Energies and moments of giant resonances for isoscalar monopole and quadrupole excitations: A sum-rule approach

An approach to isoscalar giant resonances in terms of their energy moments is proposed. Besides the well-known moment containing the energy to power plus one, moments with powers plus three and minus one are evaluated. Values for the giant resonance energy and a limit on its width are obtained. The approach systematises and unifies various collective theories, and gives a simple derivation of the quadrupole energy as √2 times the oscillator quantum.     

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.     

Theoretical investigation of giant resonances by inelastic proton scattering

A fully microscopic, antisymmetrized DWBA analysis of (p, p') spectra in the giant resonance region of ¹⁶O, ⁴⁰Ca and ²⁰⁸Pb is presented. The nuclear structure information is derived from RPA wave functions calculated in large configuration spaces. The theoretical spectra are in general in agreement with the experimental results. A new interpretation follows from our. investigation for the spectrum of the giant dipole region in the heavy nuclei: This resonance structure is mainly due to the breathing mode, whereas the electric dipole contribution is much smaller.     

201 MeV proton excitation of giant resonances in 208Pb: Macroscopic and microscopic analysis

The region of the giant resonances in ²⁰⁸Pb has been investigated by inelastic scattering of 201 MeV protons. To test the analysis, angular distributions were measured for the low-lying 3^?, 5^?, 2⁺ and 4⁺ collective states. The giant isoscalar quadrupole resonance (ISGQR) is split into two structures, one at 9.0 MeV with a full width at half-maximum Γ = 1.0 MeV, the other one at 10.6 MeV (Γ = 2.0 MeV), with fine structures at 8.9, 9.3, 10.1, 10.6 and 11 MeV. A macroscopic analysis using the distorted-wave Born approximation (DWBA) leads for the low-lying collective levels, as well as for the ISGQR, to transition probabilities too small by a factor of two, compared with those obtained in other reactions. Microscopic analysis using the distorted-wave impulse approximation (DWIA), with three different sets of random phase approximation (RPA) transition densities, is in very good agreement with the data. At forward angles, in the 12 to 16 MeV excitation energy region, a strong resonance at 13.5 MeV (Γ = 3.6 MeV) is accounted for by the Coulomb excitation of the isovector giant dipole resonance (IVGDR); at larger angles the results are compatible with the excitation of the isoscalar monopole resonance (ISGMR) located at 13.9 MeV (Γ = 2.6 MeV).A resonance located at 21.5 MeV (Γ = 5.7 MeV) appears as the superposition of an isovector quadrupole resonance (IVGQR) excited by Coulomb interaction and a resonance of multipolarity L = 1 ΔT = 0 (ISGDR “squeezing mode”).     

Multipole sum rules and giant resonances with skyrme's interaction

Energy-weighted and inverse energy-weighted (polarizability) sum rules are calculated with Skyrme's effective interaction. The electric dipole, and the isoscalar and isoveetor monopole and quadrupole excitations are considered. A simple analytic treatment of stiffness parameters and giant resonances is given using the Thomas-Fermi approximation. Results are compared with experiment and with other calculations based on RPA.     

