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P. Van Isacker

Publications and source records attributed to P. Van Isacker.

At least 37 records · Page 2Linked to original sources
arXiv2018

Quadrupole Phonons in the Cadmium Isotopes

A key question concerning the spherical-vibrator attributes of states in Cadmium isotopes is addressed by means of a boson Hamiltonian encompassing U(5) partial dynamical symmetry. The U(5) symmetry is preserved in a segment of the spectrum and is broken in particular non-yrast states, and the resulting mixing with the intruder states is small. The vibrational character is thus maintained in the majority of low-lying normal states, as observed in $^{110}$Cd.

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arXiv2018

Partial dynamical symmetry and the vibrational structure of Cd isotopes

The recently reported deviations of selected non-yrast states in $^{110}$Cd from the expected spherical-vibrator behaviour, is addressed by means of an Hamiltonian with U(5) partial dynamical symmetry. The latter preserves the U(5) symmetry in a segment of the spectrum and breaks it in other states. The effect of intruder states is treated in the framework of the interacting boson model with configuration mixing.

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arXiv2018

Symmetries of the interacting boson model

In this contribution the symmetry properties of the interacting boson model of Arima and Iachello are reviewed. While the concept of a dynamical symmetry is by now a familiar one, this is not necessarily so for the extended notions of partial dynamical symmetry and quasi dynamical symmetry, which can be beautifully illustrated in the context of the interacting boson model. The main conclusion of the analysis is that dynamical symmetries are scarce while their partial and quasi extensions are ubiquitous.

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arXiv2018

Is Seniority a Partial Dynamic Symmetry in the First $νg_{9/2}$ Shell?

The low-lying structures of the midshell $νg_{9/2}$ Ni isotopes $^{72}$Ni and $^{74}$Ni have been investigated at the RIBF facility in RIKEN within the EURICA collaboration. Previously unobserved low-lying states were accessed for the first time following $β$ decay of the mother nuclei $^{72}$Co and $^{74}$Co. As a result, we provide a complete picture in terms of the seniority scheme up to the first $(8^+)$ levels for both nuclei. The experimental results are compared to shell-model calculations in order to define to what extent the seniority quantum number is preserved in the first neutron $g_{9/2}$ shell. We find that the disappearance of the seniority isomerism in the $(8^+_1)$ states can be explained by a lowering of the seniority-four $(6^+)$ levels as predicted years ago. For $^{74}$Ni, the internal de-excitation pattern of the newly observed $(6^+_2)$ state supports a restoration of the normal seniority ordering up to spin $J=4$. This property, unexplained by the shell-model calculations, is in agreement with a dominance of the single-particle spherical regime near $^{78}$Ni.

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arXiv2018

Generic features of the neutron-proton interaction

We show that fully aligned neutron-proton pairs play a crucial role in the low-energy spectroscopy of nuclei. with valence nucleons in a high-j orbital. Their dominance is valid in nuclei with valence neutrons and protons in different high-j orbitals as well as in N = Z nuclei, where all nucleons occupy the same orbital. We demonstrate analytically this generic feature of the neutron-proton interaction for a variety of systems with four valence nucleons interacting through realistic, effective forces. The dominance of fully aligned neutron-proton pairs results from the combined effect of (i) angular momentum coupling and (ii) basic properties of the neutron-proton interaction.

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arXiv2018

Gamow-Teller transitions and neutron-proton-pair transfer reactions

We propose a schematic model of nucleons moving in spin--orbit partner levels, $j=l\pm{\sfrac12}$, to explain Gamow--Teller and two-nucleon transfer data in $N=Z$ nuclei above $^{40}$Ca. Use of the $LS$ coupling scheme provides a more transparent approach to interpret the structure and reaction data.We apply the model to the analysis of charge-exchange, $^{42}$Ca($^3$He,t)$^{42}$Sc, and np-transfer, $^{40}$Ca($^3$He,p)$^{42}$Sc, reactions data to define the elementary modes of excitation in terms of both isovector and isoscalar pairs, whose properties can be determined by adjusting the parameters of the model (spin--orbit splitting, isovector pairing strength and quadrupole matrix element) to the available data. The overall agreement with experiment suggests that the approach captures the main physics ingredients and provides the basis for a boson approximation that can be extended to heavier nuclei. Our analysis also reveals that the SU(4)-symmetry limit is not realized in $^{42}$Sc.

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arXiv2018

A geometry for the shell model

A geometric interpretation is given of matrix elements of a short-range interaction between states that are written in terms of aligned neutron-proton pairs.

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arXiv2017

Neutron-proton pairing and double-beta decay in the interacting boson model

Background: The interacting boson model (IBM) has been used extensively to calculate the matrix elements governing neutrinoless double-beta decay. Studies within other models indicate that a good description of neutron-proton pairing is essential for accurate calculations of those matrix elements. The usual interacting boson model is based only on like-particle pairs, however, and the extent to which it captures neutron-proton pairing is not clear. Purpose: To determine whether neutron-proton pairing should be explicitly included as neutron-proton bosons in IBM calculations of neutrinoless double-beta decay matrix elements. Method: An isospin-invariant version of the nucleon-pair shell model is applied to carry out shell-model calculations in a large space and in a collective subspace, and to define effective operators in the latter. A democratic mapping is then used to define corresponding boson operators for the IBM, with and without an isoscalar neutron-proton pair boson. Results: IBM calculations with and without the isoscalar boson are carried out for nuclei near the beginning of the $pf$ shell, with a realistic shell-model Hamiltonian and neutrinoless double-beta-decay operator as the starting point. Energy spectra and double-beta matrix elements are compared to those obtained in the underlying shell model. Conclusions: The isoscalar boson does not improve energy spectra but does improve double-beta matrix elements. To be useful at the level of precision we need, the mapping procedure must be further developed to better determine the dependence of the boson Hamiltonian and decay operator on particle number and isospin. But the benefits provided by the isoscalar boson suggest that through an appropriate combination of mappings and fitting, it would make IBM matrix elements more accurate for the heavier nuclei used in experiments.

