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Register a new userGround-state energies and charge radii of $^{4}$He, $^{16}$O, $^{40}$Ca, and $^{56}$Ni in the unitary-model-operator approach
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We study the nuclear ground-state properties by using the unitary-model-operator approach (UMOA). Recently, the particle-basis formalism has been introduced in the UMOA and enables us to employ the charge-dependent nucleon-nucleon interaction. We evaluate the ground-state energies and charge radii of $^{4}$He, $^{16}$O, $^{40}$Ca, and $^{56}$Ni with the charge-dependent Bonn potential. The ground-state energy is dominated by the contributions from the one- and two-body cluster terms, while, for the radius, the one-particle-one-hole excitations are more important than the two-particle-two-hole excitations. The calculated results reproduce the trend of experimental data of the saturation property for finite nuclei.
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Inclusive as well as exclusive energy spectra of the light charged particles emitted in the $^{28}Si(E_{lab}=112.6 MeV) + ^{28}Si,^{12}C$ reactions have been measured at the Strasbourg VIVITRON facility in the angular range 15^0 - 150^0, using the ICARE multidetector array. The experimental energy spectra of $alpha$-particles are generally well reproduced by the statistical model with a spin-dependent level density indicating the onset of defomations at high spin.
The ground-state energies and radii for $^{4}$He, $^{16}$O, and $^{40}$Ca are calculated with the unitary-model-operator approach (UMOA). In the present study, we employ the similarity renormalization group (SRG) evolved nucleon-nucleon ($NN$) and three-nucleon ($3N$) interactions based on the chiral effective field theory. This is the first UMOA calculation with both $NN$ and $3N$ interactions. The calculated ground-state energies and radii are consistent with the recent {it ab initio} results with the same interaction. We evaluate the expectation values with two- and three-body SRG evolved radius operators, in addition to those with the bare radius operator. With the aid of the higher-body evolution of radius operator, it is seen that the calculated radii tend to be SRG resolution-scale independent. We find that the SRG evolution gives minor modifications for the radius operator.
The reformulated coupled-cluster method (CCM), in which average many-body potentials are introduced, provides a useful framework to organize numerous terms appearing in CCM equations, which enables us to clarify the structure of the CCM theory and physical importance of various terms more easily. We explicitly apply this framework to $^4$He, retaining one-body and two-body correlations as the first illustrating attempt. Numerical results with using two modern nucleon-nucleon interactions (AV18 and CD-Bonn) and their low-momentum interactions are presented. The characters of short-range and many-body correlations are discussed. Although not considered explicitly, the expression of the ground-state energy in the presence of a three-nucleon force is given.
In the earlier unitary-model-operator approach (UMOA), one-body correlations have been taken into account approximately by the diagonalization of unitary-transformed Hamiltonians in the $0p0h$ and $1p1h$ space. With this prescription, the dependence of the harmonic-oscillator energy ($hbaromega$) on calculated observables is not negligible even at larger model spaces. In the present work, we explicitly introduce the one-body correlation operator so that it optimizes the single-particle basis states and then reduces the $hbaromega$-dependence. For an actual demonstration, we calculate the energy and radius for the $^{4}$He ground state with the softened nucleon-nucleon ($NN$) interactions from Argonne v18 (AV18) and chiral effective field theory ($chi$EFT) up to the next-to-next-to-next leading order (N$^{3}$LO). As a result, we obtain practically $hbaromega$-free results at sufficiently large model spaces. The present results are reasonably close to those by the other ab initio calculations with the same $NN$ interactions. This methodological development enables us more systematic analysis of calculation results in the UMOA. We also discuss qualitatively the origin of the $hbaromega$-dependence on calculated observables in a somewhat simplified way.
We demonstrate the capability of coupled-cluster theory to compute the Coulomb sum rule for the $^4$He and $^{16}$O nuclei using interactions from chiral effective field theory. We perform several checks, including a few-body benchmark for $^4$He. We provide an analysis of the center-of-mass contaminations, which we are able to safely remove. We then compare with other theoretical results and experimental data available in the literature, obtaining a fair agreement. This is a first and necessary step towards initiating a program for computing neutrino-nucleus interactions from first principles and supporting the experimental long-baseline neutrino program with a state-of-the-art theory that can reach medium-mass nuclei.
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