arXiv subjects

J. G. Hirsch

Publications and source records attributed to J. G. Hirsch.

At least 37 records · Page 2Linked to original sources

arXiv2011

No singularities at the phase transition in the Dicke model

The Dicke Hamiltonian describes the simplest quantum system with atoms interacting with photons: N two level atoms inside a perfectly reflecting cavity which allows only one electromagnetic mode. It has also been successfully employed to describe superconducting circuits which behave as artificial atoms coupled to a resonator. The system exhibits a transition to a superradiant phase at zero temperature. When the interaction strength reaches its critical value, both the number of photons and of atoms in excited states in the cavity, together with their fluctuations, exhibit a sudden increase from zero. Employing symmetry-adapted coherent states it is shown that these properties scale with the number of atoms, that their reported divergences at the critical point represent the limit when this number goes to infinity, and that in this limit they remain divergent in the superradiant phase. Analytical expressions are presented for all observables of interest, for any number of atoms. Comparisons with exact numerical solutions strongly support the results.

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arXiv2010

Quadrupolar correlations and deformation effect on two neutrino $\varepsilon β^{+}$ and $\varepsilon \varepsilon $ modes of $^{156}$Dy isotope

The two-neutrino positron double-$β$ decay modes of $^{156}$Dy isotope are studied in the Projected Hartree-Fock-Bogoliubov framework for the $0^{+}\to 0^{+}$ transition. Theoretically calculated half-lives of electron-positron conversion and double-electron capture modes are presented. The effect of the quadrupolar deformation on nuclear transition matrix element $M_{2ν}$ is also investigated.

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arXiv2009

Deformation effects and neutrinoless positron $ββ$ decay of $^{96}$Ru, $^{102}$Pd, $^{106}$Cd, $^{124}$Xe, $^{130}$Ba and $^{156}$Dy isotopes within Majorona neutrino mass mechanism

The $(β^{+}β^{+})_{0ν}$ and $(\varepsilon β^{+})_{0ν}$ modes of $^{96}$Ru, $^{102}$Pd, $^{106}$Cd, $^{124}$Xe, $^{130}$Ba and $^{156}$Dy isotopes are studied in the Projected Hartree-Fock-Bogoliubov framework for the $0^{+}\to 0^{+}$ transition. The reliability of the intrinsic wave functions required to study these decay modes has been established in our earlier works by obtaining an overall agreement between the theoretically calculated spectroscopic properties, namely yrast spectra, reduced $B(E2$:$0^{+}\to 2^{+})$ transition probabilities, quadrupole moments $Q(2^{+})$ and gyromagnetic factors $g(2^{+})$ and the available experimental data in the parent and daugther even-even nuclei. In the present work, the required nuclear transition matrix elements are calculated in the Majorana neutrino mass mechanism using the same set of intrinsic wave functions as used to study the two neutrino positron double-$β$ decay modes. Limits on effective light neutrino mass $< m_ν >$ and effective heavy neutrino mass $< M_{N} >$ are extracted from the observed limits on half-lives $T_{1/2}^{0ν}(0^{+}\to 0^{+})$ of $(β^{+}β^{+})_{0ν}$ and $(\varepsilon β^{+})_{0ν}$ modes. We also investigate the effect of quadrupolar correlations vis-a-vis deformation on NTMEs required to study the $(β^{+}β^{+})_{0ν}$ and $(\varepsilon β^{+})_{0ν}$ modes.

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arXiv2009

Nuclear deformation and neutrinoless double-$β$ decay of $^{94,96}$Zr, $^{98,100}$Mo, $^{104}$Ru, $^{110}$Pd, $^{128,130}$Te and $^{150}$Nd nuclei in mass mechanism

