Studies of nuclear second moments for pre-equilibrium nuclear reaction theories

The nuclear second moments, important inputs to pre-equilibrium reaction theories, are evaluated by assuming a simple model. The positive definite nature of the second moments is examined, and the nuclear level densities are calculated using positive definite second moments.     

Comments on the state densities and the transition rates in the pre-equilibrium exciton model

It is proposed to renormalize the exciton-state densities used in models for precompound decay such that the summed state densities agree with the expressions employed in equilibrium statistical models. In this way a close fit can be guaranteed between preequilibrium model calculations and the results of equilibrium statistical models for the evaporative stage of the reaction. The consequences of this proposal for the internal transition rates of the pre-equilibrium exciton model are analyzed. The matrix element for the residual interaction is obtained not from a phenomenological parametrization, but from the nucleon mean free path in nuclear matter. It is demonstrated that the proposed renormalization, from one-component Fermi-gas formulas to two-fermion expressions for the state densities, leads to strongly improved agreement of the effective exciton-model values for the nucleon mean free path in nuclear matter with realistic estimates. It is proved that the particle-hole state densities for a two-component Fermi gas, summed over the allowed exciton-state numbers, agree with the phenomenological state-density expressions used in statistical Hauser-Feshbach models.     

Tensor polarization of 6Li(2.186 MeV, 3+) states produced in the reaction 9Be(p, α)6Li* at 40 MeV

A consistent theoretical analysis of polarization moments t _kq is performed for the ⁶Li(2.186 MeV, 3⁺) states produced in the reaction ⁹Be(p, α)⁶Li*. The analysis is based on the distorted-wave Born approximation implemented for finite-range forces with allowance for spin-orbit interaction. The calculated tensor moments are compared with relevant experimental data. Particle-particle angular-correlation functions and tensor moments are shown to provide radically new information about reaction mechanisms and about nuclear interactions.     

Li NMR in lithium borate glasses

In anticipation of using fluctuations in the nuclear dipolar and quadrupolar interaction as a probe of lithium ion motion in lithium borate glasses, the static values of these interactions were measured using a variety of echo techniques. The static quadrupolar echo spectrum of ⁷Li and a calculation of the dipolar interaction in crystalline Li₂B₄O₇ (same chemical composition as the glass under study) were used to estimate the strength of the two interactions. These indicate that the dipolar and quadrupolar interactions for ⁶Li will be of similar size and the dipolar interaction will be dominated by the unlike spin interaction between the ⁶Li and the ¹⁰B, ¹¹B spins. An appropriate theoretical model is proposed and explicit expressions for the echo amplitude are calculated in terms of the dipolar and quadrupolar second moments. This single spin model takes into account the quadrupolar interaction but treats the dipolar interaction as an effective magnetic field. Experimental results are presented which show the essential validity of the model and measurements lead to reasonable values for the dipolar and quadrupolar second moments. The relative merits of the various echo techniques are discussed.     

6Li NMR in lithium borate glasses

In anticipation of using fluctuations in the nuclear dipolar and quadrupolar interaction as a probe of lithium ion motion in lithium borate glasses, the static values of these interactions were measured using a variety of echo techniques. The static quadrupolar echo spectrum of ⁷Li and a calculation of the dipolar interaction in crystalline Li₂B₄O₇ (same chemical composition as the glass under study) were used to estimate the strength of the two interactions. These indicate that the dipolar and quadrupolar interactions for ⁶Li will be of similar size and the dipolar interaction will be dominated by the unlike spin interaction between the ⁶Li and the ¹⁰B, ¹¹B spins. An appropriate theoretical model is proposed and explicit expressions for the echo amplitude are calculated in terms of the dipolar and quadrupolar second moments. This single spin model takes into account the quadrupolar interaction but treats the dipolar interaction as an effective magnetic field. Experimental results are presented which show the essential validity of the model and measurements lead to reasonable values for the dipolar and quadrupolar second moments. The relative merits of the various echo techniques are discussed.     

