Anharmonicity of multi–octupole-phonon excitations inPb208: Analysis with multireference covariant density functional theory and subbarrier fusion ofO16

Abstract

We discuss anharmonicity of the multi-octupole-phonon states in 208 Pb based on a covariant density functional theory, by fully taking into account the interplay between the quadrupole and the octupole degrees of freedom. Our results indicate the existence of a large anharmonicity in the transition strengths, even though the excitation energies are similar to those in the harmonic limit. We also show that the quadrupole-shape fluctuation significantly enhances the fragmentation of the two-octupole-phonon states in 208 Pb. Using those transition strengths as inputs to coupled-channels calculations, we then discuss the fusion reaction of 16 O+ 208 Pb at energies around the Coulomb barrier. We show that the anharmonicity of the octupole vibrational excitation considerably improves previous coupled-channels calculations in the harmonic oscillator limit, significantly reducing the height of the main peak in the fusion barrier distribution.PACS numbers: 21.60. Jz, 21.10.Re, 25.70.Jj Collective vibrational excitations exist commonly in many-fermion systems [1]. Here, the concept of phonon is an important keystone to understand these excitations. For instance, for finite nuclear systems, vibrations of the nuclear surface are treated as elementary excitations [2,3]. The phonons for these vibrations are bosonlike in character and multiple excitations of the same type are possible, resulting in multi-phonon states [2]. In a harmonic vibration, all the levels in a phonon multiplet are degenerate in energy and the energy spacing between neighboring multiplets is a constant. The energy patterns close to such harmonic vibration have been observed in nearly spherical nuclei in different mass regions, and these states have been primarily interpreted as multipole phonon states [2,4,5].From a microscopic viewpoint, however, the collective excitations are generated by a coherent superposition of quasiparticle excitations of fermions in orbits close to the Fermi surface. The Pauli principle correction, together with residual interactions among phonons (that is, modemode couplings), modifies the structure of multi-phonon states and make them highly fragmented [6]. To assess the degree of such anharmonicity is a fundamental question in nuclear physics, that needs to be studied more extensively. In particular, we mention that recent studies on the anharmonicity in the multi-quadrupole-phonon states have questioned the concept of low-energy vibrational modes in atomic nuclei [7,8]. The double-magic nucleus208 Pb provides an ideal laboratory to examine the concept of multi-octupolephonon excitations in nuclear systems, as the first excited 3 − state of this nucleus has long been interpreted as a collective one-octupole-phonon state [9]. In the past decades, several experimental searches for the twooctupole-phonon (TOP) states in 208 Pb have been carried out [10][11][12][13]. Even though many of the TOP members have been identified, the multi-phonon excitations in 208 Pb have not yet been understood completely. This is the case especia...

Odd-even parity splittings and octupole correlations in neutron-rich Ba isotopes

“…Besides, it is interesting to notice that the 3 − state is predicted to be the first excited state for the configuration with β 2 = 0 and β 3 = 0.1, or 0.2. This is exactly the case that has been found in closed-shell nucleus like 208 Pb [34].…”

“…This beyond mean-field method is often called MR-CDFT, which has been applied to study the collective excitations of axially [29] and triaxially deformed nuclei [30][31][32][33]. Recently, this method has been extended to understand the spin-dependent parity splittings in the octupole deformed nucleus 224 Ra [13], the anharmonicity of multi-octupole-phonon excitations in 208 Pb [34], the molecular-like clustering structure in 20 Ne [35], the nuclear matrix elements of neutrinoless double beta decay [36][37][38][39], and the low-lying states of hypernuclei [40,41].…”

How the Pauli exclusion principle affects fusion of atomic nuclei

“…Here, the CC calculations are kept simple and include only the most relevant couplings. Improvements could be obtained, e.g., by including anharmonicity of the multiphonon states [61]. The resulting fusion cross-sections are plotted in Figs.…”

Symmetry restoration in mean-field approaches

“…In the microscopic calculations, the transition rates are calculated in the full configuration space without effective charges and show excellent agreement with the experimental data. This model based on covariant density functional was further extended to consider triaxial intrinsic states in (Yao et al, 2011(Yao et al, , 2009(Yao et al, , 2010, to reflection asymmetric ones in (Yao and Hagino, 2016;Yao et al, 2015b;Zhou et al, 2016) and to the admixture of projected two-quasiparticle configurations (Zhao et al, 2016) for the description of band-crossing phenomena in rotating nuclei. It also has been used to study nuclear matrix elements for 0νββ decay (Song et al, 2014;Yao et al, 2015a).…”