The $(β^{-}β^{-})_{0ν}$ decay of $^{94,96}$Zr, $^{98,100}$Mo, $^{104}$Ru, $^{110}$Pd, $^{128,130}$Te and $^{150}$Nd isotopes for the $0^{+}\to 0^{+}$ transition is studied in the Projected Hartree-Fock-Bogoliubov framework. In our earlier work, the reliability of HFB intrinsic wave functions participating in the $β^{-}β^{-}$ decay of the above mentioned nuclei has been established by obtaining an overall agreement between the theoretically calculated spectroscopic properties, namely yrast spectra, reduced $B(E2$:$0^{+}\to 2^{+})$ transition probabilities, quadrupole moments $Q(2^{+})$, gyromagnetic factors $g(2^{+})$ as well as half-lives $T_{1/2}^{2ν}$ for the $0^{+}\to 0^{+}$ transition and the available experimental data. In the present work, we study the $(β^{-}β^{-})_{0ν}$ decay for the $0^{+}\to 0^{+}$ transition in the mass mechanism and extract limits on effective mass of light as well as heavy neutrinos from the observed half-lives $T_{1/2}^{0ν}(0^{+}\to 0^{+})$ using nuclear transition matrix elements calculated with the same set of wave functions. Further, the effect of deformation on the nuclear transition matrix elements required to study the $(β^{-}β^{-})_{0ν}$ decay in the mass mechanism is investigated. It is noticed that the deformation effect on nuclear transition matrix elements is of approximately same magnitude in $(β^{-}β^{-})_{2ν}$ and $(β^{-}β^{-})_{0ν}$ decay.

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arXiv2009

Multipolar correlations and deformation effect on nuclear transition matrix elements of double-$β$ decay

The two neutrino and neutrinoless double beta decay of $^{94,96}$Zr, $^{98,100}$Mo, $^{104}$Ru, $^{110}$Pd, $^{128,130}$Te and $^{150}$Nd isotopes for the $0^{+}\to 0^{+}$ transition is studied within the PHFB framework along with an effective two-body interaction consisting of pairing, quadrupole-quadrupole and hexadecapole-hexadecapole correlations. It is found that the effect of hexadecapolar correlations can be assimilated substantially as a renormalization of the quadrupole-quadrupole interaction. The effect of deformation on nuclear transition matrix elements is investigated by varying the strength of quadrupolar correlations in the parent and daughter nuclei independently. The variation of the nuclear transition matrix elements as a function of the difference in deformation parameters of parent and daughter nuclei reveals that in general, the former tend to be maximum for equal deformation and they decrease as the difference in deformation parameters increases, exhibiting a very similar trend for the $(β^{-}β^{-})_{2ν}$ and $(β^{-}β^{-})_{0ν}$ transition matrix elements.

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arXiv2009

How good are the Garvey-Kelson predictions of nuclear masses?

The Garvey-Kelson relations are used in an iterative process to predict nuclear masses in the neighborhood of nuclei with measured masses. Average errors in the predicted masses for the first three iteration shells are smaller than those obtained with the best nuclear mass models. Their quality is comparable with the Audi-Wapstra extrapolations, offering a simple and reproducible procedure for short range mass predictions. A systematic study of the way the error grows as a function of the iteration and the distance to the known masses region, shows that a correlation exists between the error and the residual neutron-proton interaction, produced mainly by the implicit assumption that $V_{np}$ varies smoothly along the nuclear landscape.

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arXiv2008

Influence of the hexadecapole deformation on the two neutrino double-$\be ta $ decay

The two neutrino double beta $(β^{-}β^{-})_{2ν}$ decay of $ ^{94,96}$Zr, $^{98,100}$Mo, $^{104}$Ru, $^{110}$Pd, $^{128,130}$Te and $^{150}$Nd nuclei for the $0^{+}\to 0^{+}$ transition is studied in the PHFB model in conjunction with the pairing plus quadrupole-quadrupole plus hexadecapole-hexadecapole effective two-body interaction and the effect of the latter is investigated on the calculation of nuclear transition matrix elements $M_{2ν}$. The reliability of the intrinsic wave functions of parent and daughter nuclei involved in the $(β^{-}β^{-})_{2ν}$ decay of above mentioned nuclei is established by obtaining an overall agreement between a number of theoretically calculated spectroscopic properties, namely the yrast spectra, reduced $B(E2$:$0^{+}\to 2^{+})$ transition probabilities, static quadrupole moments $Q(2^{+})$ and $g$-factors $g(2^{+})$ and the available experimental data. The effect of deformation on $M_{2ν}$ is also investigated to inveterate its inverse relation with nuclear deformation.

