Partial escape width for nuclei with neutron excess

NUCLEAR STRUCTURE

Partial escape width for nuclei with neutron excess

T. N. Leite^I; N. Teruya^II

^IFundação Universidade Federal do Vale do São Francisco (UNIVASF), Colegiado de Engenharia Civil, Juazeiro, BA, Brazil

^IIDepartamento de Física, Universidade Federal da Paraíba, CP 5008, 58051-970 João Pessoa, PB, Brazil

ABSTRACT

In this work, the escape width for nuclei with neutron excess is calculated by continuum Random Phase Approximation (RPA) with a careful treatment on the differences between the densities of neutrons and protons.

I. INTRODUCTION

In this work, the escape width for nuclei with neutron excess is calculated by continuum Random Phase Approximation (RPA) of the Ref.[1] with a careful treatment on the differences between the densities of neutrons and protons [2]. The calculation of partial escape width for each single-hole gives a good estimate of the escape width composition for the population of several single-holes in the residual nucleus. We have applied this method in order to estimate the energy location and the partial escape widths for pygmy dipole resonance (PDR) in the exotic nucleus ⁶⁰Ca and for isoscalar giant dipole resonance (ISGDR) in the ²⁰⁸Pb.

In the Sect. II of this work, we presented a summary of the continuum RPA formalism that accommodates the differences between neutron and proton densities. We present and comment our results in the Sect. III.

II. RPA FORMALISM

The continuum effects in our microscopic calculations are taken into account through a discrete particle-hole basis which accomodates the single-particle resonance widths, resulting in a diagonalization of RPA-like complex matrixes of standard size [1]. The excited states are implemented in the particle-hole excitation space, and the open channels correspond to unbound particle-hole states with complex energies, of which the imaginary parts give the single-particle escape widths.

The complex particle-hole modes are solved by a diagonalization of the discrete RPA equations:

where:

and

_p (_p = e_p-iG_p) are the complex energies of the single-particle resonances [3, 4]. Diagonalizing the complex Eq.(1), we have the complex eigenvectors given by complex and amplitudes and complex eigenvalues _n = . Thus, in this discrete particle-hole subspace, the escape width is associated with the contribution of all allowed unbound particles coupled to their respective single-holes. The partial escape width for each single-hole can be approximate for , what gives a good estimate of the escape width composition for the population of several single-holes in the residual nucleus.

The single-particle energies are evaluated by solving the Schrödinger equation with Woods-Saxon potential, including the centrifugal and Coulomb (as a uniformly charged sphere) terms [3, 4]. The RPA calculation is done by utilizing the Landau-Migdal residual interaction with density dependent parameters. Since the neutron and proton densities are too different in exotic nuclei, it is more appropriate to separate the nucleon density into neutron and proton parts, , where each part is given by , with k = n(p) for neutron (proton) [2].

In this same sense, the radial single-particle orbits are represented by harmonic oscillator radial wave functions with different size parameters for neutrons and protons, , where X_k = N (Z) for k = n(p), and ár²ñ_k » [2].

III. RESULTS AND DISCUSSIONS

In this section, we present and discuss some results which we have obtained by using 1p-1h continuum RPA approach, as described in the previous section, for isovector dipole electric transition for ⁶⁰Ca and isoscalar dipole transition for ²⁰⁸Pb.

According to previous RPA calculations for ⁶⁰Ca [5-8], our calculations [2] also predict a considerable strength in the energy region around ~ 8.6 MeV with a broad neutron peak. The broad width is due to the fact of the energy of the resonance to be above of the small neutron separation energy, implicating a strong coupling of the external neutrons to the continuum region. These low-lying energy states are the natural candidates for PDR because they have a dominant contribution of 'neutron skin' (pf shell), in agreement with hydrodynamic interpretation. The wide peak in ~ 8.6 MeV is composed by the overlap of three main peaks (see TABLE 1 and 2) exhausting about 8% of the EWSR.

In relation to the isoscalar GDR in ²⁰⁸Pb, the experimental data are not well defined and present some discrepancy. There are some discussions in the recent literature in relation to its correct location and their widths . Our calculations predict a considerable strength in the energy region above 20 MeV, which is composed by the presence of various narrow peaks superposing to exhaust about 82% of the EWSR between 20-30 MeV. These peaks are mainly composed by 3w transitions involving the neutrons and protons of the externals shells. The strength of this excitation is separated in two main components, in agreement with all experimental data. The lower-energy component is due to the remaining isovector contribution. The higher-energy and broader component is identified as isoscalar GDR. The mean energy centroid and escape width of this component are 24.4 MeV and 2.7 MeV, respectively. The partial escape widths for this mode are presented in TABLE 3.

IV. ACKNOWLEDGMENTS

This work was supported in part by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil.

REFERENCES

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Received on 8 December, 2004

Publication Dates

• Publication in this collection
  07 Nov 2005
• Date of issue
  Sept 2005

History

• Received
  08 Dec 2004