Binding-energy independence of reduced spectroscopic strengths derived from (p, 2p) and (p, pn) reactions with nitrogen and oxygen isotopes

A campaign of intermediate energy (300-450 MeV/u) proton-induced nucleon knockout measurements in inverse kinematics has been recently undertaken at the R 3 B/LAND setup at GSI. We present a systematic theoretical analysis of these data with the aim of studying the quenching of the single-particle strengths and its binding-energy dependence. For that, the measured semi-inclusive (p, 2p) and (p, pn) cross sections are compared with theoretical predictions based on single-particle cross sections derived from a novel coupled-channels formalism and shell-model spectroscopic factors. A systematic reduction of about 20-30% is found, with a very limited dependence on proton-neutron asymmetry.Comment: 8 pages, 3 figure

Comprehensive analysis of large α\alpha yields observed in 6^{6}Li induced reactions

Background: Large $\alpha$ yields have been reported over the years in reactions with $^{6}$Li and $^{7}$Li projectiles. Previous theoretical analyses have shown that the elastic breakup (EBU) mechanism (i.e., projectile breakup leaving the target in its ground state) is able to account only for a small fraction of the total $\alpha$ inclusive breakup cross sections, pointing toward the dominance of non-elastic breakup (NEB) mechanisms. Purpose: We aim to provide a systematic study of the $\alpha$ inclusive cross sections observed in nuclear reactions induced by $^{6}$Li projectiles. In addition to estimating the total $\alpha$ singles cross sections, it is our goal to evaluate angular and energy distributions of these $\alpha$ particles and compare with experimental data, when available. Method: We compute separately the EBU and NEB components of the inclusive breakup cross sections. For the former, we use the continuum-discretized coupled-channels (CDCC) method, which treats this mechanism to all orders. For the NEB part, we employ the the model proposed in the eighties by Ichimura, Austern and Vincent [Phys. Rev. C32, 432 (1982)], within the DWBA approximation. Results: Overall, the sum of the computed EBU and NEB cross sections is found to reproduce very well the measured singles cross sections. In all cases analyzed, we find that the inclusive breakup cross section is largely dominated by the NEB component. Conclusions: The presented method provides a global and systematic description of inclusive breakup reactions induced by $^{6}$Li projectiles. It provides also a natural explanation of the previously observed underestimation of the measured $\alpha$ yields by CDCC calculations. The method used here can be extended to other weakly-bound projectiles, including halo nuclei.Comment: 11 pages, 16 figures, fig. 12 updated; some typos correcte

The puzzle of complete fusion suppression in weakly-bound nuclei: a Trojan Horse effect?

Experimental studies of nuclear collisions involving light weakly-bound nuclei show a systematic suppression of the complete fusion cross section by $\sim$30\% with respect to the expectation for tightly bound nuclei, at energies above the Coulomb barrier. Although it is widely accepted that the phenomenon is related to the weak binding of these nuclei, the origin of this suppression is not fully understood. In here, we present a novel approach that provides the complete fusion for weakly bound nuclei and relates its suppression to the competition between the different mechanisms contributing to the reaction cross section. The method is applied to the $^{6,7}$Li+$^{209}$Bi reactions, where we find that the suppression of complete fusion is mostly caused by the flux associated with non-elastic breakup modes, such as the partial capture of the projectile (incomplete fusion), whereas the elastic breakup mode is found to play a minor role. Finally, we demonstrate that the large $\alpha$ yields observed in these reactions can be naturally explained as a consequence of a {\it Trojan Horse} mechanism.Comment: 6 pages, 4 figures. Accepted for publication in Phys. Rev. Letter

Interplay between valence and core excitation mechanisms in the breakup of halo nuclei

The phenomenon of core excitation in the breakup of a two-body halo nucleus is investigated. We show that this effect plays a significant role in the reaction dynamics and, furthermore, its interference with the valence excitation mechanism has sizable and measurable effects on the breakup angular distributions. These effects have been studied in the resonant breakup of 11Be on a carbon target, populating the resonances at 1.78 MeV (5/2+) and 3.41 MeV (3/2+). The calculations have been performed using a recently extension of the DWBA method, which takes into account the effect of core excitation in both the structure of the halo nucleus and in the reaction mechanism. The calculated angular distributions have been compared with the available data [Fukuda et al., Phys. Rev. C70,054606]. Although each of these resonances is dominated by one of the two considered mechanisms, the angular patterns of these resonances depend in a very delicate way on the interference between them. This is the first clear evidence of this effect but the phenomenon is likely to occur in other similar reactions.Comment: 5 pages, 2 figures, (Version to appear in Physical Review Letters

Description of the 11^{11}Li(p,d)10(p,d){^{10}}Li transfer reaction using structure overlaps from a full three-body model