The decay of isoscalar giant resonances in 24Mg and 40Ca

In this paper we present data on the charged-particle decay of the isoscalar 2⁺ strength between 10 and 20 MeV excitation energy (E_x) in ²⁴Mg and ⁴⁰Ca. The isoscalar strength was excited by inelastic scattering of 120MeV α-particles at 14° and 12.5° for ²⁴Mg and ⁴⁰Ca, respectively. The charged particles originating from the decay were detected in coincidence with the α′ particles at several angles in the scattering plane. J^π assignments of the decaying states were made on the basis of the angular correlation pattern of the α₀ decay to the ground state of ²⁰Ne and ³⁶Ar, respectively, using a DWBA calculation for the m-state population of the decaying state.For ⁴⁰Ca, about 40% of the E2 EWSR is found to be located in the interval E_x = 13.5 ± 1.5 MeV, which is similar to what has been found from previous inelastic scattering experiments at E_x = 18 ± 2 MeV, but much more than such experiments located in the region E_x = 12–15 MeV. The difference for the region E_x < 16 MeV is due to the fact that from our α₀ angular correlation pattern we conclude that virtually no continuum is excited in the (α, α′) process up to E_x = 16 MeV while all previous inelastic hadron scattering experiments assumed such a continuum to be present. The E2 strength distribution for ⁴⁰Ca thus obtained is very different from what previous theoretical calculations predict. For ²⁴Mg about 30% of the E2 EWSR is present in the interval 12.5 ? E_x ? experiments. 16.5 MeV which again is about twice as much as deduced from previous inelastic scattering The observed branching ratios are compared with calculated ones assuming statistical decay. Reasonable agreement was obtained for ⁴⁰Ca, but for ²⁴Mg especially the α₀-decay branch and to a lesser extent also the p₁ one are much stronger than the statistical calculations predict, indicating that especially the α₀ decay occurs mainly in a non-statistical way.A similar conclusion can be drawn from the behaviour of the forward-backward asymmetry in the angular correlations of the decay particles as a function of the excitation energy FBA(E_x). For ⁴⁰Ca, FBA(E_x) for all decay channels increases smoothly on the average once E_x is above a well-defined threshold, which is due to the onset of knock-out processes. For ²⁴Mg, however, the FBA(E_x) for the α₀ shows a large fluctuation as a function of E_x, indicating an interference process between semi-direct decay and knock-out processes.     

Excitation of low-lying levels and giant resonances in 90Zr via 57.5 MeV polarized proton inelastic scattering

Differential cross section and analyzing power angular distributions have been measured for transitions to low-lying bound states with J^π = 2⁺, 3^?, 4⁺ and 5^?, and the giant resonance region from 6 to 27 MeV excitation energy. Collective model calculations using a full Thomas form factor reproduce the data fairly well. The so-called LEOR turns out not to be seen as pure E3 in (p, p′). In the giant resonance region the data do not reveal the presence of a sizeable monopole strength, 10–20% of the energy-weighted sum rule at most. There is strong indication for a mixture of E2 (18% of the EWSR) and E4 (16% of the EWSR). Calculations were also carried out using RPA (1p1h) wave functions. They reproduce the experimental data rather poorly, except for the general behaviour of the cross-section angular distributions.     

Stripping to analog resonances

Stripping to analog resonances is studied by expressing the DWBA cross section in terms of the resolvent operator appropriate to the system composed of the proton and the target. The resolvent operator is decomposed, by means of the Feshbach projection operator technique, into parts corresponding to the entrance channel, the analog state and the compound states. The approximation scheme is similar to that used in our previous treatment of proton scattering at an analog resonance. The complex proton form factor depends on the Green function satisfying the inhomogeneous Schrödinger equation corresponding to elastic scattering and on the Coulomb potential generated by the target. The method is applied to (³He, d) stripping to analogs in ^{93, 95, 97}Tc.     

Dynamical Thomas-Fermi theory for giant monopole resonances

Transition densities for giant monopole resonances of spherical nuclei are obtained from a linearized fluid dynamical approach. The same semiclassical energy functional is used to calculate self-consistently static and time dependent properties.     

Isomer-shift analogue in neutron resonances

For the first time, the recently predicted chemical shift of neutron resonances, to be regarded as an analogue to the Mössbauer isomer shift, has been experimentally observed studying the 6.67 eV resonance of ²³⁸U. The experimental shifts were determined by a chi-square fitting technique from the time-of-flight transmission spectra of metallic uranium and four uranium compounds measured at the Dubna IBR-30 pulsed reactor. A computational method has been applied to estimate, and compensate for, the influence of the crystal-lattice vibrations on the experimental values thus obtained. The electron density differences at the nucleus have been calculated for the various sample pairs using available data on chemical X-ray shifts in uranium compounds, on Mössbauer isomer shifts in isovalent neptunium compounds and on free-ion electron densities. The resonance shift results lead to the conclusion that the mean-square charge radius of ²³⁸U diminishes by 1.7_?0.8^+1.2 fm² upon capturing the resonance neutron.     

