

Quadrupole and hexadecapole potential deformations of rotational states in ¹²C, ²⁰Ne, ²⁴Mg, and ²⁸Si, obtained 1543 1083 V 2 using projectiles from p through ¹⁶O, are shown to be consistent with corresponding electromagnetic moments, indicating that strong-interaction and charge deformations in light nuclei are essentially equal.     

A test of charge dependent forces in nuclei

A test of the charge dependence of nuclear interactions based on a fit of Coulomb displacement energies is presented. The results seem to indicate a violation of charge independence comparable or somewhat greater than that found in scattering experiments.     

Study of the charge distribution of galactic cosmic rays and search for superheavy nuclei traces in olivine crystals from meteorites

The search for and identification of energetic nuclei of superheavy elements of cosmic rays in olivine crystals frommeteorites, currently performedwithin the Olympia project [1], are based on measurements of dynamic and geometrical parameters of tracks, i.e., chemically etchable regions of the traces of slowing down of these nuclei before their stop, using the fully automated PAVIKOM measuring system [2].     

Central depression of the nuclear charge distribution

As a systematic feature of all measured charge distributions we find a shift in the form-factor zeroes as compared to a simple folding model. To first order, this shift can be interpreted as resulting from the central depression w, caused by the Coulomb repulsion. Accounting for it leads to an increase in the surface width of nuclear charge distributions by 0.105 fm. This interpretation of the experimental findings is compared with the droplet model, which relates w with the compression modulus K and the asymmetry energy J. Accounting for w leads to an increase in the extrapolated nuclear matter density by 7.5%. However, this macroscopic model is not able to describe the experimental results in detail since w is also influenced by shell effects. HF + BCS calculations with effective Skyrme-type interactions reproduce part of the data, revealing the influence of shells on w. Here, too, there remain discrepancies in details. A level of accuracy is reached at which most probably also the skewness of the charge distribution must be taken into account.     

On the electrodisintegration of nuclei

The kinematical dependences of cross sections for the electrodisintegration of nuclei that is induced by high-energy electrons is studied within the shell model of the nucleus. It is proposed to identify the quantum numbers of nuclear shells by a method that involves the subtraction of quasielastic peaks. The effect of Coulomb resonances and quasireal photons on the formation of angular and energy distributions of electrons and protons in A(e, e′p)(A ? 1) reactions is explored. The phenomenon of quasielastic-peak shift and broadening is interpreted.     

Potential of interaction between nuclei and nucleon-density distribution in nuclei

Nuclear-interaction potentials that are calculated by using Skyrme forces within the extended Thomas-Fermi approximation and Hartree-Fock-Bardeen-Cooper-Schrieffer theory are studied in detail. It is shown that the nuclear component of the potential simulating the interaction between nuclei grows with increasing number of neutrons in colliding isotopes and with increasing diffuseness parameter of the density distribution in interacting nuclei. An increase in the diffuseness parameter of the density distribution in interacting nuclei leads to a decrease in the height of the barrier between the nuclei and to an increase in the depth of the capture well and in the fusion cross section. It is shown that the diffuseness parameter calculated for the nuclear component of the potential at large distance between interacting nuclei by using Skyrme forces exceeds the diffuseness parameter of the nucleon-density distribution in these nuclei by a factor of about 1.5. Realistic values of the diffuseness parameter of nuclear interaction between medium-mass and heavy nuclei fall within the range a ≈ 0.75–0.90 fm.     

Quark distribution in light nuclei

The distribution of quarks in light nuclei is given using the quark cluster wave function. An analytic expression for the nucleus⁴He is obtained. The distribution so obtained is compared with the one obtained using a different theoretical formulation called mapping.     

On the charge distribution in manganese borides studied by X-ray photoelectron and emission spectroscopy

For the borides of the Mn-B system the values of binding energies of Mn 3p, $\text{2p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$, $\text{2}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and B1s core levels were measured on an electron spectrometer. Depending on boride composition the variation of inner level energies is very similar, showing a change of sign in the region of the monoboride phase. The same variation has been observed for some characteristics of X-ray emission spectra from these borides. An attempt is made to understand which of the chemical bonding factors are chiefly responsible for a regular concentration dependence of the X-ray and photoelectron spectra.     

On the charge and shape polarization of fission fragments,fusioning nuclei,or scattering heavy ions near contact

The polarization of the fragments from binary fission or of scattering or fusioning heavy nuclei is investigated in the liquid drop model. Due to the mutual Coulomb repulsion near contact the fragments may be polarized with respect to their charges (electric dipole moments from inhomogeneous charge distributions) as well as with respect to their shapes (quadrupole and octupole deformations). The lowering of the minimum energy near contact due to charge polarization is in the order of 1 MeV if one takes into account the energy from the giant dipole restoring force derived from the volume symmetry energy in addition to the liquid drop energies. The question whether one obtains prolate or oblate shapes is entirely due to the restriction in deformation space (fixed distance between centers-of mass or between the tips of the fragments).