arXiv subjects

R. J. Liotta

Publications and source records attributed to R. J. Liotta.

At least 19 recordsLinked to original sources

arXiv2019

The Giant Pairing Vibration in Heavy Nuclei: Present Status and Future Studies

The Giant Pairing Vibration, a two-nucleon collective mode originating from the second shell above the Fermi surface, has long been predicted and expected to be strongly populated in two-nucleon transfer reactions with cross sections similar to those of the normal Pairing Vibration. Recent experiments have provided evidence for this mode in $^{14,15}$C but, despite sensitive studies, it has not been definitively identified either in Sn or Pb nuclei where pairing correlations are known to play a crucial role near their ground states. In this paper we review the basic theoretical concepts of this "elusive" state and the status of experimental searches in heavy nuclei. We discuss the hindrance effects due to Q-value mismatch and the use of weakly-bound projectiles as a way to overcome the limitations of the (p,t) and (t,p) reactions. We also discuss the role of the continuum and conclude with some possible future developments.

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arXiv2016

A simple approach to $α$-decay fine structure

We propose a simple method to evaluate $α$-transition rates to low-lying excited states in even-even nuclei. For this a realistic $α$-daughter double folding interaction is approximated by a parabola in the region where the decay process takes place. This allows us to evaluate the penetration probability analytically. The main experimental features of branching ratios to excited states are reproduced by this simple approach.

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arXiv2014

On the Validity of the Geiger-Nuttall Alpha-Decay Law and its Microscopic Basis

The Geiger-Nuttall (GN) law relates the partial $α$-decay half-life with the energy of the escaping $α$ particle and contains for every isotopic chain two experimentally determined coefficients. The expression is supported by several phenomenological approaches, however its coefficients lack a fully microscopic basis. In this paper we will show that: 1) the empirical coefficients that appear in the GN law have a deep physical meaning and 2) the GN law is successful within the restricted experimental data sets available so far, but is not valid in general. We will show that, when the dependence of logarithm values of the $α$ formation probability on the neutron number is not linear or constant, the GN law is broken. For the $α$ decay of neutron-deficient nucleus $^{186}$Po, the difference between the experimental half-life and that predicted by the GN Law is as large as one order of magnitude.

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arXiv2012

Analytic proof of partial conservation of seniority in $j=9/2$ shells

A partial conservation of the seniority quantum number in $j=9/2$ shells has been found recently in a numerical application. In this paper a complete analytic proof for this problem is derived as an extension of the work by Zamick and P. Van Isacker [Phys. Rev. C 78 (2008) 044327]. We analyze the properties of the non-diagonal matrix elements with the help of the one-particle and two-particle coefficients of fractional parentage (cfp's). It is found that all non-diagonal (and the relevant diagonal) matrix elements can be re-expressed in simple ways and are proportional to certain one-particle cfp's. This remarkable occurrence of partial dynamic symmetry is the consequence of the peculiar property of the $j=9/2$ shell, where all $v=3$ and 5 states are uniquely defined.

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arXiv2012

Coherence features of the spin-aligned neutron-proton pair coupling scheme

The seniority scheme has been shown to be extremely useful for the classification of nuclear states in semi-magic nuclei. The neutron-proton ($np$) correlation breaks the seniority symmetry in a major way. As a result, the corresponding wave function is a mixture of many components with different seniority quantum numbers. In this contribution we show that the $np$ interaction may favor a new kind of coupling in $N=Z$ nuclei, i.e., the so-called isoscalar spin-aligned $np$ pair mode. Shell model calculations reveal that the ground and low-lying yrast states of the $N = Z$ nuclei $^{92}$Pd and $^{96}$Cd may mainly be built upon such spin-aligned $np$ pairs each carrying the maximum angular momentum $J = 9$ allowed by the shell $0g_{9/2}$ which is dominant in this nuclear region.

