Dynamics of single-particle and collective excitations in heavy nuclei

The propagation of single-particle and small-amplitude collective excitations in a heavy nucleus is considered. We calculate perturbatively corrections to the mean-field approximation induced by the coupling of one-particle and collective motion via the residual particle-hole interaction. Special attention is paid to the energy variation of the quasiparticle effective mass near Fermi energy. We conclude from the calculation that particles and holes excited in low multipolarity giant resonances have average effective masses of the order of 0.8 m rather than m. The mechanism for the decrease is provided by the enforced decoupling of the quasiparticles from surface oscillations due to the high frequency of the giant resonances. We also study the role of surface modes in the decay of giant resonances. Considerable reduction of the damping into 2p-2h states expected from the absorptive part of the optical potential is found. The correlated particle-hole pairs interact with each other by exchanging surface oscillations which adds a destructive interference term to the decay widths of giant resonances. The reduction depends on the multipolarity of the mode and is only large for low angular momenta.     

A STUDY OF THE ISOSCALAR GIANT RESONANCE IN 40Ca

The strength functions of the isoscalar giant resonance monopole resonance and giant quardropole resonance in ⁴⁰Ca are calculated by coupling the 1p-1h states to 2p-2h states. The results can explain the recent experimental data.     

Muonic atoms in the neighbourhood of lead

In a previous paper the electroexcitation of various giant multipole resonances in heavy nuclei has been discussed in Born approximation. This has given only the qualitative features of the cross section, since the electron wave functions in heavy nuclei are considerably distorted by the nuclear charge. Therefore we derive in this paper the corresponding cross sections using a phase shift analysis for the electron wave functions. Moreover, the coupling between giant resonances and surface oscillations has been taken into account. This leads to transitions not only to the several giant resonances itself but also to their “satellites” (i.e. giant resonance plus surface oscillations). Since the giant resonances have rather large widths, the calculated differential cross sections have been folded using a Lorentz shape and plotted against excitation energy. It is shown that the quadrupole giant resonance levels should be observed very clearly at scattering angles of the electron of about 40° (primary energy of the electrons about 200 MeV). It seems, however, unlikely to observe the monopole giant resonance as a distinct peak of the electron cross section because of the relatively large damping to be expected.     

On the damping of giant resonances and the independent propagation of particles and holes

In the literature, damping of nuclear collective motion has been attributed to the imaginary part of the self-energies of particles and holes, when assumed to move independently. We examine this picture within a schematic model adapted to the case of giant resonances. In this model we take degenerate 1p-1h states and dress them by a simple analytical form for the self-energies. We are able to calculate the intrinsic response function analytically and thus to study various approximations. We demonstrate that the on-shell approximation appreciably overestimates the widths of the collective vibrations.     

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.     

Microscopic study of Gamow-Teller and spin-dipole states in 208Bi

Gamow-Teller (GT) and spin-dipole (SD) states in ²⁰⁸Bi are studied by using self-consistent Hartree-Fock + Tamm-Dancoff approximation taking into account the coupling to the continuum. Most of SD strength is found at the excitation energy E _x≈ 25MeV with a very broad width, which agrees with recent experimental observations. It is shown that Landau damping effect is responsible for the large width of SD peak, while the escape width is found to be at most 1MeV. We study also electric dipole (E1) transitions between GT and SD states in ²⁰⁸Bi. Main E1 transitions for 0^- and 1^- states are found near excitation energy expected from Brink's hypothesis in which SD states are considered as E1 resonances built on the GT state. Calculated E1 transition strengths between GT and SD states are compared with the analytic sum rules within one-particle one-hole (1p-1h) configuration space and within both 1p-1h and 2p-2h model space. Received: 11 April 2000 / Accepted: 30 August 2000     

Analysis of E1 and E2 radiative α-capture and giant multipole resonances

Experimental data on E1 and E2 radiative α-capture are analyzed by taking account of direct and semidirect processes as well as the compound process. Observed excitation functions for these reactions are reasonably well reproduced assuming the reactions take place mainly through giant multipole resonances. It is shown that the compound process dominates in the lower energy region especially for E1 capture whereas in the higher energy region direct and semidirect captures are the major processes especially for E2 capture. Several interesting results are obtained on α-particle spectroscopic factors of target ground states and on spreading widths and isospin-mixing coefficients of the giant multipole resonance states. The data are shown to be consistent with the existence of the isoscalar giant quadrupole resonances. The applicability of direct and semidirect capture theories to α-capture is examined.     