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arXiv2017

A revised $B(E2; 2^+_1 \to 0^+_1)$ value in the semi-magic nucleus $^{210}$Po

The lifetimes of the $2^+_1$, the $2^+_2$ and the $3^-_1$ states of $^{210}$Po have been measured in the $^{208}$Pb($^{12}$C,$^{10}$Be)$^{210}$Po transfer reaction by the Doppler-shift attenuation method. The results for the lifetime of the $2^+_1$ state is about three times shorter than the adopted value. However, the new value still does not allow for consistent description of the properties of the yrast $2^+_1$, $4^+_1$, $6^+_1$, and $8^+_1$ states of $^{210}$Po in the framework of nuclear shell models. The Quasi-particle Phonon Model (QPM) calculations also cannot overcome this problem thus indicating the existence of a peculiarity which is neglected in both theoretical approaches.

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arXiv2016

Properties of isocalar-pair condensates

It is pointed out that the ground state of n neutrons and n protons in a single-j shell, interacting through an isoscalar (T=0) pairing force, is not paired, J=0, but rather spin-aligned, J=n. This observation is explained in the context of a model of isoscalar P (J=1) pairs, which is mapped onto a system of p bosons, leading to an approximate analytic solution of the isoscalar-pairing limit in jj coupling.

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arXiv2015

Shape coexistence in the microscopically guided interacting boson model

Shape coexistence has been a subject of great interest in nuclear physics for many decades. In the context of the nuclear shell model, intruder excitations may give rise to remarkably low-lying excited $0^+$ states associated with different intrinsic shapes. In heavy open-shell nuclei, the dimension of the shell-model configuration space that includes such intruder excitations becomes exceedingly large, thus requiring a drastic truncation scheme. Such a framework has been provided by the interacting boson model (IBM). In this article we address the phenomenon of shape coexistence and its relevant spectroscopy from the point of view of the IBM. A special focus is placed on the method developed recently which makes use of the link between the IBM and the self-consistent mean-field approach based on the nuclear energy density functional. The method is extended to deal with various intruder configurations associated with different equilibrium shapes. We assess the predictive power of the method and suggest possible improvements and extensions, by considering illustrative examples in the neutron-deficient Pb region, where shape coexistence has been experimentally studied.

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arXiv2015

Partial dynamical symmetry in Bose-Fermi systems

We generalize the notion of partial dynamical symmetry (PDS) to a system of interacting bosons and fermions. In a PDS, selected states of the Hamiltonian are solvable and preserve the symmetry exactly, while other states are mixed. As a first example of such novel symmetry construction, spectral features of the odd-mass nucleus $^{195}$Pt are analyzed.

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arXiv2014

Seniority in quantum many-body systems. I. Identical particles in a single shell

A discussion of the seniority quantum number in many-body systems is presented. The analysis is carried out for bosons and fermions simultaneously but is restricted to identical particles occupying a single shell. The emphasis of the paper is on the possibility of {\em partial} conservation of seniority which turns out to be a peculiar property of spin-9/2 fermions but prevalent in systems of interacting bosons of any spin. Partial conservation of seniority is at the basis of the existence of seniority isomers, frequently observed in semi-magic nuclei, and also gives rise to peculiar selection rules in one-nucleon transfer reactions.

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arXiv2014

Linking partial and quasi dynamical symmetries in rotational nuclei

Background: Quasi dynamical symmetries (QDS) and partial dynamical symmetries (PDS) play an important role in the understanding of complex systems. Up to now these symmetry concepts have been considered to be unrelated. Purpose: Establish a link between PDS and QDS and find an emperical manifestation. Methods: Quantum number fluctuations and the intrinsic state formalism are used within the framework of the interacting boson model of nuclei. Results: A previously unrecognized region of the parameter space of the interacting boson model that has both O(6) PDS (purity) and SU(3) QDS (coherence) in the ground band is established. Many rare-earth nuclei approximately satisfying both symmetry requirements are identified. Conclusions: PDS are more abundant than previously recognized and can lead to a QDS of an incompatible symmetry.

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arXiv2014

Partial and Quasi Dynamical Symmetries in Nuclei

One of the interesting aspects in the study of atomic nuclei is the strikingly regular behaviour many display in spite of being complex quantum-mechanical systems, prompting the universal question of how regularity emerges out of complexity. It is often conjectured that symmetries play a pivotal role in our understanding of this emerging simplicity. But most symmetries are likely to be broken, partial or both. Under such more realistic conditions, does the concept of symmetry still provide a basis for our understanding of regularity? I suggest that this requires the enlarged concepts of partial and quasi dynamical symmetry.

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arXiv2014

Exactly solvable models of nuclei

In this paper a review is given of a class of sub-models of both approaches, characterized by the fact that they can be solved exactly, highlighting in the process a number of generic results related to both the nature of pair-correlated systems as well as collective modes of motion in the atomic nucleus.

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arXiv2013

Neutron-proton pairs in nuclei

A review is given of attempts to describe nuclear properties in terms of neutron--proton pairs that are subsequently replaced by bosons. Some of the standard approaches with low-spin pairs are recalled but the emphasis is on a recently proposed framework with pairs of neutrons and protons with aligned angular momentum. The analysis is carried out for general $j$ and applied to $N=Z$ nuclei in the $1f_{7/2}$ and $1g_{9/2}$ shells.

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