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. Collective isovector 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. Congresso del Dipartimento di Fisica Highlights in Physics –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 What are charge-exchange excitations? 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. 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. pn -1 p p n pn ISOSPIN SYMMETRY particle-hole channel charge-independence and charge-symmetry breaking forces (CIB-CSB), electromagnetic spin-orbit particle-particle channel proton-neutron pairing 3 A. Bohr and B. Mottelson Nuclear Structure vol. 1 (New York: Benjamin 1969 ) 4 T. Babacan et al. J. Phys. G 30, 759 (2004) The operators which rule these transitions are the same of the allowed β-decay: Z N Nuclear charge-exchange transitions from the (N,Z) ground state excite states in the neighbour (N 1,Z 1) 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. ± ± The Isobaric Analog and the Gamow-Teller Resonances The IAR is strictly related to the isospin symmetry, since it belongs to the parent ground state isobaric multiplet: 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). The isospin mixing IVGDR IVGMR IVGQR IVSGMR IVSGDR ΔL=0 ΔL=1 ΔL=2 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. 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). p n p p n n (a)(b) p n n Theoretical framework: the Self-Consistent QRPA Interactions Skyrme effective interaction with all the residual terms In this sense, the method is fully Self-Consistent. Terms neglected in the previous literature have now been included. Self-consistency 1 Restoration of spontaneously broken symmetry Increase in predictive power No spurious contributions Extrapolation to unstable systems HF-BCS QRPA Ground state Excited states Z N Isospin mixing breaking of transition selection rules (appearance of new E1 in N=Z nuclei) influence on superallowed Fermi transitions weak vector coupling constant GV unitarity of Cabibbo-Kobayashi-Maskawa (CKM) matrix 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]. FIGURE 2. Dependence of the Gamow-Teller transition strength in 124 Sn on the strength (in MeV fm 3 ) of the residual isoscalar pairing (left) and on different Skyrme parametrizations (right). The arrow indicates the experimental value of the GT main peak [1]. In the p-p channel, the results for 124 Sn show that isoscalar pairing plays a role, but that here GTR is not sensitive to its strength variation (Fig. 2.a). 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. These results are only sensitive to the charge-breaking terms in the Hamiltonian. 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. These resonances occur at zero angular momentum transfer (ΔL=0) as, respectively, pure isospin and spin-isospin fluctuation. 1 2 IAR GTR 2 S. Fracasso and G. Colò, Phys. Rev. C (in press) 1 2 Z N 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 : 1.the energy density functional is built; 2.subsequent derivatives of provide both the mean-field and the residual interaction, responsible for collective motion. 0°- 2° 1 K. Pham et al. Phys. Rev. C 51, 526 (1995) 118 Sn( 3 He,t) 118 Sb 0°-2°