Characterization of vorticity in pygmy resonances and soft-dipole modes with two-nucleon transfer reactions

The properties of the two-quasiparticle-like soft E1-modes and PDR have been and are systematically studied with the help of inelastic and electromagnetic experiments which essentially probe the particle-hole components of these vibrations. It is shown that further insight in their characterisation can be achieved with the help of two-nucleon transferreactions, in particular concerning the particle-particle components of the modes, in terms of absolute differential cross sections which take properly into account successive and simultaneous transfer mechanisms corrected for non-orthogonality, able to reproduce the experimental findings at the 10% level. The process $^9$Li$(t,p)^{11}$Li(1$^-$) is discussed, and absolute cross sections predicted.Comment: Typo corrected with respect to previous versio

Radioactive beams and inverse kinematics: probing the quantal texture of the nuclear vacuum

The properties of the quantum electrodynamic (QED) vacuum in general, and of the nuclear vacuum (ground) state in particular are determined by virtual processes implying the excitation of a photon and of an electron--positron pair in the first case and of, for example, the excitation of a collective quadrupole surface vibration and a particle--hole pair in the nuclear case. Signals of these processes can be detected in the laboratory in terms of what can be considered a nuclear analogue of Hawking radiation. An analogy which extends to other physical processes involving QED vacuum fluctuations like the Lamb shift, pair creation by $\gamma-$rays, van der Waals forces and the Casimir effect, to the extent that one concentrates on the eventual outcome resulting by forcing a virtual process to become real, and not on the role of the black hole role in defining the event horizon. In the nuclear case, the role of this event is taken over at a microscopic, fully quantum mechanical level, by nuclear probes (reactions) acting on a virtual particle of the zero point fluctuation (ZPF) of the nuclear vacuum in a similar irreversible, no--return, fashion as the event horizon does, letting the other particle, entangled with the first one, escape to infinity, and eventually be detected. With this proviso in mind one can posit that the reactions $^1$H($^{11}$Be,$^{10}$Be$(2^+$;3.37 ${\rm MeV}$))$^2$H and $^{1}$H($^{11}$Li,$^9$Li($1/2^-$; 2.69 ${\rm MeV}$))$^3$H together with the associated $\gamma-$decay processes indicate a possible nuclear analogy of Hawking radiation

Folding and Misfolding of Designed Heteropolymer Chains with Mutations

We study the impact of mutations (changes in amino acid sequence) on the thermodynamics of simple protein-like heteropolymers consisting of N monomers, representing the amino acid sequence. The sequence is designed to fold into its native conformation on a cubic lattice. It is found that quite a large fraction, between one half and one third of the substitutions, which we call 'cold errors', make important contributions to the dynamics of the folding process, increasing folding times typically by a factor of two, the altered chain still folding into the native structure. Few mutations ('hot errors'), have quite dramatic effects, leading to protein misfolding. Our analysis reveals that mutations affect primarily the energetics of the native conformation and to a much lesser extent the ensemble of unfolded conformations, corroborating the utility of the ``energy gap'' concept for the analysis of folding properties of protein-like heteropolymers.Comment: 12 pages, Latex (Revtex

Structure and reactions of 11Be: many-body basis for single-neutron halo

The exotic nucleus 11Be has been extensively studied and much experimental information is available on the structure of this system. Treating, within the framework of empirically renormalised nuclear field theory in both configuration and 3D-space, the mixing of bound and continuum single-particle states through the coupling to collective particle-hole (p,h) and pairing vibrations of the 10Be core, as well as Pauli principle acting not only between the particles explicitly considered and those participating in the collective states, but also between fermions involved in two-phonon virtual states it is possible, for the first time, to simultaneously and quantitatively account for the energies of the 1/2+,1/2- low-lying states, the centroid and line shape of the 5/2+ resonance, the one-nucleon stripping and pickup absolute differential cross sections involving 11Be as either target or residual nucleus, and the dipole transitions connecting the 1/2+ and 1/2- parity inverted levels as well as the charge radius, thus providing a unified and exhaustive characterisation of the many-body effects which are at the basis of this paradigmatic one-neutron halo system.Comment: Supplemental materials include

