Three-body continuum structure and response functions of halo nuclei (I): 6He

Danilin, B. V.; Thompson, I. J.; Vaagen, J. S.; Zhukov, M. V.

doi:10.1016/s0375-9474(98)00002-5

Cited by 192 publications

(189 citation statements)

References 66 publications

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“…This is consistent with the calculations in Refs. [8] and [19]. Compared to the experiment [18], the theory overestimates the strength at around 1 MeV and, consistent with the sum rule, underestimates the strength at higher energies.…”

Section: A Dipole Strength Functionsupporting

confidence: 56%

Cluster sum rules for three-body systems with angular-momentum dependent interactions

et al. 2008

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We derive general expressions for non-energy-weighted and energy-weighted cluster sum rules for systems of three charged particles. The interferences between pairs of particles are found to play a substantial role. The energy-weighted sum rule is usually determined by the kinetic energy operator, but we demonstrate that it has similar additional contributions from the angular momentum and parity dependence of two-and three-body potentials frequently used in three-body calculations. I. MOTIVATIONThe use of sum rules in quantum mechanics is well established and abundantly applied for many different systems [1,2]. The prominent examples are the transitions from a given quantum state induced by an electromagnetic multipole operator. For any multipole operator acting on an initial state, the sum of all the related transition probabilities multiplied by powers of the excitation energy are completely determined by the properties of the initial state [3,4].The sum rules exist in general for any many-body quantum system. Of specific interest are those systems where the constituents clusterize, such that the degrees of freedom can be divided into the internal ones corresponding to each cluster and those associated with the relative motion of the clusters [5]. Then the different multipole operators can be decomposed into terms depending on the intrinsic coordinates of each cluster and an additional term depending only on the relative coordinates of the centers of mass of the clusters. This operator structure then leaves two sum rules showing the same decomposition: the sum rules associated with each individual cluster (depending only on the properties of the initial cluster state) plus the cluster sum rule (depending on the properties of the few-body initial wave function). Examples are found in Refs. [6,7], where the dipole non-energy-weighted and dipole energy-weighted sum rules are obtained for many-body systems clusterizing into a two-body system. When a clusterized system can be properly described as a few-body system where the internal cluster degrees of freedom are frozen, only the cluster sum rules remain, corresponding to the much smaller Hilbert space of ground and excited states of the relative cluster motion. This kind of few-body descriptions have been extensively used in nuclear physics during the past 10-15 years in connection with halos and weakly bound states in general [5]. The most interesting and frequently investigated of these systems are approximated by a three-body structure. Extensions to excited three-body continuum states are now being pursued and attracting a lot of attention [8][9][10][11][12]. To get accurate three-body wave functions the Faddeev decomposition with different Jacobi coordinates is employed in coordinate space computations [13]. The unavoidable transformation from one set of Jacobi coordinates to another complicates the structure of the cluster sum rules, especially when more than one of the three particles is charged.The purpose of this work is to generalize the dipole twobody...

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Section: A Dipole Strength Functionsupporting

confidence: 56%

Cluster sum rules for three-body systems with angular-momentum dependent interactions

et al. 2008

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“…In this system, L i = K i + 3/2 are the generalized orbital angular momenta, where K i is the hypermoment in the ith channel, and the matrix elements V ij (ρ) (containing all intercluster interactions) in the basis of hyperspherical harmonics depend only on the hyperradius ρ. More details about the development of the model and applied interactions can be found in [23].…”

Section: Discussionmentioning

confidence: 99%

“…Equations (15) and (23) [ (18) and (24)] have similar structure, but only logarithmic derivatives from irregular functions g i (k r) appear in the first case (15) [ (18)] and from regular functions f i (k r) in the second case (23) [ (24)]. We demand that at some (matching) point r m , a linear combination of wave functions and derivatives for both sets become equal,…”

Section: A Solutions For Bound Statesmentioning

confidence: 99%

Modified variable phase method for the solution of coupled radial Schrödinger equations

2011

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A modified variable phase method for the numerical solution of coupled radial Schrödinger equations, which maintains linear independence for different sets of solution vectors, is suggested. The modification involves rearrangement of coupled equations to avoid the usual numerical instabilities associated with components of the wave function in their classically forbidden regions. The modified method is applied to nuclear structure calculations of halo nuclei within the hyperspherical harmonics approach.

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“…However, for two-neutron halo nuclei, like 6 He, 11 Li, and 14 Be, a three-body picture is more appropriate but also more complicated. Microscopic three-cluster calculations of the E1 strength function were performed for, e.g., 6 He [9,12]. However, many difficulties and questions caused by incomplete knowledge of the cluster dynamics are still to be resolved.…”

Section: Introductionmentioning

confidence: 99%

Analytical E1 strength functions of two-neutron halo nuclei: the 6He example

Forssén¹,

Efros²,

Zhukov³

2002

Nuclear Physics A

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An analytical model is developed to study the spectra of electromagnetic dissociation of two-neutron halo nuclei without precise knowledge about initial and final states. Phenomenological three-cluster bound state wave functions, reproducing the most relevant features of these nuclei, are used along with no interaction final states. The 6 He nucleus is considered as a test case, and a good agreement with experimental data concerning the shape of the spectrum and the magnitude of the strength function is found.

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Three-body continuum structure and response functions of halo nuclei (I): 6He

Cited by 192 publications

References 66 publications

Cluster sum rules for three-body systems with angular-momentum dependent interactions

Cluster sum rules for three-body systems with angular-momentum dependent interactions

Modified variable phase method for the solution of coupled radial Schrödinger equations

Analytical E1 strength functions of two-neutron halo nuclei: the 6He example

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