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Register a new userShell model and deformed shell model spectroscopy of $^{62}$Ga
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Praveen Chandra Srivastava Dr.
Publication date
2014
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English
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In the present work we have reported comprehensive analysis of recently available experimental data [H.M. David et al., Phys. Lett. B {bf 726}, 665 (2013)] for high-spin states up to $17^+$ with $T=0$ in the odd-odd $N=Z$ nucleus $^{62}$Ga using shell model calculations within the full $f_{5/2}pg_{9/2}$ model space and deformed shell model based on Hartee-Fock intrinsic states in the same space. The calculations have been performed using jj44b effective interaction developed recently by B.A. Brown and A.F. Lisetskiy for this model space. The results obtained with the two models are similar and they are in reasonable agreement with experimental data. In addition to the $T=0$ and $T=1$ energy bands, band crossings and electromagnetic transition probabilities, we have also calculated the pairing energy in shell model and all these compare well with the available theoretical results.
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A systematic shell model description of the experimental Gamow-Teller transition strength distributions in $^{42}$Ti, $^{46}$Cr, $^{50}$Fe and $^{54}$Ni is presented. These transitions have been recently measured via $beta$ decay of these $T_z$=-1 nuclei, produced in fragmentation reactions at GSI and also with ($^3${He},$t$) charge-exchange (CE) reactions corresponding to $T_z = + 1$ to $T_z = 0$ carried out at RCNP-Osaka.The calculations are performed in the $pf$ model space, using the GXPF1a and KB3G effective interactions. Qualitative agreement is obtained for the individual transitions, while the calculated summed transition strengths closely reproduce the observed ones.
The uncertainty quantifications of theoretical results are of great importance to make meaningful comparisons of those results with experimental data and to make predictions in experimentally unknown regions. By quantifying uncertainties, one can make more solid statements about, e.g., origins of discrepancy in some quantities between theory and experiment. We propose a novel method for uncertainty quantification for the effective interactions of nuclear shell-model calculations as an example. The effective interaction is specified by a set of parameters, and its probability distribution in the multi-dimensional parameter space is considered. This enables us to quantify the agreement with experimental data in a statistical manner and the resulting confidence intervals show unexpectedly large variations. Moreover, we point out that a large deviation of the confidence interval for the energy in shell-model calculations from the corresponding experimental data can be used as an indicator of some exotic property, e.g. alpha clustering, etc. Other possible applications and impacts are also discussed.
The configuration interaction method, which is well-known as the shell-model calculation in the nuclear physics community, plays a key role in elucidating various properties of nuclei. In general, these studies require a huge number of shell-model calculations to be repeated for parameter calibration and quantifying uncertainties. To reduce these computational costs, we propose a new workflow of shell-model calculations using a method called eigenvector continuation (EC). It enables us to efficiently approximate the eigenpairs under a given Hamiltonian by previously sampled eigenvectors. We demonstrate the validity of EC as an emulator of the shell-model calculations for a valence space, where the dimension of parameters is relatively large compared to the previous studies using EC. We also discuss its possible applications to the quantification of theoretical uncertainty, using an example of Markov chain Monte Carlo sampling for a simplified problem. Furthermore, we propose a new usage of EC: preprocessing, in which we start the Lanczos iterations from the approximate eigenvectors, and demonstrate that this can accelerate the shell-model calculations and the subsequent research cycles. With the aid of the eigenvector continuation, the eigenvectors obtained during the parameter optimization are not necessarily to be discarded, even if their eigenvalues are far from the experimental data. Those eigenvectors can become accumulated knowledge. In order to enable efficient sampling of shell-model results and to demonstrate the usefulness of the methodology described above, we developed a new shell-model code, ShellModel.jl. This code is written in Julia language and therefore flexible to add extensions for the users purposes.
The role of discrete (or point-group) symmetries is discussed in the framework of the Cluster Shell Model which describes the splitting of single-particle levels in the deformed field of cluster potentials. We discuss the classification of the eigenstates for the cases of a triangular and tetrahedral configuration of alpha-particles in terms of the irreducible representations of the double point groups D(3h) and T(d), respectively, and show how the discrete symmetry of a given eigenstate can be determined. Finally, we derive the Coriolis coupling for each one of these geometrical configurations.
In this contribution, we present the cluster shell model which is analogous to the Nilsson model, but for cluster potentials. Special attention is paid to the consequences of the discrete symmetries of three alpha-particles in an equilateral triangle configuration. This configuration is characterized by a special structure of the rotational bands which can be used as a fingerprint of the underlying geometric configuration. The cluster shell model is applied to the nucleus 13C.
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