Isovector giant dipole resonances in proton-rich Ar and Ca isotopes

The isovector giant dipole resonances(IVGDR)in proton-rich Ar and Ca isotopes have been systematic-ally investigated using the resonant continuum Hartree-F ock+BCS(HF+BCS)and quasiparticle random phase ap-proximation(QRPA)methods.The Skyrme SLy5 and density-dependent contact pairing interactions are employed in the calculations.In addition to the giant dipole resonances at energy around 18 MeV,pygmy dipole resonances(PDR)are found to be located in the energy region below 12 MeV.The calculated energy-weighted moments of PDR in nuclei close to the proton drip-line exhaust about 4%of the TRK sum rule.The strengths decrease with in-creasing mass number in each isotopic chain.The transition densities of the PDR states show that motions of pro-tons and neutrons are in phase in the interiors of nuclei,while the protons give the main contribution at the surface.By analyzing the QRPA amplitudes of proton and neutron 2-quasiparticle configurations for a given low-lying state,we find that only a few proton configurations give significant contributions.They contribute about 95%to the total QRPA amplitudes,which indicates that the collectivity of PDR states is not strong in proton-rich nuclei in the present study.     

The nucleon-antinucleon interaction and resonances

We present predictions for nucleon-nucleon elastic scattering phase parameters based on a unitary, relativistic, one-pion-exchange model, which takes single-pion-production inelasticity into account. The agreement of the high-L phase shifts with data is considerably improved at intermediate energies by inclusion of the NΔ inelastic channel. Our predicted inelasticities are in generally good agreement with the data, but are smaller than the predictions of Green and Sainio. The Argand plots of the ¹D₂, ³F₃, ³P₁, and ¹G₄ all show counterclockwise motion resulting from the onset of inelastic channels.     

A study of isobaric analogue resonances in 71Ga

Differential cross-section and analysing-power excitation functions were measured for elastic proton scattering from E_p = 3.6–6.4 MeV at θ_c.m. = 90°, 115.8°, 129.8° and 155.3°. Differential cross-section angular distributions were measured at 3.56, 3.94, 5.78 and 8.98 MeV and analysing-power angular distributions at 5.78 and 8.98 MeV. Optical-model parameters were deduced from these distributions. Resonance parameters were determined for eight analogue resonances in ⁷¹Ga and neutron spectroscopic factors were calculated. These were compared with the results of previous (p, p) cross-section analyses and the results of (d, p) reactions leading to states in ⁷¹Zn.     

Alpha capture to the giant dipole resonances of 42Ca, 44Ca and 52Cr

Differential cross sections for the ${}^{38}\text{Ar}\text{(α, γ}{}_0\text{)}{}^{42}\text{Ca}\text{,}{}^{40}\text{Ar}\text{(α, γ}{}_{\mathrm{0,\; 1}}\text{)}{}^{44}\text{Ca and}{}^{48}\text{Ti}\text{(α, γ}{}_{\mathrm{0,\; 1}}\text{)}{}^{52}\text{Cr}$ reactions were measured at 90° to the beam direction in 50 or 100 keV steps over the bombarding energy ranges 6.0–15.0 MeV, 5.5–11.1 MeV and 6.0–12.0 MeV respectively. Gamma-ray angular distributions were measured at forty bombarding energies. These show that the (α, γ₀) reaction proceeds through 1^? levels and to a lesser extent 2⁺ levels, whereas the (α, γ₁) reaction most probably proceeds through 1^? and 3^? levels. It is deduced that 〈Γ〉/〈D〉 ≦ 1 for the ⁴⁰Ar(α, γ)⁴⁴Ca. reaction whereas the fine structure observed in the ⁴⁸Ti(α, γ)⁵²Cr reaction is probably due to fluctuations. From a comparison with other data it is shown that the (α, γ) reaction is most probably statistical in nature. Using Hauser-Feshbach theory it is deduced that the ³⁶Ar(α, γ)⁴⁰Ca. reaction is inhibited by isospin selection rules and an estimate is made of isospin mixing in the ⁴⁰Ca giant dipole resonance. The ${}^{38}\text{Ar}\text{(α, γ)}{}^2{}^{42}\text{Ca and}{}^{40}\text{Ar}\text{(α, γ)}{}^{44}\text{Ca}$ data are considered with respect to theories of isosopin splitting of the giant dipole resonance.     