Giant dipole resonances of nonmagic nuclei

A method is described for calculating giant dipole resonances of nonmagic nuclei by constructing the nuclear wave functions on the basis of deformed one-particle orbitale. The residual-interaction potential, which is taken into account in the calculation of the dipole states, includes the dependence on the quantum numbers K, which are integrals of motion in this method. Oscillator strengths are calculated as functions of the energy of the giant resonance.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 1, pp. 7–13, January, 1970.     

Damping of single-particle states and giant resonances in208Pb

The damping width of single-particle states and of giant resonances is estimated in ²⁰⁸Pb, based on the excitation of surface modes and T = 1 pairs. The damping is dominated by the collectivity of the surface modes, with the pairing modes playing a weaker role. For both the single-particle states and giant resonances, the predicted damping is somewhat small. This could be due to the neglect of T = 0 particle-particle correlations or to the neglect of the volume modes. The damping for the giant resonances is reduced by the coherence between particle and hole.     

Shell-model calculation with Hartree-Fock condition

Giant resonances and spectroscopic factors of ¹⁶O are studied in the framework of the shell model with (0 + 2)ħω model space. It is found that the Hartree-Fock condition is crucial in order to obtain reasonable excitation energies of giant resonances in ¹⁶O. The calculated spectroscopic factors in ¹⁵N are quenched only by 10% due to the coupling to 1p-2h states. The spectroscopic factor of the s-state in ¹¹B is also discussed.     

Proton capture by 11B above the giant resonance

The cross sections for proton capture by ¹¹B to the ground and excited states of ¹²C have been measured in the proton energy interval between 18 and 43 MeV. The ground-state cross section shows good agreement with theoretical calculations including correlations. Capture photons have also been observed to all the residual 1p-1h states of ¹²C having a dominant $\text{1}\text{p}{}^{\mathrm{?1}}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ hole: the corresponding cross sections systematically show a giant resonance whose energy increases with the increasing excitation energy of the “background” level. The resonances at 27.4, 31, 33.2, 37 and 43 MeV, seem to show observable interference effects.     

Isospin mixing during the decay of the giant dipole resonance: A case-study in 28Si

The magnitude of the isospin mixing in the initial 1p-1h doorway state and in the underlying compound states of the ²⁸Si giant dipole resonance is estimated from (γ, p), (γ, α) and (γ, n) cross sections. From the mixing coefficients, mixing widths of about 40 keV and 25 keV are deduced for the 1p-1h state and for the compound states respectively. This seems to indicate that the isospin mixing widths are roughly independent of the complexity and lifetime of the state involved.     

Total nuclear photon absorption cross sections for some light elements

Absolute nuclear photon absorption cross sections have been measured for the elements Li, Be, C, O, Al, Si and Ca from 10 MeV up to photon energies beyond the meson production threshold. Magnetic Compton spectrometers and a bremsstrahlung spectrum with fixed end-point energy were used. The cross sections show structure in the region of the giant resonance and fall off smoothly towards higher energies. In the giant resonance region recent 1p-1h calculations are in poor agreement with these measurements except for one calculation for carbon, which included low lying excited states of the residual mass-11 system. The cross section in the intermediate region (40 to 140 MeV) can be described by the quasideuteron model with the density of deuteron-like structures taken as 8 NZ/A. The moments of the measured cross sections are compared with sum rule predictions. The integrated cross sections from 10 MeV up to the meson production threshold (140 MeV) exceed the classical dipole sum by a factor of 1.4 to 2.     

A generalized r-matrix interpretation of the 89Y + n total cross section at low incident energies

The resonance structure observed in the ⁸⁹Y(n, n)⁸⁹Y total cross-section measurements in the range of 0.9 to 1.2 MeV neutron energy is investigated using a comprehensive theory of nuclear reactions. A shell-model calculation which formed the initial stage of this study predicts satisfactorily the energies of the negative-parity states that contribute to the observed anomalies. The neutron decay widths for these resonances are evaluated using the model wave functions. The general trends in the energy dependence of the total cross section are satisfactorily reproduced by the theory. The factors that could contribute to the discrepancies between theory and experiment are discussed. The theoretical estimates of the damping widths for the two 1^? anomalies that occur in this region were within 20 to 25% of the experimental values and support the view that these are intermediate-type resonances. Their configurational structure as predicted by the model calculation suggests that they are the parent states of the T_> components of the giant dipole resonance near 21.0 MeV in ⁹⁰Zr. The distribution of E1 widths calculated for a proposed 1^? → 2⁺ (at 0.78 MeV) transition in ⁹⁰Y indicates that an anomaly corresponding to these 1^? states can also be expected in the (n, γ) reaction.     

