arXiv subjects

Mihai Horoi

Publications and source records attributed to Mihai Horoi.

35 records · Page 2Linked to original sources

arXiv2012

Shell model analysis of competing mechanism to the double-beta decay of $^{48}$Ca

Background: Neutrinoless double beta decay, if observed, would reveal physics beyond the Standard Model (SM) of particle physics, namely it would prove that neutrinos are Majoran fermions and that the lepton number is not conserved. Purpose: The analysis of the results of neutrinoless double beta decay observations requires an accurate knowledge of several nuclear matrix elements (NME) for different mechanism that may contribute to the decay. We provide a complete analysis of these NME for the decay of the ground state (g.s.) of $^{48}$Ca to the g.s. $0^+_1$ and first excited $0^+_2$ state of $^{48}$Ti. Method: For the analysis we used the nuclear shell model with effective two-body interactions that were fine-tuned to describe the low-energy spectroscopy of $pf$-shell nuclei. We checked our model by calculating the two-neutrino transition probability to the g.s. of $^{48}$Ti. We also make predictions for the transition to the first excited $0^+_2$ state of $^{48}$Ti. Results: We present results for all NME relevant for the neutrinoless transitions to the $0^+_1$ and $0^+_2$ states, and using the lower experimental limit for the g.s. to g.s. half-life we extract upper limits for the neutrino physics parameters. Conclusions: We provide accurate NME for the two-neutrino and neutrinoless double beta decay transitions in A=48 system, which can be further used to analyze the experimental results of double beta decay experiments when they become available.

nucl-th↗

arXiv2012

Fast, Efficient Calculations of the Two-Body Matrix Elements of the Transition Operators for Neutrinoless Double Beta Decay

To extract information about the neutrino properties from the study of neutrinoless double-beta (0νββ) decay one needs a precise computation of the nuclear matrix elements (NMEs) associated with this process. Approaches based on the Shell Model (ShM) are among the nuclear structure methods used for their computation. ShM better incorporates the nucleon correlations, but have to face the problem of the large model spaces and computational resources. The goal is to develop a new, fast algorithm and the associated computing code for efficient calculation of the two-body matrix elements (TBMEs) of the 0νββ decay transition operator, which are necessary to calculate the NMEs. This would allow us to extend the ShM calculations for double-beta decays to larger model spaces, of about 9-10 major harmonic oscillator shells. The improvement of our code consists in a faster calculation of the radial matrix elements. Their computation normally requires the numerical evaluation of two-dimensional integrals: one over the coordinate space and the other over the momentum space. By rearranging the expressions of the radial matrix elements, the integration over the coordinate space can be performed analytically, thus the computation reduces to sum up a small number of integrals over momentum. Our results for the NMEs are in a good agreement with similar results from literature, while we find a significant reduction of the computation time for TBMEs, by a factor of about 30, as compared with our previous code that uses two-dimensional integrals.

nucl-th↗

arXiv2010

Can one identify the intrinsic structure of the yrast states in $^{48}$Cr after the backbending?

The backbending phenomenon in $^{48}$Cr has been investigated using the recently developed Projected Configuration Interaction (PCI) method, in which the deformed intrinsic states are directly associated with shell model (SM) wavefunctions. Two previous explanations, (i) $K=0$ band crossing, and (ii) $K=2$ band crossing have been reinvestigated using PCI, and it was found that both explanations can successfully reproduce the experimental backbending. The PCI wavefunctions in the pictures of $K=0$ band crossing and $K=2$ band crossing are highly overlapped. We conclude that there are no unique intrinsic states associated with the yrast states after backbending in $^{48}$Cr.

nucl-th↗

arXiv2009

Shell Model Analysis of the Neutrinoless Double Beta Decay of $^{48}$Ca

The neutrinoless double beta ($0νββ$) decay process could provide crucial information to determine the absolute scale of the neutrino masses, and it is the only one that can establish whether neutrino is a Dirac or a Majorana particle. A key ingredient for extracting the absolute neutrino masses from $0νββ$ decay experiments is a precise knowledge of the nuclear matrix elements (NME) describing the half-life of this process. We developed a new shell model approach for computing the $0νββ$ decay NME, and we used it to analyze the $0νββ$ mode of $^{48}$Ca. The dependence of the NME on the short range correlations parameters, on the average energy of the intermediate states, on the finite-size cutoff parameters, and on the effective interaction used for the many-body calculations is discussed.

