Scattering length and effective range for collisions between light ions within a microscopic model

Kamouni, Rachid; Baye, Daniel Jean

doi:10.1016/j.nuclphysa.2007.04.009

Cited by 29 publications

(58 citation statements)

References 32 publications

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“…However, the procedures to reach the reduction into the three-body structure are rather different. Microscopic derivations start from nucleon-nucleon interactions and integrate away the unwanted degrees of freedom while simultaneously leaving corresponding effective interactions [16][17][18][19][20]. The mean-field model is also used for two-proton decay in the formulation named the Gamow shell model where the nucleon degrees of freedom are present and the interactions are phenomenological adjusted within the mean field [21][22][23].…”

Section: A Basic Conceptmentioning

confidence: 99%

“…The number of partial waves is then immediately rather large owing to the many allowed spin couplings. The most important interactions for the resonance structure are the s, p, and d waves of the proton- 15 O system, each producing two low-lying resonances in 16 F. The lowest adiabatic effective potential for the 3/2 − resonance is shown in Fig. 4.…”

Section: A Interaction Dependencementioning

confidence: 99%

“…This symmetry breaking is especially problematic in cases where one spin-orbit partner is occupied by core nucleons while the other is available for the valence nucleons. Then the d 5/2 and d 3/2 resonances in 17 Ne are mixed in the two-body description of the 1 − and 2 − resonances of 16 F. In the three-body problem of 17 Ne the two valence protons are then forced to partly occupy the same orbits. The Pauli principle between core and valence protons is violated and unwanted properties may appear (see Ref.…”

Section: -7mentioning

confidence: 99%

“…[30], where the potentials obtained with symmetry-breaking spin operators are adjusted with three-body potentials to reproduce the known two-body spectrum in 16 F. However, this simultaneously results in an additional 2 − resonance in 16 F at 2.8 MeV with a width of 0.26 MeV. This resonance and the corresponding bound state in 16 N at −0.38 MeV are not mentioned in the description of the interaction [30], and furthermore they are not known experimentally. Figure 4 shows how such exceedingly different two-body interactions lead to effective potentials in almost perfect agreement, provided that the same basis is used.…”

Section: -7mentioning

confidence: 99%

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Necessary conditions for accurate computations of three-body partial decay widths

2008

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The partial width for decay of a resonance into three fragments is largely determined at distances where the energy is smaller than the effective potential producing the corresponding wave function. At short distances the many-body properties are accounted for by preformation or spectroscopic factors. We use the adiabatic expansion method combined with the WKB approximation to obtain the indispensable cluster model wave functions at intermediate and larger distances. We test the concept by deriving conditions for the minimal basis expressed in terms of partial waves and radial nodes. We compare results for different effective interactions and methods. Agreement is found with experimental values for a sufficiently large basis. We illustrate the ideas with realistic examples from α emission of 12 C and two-proton emission of 17 Ne. Basis requirements for accurate momentum distributions are briefly discussed.

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Section: A Basic Conceptmentioning

confidence: 99%

Section: A Interaction Dependencementioning

confidence: 99%

Section: -7mentioning

confidence: 99%

Section: -7mentioning

confidence: 99%

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Necessary conditions for accurate computations of three-body partial decay widths

2008

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“…[18]. Other theoretical investigations of p-4 He scattering include microscopic calculations with phenomenological interactions [19][20][21] as well as ab initio calculations based on accurate nucleon-nucleon (N N ) [22] and three-nucleon (3N ) [23] forces. However, both sets of calculations have limited predictive power.…”

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confidence: 99%

Predictive theory for elastic scattering and recoil of protons fromHe4

2014

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Low-energy cross sections for elastic scattering and recoil of protons from4 He nuclei (also known as α particles) are calculated directly by solving the Schrödinger equation for five nucleons interacting through accurate two-and three-nucleon forces derived within the framework of chiral effective field theory. Precise knowledge of these processes at various proton backscattering/recoil angles and energies is needed for the ion-beam analysis of numerous materials, from the surface layers of solids, to thin films, to fusion-reactor materials. Indeed, the same elastic scattering process, in two different kinematic configurations, can be used to probe concentrations and depth profiles of either hydrogen or helium. We compare our results to available experimental data and show that direct calculations with modern nuclear potentials can help to resolve remaining inconsistencies among different data sets and can be used to predict these cross sections when measurements are not available. He proton elastic recoil reactions are the leading means for determining the concentrations and depth profiles of, respectively, helium and hydrogen at the surface of materials or in thin films. Such analyses, known among specialists as (non-)Rutherford backscattering spectroscopy and elastic recoil detection analysis, are very important for characterizing the physical, chemical and electrical behavior of materials, for which hydrogen is one of the most common impurities, and for studying the implantation of helium for applications in, e.g., waveguides or fusion energy research [1,2]. To achieve good resolution e.g. in the case of thick samples, measurements are often performed at energies above the Rutherford threshold where the purely Coulomb elastic scattering paradigm does not hold anymore. In this regime, in which the incident particle energy is on the order of a few MeV per nucleon, nuclear physics becomes the main driver of the scattering process, particularly near low-lying resonances where the cross section can be enhanced by orders of magnitude with respect to the Rutherford rate. Therefore, the availability of accurate reference differential cross sections for a variety of proton/ 4 He incident energies and detection angles are key to the feasibility and quality of these analyses.

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Elastic Scattering by a Conservative Potential

Friedrich

2013

Scattering Theory

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Scattering length and effective range for collisions between light ions within a microscopic model

Cited by 29 publications

References 32 publications

Necessary conditions for accurate computations of three-body partial decay widths

Necessary conditions for accurate computations of three-body partial decay widths

Predictive theory for elastic scattering and recoil of protons fromHe4

Elastic Scattering by a Conservative Potential

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