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We study the spatial correlations between two particles (or two holes) around a closed shell core in terms of the probability distribution expressed as a function of the c.m. coordinate R of the two particles and of their relative coordinate r. We find that the mixing of configurations induced by the pairing force leads to a probability distribution centered in regions corresponding to larger values of R and smaller values of r, as compared to the case of a pure (j)02 configuration. This tendency to a "surface clustering" is mainly due to the interference of the contributions coming from levels with different parity. However, even with the inclusion of a large number of configurations, the size of the localized "cluster" is much larger than that of a free dinucleon system. NUCLEAR STRUCTURE Pairing correlations, correlation in space, two-particle transfer reactions.Two-particle transfer reactions are usually considered a typical tool for the study of particle-particle correlations in nuclei. In such reactions [we are thinking, in particular, of reactions induced by light ions, such as (p, t), (t,p), or (3He, n)] a dinucleon system with J = 0, very confined in space, is transferred on to (or from) the nuclear surface. It is, therefore, of interest to study to what extent the pairs of particles in the nucleus move closely in space toward each other, in particular in the surface region, where the Pauli principle is less effective and the probability of formation of few-nucleon correlated substructures should increase. We want to clarify the effect on this correlation in space of the particle-particle residual interaction, which is known to strongly enhance the two-particle transfer cross section. This should shed some light on the more general problem of the relation between correlations in spin, isospin, and angular momentum and clusterization in space.We consider the case of two identical particles (or two holes), coupled to angular momentum I = 0 and moving in single particle orbitals around a closed-shell core. The problem has been approached in Refs. 2 and 4 by selecting the S =0 part of the two-particle wave function and assuming the two particles at equal distance from the center of the nucleus, and then studying the behavior of the two-particle wave function as a function of the relative angle between I be the general antisymmetrized wave function describing the two-particle system. The index o. stands for the set [n I j ) of quantum numbers characterizing the single particle wave function +"t/ ( r, X) =@. ]/(r)[ I ]( f) X]/2( X)ljIn order to study the spatial correlations between the two particles we introduce the coordinates R =~r ]+ r q~/J2 and r =~r ] -r q[/v 2 associated with the center of mass and relative motion, respectively, and consider the probability distribution P(r, R) = &~' P( r ], X]', r q, Xq)~r R dr" dR dX]dXqIn the case of harmonic oscillator (HO) wave functions the coordinate transformation and the integration over the angular variables can be performed analytically and the probability di...

The absolute decay width of a single-particle level in a deformed potential is evaluated exactly. Experimental data are analyzed by using the formalism developed here. It is found that proton decay is a powerful tool to determine the deformation of nuclei as well as to probe small components of the wave functions of the decaying states. This will allow one to study the behavior of single-particle resonances in nuclei close to the drip line, and may guide future experiments. [S0031-9007(98)

The lifetimes of the first excited states of the N = 30 isotones (50)Ca and (51)Sc have been determined using the Recoil Distance Doppler Shift method in combination with the CLARA-PRISMA spectrometers. This is the first time such a method is applied to measure lifetimes of neutron-rich nuclei populated via a multinucleon transfer reaction. This extends the lifetime knowledge beyond the f_{7/2} shell closure and allows us to derive the effective proton and neutron charges in the fp shell near the doubly magic nucleus (48)Ca, using large-scale, shell-model calculations. These results indicate an orbital dependence of the core polarization along the fp shell.

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The neutron-rich lead isotopes, up to 216 Pb, have been studied for the first time, exploiting the fragmentation of a primary uranium beam at the FRS-RISING setup at GSI. The observed isomeric states exhibit electromagnetic transition strengths which deviate from state-of-the-art shell-model calculations. It is shown that their complete description demands the introduction of effective three-body interactions and two-body transition operators in the conventional neutron valence space beyond 208 Pb. The shell model is nowadays able to provide a comprehensive view of the atomic nucleus [1]. It is a many-body theoretical framework, successful in explaining various features of the structure of nuclei, based on the definition of a restricted valence space where a suitable Hamiltonian can be diagonalized. This effective interaction originates from realistic two-body nuclear forces based on phenomenological nucleon-nucleon potentials, renormalized to be adapted to the truncated model space. Although the renormalization process can be treated in a rigorous mathematical way, the appearance of effective terms is often neglected in calculations, as a common but incorrect practice. The presence and relevance of these effective forces is well known also in other fields of physics, as for example in condensed matter studies [2]. Indeed, effective three-body terms appear already at the lower perturbation order [3]: PRL 109, 162502 (2012) P H Y S I C A L