Giant Gamow-Teller resonance in neutron-rich nuclei

The giant Gamow-Teller resonance and other branches of collective nuclear excitations are described on the basis of the theory of finite Fermi systems. A connection between the Gamow-Teller resonance and Wigner SU(4) symmetry is proven. The beta-decay strength function and processes accompanying the β ⁻ decay of neutron-rich nuclei are described. The effect of the satellites of the Gamow-Teller resonance on the decay properties of neutron-rich nuclei is analyzed.     

The Gamow-Teller resonance in finite nuclei in the relativistic random phase approximation

Gamow-Teller (GT) resonances in finite nuclei are studied in a fully consistent relativistic random phase approximation (RPA) framework. A relativistic form of the Landau-Migdal contact interaction in the spin-isospin channel is adopted, which has a vector part as well as a time-like component. This choice ensures that the GT excitation energy in nuclear matter is correctly reproduced in the non-relativistic limit. The GT response functions of doubly magic nuclei ⁴⁸Ca, ⁹⁰Zr and ²⁰⁸Pb are calculated using the parameter set NL3 and g = 0.6. It is found that the effects related to Dirac sea states account for a reduction of 6-7% in the GT sum rule. The quenching of the GT strength in finite nuclei implies that the value of g in the relativistic model might be enlarged about 7%. The time component in the relativistic form of the Landau-Migdal force plays a little role in GT resonance energies.Received: 20 November 2003, Published online: 26 May 2004PACS: 21.60.-n Nuclear structure models and methods - 21.60.Jz Hartree-Fock and random-phase approximations - 24.10.Jv Relativistic models - 24.30.Cz Giant resonances     

Low-lying Gamow-Teller transitions in spherical nuclei

The Pyatov Method has been used to study the low-lying Gamow-Teller transitions in the mass region of 98 ⩽ A ⩽ 130. The eigenvalues and eigenfunctions of the total Hamiltonian have been solved within the framework of proton-neutron quasiparticle random-phase approximation. The low-lying β decay log(ft) values have been calculated for the nuclei under consideration.     

The giant Gamow-Teller resonance states

The mean energy of the giant Gamow-Teller resonance state (GTS) is studied, which is defined by the non-energy-weighted and the linearly energy-weighted sum of the strengths for Σ^A_i = 1^τi?σⁱ? Using Bohr and Mottelson's hamiltonian with the ξl· σ force, the difference between the mean energies of GTS and the isobaric analog state (IAS) is expressed as$\text{E}{}_{\mathrm{GTS}}\text{?E}{}_{\mathrm{IAS}}\text{,≈ 2〈π¦Σ}{}^{\mathrm{A}}{}_{\mathrm{i}}\text{=1ξ}{}_{\mathrm{i}}\text{l}{}_{\mathrm{i}}\text{· σ}{}_{\mathrm{i}}\text{¦π〉/ (3T}{}_0\text{-4(k}{}_{\mathrm{\tau }}\text{?k}{}_{\mathrm{\sigma \tau }}\text{) T}{}_0$. The observed energy systematics is well explained by k_τ?k_{στ≈ 4/A MeV}. The relationship between the mean energies and the excitation energies of the collective states in the random phase approximation for charge-exchange excitations is discussed in a simple model. From the excitation energy systematics of GTS, the values of k_στ and the Migdal parameter g′ are estimated to be about $\text{k}{}_{\mathrm{\sigma \tau }}\text{=}\text{(16–24)}\text{A}\text{MeV and}\text{g′ = 0.49–0.72}$, respectively.     

Giant-dipole resonance and the deformation of hot,rotating nuclei

The development of nuclear shapes under the extreme conditions of high angular momentum and/or temperature is examined. Scaling properties are used to demonstrate universal properties of both thermal expectation values of nuclear shapes as well as the minima of the free energy, which can be used to understand the Jacobi transition. A universal correlation between the width of the giant-dipole resonance and quadrupole deformation is found, providing a novel probe to measure the nuclear deformation in hot nuclei.     

On allowed Gamow-Teller and first-forbidden β-decay in deformed nuclei

A method of evaluating strength functions in the RPA without actually solving the RPA equations is applied to Gamow-Teller β-decay. This method is numerically simpler than the conventional method and is the only practically possible procedure for more complicated applications. Further, we develop a method for solving the strength function (RPA) problem for an interaction which is a sum of several separable interactions. These two methods are then combined and, as an illustration, applied to first-forbidden β-decay.     

