Collective isovector vibrational states, in which protons and neutrons move in

1. 0°- 2° p n p n p n-1 p n-1 n n n n p p Nuclear charge-exchange transitions from the (N,Z) ground state excite states in the neighbour (N 1,Z1) systems. They can spontaneously occur in nature as β-decay or be the nuclear response to an external field in a (p,n) or (n,p) type reaction. (a) (b) ± ± n p p N N Z Z IVGMR IVSGMR ΔL=0 IVGDR IVSGDR ΔL=1 IVSGDR IVGQR ΔL=2 1 2 2 S. Fracasso and G. Colò, Phys. Rev. C (in press) • The general framework is based on the Density-Functional Theory, using a Skyrme force as effective • interaction in the particle-hole (p-h) channel and a density dependent pairing in the particle-particle (p-p) • channel : • the energy density functional is built; • subsequent derivatives of provide both the mean-field and the residual interaction, responsible • for collective motion. HF-BCS Ground state Z N QRPA Excited states Isospin mixing breaking of transition selection rules (appearance of new E1 in N=Z nuclei) influence on superallowed Fermi transitions unitarity of Cabibbo-Kobayashi-Maskawa (CKM) matrix ISOSPIN SYMMETRY weak vector coupling constant GV Congresso del Dipartimento di Fisica Highlights in Physics 2005 11–14 October 2005, Dipartimento di Fisica, Università di Milano Microscopic theory of charge-exchange nuclear excitations S. Fracasso* and G. Colò* * Dipartimento di Fisica, Università di Milano and INFN – Sezione di Milano The Isobaric Analog and the Gamow-Teller Resonances What are charge-exchange excitations? These resonances occur at zero angular momentum transfer (ΔL=0) as, respectively, pure isospin and spin-isospin fluctuation. 0°-2° The operators which rule these transitions are the same of the allowed β-decay: 118Sn(3He,t)118Sb 1 K. Pham et al. Phys. Rev. C51, 526 (1995) The IAR is strictly related to the isospin symmetry, since it belongs to the parent ground state isobaric multiplet: Collectiveisovector vibrational states, in which protons and neutrons move in opposition of phase (T=1), are excited. Besides energy and angular momentum, also a spin transfer can occur (S=1), leading to spin-flip modes. For this reason, the calculation of IAR is a very serious benchmark for testing models. When the Coulomb force and the other charge-breaking forces are switched on in the nuclear Hamiltonian, a strong energy displacement is produced (Fig. 1), without however inducing a large isospin mixing (see below). IAR Theoretical framework: the Self-Consistent QRPA 1 These results are only sensitive to the charge-breaking terms in the Hamiltonian. 2 The linear response theory known as Random Phase Approximation (RPA) is a standard approach to calculate collective nuclear excitations when they occur as small amplitude oscillations of the ground state in magic nuclei. The extension to open shell systems is the Quasiparticle-RPA, which includes the treatment of pairing correlations, responsible for nuclear superfluidity. Solving the QRPA equations, the excited states are written as a linear superposition of two quasiparticle states, the simplest excitations around the Hartree-Fock-Bardeen-Cooper-Schrieffer (HF-BCS) ground state. FIGURE 1.Results obtained [2] for the IAR energy along the Sn isotopic chain by using our model (full dots), compared with the experimental results (open squares) taken from [1]. Unlike the case of IAR, the GTR is sensitive to the choice of the Skyrme parametrization (Fig. 2.b). It should be due to the different treatment of spin and spin-isospin dependent terms of the forces. This could help to improve the understanding of the isospin dependence of the effective interaction, which is still an open question. Besides nuclear structure, it also rules many astrophysical processes. GTR In the p-p channel, the results for 124Sn show that isoscalar pairing plays a role, but that here GTR is not sensitive to its strength variation (Fig. 2.a). In this sense, the method is fully Self-Consistent. Terms neglected in the previous literature have now been included. FIGURE 2.Dependence of the Gamow-Teller transition strength in 124Sn on the strength (in MeV fm3 ) of the residual isoscalar pairing (left) and on different Skyrme parametrizations (right). The arrow indicates the experimental value of the GT main peak [1] . Restoration of spontaneously broken symmetry 1 No spurious contributions Self-consistency Increase in predictive power Extrapolation to unstable systems The isospin mixing The calculation of Fermi transitions allows a microscopic estimation (Fig. 3) of the isospin mixing amount in the parent ground state, defined as the probability to find a |T+1,T> component admixed in the |T,T> ground state. Interactions particle-hole channel 3 A. Bohr and B. Mottelson Nuclear Structure vol. 1 (New York: Benjamin 1969 ) 4 T. Babacan et al. J. Phys. G30, 759 (2004) Skyrme effective interaction with all the residual terms charge-independence and charge-symmetry breaking forces (CIB-CSB), electromagnetic spin-orbit particle-particle channel proton-neutron pairing FIGURE 3. Results obtained for the isospin mixing in the Sn isotopic chain employing different Skyrme parametrizations (full marks), compared with the hydrodinamical estimate [3] (open diamonds) and a phenomenological QRPA [4] (open circles). We have a valuable tool: the calculation of other states is envisaged, in order to extract information about the isovector effective NN interaction and the associated physical observables.