QPM Analysis of 205 Tl Nuclear Excitations below the Giant Dipole Resonance

We analysed our experimental recent findings of the dipole response of the odd-mass stable nucleus 205Tl within the quasi-particle phonon model. Using the phonon basis constructed for the neighbouring 204Hg and wave function configurations for 205Tl consisting of a mixture of quasiparticle ⊗ N-phonon configurations (N=0,1,2), only one group of fragmented dipole excited states has been reproduced at 5.5 MeV in comparison to the experimental distribution which shows a second group at about 5 MeV. The computed dipole transition strengths are mainly of E1 character which could be associated to the pygmy dipole resonance.


Introduction
The nuclear structure of low-lying states consists of pure single quasiparticle states in odd-mass nuclei and onephonon or two-quasiparticle configurations in even-mass nuclei.At higher excitation energy due to the high level density and to the quasiparticle-phonon interaction, the wave function is more complex [1].Different coupling of quasi-particle and phonon states may result to different configurations with the same spin and parity.This is the case of the Pygmy states distribution which appears on the low-energy tail of the Giant dipole resonance [2].The corresponding dipole transition strengths may increase considerably the reaction rates of elements nucleosynthesis [3].Although the nature of the Pygmy is still under debate, the Quasiparticle-Phonon Model (QPM) [1] has successfully reproduced the general features as for instance in the lead isotopes [4], [5].This has been complemented by the recent nuclear resonance fluorescence (NRF) measurements on the neighboring Z=81 205 Tl nucleus.In this work, we report on the analysis of the results within the QPM model.

(γ, γ ) measurements
The dipole response of 205 Tl has been investigated in Nuclear Resonance Fluorescence experiments (NRF) using a bremsstrahlung photon beam with an end-point energy of 7.5 MeV at the Darmstadt High Intensity Photon Setup (DHIPS).The NRF technique [6] is very selective to dipole transitions.Two NRF measurements have been conducted for about 80 hours with a natural Tl target (2060.0mg) and a target enriched to 99.9% in 205 Tl (1938.4mg), respectively.For the photon flux calibration both targets were sandwiched between two boron disks with a total mass of 240.8 mg (natural) and 394.3 mg (enriched to 99.5% in 11 B), respectively.The scattered photon intensities were measured by high-resolution HPGe γ-ray detectors positioned around the target at 90 • , 95 • and 130 • with respect to the incident beam.
From the transition intensities observed in the spectrum (Fig. 1), elastic scattering cross sections are extracted.These are proportional to the g • total decay width and g is a spin factor.Knowing the branching transitions, the reduced transition probabilities are directly deduced.However, due to the detection limit most of the weak branching transitions are undetectable and only a lower limit of the dipole strengths can be obtained.In our case of odd-nucleus, the angular distributions of the ground-state transitions are nearly isotropic.
As a consequence, it was not possible to deduce the multipolarity and therefore we assume an electric dipole character for the corresponding transitions (Fig. 2a).

Quasiparticle-phonon model calculations
The ground and excited states of 205 Tl have been described by the wave function ( where α † j is an operator which creates quasi-particle (qp) on a mean field level j = |nl j and Q † λi describes phonon (ph) excitation of the core nucleus 204 Hg with multipolarity λ and QRPA root number i. Diagonalization of the QPM Hamiltonian on the set of wave functions (1) yields the spectrum of states for each particular j π and coefficients C, D, and F for all of these states.We refer for details to review article [7].
In the present calculations, we have used natural parity phonons with multipolarity λ π from 1 − to 7 − and unnatural parity 1 + phonons.The density of configurations in 205 Tl is very high and to make calculations possible we have had to truncate complex qp ⊗ ph, qp ⊗ 2ph configurations at 6.5 and 7.5 MeV, respectively.
Although the number of components of the wave function (1) is of the order of a few thousand for each j π , only a few of them carry noticeable dipole excitation strength.They are qp components corresponding to the valence ] j π which correspond to the dipole excitation of the core when the unpaired quasiparticle plays the role of a spectator.The other components of (1) provide fragmentation of the strength carried by the abovementioned components, via interaction with them.
The main part of the E1 strength in Fig. 2b is due to the fragmentation of the strength of the 1 phonon in 204 Hg has excitation energy 5.5 MeV and B(E1) = 0.46 e 2 fm 2 .This state corresponds to the very strong 1 − ground state transition in 208 Pb at the same energy.Other 1 − phonons in 204 Hg have either very small B(E1) values or are located above 7 MeV without noticeable contribution for 205 Tl below 6.5 MeV.The role of the valence E1-transitions are also of marginal importance because of high energies of the 3p 3/2 and 3p 1/2 qp-levels.
The M1 strength in Fig. 2c  We conclude from our analysis that the dipole transitions observed experimentally are mainly of E1 character.The main transitions are of 3s 1/2 → 3s 1/2 ⊗ 1 − i nature.The fragmentation of the strength distribution is underestimated in calculation as compared to data.This is not surprising because qp ⊗ 3ph configurations are omitted in the wave function (1) due to a very high density of them.But in general, we may speak about a good qualitative agreement between the results of calculations and data.*This work has been supported by the Deutsche Forschungsgemeinschaft under grant No. SFB 634.
+ phonon in 204 Hg at 5.82 MeV corresponds to the well-known isoscalar 1 + state in 208 Pb at 5.85 MeV.The other 1 + phonons in 204 Hg at lower energies have much smaller B(M1) values.