The convergence of no-core shell model (NCSM) calculations using renormalization group evolved low-momentum two-nucleon interactions is studied for light nuclei up to Li-7. Because no additional transformation was used in applying the NCSM framework, the energy calculations satisfy the variational principle for a given Hamiltonian. Dramatic improvements in convergence are found as the cutoffs are lowered. The renormalization group equations are truncated at two-body interactions, so the evolution is only approximately unitary and converged energies for A > 2 vary with the cutoff. This approximation is systematic, however, and for useful cutoff ranges the energy variation is comparable to natural-size truncation errors inherent from the initial chiral effective field theory potential.
Algebraic models are proposed for the description of the shell-like quarteting of the nucleons both on the phenomenologic and on the semimicroscopic levels. In the previous one the quartet is considered as a structureless object, while in the latter one its constituents are treated explicitely. The excitation spectrum is generated by the SU(3) formalism in both cases. An application to the $^{20}$Ne nucleus is presented.
We perform \textit{ab initio} no-core shell-model calculations for $A=18$ and $19$ nuclei in a $4\hbarΩ$, or $N_{\rm max}=4$, model space by using the effective JISP16 and chiral N3LO nucleon-nucleon potentials and transform the many-body effective Hamiltonians into the $0\hbarΩ$ model space to construct the $A$-body effective Hamiltonians in the $sd$-shell. We separate the $A$-body effective Hamiltonians with $A=18$ and $A=19$ into inert core, one-, and two-body components. Then, we use these core, one-, and two-body components to perform standard shell-model calculations for the $A=18$ and $…
Spectroscopic Amplitudes for One--Nucleon Transfer Between 1p0f--Shell Nuclei
本文计算了1 p $0\,$ f壳层下半部分核的正常低宇称态之间单核子转移的光谱振幅。用壳模型波函数进行计算，该波函数是从核哈密顿量在由1 p $_{3/2}$，1 p $_{1/2}$，$0\,$ f $_{7/2}$和$0\,$ f $_{5/2}$轨道产生的完整态集给出的空间中的对角化过程中得到的。哈密顿量包含了Richter \etal最近导出的一体和两体相互作用。给出了单核子拾取和剥离反应的求和规则。讨论了单核子拾取或剥离引起的末态激发的选择性。
The nucleon pair shell model (NPSM) is casted into the so-called M-scheme for the cases with isospin symmetry and without isospin symmetry. The odd system and even system are treated on the same foot. The uncoupled commutators for nucleon-pairs, which are suitable for M-scheme, are given. Explicit formula of matrix elements in M-scheme for overlap, one-body operators, two-body operators are obtained. It is found that the $cpu$ time used in calculating the matrix elements in M-scheme is much shorter than that in the J-scheme of NPSM.
Spectroscopic factors involving well bound nucleons in light nuclei are calculated with standard shell model, no-core shell model and Gamow shell model. Continuum coupling is included exactly in the Gamow shell model, due to the use of the Berggren basis, which contains bound, resonance and scattering states. Conversely, it is absent from standard and no-core shell models, where a basis of harmonic oscillator states is used. As the A - 1 nuclei for which spectroscopic factors are calculated are either weakly bound or unbound, coupling to continuum is prominent, even though the A nuclei are wel…
The effect of the two-nucleon excitation from $p$ to $sd$ shell is discussed in $^{12}$C and $^{14}$C in the frame work of shell model. The recently suggested shell-model Hamiltonian YSOX provides an suitable tool to investigate the $2~\hbarω$ excitation in $psd$ region. Because the strength of the $<pp|V|sdsd>$ interaction, which represents the interaction between the $0~\hbarω$ and $2~\hbarω$ configurations, is considered in the construction of the YSOX. The level of $^{12}$C is almost independent on the $<pp|V|sdsd>$ interaction, but excitation energies of certain states in $^{14}$C are str…
Applications of rotational $SU(3)$ symmetry in nuclei, using Elliott's $SU(3)$ or pseudo-$SU(3)$ or proxy-$SU(3)$ model, often need just the lowest or leading $SU(3)$ irreducible representation (irrep) $(λ_H, μ_H)$. For nucleons in an oscillator shell $η$, with ${\cal N}=(η+1)(η+2)/2$, we have the algebra $U(r{\cal N}) \supset [U({\cal N}) \supset SU(3)] \otimes SU(r)$; $r=2$ when there are only valence protons or neutrons and $r=4$ for nucleons with isospin $T$. Presented in this paper is a simple general formula for the leading $SU(3)$ irrep $(λ_H, μ_H)$ in any given irrep $\{f\}$ of $U({\ca…
Constructing microscopic effective interactions (`optical potentials') for nucleon-nucleus (NA) elastic scattering requires in first order off-shell nucleon-nucleon (NN) scattering amplitudes between the projectile and the struck target nucleon and nonlocal one-body density matrices. While the NN amplitudes and the {\it ab intio} no-core shell-model (NCSM) calculations always contain the full spin structure of the NN problem, one-body density matrices used in traditional microscopic folding potential neglect spin contributions inherent in the one-body density matrix. Here we derive and show th…
We present No-Core Full Configuration results for the ground state energies of all particle-stable p-shell nuclei, as well as the excitation energies of more than 40 narrow states, excluding isobaric analog states. We used the chiral LENPIC nucleon-nucleon plus three-nucleon interaction at N2LO with semi-local coordinate space regulators, and also the phenomenological Daejeon16 nucleon-nucleon potential. With simple exponential extrapolations of the total energies of each state, binding energies and spectra are found to be in good agreement with experiment. Both interactions produce a trend to…
用组成质子和中子通过核子-核子和三核子力相互作用来描述轻核的结构性质和反应是核理论长期追求的目标。我将简要介绍一个有前途的技术，建立在{ \em ab initio}无核壳模型，最近出现的候选人，以达到这样一个目标：无核壳模型/共振群方法。这种方法，能够同时描述轻核中的束缚态和散射态，补充了微观集群技术与使用两个核子现实的相互作用，和微观和一致的描述的核子集群。我将讨论应用轻核二进制散射过程和聚变反应的权力恒星和地球上的聚变设施，如氘- $^3$他融合，并概述了进展，包括三核子力的形式主义和三体集团的治疗。
The relativistic particle-vibration coupling (RPVC) model is extended by the inclusion of spin- and isospin-flip excitation modes into the phonon space, introducing a new mechanism of dynamical interaction between nucleons with different isospin in the nuclear medium. Protons and neutrons exchange by collective modes which are formed by isovector $π$ and $ρ$-mesons, in turn, softened considerably because of coupling to nucleons of the medium. These modes are investigated within the proton-neutron relativistic random phase approximation (pn-RRPA) and relativistic proton-neutron time blocking ap…
