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.     

The isovector monopole state and the escape width of double analog resonances

An irreducible vector operator is used to generate isovector monopole states with welldefined values of T and T_z in N > Z nuclei. Reduced transition strengths are calculated in two different ways and the results seem compatible. The Wigner-Eckart theorem is used to derive expressions for the mixing of the monopole states with the ground state and its analog states. Expressions for the escape widths of the monopole states are also derived. An application is made to double analog resonances, and it is found, contrary to expectations, that the mixing with the T?1 monopole state is unable to account for the observed elastic partial width of these resonances in medium and heavy nuclei. The reason for this is the small escape width of the monopole state.     

A microscopic theory of giant electric isovector resonances

The electric multipole isovector (τ = 1) giant resonances for Δτ_z = 0, ± 1 are studied using the self-consistent HF-RPA theory.The distributions of strength, energies, the isospin compositions and other properties of the J = 0⁺, 1^?, 2⁺ resonances in the ⁴⁸Ca, ⁹⁰Zr, ¹²⁰Sn and ²⁰⁸Pb regions are calculated. Sum rules for the charge-exchange Δτ_z = ±1 excitations are derived.     

The radiative capture of fast protons by medium-mass nuclei

High-energy photon spectra were obtained with moderate resolution for a number of neighboring nuclei: ⁵⁶Fe, ⁵⁹Co, ⁵⁸Ni, ⁶⁰Ni, ⁶¹Ni, ⁶³Cu and ⁶⁴Zn in bombardments with protons (8 to 22 MeV). The shapes, magnitudes and energy dependence of the observed spectra are found to be consistent in most of their essential features with the implications of the semidirect model for fast nucleon capture.     

A microscopic description of the negative parity resonances in the mass-4 system by the coupled-channels method (II)

The coupled-channels method for the treatment of the continuum is used to study the negative parity excited states of the ⁴He nucleus in the Tamm-Damcoff approximation. It is shown that the splittings within the SU(4) supermultiplet are well reproduced in this calculation when the spin-dependent forces responsible for the removal of the degeneracy are taken appropriately into account. The location of the T = 0, 1^? resonance and the admixture of spurious c.m. excitation in the intrinsic excitation are discussed. In addition to interpreting the observed spectrum, the available experimental data for the particle channels are well described by the theory.     

A quantum model of collective motion in nuclei and its dequantization

Collective coherent states of Perelomov type are denned by acting with unitary operators from a representation of the symplectic group on the ground state of closed-shell nuclei. A dequantization scheme associates with quantum observables classical ones, and with the state space a phase space and a generalized classical dynamics. Applications to the nuclei ⁴He, ¹⁶O and ⁴⁰Ca are derived from microscopic interactions.     

Application of a microscopic interacting boson model to single-closed-shell nuclei

The microscopic treatment of an extended IBM including the pairing vibrational modes is applied to single-closed-shell nuclei with N = 50 or Z = 50. The low-lying spectra in the N = 50 isotones are well described in terms of the quadrupole phonon and the pairing vibration. The Sn isotopes roughly resemble the N = 50 isotones. The behavior of the 0₂⁺, 0₃⁺ and 2₁⁺ levels can be explained fairly well by the present model. Introduction of the pairing-vibrational modes into the IBM is essential for describing the single-closed-shell nuclei.     

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.     

New method for precise determination of the isovector giant quadrupole resonances in nuclei

The intense, nearly monoenergetic, 100% polarized γ-ray beams available at the HIγS facility, along with the realization that the E1-E2 interference term that appears in the Compton scattering polarization observable has opposite signs in the forward and backward angles, make it possible to obtain an order-of-magnitude improvement in the determination of the parameters of the isovector giant quadrupole resonance (IVGQR). Accurate IVGQR parameters will lead to a more detailed knowledge of the symmetry energy in the nuclear equation of state which is important for understanding nuclear matter under extreme conditions such as those present in neutron stars. Our new method is demonstrated for the case of (209)Bi.     

Giant resonances on excited states

We derive modified RPA equations for small vibrations about excited states. The temperature dependence of collective excitations is examined. The formalism is applied to the ground state and the first excited state of ⁹⁰Zr in order to confirm a hypothesis which states that not only the ground state but every excited state of a nucleus has a giant resonance built upon it.     

Microscopic description of giant resonances in highly excited nuclei

Giant resonances of general multipolarity in highly excited nuclei, which are produced in compound nuclear and deep inelastic heavy ion reactions, are described microscopically in the finite temperature linear response formalism. The linear response function is calculated in the finite temperature (FT) quasi-particle RPA approximation (FT-HFB-RPA) and is based on the corresponding self-consistent quasi-particle basis (FT-HFB). The theory is derived from the small amplitude limit of FT-TDHFB. The inclusion of cranking constraints allows the investigation of giant resonances in nuclei with large intrinsic excitation energy and high spin. A schematic model for the FT-HFB-RPA is developed and applied to the isovector giant dipole resonance in hot spherical nuclei. It is shown that the energy of the resonance depends only weakly on temperature in these systems. The experimentally observed lowering of the giant mode in highly excited nuclei is to be attributed to different effects. The descritpion of resonance damping lies beyond the scope of the random phase approximation. Possible extensions in this direction and qualitative features of the width of giant resonances at finite temperature are discussed.     