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arXiv2007

Nuclear deformation and the two neutrino double-βdecay in ^{124,126}Xe,^{128,130}Te, ^{130,132}Ba and ^{150}Nd isotopes

The two neutrino double beta decay of $^{124,126}$Xe,$^{128,130}$Te, $ ^{130,132}$Ba and $^{150}$Nd isotopes is studied in the Projected Hartree-Fock-Bogoliubov (PHFB) model. Theoretical 2$ν$ $β^{-}β^{-}$ half-lives of $^{128,130}$Te, and $^{150}$Nd isotopes, and 2$νβ^{+}β^{+}$, 2$ν$ $β^{+}EC$ and 2$ν$ $ECEC$ for $ ^{124,126}$Xe and $^{130,132}$Ba nuclei are presented. Calculated quadrupolar transition probabilities B(E2: $0^+\to 2^+$), static quadrupole moments and $g$ factors in the parent and daughter nuclei reproduce the experimental information, validating the reliability of the model wave functions. The anticorrelation between nuclear deformation and the nuclear transition matrix element $M_{2ν} $ is confirmed.

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arXiv2006

The $0^{+}\to 0^{+}$ positron double-$β$ decay with emission of two neutrinos in the nuclei $^{96}$Ru, $^{102}$Pd, $^{106}$Cd and $^{108}$Cd

Theoretical results for %the $0^{+}\to 0^{+}$ positron double-$β$ decay with emission of two neutrinos in the nuclei $^{96}$Ru, $^{102}$Pd, $^{106}$Cd and $^{108}$Cd are presented. The study employs the Hartree-Fock-Bogoliubov model to obtain the wave functions of the parent and daughter nuclei, in conjunction with the summation method to estimate the double beta decay nuclear matrix elements. The reliability of the intrinsic wave functions of $^{96,102}$Ru, $% ^{96}$Mo, $^{102,106,108}$Pd and $^{106,108}$Cd nuclei are tested by comparing the theoretically calculated spectroscopic properties with the available experimental data. Calculated half-lives $T_{1/2}^{2ν}$ of $% ^{96}$Ru, $^{102}$Pd, $^{106}$Cd and $^{108}$Cd nuclei for 2$ν$ $β^{+}β^{+}$, 2$ν$ $β^{+}EC$ and 2$ν$ $ECEC$ modes are presented. The effect of deformation on the nuclear transition matrix element $M_{2ν}$ is also studied.

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arXiv2004

Two neutrino double $β$ decay of 94v$\leq A\leq $110 nuclei for $0^+ \to 0^+$ transition

The two neutrino double beta decay of $ ^{94,96}$Zr$,^{98,100}$Mo$,^{104}$% Ru and $ ^{110}$Pd nuclei for $0^{+}\to 0^{+}$ transition is studied in the PHFB model in conjunction with the summation method. In the first step, the reliability of the intrinsic wave functions has been established by obtaining an overall agreement between a number of theoretically calculated spectroscopic properties and the available experimental data for $ ^{94,96}$% Zr$,^{94,96,98,100}$Mo, $^{98,100,104}$Ru, $^{104,110}$Pd and $^{110}$Cd isotopes. Subsequently, the PHFB wave functions of the above mentioned nuclei are employed to calculate the nuclear transition matrix elements $M_{2ν}$ as well as half-lives $T{_{1/2}^{2ν}}$. Further, we have studied the effects of deformation on the $M_{2ν}$.

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arXiv2004

Two neutrino positron double beta decay of $^{106}$Cd for $0^+ \to 0^+$ transition

The two neutrino positron double beta decay of $^{106}$Cd for 0$^{+} \to $ 0$^{+}$ transition has been studied in the Hartree-Fock-Bogoliubov model in conjunction with the summation method. In the first step, the reliability of the intrinsic wave functions of $^{106}$Cd and $^{106}$Pd nuclei has been tested by comparing the theoretically calculated results for yrast spectra, reduced $B(E2$:$0^{+}\to 2^{+})$ transition probabilities, quadrupole moments $Q(2^{+})$ and gyromagnetic factors $g(2^{+})$ with the available experimental data. In the second step, the nuclear transition matrix element $M_{2ν}$ and the half-life $T_{1/2}^{2ν}$ for 0$^{+}\to$ 0$^{+}$ transition have been calculated with these wave functions. Moreover, we have studied the effect of deformation on nuclear transition matrix element M$_{2ν}.$

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arXiv2002

Excited bands in odd-mass rare-earth nuclei

Normal parity bands are studied in 157Gd, 163Dy and 169Tm using the pseudo SU(3) shell model. Energies and B(E2) transition strengths of states belonging to six low-lying rotational bands with the same parity in each nuclei are presented. The pseudo SU(3) basis includes states with pseudo-spin 0 and 1, and 1/2 and 3/2, for even and odd number of nucleons, respectively. States with pseudo-spin 1 and 3/2 must be included for a proper description of some excited bands.