nucl-th↗

arXiv2009

Predominance of Prolate Nuclear Deformations Emerging from Many-Body Interactions

A new approach to the old problem of the predominance of prolate deformations among well deformed nuclei is proposed within the shell model framework. The parameter space is explored using the ensemble of random rotationally-invariant interactions. Subsets with rotational energy ratio $E(4^{+})/E(2^{+})$ and the rigid-rotor relation between the quadrupole moment $Q(2^{+})$ and the transition probability $B(E2;2^{+}\to 0^{+}))$ are found exhibiting prolate predominance. We identify matrix elements of the effective forces responsible for the predominance of prolate deformation.

nucl-th↗

arXiv2009

Improved basis selection for the Projected Configuration Interaction method applied to heavy nuclei

In a previous paper we proposed a Projected Configuration Interaction method that uses sets of axially deformed single particle states to build up the many body basis. We show that the choice of the basis set is essential for the efficiency of the method, and we propose a newly improved algorithm of selecting the projected basis states. We also extend our method to model spaces that can accomodate both parities, and can include odd-multipole terms in the effective interaction, such as the octupole contributions. %A universal algorithm of the choice of the PCI basis was presented in details. Examples of $^{52}$Fe, $^{56}$Ni, $^{68}$Se, $^{70}$Se and $^{76}$Se are calcualted showing good agreement with the full Configuration Interaction results.

nucl-th↗

arXiv2009

Angular Momentum Projected Configuration Interaction with Realistic Hamiltonians

The Projected Configuration Interaction (PCI) method starts from a collection of mean-field wave functions, and builds up correlated wave functions of good symmetry. It relies on the Generator Coordinator Method (GCM) techniques, but it improves the past approaches by a very efficient method of selecting the basis states. We use the same realistic Hamiltonians and model spaces as the Configuration Interaction (CI) method, and compare the results with the full CI calculations in the sd and pf shell. Examples of 24Mg, 28Si, 48Cr, 52Fe and 56Ni are discussed.

nucl-th↗

arXiv1998

Chaotic wave functions and exponential convergence of low-lying energy eigenvalues

We suggest that low-lying eigenvalues of realistic quantum many-body hamiltonians, given, as in the nuclear shell model, by large matrices, can be calculated, instead of the full diagonalization, by the diagonalization of small truncated matrices with the exponential extrapolation of the results. We show numerical data confirming this conjecture. We argue that the exponential convergence in an appropriate basis may be a generic feature of complicated ("chaotic") systems where the wave functions are localized in this basis.

nucl-th↗

arXiv1994

Parity Mixed Doublets in A = 36 Nuclei

The $γ$-circular polarizations ($P_γ$) and asymmetries ($A_γ$) of the parity forbidden M1 + E2 $γ$-decays: $^{36}Cl^{\ast} (J^π = 2^{-}; T = 1; E_{x} = 1.95 $ MeV) $\rightarrow$ $^{36}Cl (J^π = 2^{+}; T = 1; g.s.)$ and $^{36}Ar^{\ast} (J^π = 2^{-}; T = 0; E_{x} = 4.97 $ MeV) $\rightarrow$ $^{36}Ar^{\ast} (J^π = 2^{+}; T = 0; E_{x} = 1.97 $ MeV) are investigated theoretically. We use the recently proposed Warburton-Becker-Brown shell-model interaction. For the weak forces we discuss comparatively different weak interaction models based on different assumptions for evaluating the weak meson-hadron coupling constants. The results determine a range of $P_γ$ values from which we find the most probable values: $P_γ$ = $1.1 \cdot 10^{-4}$ for $^{36}Cl$ and $P_γ$ = $3.5 \cdot 10^{-4}$ for $^{36}Ar$.

nucl-th↗

arXiv1994

Staggering of the Nuclear Charge Radii in a Superfluid Model with Good Particle Number

A simple superfluid model with an effective four body interaction of monopole pairing type is used to explain the staggering of the charge radii in the isotope chains. The contribution of deformation and of the particle number projection are analyzed for the Sn isotopes. Good results are obtained for the staggering parameters and neutron pairing energies.