From the NN interaction to nuclear structure and reactions

We present a novel approach for the treatment of realistic nucleon-nucleon interactions in nuclear many-body systems. A unitary correlation operator is used to explicitly introduce short-range central and tensor correlations in many-body states. The correlated interaction is used as an effective interaction in nuclear structure calculations. Results for Lithium isotopes including proton and neutron distributions, radii as well as magnetic moments and quadrupole moments are shown. Molecular resonances in the ¹⁶O?¹⁶O system are given as a first application in reaction theory.     

Calculations of the excitation functions and isomer ratios of the K(α, n)Sc reaction in the equilibrium and pre-equilibrium statistical models

Angular-momentum effects are incorporated in the pre-equilibrium statistical model using Williams' spin-dependent level density as a function of the particle and hole numbers. Excitation functions and isomer ratios for the ⁴¹K(α, n)⁴⁴Sc reaction are analyzed both in the equilibrium and pre-equilibrium models in the energy range 8 to 40 MeV. Conventional pairing-energy corrections are introduced and their influence on the pre-equilibrium decay is investigated. The results are compared with published experimental data. The best fit was obtained for almost-pure pre-equilibrium decay with the initial excited-particle-plus-hole number n_o = 5 when pairing corrections were taken into account. No success was achieved in fitting the decrease of the isomer ratios at high energies, which is probably caused by the contribution from direct processes.     

Stuty on the Process of the Fast Neutron Radiative Capture for 40Ca and 208Pb

The pre-equilibrium correction for the nuclear reactions induced by fast neutron is considered as follows: the nuclear reaction processes with the exciton number equal to or larger than five can still be described by the statistical theory of the nuclear reaction. The particle emission processes, in which less than five excitons are involved, are calculated by means of the exciton model and the γ emission of one exciton state is calculated by the direct capture mechanism. For the three-exciton state, only the semidirect capture mechanism, which plays the main role in the researched energy region, is taken into account. The interference effect between the direct and semidirect capture is also considered. The radiative capture cross sections for ⁴⁰Ca and ²⁰⁸Pb in the neutron incident energy region from 3 MeV to 20 MeV are calculated and a better coincidence with the experimental values is obtained. At the same time, the contribution to the (n, γ) reaction cross sections of the γ emissions before and after statistical equilibriums as well as the characteristics of the direct capture, semidirect capture and their interferece terms are discussed.     

Pre-equilibrium emission effect in (n,p) reaction cross-sections at 14.8 MeV

The influence of pre-equilibrium emission on (n, p) reaction cross-sections at 14.8 MeV has been studied. Cross-sections for (n, p) reactions have been measured by the activation technique at 14.8 .1; 0.5 MeV neutron energy. The experimental cross-section values have been compared with the calculated values at 14.8 MeV with and without considering the pre-equilibrium emission. Equilibrium calculations have been performed according to the statistical model of Hauser and Feshbach while the hybrid model has been used to include the pre-equilibrium contribution. Pre-equilibrium emission has been considered only in the first emission step. The comparison of experimental and calculated values clearly indicates the presence of pre-equilibrium emission.     

Neutron skin effect of some Mo isotopes in pre-equilibrium reactions

The neutron skin effect has been investigated for even isotopes of molybdenum at 25.6 MeV ^{94 − 100}Mo(p, xn) reaction using the geometry-dependent hybrid model of pre-equilibrium nuclear reactions. Here the initial neutron/proton exciton numbers were calculated from the neutron/ proton densities obtained from an effective nucleon–nucleon interaction of the Skyrme type. Initial exciton numbers from different radii of even Mo isotopes were used to obtain the corresponding neutron emission spectra. In this investigation the calculated results are compared with the experimental data as also with each other. The results using central densities in the geometry-dependent hybrid model are in better agreement with the experimental data.     