Semimicroscopic description of giant octupole resonances in deformed nuclei

The strength functions b(E3, ω) are calculated, and the positions and widths of giant octupole resonances in deformed nuclei are found. It is shown that the giant octupole isoscalar resonances have energies (19–20) MeV for the rare-earth nuclei and (17–18) MeV for the actinides and the widths (5–7) MeV. The energies of the giant octupole isovector resonances are defined by the value of the isovector constant κ⁽³⁾₁.     

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.     

Investigation of α-particle emission from the interactions of fast neutrons with 161Dy and 163Dy nuclei

The energy spectra of α-particles emitted in the ¹⁶¹Dy(n, α)¹⁶¹Gd and ¹⁶³Dy(n,α)¹⁶⁰Gd reactions have been measured at neutron energies equal to 14.1 and 18.2 MeV. The results have been analysed in terms of Hauser-Feshbach, pre-equilibrium and knock-on models. The experimental data can be described assuming the existence of preformed α-clusters in target nuclei and the processes involving only few degrees of freedom.     

Constraining symmetry energy at subnormal density by isovector giant dipole resonances of spherical nuclei

In our previous study, the deduced Langevin equation has been applied to investigate the isoscalar giant monopole resonance. In the current study, the framework is extended to study the isovector giant dipole resonance(IVGDR). The potential well in the IVGDR is calculated by separating the neutron and proton densities based on the Hartree-Fock ground state. Subsequently, the Langevin equation is solved self-consistently, resulting in the centroid energy of the IVGDR without width. The symmetry energy around the density of 0.02 fm~(-3) contributes the most to the potential well in the IVGDR. By comparison with the updated experimental data of IVGDR energies in spherical nuclei, the calculations within 37 sets of Skyrme functionals suggest the symmetry energy to be in the range of 8.13-9.54 MeV at a density of 0.02 fm~(-3).     

The (γ, p0) reactions in the giant dipole resonance region of 51V and 52Cr nuclei

The differential cross sections at 90° for the ⁵¹V(e, p₀)⁵⁰Ti and ⁵²Cr(e, p₀ + p₁)⁵¹V reactions have been measured over the giant dipole resonance region. These cross sections were used to obtain the differential cross sections of the ⁵¹V(γ, p₀)⁵⁰Ti and ⁵²Cr(γ, p₀ + p₁)⁵¹V reactions. The results show two peaks that appear at the same energies as the main peaks of the (γ, n) and (γ, p) cross section for both nuclei. The angular distributions of protons from the (e, p) reaction have also been measured at several points of the incident electron energy. The coefficients A₂ obtained by fitting with a series of Legendre polynomials, W(θ) = 1 + A₁P₁(cos θ)+A₂P₂(cos θ), varies with excitation energy. These results are discussed in terms of the direct-semidirect process considering isospin effects in the giant dipole resonance.     

Electromagnetic transitions in some odd-proton deformed nuclei

In-beam measurements of nanosecond lifetimes applying the method of delayed γ-γ coincidences were performed in the (p, n) reaction. Analysing the time spectra with the centroid shift method, the following half-lives of excited nuclear states in the subnanosecond region could be found: $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(353.2}\text{keV in}{}^{161}\text{Ho}\text{) = 0.52±0.15}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(252.7}\text{keV in}{}^{161}\text{Ho}\text{) ≦ 0.2}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(579.4}\text{keV in}{}^{161}\text{Ho}\text{) ≦ 0.2}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(431.2}\text{keV in}{}^{163}\text{Ho}\text{) = 0.37±0.15}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(439.9}\text{keV in}{}^{163}\text{Ho}\text{) = 0.35±0.15}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(471.3}\text{keV in}{}^{163}\text{Ho}\text{) ? 0.2}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(612.8}\text{keV in}{}^{163}\text{Ho}\text{) ? 0.3}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(295.6}\text{keV in}{}^{171}\text{Lu}\text{) = 0.85±0.20}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(469.2}\text{keV in}{}^{171}\text{Lu}\text{) ≦ 0.2}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(357.0}\text{keV in}{}^{173}\text{Lu}\text{) = 0.40±0.08}\text{ns and}\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(449.0}\text{keV in}{}^{173}\text{Lu}\text{) = 0.58±0.12}\text{ns}$. Following half-lives in ¹⁷³Lu have been remeasured: $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(425.3}\text{keV}\text{) = 0.84±0.20}\text{ns and}\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(434.9}\text{keV}\text{) = 0.38±0.10}\text{ns}$. Absolute γ-ray transition probabilities are deduced and compared with Nilsson model predictions including pairing correlations. Coriolis mixing calculations are performed for K-allowed as well as for K-forbidden transitions.     

Nucleon currents between highly excited nuclei

A finite temperature Thomas-Fermi method has been used to study the nucleon transfer between two hot slabs of symmetric nuclear matter. Special attention has been paid to temperature effects neglected in earlier calculations. As a result, closed and ready-to-use formulas for the exchange and transfer nucleon flux at zero relative momentum are given as a function of the temperature.