One- and two- neutron halo at the dripline. From 11Be to 11Li and back: 10Li and parity inversion

The nuclei 11Be and 11Li provide paradigmatic examples of one-and two- neutron halo systems. Because the reaction 1H(11Li,9Li)3H is dominated by successive transfer, one can use the quantitative picture emerging from a nu- clear field theory description of the structure and reaction mechanism of the above Cooper pair transfer process and of the 2H(10Be,11Be)1H and 1H(11Be,10Be)2H reactions, to shed light on the structure of 10Li. This analysis provides important support for a parity inverted scenario with a 1/2+ virtual state at about 0.2 MeV.Comment: Proceedings of the 15th Varenna Conference on Nuclear Reaction Mechanism

The 9Li(d,p) reaction, a specific probe of 10Li, paradigm of parity--inverted nuclei around N=6 closed shell

We show, within the framework of renormalized nuclear field theory and of the induced reaction surrogate formalism, that the highly debated $^{10}$Li structure, observed in a recent $^9$Li(d,p)$^{10}$Li one--neutron transfer experiment is consistent with or better, requires the presence of a virtual $1/2^+$ state of similar single--particle strength than that of the $1/2^-$ resonance at 0.45$\pm$ 0.03 MeV. Based on continuum spectroscopy self-energy techniques, we find that the physical mechanism responsible for parity inversion in $^{10}_3$Li is the same as that at the basis of the similar phenomenon observed in $^{11}_4$Be and to that needed in $^{11}$Li to have an important $s$--wave ground state component. Furthermore, it is also consistent with the (normal) sequence of the $1p_{1/2}$ and $2s_{1/2}$ levels in the $N=7$ isotones $^{12}_5$B and $^{13}_6$C.Comment: Revised text and figures. The paper includes supplemental materia

Inversion Formulas for the Dunkl Intertwining Operator and Its Dual on Spaces of Functions and Distributions

In this paper we prove inversion formulas for the Dunkl intertwining operator $V_k$ and for its dual ${}^tV_k$ and we deduce the expression of the representing distributions of the inverse operators $V_k^{-1}$ and ${}^tV_k^{-1}$, and we give some applications.Comment: This is a contribution to the Special Issue on Dunkl Operators and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

The halo of the exotic nucleus 11Li: a single Cooper pair

If neutrons are progressively added to a normal nucleus, the Pauli principle forces them into states of higher momentum. When the core becomes neutron-saturated, the nucleus expels most of the wavefunction of the last neutrons outside to form a halo, which because of its large size can have lower momentum. It is an open question how nature stabilizes such a fragile system and provides the glue needed to bind the halo neutrons to the core. Here we show that this problem is similar to that of the instability of the normal state of an electron system at zero temperature solved by Cooper, solution which is at the basis of BCS theory of superconductivity. By mimicking this approach using, aside from the bare nucleon-nucleon interaction, the long wavelength vibrations of the nucleus $^{11}$Li, the paradigm of halo nuclei, as tailored glues of the least bound neutrons, we are able to obtain a unified and quantitative picture of the observed properties of $^{11}$Li.Comment: 16 pages, 1 b/w figures, 2 colour figure

Testing two-nucleon transfer reaction mechanism with elementary modes of excitation in exotic nuclei

Nuclear Field Theory of structure and reactions is confronted with observations made on neutron halo dripline nuclei, resulting in the prediction of a novel (symbiotic) mode of nuclear excitation, and on the observation of the virtual effect of the halo phenomenon in the apparently non-halo nucleus $^7$Li. This effect is forced to become real by intervening the virtual process with an external (t,p) field which, combined with accurate predictive abilities concerning the absolute differential cross section, reveals an increase of a factor 2 in the cross section due to the presence of halo ground state correlations, and is essential to reproduce the value of the observed $d \sigma(^7$Li(t,p)$^9$Li)/d$\Omega$.Comment: Submitted to CERN proceedings for the 14th International Conference on Nuclear Reaction mechanisms, Varenna, June 15 - 19, 201