Abstract
We apply the hybrid-multi-determinant method using the recent chiral two-body interactions of Entem–Machleidt–Nosyk without renormalization to few nuclei up to
A
= 48. Mostly we use the bare ...fifth order NN interaction N4LO-450. For
24
Mg and
48
Cr the excitation energies of the
2
1
+
states are far larger than the corresponding experimental values.
In the past few years, in-medium similarity renormalization group methods have been introduced and developed. In these methods the Hamiltonian is evolved using a unitary transformation in order to ...decouple a reference state from the rest of the Hilbert space. Even if we start from a two-body interaction, the evolution by itself will generate many-body forces which are usually neglected. In this work we estimate the effect of these residual many-body forces by comparing results obtained with the hybrid multi-determinant method, which keeps the Hamiltonian within the two-body sector, with the corresponding results obtained with the in-medium similarity renormalization group. Although percentage-wise the effect of neglecting these induced many-body forces is not too large, they can be appreciable depending on the nucleus, the shell model space and the harmonic oscillator frequency.
Predominantly, harmonic oscillator single-particle wave functions are the preferred choice for a basis in ab initio nuclear many-body calculations. These wave-functions, although very convenient in ...order to evaluate the matrix elements of the interaction in the laboratory frame, have too fast a fall-off at large distances. In the past, as an alternative to the harmonic oscillator, other single-particle wave functions have been proposed. In this work, we propose a new single-particle basis, directly linked to nucleon-nucleon interaction. This new basis is orthonormal and complete, has the proper asymptotic behavior at large distances and does not contain the continuum which would pose severe convergence problems in nuclear many body calculations. We consider the newly proposed NNLO-opt nucleon-nucleon interaction, without any renormalization. We show that, unlike other bases, this single-particle representation has a computational cost similar to the harmonic oscillator basis with the same space truncation and it gives lower energies for 6He and 6Li.
We use the recently introduced single-particle states obtained from localized deuteron wave-functions as a basis for nuclear many-body calculations. We show that energies can be substantially lowered ...if the natural orbits (NOs) obtained from this basis are used. We use this modified basis for 10 B , 16 O and 24 Mg employing the bare NNLOopt nucleon-nucleon interaction. The lowering of the energies increases with the mass. Although in principle NOs require a full scale preliminary many-body calculation, we found that an approximate preliminary many-body calculation, with a marginal increase in the computational cost, is sufficient. The use of natural orbits based on an harmonic oscillator basis leads to a much smaller lowering of the energies for a comparable computational cost.
The energy variance extrapolation method consists of relating the approximate energies in many-body calculations to the corresponding energy variances and inferring eigenvalues by extrapolating to ...zero variance. The method needs a fast evaluation of the energy variances. For many-body methods that expand the nuclear wavefunctions in terms of deformed Slater determinants, the best available method for the evaluation of energy variances scales with the sixth power of the number of single-particle states. We propose a new method which depends on the number of single-particle orbits and the number of particles rather than the number of single-particle states. We discuss as an example the case of 4He using the chiral N3LO interaction in a basis consisting up to 184 single-particle states.
Young patients with early osteoarthritis (OA) represent a challenging population due to a combination of high functional demands and limited treatment options. Conservative measures such as injection ...and physical therapy can provide short-term pain relief but are only palliative in nature. Joint replacement, a successful procedure in the older population, is controversial in younger patients, who are less satisfied and experience higher failure rates. Therefore, while traditionally not indicated for the treatment of OA, cartilage repair has become a focus of increased interest due to its potential to provide pain relief and alter the progression of degenerative disease, with the hope of delaying or obviating the need for joint replacement. The field of cartilage repair is seeing the rapid development of new technologies that promise greater ease of application, less demanding rehabilitation and better outcomes. Concurrent procedures such as meniscal transplantation and osteotomy, however, remain of crucial importance to provide a normalized biomechanical environment for these new technologies.
Level of evidence
Systematic review, Level II.
The Broyden-Fletcher-Goldhaber-Shanno (BFGS) quasi-Newtonian scheme is known as the most efficient scheme for variational calculations of energies. This scheme is actually a member of a one-parameter ...family of variational methods, known as the Broyden
-family. In some applications to light nuclei using microscopically derived effective Hamiltonians starting from accurate nucleon-nucleon potentials, we actually found other members of the same family which have better performance than the BFGS method. We also extend the Broyden
-family of algorithms to a two-parameter family of rank-three updates which has even better performances.
.
We perform an
ab initio
calculation for the binding energy of
6
Li using the CD-Bonn 2000 NN potential renormalized with the Lee-Suzuki method. The many-body approach to the problem is the hybrid ...multideterminant method. The results indicate a binding energy of about 31MeV, within a few hundreds keV uncertainty. The center-of-mass diagnostics are also discussed.
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