α-decay spectroscopy of deformed nuclei reexamined

We perform an extensive analysis of $\ensuremath{\alpha}$-decays to ${2}^{+}$ and ${4}^{+}$ states in deformed even-even nuclei by using the stationary coupled channels approach. Collective excitations are described within the rigid rotor model. The $\ensuremath{\alpha}$-nucleus interaction is given by a double folding procedure with M3Y plus Coulomb nucleon-nucleon forces. We use a repulsive potential with one independent parameter in order to localize the $\ensuremath{\alpha}$-particle on the nuclear surface and to fit the experimental $Q$-value. The decaying state is identified with the first resonance inside the resulting pocket-like potential, as suggested by microscopic calculations. …

Folding description of the fine structure of α decay to2+vibrational and transitional states

We analyze \ensuremath{\alpha}-decays to ground and ${2}^{+}$ vibrational states in even-even nuclei by using a coupled channels formalism. The \ensuremath{\alpha}-nucleus interaction is simulated by a double folding procedure using M3Y plus Coulomb two-body forces. Collective excitations are described by vibrations of the nuclear surface. We use a repulsive potential, with one independent parameter, in order to simulate Pauli principle and to adjust the energy of the resonant state to the experimental $Q$-value. The decaying state is identified with the zero nodes resonance inside the resulting pocket-like potential. We have found that the fine structure is very sensitive to the strength o…

Description of the two-neutrino ββ decay of100Mo by pnMAVA

The microscopic anharmonic vibrator approach (MAVA) is a scheme where the one- and two-phonon states of an even–even nucleus are treated consistently by using a realistic microscopic nuclear Hamiltonian. This model has recently been extended to describe odd–odd nuclei by adding proton–neutron phonons in a scheme called the proton–neutron MAVA (pnMAVA). In this paper, we apply pnMAVA to compute the nuclear matrix elements corresponding to the two-neutrino double beta (2νββ) decay of 100Mo to the ground state and the first excited 0+ state of 100Ru in a realistic single-particle space. We also compute the GT− and GT+ Gamow–Teller strength functions and compare them with the plain pnQRPA (prot…

Microscopic description of α-like resonances

A description of $\ensuremath{\alpha}$-like resonances is given in terms of single-particle states including narrow Gamow resonances in continuum. The equations of motion are derived within the multistep shell-model approach; the lowest collective two-particle eigenmodes are used as building blocks for the four-particle states. A good agreement with the low-lying states in ${}^{212}\mathrm{Po}$ is obtained. A new technique to estimate the $\ensuremath{\alpha}$-particle formation amplitude for any multipolarity is proposed. The spectroscopic factor of the $\ensuremath{\alpha}$-decay between ground states is reproduced, but the total width is by two orders of magnitude less than the experimen…

Microscopic calculation of the electric decay properties of low-energy vibrational states in even110−120Cdisotopes

Low-lying collective states inRu98–106isotopes studied using a microscopic anharmonic vibrator approach

Anharmonic features of the low-lying collective states in the $^{98--106}\mathrm{Ru}$ isotopes have been investigated systematically by using the microscopic anharmonic vibrator approach (MAVA). MAVA is based on a realistic microscopic $G$-matrix Hamiltonian, only slightly renormalized in the adopted large realistic single-particle spaces. This Hamiltonian is used to derive equations of motion for the mixing of one- and two-phonon degrees of freedom starting from collective phonons of the quasiparticle random-phase approximation. Analysis of the level energies and the electric quadrupole decays of the two-phonon type of states indicates that $^{100}\mathrm{Ru}$ can be interpreted as being a…

Two-neutrinoββdecays and low-lying Gamow-Tellerβ−strength functions in the mass rangeA=70–176

Systematics of the α-decay to rotational states

We analyze \ensuremath{\alpha} decays to rotational states in even-even nuclei by using the stationary coupled channels approach. Collective excitations are described by the rigid rotator model. The \ensuremath{\alpha}-nucleus interaction is given by a double folding procedure using M3Y plus Coulomb nucleon-nucleon forces. We use a harmonic oscillator repulsive potential with one independent parameter, to simulate the Pauli principle. The decaying state is identified with the first resonance inside the resulting pocketlike potential. The energy of the resonant state is adjusted to the experimental Q value by using the depth of the repulsion. We obtained a good agreement with existing experi…

Microscopic description of low-lying two-phonon states: Electromagnetic transitions

