Extended interacting boson model description of Pd nuclei in the A ∼ 100 transitional region

Studies of even-even nuclei in the A∼100 transitional mass region within the framework of the interacting boson model-1 (IBM-1) have been expanded down to 98Pd nuclei to compare the calculation with new experimental results from measurements obtained at the Institute of Nuclear Physics in Cologne. The low-lying energy levels and the E2 transition rates of 98−100Pd nuclei are investigated and their geometric structures are described in the present work. We have also focused on the new B(E2:2+1 → 0+1 ) values of 112,114Pd nuclei to compare with previously calculated values.


Introduction
The structure of the even-even nuclei in the A∼100 region were studied both theoretically and experimentally during the last years [1][2][3][4][5][6][7][8][9].The ratio of the energy of the 4 + over 2 + in the ground state band, E 4 + /E 2 + , is always used to investigste whether the nuclei are spherical or not.Three possible dynamical symmetries, U (5), SU (3), O (6), of the interacting boson model (IBM) [10] are associated with these ratios; E 4 + /E 2 + = 2.0, 3.33, 2.5 indicate spherical, axially deformed, γ-unstable nuclei, respectively.It is also possible to get hints for the geometry of nuclei by plotting potential energy surface in terms of deformation parameters β and γ.Actually, the even-even Pd, Ru and Mo nuclei around the N=50 shell show the spherical behaviour according to the interacting boson model-1 (IBM-1) calculation in Ref. [6].
The main purpose of this paper is to complete the investigations of all nuclei in the isotopic chain of Pd with Z=46 by expanding the previous work [6].The energy levels and B(E2) values of 98,100 Pd isotopes have been calculated with refitted IBM-1 parameters and compared to new experimental results [8,9].The new experimental results for the B(E2:2 + 1 → 0 + 1 ) values of 112,114 Pd nuclei [1,2] are compared to the earlier experimental data and the calculated ones, too.We have also briefly mentioned about the new experiment on 98 Pd nucleus in this work but the detailed discussion will be presented in a forthcoming paper [14] a e-mail: boyukata@comu.edu.tr

The Interacting Boson Model
The interacting boson model [10], based on the group theoretical approaches, is useful to describe the properties of collective phenomena in the valance space.This semi-microscopic theory describes even-even nuclei by N bosons with N equal to the number of valence nucleons divided by two.In the original version of IBM-1 (no distinction between neutron and proton bosons), applicable to eveneven nuclei, the basic building blocks are s and d bosons, with angular momentum L=0 and L=2.It is successful in the description of energy spectra and also electromagnetic transition strengths in a wide range of the nuclear chart.In the present calculation, the following multipole form of the Hamiltonian in the sd-boson space has been used where nd , Q, L, T3 and T4 terms are the d-boson number operator, the quadrupole operator, the angular momentum operator and the octupole and hexadecapole operators, respectively, and they are defined in terms of s and d bosons [10] nd The electric quadrupole transition rates in the IBM-1 have been calculated with T (E2) = e b • Q, and by using the expression for the quadrupole operator Q from (2) we deduce as where e b is the boson effective charge and χ is another free parameter.
A geometric shape visualization of the even-even nuclei is made by plotting the potential energy surface in the (β,γ) plane.The V(β, γ) can be obtained by calculating the expectation value of the Hamiltonian (1) in the coherent state [13] and is given in the following form where N is number of bosons, β, γ are deformation parameters (usually, β ≥ 0, 0 • ≤ γ ≤ 60 • ) and other terms are the same as in the Hamiltonian (1).For the β = 0, nucleus is spherical, for the β > 0 it is axially deformed and in this case for γ = 0 • , 30 • , 60 • the nucleus has correspondingly prolate, triaxial, oblate shape.

New experimental data on 98 Pd
An experiment on 98 Pd using the recoil distance Doppler-shift method (RDDS) has been performed at the Cologne Tandem accelerator with the Cologne plunger device [9].The aim of the experiment was to deduce for the first time E2 transition strengths between the lowest yrast states in 98 Pd from measured lifetimes of these states.The fusion-evaporation reaction 92 Mo( 10 B,3np) 98 Pd was used to produce the excited 98 Pd nuclei with a beam energy of E( 10 B)=54 MeV.To determine the lifetimes Table 1.Hamiltonian parameters used in the ibm1-code [12] (in units of keV and χ = 0.02).

DOI: 10
.1051/ C Owned by the authors, published by EDP Sciences,

02013-p. 2 EPJFigure 1 .
Figure1.The experimental[8,9,14] and calculated energy spectrum.The potential energy surface in β,γ plane of 98−100 Pd nuclei are also given in the right side of each panel.