A microscopic study of the dipole giant resonance in fissioning nuclei

Microscopic calculations of the dipole giant resonance in fissioning nuclei give a splitting of the dipole strength into three collective branches, contrary to two branches as predicted by the hydrodynamical model. These collective phenomena have been studied with simplifying separable interactions and sum-rule approaches, and found to be fairly independent of mass number and shell structure. The detailed dependence of excitation energies, dipole strengths and transition densities on the fission coordinate could give rise to interesting phenomena, particularly in electrofission experiments.     

Alpha decay of light nuclei

Theoretical α spectroscopic amplitudes are calculated in jj coupling and isotopic spin formalism. The formulae obtained are applied for calculating the α reduced width amplitudes of the lowest lying 2⁺ levels of ¹⁶O using the shell-model wave functions of Zuker, Buck and McGrory.     

The damping of the giant resonances in heavy and medium-heavy nuclei

The damping of the giant resonances in heavy and medium-heavy nuclei can be described by thermalization and cooling-off processes. The direct emission of particles, which is strongly inhibited by Coulomb and centrifugal barriers is neglected here. In the damping process, which begins with the thermalization, the 1p-1h giant resonance states induced by the incoming electromagnetic field are scattered inelastically due to the presence of two-body residual forces into other 1p-1h and 2p-2h states. In heavy nuclei there exist, at the energy of the giant resonance, several hundreds of such 2p-2h states. The 1p-1h dipole and quadrupole basis states for the diagonalization of the Hamiltonian are obtained from a spherical Nilsson potential. The density of the 2p-2h states obtained from the same potential are then used to determine the energy dependence of the widths of the giant resonances.     

Shell-model study of giant dipole resonances in open-shell nuclei using the Lancgos method

A microscopic investigation of giant-resonance states in open-shell nuclei is proposed using for the representation of the wave functions the shell-model basis in a large model space. Instead of an exact diagonalization of the hamiltonian, which is essentially impossible for the large model spaces considered, an iterative procedure is used, which is based on the Lanczos algorithm for matrix diagonalization. The choice for the initial state in this iteration ensures that the complete transition strength to the resonance of interest is taken into account, and the iteration allows an increasingly accurate estimate of the spreading of this transition strength to more complicate configurations. An application of this method to the giant dipole resonance in ²⁰Ne yields stable results after a few iteration steps and demonstrates the efficiency of this method.     

Five-nucleon spectroscopic amplitudes for 1p-shell nuclei

Spectroscopic amplitudes of the ⁵He or ⁵Li cluster in the ground and first excited states are given for lp-shell nuclei. These Spectroscopic amplitudes are calculated with the aid of intermediate-coupling wave functions of initial and final nuclei. Sum rules for pickup and stripping reactions are presented. The selectivity in excitation of the final states in pickup and stripping reactions of the ⁵He or ⁵Li cluster for some targets are discussed.     

Velocity dependence of the nucleon-nucleon interaction,exchange currents and enhancement of the dipole sum rule in nuclei

A model is employed to describe the velocity dependence of the effective nucleon-nucleon interaction in nuclear matter. The interactions in this model consist of π^? and ρ-meson exchange, together with short-range correlations induced by the strongly repulsive potential resulting from ω-meson exchange. With known coupling strengths, these interactions produce an effective mass $\text{m}{}^1\text{/m = 0.75}$ in nuclear matter.Through the formalism of Fermi liquid theory, the exchange-current correction to the orbital g-factor, δg_l, can be described in terms of the velocity dependence in the neutron-proton interaction, and, within the model, this can be related to the effective mass $\text{m}{}^1$. With $\text{m}{}^1\text{/m = 0.75}$, the δg_l for the proton turns out to be 0.22, 45% of it coming from π-meson exchange.Additional contributions to $\text{m}{}^1\text{/m}$ in nuclei come from the coupling of vibrations to quasiparticles; these are especially important in the nuclear surface, and tend to increase the effective mass, when averaged over both nuclear volume and surface, so that $\text{〈m}{}^1\text{/m〉}{}_{\mathrm{<mtext>av.</mtext>}}\text{? 1}$. In so far as these contributions arise from isovector vibrations, we can use the same model as for π- and ρ-meson exchange, and show that the same relation between $\text{m}{}^1\text{/m}$ and δg_l holds, so that for $\text{〈m}{}^1\text{/m〉}{}_{\mathrm{<mtext>av.</mtext>}}\text{= 1}$, δg_l = 0. The contributions from coupling to vibrations will depend upon the single-particle state, however; states of high-angular momentum will tend to have $\text{〈m}{}^1\text{/m〉}{}_{\mathrm{<mtext>av.</mtext>}}\text{< 1}$ and δg_l > 0.Finally, the enchancement δg_l in gl can be connected with the enhancement k in the dipole sum rule originating from the giant-resonance region. This connection is not very precise, but gives a small positive κ ～ 0.2.     