Microscopic description of low-lying two-phonon states in even-even nuclei is introduced. The main building blocks are the quasiparticle random-phase approximation (QRPA) phonons. A realistic microscopic nuclear Hamiltonian, based on the Bonn one-boson-exchange potential, is diagonalized in a basis containing one-phonon and two-phonon components, coupled to a given angular momentum and parity. The QRPA equations are directly used in deriving the equations of motion for the two-phonon states. The Pauli principle is taken into account by diagonalizing the metric matrix and discarding the zero-norm states. The electromagnetic transition matrix elements are derived in terms of the metric matrix…

Two-neutrino double-beta decay of76Ge in an anharmonic vibrator approach

We have calculated the nuclear matrix element of two-neutrino double-beta (2???) decay of 76Ge by using the proton?neutron microscopic anharmonic vibrator approach (pnMAVA). In the pnMAVA the wavefunctions of the intermediate 1+ states in 76As have a one-phonon part containing the proton?neutron QRPA (pnQRPA) phonons and a two-phonon part built by coupling the pnQRPA and charge-conserving QRPA phonons. We compare the measured GT? and GT+ Gamow?Teller strength functions with the measured ones. The two-phonon components of the pnMAVA wavefunctions cause the pnQRPA strength to redistribute over a finite energy range. This has only a small effect on the value 2??? nuclear matrix element. This s…

Effective axial-vector strength within proton-neutron deformed quasiparticle random-phase approximation

We use the available experimental Gamow-Teller β− and β+/EC (electron-capture) decay rates between 0+ and 1+ ground states in neighboring even-even and odd-odd nuclei, combined with 2νββ half-lives, to analyze the influence of the nuclear environment on the weak axial-vector strength gA. For this purpose, the proton-neutron deformed quasiparticle random-phase approximation (pn-dQRPA), with schematic dipole residual interaction is employed. The Hamiltonian contains particle-hole (ph) and particle-particle (pp) channels with mass-dependent strengths. In deriving the equations of motion we use a self-consistent procedure in terms of a single-particle basis with projected angular momentum provi…

Study of the low-lying collective states in 94–100Mo isotopes using the MAVA

Abstract A systematic investigation of reduced electric quadrupole decay strengths, B ( E 2 ) and level energies of even 94–100 Mo isotopes is performed using the microscopic anharmonic vibrator approach (MAVA). The MAVA is suited for dynamical microscopic description of two-phonon-like states and their energy splitting due to interaction with low-lying one-phonon states. The starting point for the model is a realistic single-particle valence space and a microscopic many-body Hamiltonian which is used to generate the one-phonon states by the use of the quasiparticle random-phase approximation (QRPA). The same Hamiltonian generates also the interaction between the one- and two-phonon states.…

Microscopic description ofα+40Caquasimolecular resonances

A multistep microscopic approach describing the dynamics of quasimolecular resonances is applied to the $\ensuremath{\alpha}{+}^{40}\mathrm{Ca}$ system. The lowest collective two-particle eigenmodes are used as building blocks of the four-particle states. The pair states are built on mean-field single-particle orbitals including also sharp resonances in continuum. The structure of ${}^{44}\mathrm{Ti}$ is analyzed and strong high-lying $\ensuremath{\alpha}$-like resonances are found in good agreement with the experimentally observed quasimolecular spectrum. The resonances turn out to be very collective and contain mostly proton-neutron pairs where the lowest proton single-particle resonance,…

Two-neutrino ββ decays and low-lying Gamow-Teller β− strength functions in the mass range A=70–176

We apply the proton-neutron deformed quasiparticle random-phase approximation (pn-dQRPA) to describe the low-lying (E 6 MeV) 1+ Gamow-Teller (GT) strength functions in odd-odd deformed nuclei which participate as intermediate nuclei in two-neutrino double-β-decay (2νββ) transitions within the mass range A = 70–176. In deriving equations of motion we use a single-particle basis with projected angular momentum, provided by the diagonalization of a spherical mean field furnished with a quadrupole-quadrupole interaction. The schematic residual Hamiltonian contains pairing and proton-neutron interaction terms in particle-hole (ph) and particle-particle (pp) channels, with constant strengths. By …

Effective axial-vector strength and β -decay systematics

We use the weak axial-vector coupling strength as a key parameter to reproduce simultaneously the available data for both the Gamow-Teller and decay rates in nine triplets of isobars with mass numbers . We use the proton-neutron quasiparticle random-phase approximation (pnQRPA) with schematic dipole interaction containing particle-particle and particle-hole parts with mass-dependent strengths. Our analysis points to a strongly quenched effective value , with a relative error of 28%. We then perform a systematic computation of 218 experimentally known and decays with quite a remarkable success. The presently extracted value of should be taken as an effective one, specific for a given nuclear…