Efficient algorithm for representations of U(3) in U(N)

Langr, Daniel; Dytrych, Tomáš; Draayer, J. P.; Launey, Kristina D.; Tvrdík, Pavel

doi:10.1016/j.cpc.2019.05.018

Cited by 19 publications

(26 citation statements)

References 8 publications

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“…Then using the spherical harmonics representation of the vector ( nα = | n| 4π/3Y 1 α ( n)), and taking into consideration the spatial configuration of n, the expression of S n (q, K) can be further simplified as given in Eq. (13).…”

Section: Discussionmentioning

confidence: 99%

“…The development of nucleon-nucleon (N N ) and three-nucleon (3N ) interactions derived from chiral effective field theory (see, e.g., [7][8][9][10][11][12]) together with the utilization of massively parallel computing resources (e.g., see [13][14][15][16][17]), have placed ab initio large-scale simulations at the frontier of nuclear structure and reaction explorations. Among other successful many-body theories, the ab initio no-core shell-model (NCSM) approach (see, e.g., [18][19][20][21]), has over the last decade taken center stage in the development of microscopic tools for studying the structure of atomic nuclei.…”

Section: Introductionmentioning

confidence: 99%

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Ab initio Leading Order Effective Potentials for Elastic Nucleon-Nucleus Scattering

Burrows,

Baker,

Elster

et al. 2020

Preprint

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Background: Calculating microscopic effective interactions (optical potentials) for elastic nucleon-nucleus scattering has already in the past led to a large body of work. For first-order calculations a nucleon-nucleon (NN ) interaction and a one-body density of the nucleus were taken as input to rigorous calculations of microscopic full-folding calculations.Purpose: Based on the spectator expansion of the multiple scattering series we employ a chiral next-to-next-toleading order (NNLO) nucleon-nucleon interaction on the same footing in the structure as well as in the reaction calculation to obtain an in leading-order consistent effective potential for nucleon-nucleus elastic scattering, which includes the spin of the struck target nucleon. Methods:The first order effective folding potential is computed by first deriving a nonlocal scalar density as well as a spin-projected momentum distribution. Those are then integrated with the off-shell Wolfenstein amplitudes A, C, and M . The resulting nonlocal potential serves as input to a momentum-space Lippmann-Schwinger equation, whose solutions are summed to obtain the nucleon-nucleus scattering observables.Results: We calculate elastic scattering observables for 4 He, 6 He, 8 He, 12 C, and 16 O in the energy regime between 100 and 200 MeV projectile kinetic energy, and compare to available data. We also explore the extension down to about 70 MeV, and study the effect of ignoring the spin of the struck nucleon in the nucleus. Conclusions:In our calculations we contrast elastic scattering off closed-shell and open-shell nuclei. We find that for closed-shell nuclei the approximation of ignoring the spin of the struck target nucleon is excellent. We only see effects of the spin of the struck target nucleon when considering 6 He and 8 He, which are nuclei with a N/Z ratio larger than 1.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Ab initio Leading Order Effective Potentials for Elastic Nucleon-Nucleus Scattering

Burrows,

Baker,

Elster

et al. 2020

Preprint

View full text Add to dashboard Cite

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“…The SA-NCSM adopts powerful mathematical algorithms of group theory [6,7] to decompose a given model space in terms of U(3) irreps constructed in proton-neutron formalism with the spatial part of basis classified by the SU(3) ⊃ SO(3) group-subgroup chain [8]. Thereby each many-nucleon basis state can be schematically labeled as…”

Section: U(3) U(3) U(3) Symmetry-adapted Basismentioning

confidence: 99%

Ab initio View of Emergent Symplectic Symmetry and Its Crutial Role in Nuclear Dynamics

Dytrych¹

2022

Bulg.J.Phys.

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Results of large-scale first principle nuclear structure studies using the symmetry-adapted no-core shell model are reported. It is shown that nuclei up through the intermediate-mass region display highly regular and ubiquitous patterns of dominant nuclear shapes that vibrate and rotate. This emergent structure is tied to an approximate symplectic Sp(3, R) symmetry, and it is shown to determine dominant features of low-lying states, even in close-to-spherical nuclear states without any recognizable rotational properties.

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“…Progress in ab initio nuclear structure, both in terms of the development of more specialized realistic interactions [20][21][22][23] and numerical improvements in the many-body methods [24][25][26][27], have illustrated the large extent to which first principles calculations can describe nuclear states. In particular, the properties of excited states are increasingly well described from first principles, including collectivity in light to medium-mass nuclei [7,8] and the emergence of rotational bands [28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Nuclear spin features relevant to ab initio nucleon-nucleus elastic scattering

Baker,

Burrows,

Elster

et al. 2021

Preprint

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Background: Effective interactions for elastic nucleon-nucleus scattering from first principles require the use of the same nucleon-nucleon interaction in the structure and reaction calculations, as well as a consistent treatment of the relevant operators at each order.Purpose: Previous work using these interactions has shown good agreement with available data. Here, we study the physical relevance of one of these operators, which involves the spin of the struck nucleon, and examine the interpretation of this quantity in a nuclear structure context.Methods: Using the framework of the spectator expansion and the underlying framework of the no-core shell model, we calculate and examine spin-projected, one-body momentum distributions required for effective nucleonnucleus interactions in J = 0 nuclear states. Results:The calculated spin-projected, one-body momentum distributions for 4 He, 6 He, and 8 He display characteristic behavior based on the occupation of protons and neutrons in single particle levels, with more nucleons of one type yielding momentum distributions with larger values. Additionally, we find this quantity is strongly correlated to the magnetic moment of the 2 + excited state in the ground state rotational band for each nucleus considered.Conclusions: We find that spin-projected, one-body momentum distributions can probe the spin content of a J = 0 wave function. This feature may allow future ab initio nucleon-nucleus scattering studies to inform spin properties of the underlying nucleon-nucleon interactions. The observed correlation to the magnetic moment of excited states illustrates a previously unknown connection between reaction observables such as the analyzing power and structure observables like the magnetic moment.

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Efficient algorithm for representations of U(3) in U(N)

Cited by 19 publications

References 8 publications

Ab initio Leading Order Effective Potentials for Elastic Nucleon-Nucleus Scattering

Ab initio Leading Order Effective Potentials for Elastic Nucleon-Nucleus Scattering

Ab initio View of Emergent Symplectic Symmetry and Its Crutial Role in Nuclear Dynamics

Nuclear spin features relevant to ab initio nucleon-nucleus elastic scattering

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