The dipole response of proton-rich nuclei

We propose to search for proton dipole pygmy resonances in nuclei near the proton drip line. Experimental evidence only exists for neutron pygmy resonances, but calculations infer the occurrence of proton pygmy resonances in proton-rich nuclei in the mass region A = 30 – 50. According to recent RQRPA calculations, low-lying E1 transitions, well below the giant dipole resonance, reveal the dynamics of excess protons oscillating versus the core. The experiment uses Coulomb projectile excitation of secondary Ar and Ar beams of 700 MeV/u energy from the FRS in-flight separator and the upgraded LAND reaction setup in Cave C. In total, 10 days of beam time are requested. 1. Physics background The occurrence of the pygmy dipole resonances, pictured as the resonant dipole oscillation of a neutron or proton skin against the isospin-symmetric proton-neutron core in exotic nuclei is currently much under debate and subject to theoretical and experimental investigations. In fact, the onset of low-lying E1 strength assigned to a neutron pygmy resonance was already observed in stable nuclei, Ca, Pb [Rye02][End-03][Har-04], and some N=82 isotones [Zil-01], all of which exhibit an only moderate neutron excess. As far as unstable nuclei of large neutron excess are concerned, the LAND collaboration observed a sizeable fraction of low-lying E1 strength in O [Lei-01] and, very recently, in Sn [Adr-05] isotopes. In general, microscopic calculations conclude that in lighter neutron-rich nuclei the low-lying dipole strength is not collective, but arises from single-neutron excitations. In contrast, the low-lying dipole states in (medium-) heavy neutron-rich nuclei such as Sn display to some extent the features of a neutron pygmy resonance [Par-03][Par-05a]. One of the main questions behind studies of neutron skins and, in turn, of skin vibrations such as the dipole pygmy mode is that of the density dependence of the symmetry energy. The density dependence of the symmetry energy is strongly correlated to the skin thickness in heavy nuclei. The slope of the symmetry energy, for instance, was shown to be directly related with the neutron radius in heavy nuclei [Bro-00]. Measurements of neutron radii and thus of skin thicknesses with sufficient precision, however, are presently not available. But recently, it was shown by Piekarewicz [Pie-06] that data on the strength of the pygmy resonance can constrain the density dependence of the symmetry energy: From the pygmy strength observed in our experiment for Sn [Adr-05], Piekarewicz concluded that an overly stiff symmetry energy can be discarded. Turning to proton-rich nuclei, at a first glance, the circumstances for the evolution of low-lying dipole strength and proton pygmy resonance appear less favorable. The proton drip line is much closer to the line of β stability than the neutron drip line, and bound nuclei with an excess of protons over neutrons are found only for nuclei with Z < 50. In addition, because of the presence of the Coulomb barrier, nuclei close to the proton drip line generally do not exhibit a pronounced proton skin, except for very light elements. Since in light nuclei, the multipole response is less collective, all these effects seem to preclude the formation of proton pygmy states. Nevertheless, in a recent publication [Par05b], Paar, Vretenar and Ring showed that according to their calculations, a proton pygmy resonance should clearly evolve in nuclei of mass numbers A = 30 – 50 if located close to the proton drip line. For example, a pronounced proton pygmy resonance is observed in their calculation for the two even isotopes Cr and Fe right at the proton drip line, both, however, out of experimental reach. They performed also calculations for the chain of even-even proton-rich Ar isotopes, see Figs. 1 and 2. Starting from the lightest isotopes, a proton pygmy resonance is revealed in the calculation up to the Ar isotope, for Ar the pygmy strength drops sharply and vanishes for the N=Z nucleus Ar and the heavier isotopes. For the case of Ar, Fig. 2 illustrates that the low-lying states at excitation energies between 8 to 10 MeV indeed exhibit the expected characteristics of a vibrating proton skin. As seen from the transition densities, protons and neutrons in the nuclear interior vibrate in phase while only protons contribute to the transition density at the nuclear surface. The corresponding distributions in the contributing unperturbed2qp Fig.1: The isovector dipole strength distribution in Ar, calculated in the framework of RHB and RQRPA (left panel). In the right panel the mass dependence of the pygmy peak and the corresponding integrated dipole strength below 10 MeV are shown. From [Paa-05b]. Fig. 2: Proton and neutron transition densities (left panel) and RQRPA amplitudes as a function of the unperturbed energies of 2qp configurations (right panel) for selected 1 states [Paa-05b]. The lowest panel is for that a state in the giant dipole regime at 18.01 MeV, the upper panels for states in the energy regime of the pygmy resonance (8.3 – 9.6 MeV). states reflects the fact that the low-lying states in the pygmy domain gain strength, i.e., are of collective nature, and are down shifted. For comparison, Fig. 2 shows also one of the prominent states in the giant dipole resonance energy domain. Ar is the lightest known even Ar isotope, discovered in 1977 [Hag-77]. Its half life of τ1/2=98 ±2 ms and its Gamow-Teller beta decay properties were investigated with high resolution [Bjö-85]. Ar plays an important role in the search for scalar weak interactions in 0→0 decays [Ade-99][Bor-89]. A Coulomb excitation experiment at intermediate energies on Ar determined the strength for the transition to the first excited 2 state [Cot-02] and a precise mass measurement was carried out using ISOLTRAP [Bla-03], serving as a test of the isobaric-multiplet mass equation. From a measurement of the interaction cross section together with results on the optical isotope shifts, a proton-skin thickness of ∆R=0.362±0.221 fm was deduced for Ar (see [Oza-02] and ref. therein). For Ar (τ1/2=845 ms) a value of ∆R=0.132±0.086 fm was derived. Recently further studies of the ground state properties, the occupancy of the 0d5/2 neutron state in Ar have been performed [Gad-04]. In this paper we propose to study the dipole response of Ar over a wide range of excitation energies, covering the region of the predicted pygmy resonance and the giant dipole resonance.