We propose an importance-truncation scheme for the large-scale nuclear shell model that extends its range of applicability to larger valence spaces and mid-shell nuclei. It is based on a perturbative measure for the importance of individual basis states that acts as an additional truncation for the many-body model space in which the eigenvalue problem of the Hamiltonian is solved numerically. Through a posteriori extrapolations of all observables to vanishing importance threshold, the full shell-model results can be recovered. In addition to simple threshold extrapolations, we explore extrapolations based on the energy variance. We apply the importance-truncated shell model for the study of 56-Ni in the pf valence space and of 60-Zn and 64-Ge in the pfg9/2 space. We demonstrate the efficiency and accuracy of the approach, which pave the way for future shell-model calculations in larger valence spaces with valence-space interactions derived in ab initio approaches.
Trace formulas for the contributions of degenerate periodic-orbit families to the semiclassical level density in truncated spherical hard-wall potentials are derived. In addition to the portion of the continuous periodic-orbit family contribution which persists after truncation, end-point corrections to the truncated family should be taken into account. I propose a formula to evaluate these end-point corrections as separate contributions of what I call marginal orbits. Applications to the two-dimensional billiard and three-dimensional cavity systems with the three-quadratic-surfaces shape para…
We explore the systematics of ground-state and excitation energies in singly-strange hypernuclei throughout the helium and lithium isotopic chains --- from $^5_Λ$He to $^{11}_Λ$He and from $^7_Λ$Li to $^{12}_Λ$Li --- in the ab initio no-core shell model with importance truncation. All calculations are based on two- and three-baryon interaction from chiral effective field theory and we employ a similarity renormalization group transformation consistently up to the three-baryon level to improve the model-space convergence. While the absolute energies of hypernuclear states show a systematic vari…
Solution of the Nuclear Shell Model by Symmetry-Dictated Truncation
利用费米子动力学对称模型的动力学对称性作为球壳模型的截断原理。利用通常的原则，能量决定截断选择一个价空间，和dedicated截断选择一个集体的子空间的价空间，我们能够减少全壳模型空间的管理与现代超级计算机的尺寸之一，即使是最重的核。由此产生的壳模型，然后包括对角化的限制子空间内的有效哈密顿量。该理论不受任何对称性限制，如果截断空间的有效相互作用可以确定，则该理论代表了原壳模型的完整解。作为构建这种相互作用的第一步，我们提出了一个经验确定其矩阵元素的集体子空间中没有破碎的对一组具有代表性的原子核与$130\le A \le 250$。我们证明，这种有效的相互作用可以参数化的几个数量随粒子数缓慢变化，并能够描述这些核的低能量观测范围广泛。最后，我们给出了一个简短的讨论扩展这些方法，包括一个单一的破碎集体对。
We have reported a systematic shell model description of the experimental Gamow-Teller transition strength for $^{44}$Sc $\rightarrow$ $^{44}$Ca, $^{45}$Ti $\rightarrow$ $^{45}$Sc, $^{48}$Ti $\rightarrow$ $^{48}$V, $^{66}$Co $\rightarrow$ $^{66}$Ni, and $^{66}$Fe $\rightarrow$ $^{66}$Co transitions using KB3G and GXPF1A interactions for $fp$ model space. In order to see the importance of higher orbital for $^{66}$Co $\rightarrow$ $^{66}$Ni and $^{66}$Fe $\rightarrow$ $^{66}$Co transitions, we have reported the shell model results with $fpg_{9/2}$ space using GXPF1Br+$V_{MU}$ interaction. We ha…
In the present work, we have reported shell model results for open shell nuclei Ne, Mg and Si isotopes with $10 \leq N \leq 20$ in $sd$-shell model space. We have performed calculations in $sd$ shell with two $ab~initio$ approaches: in-medium similarity renormalization group (IM-SRG) and coupled-cluster (CC) theory. We have also performed calculations with phenomenological USDB interaction and chiral effective field theory based CEFT interaction. The results for rotational spectra and $B(E2;2_1^+\rightarrow 0_1^+)$ transitions are reported for even-mass isotopes. The IM-SRG and CC results are …
We extend the No-Core Shell Model (NCSM) methodology to incorporate strangeness degrees of freedom and apply it to single-$Λ$ hypernuclei. After discussing the transformation of the hyperon-nucleon (YN) interaction into Harmonic-Oscillator (HO) basis and the Similarity Renormalization Group transformation applied to it to improve model-space convergence, we present two complementary formulations of the NCSM, one that uses relative Jacobi coordinates and symmetry-adapted basis states to fully exploit the symmetries of the hypernuclear Hamiltonian, and one working in a Slater determinant basis o…
Expansion many-body methods correspond to solving complex tensor networks. The (iterative) solving of the network and the (repeated) storage of the unknown tensors requires a computing power growing polynomially with the size of basis of the one-body Hilbert space one is working with. Thanks to current computer capabilities, ab initio calculations of nuclei up to mass $A\sim100$ delivering a few percent accuracy are routinely feasible today. However, the runtime and memory costs become quickly prohibitive as one attempts (possibly at the same time) (i) to reach out to heavier nuclei, (ii) to e…
In the shell-model framework, valence-space Hamiltonians connecting multiple major-oscillator shells are of key interest for investigating the physics of neutron-rich nuclei, which have been the subject of intense experimental activity for decades. Here we present an extension of the ab initio valence-space in-medium similarity renormalization group which allows the derivation of such Hamiltonians nonperturbatively. Starting from initial two- and three-nucleon forces from chiral effective field theory, we then calculate properties of nuclei in the important island-of-inversion region above oxy…
An exact relation which links the ideal model space to be used in A-body calculations when the two-body interaction is given in a truncated model space is derived. Its implications on the effective field theory (EFT) approach to no-core-shell-model (NCSM) is analyzed. Some insights regarding whether details of two-body interaction becomes less important in the calculations of many-body system are given. The result suggests that there might be a way to establish an EFT expansion for heavy nuclei and nuclear matter with an effective intereaction which has a much simpler form than the nucleon-nuc…
Recent investigations have emphasized the importance of uncertainty quantification (UQ) to describe errors in nuclear theory. We carry out UQ for configuration-interaction shell model calculations in the $1s$-$0d$ valence space, investigating the sensitivity of observables to perturbations in the 66 parameters (matrix elements) of a high-quality empirical interaction. The large parameter space makes computing the corresponding Hessian numerically costly, so we compare a cost-effective approximation, using the Feynman-Hellmann theorem, to the full Hessian and find it works well. Diagonalizing t…