Coulomb displacement energies and the structure of the low-lying negative-parity states in 2s-1d shell nuclei

Negative-parity states in A = 13–33 nuclei are described as two-component wave functions, one containing a hole in the 1p shell, the other a particle in the 1f–2p shell. The large difference in Coulomb displacement energy (CDE) for both components has been used to determine the relative intensities by fitting the experimental CDE. For the lowest-lying states these intensities are compared to experimental ones derived from spectroscopic factors for pick-up reactions. Strong binding-energy effects seem to play an important role for these states.     

A treatment of renormalization,potential energy of intermediate states and re-arrangement effects in brueckner calculations of closed shell nuclei

In the Brueckner-Hartree-Fock theory of finite nuclei, the problems of renormalization, potential energy of intermediate states and re-arrangement effects are examined. For practical calculations it is shown that satisfactory solutions to them can be obtained if the parametrization chosen for the single-particle potential in finite nuclei is linked closely to nuclear matter results. We make the link with similar problems in the density dependent Hartree-Fock theory and emphasize the possibility of such a parametrization by recalling the existence of a formal solution for the Hartree-Fock single-particle potential if the effective interaction is of the δ-function type. A method of solution of the Bethe-Goldstone equation is then presented which separates the intermediate states into those of an “open shell” and of a “continuum”. Finally results of model calculations of ¹⁶O and ⁴⁰Ca with harmonic oscillator functions are presented in which the parametrization chosen for the BHF single-particle potential is taken from the Skyrme-Vautherin δ-function force. A self-consistent determination of certain parameters of this form of force leads to values in close agreement with the empirical estimate made by Vautherin and Brink in ¹⁶O, with the exception of the spin-orbit splittings. Limitations and possible improvements of this type of approach are discussed for ⁴⁰Ca.     

Investigation of spin dependence of neutron cross sections and of strength functions for rare earth nuclei in experiments with polarized neutrons and nuclei

Experiments on the spin dependence of the interaction of resonance neutrons (up to 100 keV) with the rare earth nuclei ¹⁴¹Pr, ¹⁵⁹Tb, ¹⁶⁵Ho, ¹⁶⁷Er and ¹⁶⁹Tm are reported. The measurements were performed with polarized neutrons and nuclei. The spin dependence of S-wave strength functions was investigated, and the imaginary part of the spin-spin potential (W_ss = 0.10 ± 0.06 MeV) was estimated in optical-model calculations with a potential in the form of a rectangular well. The energy dependence of the difference of strength functions for two J-states shows possible intermediate states in the formation of the compound nucleus. The J-values of about 230 resonances were determined.     

Collective model description of transitional odd-A nuclei: (I). The triaxial-rotor-plus-particle model

The energy spectrum of an odd nucléon coupled to a triaxial rotating core has been calculated as a function of the deformation β, the asymmetry γ and the Fermi energy λ_f. Results are presented in a series of plots with the odd nucleon restricted to a single j-shell and the parameters covering the area which is of most interest for transitional odd-A nuclei in the A = 135 and the A = 190 mass regions. The results apply to unique-parity spectra which are based either on particle or hole states in a. $\text{j =}\text{11}\text{2}$ shell, but hold also for $\text{j =}\text{9}\text{2}\text{and}\text{j =}\text{13}\text{2}$. In addition, results on moments and transition probabilities are given. The quasiparticle-rotor Hamiltonian is derived with special emphasis on the particle-hole symmetry. The analytic solution for the even triaxial rotor at γ = 30° is given. Concerning the odd-A spectrum, characteristics which can be tested experimentally are discussed, and a qualitative physical interpretation is given. In particular, band structures in the triaxial region and their approximate classification are pointed out.     

An analysis of electrodisintegration of nuclei using E1 virtual radiation spectra evaluated with coulomb distorted waves

Data on the ratio of photodisintegration to electrodisintegration of several nuclei (¹²C, ⁶³Cu, ⁶⁴Zn, ¹⁰⁹Ag, ¹⁸¹Ta and ¹⁹⁷Au) are compared with the theoretical ratios predicted by plane-wave and distorted-wave calculations. The analysis with distorted waves shows that all data are compatible with photoabsorption through dominant E1 transitions, as can be explained by the electric dipole sum rule. This outcome does not agree with published conclusions for high Z using the plane-wave approximation.     

T=1, spin-dipole strength in40Ca

Spin-dipole strength in⁴⁰Ca has been studied by inelastic scattering of 500-MeV protons and the dipole response in⁴⁰Ca is compared with the spin-dipole data from the⁴⁰Ca(p, n) reaction and nonspin-dipole data from photonuclear studies.     

Multiparticle emission in the interactions of hadrons with complex nuclei at incident momenta from 2 to 4 GeV/c

The charged secondary particles emitted in inelastic reactions of 4 GeV/cπ⁺ and π^? with the nuclei Be, Cu and Ta are thoroughly studied in their multiplicities, particle correlations and the distributions of kinematical variables, with the 1 m hydrogen bubble chamber into which the three nuclear target plates were installed. The numbers of charged secondaries emitted in the π^?(2.3 GeV/c), π⁺(2 GeV/c) and p(4 GeV/c) reactions are also investigated. From these data, characteristic features of the multiplication process of secondaries in nuclear matter are clarified. The experimental results are compared with the calculation of an intra-nuclear cascade model which takes into account the process of pion absorption by two-nucleon clusters in the nucleus. It is found that the experimental results on the properties of charged secondaries are consistently explained by the model. The model can also give an account of the experimental finding that fairly high momentum protons are emitted from the heavier nuclei into the backward hemisphere in the lab system.     