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arXiv2002

A study of randomness, correlations and collectivity in the nuclear shell model

A variable combination of realistic and random two-body interactions allows the study of collective properties, such as the energy spectra and B(E2) transition strengths in 44Ti, 48Cr and 24Mg. It is found that the average energies of the yrast band states maintain the ordering for any degree of randomness, but the B(E2) values lose their quadrupole collectivity when randomness dominates the Hamiltonian. The high probability of the yrast band to be ordered in the presence of pure random forces exhibits the strong correlations between the different members of the band.

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arXiv2002

The Pairing interaction in nuclei: comparison between exact and approximate treatments

As a model for a deformed nucleus the many level pairing model (picket fence model with ~100 levels) is considered in four approximations and compared to the exact solution given by Richardson long time ago. It is found that, as usual, the number projected BCS method improves over standard BCS but that it is much less accurate than the more sophisticated many-body-approaches which are Coupled Cluster Theory (CCT) in its SUB2 version or Self-Consistent Random Phase Approximation (SCRPA).

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arXiv2001

Inter-band B(E2) transition strengths in odd-mass heavy deformed nuclei

Inter-band B(E2) transition strengths between different normal parity bands in 163Dy and 165Er are described using the pseudo-SU(3) model. The Hamiltonian includes Nilsson single-particle energies, quadrupole-quadrupole and pairing interactions with fixed, parametrized strengths, and three extra rotor terms used to fine tune the energy spectra. In addition to inter-band transitions, the energy spectra and the ground state intra-band B(E2) strengths are reported. The results show the pseudo-SU(3) shell model to be a powerful microscopic theory for a description of the normal parity sector in heavy deformed odd-A nuclei.

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arXiv2001

E2 and M1 strengths in heavy deformed nuclei

Energy levels of the four lowest bands in 160,162,164Dy and 168Er, B(E2) transition strengths between the levels, and the B(M1) strength distribution of the ground state, all calculated within the framework of pseudo-SU(3) model, are presented. Realistic single-particle energies and quadrupole-quadrupole and pairing interaction strengths fixed from systematics were used in the calculations. The strengths of four rotor-like terms, all small relative to the other terms in the interaction, were adjusted to give an overall best fit to the energy spectra. The procedure yielded consistent parameter sets for the four nuclei.

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arXiv2000

Quasi-SU(3) truncation scheme for odd-even sd-shell nuclei

The quasi-SU(3) symmetry, as found in shell model calculations, refers to the dominance of the single particle plus quadrupole-quadrupole terms in the Hamiltonian used to describe well deformed nuclei, and to the subspace relevant in its diagonalization. It provides a very efficient basis truncation scheme. It is shown that a small number of SU(3) coupled irreps, those with the largest C_2 values within the direct product of the proton and neutron SU(3) irreps with spin 0 and 1 (for even number of particles), and spin 1/2 and 3/2 for (for odd number of nucleons), are enough to describe the low energy spectra and B(E2) transition strengths of 21Ne, 23Na and 25Mg. A simple but realistic Hamiltonian is employed. Results compare favorably both with experimental data and with full shell model calculations. Limitations and possible improvements of the schematic Hamiltonian are discussed.

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arXiv2000

Shell Model Description of $^{158}$Gd

The pseudo-SU(3) model is used to describe the low-energy spectra as well as $E2$ and $M1$ transition strengths in $^{158}$Gd. The Hamiltonian includes spherical single-particle energies, the quadrupole-quadrupole and proton and neutron pairing interactions, plus four rotor-like terms. The parameters of the Hamiltonian were fixed by systematics with the rotor-like terms determined through a least-squares analysis. The basis states are built as linear combinations of SU(3) states which are the direct product of SU(3) proton and neutron states with pseudo-spin zero. The calculated results compare favorably with the available experimental data, which demonstrates the ability of the model to describe such nuclei.

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