Vol 79, No 6 (2016)

The pairing correlations of the nucleus ¹²⁰Sn are calculated by solving the Nambu–Gor’kov equations, including medium polarization effects resulting from the interweaving of quasiparticles, spin and density vibrations, taking into account, within the framework of nuclear field theory (NFT), processes leading to self-energy and vertex corrections and to the induced pairing interaction. From these results one can not only demonstrate the inevitability of the dual origin of pairing in nuclei, but also extract information which can be used at profit to quantitatively disentangle the contributions to the pairing gap Δ arising from the bare and from the induced pairing interaction. The first is the strong ¹S₀ short-range NN potential resulting from meson exchange between nucleons moving in time reversal states within an energy range of hundreds of MeV from the Fermi energy. The second results from the exchange of vibrational modes between nucleons moving within few MeV from the Fermi energy. Short- (v_p^bare) and long-range (v_p^ind) pairing interactions contribute essentially equally to nuclear Cooper pair stability. That is to the breaking of gauge invariance in open-shell superfluid nuclei and thus to the order parameter, namely to the ground state expectation value of the pair creation operator. In other words, to the emergent property of generalized rigidity in gauge space, and associated rotational bands and Cooper pair tunneling between members of these bands.

We study statistical properties of the 0⁺ spectrum of ²⁰⁸Pb in the energy region E_x ≤ 20 MeV. We use the Skyrme interaction SLy4 as our model Hamiltonian to create a single-particle spectrum and to analyze excited states. The finite-rank separable approximation for the particle–hole interaction enables us to perform the calculations in large configuration spaces. We show that while the position of the monopole resonance centroid is determined by one-phonon excitations of 0⁺, the phonon–phonon coupling is crucial for the description of the strength distribution of the 0⁺ spectrum. In fact, this coupling has an impact on the spectral rigidity Δ₃(L) which is shifted towards the random matrix limit of the Gaussian orthogonal ensembles.

The role of the nucleon correlations in the ground states of even–even nuclei on the properties of low-lying states in odd–even spherical and transitional nuclei is studied. We reason about this subject using the language of the quasiparticle–phonon model which we extend to take account of the existence of quasiparticle⊗phonon configurations in the wave functions of the ground states of the even–even cores. Of paramount importance to the structure of the low-lying states happens to be the quasiparticle–phonon interaction in the ground states which we evaluated using both the standard and the extended random phase approximations. Numerical calculations for nuclei in the barium and cadmium regions are performed using pairing and quadrupole–quadrupole interaction modes which have the dominant impact on the lowest-lying states’ structure. It is found that states with same angular momentum and parity become closer in energy as compared to the predictions of models disregarding the backward amplitudes, which turns out to be in accord with the experimental data. In addition we found that the interaction between the last quasiparticle and the ground-state phonon admixtures produces configurations which contribute significantly to the magnetic dipolemoment of odd-A nuclei. It also reveals a potential for reproducing their experimental values which proves impossible if this interaction is neglected.

A short review on the self-consistent RPA based on the energy-density functional of the Skyrme type is given. We also present an extension of the RPA where the coupling of phonons to the single-particle states is considered. Within this approach we present numerical results which are compared with data. The self-consistent approach is compared with the Landau–Migdal theory. Here we derive from the self-consistent ph interaction, the Landau–Migdal parameters as well as their density dependence. In the Appendix a new derivation of the reduced matrix elements of the ph interaction is presented.

The probabilities for E2 transitions between low-lying excited 3⁻ and 5⁻ single-phonon states in the ²⁰⁸Pb and ¹³²Sn magic nuclei are estimated on the basis of the theory of finite Fermi systems. The approach used involves a new type of ground-state correlations, that which originates from integration of three (rather than two, as in the random-phase approximation) single-particle Green’s functions. These correlations are shown to make a significant contribution to the probabilities for the aforementioned transitions.

For the particle–hole dispersive optical model developed recently, a method is proposed for restoring unitarity weakly violated by a phenomenological description of the spreading effect. The method is implemented by performing a quantitative analysis of the energy-averaged isoscalar monopole double transition density and strength functions over a broad energy range including the isoscalar giant monopole resonance and its overtone in the ²⁰⁸Pb nucleus.

A universal theoretical model intended for calculating internal-bremsstrahlung spectra is proposed. In this model, which can be applied to describing nuclear decays of various type (such as alpha decay, cluster decay, and proton emission), use is made of realistic nucleus–nucleus potentials. Theoretical internal-bremsstrahlung spectra were obtained for the alpha decay of the ²¹⁴Po nucleus, as well as for the decay of the ²²²Ra nucleus via the emission of a ¹⁴C cluster and for the decay of the ¹¹³Cs nucleus via proton emission, and the properties of these spectra were studied. The contributions of various regions (internal, subbarrier, and external) to the internal-bremsstrahlung amplitude were analyzed in detail. It is shown that the contribution of the internal region to the amplitude for internal bremsstrahlung generated in nuclear decay via proton emission is quite large, but that this is not so for alpha decay and decay via cluster emission. Thus, a process in which strong interaction of nuclear particles affects the internal-bremsstrahlung spectrum if found.

A cluster approach is used to describe ground-state-based alternating-parity bands in even–even nuclei and to study the band-termination mechanism. A method is proposed for testing the cluster nature of alternating-parity bands.

Recent experiment by A1 Collaboration at Mainz, namely identification of _Λ⁴H hyperfragment from primary _Λ⁹Li hypernucleus produced in reaction (e, e′K⁺), stirred renewed interest in baryonic decay of hypernuclei. The important role of s⁻¹s_Λ excitation in p-shell hypernuclei as well as the existence of selection rules connected with [f] (Young diagram) was noted earlier within Translational Invariant Shell Model (TISM). The particular conditions of the present experiment (reaction is not selective and produces highly excited states) dictate extension of the simplest TISM: expansion of the harmonic oscillator basis space and compression of multiplets (to only (λμ) for L and [f] for S, T). Such modified TISM explains abundance production of _Λ⁴H hyperfragment and predicts production of another Hyper Hydrogen _Λ⁶H.

In a three-body system, transitions between different sets of normalized Jacobi coordinates are described as general kinematic transformations that include an orthogonal or a pseudoorthogonal rotation. For such rotations, the Raynal–Revai coefficients execute a unitary transformation between three-body hyperspherical functions. Recurrence relations that make it possible to calculate the Raynal–Revai coefficients for arbitrary angular momenta are derived on the basis of linearized representations of products of hyperspherical functions.

Recent results obtained on the basis of the self-consistent theory of finite Fermi systems by employing the energy density functional proposed by Fayans and his coauthors are surveyed. These results are compared with the predictions of Skyrme–Hartree–Fock theory involving several popular versions of the Skyrme energy density functional. Spherical nuclei are predominantly considered. The charge radii of even and odd nuclei and features of low-lying 2⁺ excitations in semimagic nuclei are discussed briefly. The single-particle energies ofmagic nuclei are examined inmore detail with allowance for corrections to mean-field theory that are induced by particle coupling to low-lying collective surface excitations (phonons). The importance of taking into account, in this problem, nonpole (tadpole) diagrams, which are usually disregarded, is emphasized. The spectroscopic factors of magic and semimagic nuclei are also considered. In this problem, only the surface term stemming from the energy dependence induced in the mass operator by the exchange of surface phonons is usually taken into account. The volume contribution associated with the energy dependence initially present in the mass operator within the self-consistent theory of finite Fermi systems because of the exchange of high-lying particle–hole excitations is also included in the spectroscopic factor. The results of the first studies that employed the Fayans energy density functional for deformed nuclei are also presented.