Fragmentation and multifragmentation of 10.6A GeV gold nuclei

The experimental data on the interactions of 10.6A GeV gold nuclei in nuclear emulsions are analyzed with particular emphasis of target separation interactions and study of critical exponents. Charged fragment moments, conditional moments as well as two and three – body asymmetries of the fast moving projectile particles are determined in terms of the total charge remaining bound in the multiply charged projectile fragments. Some differences in the average yields of helium nuclei and heavier fragments are observed, which may be attributed to a target effect. However, two and three-body asymmetries and conditional moments indicate that the breakup mechanism of the projectile seems to be independent of target mass. We looked for evidence of critical point observable in finite nuclei by study the resulting charged fragments distributions. We have obtained the values for the critical exponents γ, β and τ and compare our results with those at lower energy experiment (1.0A GeV data). The values suggest that a phase transition like behavior, is observed. Received: 2 July 1998 / Revised version: 26 March 1999     

Further Analysis of Neutron Double-Differential Cross Section of n ＋ ^16O at 14.1 MeV and 18 MeV

By using a new reaction model for light nuclei, the double-differential cross section of total outgoing neutron with LUNF code for n＋^16O reactions at En=14.1 MeV and 18 MeV have been calculated and analyzed. In this paper the opened reaction channels, which have contribution to emitting the neutrons, are listed in detail. To improve the fitting results the direct inelastic scattering mechanism is involved. The calculating results agree fairly well with the experimental data at E,~ = 14.1 MeV and the deviation from calculated results and experimental data in low energy region at En= 18 MeV has been analyzed. Since the possibility of 5He has been affirmed theoretically [J.S. Zhang, Sci. Chin. G 47 （2004） 137], so 5He emission from n＋ ^16O reaction is taken into account, which plays an important role at the region of the outgoing neutron energy εn〈3 MeV in total outgoing neutron energy-angular spectrum. The calculated results indicate that the pre-equilibrium mechanism dominates the whole reaction processes, and the recoil effect in light nuclear reactions is essentially important.     

A many-body calculation of the hyperfine interaction in the lowest2 S and2 P states of li-like systems

A non-relativistic perturbation method of Brueckner-Goldstone type is used to calculate the hyperfine interactions in the lowest² S and² P states of the Li-like systems, Li, Be⁺, B²⁺, C³⁺, N⁴⁺, O⁵⁺ and F⁶⁺. The effect of the polarization of the closed shell is treated to all orders of perturbation, while the correlation effect is calculated in the lowest order, i.e. in the third order of the perturbation expansion. Experimental data are at present available only for Li, Be⁺ and F⁶⁺, and the agreement with the calculated values is in these cases very good, usually within the experimental uncertainties. This implies that the predictions made in the remaining cases should be quite reliable, which may simplify the experimental determination of these quantities. Theoretical values are also given for the quadrupole interaction, which can be used to determine the nuclear quadrupole moments, when accurate experimental information becomes available.     

Rare-earth nuclei and the pseudo-SU(3) model

An extended version of the pseudo-SU(3) model is used to describe low-energy positive-parity states of three rare-earth nuclei in a full proton-neutron formalism. Along with other residual interactions, the Hamiltonian includes the pairing which induces mixing between different representations of SU(3). Excitation energies, B(E2) values, B(M1) values, quadrupole moments, andg _R factors of¹³⁶Xe,¹³⁸Ba, and²⁰⁴Hg are calculated in a truncation free environment and the results are compared with the experimental data and other theories.     

Calculation of excitation functions of the 5 4 , 5 6 , 5 7 , 5 8 Fe(p,n) reaction from threshold to 30 MeV

The cross-sections for the formation of ^54,56,57,58Co in the ^54,56,57,58Fe(p, n) reaction from threshold to 30 MeV protons have been theoretically calculated using the TALYS-1.4 nuclear model code, whereby we have studied major nuclear reaction mechanisms, including direct, pre-equilibrium and compound nuclear reaction. Subsequently, the level density and shell damping parameters have been adjusted and at the same time, the odd–even effects are well comprehended. The excitation functions have been compared with experimental nuclear data. It is observed that the theoretical cross-sections match fairly well. Proton-induced reaction cross-sections provide clues to understand the nuclear structure and offers a good testing ground for ideas about nuclear forces. In addition, complete information in this field is very much required for application in accelerator-driven subcritical system.     