Proton induced resonances on 21Ne

Excitation curves for the ${}^{21}\text{Ne}\text{(}\text{p}\text{, γ)}{}^{22}\text{Na}\text{,}{}^{21}\text{Ne}\text{(}\text{p, p}\text{′γ)}{}^{21}\text{Ne and}{}^{21}\text{Ne}\text{(}\text{p, p}\text{)}{}^{21}\text{Ne}$ reactions have been obtained for E_p = 0.4–1.6 MeV. Neon gas enriched to 92 % in ²¹Ne was recirculated in a differentially pumped gas target system. The fifteen previously reported (p, γ) resonances were established and nineteen new (p, γ) resonances found. Anomalies in the elastic scattering yield were observed for fourteen resonances. The reported state at E_x = 7278 ± 7 keV in ²²Na was resolved into a doublet separated by 1 keV. All unbound states in ²²Na, observed previously in other reactions, have been confirmed as resonance states in the energy range covered, with the exception of the E_x = 7942 ± 7 keV state. The new E_p = 663, 694, 1235, 1432 and 1543 keV resonances correspond to new unbound states in ²²Na. Excitation energies, γ-ray decay schemes, resonance widths and strengths as well as limits on J^π assignments are reported for all the resonances. From the Coulomb excitation of the E_x = 350 keV, first excited state in ²¹Ne a value of B(E2) = 0.014 ± 0.002 e² · b² is deduced. The astrophysical as well as the nuclear structure implications of the present results are discussed.     

Collisional damping of giant monopole and quadrupole resonances

Collisional damping widths of giant monopole and quadrupole excitations for ¹²⁰Sn and ²⁰⁸Pb at zero and finite temperatures are calculated within Thomas-Fermi approximation by employing the microscopic in-medium cross-sections of Li and Machleidt and the phenomenological Skyrme and Gogny forces, and are compared with each other. The results for the collisional widths of giant monopole and quadrupole vibrations at zero temperature as a function of the mass number show that the collisional damping of giant monopole vibrations accounts for about 30 - 40% of the observed widths at zero temperature, while for giant quadrupole vibrations it accounts for only 20 - 30% of the observed widths at zero temperature. Received: 9 January 2001 / Accepted: 29 March 2001     

Spins of low-energy neutron resonances in 235U

The spins of 15 resonances in the ²³⁵U slow neutron cross section lying in the neutron energy range between 0.1 and 15 eV were determined by measuring the transmission of polarized monoenergetic neutrons through a target in which the ²³⁵U nuclei were polarized. The magnetic moment of ²³⁵U is concluded to be negative.     

Isobaric analogue resonances in proton scattering on Ba

Extensive experimental data for the resonance scatttering of protons to the ground state and first excited state in ¹³⁸Ba are presented. A Breit Wigner analysis with a background term of the form Σ_n(a_n/Eⁿ) is performed and the extracted background function is compared with optical-model calculations using the parameters given in a detailed investigation by Perey. Neutron spectroscopic factors calculated in different ways from this data are compared with the corresponding factors from (d, p). An accurate determination of resonance energies for the first two resonances reveals a deviation from a constant Coulomb shift of the order of 10 keV.     

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.     

The study of the (α, α'f) reaction at 120 MeV on 232Th and 238U: (I). Fission probabilities and angular distributions in the region of the giant quadrupole resonances

The fission decay channel of ²³²Th and ²³⁸U has been investigated, using the (α, α'f) reaction at 120 MeV bombarding energy. The angular distributions of the fission fragments and the fission probabilities up to around 15 MeV excitation have been measured. No evidence for the fission decay of the giant quadrupole resonance has been found, although for ²³⁸U, a weakly excited structure is seen in the (α, α'f) spectrum at about 9.5 MeV excitation at backward angles with respect to the recoil axis. This effect is similar to what has been found in a (⁶Li, ⁶Li'f) experiment reported recently. The over-all feature of the fission probability for excitation energies above the fission barrier are well reproduced by statistical calculations.