Fragmentation energy shift of giant nuclear resonances
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Fragmentation Energy Shift of Giant Nuclear Resonances B. А. Tulupov and M. H. Urin1)* Institute for Nuclear Research, Russian Academy of Sciences, pr. Shestidesyatiletiya Oktyabrya 7a, Moscow, 117312 Russia Received October 13, 2008; in final form, October 23, 2008
PACS numbers: 21.60.Jz, 24.30.Cz, 25.20.-x DOI: 10.1134/S106377880904019X
As a universal phenomenon, giant resonances in nuclei are formed owing to the concentration of the corresponding particle–hole (1p1h) strength in a relatively narrow energy interval and owing to the coupling of configurations of the 1p1h type to a singleparticle continuum and to multiquasiparticle configurations. In describing giant resonances, one can take into account the first two effects in the continuum random-phase approximation (CRPA), choosing, in one way or another, a nuclear mean field and interaction in the particle–hole channel. There are two approaches to taking into account coupling to multiquasiparticle configurations (fragmentation effect), a microscopic and a phenomenological one. Within the microscopic approach, one takes directly into account the coupling of 1p1h collective states to some number of 2p2h configurations. With allowance for a single-particle continuum, this approach was implemented in [1] in describing giantresonance strength functions. As a matter of fact, it is hardly possible within the microscopic approach to correctly take into account the shift of the giantresonance energy because of the fragmentation effect since, in order to describe the fragmentation shift within this approach, it is necessary to formally take into account a complete basis of 2p2h configurations, which are doorway states for coupling to more complicated configurations. The phenomenological approach to taking into account the contribution of the fragmentation effect to the total width of a giant resonance and the probability of its direct nucleonic decay was formulated in [2] in the spirit of the optical model of nucleon–nucleus scattering. In this version, the fragmentation-effect fraction that leads to the broadening of a giant resonance in the energy dependence of the corresponding energy-averaged 1)
Moscow Engineering Physics Institute (State University), Kashirskoe sh. 31, Moscow, 115409 Russia. * E-mail: [email protected]
strength function is taken into account via the subı stitution ω → ω + I in the CRPA equations, the 2 excitation-energy-dependent single-particle quantities (Green’s functions and scattering-problem wave functions) that appear in the CRPA equations being calculated with allowance for the imaginary addition ı ∓ I(ω, r) to the nuclear mean field (effective optical 2 potential), where ω is the excitation energy. Opposite signs of this addition are related to the above sub¨ stitution in the single-particle Schrodinger equation that determines the Green’s functions g(ε ± ω) for this equation. The Green’s functions appear in the expression for the free particle–hole propagator, which is the main ingredient in the CRPA equations [2]. This procedu
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