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arXiv2012

Competition of different coupling schemes in atomic nuclei

Shell model calculations reveal that the ground and low-lying yrast states of the $N=Z$ nuclei $^{92}_{46}$Pd and $^{96}$Cd are mainly built upon isoscalar spin-aligned neutron-proton pairs each carrying the maximum angular momentum J=9 allowed by the shell $0g_{9/2}$ which is dominant in this nuclear region. This mode of excitation is unique in nuclei and indicates that the spin-aligned pair has to be considered as an essential building block in nuclear structure calculations. In this contribution we will discuss this neutron-proton pair coupling scheme in detail. In particular, we will explore the competition between the normal monopole pair coupling and the spin-aligned coupling schemes. Such a coupling may be useful in elucidating the structure properties of $N=Z$ and neighboring nuclei.

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arXiv2012

Multistep shell model in the complex energy plane

We have adopted the multistep shell model in the complex energy plane to study nuclear excitations occurring in the continuum part of the spectrum. In this method one proceeds by solving the shell model equations in a successive manner. That is, in each step one constructs the building blocks to be used in future steps. We applied this formalism to analyze the unbound nuclei $^{12,13}$Li starting from the one-particle states in $^{10}$Li and two-particle states in $^{11}$Li. In the former case the excitations correspond to the motion of three particles partitioned as the product of a one-particle and two-particle systems. The ground state of $^{12}$Li is thus calculated to be an antibound (virtual) state. In the four-particle system $^{13}$Li the states can be constructed as the coupling of two correlated pairs. We found that there is no bound or antibound state in $^{13}$Li.

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arXiv2011

Multistep shell model description of spin-aligned neutron-proton pair coupling

The recently proposed spin-aligned neutron-proton pair coupling scheme is studied within a non-orthogonal basis in term of the multistep shell model. This allows us to identify simultaneously the roles played by other configurations such as the normal pairing term. The model is applied to four-, six- and eight-hole $N=Z$ nuclei below the core $^{100}$Sn.

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arXiv2011

Spin-aligned neutron-proton pair mode in atomic nuclei

Shell model calculations using realistic interactions reveal that the ground and low-lying yrast states of the $N=Z$ nucleus $^{92}_{46}$Pd are mainly built upon isoscalar neutron-proton pairs each carrying the maximum angular momentum J=9 allowed by the shell $0g_{9/2}$ which is dominant in this nuclear region. This structure is different from the ones found in the ground and low-lying yrast states of all other even-even nuclei studied so far. The low-lying spectrum of excited states generated by such correlated neutron-proton pairs has two distinctive features: i) the levels are almost equidistant at low energies and ii) the transition probability $I\rightarrow I-2$ is approximately constant and strongly selective. This unique mode is shown to replace normal isovector pairing as the dominating coupling scheme in $N=Z$ nuclei approaching the doubly-magic nucleus $^{100}$Sn.

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arXiv2010

Analysis of the unbound spectrum of $^{12}$Li

The unbound nucleus $^{12}$Li is evaluated by studying three-neutron one-proton excitations within the multistep shell model in the complex energy plane. It is found that the ground state of this system consists of an antibound $2^-$ state. A number of narrow states at low energy are found which ensue from the coupling of resonances in $^{11}$Li to continuum states close to threshold.

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arXiv2010

Alternate proof of the Rowe-Rosensteel proposition and seniority conservation

For a system with three identical nucleons in a single-$j$ shell, the states can be written as the angular momentum coupling of a nucleon pair and the odd nucleon. The overlaps between these non-orthonormal states form a matrix which coincides with the one derived by Rowe and Rosensteel [Phys. Rev. Lett. {\bf 87}, 172501 (2001)]. The propositions they state are related to the eigenvalue problems of the matrix and dimensions of the associated subspaces. In this work, the propositions will be proven from the symmetric properties of the $6j$ symbols. Algebraic expressions for the dimension of the states, eigenenergies as well as conditions for conservation of seniority can be derived from the matrix.