Recent data on the differential angular distribution for the transfer reaction $^{11}$Li(p,d)$^{10}$Li at $E/A=5.7$ MeV in inverse kinematics are analysed within the DWBA reaction framework, using the overlap functions calculated within a three-body model of $^{11}$Li. The weight of the different $^{10}$Li configurations in the system's ground state is obtained from the structure calculations unambiguously. The effect of the $^{9}$Li spin in the calculated observables is also investigated. We find that, although all the considered models succeed in reproducing the shape of the data, the magnitude is very sensitive to the content of $p_{1/2}$ wave in the $^{11}$Li ground-state wave function. Among the considered models, the best agreement with the data is obtained when the $^{11}$Li ground state contains a $\sim$31\% of $p_{1/2}$ wave in the $n$-$^9$Li subsystem. Although this model takes into account explicitly the splitting of the $1^+$ and $2^+$ resonances due to the coupling of the $p_{1/2}$ wave to the $3/2^-$ spin of the core, a similar degree of agreement can be achieved with a model in which the $^{9}$Li spin is ignored, provided that it contains a similar p-wave content.Comment: 8 pages, 3 figures. Final versio

Linking structure and dynamics in (p,pn)(p,pn) reactions with Borromean nuclei: the 11^{11}Li(p,pn)10(p,pn){^{10}}Li case

One-neutron removal $(p,pn)$ reactions induced by two-neutron Borromean nuclei are studied within a Transfer-to-the-Continuum (TC) reaction framework, which incorporates the three-body character of the incident nucleus. The relative energy distribution of the residual unbound two-body subsystem, which is assumed to retain information on the structure of the original three-body projectile, is computed by evaluating the transition amplitude for different neutron-core final states in the continuum. These transition amplitudes depend on the overlaps between the original three-body ground-state wave function and the two-body continuum states populated in the reaction, thus ensuring a consistent description of the incident and final nuclei. By comparing different $^{11}$Li three-body models, it is found that the $^{11}$Li$(p,pn){^{10}}$Li relative energy spectrum is very sensitive to the position of the $p_{1/2}$ and $s_{1/2}$ states in $^{10}$Li and to the partial wave content of these configurations within the $^{11}$Li ground-state wave function. The possible presence of a low-lying $d_{5/2}$ resonance is discussed. The coupling of the single particle configurations with the non-zero spin of the $^{9}$Li core, which produces a spin-spin splitting of the states, is also studied. Among the considered models, the best agreement with the available data is obtained with a $^{11}$Li model that incorporates the actual spin of the core and contains $\sim$31\% of $p_{1/2}$-wave content in the $n$-$^9$Li subsystem, in accord with our previous findings for the $^{11}$Li(p,d)$^{10}$Li transfer reaction, and a near-threshold virtual state.Comment: 7 pages, 4 figures, submitted to PL

Investigating the 10Li continuum through 9Li(d,p)10Li reactions

The continuum structure of the unbound system $^{10}$Li, inferred from the $^{9}$Li$(d,p)^{10}$Li transfer reaction, is reexamined. Experimental data for this reaction, measured at two different energies, are analyzed with the same reaction framework and structure models. It is shown that the seemingly different features observed in the measured excitation energy spectra can be understood as due to the different incident energy and angular range covered by the two experiments. The present results support the persistence of the $N=7$ parity inversion beyond the neutron dripline as well as the splitting of the well-known low-lying $p$-wave resonance. Furthermore, they provide indirect evidence that most of the $\ell=2$ single-particle strength, including possible $d_{5/2}$ resonances, lies at relatively high excitations energies.Comment: accepted for publication in Physics Letters

Beyond quantum microcanonical statistics

Descriptions of molecular systems usually refer to two distinct theoretical frameworks. On the one hand the quantum pure state, i.e. the wavefunction, of an isolated system which is determined to calculate molecular properties and to consider the time evolution according to the unitary Schr\"odinger equation. On the other hand a mixed state, i.e. a statistical density matrix, is the standard formalism to account for thermal equilibrium, as postulated in the microcanonical quantum statistics. In the present paper an alternative treatment relying on a statistical analysis of the possible wavefunctions of an isolated system is presented. In analogy with the classical ergodic theory, the time evolution of the wavefunction determines the probability distribution in the phase space pertaining to an isolated system. However, this alone cannot account for a well defined thermodynamical description of the system in the macroscopic limit, unless a suitable probability distribution for the quantum constants of motion is introduced. We present a workable formalism assuring the emergence of typical values of thermodynamic functions, such as the internal energy and the entropy, in the large size limit of the system. This allows the identification of macroscopic properties independently of the specific realization of the quantum state. A description of material systems in agreement with equilibrium thermodynamics is then derived without constraints on the physical constituents and interactions of the system. Furthermore, the canonical statistics is recovered in all generality for the reduced density matrix of a subsystem