Influence of one-particle states in the continuum on the low-lying, negative-parity states in O

Balashov's resonance approximation is used to calculate the level shifts and widths of the low-lying, negative-parity states in ¹⁷O, assuming these states to be 2p-1h structure. It turns out that the coupling to one-particle continuum states is very important not only for the widths but also for the positions of most of the levels. The results prove to be very sensitive to the positions of the single-particle resonances in the (2p, 1f) shell.     

Nuclear structure at finite temperature: A review

Information on nuclear structure at finite temperature is obtained from the physics of the level density, of the rotational damping, and of the giant dipole resonance thermally excited on a compound nucleus at very large excitation energy (and angular momentum). The current understanding in terms of mean-field theories and beyond is reviewed. The coupling to doorway states and the coupling to many-particle-many-hole states in the random-matrix-theory limit are discussed. Emph asis will be on the close relation between the single-particle damping and the damping of collective vibrations. The coherence between the particle and the hole strongly suppresses the vibrational damping, in particular, the temperature dependence.     

Role of the nuclear surface in a unified description of the damping of single-particle states and giant resonances

The damping widths of single-particle states and of giant resonances are estimated in spherical nuclei, based on the excitation of surface modes.A Skyrme III interaction with an effective mass consistent with that resulting from infinite nuclear matter calculations with “realistic” forces $\text{(m}{}^1\text{/m = 0.76)}$, was utilized. The single-particle basis needed to construct the unperturbed nuclear response function for each multipolarity was obtained, treating this force in the Hartree-Fock approximation. Diagonalizing a schematic interaction in this basis, the surface modes were calculated. They are used to dress the single-particle and single-hole states and to renormalize the vertex interaction, taking into account the proper energy dependence of the couplings.The essential new feature of the present calculation as compared to the calculations reported in ref.¹) is that the energy dependence of the real and imaginary part of the self-energy is taken into account. This is done utilizing a strength function model.About 70 % of the damping widths arise from the coupling to specific intermediate states containing one low-lying collective surface vibration. The rest, from the coupling to many nonspecific states.Qualitative agreement is found with the experimental data for spherical nuclei throughout the mass table for both the single-particle states and the giant resonances. The model seems however to predict widths which are smaller than those experimentally observed.     

Evidence of an isoscalar E3 giant resonance in 16O

Differential cross sections and analyzing powers for the inelastic scattering of polarized protons from ¹⁶O leading to the 2^? state at 8.88 MeV excitation have been measured at incident energies of 31.7, 33.8, 35.8, 36.8 and 39.9 MeV. These data have been analyzed using a distorted wave theory in which the effects of virtual excitation of E1, E2 and E3 giant resonances as doorway states are included explicitly. This analysis shows that the strong energy variation in the data between 30 and 40 MeV may be predominantly due to a new isoscalar E3 resonance with the contributions from the E1 and E2 resonances corroborating earlier findings.     

相对论核多体理论中的自洽问题和求和规则

着重讨论了建立在相对论平均场基态上的相对论无规位相近似的自洽处理 .自洽处理要求基态和巨共振激发态的研究从同一个拉氏量出发,采用同一种建立在相对论下的完备基上的近似 .同时也讨论了自洽条件下Dirac海核子态的作用 ,指出 Dirac海核子态的贡献不能忽略 ,特别是在核的巨单极共振的情况.用约束的相对论平均场方法得到核的巨单极共振的能量逆权重的求和规则 ,从数值上验证了 Dirac海核子态的贡献. A consistent treatment is extremely important in relativistic approaches. We emphasized the consistent approach in relativistic random phase approximation built on relativistic mean filed ground states. The consistent treatment requires that the studies of the ground state and excited states of giant resonances are based on same effective Lagrangian, and on a same complete set of basis. It was found that the effect of the Dirac states could not be neglected, especially in the case of giant...