The Dold-Lashof-Fuchs construction revisited

Sia dato uno spazio topologicoE con azione di un monoide topologicoH e siaE→B una funzione continue che, su ogni apertoU di una partizione dell'unità diB, sia, a meno di omotopia, la proiezioneU×H→U (ovvero una fibrazione numerabile). Un classico risultato di A. Dold e R. Lashof (1959) permette di costruire, a partire daE→B, una funzione continuaE _∞→B_∞, conE _∞ debolmente contraibile e munito di azione diH: laH-fibrazione universale associata daH. Tale funzione, in generale, non è purtroppo numerabile e quindi non si presta alla classificazione delleH-fibrazioni numerabili. Successivamente (1971), M. Fuchs ha trovato un modo di modificare la costruzione di Dold-Lashof per recuperare la numerabilità. La costruzione di Dold-Lashof-Fuchs è, da allora, uno dei principali strumenti nella teoria degli spazi classificanti di monoidi topologici, anche se vi è un uso di topologie alquanto complesse e quindi poco maneggevoli. In questo lavoro ci proponiamo di mostrare come, lavorando nella categoria conveniente deik-spazi, sia possibile descrivere la costruzione di Dold-Lashof-Fuchs in modo estremamente semplificato ed adattarla anche alla classificazione delleF-fibrazioni numerabili.

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Conferenza tenuta da R. Piccinini il 15 maggio 1995     

NN final-state interaction in two-nucleon knockout from <Superscript>16</Superscript><Emphasis Type="Italic">O</Emphasis>

The influence of the mutual interaction between the two outgoing nucleons (NN-FSI) in electro- and photoinduced two-nucleon knockout from ¹⁶O has been investigated perturbatively. It turns out that the effect of NN-FSI depends on the kinematics and on the type of reaction considered. The effect is generally larger in pp- than in pn-knockout and in electroinduced than in photoinduced reactions. In superparallel kinematics NN-FSI leads in the (e,epp) channel to a strong increase of the cross-section, that is mainly due to a strong enhancement of the -current contribution. In pn-emission, however, this effect is partially cancelled by a destructive interference with the seagull current. For photoreactions NN-FSI is considerably reduced in superparallel kinematics and can be practically negligible in specific kinematics.Received: 1 July 2003, Published online: 10 February 2004PACS: 13.75.Cs Nucleon-nucleon interactions (including antinucleons, deuterons, etc.) - 21.60.-n Nuclear structure models and methods - 25.30.Fj Inelastic electron scattering to continuum     

Electromagnetic proton-neutron knockout off <Superscript>16</Superscript>O : New achievements in theory

Results for the cross-sections of the exclusive ¹⁶O(e, e'pn)¹⁴N and ¹⁶O(γ, pn)¹⁴N knockout reactions are presented and discussed in different kinematics. In comparison with earlier work, a complete treatment of the center-of-mass (CM) effects in the nuclear one-body current is considered in connection with the problem of the lack of orthogonality between initial bound and final scattering states. The effects due to CM and orthogonalization are investigated in combination with different treatments of correlations in the two-nucleon overlap function and for different parametrizations of the two-body currents. The CM effects lead in super-parallel kinematics to a dramatic increase of the ¹⁶O(e, e'pn) cross-section to the 1₂ ⁺ excited state (3.95MeV) of ¹⁴N . In all the situations considered the results are very sensitive to the treatment of correlations. A crucial role is played by tensor correlations, but also the contribution of long-range correlations is important.     

On the NN final-state interaction in the <Superscript>16</Superscript>O (e,e<Superscript>′</Superscript>pp) reaction

The influence of the mutual interaction between the two outgoing nucleons (NN-FSI) in the ¹⁶O(e, e'pp) reaction has been investigated. Results for various kinematics are discussed. In general, the effect of NN-FSI depends on kinematics and the chosen final state in the excitation spectrum of ¹⁴C. Received: 19 December 2002 / Accepted: 6 February 2003 / Published online: 15 April 2003     

Spin-orbit distortion of the emerging nucleon in quasi-free electron scattering

Spin-orbit distortion of the emerging nucleon in quasi-free electron scattering is considered in the frame of a program aiming at examining the approximations involved in the theoretical treatment. The imaginary part of the spin-orbit coupling in the optical-model potential felt by the knocked out nucleon appears here to have a significant role. Its consequences in the case of the reaction ¹²C(e, e′p)¹¹B are discussed.     

Realistic one-particle density matrix and single-particle description of nuclei

Starting from the experimental data on elastic electron scattering, realistic one-particle density matrices for ¹⁶O and ⁴⁰Ca are obtained, both with fractional occupation numbers and full occupation of the first A natural orbitals. A phenomenological single-nucleon Hamiltonian is then constructed and diagonalized. The deduced single-particle energies are compared with those obtained in the Hartree-Fock approximation. The consistency of all experimental data concerning the ground state is checked with the aid of a sum rule for the total binding energy involving only the one-particle density matrix and the hole energies.     

Charge exchange in the final state of direct (γ, n) reactions

The two-step charge-exchange contribution coming from a direct (γ, p) reaction followed by a (p, n) transition due to isospin dependence of the optical-model potential is studied for photonuclear reactions. The charge-exchange mechanism appears to be substantial: its contribution is strongly dependent on the rather uncertain isospin term in the phenomenological optical-model potential, but is still insufficient to make the size of the (γ, n) cross section comparable with the (γ, p) one as found experimentally.