On the Fermi and Gamow-Teller strength distributions in medium-heavy mass nuclei

An isospin-self-consistent approach based on the continuum-random-phase approximation (CRPA) is applied to describe the Fermi and Gamow-Teller strength distributions within a wide excitation-energy interval. To take into account nucleon pairing in open-shell nuclei, we formulate an isospin-self-consistent version of the proton-neutron-quasiparticle-CRPA (pn-QCRPA) approach by incorporating the BCS model into the CRPA method. The isospin and configurational splittings of the Gamow-Teller giant resonance are analyzed in single-open-shell nuclei. The calculation results obtained for the ²⁰⁸Bi, ⁹⁰Nb, and Sb isotopes are compared with the available experimental data.     

Damping of the giant dipole resonance in hot,strongly rotating nuclei

The isovector dipole density-density response of hot rotating nuclei is calculated applying a cranked deformed Nilsson potential together with a separable dipole-dipole residual interaction. The transformation of the response function from the internal rotating coordinate frame to the laboratory frame is discussed and illustrated by classical results for a charged particle moving in a harmonic-oscillator potential. Calculations for ¹⁰⁸Sn, ¹⁵²Dy and ¹⁹⁶Pb are presented. For ¹⁰⁸Sn at high excitation energy thermal fluctuations of the shape gives rise to a rather structureless strength function with a considerable width. For ¹⁵²Dy and ¹⁹⁶Pb superdeformed minima of the potential surface are predicted. The coupling of the giant dipole resonance to the shape degrees of freedom of superdeformed nuclei can split the vibration by ≈ 10 MeV, the lowest peak being expected at an excitation energy of ≈ 7–8 MeV and carrying ≈ 30% of the energy-weighted sum rule.     

Chiral two-body currents in nuclei: Gamow-Teller transitions and neutrinoless double-beta decay

We show that chiral effective field theory (EFT) two-body currents provide important contributions to the quenching of low-momentum-transfer Gamow-Teller transitions, and use chiral EFT to predict the momentum-transfer dependence that is probed in neutrinoless double-beta (0νββ) decay. We then calculate for the first time the 0νββ decay operator based on chiral EFT currents and study the nuclear matrix elements at successive orders. The contributions from chiral two-body currents are significant and should be included in all calculations.     

Beta-decay properties of exotic nuclei and the astrophysical r-process

The r-process abundances are evaluated with the use of three different β-decay models, i.e., the second version of the Gross Theory, the semi-Gross Theory and a QRPA approach. The necessary Q_β-values, as well as the neutron separation energies, are obtained from the TUYY, ETFSI and FRDM mass predictions. A comparison is made among the β-decay half-lives predicted by these β-decay models for the nuclei on a typical r-process path, as well as among the resulting r-process abundances.     

Excitation energies of the giant Gamow-Teller resonance states

The energy difference between the giant Gamow-Teller resonance state and the isobaric analog state is estimated by calculating the energy-weighted and the non-energy-weighted sum of the strengths. The observed energy systematics is well reproduced in a simple model assuming κ_στ ≈ 28 MeV.     

Study of the Gamow-Teller resonance in 90Nb and 208Bi

An approach is proposed for studying the spreading properties of the Gamow-Teller resonance (GTR) in heavy nuclei including the coupling to 2p2h configurations and the ground-state correlations beyond RPA. The GTR is generated by a proton p-neutron h (πp-νh) phonon within the renormalized RPA. The second-order configuration mixing beyond RPA is realized by constructing two-phonon configurations, in which one of two intermediate phonon states is a πp-νh phonon. The numerical calculations are performed in the parent nuclei ⁹⁰Zr and ²⁰⁸Pb making use of M3Y nucleon-nucleon interaction and the single-particle wave functions obtained in the standard harmonic oscillator potential. The single-particle energies around the Fermi surface are substituted with the empirical values or those given by a Woods-Saxon potential. The results obtained provide a reasonable account for recent experimental findings on the GTR in these nuclei. The extension of the present approach to highly excited (hot) nuclei is also provided. The GTR is found to be stable against temperatures up to T = 6 MeV.