Analysis of Neutron Double-Differential Cross Section of n+14N at 14.2 MeV

By using a new reaction model for light nuclei, the double-differential cross section of n 14N reactions at En = 14.2 MeV has been analyzed. In the case of n 14N reactions, the reaction mechanism is very complex, there are over one hundred opened partial reaction channels even at incident energy En = 14.2 MeV. In this paper the opened reaction channels are listed in detail. With LUNF code the model calculation is performed to analyze the doubledifferential cross sections of total outgoing neutron. The calculated results agree fairly with the experimental data. The results indicate that the pre-equilibrium mechanism dominates the whole reaction processes, and the recoil effect in light nuclear reactions is essentially important. 5He emission has been considered, but it is only a small contribution to the double-differential cross section at incident energy En = 14.2 MeV.     

73Ge NMR spectra in germanium single crystals with different isotopic composition

We have studied the influence of isotopic disorder on the local deformations in Ge single crystals from both experimental and calculation points of view. The nuclear magnetic resonance (NMR) spectra of⁷³Ge nuclei (the nuclear spin equals 9/2) in perfect single crystals of germanium with different isotopic content were measured at temperatures 80, 300 and 450 K. Abnormal broadening of the spectrum was found to occur when the magnetic field was aligned along the [111] axis of a crystal. The observed specific angular dependence of the quadrupole broadening was attributed to isotopic disorder among atoms of germanium sited around the⁷³Ge NMR probe. Local lattice deformations in germanium crystal lattice due to isotopic impurity atoms were calculated in the framework of the adiabatic bond charge model. The results obtained were applied to study random noncubic crystal field interactions with the nuclear quadrupole moments and corresponding effects in NMR spectra. Simulated second and fourth moments of resonance frequency distributions caused by the magnetic dipole-dipole and electric quadrupole interactions are used to analyze the lineshapes, theoretical predictions agree qualitatively with the experimental data.     

The understanding of nuclear structure through Mössbauer experiments

Mössbauer's discovery vitalized the study of hyperfine interactions on nuclear states. The technique has been used to measure the electromagnetic moments of scores of nuclear levels and the results, especially on rotational states, have been important to our understanding of nuclear structure. Equally signicant for nuclear physics has been the deep insight which Mössbauer studies have given us of the hyperfine interaction itself; using that knowledge, and a variety of techniques, the measurements of nuclear magnetic moments are now reliable and routine.     

Collinear laser ion beam spectroscopy

Collinear Laser Ion Beam Spectroscopy (CLIBS) investigates hyperfine structures (hfs) and isotope shifts (IS) in spectral lines and is well suited for the study of nuclear moments of short-lived isotopes. It is fast, highly selective, highly sensitive and allows many experimental alternatives. The high accuracy makes it also an interesting tool for atomic physics. A basic experimental setup is described. Results for nuclear moments and radii in Sm, Eu, Gd show that the accuracy of hfs and IS data is much better than the resulting moments. We discuss the hfs-anomaly and its dependence on atomic quantum numbers (L, S, J) and show that its determination is possible without the knowledge of the nuclear magnetic moments. A hfs-anomaly in respect of the nuclear quadrupole moment was not found. IS-measurements are used to determine permanent and fluctuating nuclear deformation. The standard interpretation is inconsistent in the case of Eu. Modifications of the theory are suggested. Crossed second order (CSO) effects affect the IS values. We show that CSO-effects may help to determine the field effect of the IS experimentally.     

The Second Moments of the Line Shapes of Multiple Quantum NMR Coherences in One-Dimensional Systems

The second moments of the line shapes of the zeroth- and second-order multiple quantum NMR coherences determined by the dipole–dipole interactions of nuclear spins in crystals have been calculated. The second moments determined by the zz part of the dipole–dipole interaction have been derived both by a direct calculation and based on the exact solution (in terms of the zz model) for the decay of the multiple quantum coherence intensities on the evolution period of a multi-quantum NMR experiment. The decay of the multiple quantum NMR coherence intensities in a single crystal of calcium fluorapatite is well described by the Gaussian curves with the calculated second moments.