Phenomenological α-α potentials

Ali, S.; Bodmer, A.R.

doi:10.1016/0029-5582(66)90829-7

Cited by 399 publications

(251 citation statements)

References 30 publications

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“…The α-particle studies use an effective α-α interaction that is typically a parametrisation as in (Ali & Bodmer 1966). Small changes in this interaction can thus cause large deviations in the condensate fraction.…”

Section: Nuclear α-Particle Condensatesmentioning

confidence: 99%

Comparing and contrasting nuclei and cold atomic gases

Zinner¹,

Jensen²

2013

J. Phys. G: Nucl. Part. Phys.

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Abstract. The experimental revolution in ultracold atomic gas physics over the past decades have brought tremendous amounts of new insight to the world of degenerate quantum systems. Here we compare and constrast the developments of cold atomic gases with the physics of nuclei since many concepts, techniques, and nomenclatures are common to both fields. However, nuclei are finite systems with interactions that are typically much more complicated than those of ultracold atomic gases. The simularities and differences must therefore be carefully addressed for a meaningful comparison and to facilitate fruitful crossdisciplinary activity. We first consider condensates of bosonic and paired systems of fermionic particles with the mean-field description but take great care to point out potential problems in the limit of small particle numbers. Along the way we review some of the basic results of BEC and BCS theory, as well as the BCS-BEC crossover and the Fermi gas in the unitarity limit, all within the context of ultracold atoms. Subsequently, we consider the specific example of an atomic Fermi gas from a nuclear physics perspective, comparing degrees of freedom, interactions, and relevant length and energy scales of cold atoms and nuclei. Next we address some attempts in nuclear physics to transfer the concepts of condensates in nuclei that can in principle be built from bosonic alpha-particle constituents. We also consider Efimov physics, a prime example of nuclear physics transfered to cold atoms, and consider which systems are more likely to show interesting bound state spectra. Finally, we address some recent studies of the BCS-BEC crossover in light nuclei and compare them to the concepts used in ultracold atomic gases. While many-body concepts such as BEC or BCS states are applicable in both subfields, we find that the interactions and finite particle numbers in nuclei can obscure the clear meaning they have in cold atoms. On the other hand, universal results from atomic physics should have impact in certain limits of the nuclear domain. In particular, with advances in the trapping of few-body atomic systems we expect a more direct exchange of ideas and results.

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Section: Nuclear α-Particle Condensatesmentioning

confidence: 99%

Comparing and contrasting nuclei and cold atomic gases

Zinner¹,

Jensen²

2013

J. Phys. G: Nucl. Part. Phys.

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“…It is assumed that this effect is small and that it can be effectively taken into account by phenomenological αΛ potential. Nuclear αα interaction is given by the phenomenological Ali-Bodmer (AB) potential [18]. This potential has the following form: V αα (r) = l=0,2,4 V l αα (r)P l , where P l is a projector onto the state of the αα pair with the orbital momentum l. The functions V l αα (r) have the form of one or two range Gaussians:…”

Section: Potentialsmentioning

confidence: 99%

“…There are different sets of the parameters for partial components V l αα (r) [18]. The parameters of version "e" of the Ali-Bodmer potential (ABe) are given in Table 1.…”

Section: Potentialsmentioning

confidence: 99%

“…We used various potential models in these calculations. In particular three variants of the αα Ali-Bodmer potential are used [18] (ABa, ABd, ABe). Note that the model "a*" of the ABa potential is modified in [31].…”

Section: Bound Statesmentioning

confidence: 99%

“…For description of αα nuclear interaction the Ali -Bodmer potential [18] is used. This potential with s, d and g-wave components has strong repulsive s-wave core that simulates the Pauli blocking for two α particles.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Faddeev calculations for the_Λ⁹Be spectrum

Filikhin

Suslov

Vlahović

2010

EPJ Web of Conferences

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Abstract. An α-cluster model is applied to study low-lying spectrum of the 9 Λ Be hypernicleus. The ααΛ threebody problem is numerically solved by the Faddeev equations in configuration space using phenomenological pair potentials. Found is a set of the potentials that reproduces experimental data for the ground state ( 1 2 + ) binding energy and excitation energy of the 5 2 + and 3 2 + states, simultaneously. This set includes the Ali-Bodmer potential of version "e" for αα and modified Tang-Herndon potential for αΛ interactions. The spin-orbit αΛ interaction is given by modified Scheerbaum potential. Low-lying energy levels are evaluated applying a variant of the analytical continuation method in coupling constant, and the experimental data for excitation energies are well reproduced by our calculations. This result improves previous α-cluster calculations. It is shown that the spectral properties of 9 Λ Be can be classified as an analog of 9 Be spectrum with the exception of several "genuine hypernuclear states", which agrees qualitatively with previous studies. The energy splitting of spin-flip doublet ( 9 2 + , 7 2 + ) is predicted.

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Few electron systems confined in Gaussian potential wells and connection to Hooke atoms

Telleria‐Allika

Mercero

Ugalde

et al. 2022

Int J of Quantum Chemistry

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In this work, we have computed and implemented one-body integrals concerning Gaussian confinement potentials over Gaussian basis functions. Then, we have set an equivalence between Gaussian and Hooke atoms and we have observed that, according to singlet and triplet state energies, both systems are equivalent for large confinement depth for a series of even number of electrons n = 2, 4, 6, 8 and 10.

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Phenomenological α-α potentials

Cited by 399 publications

References 30 publications

Comparing and contrasting nuclei and cold atomic gases

Comparing and contrasting nuclei and cold atomic gases

Faddeev calculations for the_Λ⁹Be spectrum

Few electron systems confined in Gaussian potential wells and connection to Hooke atoms

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Phenomenological α-α potentials

Cited by 399 publications

References 30 publications

Comparing and contrasting nuclei and cold atomic gases

Comparing and contrasting nuclei and cold atomic gases

Faddeev calculations for theΛ9Be spectrum

Few electron systems confined in Gaussian potential wells and connection to Hooke atoms

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Product

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Faddeev calculations for the_Λ⁹Be spectrum