The lowest five levels of 25Na: Lifetime,spin and transition strength measurements

Particle-gamma angular correlations and lifetime measurements (delayed coincidences and DSAM) have been performed in the ²⁶Mg(t, α)²⁵Na reaction. The results for J^π (and τ_m) are $\text{3}\text{2}{}^{\mathrm{+}}\text{or}\text{5}\text{2}{}^{\mathrm{+}}\text{(7.4±0.4}\text{ns}\text{),}\text{1}\text{2}{}^{\mathrm{+}}\text{(2.3}{}_{\mathrm{?0.8}}{}^{\mathrm{+2.0}}\text{ps}\text{),}\text{3}\text{2}{}^{\mathrm{+}}\text{(<25}\text{fs}\text{),}\text{7}\text{2}{}^{\mathrm{+}}\text{(200±140}\text{fs}\text{)}\text{and}\text{3}\text{2}\text{or}\text{7}\text{2}$ for the levels at 90, 1069, 2202, 2417 and 2788 keV respectively. Branching and mixing ratios have been measured, and strengths of the transitions calculated. Evidence for configuration mixing is given. The results are compared with shell-model calculations.     

(γ, p) cross sections and isospin splitting of the giant dipole resonance in N = 50 nuclei

The differential (e, e'p) cross sections of ⁸⁸Sr, ⁸⁹Y, ⁹⁰Zr and ⁹²Mo have been measured at θ = 90°. The results are used to obtain the (γ, p) cross sections by correcting with the angular distribution data. The (γ, p) cross sections are compared with the (γ, n) cross sections. A resonance corresponding to the T_< GDR is found and another resonance is separated by fitting a Lorentz line with a width equal to that of the (γ, n) GDR. The ratios σ(γ, p)/σ(γ, n) and σ(γ, p₀)/σ(γ, p) show differences between the two resonances. The two GDR resonances are studied from the isospin splitting point of view. The sum rule and splitting energy of the (γ, p) GDR agree well with theory. However, when the sum of the (γ, p) and (γ, n) experimental data is taken, the results are too large to be explained by the T_> GDR.     

A study of the giant dipole resonance of vibrational nuclei in the 103 ≦ A ≦ 133 mass region

This paper presents a set of experimental data concerning the giant dipole resonance of nuclei (GDR) in the 103 ≦ A ≦ 133 mass region. The cross sections σ(γ,n) and σ(γ, 2n) were obtained in the energy region 8–30 MeV by means of a monochromatic photon beam produced by annihilation in flight of positons. This paper attempts also to give an interpretation of the experimental behaviour of the GDR for vibrational nuclei in the 103 ≦ A ≦ 133 mass region in terms of the simple dynamic collective model. In particular it is shown that the width of the GDR increases as β increases and as E₂₊ decreases and that the theoretically predicted spreading of the dipole strength is confirmed by our experimental results. As to the characteristic behaviour of the GDR above its peak value at E₀, we come to the conclusion that the actual state of the art in (γ, xn) research does not allow one to make an unambiguous choice between isospin splitting or electric quadrupole absorption. Finally the numerical evaluations of the different sum rules are given and some empirical results concerning the average energy of the GDR as a function of A are also presented.     

Giant dipole resonance and shape transitions in warm and rapidly rotating nuclei

We discuss the shape transitions in few medium heavy-mass nuclei with emphasis on low-temperature behaviour of the giant dipole resonance (GDR) observables. We employ a macroscopic approach towards GDR in which the GDR observables are related to the nuclear shapes. Shape calculations were done using the cranked Nilsson-Strutinsky method (CNSM) extended to finite temperature. Thermal shape fluctuations are computed with free energies calculated employing Landau parameterization as well as those calculated exactly (without using parameterizations) at given spin and temperature. The results obtained are confronted with the experimental data wherever available. Our study reveals that if the fluctuations are treated properly, then, in spite of thermal fluctuations, GDR observables could very well reflect the shape transitions at low temperature.     

Search for M1 strength in 51V and the difference in 51V(e,e′) and 51V(p,p′) spectra

Following the studies of the distribution of M1 strength in the even-even N = 28 isotones ⁴⁸Ca, ⁵⁰Ti, ⁵²Cr and ⁵⁴Fe by inelastic electron scattering, the result of a search for M1 transitions in the odd-even N = 28 nucleus ⁵¹V is reported. No strong M1 excitation has been detected, in contrast to a recent (p, p') experiment. There is no immediate explanation for this discrepancy. Shell-model calculations indicate that a part of it might be accounted for by an interference between the spin and orbital term of the electromagnetic transition operator in the (e, e') experiment.