nucl-th↗

arXiv1994

Chaos {\sl vs} Thermalization in the Nuclear Shell Model

Generic signatures of quantum chaos found in realistic shell model calculations are compared with thermal statistical equilibrium. We show the similarity of the informational entropy of individual eigenfunctions in the mean field basis to the thermodynamical entropy found from the level density. Mean occupation numbers of single-particle orbitals agree with the Fermi-Dirac distribution despite the strong nucleon interaction.

nucl-th↗

arXiv1994

Downloading the Nuclear Structure Shell Model Code OXBASH from INTERNET

This document explains how to download the OXBASH code for nuclear structure calculations from the NSCL anonymous server and get it running on VAX (VMS), ALPHA (OpenVMS) and IBM RS/6000 (aix) computers. The physics behind the code is explained in the OXBASH manual, which is part of the downloading package. Everybody is welcome to download the code and use it under the conditions described below.

nucl-th↗

arXiv1994

Truncation Method for the Shell Model Calculation

A method of truncating the large shell model basis is outlined. It relies on the order given by the unperturbed energies of the basis states and on the constancy of their spreading widths. Both quantities can be calculated by a simple averaging procedure. The method is tested in the sd shell where the JT dimensions are of the order of a few thousand. It proves to be very effective in the middle of the fp shell where JT dimensions of the order of a few million are truncated to a few thousand.

nucl-th↗

arXiv1994

Chaos and Order in the Shell Model Eigenvectors

The energies and wave functions of stationary many-body states are analyzed to look for the signatures of quantum chaos. Shell model calculations with the Wildenthal interaction are performed in the $J-T$ scheme for 12 particles in the $sd$-shell. The local level statistics are in perfect agreement with the GOE predictions. The analysis of the amplitudes of the eigenvectors in the shell model basis with the aid of the informational entropy and moments of the distribution function shows evidence for local chaos with a localization length reaching 90\% of the total dimension in the middle of the spectrum. The degree of chaoticity is sensitive to the the strength of the residual interaction as compared to the single particle energy spacing.

nucl-th↗

arXiv1994

Toward a Consistent Description of the PNC Experiments in A=18-21 Nuclei

The experimental PNC results in $^{18}$F, $^{19}$F, $^{21}$Ne and the current theoretical analysis show a discrepancy . If one interprets the small limit of the experimentally extracted PNC matrix element for $^{21}$Ne as a destructive interference between the isoscalar and the isovector contribution, then it is difficult to understand why the isovector contribution in $^{18}$F is so small while the isoscalar + isovector contribution in $^{19}$F is relatively large. In order to understand the origin of this discrepancy a comparison of the calculated PNC matrix elements was performed. It is shown that the $^{18}$F and $^{21}$Ne matrix elements contain important contributions from 3$\hbar ω$ and 4$\hbar ω$ configuration and that the (0+1)$\hbar ω$ calculations give distorted results.

nucl-th↗

arXiv1994

Scaling Law in Cluster Decay

A recently proposed scaling law for the decay time of alpha particles is generalized for cluster decay. It is shown that for the decay of even-even parents, $logT_{1/2}$ depends linearly on the scaling variable S=(Z$_{c}$Z$_{d})^{0.6}/\sqrt{Q_{c}}$ and on the square root of the reduced mass of cluster and daughter.

nucl-th↗

arXiv1994

New calculations of the PNC Matrix Element for the $J^πT$ 0$^{+}1,0^{-}1$ doublet in $^{14}$N

A new calculation of the predominantly isoscalar PNC matrix element between the $J^πT$ $0^{+}1,0^{-}1$ (E$_{x} \approx$ 8.7 MeV) states in $^{14}$N has been carried out in a (0+1+2+3+4)$\hbar ω$ model space with the Warburton-Brown interaction. The magnitude of the PNC matrix element of 0.22 to 0.34 eV obtained with the DDH PNC interaction is substantially suppressed compared with previous calculations in smaller model spaces but shows agreement with the preliminary Seattle experimental data. The calculated sign is opposite to that obtained experimentally, and the implications of this are discussed.

nucl-th↗