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arXiv2010

Molecular structure of highly-excited resonant states in $^{24}$Mg and the corresponding $^8$Be+$^{16}$O and $^{12}$C+$^{12}$C decays

Exotic $^8$Be and $^{12}$C decays from high-lying resonances in $^{24}$Mg are analyzed in terms of a cluster model. The calculated quantities agree well with the corresponding experimental data. It is found that the calculated decay widths are very sensitive to the angular momentum carried by the outgoing cluster. It is shown that this property makes cluster decay a powerful tool to determine the spin as well as the molecular structures of the resonances.

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arXiv2010

Abrupt changes in alpha decay systematics as a manifestation of collective nuclear modes

An abrupt change in $α$ decay systematics around the N=126 neutron shell closure is discussed. It is explained as a sudden hindrance of the clustering of the nucleons that eventually form the $α$ particle. This is because the clustering induced by the pairing mode acting upon the four nucleons is inhibited if the configuration space does not allow a proper manifestation of the pairing collectivity.

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arXiv2010

Calculation of the spectrum of 12Li by using the multistep shell model method in the complex energy plane

The unbound nucleus $^{12}$Li is evaluated by using the multistep shell model in the complex energy plane assuming that the spectrum is determined by the motion of three neutrons outside the $^9$Li core. It is found that the ground state of this system consists of an antibound $1/2^+$ state and that only this and a $1/2^-$ and a $5/2^+$ excited states are physically meaningful resonances.

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arXiv2008

Effects due to Resonant and Continuum States on the Neutrino-Nucleus Cross Section

Estimates of the neutrino-nucleus cross section, for the charged-current process nu+208Pb-> e+208Bi, are presented. The nuclear structure calculations have been performed by considering bound, resonant, and continuum states in the single-particle basis used to construct correlated proton-particle neutron-hole configurations. The observed features of the spectrum of 208Bi have been reproduced, as accurately as possible, by diagonalizing a phenomenological multipole-multipole interaction. Calculations of the cross section, for values of q 200 $ MeV, were performed, and the dependence of the results upon the choice of the residual proton-neutron interaction was investigated. It is found that the inclusion of resonant states in the calculation of the nuclear wave functions increases the neutrino-nucleus cross section, and that the contribution of the continuum is negligible.

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arXiv2006

Systematics of proton emission

A very simple formula is presented that relates the logarithm of the half-life, corrected by the centrifugal barrier, with the Coulomb parameter in proton decay processes. The corresponding experimental data lie on two straight lines which appear as a result of a sudden change in the nuclear shape marking two regions of deformation independently of the angular momentum of the outgoing proton. This feature provides a powerful tool to assign experimentally quantum numbers in proton emitters.

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arXiv2005

A Complex Shell Model Representation Including Antibound States

A generalization of the Complex Shell Model formalism is presented which includes antibound states in the basis. These states, together with bound states, Gamow states, and the continuum background, represented by properly chosen scattering waves, form a representation where all states are treated on the same footing. Two-particle states are evaluated within this formalism and observable two-particle resonances are defined. The formalism is illustrated in the well known case of $^{11}$Li in its bound ground state and in $^{70}$Ca(gs), which is also bound. Both cases are found to have a halo structure. These halo structures are described within the generalized Complex Shell Model. We investigated the formation of two-particle resonances in these nuclei, but no evidence of such resonances was found.

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arXiv2004

Alpha Decay Hindrance Factors: A Probe of Mean Field Wave Functions

A simple model to calculate alpha-decay Hindrance Factors is presented. Using deformation values obtained from PES calculations as the only input, Hindrance Factors for the alpha-decay of Rn- and Po-isotopes are calculated. It is found that the intrinsic structure around the Fermi surface determined by the deformed mean field plays an important role in determining the hindrance of alpha-decay. The fair agreement between experimental and theoretical Hindrance Factors suggest that the wave function obtained from the energy minima of the PES calculations contains an important part of the correlations that play a role for the alpha-decay. The calculated HF that emerges from these calculations render a different interpretation than the commonly assumed n-particle n-hole picture.

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